Ilg Jens Patrick
Ilg Jens Patrick
Ilg Jens Patrick
genehmigte
D ISSERTATION
von
Jens Patrick Ilg
Karlsruhe, 2014
Contents
1
Introduction
1.1 Power Grid Investment and Operation . . . . . . . . . . . . . . . .
1.2 Challenges in Power System Transformation . . . . . . . . . . . .
1.3 Opportunities for Efficient Use and Development of Power Grids
1.3.1 Efficient Use of Capacity . . . . . . . . . . . . . . . . . . . .
1.3.2 Efficient Investment Planning . . . . . . . . . . . . . . . . .
1.4 Structure of the Thesis . . . . . . . . . . . . . . . . . . . . . . . . .
1.5 Research Path . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
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43
ii
Contents
3.3.3
3.3.4
44
46
49
51
52
53
55
57
57
59
61
62
68
71
74
75
87
92
95
98
98
99
106
111
111
112
115
Contents
5.3.3
5.4
5.5
6
iii
136
138
140
144
146
151
152
155
157
158
160
161
Conclusion
165
6.1 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 165
6.2 Outlook . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 167
References
169
List of Figures
191
List of Tables
195
List of Abbreviations
197
Appendix
A
Optimization program used for SB, SLC, DLC, DLP . . . . . . . .
B
Optimization program used for SLPmax . . . . . . . . . . . . . . .
C
Optimization program used for SLPt . . . . . . . . . . . . . . . . .
D
Optimization program used for OPT . . . . . . . . . . . . . . . . .
E
Comparison of Charging Coordination Outcomes at Work Location
201
201
202
203
204
206
Chapter 1
Introduction
Climate change, resource scarcity as well as public and political opinion necessitate changes to the current energy system. Ambitious political goals to reduce
carbon emissions are omnipresent. The Kyoto Protocol to the United Nations
Framework Convention on Climate Change (UNFCCC) is the largest international treaty on the reduction of greenhouse gas (GHG) emissions (United
Nations, 1998). The second commitment period of the Kyoto Protocol aims at
reducing GHG emissions against 1990 levels by at least 18% until 2020 (United
Nations, 2012).1 Besides the reduction of carbon emissions, many countries
reinforce the restructuring of the energy system to limit dependency on fossil
fuel imports (e.g., oil, natural gas) or avoid possibly hazardous technologies
(e.g., nuclear). Some examples in addition to Kyoto targets are Japanss aim
to cut 10% of electricity consumption by 2030, Chinas target to reduce energy
intensity by 16% until 2015 and the new fuel economy standards in the United
States (IEA, 2012b).
The power sector globally accounts for a large share of the total primary energy consumption and carbon emissions. In the United States, the electric power
sector accounts for approximately 40% of total primary energy consumption
(US Energy Information Administration, 2012)2 and 33% of total greenhouse gas
emissions (US Environmental Protection Agency, 2013). In the European Union,
the energy used by power producers accounts for approximately one third of
gross inland consumption.3 Figure 1.1 depicts the primary sources of energy
and distribution to different sectors in the EU-27. The electric power system is
a crucial starting point in achieving the targets and ensuring reliable electricity
supply at the same time.
1 Many
countries with binding targets in the Kyoto Protocol are members of the European
Union which is reflected in the EU Roadmap 2050 targets of reducing carbon emissions below
1990 levels by 20% until 2020 and 8095% until 2050 (European Commission, 2011).
2 This figure actually represents developed countries. According to IEA (2012a), electricity accounts for approximately 18% of total energy consumption.
3 For more details on assumptions, see http://epp.eurostat.ec.europa.eu/statistics_
explained/index.php/Consumption_of_energy#Further_Eurostat_information.
Introduction
Oil (617)
Transport (20.8%)
Gas (442)
Residential (17.4%)
Nuclear (237)
Industry (16.6%)
Lignite (90)
RES (172)
Services (8.6%)
Other (2.1%)
Figure 1.1: EU-27 gross inland consumption by fuel and final energy consumption by
sector 2010 in Mtoe (Data source: Eurostat, 2012)4
A prominent example of the power system paradigm change is the Energiewende (energy transition) in Germany. The German government has set a goal
to reduce greenhouse gas emissions by 8095% in comparison to 1990 levels by
2050 (BMWi and BMU, 2010), with a set nuclear phase-out by 2022 (German Federal Government, 2011). Being a densely populated, industrialized country with
limited potentials for generating electricity from continuously available renewable energy sources (e.g., hydro) in comparison to countries like Norway5 , this
is an ambitious goal for Germany. Consequently, Germany serves as an international role model and is closely observed and discussed internationally (The
Economist, 2012).
Million tons of oil equivalent (Mtoe) is equal to 11.63 TWh. Missing values to 100% are
served by other fuels.
5 In Norway hydro accounts for 94.7% of total domestic electricity generation (IEA, 2012a).
Introduction
the same range and show that the power sector accounts for a large share of
total infrastructure investments globally (Figure 1.2). In Germany, major investments in grid capacity and new technologies are identified as crucial building
blocks for the integration of renewable energy sources, with cost drivers in the
distribution as well as in the transmission grid (BNetzA, 2012).
In the context of these investments, the overall goal should be to meet future requirements with an efficient set of measures. Therefore, many parties in
the power system are involved and need to be coordinated to achieve efficient
capacity management. A grid operator faces the fundamental choice between
capacity utilization and capacity provision under uncertainty:
Infrastructure investments build additional power grid capacity efficiently
System operations use existing infrastructure capacity efficiently
In the long-run, regulatory conditions need to establish incentives for different actors to incorporate the grid infrastructure cost into their decisions. In the
short-term, Transmission System Operators (TSOs) and Distribution System Operators (DSOs) can apply coordination measures to fulfill their responsibility of
maintaining a balanced power grid and making the most out of infrastructure
capacity. These targets get even more important in the light of increasing penetration of intermittent renewable energy sources (RES), which have less or even
equal to zero marginal production cost and hence increase the relative weight of
capacity investment costs.
57
Ports
Airports
Rail
Total
Telecom
Water
Power
External
estimates
Roads
0.7
2.0
4.5
9.5
11.7
12.2
16.6
Introduction
direct current
Introduction
balancing of RES. These investments need economic justification to ensure a selection of most beneficial investments. In addition, all investments need a fair
balancing against other measures aiming to use infrastructure more efficiently.
Introduction
competition details, grid operators may or may not have incentives for pursuing
efficient investment choices (Ehrenmann and Neuhoff, 2009).
However, even with the right incentives for grid operators, investments can
still be inefficient due to other actors in the power system. An important influencing factor is the future development of demand and generation. Depending
on the location and the fluctuations over time, these may be beneficial for the
utilization of infrastructure or may lead to additional investment needs. In the
long-run, the incentives to efficiently locate demand and supply may play a major role. In addition, grid planning needs to consider opportunities provided by
new technologies, actors, energy services and business models. Enabling the efficient use of capacity provides ample opportunities to reduce the need for grid
investments.
Introduction
Chapter 1: Introduction
Chapter 6: Conclusion
and challenges of the grid. Serving as the foundation for the subsequent
chapters, it highlights the special features that differentiate the power sector
from other network industries.
Chapter 3 recapitulates on the state-of-the-art of pricing and incentives. It
discusses opportunities to resolve challenges in the power system as well as
acceptance issues and presents the current progress of implementation.
The main focus of Chapter 4 is local load coordination approaches. EV charging loads are used as an exemplary flexible load to analyze the potential of different incentive schemes to mitigate overloads. Chapter 4 mainly addresses the
following research questions:
Introduction
Investment incentives for generators and grid cost allocation under different
regulatory regimes are covered in Chapter 5. Motivated by diverse regulatory
solutions in different countries, micro-economic models are used to explore the
effects on different stakeholders and the power system development. Chapter 5
specifically addresses the following research questions:
What is the influence of different cost allocation options (e.g., generation or load) on welfare?
Which allocation of transmission and generation assets results under
different regulatory regimes?
Chapter 6 presents a short synthesis of the research outcomes. In addition, it
discusses the implications and provides an outlook on open research questions
and possible extensions.
Introduction
on a formal model of demand and supply and in a simple numerical example applies the approach to a fictitious neighborhood with limited grid
capacity.
Basse, H., F. Salah, and J. Ilg (2012). Nutzung von Demand-Side-Management
fr Leistungsausgleich und Netzausbauvermeidung: ein komplexer Spagat (Teil
1). EW-das Magazin fr die Energie Wirtschaft 22, 4851
This article explores the trade-offs between demand-side management incentives for fostering the consumption of RES and reducing grid utilization
from an industry perspective. In addition, it explains the main thoughts
and ideas of the EV charging simulation in the Swiss grid planning case
study from Section 4.4.
Ilg, J. P., H. Lange, and C. M. Flath (2013). Reduction of Congestion in Power
Grids. Working paper
This working paper focuses on congestions in power grids. It explains and
discusses alternative actions for each actor to resolve a congested situation
in power grids.
Publications that deal with different coordination mechanisms for EV charging, especially the influence of EV charging on local grid infrastructure and local
infrastructure pricing to avoid overloads:
Flath, C. M., J. P. Ilg, and C. Weinhardt (2012). Decision Support for Electric Vehicle Charging. In Proceedings of the 18th Americas Conference on Information
Systems (AMCIS)
The paper develops a more detailed model of flexible EV charging demand
in the form of different charging strategies based on real mobility data.
With these strategies it is possible to model different levels of information
availability (e.g., price forecasts) or risk propensity (e.g., minimum range).
This is valuable for more realistic models and provides a basis for the resulting charging load simulations.
Salah, F., J. P. Ilg, C. M. Flath, H. Basse, and C. van Dinther (2013). Impact of
Electric Vehicles in High-Voltage Grids: A Swiss Case Study. Working Paper
The potential impact of EV charging on the power grid and grid planning
are presented in this working paper based on Swiss load, grid, and mobility data. In cooperation with BKW FMB Energy Ltd. (BKW) the paper investigates the impact of flexible EV loads on high-voltage substation
transformers in 2040, given different scenarios.
Flath, C. M., J. P. Ilg, S. Gottwalt, H. Schmeck, and C. Weinhardt (2013). Improving Electric Vehicle Charging Coordination Through Area Pricing. Transportation
Science (available online), 116
10
Introduction
The main results on local area pricing for EV charging are published in this
article. It employs the EV charging strategies to evaluate a local infrastructure coordination mechanism in a single transformer setting. The mechanism combines generation price-based and local utilization-based incentives to foster the use of RES and at the same time adhere to infrastructural
constraints.
Ilg, J. P., C. M. Flath, F. Salah, and H. Basse (2013). Electric Vehicle Charging
Coordination and Local Power Grid Utilization. Working paper and
Salah, F., H. Basse, and J. Ilg (2012). Auswirkungen der Elektromobilitt auf die
Auslastung von Stromnetzen an einem Schweizer Fallbeispiel. In VDE-Kongress
2012, Stuttgart, Germany. VDE VERLAG GmbH
Based on the potential grid impact of EV charging (Salah et al., 2013),
different coordination mechanisms are evaluated in these articles
including the area pricing mechanism presented in Flath et al. (2013).
Publications dealing with transmission pricing, cost allocation of infrastructure, and efficient investment incentives:
Ilg, J. P., C. M. Flath, and J. Krmer (2012). A Note on the Economics of Metered
Grid Pricing. In Proceedings of the 9th International Conference on the European
Energy Market (EEM), pp. 16
Different cost allocation methods influence competition outcomes and welfare distribution between generation and demand. This paper analyzes the
welfare distribution in the case of preexisting investments based on a twonode model.
Ilg, J.; Flath, C.; Krmer, J. (2013) Investment and Grid Cost Allocation. Working
Paper.
Investors factor the regulatory design into their decisions on new investments in generation and transmission capacity. Based on different regulatory regimes on grid cost allocation, the implications on investment behavior are analyzed and discussed in this paper.
Some paragraphs and sections in this thesis are previous versions, extensions,
or direct reproductions of own publications or working papers. In addition to
this provided list, their use is mentioned explicitly at the end of the introductory
paragraphs of each chapter.
Chapter 2
Electric Power System Fundamentals
Similar to other industries, the power sector has a life cycle or value chain for
its core product electric power: generation, transmission, distribution, and consumption. Generators that produce electricity, grid operators on different levels
that transport and distribute electricity, and consumers who employ electric energy in various applications. Interaction between these core functions depends
on the level of vertical integration of different functions and therefore the regulatory design. Nowadays, the interaction also involves wholesale markets as
well as sales and distribution functions which are not examined in detail in this
thesis. The major difference of the power sector in comparison to many other
industries is that electric energy is not easily storable1 and the delivery time is
nearly instantaneous (Stoft, 2002). Therefore, power supply has to equal system
load at any time. If not, the system frequency will either decrease in case of excess demand or increase in case of excess supply. In essence, this leads to a much
closer coupling of all actors in the power sector than in other industries. Besides
non-storability, electricity has additional special characteristics that influence the
structure, operation, and development of the power sector (e.g., Erdmann and
Zweifel, 2008):
Usable for many services
Not easily substitutable
Technically homogenous, economically heterogeneous
Variety of generation technologies with different costs
Variety of transformation options into other energy forms (e.g., chemical,
thermal, mechanical)
Grid-bound transportation
1 Electric
12
This chapter provides an overview on the current state and the development
of the power sector. It introduces the main actors, the high-level regulatory development and how the actors interact to achieve a stable and secure electricity
system as it exists in developed countries. The intention is not to cover all details of the electric power system but rather provide the basis for the research
covered in this thesis. It is to support the understanding of the history of the
power sector, its rough functionality as well as recent developments influencing the actors. The German power sector serves as a practical example for an
industrialized country which is particularly challenged due to the Energiewende.
At some points own existing publications are used in this chapter. In detail,
some paragraphs in Section 2.5 are based on Flath et al. (2013).
2.1 Regulation
Power system regulation by itself is a huge topic for research and discussion due
to the large variety in regulatory approaches globally. The seminal work of Kahn
(1988), The Economics of Regulation, provides a deeper understanding of the core
principles in regulation. This section provides a high-level description of some
regulatory notions relevant for this thesis. Therefore, the main focus is on the
German electricity market regulation. If a more detailed inspection is necessary,
the paragraphs are mentioned and discussed in the respective chapter.
list is not exhaustive, but merely a compilation of typical actions. Jamasb et al. (2005) and
Joskow (2008) provide similar lists.
13
14
ergiewirtschaftsgesetz (EnWG Energy Industry Act).9 This included accounting unbundling as well as non-discriminating network access for retail electricity suppliers which led to retail competition. In 2005, the Bundesnetzagentur
(BNetzA Federal Network Agency) took on responsibility as a regulator in the
energy sector with the commencement of the Energiewirtschaftsgesetz (EnWG
Energy Industry Act). This was accompanied by the switch from negotiated
third-party access to regulated third-party access. With the changes since then,
further unbundling of the grid activities on transmission and distribution level
were put into force in national law. In summary, Germany has basically implemented all main actions of electricity market restructuring.
GeneralInformationOnEnergyRegulation/HistoryOfLiberalisation/
historyofliberalisation_node.html
10 See press release of the Federal Network Agency from April 30, 2013:
http:
//www.bundesnetzagentur.de/SharedDocs/Downloads/DE/Allgemeines/Presse/
Pressemitteilungen/2013/130430_EinspVerguetg_PV_Anl_pdf.pdf;jsessionid=
40E1FE78C89CBB121C7C53D5BF8E7AA3?__blob=publicationFile&v=2
15
(EU ETS), which favors energy sources with low greenhouse gas emissions. The
European Commission (2009) describes details on the mechanisms and realization. Another development in regulation is the nuclear phase-out decisions (e.g.,
Germany and Switzerland). Whereas the current strategies of other countries are
directly opposed to this decision (e.g., France and Great Britain).
Other regulations and subsidies for green technologies are being implemented
or currently discussed, with the magnitude of influence is still to be seen. This
includes, amongst others, technology regulation (e.g., consumption efficiency
for home appliances), tariff regulation (e.g., grid charge reduction for curtailable
loads), exemptions from fees and levies (e.g., large consumers), or tax reductions
(e.g., Hybrid or Battery EVs), .
2.2 Generation
Generators represent the supply side in the power system, producing the commodity electricity in power generation plants. This section describes generation
characteristics and development with focus on Germany.
2.2.1 Structure
Based on resource availability and historical development, various generation
technologies are employed to generate electric energy, leading to fundamentally differing supply mixes. Some countries have enough potential from renewable sources to serve a large share of their load, e.g., Norway with more
than 95% from hydro (IEA, 2011a). Other countries follow a nuclear power strategy, e.g., France with approximately 77% generation from nuclear power plants
(IEA, 2009). Other industrialized countries rely on a more diverse mix of generation units an example is the German generation mix (Figure 2.1). On an
aggregate level, this roughly corresponds to the average generation portfolio for
OECD countries, which generate 61% from fossil fuel, 21% from nuclear, and
18% from renewable sources11 (IEA, 2012a). The difference in generation mixes
led to differing levels of emission and self-sufficiency per country.
Because of existing economies of scale in most generation technologies (Stoft,
2002), a large share of generated electricity stems from large and often fossil
fuel-based generation blocks. Figure 2.2 depicts the distribution of power
plant unit sizes by generation technology in Germany 2012. The three main
generation technologies, lignite, coal and nuclear also have the largest unit
sizes in the German power sector. The historically developed mix required
11 In
16
Lignite
118.0
158.0
20.5
28.5
99.0
Nuclear
70.0
36.0
Hydro
Solar
42.0 45.0
Biomass
Gas
Other
Wind
Figure 2.1: Gross power generation by power plant type in Germany 2012 617 TWh
total with main renewable sources highlighted (Data source: Bundesministerium fr
Wirtschaft und Technologie, 2013)
1500
Capactiy [MW]
1000
500
100
10
Wind
Solar
Biomass Waste
Hydro
Gas
Oil
Other
Coal
Lignite
Nuclear
Figure 2.2: Block capacities > 10 MW by power plant type in Germany 2012 (Data source:
BNetzA, 2013)12
major investments due to the size and long economic lifetime of generation
assets. This led to a dominant position of four big generation companies (RWE,
E.ON, Vattenfall, EnBW), accounting for >80% of total installed capacity as well
as electricity feed-in (Bundeskartellamt, 2011). When focusing on competing
generation capacities only, i.e., ignoring RES generators with priority feed-in,
12 The block capacities are sometimes sums, in cases where one operator combines several power
plants. This applies mainly to wind and PV and leads to the unexpectedly high capacity
outliers.
17
[EUR/MWh]
Pumped
Storage,
Oil
Gas
Marginal cost
Offpeak demand
Coal
Peak
demand
Lignite
Nuclear
Wind, Hydro
[MW]
Power capacity
Figure 2.3: Stylized merit order for dispatching (based on Erdmann and Zweifel, 2008)
1
17.06.2013
eEnergy:
Markets,
Services
Systems
Institute ofafter
Information
Systems and
they
still account
for
73%
of and
total
generation capacity, even
retiring
eight
PD Dr. Clemens van Dinther
Management
nuclear power plants in 2011 (Bundeskartellamt and Bundesnetzagentur, 2012).
18
Electricity markets
Wholesale
OTC (over-the-counter)
Futures market
Forwards/options/
structured products
Financial and physical
settlement
Other services
Grid services
Exchange
Futures market
Futures/options
Financial settlement
Balancing power
Spot market
Physical settlement
Day-ahead market
Hourly auctions
Other services
Intraday market
Continuous trading
Figure 2.4: Different products on electricity markets, transactions and services for power
delivery Judith et al. (2011)
Source: http://www.bundeskartellamt.de/wDeutsch/download/pdf/Stellungnahmen/110113_Bericht_SU_Strom__2_.pdf
to
physical
delivery.
Figure 2.4 exemplarily depictsInstitute
different
transactions and
1
16.06.2013
eEnergy: Markets, Services and Systems
of Information Systems and
PD Dr. Clemens van Dinther
Management
products traded.
On the long-term end there are bilateral delivery contracts and the scheduling
of generation units, but also the planning of generation investment, e.g., type,
size, location. On the other extreme, TSOs need to call ancillary services like
spinning reserves to balance supply and demand and adhere to physical system
limits. A detailed analysis exceeds the dimension of this thesis, since all different
types of power transactions have different rules and renumeration schemes.
For details on specific electricity markets and rules, please refer to publications
about the specific topic, e.g., Stephenson and Paun (2001) on electricity market
trading in general, Swider (2006) on trading on markets for grid operators and
generators, Ockenfels et al. (2008) on electricity market design.
In addition to the revenue criterion, physical constraints influence the generation schedule for some generation technologies. Many renewable generators
are supply-dependent and therefore intermittent. Exemplary patterns of wind
and solar generation are depicted in Figures 2.5 and 2.6. The examples illustrate
the daily pattern of PV in contrast to the stochastic wind generation. However,
both generation types have large short-term variability, which emphasizes the
intermittency. In addition to the depicted examples, both generation types experience seasonal differences, e.g., on average lower solar radiation and higher
wind speed in winter.
Fossil fuel-based plants need to take into account the cost of their ramping
19
Generation [MW]
4000
3000
2000
1000
0
Feb 06
Feb 13
Feb 20
Feb 27
Time
Figure 2.5: Wind power output variability based on total wind generation in Bonneville
Power Administration (BPA) control area during an example month in February 2012 13
Generation [W]
6000
4000
2000
0
May 27
Jun 03
Jun 10
Jun 17
Jun 24
Time
Figure 2.6: Photovoltaic power output variability based on a single rooftop panel installation during example weeks in June 2013 14
time, since these generators cannot be switched on and off instantaneously (e.g.,
nuclear, coal, lignite).
These plants provide constant generation curves over
time, so called baseload. To serve varying demand, the long-term stable and in13 Wind
generation data from 2012 at 5-minute increments from Bonneville Power Administration (mainly Washington, Oregon and Idaho) available at http://transmission.bpa.gov/
business/operations/wind/. This data is used because it is a vailable in high 5-minutes
resolution.
14 PV generation data from 2013 at 5-minute increments from a single rooftop installation near
Stuttgart, Germany (own source).
