Frequency Bias

eeh power systems
laboratory
Andreas Ritter
Deterministic Sizing of the Frequency

Bias Factor of Secondary Control
Semester Thesis
PSL1106
EEH – Power Systems Laboratory

Swiss Federal Institute of Technology (ETH) Zurich
In Cooperation with swissgrid ag
Expert: Prof. Dr. Göran Andersson

Supervisors: MSc ETH Marc Scherer,
MSc ETH Emil Iggland
Zurich, June 1, 2011

Abstract
An important challenge of grid control is the prediction of the frequency

bias factor Ki so as to be as well matched to the actual frequency response
characteristic βi of an area i as possible, in order to adhere to the principle
of non-interaction in Secondary Control. In this report, new semi-online
sizing methods based on extensive previous research and on the current
operation policies in Continental Europe are presented. Data directly from
Switzerland’s TSO swissgrid is analyzed and used as basis for an evaluation
of the sizing methods in a purpose-designed simulation.
i
Contents
1 Introduction 1
2 Frequency Control Theory 2

2.1 Need for Constant Frequency . . . . . . . . . . . . . . . . . . 2
2.2 Without Speed Governing . . . . . . . . . . . . . . . . . . . . 3
2.3 Three Tiered Approach . . . . . . . . . . . . . . . . . . . . . 4
2.4 Primary Control Using Speed Droop Control . . . . . . . . . 5
2.5 Frequency Response Characteristic . . . . . . . . . . . . . . . 8
2.6 Secondary Control . . . . . . . . . . . . . . . . . . . . . . . . 9
2.7 Tertiary Control . . . . . . . . . . . . . . . . . . . . . . . . . 10
3 Automatic Generation Control 11

3.1 Classic Automatic Generation Control . . . . . . . . . . . . . 11
3.1.1 Linear Area Control Error . . . . . . . . . . . . . . . . 12
3.1.2 Non-Interactive Control . . . . . . . . . . . . . . . . . 13
3.2 Current Practice in the RGCE . . . . . . . . . . . . . . . . . 15
3.2.1 Network Characteristic Method . . . . . . . . . . . . . 15
3.2.2 Change in Load-Frequency Control Policy . . . . . . . 15
3.2.3 Measurements of Performance . . . . . . . . . . . . . . 18
3.3 Proposed Improvements and New Schemes . . . . . . . . . . . 18
3.3.1 Changes to Classic AGC . . . . . . . . . . . . . . . . . 18
3.3.2 Fundamentally New AGC Schemes . . . . . . . . . . . 20
3.3.3 Example of New Implementations outside ENTSO-E . 20
3.3.4 Applicability to the RGCE and Switzerland . . . . . . 21
4 Estimation Errors of β 23
4.1 Sources of Estimation Errors . . . . . . . . . . . . . . . . . . 23
4.1.1 Assumptions of Classic AGC by the RGCE . . . . . . 23
4.1.2 Research Performed in the Union for the Coordination
of Production and Transmission of Electricity (UCPTE) 24
4.1.3 Non-Linearities from Generators . . . . . . . . . . . . 27
4.1.4 Contribution Factor ci from UCTE Data . . . . . . . 30
4.1.5 Research on Load Self-Regulation . . . . . . . . . . . 31
ii
CONTENTS iii
4.2 Effects of Estimation Errors on Network Operations . . . . . 32
5 Deterministic, Semi-Online Sizing of Ki 35

5.1 Updating ci Regularly . . . . . . . . . . . . . . . . . . . . . . 35
5.2 Scaling λu with Generation . . . . . . . . . . . . . . . . . . . 36
5.3 Construction of βi by Parts . . . . . . . . . . . . . . . . . . . 37
5.3.1 Using Default Values . . . . . . . . . . . . . . . . . . . 37
5.3.2 Predicting Primary Control . . . . . . . . . . . . . . . 38
5.3.3 Additional Primary Control . . . . . . . . . . . . . . . 40
5.3.4 Measuring Surplus Generation . . . . . . . . . . . . . 40
5.3.5 Load Self-Regulation . . . . . . . . . . . . . . . . . . . 41
5.3.6 Sensitivity to Parameter-Changes . . . . . . . . . . . . 41
5.4 Measuring βi . . . . . . . . . . . . . . . . . . . . . . . . . . . 42
5.4.1 Analysis of Large Outages . . . . . . . . . . . . . . . . 43
5.4.2 Linearity in Random Disturbances . . . . . . . . . . . 43
6 Calculation, Modeling and Simulation 47

6.1 Reduced-Size Power System Model . . . . . . . . . . . . . . . 47
6.1.1 Power System Dynamics and Tie-Line Flows . . . . . 50
6.1.2 Primary and Secondary Control . . . . . . . . . . . . 50
6.2 Implementation of Ki -factor Algorithms . . . . . . . . . . . . 50
6.2.1 Operation Handbook (OpHB) Definition . . . . . . . . 50
6.2.2 Updating ci and scaling λu . . . . . . . . . . . . . . . 52
6.2.3 Simple Partwise Construction . . . . . . . . . . . . . . 52
6.2.4 Non-Linear partwise Ki (f ) . . . . . . . . . . . . . . . 52
6.3 Evaluation Result Output . . . . . . . . . . . . . . . . . . . . 52
6.4 Input Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55
6.4.1 Large Disturbance . . . . . . . . . . . . . . . . . . . . 57
6.4.2 Random Disturbances . . . . . . . . . . . . . . . . . . 60
7 Discussion and Conclusion 65

7.1 Results from the Simulation . . . . . . . . . . . . . . . . . . . 65
7.2 Further Research . . . . . . . . . . . . . . . . . . . . . . . . . 65
7.3 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66
A Evaluation Results 67
Acronyms 72
Bibliography 77
Chapter 1
Introduction
Maintaining the balance between mechanical power fed into all generators
and the active power consumed by all loads is one of the most crucial con-
trol problems in a synchronous grid. In the former UCPTE and Union
for the Co-ordination of Transmission of Electricity (UCTE)1 , a fast act-
ing frequency-dependent Primary Control loop combined with a slower but
error-free Secondary Control loop has been maintaining this balance for over
50 years. With the advent of liberalization, electricity trading and uncon-
trollable renewable energies, the fundamentals of the interconnection have
changed beyond regular expansion to new countries, while the frequency
control mechanisms remain in their original form.
This project focuses on the sizing of the frequency bias factor Ki , a funda-
mental component of Secondary Control, which has seen little change over
the last decades.
To determine shortcomings of the currently implemented methods and to
outline potential improvements, this project was completed at the request
of Switzerland’s Transmission System Operator (TSO) swissgrid ag in co-
operation with the Power Systems Laboratory at ETH Zurich.
1
Now referred to as the Regional Group Continental Europe (RGCE) of European
Network of Transmission System Operators for Electricity (ENTSO-E).
1
Chapter 2
Frequency Control Theory
It is well established that a mismatch between mechanical energy fed into

electric generators Pm (t) and active electric power consumed by loads and
losses Pe (t) is balanced by reducing or increasing the energy stored in the
rotating masses Wrot in the electric power system according to equation
(2.1). From equation (2.2) it is clear that a change in the rotational energy
can only result in a change of the system frequency f .
dWrot
Pm (t) + − Pe (t, f ) = 0 ∀t (2.1)
dt
1
Wrot = J(2πf )2 (2.2)
2
Detailed analyses of these dynamics can be found in [1] and [2]. The notation
in this chapter will closely follow [2].
2.1 Need for Constant Frequency

Equipment, from home appliances to steam turbines, connected to a syn-
chronous grid, is designed to operate at this grid’s nominal frequency which
is 50 Hz in Europe. Small deviations from the nominal frequency, in the
range of a few millihertz, are a normal result of stochastic variations in
loads and should not affect the behavior of any component in the network.
Large deviations, in the range of one Hertz or above, however, carry a num-
ber of dangers and have to be avoided. Especially large electric motors and
generators, whose rotational speed are directly proportional to the square
of the electric frequency, are at risk from vibratory stress due to resonances.
Another hazard stems from magnetic saturation in power transformers and
induction motors [1].
According to the 2009 Union for the Co-ordination of Transmission of Elec-
tricity (UCTE) Operation Handbook (OpHB) [3], as a result of the “maxi-
mum instantaneous power deviation between generation and demand in the
2
CHAPTER 2. FREQUENCY CONTROL THEORY 3
un-split synchronous area, [. . . ] undisturbed operation depends on the size

of the synchronous area and the largest generation unit or generation capac-
ity connected to a single bus bar”1 . The frequency is allowed to deviate no
more than 800 mHz in either direction immediately after the incident and
no more than 200 mHz in the quasi-steady state following the disturbance.
If the system frequency drops below 49 Hz, the 2004 UCTE OpHB recom-
mends TSOs disconnect between 10 and 20 % of their loads (load shedding)
and again 10 to 15 % more at the trigger frequencies 48.7 Hz and 48.4 Hz as
emergency actions. Below frequencies of 47.5 Hz power plants are advised
to disconnect immediately to avoid damage [4].
2.2 Without Speed Governing

In steady state, Pm = Pe which results in a constant rotational energy and
therefore constant mechanical and electrical frequencies. In an intercon-
nected system, a sudden loss of electric power produced in one generator
(i.a. resulting from a generator trip) is compensated by all other genera-
tors releasing energy stored as inertia of their rotating masses. Equation
(2.2) shows that the frequency f will decrease with the square root of the
rotational energy. This collapse of the system frequency is somewhat coun-
teracted by the self-regulation effect of electric loads, leading to a reduced
consumption of electrical power at decreased frequencies. As a result of this
effect, a new steady state will be reached at a lower frequency. Self-regulation
is the subject of numerous research efforts, for network modeling it is gener-
ally assumed that the load changes proportionally to the frequency according
to equation (2.3)2 . The load damping factor Dl as defined in equation (2.4),
is generally found to be between 0%/Hz and 4%/Hz (0−2%/%) [2]; it is
sometimes given directly in the unit of MW/Hz when referring to a defined
network3 .
∆Pe = Dl · ∆f (2.3)
h i P0 −P
% P0
Dl Hz = (2.4)
f0 − f
In order to illustrate this effect, the steady state frequency at which the Swiss
network would settle if it were not interconnected with other networks and
had no frequency control is calculated. Data from ENTSO-E’s Statistical
1
This “Reference Incident” is currently defined as 3000 MW in European Network of
Transmission System Operators for Electricity (ENTSO-E).
2
[2] features an additional term from rotating mass loads, which depends on df
dt
. While
it influences the time-characteristics of the decrease, it does not influence the resulting
steady state frequency.
3
In this report, bold Dl refers to values given in the relative unit of %/Hz and %/%,
while regular Dl refers to load dampings in the unit of MW/Hz.
Yearbook 2009 [5] was used for an exemplary calculation. The highest mea-
sured load in Switzerland in 2009 was Ptotal = 10261 MW, the largest single
producer in operation is the nuclear plant in Leibstadt with a generator rat-
ing of Pmissing = 1165 MW. If the self-regulation effect of the load is assumed
to be Dl = 2%/Hz, the frequency would settle at 44.3 Hz, 5.7 Hz below the
nominal frequency of 50.0 Hz according to (2.5). This is clearly far below
the tripping point of most power plants and thus unacceptable.
Pmissing 1 1
· = f0 − f = 11.4 % · % = 5.7 Hz (2.5)
Ptotal Dl 2 Hz
2.3 Three Tiered Approach

In most large interconnections, frequency control is split into three feedback
loops which have distinct goals, time-scales and activation mechanisms. The
differences in time-scales uncouples the three control loops so that they can
be dimensioned and analyzed separately.
Figure 2.1 shows an interconnection consisting of three synchronously con-
nected areas. Every area has multiple generators (G) and one load (L1-L3),
representing the sum of all loads in the area. The tie-lines connecting the
areas carry power between the areas according to a previously defined sched-
ule. Figure 2.2 shows the cooperation of the three control loops in case of
a generator failure in area 1, to restore pre-failure conditions according to
ENTSO-E regulations. As explained previously, a lack of generation will
lead to a frequency decrease. This decrease will be limited by the activa-
tion of Primary Control in all synchronously connected areas, which in turn
changes the flow of tie-line power to help the area in need. Primary Control
does not aim to restore the frequency to its pre-fault value but merely to
dampen the system’s dynamics and to settle the frequency at an acceptable
quasi-steady state until it can be restored. It has to be fully available after
30 s and last for at least 15 min. Summed up over the whole synchronous
area, the available Primary Control reserve is usually chosen to be as large as
the biggest generation and load loss that can occur from one single fault (e.g.
bus-bar failure, unprovoked load shedding). This assures that the frequency
does not reach dangerous levels after a single outage. Multiple outages in
short succession, however, can compromise the system’s security, which is
why the Primary Control has to be relieved shortly after the quasi-steady
state frequency has been reached.
After a quasi-steady state frequency has been reached, the Secondary Con-
trol loop steps in to restore the tie-line power flows to pre-fault levels and to
bring the frequency back to the nominal value, releasing the Primary Con-
trol reserves for further disturbances. Both Primary and Secondary Control
Area 1
L1 G
G
G G
Area 2
Area 3
L2
G L3
G G
G
G
Figure 2.1: Three Area System with Tie-Lines and individual Loads (L1-3) and
Generators (G).
are usually4 applied automatically.

A third reserve, the so called Tertiary Control reserve, can be activated by
an operator in the affected area to support Secondary Control and to re-
lease its resources until the missing generation or load can be balanced by
changing the operation schedule of a regular (i.e. non-control) power plant.
Secondary Control Reserves (oftentimes with the help of Tertiary) have to
be able to replace the largest possible generation and load failure in their
area as defined by the OpHB.
2.4 Primary Control Using Speed Droop Control

Primary Control is implemented by a simple proportional feedback loop
between the electric frequency and the turbine governor. Equation (2.6)
defines the speed droop “S”, usually given in the unit of (% frequency devia-
tion)/(100% power deviation) or simply %, of a generator or (Hz frequency
deviation)/(MW power deviation) for a network of generators5 . Speed droop
is defined to be the relationship between system frequency deviation and re-
sulting generator power output change and as such is used as proportionality
4
In the Regional Group Continental Europe, all Primary and Secondary Control is ac-
tivated and controlled automatically while some other interconnections choose to activate
Secondary Control manually.
5
As with the load damping factor Dl , bold S refers to relative speed droops in (%
frequency)/(100% power), while regular S implies the more common unit of Hz/MW
Operator
of A1
activate
activ Tertiary Control
ate A1
rest
support
Frequency ore
activa
f te
limit Primary Secondary

free
Control Control
A1, A2, A3 A1
Tie-Line
Power
A2=>A1 te
A3=>A1 activa
t=0 s 15 s 30 s 30 s 15 min
Figure 2.2: Interactions in Frequency Controls. Red Arrows: Control Inputs;

Black Arrows: Effects of Control Actions.
constant in the control loop of turbine governors. It determines the genera-

tor’s change in power output ∆P from its scheduled value Psched for every
frequency f as seen in figure 2.3 after the various turbine dynamics have
decayed.
∆f
fN om
S=− ∆P
(2.6)
PGen
If the frequency deviates too far from its nominal value however, Primary
Control generators are required to fully activate their primary reserve regard-
less of their speed droop. This requirement introduces non-linear jumps,
leaving only a certain frequency range for linear control as illustrated in
figure 2.3. In the Regional Group Continental Europe (RGCE) this band
extends ±200 mHz around the nominal frequency.
The simplicity of this mechanism assures that participating generators in
all areas work together without competing, but it also leaves a steady state
error, which has to be corrected by another control loop. As mentioned in
section 2.2, in addition to the change in power produced by generators, the
power consumed by the loads of a system also changes with its frequency.
Equation (2.7) sums up these two effects for a change in load power of
∆Pload , resulting in the quasi-steady state frequency fss in equation (2.8)
at which the interconnected network will settle after Primary Control has
full activation
(overfrequency)
fN S
Δf
f
full activation
(underfrequency)
ΔP
P
Pmin Psched Pmax
Figure 2.3: Linear Speed Droop Constant of a Generator with Underfrequency

and Overfrequency Activation.
been fully deployed and the turbine dynamics have settled.

