Energy Conversion and Management 249 (2021) 114867

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Energy Conversion and Management

journal homepage: www.elsevier.com/locate/enconman

Assessing the integration potential of new energy in river basin clean

energy corridors considering energy-power coupled complementary
operation modes
Juntao Zhang a, b, Chuntian Cheng a, b, *, Shen Yu a, Xinyu Wu a, Huaying Su c
a
Institute of Hydropower and Hydroinformatics, Dalian University of Technology, Dalian 116024, China
b
Key Laboratory of Ocean Energy Utilization and Energy Conservation of Ministry of Education, Dalian University of Technology, Dalian 116023, China
c
Guizhou Electric Power Dispatching and Control Center, Guiyang 550002, China

A R T I C L E I N F O A B S T R A C T

Keywords: Operating new energy (wind and solar) complementarily with the existing hydropower stations is a promising
Clean energy corridors way for efficient accommodation of utility-scale new energy. China plans to build a batch of river basin
Hydropower hydro–wind–solar clean energy corridors (RBCECs) by integrating new energy into the existing large hydropower
New energy
bases. This paper proposes a universal method to determine the effective complementary operation mode and the
Integration potential
Complementary operation modes
optimal capacity configuration of new energy for RBCECs. First, the energy–power coupled complementary
operation modes are proposed to fully tap the hydropower flexibility, compensating the variable new energy.
Then, an optimization model framework is constructed to determine the optimal capacity configuration of new
energy for RBCECs; the model framework can simulate the 8760–hour–time–series operation of hydro­
–wind–solar hybrid system. Moreover, the proposed operation modes can be respectively plugged into the model
framework to calculate the corresponding optimal capacity configuration of new energy for RBCECs. The Beipan
RBCEC in China, is selected as a case study, and its effective complementary operation mode and the optimal
capacity configuration of new energy are determined. Results also indicate that (1) integrating new energy into
hydropower system will change the inter-seasonal distribution of water and electricity of the hydropower sta­
tions; (2) the ability of hydropower stations to compensate variable new energy will be affected by runoff; (3) the
theoretical maximal integration potential of new energy in a RBCEC will be affected by the installed hydropower
capacity, reservoir storage, and complementary operation modes; but the actual deployment level of the theo­
retical maximum integration potential will be affected by the capacity of power transmission channels.

1. Introduction targets [6]. By the end of 2020, the cumulative installed wind and solar
power capacity of China reached 280 million kW and 250 million kW,
1.1. Motivation thereby accounting for 13% and 11% of the total installed capacity,
respectively [7]. In addition, China will increase the total installed ca­
China aims to peak its CO2 emissions before 2030 and achieve car­ pacity of new energy to over 1.2 billion kW by 2030. New energy will
bon neutrality before 2060 [1]. As the world’s largest carbon emitter become the dominant power source of the new generation power sys­
and developing country [2,3], China must devote more effort to tems in China [8].
reducing carbon emissions than developed countries, because it will However, integrating high levels of new energy into power systems
realize carbon neutrality after its carbon emissions peak in the shortest may be challenging because of their variability and limits in predict­
time period in global history [4]. China’s electricity system accounts for ability; the high variability in new energy will require power system
approximately half of the country’s energy-related CO2 emissions[5]. In flexibility to enable matching supply and demand [9]. Currently, system
this case, China will foster a new power system with new energy (i.e., flexibility is often provided by fossil fuel power plants; however, the
wind and solar power) as the mainstay to achieve its ambitious climate deep decarbonization of power systems will strongly limit their use in

* Corresponding author.
E-mail addresses: jtzhang@mail.dlut.edu.cn (J. Zhang), ctcheng@dlut.edu.cn (C. Cheng).

https://doi.org/10.1016/j.enconman.2021.114867
Received 8 August 2021; Received in revised form 30 September 2021; Accepted 9 October 2021
Available online 23 October 2021
0196-8904/© 2021 Elsevier Ltd. All rights reserved.
J. Zhang et al. Energy Conversion and Management 249 (2021) 114867

Fig. 1. Distribution of the RBCECs during the China’s 14th Five-Year Plan (2021–25).