20
30.2 (17.7%)
27.2 (16.0%)
23.8 (14.0%)
22.7 (13.3%)
21.5 (12.6%)
17.6 (10.3%)
10.4 (6.1%)
6.2
(3.7%)
5.9
(3.4%)
4.8
(2.8%)
170.2
Gross power
generation (TWh)
117.0
37.8
86.8
145.9
140.6
11.7
27.4
25.1
8.4
28.1
(18.6%)
(6.0%)
(13.8%)
(23.2%)
(22.4%)
(1.9%)
(4.4%)
(4.0%)
(1.3%)
(4.5%)
Average capacity
factor
44.3%
15.9%
41.7%
73.4%
74.6%
7.6%
29.9%
46.0%
16.3%
66.6%
628.6
Table 2.1: Installed capacity and gross power generation by source in Germany 2010
(Data source: Bundesministerium fr Wirtschaft und Technologie, 2013)15
2.2.2 Trends
The goal of reducing carbon dioxide emissions, the development of global fuel
markets, and new technologies influence the power generation mix and operation. This section provides a quick overview of current trends which are relevant
for the research results in the subsequent chapters. Most notably, the share of
renewable energy sources is rising globally. The IEA (2012b) expects RES to account for one-third of total electricity output by 2035. This development is fueled
15 Data
from 2010 is used due the start of the nuclear phase-out which has a major influence on
capacity factors. Until now, the share of RES mainly wind and solar is still increasing.
21
20
18
RES
16
Geothermal
14
Solar
12
Biowaste
10
8
Biomass
Wind
Hydro
2
0
90 91 92 93 94 95 96 97 98 99 00 01 02 03 04 05 06 07 08 09 10 11
Year
Figure 2.7: Renewables share of gross generation is steadily increasing mainly in wind,
biomass and solar (Data source: Bundesministerium fr Wirtschaft und Technologie,
2013)
The rise of renewable energy also leads to shifts of generation capacity to locations with good supply of renewable energy sources. In Germany, wind capacity
is strongly increasing in the North, whereas solar is installed mainly in the Southern part of the country. In addition, the sizes of these new generators are typically smaller than former fossil fuel-based plants, except for large offshore wind
farms. This leads to a more decentralized generation, which is already indicated
in Figure 2.2 by sizes per generator type. In addition, small Combined Heat and
Power (CHP) plants with increased energy efficiency gain market share with regulatory support (e.g., act on combined heat and power generation in Germany
- KWK). So-called Distributed Generation (DG) accounted for approximately 20%
of total power generation in Germany in 2006 and is still increasing (Bauknecht
and Brunekreeft, 2008). In Denmark, DG already represents more than 50% of
total generation (Bauknecht and Brunekreeft, 2008). In contrast to the German
Energiewende, different approaches to reduce carbon dioxide emissions influence
the generation mix: the use of carbon capture and storage (CCS) or nuclear are
22
Switzerland
Level 1
Level 2
High
Level 7
50/110/132 kV
Supra-regional distribution
10/16/20 kV
Regional distribution
0.4/1 kV
Local distribution
Transformer
Level 5
Level 6
Low
Transformer
Level 3
Level 4
Medium
Transformer
Figure 2.8: Grid and voltage levels and naming according to 2 Nr.6 StromNEV in Germany and Swissgrid in Switzerland16
also ways to adhere to the main goal of emission reduction mentioned in the
introduction (Islegen and Reichelstein, 2010; van Vuuren et al., 2007).
2.3.1 Structure
The extra-high voltage grid for long-distance transmission is operated by transmission system operators (TSOs), whereas distribution system operators (DSOs)
manage the lower-voltage levels which are originally dedicated to the distribution of electric power to end consumers (Figure 2.8). This thesis focuses on the
TSO concept, where ownership and operation of the transmission system are
integrated. Another model, which is not applied here, is the split into a transmission owner who is also responsible for physical maintenance and an independent system operator (see Brunekreeft et al. (2005) as well as Balmert and
Brunekreeft (2008)). The electric power grid for transmission and distribution
is typically divided into four different voltage levels: Extra-high, high, medium
and low voltage. Since the exact voltage levels and naming of each grid or voltage level differ by region and specific application, this thesis always refers to the
German and Swiss notation as depicted in Figure 2.8.
http://www.swissgrid.ch/swissgrid/en/home/grid/transmission_system/grid_
levels.html
16 Source
23
Extra-high voltage transmission grids are often operated by a few large TSOs
(Germany) or even just one monopolistic TSO (Switzerland). In Germany, there
are four control zones, each with one responsible TSO (see Figure 2.9).
DSOs are responsible for the distribution systems on a regional scale. In 2011,
more than 700 DSOs were responsible for approximately 1.9 million kilometers
of electric lines and nearly 48 million metering points in Germany (Table 2.2).
In comparison, the highest voltage level comprised 630 metering points, which
are mainly large industrial customers and pumped storage. Hence, the demand
directly connected to the transmission grid already accounts for approximately
10% of total consumption. Table 2.2 shows the structure and size of different
voltage levels in Germany. Large generators are typically connected to the higher
voltage levels. However, new generation units like photovoltaics or combined
heat and power (CHP) plants are increasingly connected to low-voltage grids.
All system operators are responsible for grid stability, security and reliability
within their area. TSOs are mainly responsible for providing system security
by balancing load fluctuations in the short term through ancillary services in
their control area. DSOs cover the operation, maintenance and repair in their
region, as well as mid- and long-term planning to accommodate future supply
and demand. Since the flow of power is not controllable and the German power
grid is interconnected between the control zones and with other European countries, the system stability in one region influences the whole grid. An example
of this is the system disturbance in the German transmission grid in November
Francis McLloyd [CC-BY-SA-3.0 (http://creativecommons.org/licenses/by-sa/3.0)],
via Wikimedia Commons
17 By
24
2006 that affected all European countries in the same synchronous area (ERGEG,
2007). To avoid such incidents, the N-1 criterion attempts to ensure that the
Grid data 2011
Unit
TSO
DSO
Total
System operators
[#]
4
735
739
Electric circuit length
[km] 34,404 1,869,670 1,904,074
thereof extra-high voltage
[km] 34,314
483
34,797
thereof high voltage
[km]
90
94,932
95,022
thereof medium voltage
[km]
0
532,894
532,894
thereof low voltage
[km]
0 1,241,361 1,241,361
End consumption
[TWh]
44.8
461.3
506.1
thereof commerce and industry [TWh]
34.7
334.2
368.9
thereof households
[TWh]
0
126
126
thereof pumped storage
[TWh]
10.1
1.1
11.2
End-consumer metering points
[#]
630 47,660,927 47,661,557
thereof commerce and industry
[#]
496 2,894,412 2,894,908
thereof households
[#]
134 44,766,515 44,766,649
Table 2.2: Grid length and metering points per voltage level (Data source: Bundeskartellamt and Bundesnetzagentur, 2012)18
most important grid infrastructure components are fail-safe at least on transmission and supra-regional distribution level. It ensures that at any point in
time the failure of one asset (e.g., line, transformer, generator) does not lead to
overloads in other infrastructure assets. These high security standards result in
high system stability. In Germany, the System Average Interruption Duration
Index (SAIDI) for end consumers is as low as 17.44 minutes per year in 20062010 (Bundeskartellamt and Bundesnetzagentur, 2012). Since security is crucial
in industrialized countries and the grid is a natural monopoly, TSOs and DSOs
are the most regulated actors in the power system. However, a detailed analysis
of this regulation goes beyond the scope of this thesis. An overview of the regulatory development is provided in Section 2.1. If specific norms are relevant,
they are introduced and discussed in the respective section.
2.3.2 Trends
The dominant trend in power grids are the major investments for different reasons, even in countries with existing power grids, and without considering
growing demand. First, transmission and distribution assets are aging and may
be replaced (Prez-Arriaga et al., 2013). Second, locational shifts in generation
18 Potential
small deviations from other diagrams in this thesis are due to differing data sources.
25
caused by new generation (e.g., wind offshore) or decommissioning of old assets (e.g., nuclear phase-out) lead to changes in power flows (ENTSO-E, 2012a).
Third, interconnection of markets to allow power flows for market integration
(Meeus et al., 2005). Fourth, decentralization of supply and smart distribution
grids need new investments to ensure reliable grid operation and enable new
coordination and control approaches (see Faruqui et al., 2010). The ENTSO-E
(2012a) provides a detailed overview of the reasons in the network development
plan for Europe.
The majority of these grid investments is necessary on distribution grid level
(IEA, 2011b). However, the focus of most public discussions is on the large
transmission and interconnection projects. In Germany, the main example is
the Netzentwicklungsplan (Power Grid Development Plan),19 which plans in
addition to the existing networks expansion and optimization several new
high-voltage direct current (HVDC) lines to meet the additional transmission
requirements from North to South. These huge investments affect grid operators financial planning models for the future. Therefore, different regulatory
approaches for cost recovery are discussed due to financing issues and to provide a stable framework for efficient investment (Henriot, 2013).
Consumers as ultimate sponsors will face rising grid charges (Bundeskartellamt and Bundesnetzagentur, 2012). In addition to cost, grid investments need
tremendous lead time and are often delayed in many countries especially
on the high voltage level (ENTSO-E, 2012a). In Germany, 15 out of 24 extrahigh voltage grid investments prioritized by the Energy Line Expansion Act
(EnLAG) are currently delayed between one and five years (Bundeskartellamt
and Bundesnetzagentur, 2012).
2.4 Consumption
Consumers employ electric energy for various applications such as lighting,
cooling and heating, or other electronic appliances. This section describes the
main characteristics of the consumer side with the focus on households in Germany.
2.4.1 Structure
When referring to the GHG reduction targets mentioned in the introduction,
one has to consider total energy consumption. The leverage of using all sources
of increasing energy efficiency (e.g., better insulation of buildings) is high for
achieving the targets. However, all approaches discussed in this thesis refer to
19 http://www.netzentwicklungsplan.de
26
2492
760
362
435
1887
717
Other
Coal
Electricity
District heating
Light fuel oil
Figure 2.10: Final energy consumption by energy source type in Germany 2011 in Petajoule20 8,744 PJ total (Data source: Bundesministerium fr Wirtschaft und Technologie,
2013)
223.0
8.7
16.5
141.0
Households
45.0
74.8
Agriculture
Transportation
Public facilities
Figure 2.11: Electricity consumption by consumer type in Germany 2010, excluding export, losses, internal consumption and pumped storage 509 TWh total21 (Data source:
Bundesministerium fr Wirtschaft und Technologie, 2013)
These loads have the largest impact on total consumption and the system load
pattern over time. In particular, the load curves of industrial consumers differ
20 One
petajoule (PJ) is equal to 1015 joules and 3.6 PJ = 1TWh. Hence, the final energy consumption of electricity reported here accounts for approximately 524 TWh in 2011.
21 The 2010 consumption is less than the 524 TWh in 2011 as reported in Figure 2.10.
27
0.20
Workday
0.15
0.10
Season
0.20
Saturday
Load [kW]
0.05
0.15
0.10
Summer
Transition
Winter
0.05
0.20
Sunday
0.15
0.10
0.05
00:00
06:00
12:00
18:00
00:00
Time
Figure 2.12: Synthetic H0 load profile for different days and seasons in Germany (Data
source: http://www.vsg-netz.de/vsgnetz/Stromnetz/Lastprofilverfahren.php)
substantially, since they are dependent on the industry and electricity demand in
production. Due to these differences and the amount of total consumption, load
profiles for industrial customers are measured for billing purposes and special
contracts already. The total consumption of a single household is negligible in
comparison to total system load. Often especially for infrastructure sizing
synthetic load profiles are used to account for household consumption (Figure
2.12). These profiles try to represent a typical average household load profile.
However, each consumer has his individual and unique load profile, which can
deviate considerably from this average pattern. In the face of information availability through smart grids and increasing flexibility through automation and
smart appliances, a more individual examination of load profiles seems promising (see Flath et al., 2012). From an overall system perspective, these load profiles
add up to the total system load that need to be matched by generation capacity
under given grid infrastructure capacities.
Historically, the overarching principle in the power sector was that supply
follows demand, i.e. generation capacities are scheduled to match demand.
The German load profile has a base load that is constant in the long-term. In
addition, there are some typical patterns which repeatedly occur in different
time periods (e.g., daily, weekly, monthly, yearly). The remaining fluctuations
in demand are stochastic in nature and most difficult to match by generators.
As mentioned before, the generators with lowest marginal cost should be
scheduled first. Since RES sometimes have priority feed-in by law and their
marginal cost are equal to zero, the scheduling of the remaining generation
28
capacities is based on the residual load. With the stochastic nature of demand
and the increasing share of intermittent generators, forecasting of residual load
is essential. Hahn et al. (2009) provide an overview of existing load forecasting
methods and models.
Electricity demand is often assumed to be largely independent from incentives. This is because, only large consumers or special loads like night storage
heaters receive adjusted prices which account for different marginal generation
cost. However, demand side management (DSM) has been an extensively analyzed concept in the last decade. One goal is to determine the elasticity of demand based on different incentives. An overview of different analyzes of price
elasticities is provided by Lijesen (2007). With the rise of the smart grid and
automated demand, elasticities are expected to increase. This demand side flexibility is the central element used for price coordination of demand as described
in Chapter 4.
2.4.2 Trends
Even in industrialized countries, total electricity demand is still increasing because of numerous new appliances, services and uses based on electric power.
In Germany, with some of the highest electricity prices and steady improvements
in energy efficiency of different applications, the share of electricity of the total
energy consumption increased from 17.3% in 1990 to 21.6% in 2011 (Bundesministerium fr Wirtschaft und Technologie, 2013). Some barriers for more efficiency
gains on the consumption side are imperfect information, hidden costs, uncertainty, access to capital, and split incentives (Schleich, 2009). Improved information availability can also be used in demand response management with variable
prices. The first programs are developing from research test beds to first real offers to end consumers (for details, see Section 3.3). Smart technology roll out
is accelerating (e.g., smart meters), leading to more available information and
control equipment. Directive 2009/72/EC of the European Parliament and of
the Council requires all member states to follow a timetable with a target of up
to 10 years for the implementation of intelligent metering systems and a minimum of 80% of all consumers to be equipped with intelligent metering systems
by 2020. In addition, new technologies and control algorithms are being developed to increase the flexibility in demand without influencing usage patterns.
29
23 The
30
http://www.bloomberg.com/news/2013-03-12/europe-gas-carnage-shown-by-eon-
31
tor reacted with compensation payments for fixed costs to keep these generation
capacities as reserve.25 However, in the long term, the market design needs to
ensure reasonable profitability for these flexible generators even if the load
factor is low and they serve mainly as a backup. Capacity markets are one measure currently discussed to tackle this challenge (Cramton and Ockenfels, 2012;
Stauffer, 2006).
The consumption side itself can contribute significantly to achieve the set
targets. In order to tap this potential, the market design needs to incentivize
more efficient appliances for reduction or new smart grid technologies for
flexibilization of demand. However, even given a market design that incentivizes joint collaboration of different entities, more information is stored and
exchanged for coordination. Therefore, system security is not only about reliable
supply and demand matching, but also about data security or risk of cyber
attacks (Quinn, 2009; Mohsenian-Rad and Leon-Garcia, 2011).
Inadequate market design can cause unwanted market outcomes. One example is the California electricity crisis in California with skyrocketing electricity
prices (Borenstein, 2002). In this case, the main reason was the market power of
power suppliers under the given market design (Borenstein et al., 2002). This
thesis focuses on the analyzes of few incentives based on some coordination approaches and does not attempt to solve all possible failures in market design (see
Hogan, 2002; Wilson, 2002; Woo et al., 2003; Newbery, 2010, for more information on market design challenges).
closing-3-year-old-plant-energy.html
E.ON press release http://www.eon.com/en/media/news/press-releases/2013/5/3/
2013-eon-annual-shareholders-meeting--building-the-new-eon.html
25 See
Chapter 3
Pricing and Coordination in Power
Systems
Following the last chapter on the situation and development of the power sector,
this chapter provides an overview of the state of the art in pricing and coordination. First, coordination as referred to in the context of this thesis is defined,
and different approaches are introduced. This is followed by a discussion of the
short-term and long-term opportunities to avoid grid infrastructure overloads in
generation, consumption as well as transmission and distribution. Subsequently,
a short overview of cost in electricity provision, current electricity tariffs and
prices for end consumers in Germany introduces the focus on monetary incentives. Finally, a simple pricing model with three components is introduced as the
foundation for the subsequent analyzes. This is not an exhaustive work on pricing and coordination. It rather gives an understanding of potential and missing
prerequisites to tap the potentials analyzed in the following chapters.
This chapter is partly based on own publications. Specifically, Section 3.2 is
currently included in our working paper Ilg et al. (2013), and some paragraphs
in Section 3.3.3 have previously been published in our paper Flath et al. (2013).
34
The first three items mainly refer to additional investments to secure supply.
In contrast, the last three items represent coordination options that employ the
demand side by either forcefully rationing and degrading quality or incentivizing to adjust demand.
The focus of this thesis is on mechanisms for grid capacity coordination which
either avoid any rationing/degradation and expansion/upgrade or set incentives for
and investment.
Overall, several different coordiIMefficient
Energyoperation
Group coordination
structure
nation mechanisms for limited capacities are analyzed, matching into a standard structure as depicted in Figure 3.1. Each approach tries to coordinate actors
Externalities
Mechanisms
Resources
Coordination
Actors
Information
within an environment with limited resources (e.g., grid capacity). To this end, it
uses a mechanism which could range from central control to a non-binding suggestion. To achieve coordination, data can be collected and transformed into information to be exchanged in various ways from individual local information
to globally available information or forecasts. Ideally, the amount of information
exchange necessary should be as minimal as possible. Finally, the coordination
outcome may be influenced by externalities that are neither part of the coordination process nor under control of participating actors.
Alderete (2005) names three main goals of congestion management in power
systems:
Source: IM Energy Group
19.05.2011
35
Be economically efficient
Send efficient signals to encourage transmission and generation investment
Facilitate instruments to hedge against congestion
There are helpful suggestions from other industries which may be applied. An
example is a pricing scheme for electricity networks based on quality of service
similar to DaSilva (2000). Another interesting approach is congestion pricing
(MacKie-Mason and Varian, 1995a), e.g., road congestion pricing (Arnott and
Small, 1994) based on traffic flow. All these approaches have varying similarities with power grids (e.g., network industries) but also differences (e.g., nonstorability). Therefore, they can be applied to design and test new coordination
mechanisms, but at the same time they might lead to different outcomes in the
context of power grids.
36
when transporting the necessary power d > x, even if there is enough generation capacity k to satisfy demand d < k. The second situation arises if the given
generation capacity k is the limiting factor k < d but there is still sufficient grid
infrastructure capacity k < x.
x
G
k
C
d
Typically, these bottlenecks can be distinguished into temporary and structural bottlenecks. Temporary bottlenecks may occur under special circumstances
such as maintenance activities and can be mitigated by temporary measures. On
the other hand, structural bottlenecks are long-term phenomenons and should
be addressed through structural measures of congestion reduction. Specifically,
substantial changes in regional demand or supply may cause structural bottlenecks. This can lead to a long-term difference between supply and demand for
electricity at a specific location either due to scarce grid capacity or missing
generation capacity.
37
renewable energy sources cannot be operated economically efficient at every location. The efficiency of wind turbines and solar power depends heavily on local
conditions. The same applies to gas, coal or nuclear power plants which are dependent on fuel and cooling water availability (Rious et al., 2011). In addition,
economies of scale apply to many generation technologies (Stoft, 2002), which
also influences the siting.
Transmission and Distribution
The expansion of the grid infrastructure is a measure for grid operators to increase the transmission or distribution capacity to avoid congestion. However,
grid expansion does not influence total generation capacity and location in the
grid. If the generation capacity is remote from main load centers, grid expansion is very expensive. In special cases grid expansion can even lead to additional bottlenecks due to loop flows (Blumsack et al., 2007). Therefore, power
system simulations are necessary prior to investments to analyze the effect of
more transmission capacity. A temporary instance of this measure is realistic
in special cases only (e.g., interim lines in case of damages2 ), since investment
costs are extremely high and the projects need a long time for planning as well
as construction (Erdmann and Zweifel, 2008). The structural expansion of grid
capacity is widely in use, and governments consider it as the solution to avoid
bottlenecks, e.g., the Germany Energy Line Expansion Act (EnLAG). Important
influencing factors for the decision on transmission investment are resistance in
the population against these infrastructure projects (Keller, 2004) as well as long,
complicated planning, approval and building processes (Buijs et al., 2011). In
addition, the expected shifts of supply due to the nuclear phase-out and most
notably due to RES lead to congestions that require expansion (Bruninx et al.,
2013). An example is the investment into wind power capacity in the northern
part of Germany which requires transmission grid capacity to supply load centers in the South.
Consumption
The reduction of peak demand on the consumer-side can resolve both types
of constraints: scarce transmission capacity and missing generation capacity.
A drastic variant of this is load shedding where loads are temporarily
disconnected from the electricity grid. Usually, load shedding concerns large
consumers, since their load has an effect on grid usage at a specific location and
only affects a small number of consumers that typically have special contracts.
The system operator compensates affected consumers in case of load shedding,
for example, high-voltage line damage due to local tornado: http://www.50hertz.com/
en/file/20121004_PM-Tornado_EN.pdf
2 See,
38
39
40
Price [cents/kWh]
30
20
10
Au
st
r
Be ia
lg
iu
Bu m
lg
ar
ia
Cz
C
yp
ec
ru
h
Re
s
pu
De blic
nm
ar
Es k
to
ni
Fi a
nl
an
d
Fr
an
ce
G
er
m
an
y
G
re
ec
e
Hu
ng
ar
y
Ire
la
nd
Ita
ly
La
tv
ia
Li
t
Lu hua
xe
ni
a
m
bo
ur
g
M
al
t
No a
rw
ay
Po
la
Po nd
r tu
Ro gal
m
an
ia
Sl
ov
ak
ia
Sl
ov
en
ia
Sp
ai
n
Un
S
ite we
de
d
Ki
n
ng
do
m
Country
Figure 3.3: Comparison of retail electricity prices in 2012 for households with 2,500 5,000 kWh yearly consumption (Data source: Bundesministerium fr Wirtschaft und
Technologie, 2013)
41
42
increasing share of RES which at the same time increase the EEG apportionment.