1
∆fss = −∆Pload · 1 (2.7)
Dl + S
fss = fN om + ∆fss (2.8)
In ENTSO-E’s regional group Continental Europe, the total Primary Con-

trol reserve is set to the size of the reference incident, 3000 MW, and dis-
tributed over the control blocks roughly according to their share of the total
power production in the interconnection. This distribution allows control
blocks to be protected against large frequency deviations without having to
reserve the full generation power they would need for their worst case sce-
narios.
Extending the example used in section 2.2, it is obvious that Switzerland,
were it not interconnected, would need at least 1165 MW in Primary Con-
trol reserve to protect the grid frequency from an outage of its largest power
plant, neglecting load self-regulation. This represents about 15.4 % of the
average electric power production of Switzerland in 2009. For comparison,
Switzerland’s share of the 3000 MW Continental Europe reserve is currently
77 MW, a mere 1 % of the average power [6]. This is clearly an advantage
over providing the full reserve for a worst-case scenario, as Primary Control
reserves are expensive to maintain [7]. Applying equation (2.7), it can be
calculated that an outage of the 1165 MW generator at Leibstadt would lead
to a frequency deviation of between -53 mHz and -64 mHz6 in RGCE.
2.5 Frequency Response Characteristic

The sum of the effect of speed droop governing and of the self-regulation of
loads determines the steady state frequency deviation after a disturbance, as
shown in equation (2.7). This sum is called “frequency response character-
istic” and usually labeled β 7 . Calculation for every area i is done according
to equation (2.9).
Connecting areas synchronously provides the Primary Control power and
the change in load from self-regulation available in all areas for an incident
in any of the areas. Thus the individual frequency response characteristics βi
can be summed into one frequency response characteristic β for the whole in-
terconnection as shown in equation (2.10) and equation (2.11). To compare
the behavior of a network to that of a generator, the effective speed droop
σ in [%frequency] of that network can be calculated according to equation
(2.12).
1
βi = + Dl,i (2.9)
Si
X 1
−∆Pload = ∆fss · (Dl,i + ) (2.10)
Si
i
X
β = βi (2.11)
i
1 Ptotal
σ = · · 100% (2.12)
β fN
This provides an elegant way to write equation (2.7) for interconnected areas,
equation (2.13).
∆Pload
∆fss = − (2.13)
β
That said, some caution has to be exercised when adding the speed
droops and load damping factors of different machines and networks, because
percentages can be calculated on different bases. Speed droops can easily be
converted from S [%] to S [Hz/MW] according to equation (2.14) via division
by the generator rating and multiplication by the nominal frequency. Once
given in Hz/MW speed droops can simply be summed as shown to equation
(2.15). To convert the sum of speed droops Sgen,tot to Sgen,tot [%] it has to
6
Calculated using 2 % self-regulation of the loads at the highest (405158 MW) and
lowest (201878 MW) load measured in 2009 according to [5].
7
The definition of β as ∆power /∆f requency in this report follows the notation of [1].
The UCTE OpHBs use the greek letter λ for the same definition. In some other literature,
however, the network response characteristic is definded as network speed droop S or σ,
being equivalent to β1 .
be multiplied by the combined ratings of the participating generators and

divided by the nominal frequency as illustrated in equation (2.16).
Hz
fN 1
Sgen,i MW = Sgen,i · · (2.14)
Pgen,i 100
Hz
1
Sgen,tot MW = PN 1
(2.15)
i=1 Si
PN
i=1 Pgen,i
Sgen,tot [%] = Sgen,tot · · 100% (2.16)
fN
%
Analogously, the load damping factors Dl,i [ Hz ] have to be multiplied by
their load powers Pload,i to be converted to Dl,i [ MWHz ] in order to avoid unit
mismatches. Equations (2.17) to (2.19) illustrate the necessary calculations.
%
The conversion from Dl in [ Hz ] to [ %
% ] is a simple division by two, as shown
in equation (2.20).
MW 1
Dl,i Hz Dl,i · Pload,i
= (2.17)
100
XN
MW
Dl,tot Hz = Dl,i (2.18)
i=1
h
%
i Dl,tot
Dl,tot Hz = PN · 100 (2.19)
i=1 Pload,i
h i
% 1 h i
%
Dl % = Dl Hz (2.20)
2
2.6 Secondary Control

After Primary Control has taken full effect and all interconnected areas are
assisting the affected area in coping with the outage, the Secondary Control
loop steps into action.
As mentioned previously, the two goals of Secondary Control are to restore
the frequency and the tie-line power flows to their pre-disturbance values8 .
This makes Primary Control reserves available for another disturbance. It
is necessary for the Secondary Control to act more slowly than the Primary
Control, so that the control behavior is decoupled from the fast turbine
dynamics and influences from the Primary Control. This is most often
achieved by implementing the Secondary Control loop as a PI-controller
with a large time-constant of up to several minutes.
In most interconnections, Secondary Control is invoked only by the area
8
Secondary Control is often also used for Time Control purposes [3]. To achieve this,
the frequency setpoint is adjusted to have a value slightly different from the nominal
frequency to make up for accumulated deviations. In RGCE the coordination for the
entire interconnection take place at swissgrid in Laufenburg.
causing the disturbance, by means of automatic generation control. This

mechanism will be covered in more detail in chapter 3.
2.7 Tertiary Control

As seen in figure 2.2, Tertiary Control is most often manually activated
by the operator of the area causing a disturbance. In the event of a large
disturbance, Tertiary Control reserves can support the Secondary Control
in restoring frequency and tie-line flows, particularly in cases where the
Secondary Control reserves are exhausted. When Secondary and Tertiary
Control have successfully reestablished the nominal frequency, Tertiary con-
trol also makes Secondary Control reserves available again by changing the
scheduled operating points of area power plants participating in Tertiary
Control.
The only requirement concerning Tertiary Control outlined in the UCTE
OpHB states that these reserves must be sufficent to cover the largest ex-
pected loss of power in the area.
Tertiary Control is not discussed further because it is manually activated
and because it does not affect the Automatic Generation Control (AGC)
operations below.
Chapter 3
Automatic Generation
Control
3.1 Classic Automatic Generation Control

By returning the frequency to its nominal value and the tie-line powers to
their scheduled levels, AGC frees up Primary Control reserves and reestab-
lishes the normal, pre-disturbance operation state. The classic implemen-
tation, which has been in use for several decades in many interconnections
around the globe, consists of one AGC controller per control area, which
centrally calculates a control signal ∆PAGC,i for all generators participating
in Secondary Control in its area1 . The deviation from nominal frequency
and scheduled tie-line power compose the Area Control Error (ACE) (see
section 3.1.1). Thus, driving the ACE to zero is the goal of AGC. Figure 3.1
illustrates area 1 from figure 2.1 with AGC. The controller labeled AGC1
measures the power flow on the tie-lines from area 1 to area 2 (P12 ) and to
area 3 (P13 ), as well as the network frequency f . The nominal frequency
fset and the scheduled power flows of the tie-lines, P12,sched and P13,sched ,
are used in the controller to calculate the deviation of the measured values.
AGC is implemented as a PI-controller, according to equation (3.1). A small
gain constant Cp,i in the range of 0.1 to 1.0 and a large time constant TN,i
in the range of 30 to 200 s as documented in [2] lead to a sufficiently slow
increase in the control signal PAGC,i . The large time constant stems from
the fact that Secondary Control has to be sustained until it can be relieved
by Tertiary Control, which often takes up to 15 min [4]. The speed of pro-
vision of Secondary Control power depends largely on the type and size of
the generating units. While many hydro power plants can vary their power
outputs over a large part of their output range within tens of seconds or
1
This organisation scheme is referred to as “Centralised” by [3]. There are two
schemes,“Pluralistic” and “Hierarchical”, which work in a decentralised way. These are
not discussed here but generally function along the same guidelines.
11
CHAPTER 3. AUTOMATIC GENERATION CONTROL 12
P13,sched
P12,sched
Participating in
fset
Secondary Control
G ΔPAGC1 P12
G AGC1 P13 Area 2
f
G G
L1 Area 3
G
Not Participating in Secondary Control
Figure 3.1: Area 1 Including the AGC Controller which sends the Control Signal
∆PAGC1 to all Generators Participating in Secondary Control.
minutes, coal-fired or nuclear plants employing steam turbines have longer

activation times, in the range of a few minutes [8]. In addition to the acti-
vation time, different power plant types also feature distinctive dynamics in
their power outputs. A large integration time constant in combination with
a small proportional gain make the controller robust against tracking these
short-term dynamics.
1
Z
∆PAGC,i = −(Cp,i · ACEi + ACEi · dt) (3.1)
TN,i
3.1.1 Linear Area Control Error

The sum of all deviations between the actual tie-line power exchange from
area i to j, PTj i , and their scheduled values PTj i,0 added to the weighted
difference between the momentary frequency f and the setpoint frequency
fset 2 makes up the ACE as shown in equation (3.2). The weighting factor
Ki is called “frequency bias factor”, and determines the conversion from
frequency deviation to power deviation and is given in [MW/Hz]3 . Ωi is
defined as the set of areas connected to area i.
X j
ACEi = (PT,i − PTj i,0 ) + Ki · (fi − fset ) (3.2)
j∈Ωi
It is known from measurements and calculations that the assumption of an

identical frequency everywhere in a synchronized grid is not correct dur-
2
fset is equal to the nominal frequency fN except at times when accumulated network
time error is compensated by slightly increasing or decreasing the frequency.
3
Different literature refers to the frequency bias factor in different ways. It is common
to find a factor of −B, −10B or +B instead of the Ki which is used here.
ing dynamic phenomena. Based on [8] however, we can assume that the
dynamics leading to different frequencies fi in different areas (i.a. electro-
mechanical transients and intermachine oscillations) act on much smaller
time-scales than AGC itself and are filtered out by the AGC controllers,
thus allowing the assumption of equation (3.3).
Using equation (3.3), together with the definition of total change in tie-line
power flow out of an area i given in (3.4) and the definition of deviation of
the measured frequency from the setpoint frequency in (3.5), the ACE for
area i can be simplified to (3.6).
fi = f ∀i (3.3)
X j
∆PT i = (PT i − PTj i,0 ) (3.4)
j∈Ωi
∆f = f − fset (3.5)
ACEi = ∆PT i + Ki ∆f (3.6)
3.1.2 Non-Interactive Control

According to [2], any positive value of Ki in the ACE equation (3.6) in com-
bination with an integrating AGC controller, such as given in equation (3.1)
will guarantee that all ACEi will eventually be controlled to zero.
The exact value of the frequency bias factor Ki is given by the “Non-
Interactive Control” principle, which states that only the area responsible
for a disturbance has to provide Secondary Control power to relieve Primary
Control reserves and restore the nominal frequency.
Assuming now that a synchronous grid, consisting of N areas labeled 1. . . N ,
is subject to a change in load of ∆Pload in area l. From section 2.4 it is known
that the Primary Control in all areas will act jointly and that the frequency
will settle at a steady state differing by ∆fss from the setpoint frequency
according to equation (2.13). The individual contribution in stabilizing the
frequency of every area is composed of its Primary Control power and of its
loads’ self-regulation effect and is transferred to area l via tie-lines4 . The
change in tie-line power ∆PT,i all areas i 6= l is calculated as shown in
equation (3.7) and equation (3.8).
∆fss
∆PT,i = −( + ∆fss · Dl,i ) ∀i 6= l (3.7)
Si
= −∆fss · βi (3.8)
The sum of tie-line power flows and thus also the sum of tie-line power
flow changes, as written in equation (3.9), have to equal zero in order to
4
If some areas do not have a direct connection to l, the power will flow through in-
termediate areas. ∆PT,i of the intermediate areas will not be affected by the this transit
because inflow and outflow cancel out.
comply with the conservation of energy. From this, it is clear that the total
change of tie-line power into the affected area l of −∆PT,l is obtained by
summation of all other areas’ contributions, as shown in equation (3.10).
Inserting equation (3.8) into equation (3.10), ∆PT,l can simply be written
as equation (3.11).
N
X
∆PT,i = 0 (3.9)
i=1
X
∆PT,l = − ∆PT,i (3.10)
i6=l
X
= ∆fss βi (3.11)
i6=l
Using these deviations in tie-line powers, the ACEs of all areas, before Sec-
ondary Control is activated, can be calculated by inserting equation (3.8)
and equation (3.10) into equation (3.6) resulting in equation (3.12) and
equation (3.13).
ACEi = ∆fss · (−βi + Ki ) ∀i 6= l (3.12)

X
ACEl = ∆fss · ( βi + Kl ) (3.13)
i6=l
To fulfill the Non-Interaction Control principle, the ACEs of all areas except
for area l have to be zero, so that their AGCs do not react to the disturbance
in area l. From equation (3.12) it is obvious that this can be implemented
by selecting the frequency bias factor Ki according to equation (3.14).
1
Ki = βi = + Dl,i (3.14)
Si
The ACE of area l, using Kl = βl , can be calculated by inserting equation
(2.13) into (3.15), resulting in equation (3.16).
X
ACEl = ∆fss · βi (3.15)
i
ACEl = −∆Pload (3.16)
At first glance, this solution looks deceptively simple. To setup their fre-
quency bias factor, every area has to add up its Primary Control generators’
speed droops as shown in equation (2.15) and calculate its load damping
factor according to equation (2.17).
As explained in section 3.1, AGC works on a slower timescale than Pri-

mary Control. It can be assumed that these two mechanisms are uncoupled,
meaning that for every change ∆PAGC,l in AGC power applied in area l, the
quasi steady state of Primary Control will be reached before the next change
in ∆PAGC,l is applied. Using this assumption, the frequency deviation after
deployment of AGC power in area l follows from equation (3.17). It also
implies that the ACEs of all areas i 6= l will remain zero, while ACEl will
decrease according to equation (3.18).
−∆Pload + ∆PAGC
∆fss = (3.17)
β
ACEl = −∆Pload + ∆PAGC (3.18)
3.2 Current Practice in the RGCE

The legal framework for Primary and Secondary Control in ENTSO-E’s
RGCE is currently dictated by Policy 1 of the 2009 UCTE OpHB [3]. Further
explanations of Policy 1 can be found in the appendix of the 2004 UCTE
OpHB [4].
3.2.1 Network Characteristic Method