the future. Operating new energy complementarily with the existing complementary operation mode. Therefore, this paper aims to answer
hydropower stations has been an important way promote the effective two questions about the construction and complementary operation of
accommodation of utility-scale new energy, because the existing reser­ the RBCECs:
voir hydropower has been widely regarded as a renewable alternative
resource of flexibility that can compensate for the variability of wind • To achieve the efficient accommodation of the clean energy re­
and solar power [10,11]. Furthermore, China has the worldwide largest sources and the full exploitation of hydropower flexibility, which
hydropower resources, most of which are large cascade hydropower hydro-wind-solar complementary operation mode should the RBCEC
plants with reservoirs and regulation capabilities[12]. More than 60% of adopt?
the country’s hydropower resources are concentrated in large river ba­ • How much wind and solar power can be integrated into a RBCEC
sins, mainly distributed in the southwestern regions far away from the under the support of the existing power transmission channels and
load centers [13]. China has developed the “West to the East” power the hydropower flexibility?
transmission project to transmit the clean electricity of hydropower
bases to the eastern load centers [14]. Several large river basins in China
(e.g., Jinsha River, Yalong River, Yellow River, Wu River, and Beipan 1.2. Related work
River) are also rich in wind and solar resources [15]. Therefore, during
the 14th Five-Year Plan (2021–25), China will build a batch of river Integrating new energy into the existing hydropower plants has been
basin hydro-wind-solar clean energy corridors (RBCECs) by integrating an important way to facilitate the effective new energy accommodation,
utility-scale wind and solar power into the existing large hydropower especially for the countries rich in hydropower resources[18]. However,
bases[16], as shown in the Fig. 1. The construction of RBCECs mainly how to determine the optimal sizes (also called integration potential in
servers two purpose: (1) the flexible hydropower system can compensate this paper) of new energy in hydro-wind-solar hybrid energy systems is a
for the high volatility and intermittency of wind and solar power; the key problem[19]. The related studies can be roughly classified into three
hydro-wind-solar electricity will be bundled together and transmitted to categories.
the load centers through the high-voltage direct current tie lines; this The first category evaluated the potential of integrating new energy
will help reduce the demand for system flexibility from the power supply into standalone energy systems that include hydropower. For example,
side and promote the efficient accommodation of utility-scale new en­ John et al. [20] explained a procedure for sizing components of a
ergy [17]; (2) the existing power transmission infrastructure of hydro­ standalone hybrid energy system involving hydropower, photovoltaics,
power plants will reduce the cost of new energy integration. and battery storage systems. Syahputra et al. [21] designed renewable
An effective hydro-wind-solar complementary operation mode will energy systems based on micro-hydro and solar photovoltaic for rural
play a significant role in the efficient utilization of the clean energy areas, with a case study in Yogyakarta, Indonesia. Mahmoudimehr et al.
resources and the full exploitation of the hydropower flexibility for [22] proposed a novel method to design a hybrid hydro-solar standalone
RBCECs. Moreover, integrating the wind and solar power with a energy system for coastal areas in north and south Iran. Come Zebra
reasonable capacity into the RBCEC can avoid the power transmission et al. [23] thoroughly reviewed the hybrid renewable energy systems in
congestion and ensure the sustainable accomplishment of the mini-grids for off-grid electrification in developing countries. However,
owing to the inverse distribution of clean energy resource and load

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J. Zhang et al. Energy Conversion and Management 249 (2021) 114867