At the beginning of 2013 the apportionment was raised from 3.592 cents/kWh
to 5.277 cents/kWh.
The so-called 19 levy compensates system operators for reduced revenues
due to reduced grid charges for large consumers based on 19 StromNEV.
This levy is paid by all other consumers per kWh, with reduced burden for
consumption over 100 MWh. In 2013, the levy was raised from 0.151 cents/kWh
to 0.329 cents/kWh for small consumers.
The concession fee compensates municipalities for the usage of roads. System
operators have to collect this fee, typically based on the number of inhabitants
as indicated in the Concession Fee Ordinance (Konzessionsabgabenverordnung
KAV) and pay it to the municipality. Again, some special contract customers
have to pay only limited concession fees, based on 2 KAV.
The power tax was introduced as one element of an ecological tax reform. The
generated funds are mainly intended to support the German public pension
fund. Again, some types of industrial consumers, especially those with large
electricity consumption, can get discounted charges. For all other consumers
the standard tax rate was 2.05 cents/kWh in 2012.
The CHP allocation was introduced to support the German goals for climate
protection by increasing the share of CHP electricity generation (1 KWKG)
It is structurally similar to the EEG apportionment but at a lower level. In
2013, it was raised to 0.126 cents/kWh for small consumers, with the charge for
consumption above 100 MWh being limited (9 KWKG).
43
Industry
Concession fee
CHP allocation
19 Levy
0
10
Figure 3.4: Average end consumer electricity price 2013 in Germany by element for
households and industry customers (Data source: BDEW, 2013)5
mentioned above, some industry consumers are even exempt from paying some of the
charges depicted in this figure (e.g., EEG apportionment).
44
45
that equals marginal costs at each node in the grid including transmission and
generation cost (Green, 2007; Schweppe et al., 1988). This also applies to household end consumers, since they will consume too much during peak periods
and too little during off-peak periods if their retail tariffs do not incorporate
variations in marginal costs (Joskow and Wolfram, 2012). The development in
the direction of more dynamic electricity prices as described in the previous section favors some consumers over others. However, so far, the typical flat tariff
per kWh is still being offered and the trials and rollouts mentioned above were
optional. In Germany, 40(5) EnWG also constitutes the obligation to offer a flat
tariff. This may also hinder more dynamic tariffs which are discussed in this
thesis. Dynamic tariffs offered by electricity suppliers will only be adversely selected by consumers that are flexible enough and actually save cost (Ackerlof,
1970), whereas other consumers will stay with the flat tariff. Depending on the
supply cost of electricity, this may lower the willingness to offer different dynamic tariffs. Another point of view is stated by Faruqui (2010):
the presumption of unfairness in dynamic pricing rests on an assumption of fairness in todays tariffs.
This rests on the typical socialization of cost in the electric power sector. More
precisely, consumers with flat tariffs pay the exact same price for the same
amount of consumption, independent of their individual pattern. A household
that consumes mainly in low-demand periods when there might even be excess
generation (e.g., from wind power) pays the same as a household that consumes
only in high-demand periods where expensive peaking plants need to be
dispatched.
Various researchers demonstrate efficiency gains in the electricity system with
the application of time-based pricing (Crew and Kleindorfer, 1976; Newsham
and Bowker, 2010) and spatial (i.e., nodal or locational) pricing (Green, 2007;
Lewis, 2010).
Crew and Kleindorfer (1976) show that time-based pricing is an efficient
management option under stochastic demand and generation. Newsham and
Bowker (2010) review several North American studies of time-varying pricing.
They identify the cost-effective supply of electricity demand by shifting load
from peak to off-peak hours as the main objective for its introduction. For example, Green (2007) develops a nodal pricing model, incorporating losses and
transmission constraints. For England and Wales, this model shows a welfare
increase by 1.3%. Lewis (2010) states that locational prices can be seen as an
indicator of electricity system insufficiencies. He uses locational prices as an indicator to determine locations where wind turbines could provide the greatest
benefit to the system. Bohn et al. (1984) derive optimal electricity prices over
46
space and time depending on electricity load flow. These prices influence the
patterns of production, transmission and use of electricity.
The temporal component of electricity pricing reflects the market price of generation. In wholesale electricity markets generators offer their electricity output
to retailers. As described in the previous chapter, various technologies are available for generation, and marginal costs of different power plants depend on fuel
prices, operational costs and efficiency levels. Power plants are scheduled in
order of increasing short-run marginal costs of production. Last in this order are
typically peaking plants (Holmberg and Newbery, 2010). The highest marginal
cost generator dispatched determines the market clearing price for all generators in operation (see Figure 2.3). Therefore, availability of generation from
renewable sources with zero marginal cost reduces the wholesale price (Sensfuss et al., 2008). Typically, in times with high demand, generation costs are high.
Costs of transmission and utilization of low-voltage grids are the fundamental drivers behind spatial price differences. Consideration of all operational constraints results in nodal prices. Each point where electricity is generated or consumed has a specific price (Bohn et al., 1984). However, this large number of
nodal prices may be too complex for the application to end consumers. Zonal
pricing reduces this complexity: The price within one area of the grid changes
according to the local system state. Zones can be pre-defined or dynamically
established depending on grid conditions.10 Zonal pricing allows a reasonable
trade-off between pricing complexity and the coordination ability of the pricing
scheme. Hogan (1998a) demonstrates different transmission pricing approaches,
and Leuthold et al. (2008) summarize the debate on zonal vs. nodal pricing.
similar example is congestion pricing of roads during peak hours which encourages drivers
to either use alternative routes or shift travel times to non-congested hours (see Arnott and
Small, 1994).
47
Consumer Rationing discourage the wasteful use of public utility services while promoting all the use [...] justified [...] [between] cost incurred
and benefits received
Fairness to Ratepayers fair distribution of cost ideally to beneficiaries and
without inadequate discrimination
Similar to these criteria, the objective of this thesis is to analyze new coordination
approaches that provide alternatives to current investment incentives (Capital
Attraction), use of resources (Consumer Rationing) and cost allocation (Fairness to
Ratepayers). Since physical constraints and system conditions change, the price
generally has to vary per location and over time. In a static scenario Schweppe
et al. (1985) decompose this price into three components: generation fuel and
maintenance, network losses and variable maintenance, generation and network
quality of supply (costs related to unserved energy).
Given the operational constraints of the electricity system, this thesis analyzes
three price components (for different divisions of price and cost components,
see, e.g., Houthakker, 1951; Bohn et al., 1984; Stoft, 2002; Parmesano, 2007):
Energy Price reflects the market price for generation at a specific location
Network Price reflects the price for transmission of power between locations
Local Price reflects the price for utilization of low-voltage grid at a location
In the following chapters, the effects and interaction of some instances of these
components in different scenarios are analyzed in the face of the primary criteria
of rate structure design.
As mentioned above, the supply side coordination in the electric power system exists in the form of wholesale markets, dispatching or ancillary services,
given the regulatory interventions such as priority of RES (Energy Price). Therefore, Chapter 4 focuses on coordination approaches using the remaining two
price components under a given Energy Price. Demand side flexibility has been
used so far with large industrial consumers only. Hence, the focus is on the operational demand side coordination of small consumers (Local Price), possible
through ICT-enabled information availability in real time. Structural coordination of demand, supply and the network is in focus of Chapter 5, mainly in the
form of cost allocation of long-term investments (Network Price) and the inferred
impact. The relevant structural coordination approaches are reviewed in detail
in Chapter 5.
Chapter 4
Local Load Coordination
This chapter focuses on the potential of load coordination, to ensure adherence
to local infrastructure limits in the distribution grid. The focus is on DSOs
who are responsible for grid capacity on lower voltage levels for private end
consumers. The aim is not to provide ancillary services for system stability on
low-voltage level, but to discuss demand response mechanisms for balancing
the limits of existing grid infrastructure and the optimal utilization of renewable
or low-cost generation. The terms demand response (DR) and demand side
management (DSM) are often understood as synonyms. In more detailed
definitions DSM is considered as a superset of DR going beyond load shifting
and including long-term energy efficiency measures (Palensky and Dietrich,
2011). In contrast, Albadi and El-Saadany (2008) categorize the reduction of
total electricity consumption as DR. An overview of load-shaping objectives of
DSM is provided by Gellings (1985), ranging from peak clipping (e.g., simple load
curtailment), strategic conservation/load growth (e.g., energy efficiency) to other
objectives of demand shaping, e.g., valley filling, load shifting, flexible load shape.
Energy efficiency, which leads to an overall reduction of quantities demanded,
is an important factor to reduce GHG emissions and avoid infrastructure
overloads. Efficiency measures of small consumers can provide significant
savings, since a large part of electricity consumption is wasted in households.
For example, in IAE member countries, approximately 10% of total electricity
consumption in households stems from stand-by power (IEA, 2001). However,
even with an increase in efficiency, the growth (e.g., population, economy) and
rebound effects undermine these savings.1 Hence, continued growth in total
electricity demand is projected globally (IEA, 2011b). This chapter intentionally
excludes the overall reduction of demand and uses both the terms DR and DSM
where DR mainly refers to measures of load shifting.
In their seminal work, Schweppe et al. (1988) describe the core pricing
methodologies to incentivize DR that can nowadays be exploited using smart
grid technologies. Oren (2013) categorizes two different DR paradigms: real1 For
more details about the rebound effect, see Greening et al. (2000) and Berkhout et al. (2000).
50
time prices for retail customers and load control contracts differentiated by
quality of service. Similarly, Albadi and El-Saadany (2008) classify DR programs
into price-based programs and incentive-based programs. Both paradigms are
not widespread so far, and Oren (2013) focuses on the paradigm of contracted
load control options. This chapter emphasizes the direction of real-time pricing
for demand coordination and employs direct load control options such as
curtailment as reference scenarios.
A flexible demand side is a necessary prerequisite for any DR application
scenario. Retail customers combine various load types with different flexibility.
This results in specific control characteristics: Some loads are controllable at all
times and might react immediately with continuously flexible higher or lower
demand (e.g., heating, ventilation, air-conditioning devices HVAC), whereas
other loads cannot respond instantaneously due to operating characteristics
(e.g., washing machines during a washing cycle) or can only consume in discrete
power levels (e.g., appliances with on/off-switch only). Some appliance loads
are dependent on or constrained by other devices (e.g., a dryer should only run
after a washing machine cycle). Other load types even offer the possibility of
substituting electric power consumption (e.g., switch heating from electricity to
natural gas). The most flexible devices are storage appliances, especially if their
charging pattern is not restricted by their type.
However, the mere existence of flexible loads itself is not sufficient to establish
DR successfully. Consumers need to allow and enable use of the available flexibility. Specifically, consumer reaction to dynamic prices is subject to discussions,
since electricity costs are still too low in comparison to total cost-of-living. The
low price elasticity of demand has been confirmed by several studies (Faruqui
and Sergici, 2010). Also, the willingness to accept lower quality of service in the
form of lower reliability levels for some loads seems limited, given the current
high security of supply levels in industrialized nations. However, some studies
show high demand for dynamic tariffs2 and that load control automation helps
to increase acceptance rates (Dtschke and Paetz, 2013). Hence, an essential
step to ensure consumer acceptance of demand flexibility on a household level
is the development of support tools for different load types. These tools need to
ensure that consumers utility is not impaired and that they can easily adjust the
service or tool to their personal preferences.
Based on the requirements and characteristics described above, different
coordination mechanisms are discussed in this chapter which fit into the coor2 In
one program, 93% of all customers preferred the dynamic tariff in comparison to a flat rate
(Pyry, 2012).
51
dination framework presented in Section 3.1. The main actors are consumers,
who can shift flexible parts of their demand to achieve individual targets (e.g.,
minimize cost, maximize use of RES). At the same time, system operators,
retailers and generators are responsible for power provision and want to coordinate the demand in their favor. The central resources in this chapter are local
infrastructure limits which need to be adhered to. At the same time, utilization
of renewable or low-cost generation is ideally maximized. The coordination
mechanisms discussed can be based on different levels of information, e.g.,
market prices, local prices, local infrastructure utilization, and availability of
renewable or other low-cost generation.
First, general alternatives for local load coordination are presented in Section 4.1. Section 4.2 describes electric vehicle charging loads as one practical
example. Subsequently, Section 4.3 analyzes in detail the influence of different
coordination approaches on EV charging loads in combination with local
infrastructure limits. One striking result is that decentralized approaches have
the potential to shift loads such that grid limits are adhered to. This decentralized approach can thus avoid central load shedding. Section 4.4 applies the
theoretical research results in a Swiss grid planning case study. This practical
application demonstrates the potential impact of DR and variable tariffs on
high-voltage grid planning. The main assumptions and limitations of the
research approach are discussed in Section 4.5.1. Finally, Section 4.5.2 concludes
and summarizes the main implications of this chapter.
This chapter contains parts of own publications and working papers. Namely
Section 4.2 on electric vehicles as flexible loads contains parts of our papers Flath
et al. (2012), Flath et al. (2013) and Salah et al. (2013). In Section 4.3, some subsections especially the modeling and the sections on uncoordinated, supplybased coordination and dynamic load pricing coordination are partly reproductions of Salah et al. (2013) and Flath et al. (2013). This section also comprises
the results of Flath et al. (2013). The Swiss case study presented in Section 4.4 is
an extended version of our results presented in Salah et al. (2013). Finally, the
discussion (Section 4.5.1) and conclusion (Section 4.5.2) also repeat some parts of
the respective chapters in our papers Flath et al. (2013) and Salah et al. (2013).
52
ence to infrastructure limits. To this end, this thesis defines energy consumption
e (e.g., measured in kWh or MWh) and load l (e.g., measured in kW or MW).
Naturally, the following relation applies:
e=
l (t) dt
(4.1)
i
pext
t et
(4.2)
t =1
During times of high prices (e.g., in situations with low supply from RES)
flexible individual consumers lower their consumption eit and may increase their
consumption in low-price periods. Total consumption Et = i eit is dependent
on the current prices and the price elasticity of consumers. Obviously, this
demand response can also be realized by direct control based on contracts
(Fahrioglu and Alvarado, 2000). An example are load aggregators or retailers
that have load control contracts with their customers and try to shift consumption into periods with low power prices (Kirschen, 2003). The aggregation helps
53
to reach a critical mass that can be used to participate in power markets that
follow current power market designs.
Researchers have analyzed this type of load coordination from various points
of view, using different external price signals or even direct load control. Daryanian et al. (1989) and Ahlert (2010) analyze optimal demand response strategy
of storage-type consumers based on spot prices. Gottwalt et al. (2011) compare
household demand patterns and electricity bills under flat tariffs and given variable electricity prices. They also analyze resulting load shifts and find that variable electricity prices can lead to significant shifting effects and new total load
peaks (avalanche effects or load synchronization). Kishore and Snyder (2010) show
similar results: with flexible residential demand and peak/off-peak pricing they
find new peaks in low-price periods based on individual demand optimization.
Using simulations, Sioshansi and Short (2009) find that real-time pricing can increase wind generation use and decrease wind curtailment with load demand
elasticities. Our paper (Schuller et al., 2012) also demonstrates significant increase in wind-power utilization when incentivizing flexible EV charging loads
with a wind-power-based tariff. We observe the same load avalanche effects as the
previous studies when offering a dynamic price to an EV population.
Therefore, local load limits have to be considered. Even if there is excess renewable energy feed-in in the system, some grid infrastructure components may
already operate at their limit. Demand response through direct control or monetary incentives needs to internalize this risk of overloads into the coordination
mechanisms. The next sections present the analytical descriptions of examples
for the integration of local infrastructure limits into coordination mechanisms.
These generic approaches are subsequently applied in simulation models with
electric vehicles as flexible demand.
ble.
seems unlikely, however with fully flexible loads such situations are theoretically possi-
54
location, one could limit individual loads homogeneously. Thus, the static load
limits l i for all i [1..n] loads need to fulfill the condition
li
L
n
(4.3)
L needs to be selected such that all infrastructure component limitations are considered.4 In practical applications, this approach could be implemented by installing fuses that are sized accordingly. Grid expansions are basically planned
with a similar approach in mind: The capacity is sized based on the maximum
load expected, but considering different types of loads and hence not using the
worst case simultaneity factor of unity.5
Dynamic Load Curtailment (DLC)
The aggregate load at a specific location can be simplified as Lt = in=1 lti . Depending on the load type interruptable demand contracts (switch on/off only)
or continuously controllable loads the load curtailment is dynamically adjustable based on different aggregate load levels. Baldick et al. (2006) provide a
good overview on interruptable load contracts.
This type of control can be exercised by the local DSO, typically with flexible
non-critical loads (e.g., refrigerators, HVAC, heat pumps, storage appliances).
Generally, two simple types of dynamic load curtailment are possible. The first
one follows the first-come first-serve philosophy: all loads lti are accepted until
the aggregated level L is reached. Any additional loads are curtailed completely.
The second curtailment option is reducing all loads either evenly or proportionally based on individual contracts when the limit L is reached. The latter
option is only feasible with continuously controllable loads or at least loads with
multiple power levels. Hence under DLC, individual consumers can consume
more than the static limit described in Equation 4.3 as long as the dynamic load
is lower than the limit:
n
lti L
t T
(4.4)
i =1
Multiple extensions can be added to these simple forms of dynamic load curtailment. Based on more complex contracts and communication technology, quality
of service differentiation is possible. Each customer may have a quality of service specification for each load type. Hence, the curtailment and demand levels
could be specified, e.g., based on load type or level and time (see Oren, 2013).
4 This
55
Optimization approaches can use this information, e.g., for minimizing end-user
discomfort while adhering to load limits (Ramanathan and Vittal, 2008). An example of different service levels is analyzed in our paper (Flath et al., 2012),
which applies a revenue management approach for electric vehicle charging. We
model customer segments with different valuations charging their EVs and use
two booking classes to achieve an efficient allocation of the available limited capacity.
f
l
t
t
Apart from price elasticity and consumer flexibility, the demand response
strongly depends on the load-price function. A simple constant price (per kW)
combined with the identical duration of measuring and billing period (t = tb )
leads to the same incentives as a flat external price signal of supply as introduced
in Equation 4.2. This thesis focuses on the goal of avoiding local infrastructure
6 For
sake of brevity a compact notation is used in the following, e.g., pSLP
maxttb lti .
tb
56
overloads by means of increasing marginal demand charges. These charges incentivize individual consumers to avoid demand peaks and therefore to flatten
their demand profile.
Another possibility to incorporate the individual load level are adjustments to
the energy price. The resulting price experienced by the consumer depends on
the external price and the individual load level:
pSLP,e
t
lti ,
pext
t
(4.6)
f
ptDLP
b
max { Lt }
ttb
(4.7)
(4.8)
Similar to SLP, DLP adjustments through the energy price are also possible.
The external price signal pext
t can be extended by a price signal which includes
the respective loads. The resulting energy price depends on:
ptDLP,e f Lt , pext
t
(4.9)
Given the demand charge function setup, consumers are incentivized to reduce demand when local infrastructure is utilized to a greater extent. A similar
concept is used for peak-load pricing (e.g., Boiteux, 1960) with the intention to
57
limit demand due to missing generation capacity. The static approach based on
booking classes in our paper (Flath et al., 2012) is a modification of peak-load
pricing. In this case we model two different prices only, and each consumer can
decide to book capacity at a lower price in advance or pay a higher price for
adhoc capacity requirements.
Pricing structure
Supply-based -
i
tT pext
t et
L
n
i
tT pext
t et
with SLC
li
with DLC
eit
in=1 lti L, t T tT pext
t
SLP,e i ext
i li
lt , pt eit + pSLP
l
t T pt
t
t
t
DLP,e
ext
i
DLP
i
Lt , pt et + pt
( L t ) lt
t T pt
with SLP
with DLP
Energy Efficiency
The most compelling way to compare energy effiTodays well-introduced HEV concept is the first
ciencies and GHG emissions of alternative car engine
58
Local Load Coordination
logical step from classical ICEs towards pure EVs. The
concepts with the classical combustion engine is the
number of HEVs is growing worldwide. The HEV conwell-to-wheel (WTW) analysis. This analysis is a holiscept combines
allon
advantages
ofpresented
conventional engines
tic approach(2013).
that accounts
for the the
complete
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For example,
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introduction
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the paper
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at the
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2012). ICE technology)
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cially
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7
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The next evolutionary step in HEVs (e, f) is the
Hybrid electric
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emission-free,
balance (well-to-wheel) critically
evolution towards a PHEV that allows for charging
Fuel cells driven vehicles, and
hinges on the electricity mix used for charging the vehicle. Figure 4.1 illustrates
the battery with electric energy taken directly from
Electric vehicles.
that EVs can achieve emission reduction only if the electric energy comes from
renewable energy sources (e.g., wind or solar).
20
18
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Figure 4.1: Emission statistics of different vehicle technologies (Ballentin et al., 2011)
49
59
text comprises parts of our papers (Flath et al., 2013; Salah et al., 2013; Flath et al., 2012)
and combines the technical specifications for this thesis.
60
utilization, BEVs and Plug-in Hybrid EVs (PHEV) are relevant within this thesis
because these are directly connected to the power system. An introduction with
detailed information on EV architectures is provided by Chan (2007) and Chan
et al. (2010). The internal combustion engine (ICE) in HEVs are not in scope
of this thesis but would provide further interesting applications as an outside
option. The remaining part of this thesis focuses on BEVs only.
Recently, an increasing number of electric vehicles from major OEMs have become available. The most relevant EV characteristics are distance-specific energy
consumption, battery capacity and vehicle maximum range. Most notably, battery capacity in BEVs is limited due to cost as well as size and weight, since the
volumic energy of batteries is low in comparison to fossil fuel. This results in
general in a lower maximum range than todays typical ICE vehicles. Table 4.2
lists this data for a selection of current electric vehicles.
Make and
Model
Citron C-Zero
Ford Transit Electric
Karabag Fiat 500 E
Mitsubishi i-MiEV
Mercedes A-Class E-Cell
Nissan Leaf
Peugeot iOn
Renault Fluence Z.E.
Renault Kangoo Z.E.