During normal operations5 , referred to as “Frequency Power Network Char-
acteristic Method”, Policy 1 requires every Transmission System Operator
to implement a classic AGC according to chapter 3, which has to start op-
erating no later than 30 s after a disturbance occurred and bring the ACE
to zero without overshoot in no more than 15 min.
Estimation of RGCE’s total frequency response characteristic β, referred to
by UCTE and ENTSO-E records as λu , is currently done “on a regular ba-
sis” as specified in OpHBs 2004 [9] and 2009 [3]. Apart from these updates,
usually occurring less than once per year, “it is taken to remain as constant
as possible”.
3.2.2 Change in Load-Frequency Control Policy

The 2004 UCTE OpHB defines the K-factor for every control block or area
by a specific formula (3.19). The “contribution coefficient” ci , defined as the
ratio of electrical energy produced in area i over the total production in the
interconnection in one year6 , is used to split the total frequency response
characteristic among its areas. An additional factor of 10% is introduced
to account for uncertainties in the self-regulation effect, assuming that over-
estimation of the frequency response characteristic is preferable. The overall
network frequency characteristic λu of 18000 MW/Hz is composed of the
5
Other modes of operation are only activated in case of equipment outages or emergency
conditions.
6
The factor ci is also used to determine an areas share of the 3000 MW Primary Control
reserves every year.
Primary Control speed droops, which are calculated according to the rule
that the total Primary Control reserve of 3000 MW has to be provided within
200 mHz, and the load self-regulation effect of 1 %/Hz.
Kri = 1.1 · ci · λu (3.19)
Since, by OpHB definitions, none of the factors in equation (3.19) change

on an interval shorter than one year, the frequency bias factor of every area
is supposed to stay constant for that same interval.
The revised OpHB policy on load-frequency control7 , approved in March
2009, states in its “Standards” section that “Frequency Gain Setting [. . . ]
shall reflect the best approximation of the real Network Power Frequency
Characteristic of the Control Area/Block”. It further postulates that the
K-factor calculated by multiplying ci and λu shall serve as the default value
for the frequency gain setting according to equation (3.20).
λdef
i
ault
= ci · λu (3.20)
The calculation, however, must be adjusted in case of border-crossing trad-

ing in Primary Control reserves. The computation of the λu also changed
significantly from the 2004 OpHB, resulting in an overall network frequency
response of 26680 MW/Hz for 2009. In addition to the Primary Control
reserves from equation (3.21) and the self-regulation effect from equation
(3.22), which made up λu in the previous OpHB, two new components
Sadditional −1 , equation (3.23), and Ssurplus −1 , equation (3.24), are added
in the 2009 version. The first accounts for the fact that Primary Control
delivers on average 30% more power per frequency than it is planned to.
The latter is referred to as “surplus-control of generation”, and is briefly ex-
plained to originate from a linear frequency dependency, according to figure
3.2, of roughly 50% of the generators in the network. To the knowledge of
the author, no published measurements or analyses as to the exact size or
cause of both of these effects currently exist. The most probable explana-
tion of the “Additional Primary Control” is incomplete adjustment of speed
droop controllers, which are especially hard to modify in older generators.
According to swissgrid, many power plant owners chose not to readjust their
turbine controllers to lower settings even when not taking part in the official
Primary Control reserves. Other operators, instead of completely switching
off the speed droop controllers, set the controllers’ deadbands to large values
of over ± 200 mHz. While both of these measures complicate the calculation
of the actual Primary Control behavior, they are beneficial to the perfor-
mance of the whole interconnection in the event of disturbances.
The result of the sum of these four effects is the overall network frequency
7
Load Frequency Control (LFC) is a synonym for AGC, which is used throughout the
UCTE OpHB.
2Psched,i
Psched,i
0 f
0 fN 2fN
100%
Figure 3.2: Linear Frequency Dependency which 50% of the Generators are
50 Hz
Following According to the OpHB.
response as shown in equation (3.25).

1 3000 MW
= (3.21)
Sprim 200 mHz
%
Dl = 1 · P highest (3.22)
Hz load
1 1
= 0.30 · (3.23)
Sadditional Sprim
1 50%
= · P mean (3.24)
Ssurplus 50 Hz generation
1 1 1
λu = + Dl + + (3.25)
Sprim Sadditional Ssurplus
Compared to the stringent definition of the frequency bias factor by formula

in the earlier version of the OpHB, the new standard leaves some room for
interpretation. From the definition of the ACE according to equation (3.6)
it is clear that the frequency bias factor Ki has to be changed if Primary
Control reserves are traded over borders of areas, which is explicitly specified
in the OpHB. It is not entirely clear from the new standard whether or
not cross-border trading is the only case where changing Ki is allowed. A
plausible interpretation is that any method yielding a better approximation
of the actual frequency response characteristic βi than equation (3.25), is

allowed.
3.2.3 Measurements of Performance

As previously stated, the main target of Secondary Control as defined in the
2009 UCTE OpHB is returning the system frequency and the tie-line powers
back to their set-points by reducing the ACE to zero with no overshoot,
in under 15 min. There are a number of indicators used to measure the
quality of Frequency Control employed in RGCE, as explained in [4]. During
normal operation the monthly standard deviation σ of the frequency can be
calculated by taking averages of the frequency over 15 min (fl ) and summing
the squares as in equation (3.26).
v
u n
u1 X
σ=t · (fl − f0 )2 (3.26)
n
i=1
Also the number and duration of frequency deviations of more than 50 mHz
from the frequency set-point must be measured.
In case of generation or load loss of more than 1000 MW, categorized as large
disturbance, the recovery of the system frequency by Secondary Control is
compared to a trumpet-shaped curve of the form H(t) = f0 ± A · e−t/T .
The parameters A and T are calculated from a number of constants, the
15 min maximal recovery time and the size of the disturbance Pa ; f0 is
the pre-disturbance frequency. When the system frequency stays within the
boundaries given by H(t) during recovery back to f0 , the Secondary Control
mechanism is deemed satisfactory. Figure 3.3 from [4] shows trumpet-curves
for different disturbance sizes.
3.3 Proposed Improvements and New Schemes

Since the introduction of AGC more than half a century ago, its shortcom-
ings have been well documented (see section 4.1) and a large number of
alternatives have been proposed by different parties. In 2005, Ibraheem et
al. categorized and summarized 184 different sources in “Recent Philoso-
phies of Automatic Generation Control Strategies in Power Systems” [10].
This extensive literature review provides a well informed overview of the
different approaches taken to simulate the effects of AGC, to improve on the
current implementations and to completely redesign Secondary Control.
3.3.1 Changes to Classic AGC

In [11] Quazza 1966, it is suggested that selecting Ki = βi in all areas of an n
area system fulfills the non-interaction principle between frequency and tie-
Pa (parameter)
-3200 MW
-2800 MW
50.2
-2400 MW
-2000 MW
f [Hz] -1600 MW
-1200 MW
50.1
-800 MW
-400 MW
d
50.0
400 MW
800 MW
49.9
1200 MW
1600 MW
2000 MW
2 40 0 MW
49.8
2800 MW
3200 MW
-100 0 100 200 300 400 500 600 700 800 900 1000 1100
t [s]
Figure 3.3: Trumpet-Curves for Different Incident Sizes Pa .
line power, as well as the principle of non-interaction between different areas

(at least for the low-frequency approximation). However, there was and still
is research and development carried out to improve the simple control given
by equation (3.1) and equation (3.6).
Some early research about the fundamentals of AGC, such as that carried
out by Elgerd and Fosha [12], applied new concepts of control theory, in the
case of [12], the theory of optimal control, and suggested that β might not
be the best choice of frequency bias factor Ki . These suggestions, however,
were never utilized.
At the same time, other research looked into expanding the basic definition
of ACE given in equation (3.6) by adding power system properties other than
tie-line flow and frequency deviation. One example of this is [13], in which
Cohn makes a case for adding two terms accounting for the accumulated
inadvertent energy exchange between areas and for the deviation of the grid
time from real time.
Since there are a number of sources of estimation errors when determining
a system’s frequency bias response (see section 4.1), a necessary method to
improve classic AGC is by modeling Ki as closely as possible to the actual
frequency response characteristic β. To achieve this, Kennedy et al. in 1988
in [14], proposed a non-linear frequency bias factor Ki . The goal of the non-
linearity was to emulate turbine governor dead-bands which were known to
violate the assumption of linear speed droop control8 . Another approach

consisting of an adaptive filter for online updating of β was proposed by
Chang-Chien in the publications [15] and [16].
3.3.2 Fundamentally New AGC Schemes

With the advent of control theory, a large number of AGC implementations,
partially or entirely different from the algorithm described in section 3.1,
were developed and simulated. Control methods such as neural networks,
fuzzy logic and genetic algorithms have been applied to the problem of AGC
with varying degrees of success. Again, [10] provides an overview of the ex-
tensive, ongoing research in these areas prior to the year 2005.
The article “Understanding Automatic Generation Control” by N. Jaleeli et
al. [8], and the substantial discussion following its publication in 1992, por-
trayed fundamental redesigns of AGC in a critical light. The main objections
to these redesigns were that they violate fundamentals of electric power sys-
tems or the goal of AGC itself. It was observed that many approaches to
AGC redesign neglected power plant dynamics and their shortcomings (i.a.
non-linearities, limited control range and speed), while others neglected the
long decision cycle times typical for AGC. Another flaw found by Jaleeli et
al. in many publications, was the level of detail used in the simulation of
new AGC schemes. Many of them involved dynamic phenomena, such as
tie-line interchanges due to frequency deviations between control areas, that
occur on a much smaller time-scale than AGC actions. Yet another point of
criticism was the assumption of many publications that new AGC schemes
could be introduced in an entire interconnection at once. It was pointed out
by Jaleeli et al., that especially the large interconnections of North America
and Europe have grown evolutionarily and classic AGC has been at least
partially implemented for over six decades. Changes to these systems can
thus only be established slowly and continuously.
3.3.3 Example of New Implementations outside ENTSO-E

With the ongoing expansion of interconnections and the growth of electric
power grids in certain parts of the world, AGC is currently becoming pre-
dominant in areas which previously did not employ Secondary Control or
manually dispatched reserves via an operator.
An example of newly adopted classic AGC can be found in [17]. The area
in question is the country of Montenegro which previously contracted out
Secondary Control to Serbia and has now established its own AGC. In the
report, Stojkovic presents insights into the details of Montenegro’s AGC in-
8
Even the newest UCTE OpHB regulations require turbine governors to have the small-
est possible deadband, illustrating the persistence of this issue with linear frequency bias
factors.
cluding noise management and individual generator dispatch.

When Africa’s largest power producer, ESKOM, redesigned its frequency
control in order to reduce generator activation, classic AGC was already im-
plemented in the system but performed unsatisfactorily. A complete anal-
ysis of the frequency control policy in action at the time lead to numerous
changes, such as widening of the Primary Control deadbands [18]. Ad-
ditionally the ACE calculation of the existing AGC was changed from the
established equation (3.6) to a fuzzy-logic algorithm which includes the stan-
dard ACE as well as its derivative ∆ACE, as presented in [19]. ESKOM
claims in [18], that its frequency policy and control redesign reduced daily
generator activation by as much as 80 % without any implications to their
customers. These results have to be weighed against the unique situation
ESKOM finds itself in, being by far the largest energy producer in a sparsely
interconnected grid.
The change of measurements of control performance by the North Amer-
ican Electric Reliability Council (NERC) in 1997 triggered rethinking of
the employed AGC algorithms in most of the North American interconnec-
tions. ’AGC Logic Based on NERC’s New Control Performance Standard
and Disturbance Control Standard’ [20] by Yao et al. proposed a completely
new AGC controller which specifically optimizes its output for a maximum
compliance with NERC’s new performance indicators. ACE according to
equation (3.6) is still used in this controller but only to constantly calculate
the area’s current performance indicators rather than defining the control
goal. The comparison of these real-time measurements with long-term values
results in control actions to minimize the deviation from NERC’s specifica-
tions. The promising results led Texas Utilities Electric Company and the
University of Texas at Arlington to start developing a practical implemen-
tation according to [20]. However Jaleeli and VanSlyck were quick to point
out that an optimization of performance indicators rather than the actual
frequency and tie-line error can have unforeseen consequences for all con-
nected areas, and that more simulation as well as research is needed before
the application of the proposed control system [21].
3.3.4 Applicability to the RGCE and Switzerland

Though interesting, the approaches presented in the above sections 3.3.3
and 3.3.2 are unlikely to be adopted in the control areas of the RGCE in
the near future. Member areas which have been interconnected strongly for
several decades have invested considerable resources in the existing control
system over the years. The classic scheme has proven to be reliable and
dependable. Nevertheless some of the recently developed AGC systems will
find their way into modern electric power systems which have serious prob-
lems with their current implementation or have no AGC at all.
It has therefore been decided, for the scope of this project that the ap-
proach with the greatest relevance is to build on the existing Secondary

Control scheme of AGC with the ACE calculation explained above and to
improve on it solely by proposing a new strategy for the sizing of the fre-
quency bias factor K. This change to the algorithm is small enough that
it can be incorporated easily into the existing system. This approach also
allows direct comparison between the proposed and the classic system since
it does not require large changes to the existing control architecture. Ad-
ditionally, the availability of research on the topics of non-linear frequency
bias settings and interconnection frequency response characteristics assures
a well-founded starting point.
Chapter 4
Estimation Errors of β
As explained in section 3.1, the basis of the AGC scheme currently im-
plemented in RGCE is the Non-Interactive control principle, which specifies
that only the area in which a disturbance occurred should provide Secondary
Control power to restore pre-disturbance conditions. It is, however, evident
from the presented equations that if an area cannot set its frequency bias
factor Ki to be exactly equivalent to its frequency response characteristic
βi , the Non-Interaction principle will be violated.
4.1 Sources of Estimation Errors

4.1.1 Assumptions of Classic AGC by the RGCE
The calculation of the frequency bias factor of any area according to the
the definition given by the OpHB 2004 and 2009, albeit different in their
composition, are based on the following four fundamental assumptions.
1. The frequency response characteristic β (called λu in the OpHB) of

the entire interconnection is
(a) calculable from two to four known constituents and