centers in China, the clean power of RBCECs will be bundled together complementary operation modes were used in the previously presented
and transmitted to the load centers in eastern China (see Fig. 1) [15,24]. studies to guide the complementary operation of the hydro-wind-solar
Therefore, the results of these studies on standalone energy systems are hybrid systems; these complementary operation modes can be roughly
difficult to apply to the RBCECs. classified into two categories: mitigating the fluctuation of new energy
The second category of studies focused on the integration potential of power output [27,29], and following the load [18,25,26,28,32,33,36].
new energy into a single large hydropower plant. Ming et al. [25] The aforementioned complementary operation modes are essentially
developed a systematic framework to determine the optimal sizing of a power-based complementary operation modes, in which the hydro­
utility-scale photovoltaic (PV) section of the China’s Longyangxia power flexibility is only used to compensate for the power variability of
hydro–PV plant. Fang et al. [18] proposed a method for optimal sizing of new energy. As growth in the penetration rate of new energy continues,
a PV plant integrated into the China’s Longyangxia hydropower plant by the variability of daily electricity generation from new energy will also
maximizing the net revenue during lifetime. Zhang et al. [26] estab­ seriously affect the balance between energy supply and demand in the
lished a multi-objective mathematical model, considering electricity power systems [37]. However, to the best of the authors’ knowledge,
delivery demand and reservoir characteristics; the model was used to few studies have considered the energy-power coupled complementary
determine the optimal PV capacity of a hydropower-PV hybrid system in operation modes in which the flexible hydropower system can simul­
the Upper Yellow River. Yuan et al. [27] proposed a two-layer nested taneously compensate for the high variability of new energy’s hourly
algorithm to determine the optimal size of the PV plant of Naijili hydro- power output (MW) and daily electricity generation (MWh).
PV hybrid system located in Qinghai, China. Moreover, Danso et al. [28]
assessed the potential of the Akosombo hydropower plant in Ghana to 1.3. Contributions
support the integration of solar and wind energy into West Africa. Wang
et al. [29] established a multi-objective size optimization model to To fill the knowledge gaps, this paper proposes for the first time a
investigate the optimal configuration of hydro-wind-solar hybrid sys­ universal method framework to determine the effective energy-power
tems on a global scale. The previously mentioned studies have provided coupled complementary operation mode and the integration potential
valuable methods for evaluating the potential of a single large or of new energy for RBCECs. The contributions of this paper are as follows:
medium-sized hydropower plant to support the integration of wind and
solar power into power systems. However, the operation details of the • Different from the common power-based complementary operation
hydro-wind-solar hybrid systems simulated in above studies were typi­ modes used in the previous studies which only consider the power
cally limited to several hours, days, or weeks in a year selected using variability in the new energy, we propose energy-power coupled
time series aggregation method[30]; As mentioned in the literatures complementary operation modes for RBCECs, in which the hydro­
[31,32], it’s necessary to construct a model that combines hydro-wind- power flexibility will be fully taped to compensate for the variability
solar power at hourly resolution across one or more years to consider the in both the hourly power output (power) and the daily electricity
fluctuation of water-wind-solar resource on different time scale; this will generation (energy) of new energy.
lead to a more reliable result of hydro-solar-wind power mix. Based on • An optimization model framework is constructed to calculate the
the recently developed REUVB model [32], which combines solar and optimal capacity configuration of new energy with the objective of
wind energy meteorology and hydropower dispatch at hourly resolution maximizing annual electricity generation of the RBCEC system; the
over multiple years, Sterl et al. [33] uncovered the potential of the proposed model framework can explicitly simulate the 8760-hour-
Afobaka hydropower plant in supporting wind power integration in time-series operation of the RBCEC system, which will fully cover
Suriname. the operational details of the energy-power coupled complementary
Studies of the third category evaluated the potential of large-scale operation modes. Moreover, the proposed operation modes can be
cascade hydropower plants to facilitate the utility-scale new energy respectively plugged into this optimization framework to calculate
integration. Because of the hydraulic connections between cascade the corresponding optimal capacity configuration (also called inte­
reservoirs, the models of assessing the flexibility potential of cascade gration potential in this paper) of new energy and the power gen­
hydropower plants are difficult to solve [12]. Gebretsadik et al. [34] eration results.
introduced a reliability assessment method to test if the cascade hy­ • Based on a new linear modeling method for nonlinear hydro pro­
dropower plants in the Zambezi River basin can be efficiently used to duction function[38], the original multi-period nonlinear optimiza­
offset wind power intermittence in South Africa; Hirth [35] investigated tion model is transformed into a linear programming (LP) model,
the potential of large hydropower plants in Sweden in mitigating the reducing the computational complexity.
wind power value drop in power markets. Nevertheless, hydropower • The proposed method is applied to the Beipan RBCEC under con­
system was modeled relatively roughly in the above two studies. Zhang struction in Guizhou province, China. Based on the comparative
et al. [36] proposed a large-scale hydro-solar-wind hybrid system sizing analysis of the calculated results in different operation modes, the
model considering the electricity transmission requirements and effective energy-power coupled complementary operation mode and
cascade reservoir connections; the model only considered typical daily the corresponding optimal capacity configuration of wind and solar
outputs of new energy. As previously mentioned, the REVUB model is power are determined. Moreover, the impacts of new energy inte­
based on hourly resolution for multiple years; it was used to evaluate the gration on the long-term operation of the existing hydropower sta­
potential for the cascade hydropower plants in West Africa to support tions are revealed. The sensitivity of the optimal capacity
the wind and solar power integration [32]. However, the REVUB model configuration of new energy to several key factors is also analyzed.
has a major deficiency: the hydraulic connections between cascade
reservoirs are not considered, which leads to an overly conservative The remainder of the paper is organized as follows: the method is
assessment of the flexible regulation capacity of large-scale cascade described in Section 2. Section 3 provides a brief introduction of the
hydropower plants. Beipan RBCEC and the relevant input data. Section 4 and Section 5
To the best of the authors’ knowledge, few researchers have pro­ present the case study results and discussion, respectively. Section 6
posed a method framework to assess the integration potential of new concludes this paper.
energy into RBCECs; and, the method framework can explicitly couple
the wind and solar power generation with the optimal dispatching of 2. Method
cascade hydropower plants for an entire year with hourly resolution and
consider the hydraulic connections between cascade reservoirs. Integrating new energy into the existing hydropower plants to serve
In order to mitigate the variability of new energy, different as a hybrid power source has been an important way to facilitate the