Renault Twizzy 75
Renault Zoe
Smart Fortwo Electric Drive
Tesla Roadster
Think Global Th!nk City
1,110
2,340
1,120
1,110
1,591
1,520
1,110
1,610
1,410
450
1,392
975
1,220
1,038
16
28
20
16
36
24
16
22
22
7
22
17.6
53
23
150
130
140
150
255
160
150
185
170
100
210
140
393
160
0.107
0.215
0.148
0.107
0.141
0.150
0.107
0.119
0.129
0.070
0.105
0.126
0.135
0.144
Average
1,285
23
178
0.129
Table 4.2: Technical data of current electric vehicles (Salah et al., 2013)
In addition to the technical specification of the EVs, the charging system and
battery specifications influence the impact on and interaction with the power
grid.9 The IEC standard 62196-1 specifies four charging modes, ranging from
the slow AC mode (up to 3.5 kW) to the fast DC mode (up to 240 kW). Furthermore, the charging speed of EV batteries is limited due to physical constraints
of the batteries. Most recent electric vehicles are typically capable to charge in
9 The
term plug-in gives the impression that inductive charging is excluded. This thesis abstracts from different technical alternatives and treats conductive and inductive charging connections equally.
61
slow AC mode (3.5 kW) or fast AC mode (11/22 kW). Thus, refueling is much
slower for EVs and can hardly be done en route. The German National Electric
Mobility Platform suggests that the future charging infrastructure will consist
of a mix of home charging stations, public charging stations and fast charging
stations (Nationale Plattform Elektromobilitt, 2011). Fast charging stations will
represent a very small part of the infrastructure as they are expensive and will
be required for long-distance traffic only.
Typical charging speed at home is around 3 kW, which translates into approximately 8 hours charging time for a full charge of a 24 kWh battery. Faster charging speeds at 11 kW are possible with special plugs and quick charging stations
with over 50 kW, which are in development and testing. With the fast charging
mode, vehicles batteries can be fully charged in about 30 minutes. Faster charging offers both quick mobility range for driving needs and more flexibility for
intelligent charging to support power grids. In the long-term, EVs should not
only support the power system by scheduling their charging load appropriately
but also by feeding electricity back into the grid. Several research contributions
covering that direction envision EVs to provide vehicle-to-grid (V2G) services
(Kempton and Tomic, 2005). Since vehicles are parked more than 90% of the
time, the wide scale adoption of EVs could provide a flexible storage opportunity for the power system.
section is an extended version of sections in our papers Flath et al. (2012) and Salah et al.
(2013).
11 Deviations to table 4.2 are due to different measurements of the Department of Energy and
specific manufacturers.
12 For details, see the US Energy Information Administration http://205.254.135.24/tools/
faqs/faq.cfm?id=97&t=3 and the US Department of Energy: http://www1.eere.energy.
gov/vehiclesandfuels/facts/2010_fotw618.html.
62
63
can lead to bottlenecks and power quality issues (e.g., transformer overloads,
voltage drops). Different simulations have shown that the electrification level
of the current car fleet can reach between 10 40% before inducing problems in
low-voltage distribution grids (Staats et al., 1998; Rahman and Shrestha, 1993;
Richardson et al., 2010). Many of the aforementioned publications focus on grid
capacity analysis without taking into account the possibilities of economically
motivated charging coordination (Roe et al., 2009; Richardson et al., 2010; Rahman and Shrestha, 1993).
Objective Function
The heterogeneity of actors in todays liberalized power systems leads to different objectives for EV charging coordination. From a generation perspective it is
beneficial to optimize the utilization of low-cost generation capacity or use EV
charging to smooth the load curve in order to minimize ramping cost (e.g., Guille
and Gross, 2009). Sioshansi and Denholm (2010) minimize the total system cost
consisting of generation and EV operating costs. Environmental organizations as
well as governments often propagate the use of EV charging flexibility to reduce
carbon dioxide emissions by integrating renewable energy sources, e.g., use excess wind-power in-feed for EV charging (Lund and Kempton, 2008; Caramanis
and Foster, 2009). At the same time, electrical engineers often focus on coordination to provide regulating power (Tomic and Kempton, 2007; Andersson
et al., 2010), minimize power losses (Clement et al., 2009; Sortomme et al., 2011),
maximize EV integration (Peas Lopes et al., 2009), or reduce emissions as well
(Gransson et al., 2010). In contrast, economists minimize cost for power suppliers or EV owners (Sioshansi et al., 2010; Dietz et al., 2011). From a mobility users
point of view the objective is to reduce mobility costs by optimizing the charging
schedule based on variable electricity rates (Rotering and Ilic, 2011; Flath et al.,
2013).
Coordination Approach
Approaches for EV charging coordination range from central optimal planning
(Clement et al., 2009; Lund and Kempton, 2008) to decentralized approaches like
time-of-use pricing (Peas Lopes et al., 2009; Clement-Nyns et al., 2011; Qian
et al., 2011) or coordination based on local grid parameters (Peas Lopes et al.,
2010; Flath et al., 2013). In general, the approaches abstract from direct communication of individual preferences similar to the load coordination approaches
described in Section 4.1.
Centrally controlled coordination is often based on assumptions such as a given
share of all EV owners using off-peak periods or the option of shedding (curtailing) some EVs on demand by contract (van Vliet et al., 2010; Kempton and
64
Tomic, 2005; Andersson et al., 2010; Gransson et al., 2010; Sioshansi et al., 2010).
Evaluations of EV charging based on intermittent RES infeed often apply central approaches as well (Lund and Kempton, 2008; Li et al., 2013; Markel et al.,
2009). Besides that, another model already uses centrally forecasted DR in addition to wind power integration (Wang et al., 2011). However, EV charging with
decentralized decisions based on RES price signals or online mechanisms has
been used recently (Schuller et al., 2012; Gerding et al., 2011; Dietz et al., 2011).
This chapter complements existing research with the integration and evaluation
of grid constraints in combination with decentralized coordination approaches
of individual EVs.
Grid Impact
In recent years, some research projects and field studies focused on the power
system impact of EV charging, similar to this thesis. Farmer et al. (2010) compare different studies and find that available generation capacity is sufficient
even with significant EV penetration as long as the charging activity
is coordinated. An overarching study by Kintner-Meyer et al. (2007) finds
that the US power system capacity is sufficient to provide fuel for 84% of
the total car, pickup truck and SUV fleet with a daily average drive of 33
miles. The study does not focus on grid issues. However, the authors state
that EV charging adds significant new loads and may impact overall grid
reliability due to infrastructure utilization. Taylor et al. (2009) recommend
analyses on distribution feeder level to investigate which charging behaviors
and penetration levels need to be considered or require actions by utilities,
respectively. Real data case studies on the grid impact show slightly varying
focus, approaches and results. Peas Lopes et al. (2011) propose a framework for
the EV grid integration and show in simulations that with a central aggregator
EV penetration rates up to 52% are possible in an example medium voltage
grid. Based on a reference distribution grid, Qian et al. (2011) simulate different
controlled and uncontrolled charging scenarios which result in approximately
36% peak load increase with 20% penetration rate in uncontrolled charging.
In a planning model based on two real distribution areas, Pieltain Fernandez
et al. (2011) demonstrate the increase of system investment cost and significant
energy losses in a 60% EV penetration scenario. In addition, other possible
grid impacts like power quality problems or voltage imbalances may occur
(Putrus et al., 2009). Roe et al. (2009) investigate the effect of EV charging in
a distribution circuit and, in a specific simulation scenario, find a significant
reduction of the expected life of the distribution transformer. This thesis
adds a Swiss case study which analyzes the influence of EV loads on future
grid expansions under different load coordination and EV penetration scenarios.
65
Several research publications partly use similar model features, input data and
evaluation methods as applied in this thesis. Table 4.3 provides an overview of
selected publications on EV charging coordination.
D
D
Fan (2012)
Galus et al. (2010)
Gerding et al. (2011)
al.
D
D
D
D)
D
D
D
D
D
Historic prices
Grid topology
Load profile
Driving prof.
Simulation
Key notions
D) (D)
(D) (D) D
D
D
D D
D
(
D
D (D) D
D (D)
D
D
D
D D
DDD
D D
D D
D D
D
D
Input
data
Emissions
D
D
D
D
D
Vehicle-to-grid
Grid constraints
Battery modeling
Other mechanisms
Price signals
Central control
Other
D
D
D
D
D
Model
features
D
D
D D
Heydt (1983)
D
D
Emissions
EV integration
Papadopoulos
(2012)
Generation cost
Acha et al. (2010)
Coordination
approach
66
Objective
function
Reference
and
DD D
D D D
D
D (D) D
Key notions
Historic prices
Grid topology
D D
D D
D D
DD D
Load profile
Driving prof.
Simulation
Emissions
Vehicle-to-grid
Grid constraints
Battery modeling
Other mechanisms
Price signals
Central control
Input
data
D
( )
( )
( )
D (D)
( )
Model
features
D (D) D (D) D
D (D)
Miller
Sioshansi (2012)
D (D)
D D
Sioshansi
(2011)
Other
D (D)
Emissions
EV integration
Generation cost
Peas Lopes et al. (2009,
2011)
Coordination
approach
D
D
D
Comparison of dumb charging to a dual-tariff coordination and a central smart charging coordination to maximize EV integration. Charging
coordination can increase the maximum EV integration level.
Evaluation of uncontrolled EV charging on total load at example residential, commercial and industrial feeders. Optimal smart charging with
real-time tariff only shows that most charging occurs in low-cost hours.
Impact of three simple charging models on total load: all EVs start simultaneously, EVs start sequentially in groups, EVs charge uniformly over
time. Main results indicate that distribution grid limits are reached in
residential areas at 20% EV penetration.
Analysis of cost of EV charging given cases with and without emission
constraints. Constraining the emissions induced by EV charging does not
largely increase total cost.
Evaluation of EV charging with individual agents under different tariffs
on total generation cost and emissions. RTP performs worst in total cost
due to resources with nonconvexities (e.g., ramping constraints)
Analysis of the relationship between feeder losses, load factor, and load
variance in the context of coordinated PHEV charging. Evaluation of
three central algorithms that minimize distribution system impact.
Intelligent charging optimizes costs of generation, including ramping
cost in comparison to uncontrolled charging.
Multi-agent systems (MAS) solution with negotiation on different grid
voltage levels. Hierarchical scheduling approaches of decentralized
charge intentions decrease system imbalances.
Simulation of optimally dispatched PHEV charging load demonstrates
cost reduction potential which increases with DR enabled.
67
Objective
function
Reference
68
a consumption vector i = 1i , ..., iT specifying the required electrical
energy for driving in each time slot as well as
a location vector ai = a1i , ..., aiT where ait indicates a vehicles current location area over the collection of time slots t [1..T ].
Following the time resolution of the EV profiles, all consumption (driving) and
charging actions are discretized in 15-minute intervals. In our model the time
horizon (T) is set to one week consisting of 672 time slots. The time horizon also
spans a (potentially varying) price vector p = h p1 , ..., p T i indicating the price
of electricity at each point in time. Given this discrete time structure, the EVs
charging decisions can be represented as charging vectorsh i = 1i ,i...Ti .14
The total load at location x at time t then is t,x = in=1 ti 1( x=ai ) where
t
1( x=ai ) is the indicator function on the location level. While the mobility dataset
t
13 See
Sioshansi et al. (2010) or Flath et al. (2013) for similar EV charging models.
index from i and
i
for ease of exposition.
69
2,500
2,000
State
DRIVING
Profile state
OTHER
VACATION
1,500
SHOPPING
LEISURE
WORK
HOME
1,000
500
0
Mo 0:00
Tu 0:00
We 0:00
Th 0:00
Fr 0:00
Sa 0:00
Su 0:00
Mo 0:00
Time
Figure 4.2: Distribution of vehicle locations and states over one week based on 2,966
employee driving profiles (Data source: Zumkeller et al., 2010)
our paper Flath et al. (2012) for a discussion of different charging strategies.
70
the initial model. Assuming a linear charging process and discretized time slots
of 15 minutes similar to the driving profile resolution this translates into
= 2.75 kWh per time slot. Similarly, the battery level must always be positive
and cannot exceed battery capacity SOC. The model deviates from original car
specifications (Table 4.2) and rather uses a fictitious vehicle with SOC = 30 kWh
battery capacity and a consumption of 0.15 kWh/km determining a maximum
range of 200 km. The rationale here was to better capture the capabilities of a
future standard EV. Without consideration of losses, the 11 kW mode results in
a minimum charging time of about 165 minutes for a complete charge for the 30
kWh-battery.
Objective Function
Since the focus is on economic coordination, individual charging cost minimization is the appropriate objective.16 The charge amounts with the corresponding
billing structure allow to determine the total individual charging costs C:
min C ()
(4.10)
t [1..T ]
(4.11)
Furthermore, a terminal battery level SOCT is specified to prevent the optimization from completely discharging the battery towards the end of the time horizon. The initial charge level allows us to compare the different charging coordination approaches:17
SOCT = SOC0
(4.12)
16 Alternative
17 This
71
The total charging amounts under optimal charging are then exogenously given
by total consumption and the difference between the initial and terminal SOC.
Moreover, since EVs can only be charged when connected to the grid, the vehicle location at extracted from the driving profiles governs the current charging
capacity t .18
(
if at { Home, Work},
( at ) =
0 otherwise.
This current charging capacity then constrains the range from which t can be
chosen:
t [0, ( at )] t [1..T ]
(4.13)
that while this looks like an if-else condition this is only for compactness of expression.
Each ( at ) is a static expression (i.e. no decision variable) extracted from the driving profiles
which are applied to build the set of constraints (4.13).
72
P ROGRAM C ONTROL
Start
EV A GENTS
Initialize
prices, parameters and
EVs (i=0)
Iterate i over
EVs 1..n (i++)
no
End
Save results
i=n?
Determine
is charging
amounts
Update
coordination
parameters
Update
aggregate load
yes
M ECHANISM C ONTROL
Figure 4.3: Model workflow
section is an amended version of our data description used in the paper published in
Transportation Science (Flath et al., 2013).
73
integration in distribution grids (Stoeckl et al., 2011; Gong et al., 2012). Other
physical constraints such as transmission line limits or voltage drops would
go beyond the scope of this thesis. As described above, the charging loads are
analyzed at two possible charging locations or areas, Home and Work. The load
limit for EV charging in both areas is set to lim
x = 2, 000 kW, i.e., approximately
20% of the EV population can charge simultaneously at each location at 11 kW
charging power (e.g., assuming one residential and one industrial zone). These
are instances of the total maximum load L introduced in Section 4.1. Using the
locational information of the driving profiles to determine charging locations,
this approach is similar to the analysis of residential area load as described by
Rahman and Shrestha (1993).
The simulation of individual driving habits and EVs results in high computational requirements (Richardson, 2013). To keep computability on an acceptable
level, 1,000 random employee driving profiles out of the 2,966 from the German
Mobility Panel (Zumkeller et al., 2010) depicted in Figure 4.2 serve as a model
base for EV charging load. Each vehicle is modeled individually as described
in the previous section to ensure decentralized coordination based on rational
and independent individual decision-making. However, because of excessive
trip distances or insufficient charging time between subsequent trips, a driving
profile may not be feasible with an EV. In addition, the end SOCT condition 4.12
of the optimal charging regime results in some profiles becoming infeasible.
The reason is that this thesis assumes SOCT = SOCO = SOC to be able to
compare results of uncoordinated and coordinated charging. For these reasons,
100 infeasible driving profiles have to be removed in the base scenario (charging
at home and work with charging power 11 kW).20
The population charging behavior is evaluated under a time-based variable
external price signal which is an instance of pext
t described in Section 4.1. This
thesis uses EPEX SPOT (European Power Exchange) hourly electricity prices
from 2012.21 . These prices are not directly applicable to end-consumers. However, the availability of low-cost generation capacity in the market is somehow
reflected by the price variability. This way, the electricity price data also serves as
a proxy for renewable generation availability. These prices neither include taxes
nor license or transmission fees. Therefore, the average hourly prices of 2012 are
normalized to the average retail electricity price in Germany in the same year
(approximately 0.26 e/kWh).22 In addition, the prices are interpolated linearly
20 73
profiles are removed due to excessive trip distances. Additional 25 profiles are removed
due to a T 6 {Home, Work}, and 2 profiles because the time after the last trip is insufficient
to reach SOC.
21 www.epexspot.com/en/market-data/
22 The average electricity price in 2012 for households is reported by Bundeskartellamt and
0.8
0.6
0.4
0.0
0.2
Price [Euro/kWh]
1.0
1.2
74
Mo 0:00
Tu 0:00
We 0:00
Th 0:00
Fr 0:00
Sa 0:00
Su 0:00
Mo 0:00
Time
to better map hourly prices to the 15-minute resolution of the driving profiles.
Finally, all negative prices are set to zero to avoid gains through consumption of
electricity for mobility. This is in line with the EU goals of energy efficient tariffs
that do not support the waste of energy, e.g., directive 2006/32/EC. Figure 4.4
depicts the upscaled and interpolated electricity prices for one week. This approach follows prior research on smart grid and EV applications (Hartmann and
zdemir, 2011; Gottwalt et al., 2011).
Bundesnetzagentur (2012) with 0.2606 e/kWh and by (BDEW, 2013) with 0.2589 e/kWh,
respectively.
75
(
( at ) =
if at {Home, Work},
otherwise.
(4.14)
This simple charging maximizes EV range at any given time. Moreover, it requires no information on future trips of the EV customer. It can be used to analyze the feasibility of any given driving profile under EV battery restrictions and
provides a maximum range benchmark. Therefore, all remaining driving profiles used are feasible under UC.24 Uncoordinated charging mainly depends on
the driving profiles and is expected to result in load spikes due to commuter mobility, i.e., in the morning at Work and in the evening at Home. Figure 4.5 depicts
the resulting loads at the different locations. On the left, it shows the load over
time at both charging locations Home and Work in one example week (672 time
slots). On the right, all load levels throughout the simulated 52 weeks with each
672 time slots serve as the base for each location (34,944 time slots per location).
The violin plots on the right of Figure 4.5 depict the distribution of occurred load
23 A
version of this section is also used in our working paper Salah et al. (2013).
charging approach was used to identify the 100 infeasible profiles at 11 kW charging
speed.
24 This
76
levels over all 52 weeks. This type of diagram is repeated in this chapter to allow
for visual comparison of the different load coordination mechanisms.
Distribution of loads (52 weeks)
2000
2000
1000
1500
Limit
500
1000
0
500
1500
Home
Work
Limit
Mo 0:00
Tu 0:00
We 0:00
Th 0:00
Fr 0:00
Sa 0:00
Su 0:00
Mo 0:00
Home
Work
Time
Figure 4.5: Aggregate load curve at Home and Work locations with uncoordinated charging (UC) in one example week (672 time slots) and distribution of loads over 52 weeks
(34,944 time slots)
section contains is based on parts of our paper Flath et al. (2013) where supply-based
charging also serves as reference scenario.
77
min C () =
pext
t t
(4.15)
t =1
subject to the constraints listed in Section 4.2.4. Given the individual optimization, all EV agents try to shift their charging demand to low-cost periods of the
external price signal. Consequently, the aggregate load exhibits extreme spikes
greatly exceeding 2,000 kW under wholesale electricity price coordination during low-price periods. Figure 4.6 shows the resulting load pattern for one example week and the load distribution over all 52 weeks. In addition, the exogenous
price vector for the example week is depicted below the load pattern. The lower
right corner shows the external price signal distribution over all 52 weeks in a
violin plot as well. Note that the y-axis for the full year price distribution is different from the example week account for wholesale price spikes that occurred
in other weeks of the year 2012.
10000
10000
8000
6000
4000
0
2000
4000
6000
Limit
2000
8000
Work
Mo 0:00
Tu 0:00
We 0:00
Th 0:00
Fr 0:00
Sa 0:00
Su 0:00
Mo 0:00
Home
0.0
0.4
0.2
0.8
0.4
1.2
0.0
Prices [Euro/kWh]
Work
Mo 0:00
Tu 0:00
We 0:00
Th 0:00
Fr 0:00
Sa 0:00
Su 0:00
Mo 0:00
External
Time
Figure 4.6: Aggregate load curve at Home and Work locations with supply-based coordination (SB) and external price signal in one example week (672 time slots) and distribution over 52 weeks (34,944 time slots)
The violin plot in the upper right corner shows that extreme load spikes also
occur in other weeks of the year. These effects are in line with results from prior
research on the effects of price-based coordination in retail markets (Rahman
and Shrestha, 1993; Gottwalt et al., 2011). Another interesting outcome is that
the charging mainly occurs at the Home location, even though charging is possi-
78
ble at both locations. The reason for this is that in the current electricity market
low electricity prices typically emerge during low-demand hours at night (see
Figure 4.4). Consequently, supply-based EV charging coordination leads to temporal and spatial clustering of charging activity. Therefore, the physical limits
of distribution grids may be significantly challenged in residential areas by increasing EV penetration.
Static Load Curtailment
The simple solution to avoid infrastructure overloads through EV charging is to
limit the maximum charging speed at the charging station. This is an instance of
the SLC approach described above. As indicated in Table 4.1 the pricing structure and therefore the objective function remains the same as with supply-based
charging. However, in the EV model setup, the individual charging speed is
limited to
L
2, 000kW
=
2.2kW.
(4.16)
n
900
This directly translates into = 0.55 kWh per 15 minutes time slot. Given this
additional constraint, the individual EV charging optimization leads to lower
peak demands, as depicted in Figures 4.7.
2000
2000
1000
1500
Limit
0
Mo 0:00
Tu 0:00
We 0:00
Th 0:00
Fr 0:00
Sa 0:00
Su 0:00
Mo 0:00
Home
Work
0.0
0.0
0.4
0.2
0.8
0.4
EPEX Spot
1.2
500
1000
0
500
1500
Home
Work
Limit
Mo 0:00
Tu 0:00
We 0:00
Th 0:00
Fr 0:00
Sa 0:00
Su 0:00
Mo 0:00
External
Time
Figure 4.7: Aggregate load curve at Home and Work locations with static load curtailment
(SLC) and external price signal in one example week (672 time slots) and distribution
over 52 weeks (34,944 time slots)
However, these reduced loads come at the expense of lower utilization of lowcost generation which will result in higher average wholesale prices paid by con-
79
i
lim
t,x
x
t T
i =1
where
(4.17)
lim
x = 2, 000kW
Similar to SLC, the objective function and other auxiliary conditions remain the
same. Given the strict capacity constraint, DLC succeeds in keeping the infrastructure limits as depicted in Figure 4.8. At the same time, DLC does not restrict
consumption needlessly during low-cost time slots. However, it can result in
infeasible profiles similar to SLC.