(b) remains constant for at least one year.
2. Every area’s individual frequency response characteristic βi can be

calculated by multiplication of the characteristic of the whole network
with a contribution factor ci .
3. This contribution factor ci is equal to an area’s share of the annual

energy production of the interconnection and remains constant over
the course of one year.
4. β and its constituents are linear (i.e. independent of the frequency).
23
CHAPTER 4. ESTIMATION ERRORS OF β 24
4.1.2 Research Performed in the Union for the Coordination

of Production and Transmission of Electricity (UCPTE)
Soon after implementing AGC with ACE, the operators of UCPTE encoun-
tered a number of difficulties. The UCPTE annual reports 1957-1958 [22]
and 1958-1959 [23] cover in great detail the problem of determining the
frequency response characteristic in the network which then connected Bel-
gium, West Germany, France, Italy, Luxembourg, the Netherlands, Austria
and Switzerland. At first β was estimated by summation of the linearized
speed droops of all participating power plants, as explained in section 2.51 ,
however measurements of the frequency response characteristic of the net-
work showed that it never reached more than a fraction of the calculated
value. One explanation was found to be power plant protection equipment
such as oil-breaks and opening-limiters which added non-linearities and time-
dependencies to the speed droops. They also hindered certain power plants
(i.a. hydro power plants with opening limiters) from contributing to Pri-
mary Control if they could do so at all. Subsequently, two improvements
were proposed to increase the frequency response characteristic, thus mak-
ing the frequency less susceptible to load changes. These were to deactivate
some of the protection equipment and to equip power plants with more
accurate controllers in order to reduce deadbands as well as measuring in-
sensitivities.
The first measurements listed in [22] to determine the whole interconnec-
tion’s β were done in May 1957 by switching off two generators in the after-
noon and two pumps at night, each generator and pump making up about
1 % of the UCPTE generation and load at the time. The results showed β
values of 13.1 % and 13.5 % during the day as well as values of 11.8 % and
11.9 % during the night. Over the two years following these initial tests,
many more were executed in most UCPTE member areas to determine the
individual areas’ frequency response characteristics.
The results published in 1959 in [23] demonstrated measured βi over a wide
range for the different areas, which was explained as stemming from the
different types and sizes of power plants prevalent in the different areas. It
was also found that the characteristics changed depending on the time of
day the measurement was taken. This was also explained to be attributable
to power plant scheduling depending on the amount of the load. The fact
that different types of power plants exhibit different speed droops has been
covered widely in literature; as one example, the ranges of S for the three
most prevalent types of power plants are listed in [24] as being 4 to 6 % for
nuclear power plants, 4 to 6 % for conventional thermal power plants and 2
to 6 % for hydro power plants.
With the increasing size of the UCPTE interconnection, measuring network
1
Whether or not the self-regulation effect of the loads was included as well is not exactly
specified in the report; the focus clearly lay on the generators.
parameters by switching off large generators or loads in order to find β was

deemed unsecure as well as unnecessary because naturally occurring faults
provided readily available data for analysis. A comprehensive evaluation
published in the annual report of UCPTE in 1982 [25] analyzed 1251 faults
over the course of five and a half years. A high dependence of the frequency
response characteristic on the season, the weekday and the hour of the day
was found. Figure 4.1 from [25] shows the development of the monthly av-
erage of the frequency response characteristic β in the upper curve and the
monthly maximum load in the lower curve. It is obvious from this figure
20000
]
MW/Hz
15000
c[
00
ti
3
ace
trs
i
GW]
poneChar
10000
d[
00
a
2
stLo
s
he
yRe
g
5000
Hi
0
nc
10
e
Frque
0
0
1
976 19
77 1978 1979 1
980 1981
Ye
arofOc
cur
anc
e
Figure 4.1: Monthly Average of Frequency Response Characteristics and Maxi-

mum Load in UCPTE. Upper Curve: β Using the left Scale of [MW/Hz]. Lower
Curve: Monthly Maximum Load, Using the right Scale of [GW]. Actual Measure-
ments are Given by ’+’; Dotted Lines are Spline-Interpolation; Solid Line Indicates
Linear Regression.
that assumption 1b is violated because β shows a significant seasonality.

That said, there is a noticeable correlation between the frequency response
characteristics and the total load of the network. The report explains the
seasonalities as an effect of the different types of power plants running at
different times of the day, week, and year depending on the demand by the
loads. The same measurements presented in figure 4.1 were also analyzed
for the time of day the fault occurred. Figure 4.2 shows all of the 1251 mea-
sured characteristics. Despite the noise stemming from the different times
of year when the incidents took place, a tendency of the frequency response
characteristic to be higher during peak-load (between hours 6 and 18) can
be discerned. Also in this case, the explanation was found in the additional
peak power plants which were online during the high-load hours.
2000
0
MW/ ]
Hz
00
c[
50
i
1
a
rce
trs
it
0
neCha
1000
nc s
yRepo
00
que
50
e
Fr
0 6 12 18 24
HourofDayofOc
cur
enc
e[h]
Figure 4.2: Time of Day of the Measured Frequency Response Characteristics.

Averages Over Five Years in Red.
In [26], H. Weber et al. evaluated the continued measurements of distur-

bances larger than 600 MW in the UCPTE grid between 1988 and 1996.
The absolute values of β showed the same trends as previously described,
i.e. a considerable seasonality and a net increase with overall system growth.
When calculating the frequency response characteristic relative to the total
load of the system (β) however, the effects of seasons and the growth of
the network became much less dominant, as displayed in figure 4.4. Be-
tween 1988 and 1991 the average β exhibited little change between summer
and winter. This change increased considerably after 1991, when according
to Weber et al., some operators stopped to adjust their Primary Control
reserves according to their total energy production. Albeit not mentioned
in the report, it can be assumed from earlier findings that the change in
types of power plants being online during winter or summer also has some
influence. In addition to the development of the mean values, it has to be
noted that the actual measurements tend to differ greatly from the average,
leading to large standard deviations.
In many of the previous reports it was assumed that the frequency response
of the system was linear, so that it can be calculated from any measure-
ment simply by calculating ∆Pload /∆fss . Figure 4.3 shows 1285 distur-
bances, which occured between 1988 and 1995 in the UCPTE network and
31 disturbances in 1995-1996 after UCPTE and Former synchronous area
covering Czech Republic, Hungary, Poland and Slovakia (CENTREL) were
connected. It can be seen from the figure that a linear approximation is pos-
sible but many datapoints with significant deviations exist. Figure 4.4 shows
the same analysis for the relative characteristic, which features a better cor-
relation between the linear approximation and the 1316 measurements. This
analysis adds some credibility to assumption 1b, under the conditions that
relative β is referred to and that the linearity is only an approximation.
From the detailed analysis of the frequency bias factor in the UCPTE, over a
period of four decades, it can be concluded that two of today’s basic assump-
tions are erroneous: β of the Central European interconnection is neither
constant over any period of time, nor is it exactly linear. It was shown,
however, that β can be measured retroactively by measuring the effect of
normally occurring disturbances on the frequency.
4.1.3 Non-Linearities from Generators

Even though turbine governors might use a linear speed droop such as that
shown in figure 2.3, the various non-linear elements in the control path be-
tween the governor and the actual power output result in a non-linear overall
speed droop characteristic S(f ) for any generator. Figure 4.5 from [1] shows
a simplified comparison of the ideal, linear speed droop compared to the
non-linear speed droops of steam and hydro power plants.
A second source of non-linearities in the speed droop of a generator is its
200
175
UCPTERangeofRe
qui
reme
nt
150
125
Wi
ndow ofDi
stur
banc
e
100
]
mHz
75
on[
50
vit
ai
25
yDe
0
un
ec
-
25
e
Frq
-
50
-
75
-
100
-
125
-
150
-
175 Los
sofLoa
d Los
sofGe
ner
ati
on
-
200
5000 40
00 3000 2000 1 000 0 - 100
0 -
2000 -
3000 -
4000 -
5000
Si
zeofDis
tur
banc
e[MW]
Figure 4.3: Frequency Deviation in mHz per Loss of Load in MW. White Squares:
1285 Disturbances between 1.1.1988 and 17.10.1995 in UCPTE; Blue Circles: 31
Disturbances between 19.10.1995 and 10.2.1996 in UCPTE with CENTREL; Dark
Blue Line: Linear Regression of White Squares βU CP T E = 30000 MW/Hz; Light
Blue Line: Linear Regression of Blue Circles βU CP T E+CEN T REL = 40000 MW/Hz.
[26]
200 0.
4
150 0.
3
]
%]
mHz
n[
100 0.
2
n[
i
to
io
via
50 0.
1
vit
a
yDe
yDe
0 0.
0
nc
nc
que
-
50 -
0.1
que
e
Fr
e
-
100
Fr
-
0.2
-
150 -
0.3
sofLoad Los
Los sofGe
ner
ati
on
-
200 -0.
4
2.
5 2.
0 1.
5 1.
0 0. 5 0. 0 0. 5 1.
0 1.
5 2.
0 2.
5
Rel
ati
veDi
sturbanc
eSi
ze[
%]
Figure 4.4: Frequency Deviation in mHz (Left Scale) and % of 50 Hz (Right Scale)
per Loss of Load in % of Total Load. White Squares: 1316 Disturbances between
1.1.1988 and 10.2.1996; Dark Blue Line: Linear Regression of Measurements with
β = 13 %. [26]
Figure 4.5: Left: Comparison of the Ideal, Linear Speed Droop Characteristic (1)
to the Typical Speed Droops of a Thermal Power Plant (2) and a Hydro Power
Plant (3). Right: Typical Speed Droop of a Thermal Power Plant with Added
Deadband.
deadband. The deadband of a generator, illustrated in figure 4.5, is defined

as “the percentage of steady-state speed within which no change in the po-
sition of governor-control valves or gates occurs” [1]. The position of the
generation within its deadband previous to a disturbance has been found to
be randomly distributed [27], which was found to lead to a significant overall
decrease of a network’s frequency response characteristic [28]. Continuing
improvements of governor technology (i.a. electrohydraulics) have led to
significantly lower deadbands in new generation units. That the effect of
deadbands still persists can be seen in the fact that the most recent version
of the UCTE OpHB [3] specifies a maximal deadband of ±10 mHz for any
primary controller and requires control areas to offset their deadbands.
4.1.4 Contribution Factor ci from UCTE Data

Since a network’s total frequency response characteristic β can be deter-
mined statistically from naturally occurring disturbances, as shown above,
it is used as a basis to calculate the individual frequency response character-
istic of every control area in RGCE (assumption 2 from section 4.1.1). Said
calculation is currently done on an annual basis according to every area’s
share of the total energy production over one year (assumption 3). It is clear
that this approach only leads to valid results if an area’s share of the total
energy generation does not change over the course of the year.
To ascertain whether this assumption is reasonable, data from the RGCE
section of the ENTSO-E Statistical Yearbook 2009 [5] has been compiled
into figures 4.6 and 4.7. The first shows the contribution factors calculated
0.04
0.038
0.036
0.034
Contribution Factor
Monthly 1999
0.032
Monthly 2008
0.03
Monthly 2009
0.028
Annual 1999
0.026
Annual 2008
0.024
Annual 2009
0.022
0.02
1 2 3 4 5 6 7 8 9 10 11 12
Month
Figure 4.6: Contribution Factors ci of Switzerland in RGCE, Calculated using

Annual Averages (dotted) and Monthly Averages (Solid) in 1999, 2008 and 2009.
as specified by the UCTE OpHB, by dividing the annual electrical energy

40
30
% Deviation from Annual Average
20
Switzerland
10
France
Germany
0
1 2 3 4 5 6 7 8 9 10 11 12 Italy
-10 Austria
-20
-30
Month
Figure 4.7: Deviations between Contribution Factors ci Calculated on Monthly

and Annual Basis for Switzerland an its Neighboring Countries in 2009.
production of the control area Switzerland by the total generation of RGCE

(dotted lines). For comparison, the contribution factors were also calculated
from the share of energy produced in Switzerland during every month of
the same years (solid lines). It is evident from the figure that Switzerland’s
share of the total generation is much lower in the winter months than during
the summer months. The monthly contribution factors deviate maximally
23 % in 1999, 30 % in 2008 and 34 % in 2009. The most probable explana-
tion of this phenomenon is the fact that roughly two thirds of Swiss power
production comes from hydro power plants which reach their peak power
production in the summer months. Compared to other countries in RGCE
this is a high fraction of season-dependent generation. As a result of this
seasonality, the assumption of being able to determine an area’s frequency
response characteristic using a contribution factor which is constant over the
time-scale of one year is invalid.
Figure 4.7 shows the percentage of deviation of contribution factors calcu-
lated on monthly bases from the ones calculated annually over the course of
the year 2009. While Switzerland seems to incur the largest deviations over
the course of 2009, Austria, Italy and France have months where their share
on RGCE’s total production differed by more than 10 % of the annual av-
erage. With the exception of Germany, figure 4.7 lends even more evidence
to the non-applicability of assumption 3.
4.1.5 Research on Load Self-Regulation

Most of the fundamental literature on frequency control carries only very
little information about the self-regulation effect of loads. Kundur [1] sim-
ply states that a fraction of the load is sensitive to changes in frequency and
that the factor Dl is typically between 1 and 2 %/%, while Andersson [2] lists
values between 0 and 2 %/% as plausible. The UCTE OpHB [3] assumes a
constant self-regulation of 1 %/Hz or 0.5 %/% in the RGCE interconnection.
The research about UCPTE’s frequency response characteristic carried out
in [26] determined the average β in the time between 1988 and 1996 to be
around 8 %/%. In addition to the considerable standard deviation from this
value, not being able to specify the load damping factor more accurately
than being somewhere between 0 and 2 %/% adds even more uncertainty.
Two extensive reports by Welfonder et al., [29] and [30], show the results of
a study of eight different measuring points in Germany over the course of
up to two and a half years. The results indicated a similar seasonality of
self-regulation as that already found in the frequency response characteristic.
The main reason given is the fraction of motor loads in the total load. Motor
loads generally consume less power at decreased frequency, while other loads
such as ohmic heating are frequency insensitive. The effect of this can be
seen in the fact that the average load-damping factor in summer was found
to be roughly one third higher than the average in winter. Even larger differ-
ences were found between measurements during business hours and weekend,
evening or night hours. In addition to the standard load-damping, which
measures the change in active power consumption as a result of frequency
changes, Welfonder et al. also included active power deviations resulting
from voltage variations, which were a result of frequency changes. The an-
nual average of the total load-damping resulting from frequency deviations
in all seven areas was found to be 1.5 %/%, with the average in summer
being 1.8 %/% and 1.2 %/% in winter.
4.2 Effects of Estimation Errors on Network Op-

erations
Using equation (3.12) and (3.13), the initial responses of AGC controllers
can be calculated for different frequency bias factors Ki . Table 4.1 shows
the effects of different Ki on AGC of an area i for the case when area k
causes a disturbance by loss of generation (second row) or loss of load (third
row). It is clear that when Ki is set to be exactly equal to the frequency
response characteristic βi , no power change results from AGC action2 . If
this is not possible, it is preferable to chose Ki to be larger than βi according
to the second column, because area i supports the area in need. Situations
where Ki is smaller than βi should be avoided since the AGC of area i would
worsen the disturbance by decreasing its power output in the case of missing
generation and by increasing its power in the case of excess generation in
2
The problems with fulfilling this non-interaction criterion were, however, presented
above.
area k.
For an area causing a disturbance (area k in the example above), equation
∆f Ki > βi Ki = βi Ki < βi
ACEi < 0 ACEi = 0 ACEi > 0
∆f < 0 ∆PAGC,i > 0 ∆PAGC,i = 0 ∆PAGC,i < 0
area i supports no interaction area i interferes
ACEi > 0 ACEi = 0 ACEi < 0
∆f > 0 ∆PAGC,i < 0 ∆PAGC,i = 0 ∆PAGC,i > 0
area i supports no interaction area i interferes
Table 4.1: Effects of Different Frequency Bias Factors on AGC of an Area

not Causing a Disturbance.
(3.13) shows that as long as Kk is chosen to be larger than zero, it will

always lead to correcting AGC power changes.
To find a measurement for the power which is transferred from all areas i
to an area k hit by a disturbance, N. Cohn defined the term “inadvertent
interchange” in [31] as being composed of “primary inadvertent interchange”
and “secondary inadvertent interchange”. Primary inadvertent interchange
Iii of an area i stems from that area’s non-ideal AGC, while secondary inad-
vertent Iin represents the control power which area i has to provide because
of AGC-actions in area n. The definitions of “primary inadvertent” and
“secondary inadvertent” both include Primary as well as Secondary Control
power, as defined in chapter 2.
In the scope of this report, it is of interest to know how much power is
transported over tie-lines to other areas as a result of an imperfect AGC,
to obtain a measurement for unnecessary stress on these tie-lines. This can
be calculated by integration of the absolute value of the tie-line power flow,
which is the sum of Primary Control power, Secondary Control power and
the load self-regulation effect, according to equation (4.1). This equation is
a simplification of Cohn’s primary inadvertent, neglecting measuring errors.
Additionally, it is important to know the total energy produced by AGC
alone over the time of a disturbance and if the AGC power supported the
area in need or if it interfered. To make this difference, the AGC-signal
+
∆PAGC,i can be split up in supporting power ∆PAGC,i (i.e. when ∆f and
∆PAGC,i share the same sign, as seen in table 4.1) or interfering power,
−
∆PAGC,i , as shown in equation (4.2). To then calculate the corresponding
energy, a simple integration from the start of the disturbance (t = 0) to the
time the disturbance resolved (t = T ) of the AGC-signal can be done as
demonstrated in equation (4.3).