3
J. Zhang et al. Energy Conversion and Management 249 (2021) 114867

Inflo w D am

DC R eservo ir
G
Hydropower plant Existing transmission line
AC
R elease
Turb ine

Wind power plant transmission line for new energy plant

Solar power plant Water flow

Inflow Dam Transformer

Turbine
Release

DC Control AC
AC
center DC

Inflow Inflow Dam

Turbine
Release
DC tie-lines
DC
AC
DC
AC

Inflow Dam
Inflow

Turbine Receiving-end power grids

Fig. 2. Schematic diagram of a river basin hydro-wind-solar clean energy corridor.

effective accommodation of utility-scale new energy, since the existing hydro-wind-solar power plants throughout the representative year.
reservoir hydropower is an available and economical measure that can Third, another complementary operation mode is selected to repeat
compensate for the variability of wind and solar power. As shown in the previously mentioned steps until the results of all the proposed
Fig. 2, for a RBCEC, new energy power plants are built in the neigh­ complementary operation modes have been obtained.
boring areas of each hydropower plant in the large hydropower base; Finally, the results of different complementary operation modes are
then the new energy power plants are connected to the corresponding compared and analyzed regarding the system power generation results
hydropower plant. The hydropower plants will be dispatched to and the impacts on the operation of existing hydropower reservoir.
compensate for variability of wind and solar power. On this basis, large Based on the comparative analysis, the effective energy-power coupled
hydropower base is developed into the RBCEC. Under the support of the complementary and the corresponding integration potential of new
existing power transmission channels of large hydropower base and the energy are determined for the RBCEC.
hydropower flexibility, the RBCEC will act as a hybrid power source and
the hydro-wind-solar electricity will be bundled together and trans­
2.2. Modeling energy-power coupled complementary operation modes
mitted to the receiving-end power grid; this can reduce the need for
system flexibility from the power supply side and facilitates the large-
In this section, two energy-power coupled complementary operation
scale, cross-regional, centralized accommodation of utility-scale new
modes are proposed, in which the flexible hydropower system can
energy.
simultaneously compensate for the high variability of new energy’s
hourly power output and daily electricity generation.
2.1. Research framework
2.2.1. Modeling the power-based complementary operation modes
The research framework is presented in Fig. 3.
First, an energy-power coupled complementary operation mode
(1) “Providing constant power”
(Section 2.2) is selected; the mathematical expressions of the selected
operation mode are plugged into the corresponding constrains part of
The “providing constant power” mode (PCM) means that the RBCEC
the optimization model.
will provide constant power to the receiving-end power grid every day;
Second, based on the operation mode selected in the previous step,
More specifically, the cascade hydropower plants will smooth the fluc­
the LP-based optimization model is established to optimize the capacity
tuations in wind and solar power output. The schematic of PCM is
configuration of new energy with the objective of maximizing annual
depicted in Fig. 4; the mathematical equations are as follows:
electricity generation of the RBCEC system. Then, the LP-based opti­
{ }
mization model is solved with the Gurobi Solver and the optimal results ∑H
( )
are obtained, including: 1) maximal annual power generation of the sumpmax
d = max phh,t + pwh,t + psh,t (1)
t∈Ωd
system; 2) optimal capacity configuration of wind and solar power that
h=1

can be integrated into the RBCEC; 3) the hourly operation process of

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J. Zhang et al. Energy Conversion and Management 249 (2021) 114867

Fig. 3. Framework of the proposed method.