80
2000
2000
1500
1000
0
Mo 0:00
Tu 0:00
We 0:00
Th 0:00
Fr 0:00
Sa 0:00
Su 0:00
Mo 0:00
Home
Work
0.0
0.0
0.4
0.2
0.8
0.4
EPEX Spot
1.2
500
1000
0
500
1500
Home
Work
Limit
Mo 0:00
Tu 0:00
We 0:00
Th 0:00
Fr 0:00
Sa 0:00
Su 0:00
Mo 0:00
External
Time
Figure 4.8: Aggregate load curve at Home and Work locations with dynamic load curtailment (DLC) and external price signal in one example week (672 time slots) and distribution over 52 weeks (34,944 time slots)
min C () =
t =1
pext
t
t +
max {t }
t[1..T ]
(4.18)
81
increasing marginal load cost.26 In this exemplary instance, factor which controls the influence of load price is set to unity. Similarly, the continuous load
pricing SLPt objective function for EV charging is implemented with shorter
billing periods:
T
2
min C () = pext
(4.19)
t
t
t
t =1
The constant factor determines the penalty fee for higher loads per period and
is set to = 0.1 in the current example. If it is too low, the load level influence
on the total price per period is marginal and the resulting charging patterns are
close to the purely supply-based coordination. In the case of this factor being
too high, the individual optimization tries to minimize load peaks without integrating the external price signal. The selected value ensures in this scenario that
most load peaks are reduced to adhering or only slightly exceeding the infrastructure limit. Given the maximum charging speed of = 2.75 kWh in one time
slot, the total costs are approximately split even between the SLP component
and the average external price at this limit. Such scaling is not possible for in
the SLPmax approach because the average influence of the SLP component per
kWh depends on the total consumption per week, which differs per vehicle. A
more detailed sensitivity analysis of both factors is presented in Section 4.3.3. As
depicted in the overview, Figures 4.9, and Figures 4.10, both approaches lead to
a peak load reduction.
Obviously, the SLP approaches cannot guarantee total load to stay within infrastructure limits. Depending on the implementation, the main difference is
that SLPmax results in an individual optimal selection of a maximum charging
speed for a whole week. Whereas, under SLPt the EV agents balance between
energy and load cost in each time slot separately.
26 The
next section of this thesis shortly discusses the reasons for convex cost functions.
82
2500
2500
2000
1500
1000
0
500
1000
1500
Limit
500
2000
Work
Mo 0:00
Tu 0:00
We 0:00
Th 0:00
Fr 0:00
Sa 0:00
Su 0:00
Mo 0:00
Home
0.0
0.4
0.2
0.8
0.4
EPEX Spot
1.2
0.0
Prices [Euro/kWh]
Work
Mo 0:00
Tu 0:00
We 0:00
Th 0:00
Fr 0:00
Sa 0:00
Su 0:00
Mo 0:00
External
Time
Limit
0
Mo 0:00
Tu 0:00
We 0:00
Th 0:00
Fr 0:00
Sa 0:00
Su 0:00
Mo 0:00
Home
Work
0.0
0.0
0.4
0.2
0.8
0.4
EPEX Spot
1.2
500
Limit
500
Figure 4.9: Aggregate load curve at Home and Work locations with SLPmax coordination
and external price signal in one example week (672 time slots) and distribution over 52
weeks (34,944 time slots)
Mo 0:00
Tu 0:00
We 0:00
Th 0:00
Fr 0:00
Sa 0:00
Su 0:00
Mo 0:00
External
Time
Figure 4.10: Aggregate load curve at Home and Work locations with SLPt coordination
and external price signal in one example week (672 time slots) and distribution over 52
weeks (34,944 time slots)
83
(4.20)
sections is in large parts a reproduction of our paper on area pricing (Flath et al., 2013).
84
t,x
limit itself could be time-varying. Denoting substation utilization by z = lim
x
the following pricing function parameterized by is used to determine locationspecific prices fulfilling conditions (4.20) and (4.21):
( z
e 1 loc
p
if z < 1
e 1 lim
ploc
=
(4.22)
t,x
loc
plim
if z 1
where ploc
lim is the locational surcharge at the infrastructure limit z = 1. Some
exemplary pricing functions using different values for are depicted in Figure
4.11. This DLP approach is applied in the model to update the charging prices
dynamically given the charging activity at different locations. After a customers
charging decision has been made, the adjusted price for the current location is
updated to reflect the load increase and the subsequent customers experience
adapted prices.
ploc
lim
=0.01
=3.0
=10.0
=100.0
0
0
lim
x
Figure 4.11: Examples of dynamic local pricing function for different values of
85
depicted prices represent the price level reached after the final EVs charging
decision.
2000
1000
0
500
1000
We 0:00
Th 0:00
Fr 0:00
Sa 0:00
Su 0:00
Mo 0:00
0.4
Work
0.0
0.4
0.2
0.8
EPEX Spot
0.0
Prices [Euro/kWh]
Home
1.2
Tu 0:00
Mo 0:00
Tu 0:00
We 0:00
Th 0:00
Fr 0:00
Sa 0:00
Su 0:00
Mo 0:00
Home
0.4
External
0.0
0.0
0.4
0.2
0.8
EPEX Spot
1.2
500
0
Mo 0:00
Prices [Euro/kWh]
Limit
1500
Home
Work
Limit
1500
2000
Mo 0:00
Tu 0:00
We 0:00
Th 0:00
Fr 0:00
Sa 0:00
Su 0:00
Mo 0:00
External
Work
Time
Figure 4.12: Aggregate load curve at Home and Work locations with DLP coordination
and external price signal in one example week (672 time slots) and distribution over 52
weeks (34,944 time slots)
Higher loads still occur at the Home location because low wholesale electricity
prices still occur during nighttime. Notably, the local load in all 52 simulated
weeks never reaches the limit lim at any location, which also indicates that the
local limit price ploc
lim is never reached in both locations. The distribution of the
different price elements in the lower right corner shows that the additional local
surcharges remain on low levels. Specifically, there is hardly any local surcharge
at Work, which indicates that load levels are well below the given capacity limit.
As mentioned before, the additional revenues generated by location-specific surcharges can be used for other purposes, e.g., capacity expansion. In summary,
dynamic local price increases lead to both temporal and spatial shifts in individual charging decisions and reduce load peaks significantly.
86
i
pext
t t
(4.23)
i t =1
The optimization is subject to the constraints 4.11, 4.12 and 4.13 for each individual EV. In addition, the maximum load restrictions used in DLC at Home and
Work (Equation 4.17) are directly implemented in the optimization model:
n
i
lim
t,x
x = 2, 000 kW
t T.
i =1
Given this implementation, the CPLEX solver calculates an overall cost minimizing charging pattern for each week which at the same time fulfills the grid
limits and ensures mobility needs. The introduced overview graph shows that
the load limits are always exactly reached, but never exceeded in time slots with
low wholesale prices (Figure 4.13). In the following, this central planner approach serves as a quantitative reference.
87
2000
2000
1500
1000
0
Mo 0:00
Tu 0:00
We 0:00
Th 0:00
Fr 0:00
Sa 0:00
Su 0:00
Mo 0:00
Home
Work
0.0
0.0
0.4
0.2
0.8
0.4
EPEX Spot
1.2
500
1000
0
500
1500
Home
Work
Limit
Mo 0:00
Tu 0:00
We 0:00
Th 0:00
Fr 0:00
Sa 0:00
Su 0:00
Mo 0:00
External
Time
Figure 4.13: Aggregate load curve at home and work locations given a central planner
(OPT) and external price signal in one example week (672 time slots) and distribution
over 52 weeks (34,944 time slots)
88
7500
UC
5000
2500
0
7500
SB
5000
2500
0
7500
SLC
5000
2500
0
DLC
5000
2500
0
7500
SLPmax
7500
5000
2500
0
7500
SLPt
5000
2500
0
7500
DLP
5000
2500
0
7500
OPT
5000
2500
0
Mo 0:00
Tu 0:00
We 0:00
Th 0:00
Fr 0:00
Sa 0:00
Su 0:00
Mo 0:00
Time
89
is obvious, but not within the scope of this thesis. The cost obtained under
SB charging coordination provides a lower bound for average wholesale
cost.
Average SOC: The average SOC represents the spontaneous range availability
indicates the level of guaranteed mobility. Canceling trips which are possible with other charging coordination mechanisms may induce customer
dissatisfaction. The risk of infeasible rides may even prevent EVs from
gaining share in the individual mobility market. However, there is always
the outside option of using a non-electric vehicle to fulfill mobility needs.
Overloads: The number of overloads indicates the effectiveness of congestion
mitigation. While overloads should ideally not occur at all, the grid infrastructure elements are able to cope with limited overloads for a short period
of time.
Maximum load: The maximum load occurred at each location indicates the mag-
nitude of overloads and therefore helps to understand if given grid infrastructure might tolerate this for a short period. On the other hand, low
maximum loads reveal that given capacity is not fully utilized and coordination mechanisms might be adjusted to allow higher loads.
Locational consumption: The share of total charging consumption at the loca-
tions Home and Work stands for the influence of the mechanisms to induce
locational load shifts.
The important variables characterizing the outcome of each coordination approach are compared in Table 4.4. In addition to the base case of 2,000 kW, all
approaches have been simulated using a local load limit of lim
x = 1, 000 kW to
investigate potential differences with less spare capacity.
e
Regarding the wholesale cost, the cost-optimal SB benchmark of 0.135 kWh
is a hypothetical solution only, since the goal is to avoid overloads and the
maximum load of 9,470 kW is not acceptable. The realistic benchmark which
incorporates the local infrastructure limits are results of a central planner (OPT)
e
e
with full information: 0.144 kWh
(0.159 kWh
at lim
= 1, 000 kW). The other
x
extreme in terms of average wholesale cost is uncoordinated UC charging.
90
UC
Limit 2,000 kW
SLC
SLPmax
DLC
SLPt
DLP
OPT
Home Work Home Work Home Work Home Work Home Work Home Work Home Work Home Work
Dimension
e
]
Avg. cost (whsl) [ kWh
0.307
0.135
0.155
0.145
0.149
0.163
0.154
0.144
Avg. SOC
[pct.]
98.7%
69.9%
68.2%
70.8%
71.7%
73.6%
72.1%
71.1%
[#]
52.0
1.0
Overloads
[#]
Max. Load
[kW]
Home Cons.
[pct.]
68.8%
97.0%
95.9%
96.5%
96.9%
94.9%
93.1%
95.9%
e
Avg. cost (whsl) [ kWh
]
0.307
0.135
0.175
0.159
0.149
0.163
0.172
0.159
Avg. SOC
[pct.]
98.7%
69.9%
66.9%
72.0%
71.7%
73.6%
74.7%
72.7%
[#]
105.0
5.0
Overloads
[#]
Max. Load
[kW]
Home Cons.
[pct.]
684
733
684
733
68.8%
975
19
425
50
9,470 5,361 1,812 1,071 2,000 2,000 2,465 1,327 3,146 1,057 1,804 1,428 2,000 2,000
1,501
33
9,470 5,361
97.0%
824
484
93.4%
2,636
21
1,323
26
96.9%
94.9%
Table 4.4: EV model results with different charging coordination approaches at 11kW
0
797
91.4%
1,000 1,000
94.1%
Limit 1,000 kW
SB
91
92
0.5
10
SLPmax
e
[ kWh
]
0.145
0.149
0.158
[pct.]
71.2%
71.7%
72.7%
[#]
0
0
0
[#]
917
0
425
0
0
0
[kW] 3,232 1,824 2,465 1,327 1,885 876
[pct.]
97.0%
96.9%
96.5%
0.171
74.6%
0
0
0
1,291 620
95.2%
For the scenario discussed in this thesis, the setup which avoids overloads
and still uses low-cost wholesale time slots is roughly 1 < < 3 with average
wholesale cost between 0.149 e/kWh and 0.158 e/kWh. To determine the optimal setup of parameter , the cost of overloads would need to be calculated.
Given the large investments and long service life of transformers, this goes beyond the scope of this thesis.
93
94
0.01
0.1
0.3
0.5
SLPt
e
]
0.139
0.163
0.189
[ kWh
[pct.]
70.8%
73.6%
77.0%
[#]
0
0
0
[#]
960
14
50
0
0
0
[kW] 9,389 3,649 3,146 1,057 1,429 549
[pct.]
96.8%
94.9%
91.0%
0.203
78.8%
0
0
0
1,031 415
88.4%
29 The
same would apply for uncertainty of other loads that are currently not considered in the
model.
95
0.01
Load distr. at
Home
[% of total]
e
Avg. cost (whsl) [ kWh
]
e
Avg. cost (loc) [ kWh ]
Avg. SOC [pct.]
1.00
0-100 kW (%)
64.01 64.37 68.14 75.14 83.99 85.25
100-500 kW (%)
23.55 22.97 17.13 8.40 3.76 4.56
500-1,000 kW (%)
10.06 10.20 11.37 10.69 1.62 1.80
1,000-1,500 kW (%) 2.11 2.19 3.08 5.10 5.46 1.08
1,500-2,000 kW (%) 0.25 0.26 0.28 0.67 5.17 7.26
> 2,000 kW (%)
0.00 0.00 0.00 0.00 0.00 0.05
0.10
0-100 kW (%)
94.64 94.82 96.21 97.76 98.70 98.91
100-500 kW (%)
5.20 5.01 3.60 1.95 1.08 0.91
500-1,000 kW (%)
0.12 0.12 0.13 0.21 0.06 0.05
1,000-1,500 kW (%) 0.03 0.04 0.06 0.08 0.09 0.03
1,500-2,000 kW (%) 0.00 0.00 0.00 0.00 0.07 0.10
> 2,000 kW (%)
0.00 0.00 0.00 0.00 0.00 0.00
Table 4.7: Impact of on average costs and load at Home and Work with individual EV
charging optimization
96
load shifts to desired supply (e.g., low-cost, RES) at all (). All other approaches incorporate incentives to shift load into periods with low-cost
wholesale prices. Obviously, the SB coordination serves as a benchmark in
terms of desired supply utilization (BM). However, given the individual
information base, SLC and SLP can limit loads, even if it is not necessary in
30 The
Swiss grid planning impact study, which is presented in the next section, includes these
other loads in the analysis.
97
terms of aggregate load (). In contrast, DLP and DLC influence demand
only if it is necessary due to aggregate infrastructure limits (+).
Efficiency/Fairness The efficiency or fairness criterion is more weakly defined
in this case and combines several aspects of the other criteria. Basically,
it rates whether the coordination approach is able to differentiate between
low and high load valuation. This means that in time slots with capacity constraints preferably demand with high valuation is served. UC, SB,
SLC and DLC cannot distinguish between different valuations for demand
in capacity-constrained time slots (). For UC and SB, this is because capacity is not considered at all. SLC and DLC are forms of direct control
and therefore could integrate different valuations in forms of static contracts only (i.e., only low valuation loads that can cope with curtailment
will accept these approaches). SLP adds the dynamic pricing of load and
therefore leads to prudent usage of high load levels. However, SLP still
focuses on own load only and does not lead to shifts of unnecessary loads
with low valuation in comparison to other consumers in times of high infrastructure utilization (). This target is achieved by DLP only. Given the
right setup, DLP incentivizes load shifting in times of high aggregate load
and thus tries to ensure efficient use of infrastructure in combination with
supply-based incentives (+).
Coordination
Criterion
UC
SB
SLC
DLC
SLP
DLP
Communication complexity
Tariff complexity
Infrastructure limit protection
Consumption guarantee
Comfort level
Desired supply utilization
Efficiency/Fairness
BM
BM
BM
BM
+
+
BM
BM
BM
BM
+
BM
+
BM
+
+
98
99
100
power rating of charging systems (2) determines the minimum length of a charging procedure and the maximum instantaneous impact of an individual vehicle
on the system. Another external input for the model is the electricity spot price
Swissix (3) which serves as a baseline for a variable EV charging tariff. Technical specifications and locations of high-voltage substations in the BKW grid (4)
are incorporated to account for regional differences in grid capacity. Given the
forecast of every substations load curve (5), all other loads are accounted for
as well. By considering the market penetration and regional allocation of electric vehicles (6) we can map the effects of regional differences to corresponding
substations. Swiss driving profiles (7) from the Swiss Federal Statistical Office
(SFSO) are the main source for modeling driving behavior which governs the
charging requirement for daily trips as well as the times during which charging
procedures can take place.
(4)
(5)
(3)
(1)
(6,7)
(2)
Model element
Data Source
OEM data
IEC 62196-1
Swissgrid, EPEX
BKW data
BKW data
SFSO data
SFSO census
101
Electricity Price
For the evaluation of the charging loads three pricing scenarios are applied
static pricing, SB pricing and DLP. The power price for end consumers in
Switzerland comprises 40% generation, trade and marketing costs, 46% grid
costs and 14% taxes and other dues.33 For the static electricity price scenario,
we can directly apply a price of 0.18 e/kWh to our model in the form of a flat
tariff for EV charging. However, variable electricity prices are currently not yet
readily available to retail customers. Therefore, the model uses a hypothetical
SB tariff which assumes that the entire wholesale costs follow the Swissix spot
market price. The DLP approach uses the SB price and adds a dynamic price
component to account for the current system load. To increase the temporal resolution of the prices and increase the alignment with the driving profiles, the
hourly exchange prices are linearly interpolated to obtain quarter-hourly prices.
Let p T denote the Swissix wholesale price in hour T and p T +1 the wholesale price
in the subsequent hour T + 1. The linearly interpolated price p(t) in t [ T, T + 1]
is then given by:
p ( t ) = ( T + 1 t ) p T + ( t T ) p T +1
(4.24)
For example, if two subsequent hourly prices are 50.00 e/MWh and 60.00
e/MWh, we obtain in-between quarter-hourly prices of 52.50 e/MWh, 55.00
e/MWh, and 57.50 e/MWh. These prices are then fed back into the generation
share by normalizing with the average price in 2010 and are then applied to the
dynamic electricity tariff scenario. To ensure tractability of the approach, we use
an exogenous price and in our model abstract from influencing feedback mechanisms on the electricity price. The potential development of future power prices
and the influence of flexible loads are discussed in Section 4.5.1.
Grid Infrastructure
The power grid comprises different layers ranging from high-voltage transmission lines to low-voltage distribution grids. Relevant bottlenecks in the grid are
the line limits and transformer capacities across different voltage levels. This
case study focuses on the load at substations in the high-voltage grid of BKW.
These substations comprise transformers between the high-voltage grids, that
either run on 132 or 50 kV, and the connected medium-voltage grids, that operate at 16 kV, and further aggregate the load of end consumers in the low-voltage
grid. Typical transformers have a capacity of 12.5, 25, or 40 MVA depending on
the load profile in this region.
A substation is the topological node where we measure the load to calculate
further information, we refer to the association of Swiss electricity enterprises (http://
www.strom.ch).
33 For
102
the capacity utilization. For the sake of simplicity, we abstract from the capacity utilization of overlying high-voltage lines, since this would require timeintensive load flow calculations. Thus, the utilization values reported correspond to transformer capacity and not to actual system capacity. Hence, the
values are systematically too low, as transformer capacity may be higher than
the feeding line limits. Initial calculations of the developed scenarios on the real
BKW grid model show that the lines can be an important limiting factor. We
use the (n-1)-capacity of all HV/MV transformers in each substation as 100%
capacity on our model, i.e., half of the total capacity in the case of two equal
transformers and two thirds in the case of three equal transformers.34 This is a
standard approach in high-voltage grid planning.
In Switzerland, 8 million people are supplied through approximately 250 substations with a transformer capacity of 40 MVA on average (BFE, 2010). In the
area supplied by BKW and adjacent regions35 there are 122 substations in total.
78 of these are completely or partly owned by BKW which supply approximately
350.000 people. Reasons for the deviation of people per substation ratio is that
BKW supplies rural areas with a low residential density, while cities like Bern
are supplied by other operators. For 59 of BKWs substations sufficient data
was available to be able to generate an individual load curve forecast for each of
them. Out of these 59 substations, the load forecasts of ten substations already
exceeded todays transformer capacity in 2040 without additional EV charging
loads which necessitates capacity investments to ensure reliable future operation. As the focus is on transformer substation requirements due to EV charging,
we excluded these substations from our analysis. The remaining 49 substations
(highlighted in Figure 4.17) are considered and serve as base for our model.
To capture the effect of EV charging on these substations we need to map municipalities (with their expected number of electric vehicles) to each substation.
The location of the distribution grid stations36 connected to substations determines which municipalities are supplied by which substations. The distribution
of EV charging stations within the municipalities which are connected to the low
voltage grid is not within the scope of our simulation. Our study focuses on the
aggregate charging load which can be measured on the substations level.
34 For
ease of exposition, this reference value is being referred to as substation capacity, even
though substations switchgear can represent another limiting factor besides lines and transformers.
35 Adjacent regions had to be examined in BKWs target grid planning project as they can influence BKWs grid.
36 Distribution grid stations transform between medium voltage grids and low voltage grids.
103
132 kV Grid
50 kV Grid
Modeled Substation
Other Substation
104
allocate the EVs to the substations of BKW in order to model their influence on
substation load curves. An overview of the required input data and the combination is depicted in Figure 4.18.
Input Data
Future municipality population
(Bundesamt fr Statistik,
2011c, Bundesamt fr
Statistik, 2011a)
Calculation
EV Penetration scenarios
(Estimate 16% and extreme 50/100%)
105
> 3000 electric vehicles
1000-3000 electric vehicles
100-1000 electric vehicles
50-100 electric vehicles
0-50 electric vehicles
Figure 4.19: Estimated number of EVs per municipality in the relevant regions in 2040
serves as base
data
our
model.Grids
Members of 60,000
households
were
selected
Impact of
Electricfor
Vehicles
on High-Voltage
Institute
of Information Systems
and Management
Department of Economics and Business Engineering
randomly and interviewed regarding their mobility behavior on the day before
the interview day. We use the survey questions on trip timing, distances, type
and means of transportation to extract raw trip data. Figure 4.20 depicts the
distribution of the daily driving distances.