Z T
Wtie,i = |∆PT,i |dt (4.1)
(0
± ∆PAGC,i , ∆f · ∆PAGC,i ≶ 0
∆PAGC,i = (4.2)
0, otherwise
Z T
± ±
Wagc,i = ∆PAGC,i dt (4.3)
0
Chapter 5
Deterministic, Semi-Online
Sizing of Ki
Chapters 3 and 4 have identified a number of shortcomings of the currently

implemented Secondary Control. A complete redesign of frequency control,
such as proposed by some of the research presented in section 3.3, could
potentially address most of the drawbacks of the established system but en-
tirely retrofitting a vast and complex system which has grown evolutionarily
over more than six decades requires substantial investments and long-term
planning. Therefore, solutions that can be implemented in the short-term
have to build on the existing control infrastructure and make use of the
research performed in the past.
The presented approaches focus on deterministically estimating the cur-
rent network frequency response βi of an area i in order to set the frequency
bias factor Ki of the AGC as close to βi as possible1 . In order to achieve
this, the four following methods may be utilized.
5.1 Updating ci Regularly

The simplest method of resizing Ki is the recalculation of an area’s contribu-
tion factor ci on an interval smaller than one year. The analysis performed in
section 4.1.4 found differences of up to 30 % between annually and monthly
calculated contribution factors. It is reasonable to assume that similar dis-
crepancies can be found on shorter time frames as well2 . Especially for an
area such as Switzerland which has large pumped-storage power plants that
act as generation during times of high load and as loads during times of low
1
Some of the algorithms described in the following sections will contain specific details
about a possible realization in Switzerland but should be easily adaptable to other control
areas as well.
2
Detailed data of production of electricity by area in ENTSO-E is only available as
monthly averages.
35
CHAPTER 5. DETERMINISTIC, SEMI-ONLINE SIZING OF KI 36
electricity prices, ci can change considerably over short intervals. In order to

avoid interfering with the function of the AGC’s integration component, an
update interval considerably larger than the integration time-constant has
to be selected. In addition to this restriction, the large frequency excursions
regularly appearing around the hour mark further impose difficulties on the
timing of updates.
It is thus proposed that update intervals coincide with European Energy Ex-
change (EEX)’s definition of peak and offpeak times. This results in three
contribution factors each day. One for the twelve hours of high generation
and load between 8:00 and 20:00 and two for the times of low generation and
increased pump-load between 0:00 and 8:00 and between 20:00 and 24:00.
To avoid interferences with AGC operations around the full hour, the actual
update of the K-factor should occur 30 minutes before the beginning of each
period.
Necessary for the calculation of the updated contribution factors cl,m i ,
where l and m stand for the first and last full hour covered by the factor, are
the scheduled power generation levels PG,jk for all areas j in the synchronous
grid over the hours k of the following day. cl,mi is calculated according to
equation (5.1) by dividing the generation of area i by the total generation
of all areas over the hours l to m. The frequency bias factor Kil,m results
from the multiplication of cl,m
i with the frequency response characteristic λu
determined by ENTSO-E, as shown in equation (5.2).
Pm k
l,m k=l PG,i
ci = Pm PN (5.1)
k
k=l j=1 PG,j
Kil,m = cl,m
i · λu (5.2)
The data necessary to perform the calculations to find these three factors
are available to the TSO and the balance area operator after the closing of
the spot market at 18:00 on the day before operation. This data, however,
is subject to forecast errors by the balancing areas3 and does not include
the so called intra-day trading which occurs during the day of operation.
5.2 Scaling λu with Generation

The method presented above uses λu given by ENTSO-E, which remains
constant for at least one year before being updated. From the measure-
ments performed by [25] and [26] it is evident, however, that λu has an
approximately linear dependency on the total generation active in the sys-
tem. Therefore an improvement on calculating Ki by simply updating ci as
3
Every control area typically managed by a Transmission System Operator (TSO) is
made up of multiple balancing areas managed by electric utility companies.
shown in equation (5.2) is to also scale λu with the total load in the system
at any point in time. In order to do this, λu has to be divided by the average
load of the year that was used as a base for its original calculation PG,base
and multiplied by the average load forecasted for the interval in question.
Using the nomenclature introduced above, this is demonstrated in equation
(5.3).
Pm PN k
l,m k=l j=1 PG,j λu
λu = · (5.3)
(m − l + 1) PG,base
Combining equation (5.1) and equation (5.3) into equation (5.4) results in
an updated Kil,m for the hours l to m.
Pm k
k=l PG,i
Kil,m = · λu (5.4)
(m − l + 1)Pbase
This method eliminates the need for the generation forecasts of all areas
except for area i itself. This significantly reduces the sensitivity to forecast
errors and also eliminates other risks associated with international forecast
exchange, i.a. miscommunications, strategic misinformation.
As an effect of the deregulation of electricity markets, some TSOs, such
as swissgrid, do not have full access to all generation and load data of their
balancing areas. Instead they forecast and measure the “vertical load”, which
corresponds to the total flow of electric power from the transmission system
level to all lower levels. In addition, they also forecast the tie-line power-
flows to other areas on the transmission system level. Despite the fact that
generators which are connected to a lower voltage level can cancel loads in
the lower levels and therefore do not appear in the vertical load, an approx-
imate value for the generation of such an area could be found by adding the
vertical load to the net powerflow to adjacent areas. Since no research on the
correlation of vertical load and frequency response characteristics exists to
date, this approach has to be evaluated in detail before its implementation.
5.3 Construction of βi by Parts

Instead of relying on RGCE’s annually calculated λu , which is commonly
based on two year old measurements and yearly averages, an algorithm to
construct βi from its four parts can be found by applying the formula given
in the OpHB, explained in detail in section 3.2.2, on a much shorter interval
and for only one area instead of the entire synchronous grid.
5.3.1 Using Default Values

The specific values given for Primary Control, load self-regulation effect
and surplus generation in the OpHB formulas stem from the research and
operating experience of the entire RGCE grid. Using these values for the
calculation of the frequency response characteristic of a single area should
therefore only serve as a default value if more detailed analyses do not exist.
The adaptation of equation (3.21) to (3.24) to a single area i for the hours
l to m of one day, as shown in equation (5.5) to (5.8), requires the hourly
values of the area’s forecasted load Pload,i k k
and generation Pgen,i as well as
k l,m
the area’s Primary Control reserve Pprim,i and results in Ki according to
equation (5.9).
Pm k
1 k=l Pprim,i
l,m
= (5.5)
Sprim,i (m − l + 1) · 200 mHz
Pm k
l,m % k=l Pload,i
Dl,i = 1 · (5.6)
Hz m − l + 1
1 1
l,m
= 0.30 · l,m (5.7)
Sadditional,i Sprim,i
Pm k
1 % k=l Pgen
= 1 · (5.8)
S l,m
surplus,i
Hz m − l + 1
1 1 1
Kil,m = l,m
l,m
+ Dl,i + l,m
+ l,m
Sprim,i Sadditional,i Ssurplus,i
m k
1 X Pprim,i
= (1.3 ·
m−l+1 200 mHz
k=l
m
% X k k
+1 · (Pload + Pgen )) (5.9)
Hz
k=l
To improve on this adaptation, the specifics of area i have to be taken into

consideration for all four contributing effects. In addition, non-linearities of
the frequency response characteristic can be incorporated into a frequency-
dependent bias factor Ki (f ).
5.3.2 Predicting Primary Control

Calculating Primary Control according to equation (5.5) assumes that the
activation of Primary Control occurs linearly in a way that releases the full
reserves over the specified band of 200 mHz. However, research presented in
section 4.1.3 showed that all generators have an activation deadband which
gives rise to a non-linearity in the vicinity of the steady-state frequency.
Additionally, the OpHB specification of speed droop control, as summarized
in section 2.4, gives rise to a second non-linearity by dictating that the max-
imum Primary Control has to be released at ±200 mHz. A more realistic,
step-wise linear speed droop Sj (f ) for a generator j integrating these two
factors, is presented in figure 5.1 and equation (5.10).




 Pmin,j , f < fmin,j ;
 P min,j
 fmin,j −fN −,j (f − fN −,j ), fmin,j < f < fN −,j ;



Sj (f ) = 0, fN −,j < f < fN +,j ; (5.10)
 Pmax,j
fmax,j −fN +,j (f − fN +,j ), fmax,j > f > fN +,j ;





P

, f >f
max,j max,j
ΔPj
Pmin,j
deadband
full activation
full activation
Pmax,j Sj(f)
SOpHB,j
f
fmin,j fN-,j fN fN+,j fmax,j
Figure 5.1: Non-linear Speed Droop Model Sj (f ) of One Generator compared

to the Assumption of OpHB SOpHB.j . fN +,j and fN −,j Denote the Deadband
Frequencies; fmax,j and fmin,j Are the Maximum and Minimum Frequencies where
Full Activation of Primary Control Reserves Occurs.
The deadband frequencies fN +,j and fN −,j of most generators partici-

pating in Primary Control in Switzerland are known from prequalification
tests according to swissgrid’s specification [32]. The full activation frequen-
cies fmax,j and fmin,j can be assumed to be ±200 mHz as specified in the
OpHB if more accurate values are not known; Pmax,j and Pmin,j are deter-
mined regularly by auction.
This model neglects the machine-specific non-linearities occurring between
the frequencies fN +,j and fmax,j as well as between fN −,j and fmin,j . These
non-linearities are currently not measured during prequalification4 and thus
not usable in the modeling.
4
If detailed Sj (f ) curves were available from other sources such as the manufacturer
of the turbine-controller assembly or other test, they could be used instead of the model
from figure 5.1
The sum of the inverse of Sj (f ) of all generators j participating in Primary

1
Control results in an improved term Sprim,i (f ) according to equation (5.11).
1 X 1
= (5.11)
Sprim,i (f ) Sj (f )
j
5.3.3 Additional Primary Control

Equation (5.7) adds 30% additional Primary Control to the simple formula
of (Minimal Reserves)/(200 mHz). As explained in section (3.2.2), the causes
of this effect are not well documented. For an area i to improve on OpHB’s
empirical value of 30 %, knowledge of the speed droop controllers present in
the system, as well as detailed measurements of their behavior are needed.
A non-linear factor for additional Primary Control could prove to be bene-
ficial, especially when accounting for generators which do not officially take
part in the auctioned Primary Control. According to swissgrid, many gener-
ator operators decide to widen the deadbands of the speed droop controllers,
instead of switching them off completely, in order to help sustain the fre-
quency in cases of large deviations.
Until reliable data in the area of additional Primary Control exists, the
RGCE’s default value of 30% has to be used to calculate any area’s Ki
factor.
5.3.4 Measuring Surplus Generation

Surplus generation is explained in the OpHB to originate from the speed
droop of (100%)/(50 Hz), which approximately 50% of all generators ex-
hibit. It is clear that large generators employing sophisticated speed droop
controllers count towards the other half of all generators, not included in
surplus generation.
The constant surplus generation factor of 1 %/Hz takes into account only
the size of the generation in the RGCE grid, which is then split amongst
its areas by the contribution factor ci . It is reasonable to assume, however,
that the different types of power plants have different influences the overall
1 %/Hz surplus Generation. It is further safe to assume that Switzerland’s
fraction of the surplus generation does not correlate with its contribution
factor ci because the types of power plants prevalent in Switzerland are not
proportional to those of the entire RGCE. This fact is illustrated in table
5.1 which compares the sources of primary energy converted to electricity
in 2009. A further complication comes with the time-dependence of these
shares. Switzerland in particular sees large changes in its hydro power plant
activity in correlation with the seasons and the electricity market prices. As
with additional Primary Control, because of the lack of research, there exists
no support for a value other than the OpHB’s default for surplus generation.
Type of primary power Switzerland RGCE

Nuclear 39.3 % 28.8 %
Fossil 3.1 % 51.1 %
Hydro 55.9 % 12.6 %
Other renewables 0.2% 6.9%
Table 5.1: Share of Different Power Plants on the Annual Electricity Gen-
eration in 2009, Data from [5].
5.3.5 Load Self-Regulation

As discussed in section 4.1.5, the load self-regulation factor of 0.5 %/% spec-
ified by the OpHB is not beyond doubt. Welfonder et al., [29] and [30],
showed that on average between 1989 and 1991, the load self-regulation ef-
fect measured at seven different points in Germany came to be 1.5 %/%.
However, seasonalities on average showed values 20 % higher in summer and
20 % lower in winter. In addition, intra-day variations of +11 % during office-
hours, -2 % during night-time and -8 % during evening-hours and weekends
were found.
For the lack of more current measurements, and more importantly mea-
surements performed in Switzerland, the results found by Welfonder et al.
can be used as a basis when constructing βi by parts. The author thus
proposes the following algorithm derived directly from the results of [29] to
k,n
calculate the load self-regulation factor Dl,i for the hour k on day n of the
week:
base , is set to 1.8 %/% for May-September and to 1.2 %/%
The base value Dl,i
during October-April. In order to account for changes during the hours of
the day and days of the week, a factor γik,n , defined in equation (5.12), can
k,n
be used to determine Dl,i according to equation (5.13).