Fig. 4. Schematic of PCM.

Fig. 5. Schematic of PSM.

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J. Zhang et al. Energy Conversion and Management 249 (2021) 114867

Fig. 6. Schematic of PCM + PCDE and PSM + PCDE mode.

{ }
∑
H
( ) d th day, respectively (MW); rlmax
d and rlmin
d are the maximal and minimal
sumpmin = min phh,t + pwh,t + psh,t (2)
d
t∈Ωd
h=1
residual load on the d th day, respectively (MW); in addition, ξPSM is the
control index; η is the overall percentage energy loss in the DC/AC
sumpmax − sumpmin = 0 (3) conversion and transmission lines. In this paper, for simplicity, the
d d
overall percentage energy loss is considered constant and equal to 5%
where t is the hour index; h is the index of the hydropower plant; the [39,40].
wind power plant and solar power plant integrated into the hydropower
plant h are hereinafter referred to as “wind power plant h ” and “solar 2.2.2. Modeling the “providing constant daily electricity generation” mode
power plant h ”, respectively; H is the number of hydropower plants in For the “providing constant daily electricity generation” mode
the RBCEC; d is the day index (1⩽d⩽365), and Ωd is the set of hour in­ (PCDE), the cascade hydropower plants will mitigate the fluctuations of
dexes t for the d th day, for example Ω365 = {8737, 8738, ..., 8760}; phh,t , daily electricity generation from new energy during several consecutive
pwh,t , and psh,t are the outputs of hydropower plant h, wind power plant days. In this paper, according to the operation specifications of the China
h, and solar power plant h in the t th hour respectively (MW); sumpmax Southern Power Grid, the horizon of the medium-term power generation
d
and sumpmin plan is usually a week. Therefore, in this paper, the fluctuation in daily
d are the hourly maximal and minimal total power outputs of
electricity generation of new energy is smoothed weekly for an entire
the RBCEC on the d th day, respectively (MW);
year. The mathematical equations of the mode PCDE are as follows:
(2) Peak shaving ∑∑
H
( )
sumed = phh,t + pwh,t + psh,t Δt (9)
In the “peak shaving” mode (PSM), the combined power output of
t∈Ωd h=1

RBCEC will fully respond to the peak load demands of the receiving-end
sumemax = max{sumed } (10)
power grid, relieving the peak regulation pressure. The reduction per­ w
d∈Γw

centage of the peak-valley difference of the residual load is used as the

control index. In addition, the schematic of PSM is depicted in Fig. 5; the sumemin
w = min {sumed } (11)
d∈Γw
mathematical equations are as follows:
Lmax = max{Lt } (4) sumemax min
w − sumew = 0 (12)
d
t∈Ωd

where sumed is the daily electricity generation of the RBCEC on the d th

Lmin
d = min{Lt } (5) day (MWh); w is the week index of an entire year (1⩽w⩽52); Γw is the set
t∈Ωd
of day indexes d of the w th week (e.g., Γ2 = {8,9,...,14}); sumemax
w and
{ }
∑
H
( ) sumemin
w are the maximal and minimal daily electricity generation in the
rlmax
d = max Lt − η phh,t + pwh,t + psh,t (6) w th week (MWh).
t∈Ωd
h=1

{ } 2.2.3. Modeling the energy-power coupled complementary operation modes

∑
H
( )
rlmin
d = min Lt − η phh,t + pwh,t + psh,t (7) Based on the above work, the energy-power coupled complementary
operation modes can be modeled.
t∈Ωd
h=1

( max ) For the PCM + PCDE mode, the hydropower will smooth the fluc­
rl − rlmin
( dmax d
) ⩾ξPSM (8) tuations in wind and solar power outputs and their combined power
Ld − Ldmin
output series will be a horizontal line; at the same time, the fluctuation
in the daily electricity generation of new energy will also be smoothed
where Lmax
d and Lmin
d are the maximal and minimal power grid load on the by the hydropower. Fig. 6(a) shows the Schematic of the energy-power