This trip data is wrapped in driving profiles that consist of the driving status,
the distance driven, and the location of the car in a 15-minute resolution over the
whole day. We use these driving profiles to model the EV charging requirements.
Although these profiles are based on conventional vehicle trips, we apply them
to build EV models similar to the previous section as changes in the driving
behavior have to be expected only in the long-run (Oeltze et al., 2006). In order
to allow for load shifts greater than one day, the driving profiles are extended
to a period of one week by looping them. Of the initial set of 17,087 driving
profiles, we had to remove 4.1% of the profiles, as they conflicted with certain
model assumptions:37
1.3% of the profiles featured trips that exceeded the assumed EV range in
37 This
differs from the approximately 10% of driving profiles that had to be removed from the
German Mobility Panel employee data in Section 4.3. Except for the difference of employees
only in the German Mobility Panel to a mixed population here, the underlying reasons for the
difference are not known. However, some differences may be due to the survey format. For
example, SFSO data refers to the day before the interview, which clearly excludes trips and
vacation times greater than one day. As depicted in Figure 4.20, the distribution is similar to
typical mobility behavior.
106
0.025
Density
0.020
0.015
0.010
0.005
0.000
0
50
100
150
200
250
300
Distance in km
Figure 4.20: Distribution of daily driving distances in the SFSO mobility survey
a single trip
0.4% of the profiles featured trip sequences with insufficient recharge time
and thus exceeded the assumed EV range
2.4% of the profiles did not terminate at the home location and were thus
unable to fully restore battery capacity at the end as required for optimal
EV charging
Given the limited size of the mobility survey compared with the EV penetration projection, we reused the set of driving profiles to generate the necessary
input data. To maintain integrity with respect to the driving habits, the assignment of profiles to substation is based on the municipality type as provided by
the SFSO (Schuler et al., 2005), i.e., only rural profiles are used in rural areas.
107
Substation Count
0%
16%
50%
100%
10
0
0
Figure 4.21: Substation peak load distribution with uncoordinated charging UC for different EV market penetration levels (N=49)
With the estimated progress of market penetration of EVs, we can expect that
none of the substations will be overloaded until the year 2040. Thus, load clustering due to similar driving habits does not have a large impact on peak loads
of BKW substations at a market penetration of 16%. At higher EV penetration
levels, overload situations become more likely but still remain limited in both
number as well as magnitude.
108
Substation Count
Simple Charging
Smart Charging
10
0
0
20
40
60
20
40
60
Figure 4.22: Substation peak load distribution under simple and smart charging for 16%
market penetration (N=49)
Figure 4.22 shows that at a market penetration of 16% many substations are
already overloaded under SB price-coordinated charging. Furthermore, reaching utilization levels of 150%, these overloads are more significant than the ones
under simple UC charging with 100% penetration. The strong shift of the histogram towards higher peak loads is a result of price differences over the week.
Due to the financial incentives, price-sensitive EV agents will charge their batteries at times of low electricity prices. The depicted histograms are based on the
Swissix prices of the third calendar week 2010. However, the observed effects
are robust to variations of the underlying price vector. In total we evaluated 12
different price weeks in 2010 that are depicted in Figure 4.23 four example
weeks for each season: summer, winter and transition.
Besides the aggregate view of all substations, it is also illustrative to look at
the substations individually. Figure 4.24 provides anonymized utilization boxplots based on smart charging of all 12 simulated weeks for each substation. The
solid line illustrates the peak utilization of each substation without EV charging
loads. The diverse outcomes per substation reflect the multitude of real input
data for the simulation. Some substations will be more challenged by upcoming
EV charging loads. The underlying reasons for this heterogeneity are diverse,
e.g., rural or urban areas, mobility behavior, EV distribution. Furthermore, this
analysis provides some guidance on which substations will be suited for economic coordination of charging loads (overloads arising mostly from EV charg-
Sample Week 1
109
Sample Week 2
Sample Week 3
Sample Week 4
10
Summer
Transition
Substation Count
10
0
10
Winter
0
0
Figure 4.23: Substation peak loads with optimal smart charging for sample weeks in
summer, transition and winter period under 16% market penetration (N=49)
ing), and which substations will most likely require capacity upgrades (high utilization levels even without electric vehicles).
DLP Scenario
Due to the resulting overloads of the variable SB coordination, we apply a DLP
coordination to analyze the potential overload mitigation effect. Unlike the example with Home and Work locations in Section 4.3.1, DLP is set up at each substation in the BKW grid. The parametrization is the same as in Section 4.3.1 with
= 3 and the limit price based on the median of the external price of the respective week. As expected, DLP coordination succeeds in shifting EV charging
load into times with lower grid utilization. Across all substations, the maximum
capacity is never exceeded given 16% EV market penetration in the 12 example
weeks simulated (Figure 4.25). The DLP approach allows increasing peak loads
caused by EV charging at substations with lower maximum utilization. In contrast, substations with high maximum utilization do not experience higher peak
loads through EV charging under DLP. Nevertheless, as mentioned before, substations with high utilization even if no additional load from EVs is considered
most likely will require capacity upgrades.
110
150
100
50
0
1
9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49
Substation Index
Figure 4.24: Boxplots for substation peak load distribution per substation with SB smart
charging (based on 12 simulation weeks)
150
100
50
0
1
9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49
Substation Index
Figure 4.25: Boxplots for substation peak load distribution per substation with DLP
smart charging (based on 12 simulation weeks)
111
112
4.5.1 Discussion
The modeled approaches of local load coordination have limitations mainly concerning assumptions on modeled components and individual behaviour. The
main limitations are discussed in the following.
Tariff Complexity
As noted before, spatial pricing schemes have been demonstrated to improve
system efficiency while at the same time increasing the pricing complexity that
customers are faced with. First, the discussed tariffs (e.g., SLP, DLP) are currently not realistic on a household level. Specifically, the complex tariffs require
a full smart grid roll-out as well as real-time access to load and billing data. In
addition, the regulator would need to allow one actor to charge dynamic fees
based on the local system state. Given the deregulation to foster competition,
a grid area is typically served by several electricity retailers in most countries.
Therefore, the grid operator is suited to undertake this task as a form of his grid
operation duties. So far, there is no intended introduction of such dynamic local
grid fees. Even if the technical and regulatory issues are resolved, consumers
need to accept highly variable tariffs or load curtailment for the implementation
of the discussed load coordination mechanisms. Dtschke and Paetz (2013) find
that consumers prefer simple over complex tariffs and that demand automation
is needed to tap consumers flexibility. However, EV charging constitutes an additional and flexible load which may facilitate the introduction and serve as a
reference case for load coordination approaches as well as more complex tariffs,
since it is separable from other loads through designated charging stations.
Full Price Responsiveness
Furthermore, the load clustering and coordination results, given a variable price
vector, are based on fully price-responsive EV owners with perfect knowledge
of future market prices. Unquestionably, these are benchmark results for the effects of price-responsive EV charging on the power system while still assuring
given mobility patterns. In general, load flexibility in field trials is only limited
as mentioned before. Faruqui and Sergici (2010) review 15 residential dynamic
pricing studies and report mean peak reductions of 4-44%, depending on rate
design. They find an especially high impact of dynamic pricing if supported
by enabling technologies such as automated air conditioning. However, these
studies are based on residential demand which includes load types that are less
shiftable (e.g., entertainment, cooking). In contrast, EV loads are easily shiftable
without or with only a minor loss in mobility comfort. Therefore, high load flexibility seems to be possible in the presence of appropriate incentives and tech-
113
nical support for EV owners (e.g., intuitive interfaces and automated charging
systems). Smart charging of EVs offers higher benefits than other load management approaches due to large charging energy amounts. In the future, variable
pricing can be applied to other flexible loads as well (e.g., distributed storage,
heating and cooling appliances) to leverage demand side flexibility. Another aspect may be the flexibility in mobility patterns, as this thesis assumes invariant
mobility needs. As mentioned by Sioshansi (2012), consumers may change their
driving patterns when they get used to variable tariffs. In addition, the examples assume that the entire consumer population is in the same tariff. In real
applications, a variety of different tariffs will be offered to consumers. Thus,
consumers with a preference for higher quality of service may select different
tariffs. Consequently, the load coordination effects presented may be valid for
parts of the total consumer base only. Different behaviour based on heuristic EV
charging strategies and only limited knowledge is discussed in our papers Flath
et al. (2012) and Flath et al. (2013).
Exogenous Price Vectors
In all instances of our model we assume an exogenous price vector. Depending
on the scenario, the variability and the spread between highest and lowest price
are different. However, it should be noted, that for the analysis of substation utilization, the absolute level of the dynamic prices is not essential. Price variability is crucial, as optimal charging leverages these price differentials to determine
charging schedules. In the case of completely flat price curves, these load coordination incentives vanish. This approach implicitly assumes that wholesale prices
remain unaffected by the EV loads. This is clearly a limiting assumption, as concentrated charging loads may induce system-wide load increases which should
impact wholesale prices. Other publications focus on different aspects of load
influence on wholesale prices. Boisvert et al. (2002) find in the NYISO zone that
the supply curve is hockey-stick shaped with prices exponentially increasing
in load. Whereas, Li and Flynn (2006) analyze 13 different power markets and
find that the relationship between price and load differ significantly. Nyamdash
and Denny (2013) investigate the influence of storage deployment on wholesale
prices in a unit commitment model. They find a reduction in fuel cost but an
increase in the average electricity price of the simulated power system.
Using Swissix prices as an example, a price-load relationship becomes evident. The effect greatly varies, even when controlling for season and day type as
illustrated by the large price differences present at each load level in Figure 4.26.
Both increasing amounts of intermittent generation and increased load flexibility (a result of large-scale electrification of individual transport served by renewable energy sources) will further distort the load-price relationship. Therefore,
a stable and meaningful wholesale price model based on aggregate load is not
114
Summer
Transition
Winter
weekday
100
50
100
weekend
50
0
4000
6000
8000
10000 4000
6000
8000
10000 4000
6000
8000
10000
Figure 4.26: Swissix price and Swiss total system load in 2010
available. For this reason, we avoid implementing an arbitrary model and keep
prices as an exogenous and invariant input. The wholesale prices used as input thus mainly serve to capture possible price dynamics. Other stochastic price
vectors will likely yield very similar results concerning the more frequent occurrence of substation overloads. Still, the wholesale price effect of large-scale EV
integration (and other flexible loads) offers interesting opportunities for future
research.
Power System Modeling
The impact of EV charging loads on transformer utilization in the grid is a relevant example in this thesis. This is an important step to understand opportunities and risks of flexible loads, but it is at the same time a simplification of
the complex power system. To identify other effects and constraints (e.g., losses,
line utilization, voltage drops), more detailed data and power flow analyses are
necessary. The presented model assumes EV charging to be dynamic and all
other influence factors to be static. New technologies (e.g., battery storage, home
automation) and the development of decentralized generation units (e.g., solar,
CHP) should be included to generalize the model and to obtain more robust
simulation results. In addition, the model may be further detailed by considering geographical differences in vehicle penetration (see Saarenp et al., 2013) or
long-term changes in mobility behavior.
115
116
can be used for load flow calculations, determining impact on power lines. In
fact, initial calculations of the developed scenarios on the real BKW grid model
show that already at a penetration level of 16% the lines can be an important
limiting factor. Another natural next step is to model the implications of EV
charging on other voltage levels or different high-voltage power grids to compare results. Moreover, some model assumptions may warrant closer attention
to ensure robust results. So far, the model abstracts from battery specifications
or different charging patterns which could affect battery ageing. As mentioned
above, another strong assumption is the full knowledge of future mobility patterns and prices assumed in the optimal charging strategy. Finally, the model
needs to be incorporated and aligned with other modeling efforts to support the
major restructuring of the power system. For example, the integration with models of generation capacity development including the local, intermittent supply
would allow for a combined analysis of dynamic supply and dynamic demand
on different grid levels. In addition, the real potential of the different load coordination approaches needs to be investigated, e.g., consumer acceptance of these
approaches for different services or the role of DSOs in future grid operation and
planning.
Chapter 5
Transmission Grid Cost Allocation
and Investment
Expected changes in electric power supply and demand impact future power
grids. On the one hand, the shift from fossil fuel-based generation to renewable
energy sources (RES) leads to more intermittent supply. On the other hand, demand profiles are expected to change, since new smart grid technologies enable
flexibility in consumption of electricity and provide a basis for more diversified
energy tariffs and services.
In addition to these changes in supply and demand patterns, there is also
a locational shift of generation, since RES generators are typically not built at
the same locations as existing fossil fuel plants. This relocation of generation
capacity poses additional challenges for the historically grown grid infrastructure. Massive grid infrastructure investments are necessary and grid expansion
actions are undertaken in different forms internationally.1 Regulators have
to consider both grid investments and other measures such as influencing
the siting of new generators to achieve reliable electricity supply and define
an efficient trade-off. In cases with high investment costs or extensive land
consumption, project duration and public opinion are of major concern.2 The
allocation of grid investment costs fuels public discussions, as these costs are
enormous and the beneficiaries are often not clearly identifiable, with some parties even being at a disadvantage. In essence, the individual goals of economic
efficiency and common fairness are difficult to achieve simultaneously. This
chapter is motivated by recent discussions on rising energy prices, investment
into grid infrastructure (e.g., new HVDC lines), siting of new RES generators
as well as transmission pricing and cost allocation policies (e.g., Transmission
UK http://www.nationalgrid.com/uk/Electricity/MajorProjects/, USA http://
www.tresamigasllc.com/
2 See German Grid Development Plan Consultation http://www.netzentwicklungsplan.
de/sites/default/files/NEP_2012/Factsheet.pdf and UK National Grid Undergrounding
Consultation
http://www.nationalgrid.com/uk/Electricity/
UndergroundingConsultation/
1 e.g.,
118
135
6 MASSNAHMEN ZUR BEDARFSGERECHTEN OPTIMIERUNG, VERSTRKUNG UND ZUM AUSBAU DER NETZE
119
Figure 5.1: Suggested grid expansion projects in the lead scenario of the German Grid
Development Plan 2012 (50Hertz Transmission GmbH et al., 2012)
120
Figure 5.2: Locational differences in grid charges for households in Germany 2011
(BNetzA, 2011)
fair outcomes. For example, one strange outcome may be that consumers who
have no benefit bear a large share of the grid cost. Consumers in the eastern
part of Germany, where a large share of the low-cost wind generation is located,
may have to pay a major share of investments. This would increase the cost
differences due to the building of new lines. However, in the German example, the final course is not yet set. In the context of this thesis, we contacted the
German regulator (Bundesnetzagentur) in late November 2012 to find out who
will pay for the investments into the transmission grid until 2032. So far, the
questions are officially unanswered in written form. In informal phone calls the
Bundesnetzagentur mentioned that a final answer is not yet possible, which may
indicate that there may be room for changes in the regulatory regime.
Incentivizing local generation and consumption by charging direct beneficiaries of grid investments for grid cost may be a different approach to addressing
upcoming grid challenges. The variety in cost allocation schemes under
different regulatory regimes underlines the arising complexity which leads to
public discussion and experts consultations for regulatory advice. This chapter
analyzes different cost allocation and pricing regimes in a simple network
model. Focusing on the economic behavior and implications on consumer and
total welfare, it simplifies the modeled entities as much as possible, abstracting
from rich power system modeling aspects. Important questions to be analyzed
are the influence of different cost allocation and pricing options on welfare as
well as the corresponding investments in transmission and generation assets
under different regulatory regimes.
This chapter is also an extension of own publications and working papers.
121
Specifically, Sections 5.2 5.5 are reproductions and extensions of our paper
Ilg et al. (2012) and the results presented here are currently incorporated in the
working paper Investment and Grid Cost Allocation.
122
123
critique mentioned in Leuthold et al. (2008) is that a large number of nodal prices is seen as
too complex by some researches, and therefore zonal prices may be a compromise. However,
the zonal approach is also strongly criticized by Hogan (1999), due to the fact that nodal pricing would lead to zones with similar prices if there is no difference between nodes. However,
Hogan (1999) also mentions that the focus of his argument is short-term congestion management. Finally, the magnitude of impact is again discussed by Oren (1998). For more details
on nodal and zonal pricing as well as where the concepts are applied, Leuthold et al. (2008)
provide further information.
124
principle is the following: beneficiaries or those who cause the grid cost, should
pay (see Prez-Arriaga and Smeers, 2003). However, beneficiaries are very difficult to identify in an interconnected power grid and often change over time.
In addition to the cost allocation to different stakeholders, the calculation
method for transmission charges is another dimension. An important factor is
whether cost allocation should be uniform or differentiated. One possible type
is differentiation by location of generation or consumption.
Madrigal and Stoft (2012) provide an overview of network infrastructure
pricing methodologies. Shirmohammadi and Gorenstin (1996) name similar
paradigms for calculation of transmission charges based on actual cost. They
identify three different transmission pricing paradigms:
Under a postage stamp model all transmission users pay the same rate
pro rata, independent from individual benefit or cost causality, e.g., for
consumers based on total consumption (energy-based) or maximum demand (capacity-based) (Madrigal and Stoft, 2012). A small deviation is
a license plate fee which is a regionally differentiated postage stamp rate
(Brunekreeft et al., 2005).
Usage-based methods on the other hand attempt to charge grid users in relation to their actual use of the infrastructure. Madrigal and Stoft (2012)
further divide these methods into flow-based and MW-mile calculations.
The latter also incorporate distances for rate calculations in addition to
caused flows.6 As mentioned before, the definition of usage-based can be
extremely complex in interconnected power grids.
Combined pricing approaches are a blend of postage-stamp and usagebased methods.
In summary, the discussion on who is to be charged for the usage of the transmission system is spanned by two extremes: socialization vs. beneficiary pays
(PJM, 2010). In the case of socialization, grid costs are split independently from
benefits with the main argument that every stakeholder benefits from the reliability provided by the transmission grid. By contrast, under beneficiary pays
the costs are allocated to the stakeholders who benefit the most (e.g., by usage
of capacity or low electricity prices). One has to note, that if the benefits are
widely distributed, a beneficiary-pays scheme might result in in the same cost
allocation as socialization (MIT, 2011). Obviously, it is a challenging task for regulators to create conditions and rules for transmission cost allocation that fulfill
all objectives mentioned in the previous section
6 For
more details on distances and the difference between geographical and electric distance
please refer to Prez-Arriaga and Smeers (2003).
125
126
there must be a transparent method for determining benefits and identifying beneficiaries; and
there may be different methods for different types of transmission facilities.
Olson (2012) provides an interesting interpretation of the Order 1000 and
discovers that it is still complex to allocate grid cost fairly even if the order uses
the word fair 32 times. Another example is the transmission pricing scheme in
New Zealand which has been subject to discussions and changes several times
in the last years (Electricity Authority, 2012). In contrast, other countries still
apply a socialization of large shares of grid investment cost.
Since this section cannot fully analyze and discuss all regulatory approaches,
only some selected cases on transmission cost allocation are presented. First,
LMP is not only used by the often mentioned example of PJM, but also by other
U.S. ISOs and in other countries, e.g., New Zealand, Argentina (Frontier Economics, 2009). Zonal approaches are used in the UK and also in other countries
such as Australia (National Grid, 2013; Frontier Economics, 2009; Ault et al.,
2007). In Germany, transmission injection pricing for generation nodes is prohibited by regulation (Knieps, 2013). A real example demonstrates the influence
of cost allocation methods on actual investment and also on social welfare: The
Arizona Commission rejected a transmission line the cost of which would have
had to be borne by Arizona ratepayers, whereas California customers would
have benefited from supply at lower cost (Baldick et al., 2007).
The different approaches and recent discussions show that there is currently
no generally accepted optimal approach. This is why we evaluate different scenarios where grid costs are paid by either generators or consumers. Olmos and
Prez-Arriaga (2009) summarize the current situation accurately: There is no
universal consensus on the most adequate regulatory approach for transmission
investment, access, and pricing. Or as Green (1997) puts it: None of the authors claims that they have the right answer, and it probably does not exist.
All we can do is learn from each others experience, and hope for incremental
improvements.
127
Competition
Competition in spatial models is analyzed by a multitude of models the
following selection matches the topics addressed in this chapter. Borenstein
et al. (2000) employ a two-node model with one dominating supplier at each
node and constrained grid capacity. Using Cournot competition they show
that modest additions to transmission capacity can yield large social benefits.
In addition, they discuss opportunities to extend their model and apply it to
the Californian electricity market to find that strategic congestion may be an
important issue. Wei and Smeers (1999) model a spatial oligopolistic Cournot
competition among generators with regulated transmission prices. They apply
two transmission pricing regimes namely average-cost and marginal-cost
pricing to a four node simulation representing European countries and find
that average-cost pricing yields lower supply but higher profits.
In a three-node Cournot model with loop flows, Cardell et al. (1997) find that
market power may also be exerted by increasing outputs to congest transmission
lines. Hobbs (1986) analyzes short-run spatial price equilibria in an oligopolistic
deregulated power market with the use of different models. He applies the
128
Nash-Bertrand and a limit price model to upstate New York. The comparison
of prices, profits, and social welfare to a regulated prices regime shows that
consumers experience different price effects based on their location.
Investment
Investment and expansion are often analyzed in publications using several
stages. Aflaki and Netessine (2012) present a paper on strategic investment into
RES. They use an investment and a generation stage, however, grid investment
or cost allocation is not in focus. Joskow and Tirole (2005) analyze merchant
transmission investment in detail and incorporate several dimensions to obtain more realistic models. They demonstrate also using simple economic
two-node models that merchant transmission investment may lead to inefficiencies, e.g., when market power influences nodal prices or lumpiness of
investment lead to over- or under-investment. Chao and Wilson (2012) analyze
electricity transmission and generation investments in three models: efficient
coordination, merchant transmission investment, and sequential coordination.