1.11, 0 ≤ n ≤ 5 ∧ 6 ≤ k < 18;

0.92, 6 ≤ n ≤ 7 ∧ 6 ≤ k < 18;
γik,n = (5.12)


0.92, 0 ≤ k < 6;
18 ≤ k < 0

0.98,
k,n
Dl,i = γik,n · Dl,i
base
(5.13)
5.3.6 Sensitivity to Parameter-Changes

When constructing λi as specified by the OpHB, the aforementioned four
parts contribute different shares as shown in table 5.2. In addition, these
parts also depend on different quantities of the power system, namely the
load, generation and Primary Control present in the area i. It is clear from
table 5.2 that the mandatory 3000 MW of Primary Control which have to
be delivered over 200 mHz, account for the largest share of the Frequency
Response Characteristic. Furthermore, additional primary control is directly
proportional to the Primary Control, resulting in an overall 73.1 % of λi
being made up of Primary Control. Changing the calculation of Primary
Control, as suggested in section 5.3.2, thus has significant impact on the size
and frequency-dependancy of λi .
Absolute Relative
Cause Value [ MW
Hz ] Value [%] Dependency
Primary Control 15000 56.2 −
additional Primary Control 4500 16.9 Primary Control
surplus generation 3060 11.5 Generation
Load Self-Regulation 4120 15.4 Load
Table 5.2: Analysis of the Four Parts of λu according to the OpHB.
The two remaining parts each make up considerably smaller shares of

11.5 % and 15.4 % of the total λi , however, they depend on the generation
and the load present in the system, which vary considerably over time. De-
tailed load data5 of Switzerland evaluated for 2010 shows a minimum value
of 5016 MW at 04:00 on August 18th and a maximum of 10835 MW at 18:00
on December 15th. Assuming that the generation varies similarly, it has to
be considered that surplus generation and load self-regulation, which com-
bined make up 26.9 % of λi by OpHB calculations, can deviate by as much
as 100 % when using the algorithms proposed in section 5.3.4 and 5.3.5.
Furthermore, the load self-regulation effect’s share of the total frequency
response characteristic of 15.4 % increases to between 17.0 % and 30.9 %
when using the algorithm from section 5.3.5 instead of the constant factor
of 1 %/%.
It is clear from these calculations that the major influence on recalculat-
ing λi with the algorithms described previously is the modeling of Primary
Control. However, the quality of forecasts concerning load and generation
as well as the load self-regulation factor Dl,i also carry considerable signifi-
cance.
5.4 Measuring βi
Predicting βi by using calculations such as the ones presented above, has
proven to be challenging for different reasons, the most important being
the lack of research in the area. Another major obstacle is the difficulty
of measuring the actual frequency response characteristic βi of an area i in
order to verify the accuracy of the calculation of the frequency bias factor Ki
5
ENTSO-E’s data portal [33] releases hourly measured load for every third Wednesday
of every month for every area in the RGCE.
have to be investigated. Measurements recorded during outages have served

as guidelines and as benchmarks for the calculations in the past but they
have never been used to directly update Ki factors in areas of the RGCE.
5.4.1 Analysis of Large Outages

Traditionally large outages, which were either induced deliberately or oc-
curred by accident, were used to measure β of a synchronous area according
to equation (2.13) by dividing the size of the outage by the frequency devi-
ation it caused. For this purpose, the OpHB obligates the members of the
RGCE to record data concerning every outage of more than 600 MW.
For the calculation of βi of an individual control area i within the syn-
chronous area, two cases have to be considered. Either a disturbance hap-
pens in an area k 6= i or it occurs inside the area i itself. In the first case,
the change in exported power immediately following the change in frequency
is composed of area i’s Primary Control, Load Self-Regulation and Surplus
Control and is thus proportional to βi as shown in equation (5.14). The
latter case triggers support from all areas k 6= i, which results in an import
of supporting power proportional to the load frequency response character-
istic of all areas except area i according to equation (5.15). In both cases,
the frequency deviation and the change in exported power resulting from
the outage have to be evaluated at a point in time shortly after the outage,
when Secondary Frequency Control loops are not yet active.
∆PT,i (t0+ )
βi = − (5.14)
∆f (t0+ )
∆PT,i (t0+ )
β − βi = (5.15)
∆f (t0+ )
The events leading to these large disturbances occur only seldomly and
at random times. They are therefore not appropriate as a sole method of
determining the frequency bias factor of Secondary Control. Large outages
can, however, serve as an evaluation and correction method for an algorithm
which predicts βi .
5.4.2 Linearity in Random Disturbances

Unlike the large disturbances treated in the previous section, small, random
mismatches between the mechanical power fed into generators and the elec-
tric power consumed by the sum of all loads in a grid happen constantly in
all areas. Each small disturbance only produces a minor frequency devia-
tion but summed over the total of the RGCE they can lead to considerable
changes in the system frequency at any given point in time.
The constant presence of these random disturbances provides a viable base
for constant benchmarking of βi calculation methods and potentially for an

automatted error correction algorithm.
For a small area i, such as Switzerland, which makes up only between
2 % and 3.5 % of the total generation of the synchronous area at any time,
the vast majority of random disturbances take place in other areas j ∈ Ωi .
Therefore, the frequency deviations resulting from the sum of these distur-
bances can be treated similarly to the ones resulting from large outages.
Unlike large disturbances, however, the exact size of the mismatch in me-
chanical power produced and electrical power consumed is not known. Thus,
an algorithm for the calculation of βi other than equation (5.14) has to be
derived.
Ωi = {1, . . . , N }\{i} (5.16)
As explained in chapters 2 and 3, the initial change in exported power
t0+
∆PT,i of an area i to a frequency deviation ∆f is directly proportional to
that area’s frequency response characteristic, as shown in equation (5.17).
Shortly after the initial response, the Secondary Control loop will activate
Secondary Control power ∆PAGC,i according to equation (3.1) which is also
exported to the areas Ωi causing the disturbances, resulting in the exported
power given in equation (5.18). If this area’s Ki is set to be exactly equal
to its βi , the area control error ACEi stays equal to 0 MW over the course
of the frequency disturbance according to equation (3.12). As a result, area
i does not activate Secondary Frequency Control and thus exhibits a devia-
tion in export power linear to βi .
The research presented in chapter 4 and an analysis of swissgrid’s ACE
data, however, suggests that Ki differs from βi during normal operation.
Assuming an Ki to be the actual βi plus an error factor ei as shown in equa-
tion (5.19), ACEi from equation (3.12) can be written according to equation
(5.20). Inserting this into equation (3.1) yields ∆PAGC,i (t) as a function of
∆f (t) and of its own integration, as seen in equation (5.21). Finally, in-
serting equation (5.21) into equation (5.17), gives the deviation of export
power as a function of ∆f (t) and the Secondary Control energy exported
during the deviation as shown in equation (5.22). In most literature, ∆f
is suggested to be directly influenced by ∆PT,j of any area j. However, for
areas i of very small size, the effect of ∆PT,i on the frequency deviation of
the entire interconnection can turn out to be almost negligeable. This allows
for the analysis of ∆PT,i as a function of ∆f .
t
0+
∆PT,i = − βi · ∆f (5.17)
∆PT,i (t) = − βi · ∆f (t) + ∆PAGC,i (t) (5.18)
Ki = (1 + ei ) · βi (5.19)
ACEi (t) = ei βi · ∆f (t) + ∆PAGC,i (t) (5.20)
Cp,i ei 1
∆PAGC,i (t) = − βi ∆f (t) −
1 + Cp,i TN,i (1 + Cp,i )
Z
· (ei βi ∆f (t) + ∆PAGC,i (t)) dt (5.21)
Cp,i ei 1
∆PT,i (t) = − ( + 1)βi ∆f (t) −
1 + Cp,i TN,i (1 + Cp,i )
Z Z
· ei βi ∆f (t)dt + ∆PAGC,i (t)dt (5.22)
For the error factor ei , two cases have to be distinguished: Either Ki >
βi , leading to a positive ei or Ki < βi , resulting in a negative ei . As discussed
in section 4.2, the first case will lead to Secondary Control power which
supports the activated Primary Control power, while the latter leads to an
opposite reaction of the Secondary Controller, which will lead to a partial
cancellation of the Primary Control power within the area i itself.
It is clear from equation (5.22) that for small error factors ei , the de-
viation in export power scales almost linearly with the frequency deviation
∆f (t) for any point t in time. In cases of large differences between Ki and
βi , the time dependent integrals will reduce the effect of the linear relation
between ∆f (t) and ∆PT,i . The effects of the sign of ei and the non-linearities
on ∆PT,i as a function of ∆f are shown in figure 5.2.
In addition to the non-linearity introduced by ei , pre-disturbance offsets
in ∆PT,i lead to additional noise. Especially in small areas, it is possible that
tie-line power flows occur without a resulting change in system frequency if
the power flows are compensated by another area; in figure 5.2 these offsets
can lead to ∆PT,i (∆f ) curves which are vertically displaced.
As a sizing method for Ki , the continuous analysis of ∆PT,i as a function
of ∆f could provide advantages over the current method of applying static
formulas to system properties such as load and generation volumes. In order
to implement such a method, sophisticated stochastic algorithms, as well as
artifical intelligence strategies that couple ∆PT,i and ∆f to important power
system properties such as seasonality, weather-effects and load-schedules,
have to be devised. This was deemed outside the scope of this project and
thus remains as a future research possibility for interested parties.
ΔPT,i
ei>0
βi
ei<0
Non-Linearities from
Integrations in Time
Δf
Figure 5.2: Deviation in Export Power Flow as a Function of the Frequency De-
viation. The error factor ei changes the Slope and Introduces Non-Linear Effects.
Chapter 6
Calculation, Modeling and

Simulation
In order to compare the performance of the different sizing methods for Ki

proposed in sections 5.1 to 5.3, a simple, semi-dynamic frequency control
simulation in Matlab/Simulink was derived. The model was to be set ac-
cording to specific load- and generation scenarios at which β and βi were
known.
6.1 Reduced-Size Power System Model

To simulate the behavior of an AGC employing different Ki factors, a power
system model of small size was created, closely following the models pre-
sented in [2]. Since short-term phenomena, such as power plant dynamics
and small-signal frequency swings are not of importance for AGC, as pointed
out in [8], the modeled power system shares one common frequency and em-
ploys only first-order delays as power plant models.
For the simulation, the synchronous grid of the RGCE is divided into
three different areas. The updating algorithms for the Ki factor are imple-
mented in the AGC of area one. The second area designates the control
area which sustains a step-wise discrepancy between its mechanical and its
electrical power (i.e. an outage of generation or load) and the remainder
of the RGCE load and generation is concentrated in the third area. The
simulation is designed to only calculate deviations from normal operation
values, such as frequency (∆f ) and tie-line power flows (∆PT,i ). The pre-
disturbance properties of the power system are used to determine influences,
namely the frequency response characteristics of the individual areas.
Partitioning the synchronous grid in such a way enables the simulation
of the reaction of the AGC in the first area to an outside outage, while
incorporating all of the load and generation present in the entire grid at the
time of the incident. The ideal outcome for a Ki -factor calculation would
47
CHAPTER 6. CALCULATION, MODELING AND SIMULATION 48
be to have an exact match with βi . In the simulation, this would equate to

a complete lack of reaction of the AGC in area one to a disturbance in area
two.
Df
Df
f0
system inertia
2*H*SBs
Df DPme
<Df> <Df>
DPAGC1 DPAGC3
<DPT1> <DPT3>
Df Df
DPT2
AGC1 AGC3
DPT3
<DPAGC1> <DPAGC3>
DPT1
DPT1 DPT3
DPT1
<Df> <Df>
Area1 Area3
DPT2
<Df>
DPAGC2
<DPT2>
AGC2
DPload
Step
<DPload>
<DPAGC2> DPSlack
DPSlack
<Df>
Area2
Figure 6.1: Reduced-Size Model of the RGCE Synchronous Area in Simulink.
Figure 6.1 shows the top layer of the Simulink model incorporating the
three individual areas. The blocks labeled Area1 −Area3 contain Primary
Control as well as the load self-regulation, as seen in figure 6.2 for area
three. These blocks also contain a first order delay modeling the Secondary
Control power plants. For the second and third area, Primary Control and
load self-regulation is assumed to behave linearly according to a βj which
can be specified individually for every simulation.
The blocks AGC1 −AGC3 contain the Automatic Generation Control of
each area, shown in figure 6.3 for area one, which consists of a PI controller
and an ACE calculation block depicted in figure 6.4.
DPT3 DPl3 2 In2

1 D_l3
Out1 1
In1 self-regulation 3
1
secondary gen 3
DPg3 Tt3.s+1
DPsek3
DPprim3 1
-1/S3
Tt3.s+1
primary gen 3 speed droop 3
Figure 6.2: Simulink Block of Area3 Containing Linear Primary Control via Speed
Droop and Self Regulation as well as First Order Delays which Model Power Plant
Behavior. The Sum of the Change in Generation (Primary and Secondary) is Added
to the Change in Load Self-Regulation which Results in a Change in Tie-Line Power
Flow DPT3.
In1 1
DPAGC1 ACE1
1 PI(s) Out1 In1
Out1 In2
PIAGC1
ACE1 2 In2
Figure 6.3: Model of the AGC of Area One, Where Inputs In1 and In2 Feed ∆f
and ∆Pt,1 into the ACE Calculation Block. The PI controller PIACG1 Produces
the Control Signal DPAGC1 for the Secondary Control Plants.
Kdf
1 K1 1
Out1 In1
Gain4
2
In2
Figure 6.4: Calculation of the Area Control Error of Area One with a Linear
Frequency Bias Factor K1 .
6.1.1 Power System Dynamics and Tie-Line Flows

As seen in figure 6.1, the system frequency deviation is computed as a result
of one single system inertia block. This block incorporates the sum of all
inertial constants and generator ratings of the synchornous area as to gener-
ate only one shared frequency deviation. The mismatch between electrical
and mechanical power, which defines the input of the system inertia block,
is calculated as the difference of the power of the outage in area two and the
sum of the frequency dependent power change in all areas.
In the same way, the tie-line power flows from areas one and three to the
area in need are simply calculated as the sum of the frequency dependent
power production and consumption in areas one and three. This calculation
assumes that during the outage in area two, no other outages or similar
phenomena occur.
6.1.2 Primary and Secondary Control

For area one, Primary Control was modeled as four different generators with
individual, non-linear speed droops S(∆f ), presented in figure 6.5. Gener-
ators one, two and three each account for approximately one third of the
Primary Control reserves allocated to Switzerland over a band of 200 mHz;
the fourth generator is included to model additional Primary Control. All
speed droops feature deadbands of different sizes around ∆f = 0 as well as
specific frequencies at which their control reserves are fully activated. Addi-
tionally, generator three contains a continuous non-linearity in the form of
a square-root function. The resulting speed droop of the sum of these four
generators is shown to differ from the classic assumption of linear S(∆f ),
especially for small and for large variations in frequency.
For simplicity and because their behavior is not significant for the per-
formance of AGC in area one, Primary Control in areas two and three area
assumed to be linear speed droop controlled power plants with low first-order
delays as seen in figure 6.2.
6.2 Implementation of Ki -factor Algorithms

6.2.1 OpHB Definition
In order to have a baseline for measuring any improvement, Ki of Switzer-
land as well as the Primary Control reserves and the λu of the RGCE were
taken directly from the instruction of the UCTE or ENTSO-E, depending
on the simulated year.
Non-Linear Speed Droops of Primary Control Generators
100 (S(f )Gen1 )−1

(S(f )Gen2 )−1
(S(f )Gen3 )−1
50
(S(f )Gen4 )−1
Power [MW]
(S(f )Area1 )−1

0
−50
−100
−0.3 −0.2 −0.1 0 0.1 0.2 0.3

Frequency Deviation [Hz]
Figure 6.5: Non-Linear Speed Droops of Primary Control Power Plants of Area
One.
6.2.2 Updating ci and scaling λu

The algorithms described in sections 5.1 and 5.2 were implemented in the
simulation for time intervals of 0:00-8:00, 8:00-20:00 and 20:00-0:00. The
generation during these time intervals was calculated by adding every area’s
export powerflow to its load because detailed generation data is not made
available through the ENTSO-E.
6.2.3 Simple Partwise Construction

“Simple partwise construction” refers to the calculations presented in section
5.3.1. It involves applying the definition of λu to a single area on the same
time-intervals used for the calculations of ci and λu above.
6.2.4 Non-Linear partwise Ki (f )

The fourth algorithm proposed in section 5.3.2 differs from the simple part-
wise construction by taking into account more accurate load self-regulation
measurements and non-linear Primary Control speed droops. For the latter,
it is assumed that the specifics of the deadbands and the full activations are
known for Primary Control generators one, two and three. The fourth gen-
erator accounts for the additional Primary Control and cannot be predicted
when setting Ki (f ).
In order to realize a frequency dependent Ki (f ), the calculation of the ACE
shown in figure 6.4 was changed to figure 6.6, where a Matlab function
replaces the previously linear multiplication.
Kdf MATLAB
1 1
Function
Out1 In1
K(f)
2
In2
Figure 6.6: Calculation of ACE1 for a Non-Linear Ki (f ), Using a Frequency

Dependent Matlab Function.
6.3 Evaluation Result Output

For every one of the four proposed sizing methods as well as the standard
OpHB values, the simulation program plots the time-domain behavior of
important system variables. Additionally various indicators of Secondary
Control quality introduced in chapters 2 and 4 are compared amongst the
different sizing methods. In the examples below, the information in the dif-
ferent plots is explained; the corresponding figures can be found in appendix
A.
Time-domain performance of characteristic values of area one is shown

in figures 6.7, A.1 and A.2. These figures are generated separately
for every sizing method. The first two show the frequency-dependent
change in generation and in load in area one and the resulting change in
tie-line powerflow. The last figure shows the input, internal states and
output of the AGC over time, which can be helpful in reconstructing
the area’s response in Secondary Control power.
Power Contributions in Area 1
35
30 ∆PP rimary,G1
25 ∆PP rimary,G2
Power [MW]
∆PP rimary,G3
20
∆PP rimary,G4
15
∆PSecondary
10 ∆PLoad+Surplus
5 ∆PT ie
0
0 100 200 300 400 500
Time [s]
Figure 6.7: Share of the Primary and Secondary Control Power and Load Self-
Regulation of the Tie-Line Power over Time.
Development of the total power generation and consumption is split

up into its sources in the different areas in figure 6.8. The ACE and
∆PAGC,i of the AGCs of all areas are presented in figure A.3. Both
figures can help in analyzing the interaction of the different frequency
dependencies and the performance of the AGCs in all three areas.
Comparisons of the effect of the different Ki -factor calculation methods

are shown in figures 6.9 through A.6. The different Ki (∆f ) calculated
are displayed in figure A.6. Figures 6.9 and A.4 compare the operation
of the AGC in the first area; the non-linearites in the calculated ACE
originate from the non-linear Primary Control generator models. The
plot of the change in tie-line powerflow for the different sizing methods
Power Contributions of Areas 1-3

1400
∆PPArea1
rimary
1200
∆PPArea2
rimary
1000
∆PPArea3
rimary
Power [MW]
Area1
800 ∆PAGC
Area2
∆PAGC
600
Area3
∆PAGC
Area1
400 ∆Prem.
Area2
∆Prem.
200
Area3
∆Prem.
0
0 100 200 300 400
Time [s]
Figure 6.8: Share of All Areas’ Frequency Dependent Generation and Load of the
Total Change in Power.
in figure A.5 has to be analyzed carefully because while lower values

of ∆PTArea1
ie indicate lower congestion, they can also indicate a can-
cellation of Primary Control power by interfering Secondary Control.
ACE Area1
8
0
Power [MW]
−2 OpHB Definition
−4 Updated ci
−6 Scaled λu
−8 Simple Partwise Construction
−10 Non-Linear partwise K(f )
−12
0 100 200 300 400 500
Time [s]
Figure 6.9: Area Control Errors of the First Area’s AGC for the Different Ki
Calculation Algorithms.
The summary of the performance of the different Ki -factor calculation

methods is generated in the form of a spider plot, as seen in figure 6.10.
The size of the area spanned in the spider plot is inversely proportional
to the performance of the corresponding algorithm. Interfering and
supporting AGC power and energy is calculated according to equations
(4.2) and (4.3). These values serve as an indication of how much
Secondary Control power was triggered as a result of the disturbance.
The maximum value of the ACE and its integration over time are
measurements for the mismatch between the area’s actual βi and the
AGC’s Ki .
6.4 Input Data

In order to simulate the influence of different Ki calculation algorithms, the
most important system properties, as listed below, have to be known for the
Performance Indicators of Different Algorithms
Max. Supporting AGC Interfering AGC

[MW] 11 [kWh]
300
8.6
220
5.7
150
Max. Interfering AGC 2.9 Supporting AGC
[MW] 74 [kWh]
11 8.6 5.7 2.9
74 150 220 300

2.9
74
5.7
150
8.6
220
11
Max. |ACE| 300 Integrated |ACE|
[MW] [kWh]
OpHB Definition
Updated ci
Scaled λu
Simple Partwise Construction
Non-Linear partwise K(f )
Figure 6.10: Spider Plot Comparing the Most Important Performance Indicators
of the Different Ki (f ) Calculation Algorithms. Smaller Area Correlates to Better
Performance.
specific point in time.
β and βi at the specific time, in order to compare the calculated Ki to the

actual β of the net.
Size of the disturbance in combination with β is used to simulate the

initial frequency deviation as explained above.
Load values over the course of the day when the simulation takes place
have to be known in order to calculate the load self-regulation effect
at the specific time and to calculate Ki .
Net export powerflows are added to the load to give the generation present
in every area during the simulation, is needed for the calculation of
different Ki -factors.
The load and export powerflows can be obtained through ENTSO-E’s

data portal [33]. While the load of every area in the RGCE is available as
hourly averages for every third Wednesday of the month, only snapshots
of the export powerflows at 3:00 and at 11:00 are available on these dates.
During normal operation the predictions of load and export powerflows,
which would be used to calculate Ki , always contain a forecast error which
originates from system variations between days. As a result, the error in
the simulation introduced by selecting a weekday reasonably close to the
third Wednesday can be treated as forecast error which occurs naturally in
the power system. Running the simulation for the load and export power-
flow situation on a Saturday or Sunday is not advised since the correlation
between the third Wednesday and a weekend day can be far greater than
realistic forecast errors.
6.4.1 Large Disturbance

To obtain a direct comparison between the simulation and the response of
the real power system, analyses of selected outages performed by swissgrid
employing the method presented in section 5.4.1 yielded values for β, βi and
the size of the disturbances, which are listed in table 6.1. It is evident from
the table that the frequency response characteristic of the entire network β
tends to be higher than the yearly calculated value λu . According to the
calculations performed in section 4.2, this can result in interfering Secondary
Control power being provided in some areas. However, since the exact dif-
ference between β and λu depends on the time of day and and the season,
these measurements lend some credibility to the assumption that β scales
with the generation present in the system.
Unlike β, βi varies widely between the different outages and does not
seem to be correlated to the variation of β. To analyze the accuracy of
Date Country Size βi

MW βi − Ki β
MW β − λu
[MW] Hz [%] Hz [%]
Tue. 31.07.2010 France 1294 591 -9.5 29432 10.9
09:55
Tue. 17.08.2010 France 1221 909 39.2 27750 4.6
15:23
Wed. 15.12.2010 Poland 1031 1406 115.3 32219 21.4
22:50
Tue. 18.01.2011 Italy 2250 462 -32.2 34615 31.0
17:05
Table 6.1: Details of the Different Outages Analyzed by swissgrid.
the βi measurements, different plausibility checks were applied to the data

depending on the specifics of the supplied data sets. Where available, the
ACE generated by swissgrid’s AGC was compared to the theoretical values
calculable by equations (5.20) and (3.12) when using βi calculated by swiss-
grid. In addition, for every data set, the relationship of βi to the calculations
from equation (5.14) was examined.
As an example, figures 6.11 and 6.12 show the frequency and the export
power deviations measured by swissgrid between 17:00 and 17:10 on Tuesday,
January 18th, 2011. At 17:05:44 the failure of a bus bar in Italy lead to a
momentary loss of 2250 MW of generation in the RGCE grid. In figure 6.11
System Frequency
50.06
50.04
50.02
f [Hz]
50
49.98
49.96
49.94
17:03 17:04 17:05 17:06 17:07 17:08 17:09 17:10
Time
Figure 6.11: System Frequency measured by swissgrid between 17:00 and 17:10
on January 18th 2011. Outage in Italy of 2250 MW generation occurs at 17:05:44.
the system frequency is shown to have dropped rapidly by approximately

Export Power Deviation

200
100
0
∆PT,ch [MW]
−100
−200
−300
−400
17:03 17:04 17:05 17:06 17:07 17:08 17:09 17:10
Time
Figure 6.12: Export Power Deviation from Schedule between 17:00 and 17:10 on
January 18th 2011. Outage in Italy of 2250 MW Generation Occurs at 17:05:44.
65 mHz, which according to equation (2.13) adds up to a frequency response

of the whole grid of 34615 MW/Hz, which is 31 % above the OpHB reference
of 26680 MW/Hz. Figure 6.12 shows a decrease in Switzerland’s exported
power of almost 500 MW during the decrease in frequency, which is not at all
consistent with the expected increase of supporting power of about 44 MW
according to Ki or the 30 MW according to βi calculated by swissgrid.
From the results of these plausibility checks it can be concluded that mea-
suring βi of Switzerland by applying equation (5.14) to large disturbances
does not yield realistic results.
It is possible that the data delivered by swissgrid for the four outages
was affected by technical failures, such as measurement insensitivities or
data storage corruption, however, the most plausible explanation for the
phenomenon of widely varying βi and ∆PT,i lies in the size of Switzerland’s
load and generation in comparison to the total size of the synchronous grid,
as well as the large capacity of the high voltage lines connecting Switzerland
to its neighboring areas. The share of frequency sensitive generation and
load in Switzerland is negligible compared to the transit power flows which
result from dynamics of large parts of the RGCE grid.
During these large disturbances, a power system of the extent of the RGCE
acts very dynamically. In addition to the fact that in most cases, the system
was not in a true 50 Hz equilibrium before any of the disturbances; there
are a large number of different interactions such as incorrectly configured
control loops, protection equipment and unscheduled tie-line flows which
can affect the accuracy of the results from equation (5.14) and (5.15). These
dynamics have insignificant effects on the overall β of the whole grid, but for
a small area such as Switzerland, they can dominate the natural dynamics
and subsequently lead to unusable data.
6.4.2 Random Disturbances

Since the analysis of the large disturbances provided by swissgrid did not
yield usable βi for given points in time, more detailed data was requested in
an attempt to apply the methods demonstrated in section 5.4.2. The deliv-
ered data contained measurement series of the frequency, ACE, and export
powerflow for the same days when the aforementioned outages occurred.
While the findings are consistent over all measurements, the following
figures show exemplary data of one hour on Monday, January 17th, 2011 at
which the effects presented themselves especially clearly. The first attempt
at estimating βi was to plot the ACE as a function of the frequency devia-
tion in order to find lines with a slope proportional to ei βi as suggested by
equation (5.20). In figure 6.13, there are at least seven lines with approxi-
mately the same slope, this slope corresponds exactly to Ki set in the AGC.
According to equation (5.20), however, this slope should be equal to the
error term ei multiplied by the frequency response characteristic βi , which
is equal to the difference between Ki and βi . An analysis of the data points
showed that the measurements which appear close together in the same line
of the ACE(∆f ) plot are not all proximate when analyzing the ACE as a
function of time, as done in figure 6.14. ACE(t) appears to oscillate with an
amplitude of ±50 MW around 0 MW. The deviation of the frequency from
its setpoint, shown in figure 6.15, slowly increases from almost -40 mHz to
50 mHz over the course of the hour, while exhibiting small oscillations in
the range of a few millihertz. The slope of Ki in figure 6.13 suggests that
the second term in calculating ACE, ∆PT,i , is not frequency dependent.
This was analyzed in figure 6.16 for the same interval in time. In this plot,
the only discernible lines run parallel to the frequency axis, with a slope
of 0 MW/Hz. According to equation (5.22) the only explanation for this
phenomenon is that the integration components of the frequency deviation
and the AGC power compensate the frequency dependency of the Primary
Control. A fundamentally different explanation is to use the same argumen-
tation as for large disturbances, which says that the tie-line powerflow in
and out of Switzerland is dictated by neighboring countries and cannot be
calculated according to equation (5.18), rendering the basis of the analysis
of ∆PT,i as a function of ∆f in order to find βi irrelevant. Both explana-
tions are supported by figure 6.17, which shows the export powerflow out of
Switzerland over time. If the powerflow were proportional to the frequency
deviation in some way, ∆PT,i would show a noticeable difference between the
first half and the second half of the hour as the frequency deviation changes
signs around 23:30.
ACE @23:00:00.292-23:59:59.822
150
100
50
0
ACE [MW]
−50
−100
−150
−200
−0.04 −0.03 −0.02 −0.01 0 0.01 0.02 0.03 0.04 0.05 0.06
∆f
Figure 6.13: ACE as a function of ∆f over one hour.

ACE(t) @23:00:00.292-23:59:59.822
150
100
50
ACE [MW]
−50
−100
−150
−200
23:00 23:10 23:20 23:30 23:40 23:50 00:00
Time
Figure 6.14: ACE as a Function of Time over One Hour.
∆f (t) @23:00:00.292-23:59:59.822
0.06
0.04
0.02
∆f [Hz]
−0.02
−0.04
23:00 23:10 23:20 23:30 23:40 23:50 00:00
Time
Figure 6.15: ∆f as a Function of Time over One Hour.

∆PT (∆f ) @23:00:00.292-23:59:59.822

200
150
100
50
∆PT [MW]
−50
−100
−150
−200
−0.04 −0.03 −0.02 −0.01 0 0.01 0.02 0.03 0.04 0.05 0.06
∆f
Figure 6.16: ∆PT,i as a Function of ∆f over One Hour.