They find substantial differences in welfare, prices and investments between efficient regulated and merchant investment and suggest their model as a tool for
transmission planners to evaluate different situations and regimes. They state
that when the efficiency losses of self-financed (injection fees and congestion
charges) investments are small, it might be advantageous due to the avoidance
of cost allocation discussions. Murphy and Smeers (2005) investigate different
generation investment models also including a two-stage Cournot model but
use a single node to avoid transmission challenges. Sauma and Oren (2006)
as well as Sauma and Oren (2007) propose a 3-period model for investment
and Cournot competition. The periods are transmission planning followed by
generation investment and finally an energy spot market. They investigate the
influence of transmission investment on social welfare and find that different
targets namely maximization of social welfare, minimization of market
power, and maximization of consumer or producer surplus may all lead
to different grid expansion plans. Van der Weijde and Hobbs (2012) evaluate
transmission investment for renewable energy sources under uncertainty using
a stochastic two-stage optimization model. They apply their model to the
UK transmission system and analyze the value of information and the cost of
ignoring uncertainty.
129
Practical Examples
Finally, some publications discuss transmission pricing and cost allocation in
practical examples. The following three papers give a notion of the differences
between theoretical concepts and real-life implementations. Philpott and Hoang
(2010) analyze a scheme based on auctioning physical flow rights as alternative
to the allocation of HVDC cost to South Island generators in NZ. Ault et al. (2007)
model the investment cost-related zonal pricing approach in the UK and find
that it is suitable in the future if some issues are resolved that affect some actors,
e.g., the effect of distributed generation and the re-zoning in some areas. Dietrich
et al. (2009) show for the German market that an integration of grid conditions
leads to a different siting of power plants and a social welfare gain in comparison
to the current situation with no locational signals.
Hobbs (1986)
( )
( )
Dynamic investment
Key notions
Intermittent supply
Demand elasticity
Other
Beneficiary pays
Socialized
Additional
features
D D D
D (D) (D)
D (D) D
D D D D
( )
Other
( )
Uniform
Nodal
( )
Regulatory
regime
D D (D)
( )
( )
D (D) D
D (D)
D D
D
D
Analysis of investment into RES and conventional generation under vertical integration and market competition. They find that due to intermittency of supply, market liberalization may not promote efficient generation investments.
Two-node Cournot model with constrained transmission capacity and
Bertrand extension. They find that transmission expansion mitigates
market power and reduces prices.
Spatial three-node Cournot model with loop flows that yields the result
that market power may also be exerted by increasing outputs to block
transmission.
Three-node Cournot model with two transmission lines to study efficient
transmission and generation planning. Costs are allocated to consumers
in three ways: socialized, beneficiary pays, and market-based. The authors state that when the efficiency losses of a self-financed investments
(injection fees and congestion charges) are small, it might be advantageous due to the avoidance of cost allocation discussions.
) Model of Bertrand competition and limit-pricing in spatial electricity
markets. The comparison to a price regulation model shows that consumers experience different price effects by location.
Two- and Three-node model to analyze the influence of transmission
right allocation on a congested network. They find that physical and financial transmission rights can increase market power of generators and
consumers.
A merchant transmission investment is expanded to incorporate realistic
attributes in transmission, e.g., market power. The authors find that merchant transmission investment yields inefficiencies given these attributes.
Single node model which investigates generation investment and perfect
competition as well as simultaneous and two-stage cournot competition.
Other
Perfect comp.
D D
Oligopoly
Duopoly
Monopoly
Pricing
130
Industry
model
Reference
D
D
( )
D (D)
(D) (D)
D
( )
D
D
D
D
( )
Key notions
Dynamic investment
Intermittent supply
( )
D
( )
Additional
features
Demand elasticity
Other
Beneficiary pays
Socialized
Other
D
D
D
D
Regulatory
regime
D D (D)
( )
Rubio-Odriz
and
PrezArriaga (2000)
Sauma and Oren (2006), Sauma
and Oren (2007)
Uniform
D)
Nodal
Other
Perfect comp.
Oligopoly
Duopoly
Monopoly
Pricing
D
D
D D
( )
Industry
model
Reference
Table 5.1: Summary of selected contributions on transmission grid pricing and cost allocation models
131
132
This chapter extends prior research on grid or transmission pricing and cost
allocation by investigating cost allocation and local price differentiation simultaneously. The use of price discrimination raises again the question of what is
fairness. As discussed in the beginning, one may argue that electricity is a commodity product and all types of differentiation are per se unfair. However, this
thesis rather follows the argumentation that fair prices can also be differentiated,
e.g., by time or location especially in order to yield an efficient outcome. This corresponds to the notion that current uniform pricing regimes are not per se fair in
terms of grid cost allocation (Faruqui, 2010). Different regulatory cost allocation
regimes are compared with respect to their impacts on total and consumer welfare. The intention is to present the modeling assumptions from an economic
point of view and to allow the reader to judge applicability and limitations of
the presented model.
133
GL
System Operator
Gi
Generator population
Dj
Consumer Demand
Location H
GH
DH
134
regulatory environment. Subsequently, the actors compete on the market and try
to maximize their profit under the given regulatory regime. Obviously, actors
incorporate the third stage of revenue generation into their investment decision.
To this end, we first analyze step 3, to understand the behavior of participants
given a preexisting infrastructure. This is comparable to a static case where generators and the transmission grid are already existing which is true for large
parts of most power systems. Step 2 on the other hand represents a dynamic
decision on new investments into generation and transmission capacity.
The following sections provide a description of the two different model instances we use to analyze step 2 and 3. First, step 3 with competitive dispatch
and pricing is investigated under different regulatory regimes. Based on these
results, the investment stage in step 2 is discussed. In the classification of Ventosa et al. (2005) step 3 is modeled as an equilibrium model whereas we use an
optimization model for one generator in step 2.
GL
MCL
135
System Operator
Gi
Generator population
Dj
Consumer Demand
O
CT
Location H
DH
GH
MCH
Figure 5.4: Model instance for grid pricing with preexisting investment
136
II
III
IV
Uniform supply
pricing and benefiting generators
bear grid cost
Uniform supply
pricing and benefiting consumers
bear grid cost
137
(5.1)
Owing to the Bertrand-style competition with uniform prices, all demand will
be allocated to the generator that offers the lowest price or split evenly in case of
identical prices. The demand function for the generator L is
NGL
if pl < ph
1
=
0.5 + 0.5(1 ) if pl = ph
0
if pl > ph
(5.2)
and respectively the opposite for generator H. Since identical prices would lead
to split population, which in return would change total grid cost, we abstract
from this special case in order to derive clear results. In addition, this outcome
would be somehow artificial and unstable given the multitude of different generation technologies.
Based on this demand the profit functions of the generators are
L = NGL ( pl MCL ),
H = NGH ( ph MCH ).
(5.3)
The resulting competition is a typical Bertrand competition based on the generation price. The generators will undercut prices as long as they are above
marginal cost. Similar to Peeters and Strobel (2009), we define undercutting as
the setting of lower prices to attract consumers from the opposite generator despite any additional cost such as transportation or transmission. Finally, lowcost generators will serve the whole market at a price slightly below marginal
cost of the generators at the high-cost location. Then the high-cost generator
can no longer undercut without making losses. This results in an equilibrium
generation price for all consumers of
pl = pl H = pl L = MCH e.
(5.4)
Given totally inelastic demand and marginal production cost of zero, and neglecting e, the equilibrium profit functions of the generators are
L = MCH ,
H = 0.
(5.5)
Both consumer populations have to pay the same end consumer price and
additionally finance total grid cost ct which leads to the average consumer cost
138
CT
= MCH + CT
1
(5.6)
The socialization of grid cost results in the maximum grid infrastructure to serve
0.5 of the total consumer population with low-cost generation. This result
has two interesting facets. First, generators with higher cost cannot compete
independently of grid cost levels. Second, consumers next to low-cost generation
pay for the grid like the customers next to the high-cost generation without being
beneficiaries of the transmission.
(5.7)
Equilibrium prices result from the same undercutting competition as in Scenario I, with generators anticipating their share of grid cost when serving remote
consumers. Depending on the transmission cost, the low-cost generator located
next to the smaller consumer population might not have lower total marginal
cost. Again, the generator with the lowest marginal cost will serve all consumers
at the minimum price of the opposite generator. Given the transmission cost,
minimum prices when serving all consumers are
pl = MCL + CT = CT ,
ph = MCH + (1 )CT .
(5.8)
The resulting equilibrium prices depend on both the consumer population partition () and the locational difference in generation cost (MCH ). Excluding the
possibility to split consumer populations evenly, we obtain two possible outcomes.
139
Case 1 Low-cost generator captures market If pl < ph , the low-cost generator can serve the whole market. The condition can be converted into
pl < ph
CT < MCH + (1 )CT
1
CT
>
2 1
MCH
(5.9)
GL will charge the other generators minimum price minus an infinitesimal discount. Neglecting e, the resulting price obtains:
pl = MCH + (1 )CT
if
1
CT
>
2 1
MCH
(5.10)
(5.11)
As the low-cost generator accounts for grid cost MCT when setting prices,
the resulting prices are the average consumer cost: AVCDL = AVCDH = pl =
MCH + (1 )CT .
Case 2 High-cost generator captures market In the opposite case pl > ph
the high-cost generator will capture the whole market. Thus, neglecting e, the
equilibrium price is
ph = CT
if
CT
1
<
.
2 1
MCH
(5.12)
(5.13)
Again, the grid cost (1 )CT are already included the price represents the
final average consumer cost: AVCDL = AVCDH = ph = CT .
CT
< MC
that determines the switch
H
CT
from case 1 to case 2 depending on the grid-to-generation-cost relation MC
is
H
depicted in Figure 5.6. In the area above the depicted function GH serves total
demand GL otherwise in the area below. In both cases the total industry profit
= L + H is absorbed by a single company while network costs amount to
Cases Overview
The condition
1
21
6
4
Case 2
Case 1
Condition
CT
MCH
10
140
0.5
0.6
0.7
0.8
0.9
1.0
1
21
for different
1
if pl < ph CT
0.5 + 1 if pl = ph CT
NGl =
(5.14)
1
if ph + ct > pl > ph CT
0.5(1 )
if pl = ph + CT
0
if pl > ph + CT
while GH always captures the remaining demand.
Therefore, generators need to consider expected grid cost for consumers when
setting their uniform prices (Equation 5.1). With our assumptions MCH >
MCL = 0 and CT > 0, generator pool GL is always able to capture its local consumer demand DL ; therefore the lower two lines of Equation 5.14 cannot occur,
and the high-cost generator will never capture the whole market. With respect
141
(5.15)
(5.16)
= MCH CT .
Both consumer populations will buy at this price pl from GL . Additionally, the
consumers at the high-cost location have to bear the grid cost of CT . Therefore,
the average consumption costs for each demand population are
AVCDL = MCH CT ,
AVCDH =
( MCH CT ) + CT
= MCH .
(5.17)
The population at the low-cost location has lower average cost than consumers
at the high-cost location: AVCDH > AVCDL .
Case 2 Market split In the case of CT > MCH , each generator has a local
cost advantage and could serve its local market profitably without connecting
grid infrastructure. However, generators can leverage the threat of potential
grid cost to realize higher prices at their local consumer pool. In such a case,
a Nash-Bertrand equilibrium in pure price-strategies does not exist (Shy, 2001).
However, Morgan and Shy (1996) propose the Undercut Proof Equilibrium as
an alternative solution concept. According to Peeters and Strobel (2009), the rationale behind the UPE has some similar features as the Stackelberg sequential
price setting process. Each generator assumes its own price as fixed and analyzes whether the opposite generator has an incentive to undercut in order to
capture the whole market. In the UPE each generator sets the highest price possible without giving the opposite generator an incentive to undercut and capture
the whole market. In detail that means GL has to set the price pl satisfying the
8 Again,
142
following condition
GH = ( ph MCH ) pl MCH (1 ) MCT .
(5.18)
(5.19)
(5.20)
Price
pl
ph
0.5
0.6
0.7
0.8
0.9
1.0
Figure 5.7: UPE consumer prices for different with split market and without transmission
143
for firms with a larger consumer base to sell at a lower price, e.g., discount stores.
Industry and firm profits are then given by local population share times
equilibrium price minus the generation costs:
1
MCH + CT (1 ),
L =
2 + 1
( 1)2
(5.21)
MCH + CT MCH ,
H =
2 + 1
(1 2)
= 2
MCH + CT .
+1
Cases Overview In summary, the low-cost generator can serve the whole
market if its cost advantage is large enough (Case 1). However, GL has to compare the profit with the profit of a split market (Case 2) to decide whether it is
better to serve all consumers or give up the remote customers in order to realize
higher profits. Comparing Equation 5.16 and Equation 5.21, we can determine
when it is optimal for GL to serve the whole market or when it is optimal to
forfeit the remote customers, respectively:
1
MCH + CT )(1 )
2 + 1
CT
>
2
3
MCH
2 3 + 3
MCH CT > (
(5.22)
1.0
Case 2
0.5
Condition
CT
MCH
1.5
2.0
The factor 23+32 3 is strictly increasing in [0.5; 1] and depicted in Figure 5.8. As long as the grid costs are sufficiently low in comparison to generation
0.0
Case 1
0.5
0.6
0.7
0.8
0.9
1.0
23+32 3
for different
144
cost , GL will serve the whole market (case 1). However, if the grid costs are sufficiently high, the low-cost generator will find it profitable to serve only its local
customers in a split market to realize the higher UPE prices (case 2). In addition, the switch between the two cases depends on . For small values of , the
low-cost generator tends to split the market already at lower grid cost.
This scenario has two interesting implications. First, in the case of a split market, the generators can utilize virtual grid cost as market protection and set
higher prices. This means in a split market no grid infrastructure is necessary.
However, the threat of grid pricing allows to set higher prices on the respective local market. Second, when the low-cost generator serves the whole market,
consumers at the high-cost location as beneficiaries pay higher average end consumer prices.
(5.23)
phH = MCH .
The resulting optimum prices do not depend on the relative consumer pool sizes
( and 1 ), since the markets are separated by price discrimination.
Given the assumption MCH > MCL = 0, the low-cost generator GL can al9 In
Ilg et al. (2012), we demonstrate that individual welfare is independent of cost allocation in
a price discrimination scenario.
145
ways capture the whole customer demand DL by charging the minimal price phL
minus an infinitesimal discount:
plL = phL e = MCH + CT e
(5.24)
(5.25)
(5.26)
= MCH + (1 2)CT .
The average consumer costs are higher at the low-cost location
AVCDL = plL = MCH + CT ,
AVCDH = plH = MCH .
(5.27)
Case 2 Market split In the case of CT > MCH , the high-cost generator GH
has a local cost advantage and can serve its local market profitably leveraging
the differentiating grid cost to realize higher prices by charging:
phH = plH e = CT e
(5.28)
Total industry profit is split between both generators with no transmission cost:
L = (1 )( MCH + CT ),
H = CT ,
(5.29)
= (1 ) MCH + CT .
Similar to Case 1, the average consumer costs are higher at the low-cost loca-
146
tion
AVCDL = plL = MCH + CT ,
(5.30)
AVCDH = plH = CT .
1.0
Case 2
Case 1
0.0
0.5
Condition
CT
MCH
1.5
2.0
Cases Overview For low grid cost CT the generator GL can profitably serve
CT
the whole market. As soon as CT > MCH or MC
> 1 respectively, the market is
H
split independently of the consumer demand distribution. Figure 5.9 depicts the
condition and the respective case per area. In both cases consumers at the low-
0.5
0.6
0.7
0.8
0.9
1.0
cost location face higher prices. Again, both generators can use virtual grid cost
as market protection and to set higher prices in a split market.
147
2.5
3.0
1
2 1
1.5
0.5
1.0
Scenario IV: 1
Scenario III:
2 3 + 32 3
0.0
Condition
MCT
MCH
2.0
Scenario II:
0.5
0.6
0.7
0.8
0.9
1.0
148
Pricing
Uniform Pricing
I Soc. cost
Demand served by
Condition
GL
GL
CT
1
MCH < 21
GH
CT
1
21 < MCH
CT
CT
( 1 ) CT
MCH
II Ben. Generators
CT
MCH
GL
<
23+32 3
23+32 3
Generator
MCH
MCH + (1 2)CT
MCH CT
profits
MCH + (2 1)CT
Avg. consumer
CT
MCH CT
costs
CT
MCH
<
CT
MCH
CT
MCH CT
IV Ben. Generators
Split
GL
CT
MCH < 1
Split
CT
1 < MC
H
CT
(12)
MCH
2 +1
+ CT
MCH + (1 2)CT (1 ) MCH + CT
1
MCH + CT (1 ) MCH + (1 2)CT (1 )( MCH + CT )
2
2+1
( 1)
MCH + CT + MCH
0
CT
2 +1
1
MCH
2 +1
( 1)2
MCH
2
+1
+ CT
MCH + CT
MCH + CT
+ CT
MCH
CT
Allocation Scenario
Discriminatory Pricing
149
Scenario IV
MCH = 3
Table 5.3: Industry profit of scenarios II, III and IV in comparison to the reference Scenario I given different levels of generation cost MCH
MCH = 2
MCH = 1
Scenario III
150
Scenario II
151
Consumer Cost
Obviously, consumers costs are to some extend complementary to the generation profits. However, especially their distribution is an important factor from a
regulatory perspective. Hence, the first differentiating factor of all scenarios is
whether final end consumer costs are equal or differentiated across the locations.
To this end, Table 5.2 contains final consumer cost by location. Clearly, Scenario
I and II result in final uniform end consumer cost by design. Given the Bertrand
competition, a split market is also impossible in these scenarios. Interestingly,
Scenario II results in strictly lower or equal consumer cost in comparison to Scenario I with socialized grid cost.
For Scenario III and IV, the large industry profits in a split market case as discussed above are reflected in the consumer cost. Given a split market, the final
cost always contains the grid cost CT which can be interpreted as the protection bonus due to high grid cost. Furthermore, it is interesting to look at the
locational consumer cost which differs by location in all cases of Scenario III and
IV. In most cases consumer demand D H is better off than consumer demand
DL . Given that the low-cost generator GL is situated close to consumer demand
DL , this insight seems counter-intuitive. However, it results naturally from the
possibility of product differentiation. Interestingly, this difference is most pronounced under the discriminatory pricing Scenario IV. Consumer demand DL is
only better off under Scenario III when benefiting generators bear grid cost and
CT
grid cost are low enough to fulfill the condition MC
< 23+32 3 . That is, the
H
optimal cost efficiency in Scenario IV and partly in Scenario III come at the cost
of inter-population inequality and high industry profits in case of split markets
without the need of grid infrastructure.
152
with consumer demand D H facing lower costs. Again, the case of high generation cost difference is special, yielding a unique result in Scenario III: Remote
consumers pay more than local consumers.
Our model lends itself to future extensions. The Bertrand competition model
may be replaced by alternative specifications like Cournot or Hotelling. This
may shed light on the robustness of our results. In fact, Smeers (1997) notes
that the achieved equilibrium lies between the Cournot equilibrium and the
Bertrand equilibrium. It is close to the Cournot equilibrium at peak time, when
capacities are almost saturated and close to the Betrand equilibrium when there
is significant excess capacity. Similarly, dropping the infinite capacity assumption or introducing richer cost functions (e.g., grid cost with economies of scale)
allows the analysis of more complex situations. Finally, analysis of the investment location choices as discussed in the following may enhance our understanding of the interplay between network costs and investments.
153
new generators with a certain energy output g L , whereas the second location
(H) leads to higher investment for generators with an output g H . To this end, we
introduce two investment cost factors w L and w H with w L < w H to account for
differences in investment to achieve the same output (Figure 5.11).
Location L
DL
GL
wL
MCL
System Operator
Gi
Generator population
Dj
Consumer Demand
O
wT
Location H
DH
GH
wH
MCH
Figure 5.11: Model instance for grid cost allocation and investment
This means that investment cost IL and IH at the locations are depending on
the generation capacity decision gi , i { L, H } and the investment factors:10
I L f ( w L , g L ),
I H f ( w H , g H ).
(5.31)
(5.32)
to the previous chapter, we use a more compact notation throughout the chapter, e.g.,
I L ( w L , g L ).
154
generators produce at the same constant low marginal cost of MCL = MCH per
unit of energy. Without loss of generality we normalize MCL = MCH = 0 to
reduce complexity of results. This assumption is based on the fact that maintenance costs are largely independent of energy output for renewable energy
sources like wind or solar. For ease of calculation we do not use the consumer
distribution factor in this section. The demand of the consumer populations
DL and D H at each location is represented by d j with j { L, H }. Figure 5.11
provides an overview of the model instance.
Institutional Scenarios
With the model we aim to evaluate and compare different options for grid investment cost allocation and their influence on investment in spatially diverse
electricity markets. The necessary grid investment cost T depends on the grid
investment factor wT as well as the locational distribution of demand and supply:
T f ( w T , d H , d L , g H , g L ).
(5.33)
B
Benefiting generator bears grid
cost
155
(5.34)
(5.35)
After the investment phase the generator serves consumer demand. Affected
by the location of the generation capacity and the consumer demand, transmission infrastructure is necessary. Depending on the regulatory environment, the
generation investor has to consider these costs or they are socialized across the
11 In reality this could be a price where it is cheaper for consumers to switch to generating power
156
consumer population. In our special case with inelastic demand, maximum consumer prices and total revenue are constant. This influences the investment behavior and a cost minimizing objective function is sufficient. The overall objective function of the generation investor is:
min C = T (d L , d H , g L , g H , wT ) + I ( g L , g H , w L , w H ) .
{z
} |
{z
}
|
g L ,g H
transmission cost
(5.36)
investment
gi = di , i { L, H }.
i
(5.37)
Obviously, generation output and demand are not constant in a practical setting. However, we abstract from this challenge and assume a sufficiently flexible
system that can be approximated with constant demand and supply. In practical applications, this requires, for example, sufficient storage capacity at both
locations.
To account for typical situations, we assume the majority of consumers and
therefore the main load center to be at location H with higher investment cost ,
i.e. the sites for low-cost investment into generation are remote from load centers
(d L < d H ). Therefore, d = d H d L is strictly positive. In addition, we assume
rational behavior especially that the generation investor will always install
enough generation at the low-cost location to serve the local demand (g L d L ).
With the condition for the balance of generation and demand (Equation 5.37) we
can derive the representations of necessary transmission capacity:
gL + gH = dL + d H
gL dL = d H gH 0
Given these definitions, we can set up a model with increasing linear transmission investment cost depending on the discrepancy in demand and supply per
location:
T ( d L , d H , g L , g H , wt ) = ( g L d L ) w T = ( d H g H ) w T
(5.38)
The total generation investment cost in this scenario is the sum of investment at
both locations (see Equation 5.34):
I ( g L , g H ) = w L g2L + w H g2H .
12 Another
option may be to include a term which represents expected blackout cost dependent
on supply-demand mismatches.
157
The defined terms induce varying impact on profits depending on the regulatory
regime which we will analyze in the following.
g L ,g H
(5.39)
Generation investment will occur at the location with lowest marginal investment cost until total demand d = d L + d H is served as long as marginal costs
are below the consumers reservation price threshold. With our assumption of
linearly increasing marginal investment cost the generator will invest at both locations simultaneously, disregarding locational distribution of demand. Given
the supply and demand Equation 5.37, we can calculate the optimal investment
at each location for a given demand. The share of investment depends on the
increasing marginal cost:
C = w L (d g H )2 + w H g2H
= w L d2 2w L dg H + w L g2H + w H g2H
C
!
= 2w L d + 2w L gH + 2w H gH = 0
g H
(w H + w L ) gH = w L d
wL d
gH =
wH + wL
Similarly, we obtain the optimal investment at the low-cost location as gL =
wH d
w H +w L . As expected, the major investment into generation capacity occurs at
the remote location with lower cost and a small share of total demand. Figure
5.13 illustrates how a given demand leads to a share of investment in generation
capacity at each location and demonstrates that investment is independent of
grid cost and consumer demand split. Notably, the necessary grid investment
costs that are socialized obtain as gL d L = d H gL .
158
marginal cost
IL
g L
IH
g H
= 2w H g H
= 2w L g L
d
gL
gL
gH
gH
= (d H g H ) wT + w L (d g H )2 + w H g2H
= (d H g H ) wT + w L d2 2dg H + g2H + w H g2H
= d H wT g H wT + w L d2 2w L dg H + w L g2H + w H g2H
The optimal investment split requires minimization of these cost:
C
!
= wT 2w L d + 2w L gH + 2w H gH = 0
g H
(w L + w H ) 2gH = 2w L d + wT
w L d + 0.5wT
gH =
wL + wH
Similarly, we obtain the cost function depending on g L by replacement of
159
gH = d gL :
C = ( g L d L ) wT + w L d2L + w H d2H
= ( g L d L ) wT + w L g2L + w H (d g L )2
= ( g L d L ) wT + w L g2L + w H d2 2dg L + g2L
= g L wT d L wT + w L g2L + w H d2 2w H dg L + w H g2L
And the optimal investment gL at location L:
C
!
= wT + 2w L gL 2w H d + 2w H gL = 0
g L
(w L + w H ) 2gL = 2w H d wT
w H d 0.5wT
gL =
wL + wH
In contrast to Scenario A, the generator considers transmission cost and invests more in generation at the high-cost location depending on grid cost wT .
Figure 5.14 illustrates how the grid cost influences the investment decision for
an exemplary implementation of demand distribution and marginal cost. The
costs at the low-cost location include the expected grid cost as soon as the local
market is served and transmission to the high cost location is necessary.13
marginal cost
CL
g L
CH
g H
= 2w H g H
= 2w L g L + wT
d
gL
gL
dL
gH
gH
13 Given
our assumption g L d L this is always the case for each additional capacity investment
at the low-cost location.
160
Generation
investment
Scenario A
Scenario B
gL
wH d
w H +w L
>
w H d0.5wT
w L +w H
gH
wL d
w H +w L
<
w L d+0.5wT
w L +w H
Table 5.4: Optimal locational generation investments given different transmission cost
allocation policies
Given the socialization of transmission grid investment cost (Scenario A), the
investing generator optimizes generation cost independently of location. Therefore a large share of total capacity investment occurs at location L with lowinvestment cost but also a smaller share of total demand. Hence, the model confirms that socialization reduces the systems ability to promote investment in
the best locations (MIT, 2011). As Scenario B shows, the investor can already be
incentivized to focus on overall more efficient generation capacity investments
in this first investment step. In Scenario B he has to bear the grid investment cost
which leads to lower generation investments at the low-cost location with small
consumer demand. Consequently, less grid investment is necessary, since the
generation investor trades grid investment off against generation investment.
These results are not restricted to the simple analytical model applied here.
Knieps (2013) analyzes a richer model including variable infrastructure investments with injection charges for generators and extraction prices for consumers. He argues that with injection charges incentives arise for the generators of renewable energy not only to focus on generation costs but also to choose
the proper location of electricity generators, taking into account locational different injection charges (Knieps, 2013). Another example is the recommendation
of von Hirschhausen et al. (2012) to the European Commission to at least introduce a minimum grid price component that is charged to generators. Also,
Madrigal and Stoft (2012) agree that if specific groups of renewable generators
cause expansion cost, these generators should bear the cost. A practical example
where different locational grid charges are used, is the zonal approach used in
the UK. However, as also mentioned before, countries are using various transmission cost allocation schemes, which are even further differentiated, e.g., by
161
162
The first model shows that the allocation of grid cost influences the static competition outcome, e.g., in terms of efficiency and total end consumer prices. A socialization of grid cost may lead to high industry profits if transmission costs are
low in comparison to generation cost differences. In addition, it demonstrates
that generators can use transmission cost to exercise market power in local markets. And that consumers next to low-cost generation may be unintuitively exposed to higher prices than consumers at locations with higher marginal cost of
generation. The model suggests one regulatory regime (out of four analyzed)
which leads to an expected fair outcome under the assumption of low grid
cost: When benefiting consumers that are located remote from low-cost energy sources bear the grid cost, the total prices paid by these consumers are
higher as intuitively expected.
The second model targets the incentives for generation investors into capacity
at different locations and analyzes the influence of cost allocation. It confirms
and underlines that generators have little incentive to integrate transmission cost
in their siting decision in a setting with socialized grid cost. This result is in line
with Brunekreeft et al. (2005) who state that in the absence of LMP, there is a
strong case for a locational element to grid charges.
In summary, the models provide and describe opportunities for regulators to
understand the incentives of the different actors given our model assumptions.
First, the benefiting consumers need to be charged directly in order to create
an environment where consumers who live in areas with low-cost generation
actually pay less for their consumption. Second, the transmitting generators
also need to face grid cost in order to create the incentives for them to allocate
capacity efficiently in terms of grid and generation cost.
However, countries apply different regulatory regimes. One reason may be
that the grid and competition model used here is extremely simplified and based
on many assumptions. As mentioned before, the models may be adapted to be
applicable for other research questions, for example, other competition models
(e.g., Cournot, Hotelling), different cost functions (e.g., including economies of
scale), or more complex grid representations. Another extension could tackle the
hard assumption of inelastic demand which obviously enables the exert of market power. Bompard et al. (2007) state that a small increase in demand elasticity
can mitigate market power enabled by constraints and leads to improved market
outcomes. In addition, other factors increase the uncertainty of the results and
may be analyzed in more detail, e.g, intermittent supply or stochastic demand.
Overall, for specific power sectors and markets, the theories developed in the
analytical models need to be verified in more realistic simulation models over
time. These extensions go beyond the scope of this thesis, however, the literature review in the beginning of this chapter provides some links to other models.
163
Another important reason for various regulatory regimes are different targets
and markets that regulators have to deal with as well as the possibilities and information they have to work with. For example, in complex power networks it
is difficult to identify who is benefiting from a grid expansion, which can hinder
precise cost allocation.14 In addition, if grid costs account for a small fraction of
total cost only and reliability and/or use of RES is most important, a socialization of grid cost among consumers might be seen as fair. Also, applying differentiated grid charges can influence the level playing field for generators that is
intended by investments for congestion-avoidance. Finally, the use of locations
with low-cost generation condition might have political priority. Thus, despite
the results in this chapter, there are various reasons why a regulator decides to
socialize grid cost among all consumers or use an approach with zonal differences for demand and generation. For example, Baldick et al. (2011) recommend
to change the UK cost allocation in a way that all existing grid costs (except for
shallow connection cost) should be borne by consumers to enable the level playing field. However, in the same report they also recommend a generation follows transmission planning process and an efficient locational pricing scheme
(Baldick et al., 2011). This would basically represent a centrally planned optimal
grid expansion, where planned congestion costs yield to an optimal allocation
of generation capacity. Indeed, the proposed theoretical Optimal Charging Arrangement for Energy Transmission (Baldick et al., 2011) seems a promising
approach. In another publication, Baldick et al. (2007) provide a good statement
on optimal planning: As has been noted countless times in the past, there is
virtually no transmission asset that has ever been built that has not been used in
ways its planners and builders never anticipated. Leuthold et al. (2008) apply
nodal pricing to the German network which serves as an example in this chapter.
They find that nodal prices are more efficient than uniform pricing. However,
they also state that the static nodal prices do not give incentives for efficient grid
expansion.
In summary, the optimal decision on transmission pricing and cost allocation
regulation depends on the specific situation and targets. However, given the
increasing importance of grid cost mentioned above, the allocation of grid cost
may be an important topic in challenged power systems. For that matter, one
possible approach can be to charge some parts of the grid in a different way. One
example are the costs of the HVDC connection in New Zealand which are allocated through separate charges (Electricity Authority, 2012). In line with Hogan
(1998b), the allocation problems for existing transmission assets and grid expansion could be treated differently.
14 It
Chapter 6
Conclusion
This thesis focuses on the efficient use of power grid capacity and efficient investment into grid infrastructure on different voltage levels. More specifically,
it analyzes different coordination mechanisms and incentives to achieve more
efficient short-term operation and long-term investment behavior. The analyzed
models have limitations and primarily serve as a guideline in specific cases. The
specific discussion sections for the models on local infrastructure pricing (Section 4.5.1) and transmission grid cost allocation (Section 5.5) name the limitations and ideas for future extensions. This conclusion provides a summary of
the main findings and implications of the discussed models. It finalizes with a
more comprehensive overview of the potential solutions for challenges in future
power systems and open questions in the transition to an efficient low-carbon
power sector.
6.1 Summary
Major changes in power systems over the next decades pose challenges to existing power grids and require major infrastructure investments. These challenges
are particularly complex in unbundled power markets where individual actors
generators, system operators, and consumers need to be coordinated.
Chapter 2 provides an overview of the characteristics for the major actors in
the electricity supply chain and summarizes resulting challenges in physical
operation and market design. Chapter 3 discusses coordination mechanisms
and management options for each actor to react to bottlenecks in power grids,
such as temporal or spatial load/supply shifting as well as capacity investments. Monetary incentives in the form of variable or even dynamic prices
are discussed in more detail, based on theoretical potentials and frameworks.
In addition, real-life implementations and promising recent developments are
presented.
The local infrastructure coordination approaches analyzed in Chapter 4
specifically address the challenge of using existing distribution grids efficiently.
166
Conclusion
Conclusion
167
6.2 Outlook
The approaches discussed in this thesis add insights which emphasize the
important role of the grid and may support efficiency in the transition to, as well
as in the operation of, a low-carbon power sector. Recent newspaper articles
demonstrate that grid investments and siting of new generation capacities receive increasing attention in political discussions in context of the Energiewende.1
However, besides the topics discussed, there are still many open questions and
numerous areas for further research that are either prerequisites for the success
of the presented coordination approaches or stand independently alongside.
Complementary to the discussed topics, one major goal needs to be the
advancement of efficient supply technologies, e.g., in storage, transmission,
or generation. Similarly, or even more important is an efficiency increase in
consumption. A simple raise of awareness for energy consumption can yield
significant energy savings merely by switching off unnecessary equipment or
investing in more energy-efficient equipment. To this end, rising power prices
for end consumers (e.g., in Germany due to the Energiewende) might not only
cause higher electricity bills but also yield very positive saving effects in the
long run.
Smart grid technologies that improve the ability to monitor and control in
real-time are actually prerequisites for the approaches presented in this thesis.
While these technologies are already available today, their market penetration and use is hampered by missing incentives and limited user acceptance.
When real-time data is widely available, research in energy informatics and
economics can activate efficiency potentials in addition to a simple reduction of
consumption. To foster this research, simulation frameworks and testbeds can
be used to investigate how theoretical results can be realized in more practical
settings. In addition to the overall setting, interaction with individual actors
such as consumers, operators, and generators needs to be analyzed further.
Open questions include, e.g., which type of of incentives (e.g., monetary or
non-monetary) result in what kinds of effect?, What should the communication
or interface between actors and systems look like to be accepted in terms of data
security and to be efficient in terms of the outcome?, What kind of information
on individual flexibility is most valuable?. Answers to these questions can
enable new services and business models in the future power sector. They may
also overcome the roll-out issues and lead to a dissemination of smart grid
1 See for example Handelsblatt on November 8, 2013 on the expectation that the transmission grid
168
Conclusion
technologies. In the special case of incentives for the efficient use of capacity
and investment into power grid infrastructure, it is important to analyze the
interaction of different incentives. Particularly when applying several coordination approaches in an interconnected grid they are not separate from each other
but need to be checked for compatibility and mutual influences.
In addition to the technical aspects and user acceptance, other influencing
factors need to be considered, e.g., legal issues, existing regulations, or resistance of individual stakeholders. Hence, the development of a consistent,
integrated incentive and contract system is still a long way to go. The transition
to another system needs some time and might require regulatory measures
that are temporary only. One apparent example is the Renewable Energy Act
in Germany: the necessity of modifications is widely agreed, but the detailed
implementation is being severely discussed.
In summary, more flexibility combined with the right incentives can help to
support power system transformations. However, there will be individual paths
to a sustainable energy future as well as different detailed organizations these
paths remain to be seen.
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List of Figures
1.1
1.2
1.3
EU-27 gross inland consumption by fuel and final energy consumption by sector 2010 in Mtoe . . . . . . . . . . . . . . . . . . .
Estimated global infrastructure investment in different sectors . .
Structure of the thesis . . . . . . . . . . . . . . . . . . . . . . . . . .
2.1
2.2
2.3
2.4
2
3
7
16
16
17
18
19
19
21
22
23
26
26
27
34
36
40
58
69
72
74
43
76
77
78
192
List of Figures
4.8
4.9
4.10
4.11
4.12
4.13
4.14
4.15
4.16
4.17
4.18
4.19
4.20
4.21
4.22
4.23
4.24
4.25
4.26
5.1
5.2
5.3
5.4
5.5
5.6
119
120
133
135
136
140
List of Figures
5.7
5.8
5.9
5.10
5.11
5.12
5.13
5.14
UPE consumer prices for different with split market and without
transmission . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Characteristics of condition 23+32 3 for different . . . . . . .
Characteristics of the switching condition in Scenario IV for different . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Characteristics of conditions for different . . . . . . . . . . . . .
Model instance for grid cost allocation and investment . . . . . .
Institutional scenario overview for investment analysis . . . . . .
Investment Scenario A with socialized grid cost . . . . . . . . . .
Investment Scenario B with generator bearing grid cost . . . . . .
193
142
143
146
147
153
154
158
159
List of Tables
2.1
2.2
4.1
4.2
4.3
4.4
4.5
4.6
4.7
4.8
5.1
5.2
5.3
5.4
57
60
67
90
92
94
95
97
131
148
150
160
List of Abbreviations
AC
AMCIS
ARegV
BDEW
BEV
BKW
BM
BMU
BMWi
BNetzA
CCS
CHP
CWE
DC
DG
DLC
DLP
DOE
DR
DSM
DSO
EEG
EEM
EnLAG
ENTSO-E
EnWG
EPEX
Alternating current
Americas Conference on Information Systems
Anreizregulierungsverordnung Incentive Regulation
Ordinance
Bundesverband der Energie- und Wasserwirtschaft German Association of Energy and Water Industries
Battery electric vehicle
BKW FMB Energie AG Swiss electric utility
Benchmark
Bundesministerium fr Umwelt, Naturschutz und Reaktorsicherheit Federal Ministry for the Environment, Nature
Conservation and Nuclear Safety
Bundesministerium fr Wirtschaft und Technologie
Federal Ministry of Economics and Technology
Bundesnetzagentur Federal Network Agency
Carbon capture and storage
Combined heat and power
Central Western Europe
Direct current
Distributed generation
Dynamic load curtailment
Dynamic load pricing
Department of Energy
Demand response
Demand side management
Distribution system operator
Erneuerbare-Energien-Gesetz Renewable Energy Act
European Energy Market
Energieleitungsausbaugesetz Energy Line Expansion
Act
European Network of Transmission System Operators for
Electricity
Energiewirtschaftsgesetz Energy Industry Act
European Power Exchange
198
ERGEG
EU
EU ETS
EV
FCEV
FERC
GHG
GW
HEV
HICSS
HV
HVAC
HVDC
ICE
ICT
IEA
IEEE
ISGT
KAV
KIT
KW
KWKG
LMP
MV
MVA
MW
NYISO
OECD
OECD
OEM
OPT
OTC
PES
PHEV
RES
SAIDI
SAIDI
SB
SFSO
List of Abbreviations
European Regulators Group for Electricity and Gas
European Union
European Union emission trading system
Electric vehicle
Fuel cell electric vehicle
Federal Energy Regulatory Commission
Greenhouse gas
Gigawatt
Hybrid electric vehicle
Hawaiian International Conference on System Sciences
High-voltage
Heating, ventilation, and air conditioning
High-voltage direct current
Internal combustion engine
Information and communications technology
International Energy Agency
Institute of Electrical and Electronics Engineers
Innovative Smart Grid Technology
Konzessionsabgabenverordnung Concession Fee Ordinance
Karlsruhe Institute of Technology
Kilowatt
Kraft-Wrme-Kopplungsgesetz German Combined Heat
and Power Act
Locational marginal pricing
Medium-voltage
Megavolt ampere
Megawatt
New York Independent System Operator
Organisation for Economic Co-operation and Development
Organisation for Economic Co-operation and Development
Original equipment manufacturer
Optimal
Over-the-counter
Power and Energy Society
Plug-in hybrid electric vehicle
Renewable energy sources
System Average Interruption Duration Index
System Average Interruption Duration Index
Supply-based
Swiss Federal Statistical Office
List of Abbreviations
SLC
SLP
SOC
StromEinspG
StromNEV
SUV
SysStabV
TOU
TSO
TW
UC
UNFCCC
UPE
US
V2G
VAT
VDE
199
Appendix
A Optimization program used for SB, SLC, DLC,
DLP
Based on our paper Flath et al. (2013), we used the following optimization program for SB, SLC, DLC, and DLP:
int NbPeriods = ...;
float initSoc =...;
float maxSoc = ...;
float endSoc = ...;
range Periods = 1..NbPeriods;
float Capacity[Periods] = ...;
float Demand[Periods] = ...;
float Cost[Periods] = ...;
dvar float+ PosChargeamount[Periods];
dvar float+ Soc[Periods];
minimize
sum( t in Periods )
Cost[t]*PosChargeamount[t];
subject to {
forall(t in Periods )
ctNonNegativeSoc:
Soc[t] >= 0;
forall(t in Periods )
ctMaxSoc:
Soc[t] <= maxSoc;
forall( t in Periods )
ctChargeamount:
PosChargeamount[t] <= Capacity[t];
forall( t in 2..NbPeriods )
ctStorageConstraint:
Soc[t] == Soc[t-1]+ PosChargeamount[t] - Demand[t];
ctInit:
Soc[1] == initSoc + PosChargeamount [1] - Demand[1];
ctEnd:
Soc[NbPeriods] >= endSoc;
};
202
Appendix
Appendix
203
204
Appendix
float+
float+
float+
float+
float+
PosChargeamountH[Vehicles][Periods];
PosChargeamountW[Vehicles][Periods];
Soc[Vehicles][Periods];
TotalChargingH[Periods];
TotalChargingW[Periods];
minimize
sum( t in Periods )(
sum( n in Vehicles)(
Cost[t]*PosChargeamountH[n][t]+Cost[t]*PosChargeamountW[n][t]));
subject to {
forall(v in Vehicles)
ctInitStorage:
Soc[v][1] == initSoc + PosChargeamountH[v][1] + PosChargeamountW[v][1] - Demand[v][1];
forall(v in Vehicles, t in 2..NbPeriods )
ctStorageConstraint:
Soc[v][t] == Soc[v][t-1] + PosChargeamountH[v][t] + PosChargeamountW[v][t] - Demand[v][t];
forall(v in Vehicles, t in Periods )
ctChargeamountH:
PosChargeamountH[v][t] <= ChargingPossibleH[v][t]*maxChargeAmount;
forall(v in Vehicles, t in Periods )
ctChargeamount:
PosChargeamountW[v][t] <= ChargingPossibleW[v][t]*maxChargeAmount;
forall(v in Vehicles, t in Periods )
ctMaxSoc:
Soc[v][t] <= maxSoc;
forall(v in Vehicles)
ctEnd:
Soc[v][NbPeriods] == endSoc;
forall(v in Vehicles, t in Periods )
ctNonNegativeSoc:
Soc[v][t] >= 0;
forall(v in Vehicles, t in Periods)
ctNonNegativeChargeamountH:
PosChargeamountH[v][t] >= 0;
Appendix
forall(v in Vehicles, t in Periods)
ctNonNegativeChargeamountW:
PosChargeamountW[v][t] >= 0;
forall(t in Periods )
ctTotalLoadH:
sum( n in Vehicles)(PosChargeamountH[n][t]) == TotalChargingH[t];
forall(t in Periods )
ctTotalLoadW:
sum( n in Vehicles)(PosChargeamountW[n][t]) == TotalChargingW[t];
forall(t in Periods )
ctMaxLoadH:
TotalChargingH[t] <= x;
forall(t in Periods )
ctMaxLoadW:
TotalChargingW[t] <= x;
};
205
206
Appendix
2000
0
4000
SB
2000
0
4000
SLC
2000
0
DLC
2000
0
4000
SLPmax
4000
2000
0
4000
SLPt
2000
0
4000
DLP
2000
0
4000
OPT
2000
0
Mo 0:00
Tu 0:00
We 0:00
Th 0:00
Fr 0:00
Sa 0:00
Su 0:00
Mo 0:00
Time