∆PT (t) @23:00:00.292-23:59:59.822
150
100
50
∆PT [MW]
−50
−100
−150
23:00 23:10 23:20 23:30 23:40 23:50 00:00
Time
Figure 6.17: ∆PT,i as a Function of Time over One Hour.
The conclusion of this analysis of the data supplied by swissgrid is that βi

can not easily be obtained by representing the tie-line powerflow as a func-
tion of the frequency deviation. As with the measurements taken during
large disturbances, analyzed in section 6.4.1, it is possible that this conclu-
sions is drawn based on errorneous data. In addition, small disturbances
occur stochastically and could therefore underly statistical problems which
are not treated further in the scope of this project.
Chapter 7
Discussion and Conclusion
7.1 Results from the Simulation

Due to the unforeseen difficulties encountered when determining βi for a
specific set of circumstances, the proposed improvements over the OpHB
algorithm for sizing Ki could not be evaluated using the developed simula-
tion.
If methods other than the two explained in section 6.4 for finding βi are
derived, the simulation can immediately be used to evaluate the different
algorithms as explained in section 6.3.
To develop an algorithm which does not require a measured βi for the com-
parison is conceivable, but a synthetic βi will lead to a considerable loss in
accuracy and comparability.
An entirely different approach to evaluating the performance of the Ki siz-
ing algorithms is to use the backup AGC, which is present and connected
to the network at all times but does not send signals to the generators,
to determine the usefulness of the different Ki factors in terms of minizing
ACE.
7.2 Further Research

Over the course of this project, a number of interesting topics of for future
research activities in different areas were found.
Investigation of ACE(∆f ) and ∆PT,i (∆f ) to find the origins of the ar-
tifacts presented in 6.4.
Performing thorough mathematical analysis of ∆PT,i for non-ideal
cases, such as tie-line power flows which are not accompanied by fre-
quency deviations or load swings.
Improving the accuracy of the simulation by implementing more dy-
namic phenomena such as turbine characteristics. Integrating voltage
65
CHAPTER 7. DISCUSSION AND CONCLUSION 66
magnitudes and angles in order to perform sophisticated power flow

calculations after outages.
Researching load self-regulation in Switzerland in order to find out

if the research published in [29] applies to other areas as well.
Researching surplus generation and additional Primary Control in

Switzerland to improve on the standard OpHB values.
Analyzing more measurements of outages in Europe to find realistic

values for βi and to subsequently compare the different Ki factor al-
gorithms.
Analyzing random frequency variations using stochastic mathematics

and machine learning algorithms so that βi can be “learned”.
Studying the adequacy of frequency control reserves for the case of

perfect AGC of all areas.
Developing a trading model for Secondary Control power in order

to be able to use features of specific areas, i.a. fast response times,
large reserves.
Analyzing implications of switching off Secondary Control in

Switzerland.
7.3 Conclusion
The extensive literature review, as well as the analysis of the current and
past frequency control regulations of the RGCE have shown considerable
potential for improving the sizing of Ki , bringing it closer to βi . Four differ-
ent methods developed for this task have been outlined and integrated into
a newly developed simulation program. The data delivered by swissgrid,
however, was not as applicable to the simulation environment as would be
desirable. Further analysis of said data revealed potentially fundamental
flaws in its acquisition or in the functioning of the Swiss transmission grid.
A multitude of future research directions have been elucidated, for which
this report serves as a viable basis.
Appendix A
Evaluation Results
Power Exchange from Area 1

35
30 ∆PP rimary,G1
∆PP rimary,G2
25
Power [MW]
∆PP rimary,G3
20
∆PP rimary,G4
15
∆PSecondary
10
∆PLoad+Surplus
5
0
0 100 200 300 400 500
Time [s]
Figure A.1: Development of the Primary and Secondary Control Power, the Load
Self-Regulation and the Total Power Transported over the Tie-Line over Time.
67
APPENDIX A. EVALUATION RESULTS 68
Input, States and Output of AGC-Controller

40
K · ∆f
20
∆PT ie
Power [MW]
ACE1
0
ci · ACE1
1
R
TN 1 ACE1 dt
−20
Area1
∆PAGC
−40
0 100 200 300 400 500
Time [s]
Figure A.2: Development of the AGC Inputs (K∆f , ∆PT ie ), Internal Variables
1 Area1
R
(ACE1 , ci ACE1 , TN,1 ACE1 dt) as well as its Output (∆PAGC ).
Area Control Errors and AGC Power Changes

1500
ACE1
1000 ACE2
ACE3
500
Power [MW]
Area1
∆PAGC
0 Area2
∆PAGC
Area3
−500 ∆PAGC
−1000
−1500
0 100 200 300 400 500
Time [s]
Figure A.3: Reaction of All Areas’ AGC to the Disturbance in Area Two.
Area1
∆PAGC
6
OpHB Definition
5
Updated ci
4 Scaled λu
3
Power [MW]

2
−1
−2
0 100 200 300 400 500 600 700
Time [s]
Figure A.4: Output of the First Area’s AGC for the Different Ki Calculation
Algorithms, which Controls the Secondary Control Power Plants.
∆PTArea1
ie
35
30 OpHB Definition
Updated ci
25
Scaled λu
Power [MW]

20
15
10
0
0 100 200 300 400 500
Time [s]
Figure A.5: Tie-line Powerflows out of Area One for the Different Ki Calculation
Algorithms.
Comparison of Different K-factor Algorithms

300
200
100
Power [MW]
−100
−200
−300
−0.2 −0.1 0 0.1 0.2 0.3
Frequency Deviation [Hz]
OpHB Definition
Updated ci
Scaled λu
Figure A.6: Frequency Bias Factors Ki (f ) Resulting from the Different Algo-
rithms.
Acronyms
ENTSO-E European Network of Transmission System Operators for

Electricity
RGCE Regional Group Continental Europe
UCTE Union for the Co-ordination of Transmission of Electricity
UCPTE Union for the Coordination of Production and Transmission

of Electricity
OpHB Operation Handbook
AGC Automatic Generation Control
LFC Load Frequency Control
ACE Area Control Error
CENTREL Former synchronous area covering Czech Republic, Hungary,

Poland and Slovakia
NERC North American Electric Reliability Corporation
TSO Transmission System Operator
EEX European Energy Exchange
72
List of Figures
2.1 Three Area System with Tie-Lines and individual Loads (L1-3) and
Generators (G). . . . . . . . . . . . . . . . . . . . . . . . . . . 5
2.2 Interactions in Frequency Controls. Red Arrows: Control Inputs;
Black Arrows: Effects of Control Actions. . . . . . . . . . . . . . 6
2.3 Linear Speed Droop Constant of a Generator with Underfrequency
and Overfrequency Activation. . . . . . . . . . . . . . . . . . . . 7
3.1 Area 1 Including the AGC Controller which sends the Control Sig-
nal ∆PAGC1 to all Generators Participating in Secondary Control. 12
100%
3.2 50 Hz Linear Frequency Dependency which 50% of the Generators
are Following According to the OpHB. . . . . . . . . . . . . . . . 17
3.3 Trumpet-Curves for Different Incident Sizes Pa . . . . . . . . . . . 19
4.1 Monthly Average of Frequency Response Characteristics and Max-

imum Load in UCPTE. Upper Curve: β Using the left Scale of
[MW/Hz]. Lower Curve: Monthly Maximum Load, Using the right
Scale of [GW]. Actual Measurements are Given by ’+’; Dotted Lines
are Spline-Interpolation; Solid Line Indicates Linear Regression. . . 25
4.2 Time of Day of the Measured Frequency Response Characteristics.
Averages Over Five Years in Red. . . . . . . . . . . . . . . . . . 26
4.3 Frequency Deviation in mHz per Loss of Load in MW. White Squares:
1285 Disturbances between 1.1.1988 and 17.10.1995 in UCPTE;
Blue Circles: 31 Disturbances between 19.10.1995 and 10.2.1996 in
UCPTE with CENTREL; Dark Blue Line: Linear Regression of
White Squares βU CP T E = 30000 MW/Hz; Light Blue Line: Linear
Regression of Blue Circles βU CP T E+CEN T REL = 40000 MW/Hz. [26] 28
4.4 Frequency Deviation in mHz (Left Scale) and % of 50 Hz (Right
Scale) per Loss of Load in % of Total Load. White Squares: 1316
Disturbances between 1.1.1988 and 10.2.1996; Dark Blue Line: Lin-
ear Regression of Measurements with β = 13 %. [26] . . . . . . . . 29
73
LIST OF FIGURES 74
4.5 Left: Comparison of the Ideal, Linear Speed Droop Characteristic

(1) to the Typical Speed Droops of a Thermal Power Plant (2)
and a Hydro Power Plant (3). Right: Typical Speed Droop of a
Thermal Power Plant with Added Deadband. . . . . . . . . . . . 29
4.6 Contribution Factors ci of Switzerland in RGCE, Calculated using
Annual Averages (dotted) and Monthly Averages (Solid) in 1999,
2008 and 2009. . . . . . . . . . . . . . . . . . . . . . . . . . . . 30
4.7 Deviations between Contribution Factors ci Calculated on Monthly
and Annual Basis for Switzerland an its Neighboring Countries in
2009. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31
5.1 Non-linear Speed Droop Model Sj (f ) of One Generator compared

to the Assumption of OpHB SOpHB.j . fN +,j and fN −,j Denote the
Deadband Frequencies; fmax,j and fmin,j Are the Maximum and
Minimum Frequencies where Full Activation of Primary Control
Reserves Occurs. . . . . . . . . . . . . . . . . . . . . . . . . . . 39
5.2 Deviation in Export Power Flow as a Function of the Frequency
Deviation. The error factor ei changes the Slope and Introduces
Non-Linear Effects. . . . . . . . . . . . . . . . . . . . . . . . . . 46
6.1 Reduced-Size Model of the RGCE Synchronous Area in Simulink. . 48

6.2 Simulink Block of Area3 Containing Linear Primary Control via
Speed Droop and Self Regulation as well as First Order Delays
which Model Power Plant Behavior. The Sum of the Change in
Generation (Primary and Secondary) is Added to the Change in
Load Self-Regulation which Results in a Change in Tie-Line Power
Flow DPT3. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49
6.3 Model of the AGC of Area One, Where Inputs In1 and In2 Feed
∆f and ∆Pt,1 into the ACE Calculation Block. The PI controller
PIACG1 Produces the Control Signal DPAGC1 for the Secondary
Control Plants. . . . . . . . . . . . . . . . . . . . . . . . . . . . 49
6.4 Calculation of the Area Control Error of Area One with a Linear
Frequency Bias Factor K1 . . . . . . . . . . . . . . . . . . . . . . 49
6.5 Non-Linear Speed Droops of Primary Control Power Plants of Area
One. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51
6.6 Calculation of ACE1 for a Non-Linear Ki (f ), Using a Frequency
Dependent Matlab Function. . . . . . . . . . . . . . . . . . . . . 52
6.7 Share of the Primary and Secondary Control Power and Load Self-
Regulation of the Tie-Line Power over Time. . . . . . . . . . . . . 53
6.8 Share of All Areas’ Frequency Dependent Generation and Load of
the Total Change in Power. . . . . . . . . . . . . . . . . . . . . 54
6.9 Area Control Errors of the First Area’s AGC for the Different Ki
Calculation Algorithms. . . . . . . . . . . . . . . . . . . . . . . 55
LIST OF FIGURES 75
6.10 Spider Plot Comparing the Most Important Performance Indica-

tors of the Different Ki (f ) Calculation Algorithms. Smaller Area
Correlates to Better Performance. . . . . . . . . . . . . . . . . . 56
6.11 System Frequency measured by swissgrid between 17:00 and 17:10
on January 18th 2011. Outage in Italy of 2250 MW generation
occurs at 17:05:44. . . . . . . . . . . . . . . . . . . . . . . . . . 58
6.12 Export Power Deviation from Schedule between 17:00 and 17:10 on
January 18th 2011. Outage in Italy of 2250 MW Generation Occurs
at 17:05:44. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59
6.13 ACE as a function of ∆f over one hour. . . . . . . . . . . . . . . 61
6.14 ACE as a Function of Time over One Hour. . . . . . . . . . . . . 62
6.15 ∆f as a Function of Time over One Hour. . . . . . . . . . . . . . 62
6.16 ∆PT,i as a Function of ∆f over One Hour. . . . . . . . . . . . . . 63
6.17 ∆PT,i as a Function of Time over One Hour. . . . . . . . . . . . . 64
A.1 Development of the Primary and Secondary Control Power, the

Load Self-Regulation and the Total Power Transported over the
Tie-Line over Time. . . . . . . . . . . . . . . . . . . . . . . . . 67
A.2 Development of the AGC Inputs (K∆f , ∆PT ie ), Internal Variables
1 Area1
R
(ACE1 , ci ACE1 , TN,1 ACE1 dt) as well as its Output (∆PAGC ). 68
A.3 Reaction of All Areas’ AGC to the Disturbance in Area Two. . . . 68
A.4 Output of the First Area’s AGC for the Different Ki Calculation
Algorithms, which Controls the Secondary Control Power Plants. . 69
A.5 Tie-line Powerflows out of Area One for the Different Ki Calculation
Algorithms. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70
A.6 Frequency Bias Factors Ki (f ) Resulting from the Different Algo-
rithms. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71
List of Tables
4.1 Effects of Different Frequency Bias Factors on AGC of an

Area not Causing a Disturbance. . . . . . . . . . . . . . . . . 33
5.1 Share of Different Power Plants on the Annual Electricity

Generation in 2009, Data from [5]. . . . . . . . . . . . . . . . 41
5.2 Analysis of the Four Parts of λu according to the OpHB. . . . 42
6.1 Details of the Different Outages Analyzed by swissgrid. . . . 58
76
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eeh power systems

Deterministic Sizing of the Frequency

EEH – Power Systems Laboratory

In Cooperation with swissgrid ag

Expert: Prof. Dr. Göran Andersson

Zurich, June 1, 2011

An important challenge of grid control is the prediction of the frequency

2 Frequency Control Theory 2

3 Automatic Generation Control 11

4.2 Effects of Estimation Errors on Network Operations . . . . . 32

5 Deterministic, Semi-Online Sizing of Ki 35

6 Calculation, Modeling and Simulation 47

7 Discussion and Conclusion 65

Frequency Control Theory

It is well established that a mismatch between mechanical energy fed into

2.1 Need for Constant Frequency

un-split synchronous area, [. . . ] undisturbed operation depends on the size

2.2 Without Speed Governing

2.3 Three Tiered Approach

are usually4 applied automatically.

2.4 Primary Control Using Speed Droop Control

limit Primary Secondary

Figure 2.2: Interactions in Frequency Controls. Red Arrows: Control Inputs;

constant in the control loop of turbine governors. It determines the genera-

Figure 2.3: Linear Speed Droop Constant of a Generator with Underfrequency

been fully deployed and the turbine dynamics have settled.

In ENTSO-E’s regional group Continental Europe, the total Primary Con-

to a frequency deviation of between -53 mHz and -64 mHz6 in RGCE.

2.5 Frequency Response Characteristic

be multiplied by the combined ratings of the participating generators and

2.6 Secondary Control

causing the disturbance, by means of automatic generation control. This

2.7 Tertiary Control

3.1 Classic Automatic Generation Control

Not Participating in Secondary Control

minutes, coal-fired or nuclear plants employing steam turbines have longer

3.1.1 Linear Area Control Error

It is known from measurements and calculations that the assumption of an

3.1.2 Non-Interactive Control

ACEi = ∆fss · (−βi + Ki ) ∀i 6= l (3.12)

As explained in section 3.1, AGC works on a slower timescale than Pri-

3.2 Current Practice in the RGCE

3.2.1 Network Characteristic Method

3.2.2 Change in Load-Frequency Control Policy

Kri = 1.1 · ci · λu (3.19)

Since, by OpHB definitions, none of the factors in equation (3.19) change

The calculation, however, must be adjusted in case of border-crossing trad-

response as shown in equation (3.25).

Compared to the stringent definition of the frequency bias factor by formula

of the actual frequency response characteristic βi than equation (3.25), is

3.2.3 Measurements of Performance

3.3 Proposed Improvements and New Schemes

3.3.1 Changes to Classic AGC

Figure 3.3: Trumpet-Curves for Different Incident Sizes Pa .

line power, as well as the principle of non-interaction between different areas

violate the assumption of linear speed droop control8 . Another approach

3.3.2 Fundamentally New AGC Schemes

3.3.3 Example of New Implementations outside ENTSO-E

cluding noise management and individual generator dispatch.