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J. Zhang et al. Energy Conversion and Management 249 (2021) 114867

coupled operation mode of PCM + PCDE. (2) Wind and solar power generation model
For the PSM + PCDE mode, the fluctuation and anti-peaking char­
pwh,t = cwind wind
Nh,t (16)
acteristics of new energy power output will be adjusted by the hydro­ h

power, and their combined power output will fully respond the peak
load demands of the receiving-end power grid; furthermore, the fluc­ psh,t = csolar
h
solar
Nh,t (17)
tuation in the daily electricity generation of new energy will also be
smoothed by the hydropower; Fig. 6(b) shows the Schematic of the PSM where cwind
h and csolar
h denote the capacity of the wind power plant h and
+ PCDE mode. solar power plant h (MW) to be optimized, respectively; Nwind solar
h,t and Nh,t
The mathematical equations of PCM + PCDE and PSM + PCDE are as denote the power output of the unit megawatt wind and solar power
follows: plant that has built in the study region at period t [18,26].
PCM + PCDE: Eqs. (1-3), (9-12)
PSM + PCDE: Eqs. (4-12) 2.3.2. Constraints
Moreover, the max and min form functions in the previously pre­
sented equations can be linearly modeled by introducing ancillary var­ 1. Constraints for the selected complementary operation mode
iables[41].
Different complementary operation modes can be plugged into this
2.3. Optimization model optimization framework to calculate the corresponding integration po­
tential of new energy and the power generation results. Based on the
In this section, an optimization model framework is constructed to Section 2.2, when RBCEC operates in the PCM + PCDE mode, the
optimize the capacity configuration of new energy with the objective of mathematical equations of the constraints are Eqs. (1-3) and (9-12);
maximizing annual electricity generation of the RBCEC system; the when RBCEC operates in the PSM + PCDE mode, the corresponding
proposed model framework explicitly simulates the 8760-hour-time-se­ constraints are Eqs. (4-12); when RBCEC operates in the PCM mode, the
ries operation of the RBCEC system, which can fully cover the opera­ corresponding constraints are Eqs. (1-3); when RBCEC operates in the
tional details of the energy-power coupled complementary operation PSM mode, the corresponding constraints are Eqs. (4-8);
modes. Moreover, different operation modes can be easily plugged into
this optimization framework to calculate the corresponding integration 2. Hydropower plant operation constraints
potential of new energy and the power generation results. The main (1) Reservoir water balance constraints:
{ }
variables of the model are cwindh , csolar
h , phh,t , vh,t , qph,t . cwind
h and csolar
h
( ) /
vh,t = vh,t− 1 + qih,t − qph,t − qsh,t × 3600 10000 (18)
denotes the capacity of the wind and solar power that can be integrated
into the hydropower plant h (MW), respectively; phh,t vh,t , qph,t are the where qih,t , qph,t and qsh,t are the total inflow, turbine discharge, spilled
power output (MW), reservoir storage volume (104 m3), turbine discharge of hydropower plant h in the t th hour (m3/s), respectively;
discharge(m3/s) of hydropower plant h at the t th hour, respectively.
(2) Hydraulic connections between cascade reservoirs:
2.3.1. Objective function ∑( )
The objective of the optimization model is to maximize the total qih,t = QNh,t + qpu,t− dtu,h + qsu,t− dtu,h (19)
annual electricity generation of the RBCEC; the mathematical equation
u∈Uh

is as follow:
where QNh,t is the local natural inflow of hydropower plant h in the t th
∑
T ∑
H
( ) hour (m3/s); Uh denotes the set of upstream hydropower plants directly
maxE = phh,t + pwh,t + psh,t Δt (13) connected to the hydropower plant h; dtu,h is water transportation time
periods from hydropower plant u to h.
t=1 h=1

where t is the hour index, T the number of hours in a year, T = 8760, Δt (2) Reservoir storage volume constraints:
= 1 h; h is the index of the power plant; H is the number of hydropower min
Vh,t max
⩽vh,t ⩽Vh,t (20)
plants in the RBCEC; phh,t , pwh,t , and psh,t are the outputs of hydropower
plant h, wind power plant h, and solar power plant h in the t th hour min
where Vh,t max
and Vh,t are the minimal and maximal reservoir storage
respectively (MW); E is the total annual electricity generation of the
volumes of hydropower plant h in the t th hour, respectively (104m3).
RBCEC (MWh).
(3) Total discharge constraints:
(1) Hydropower generation model
QOmin max
h,t ⩽qph,t + qsh,t ⩽QOh,t (21)
The hydropower output can be expressed as a nonlinear function of
the turbine discharge and reservoir storage volume [41,42]; the non- where QOmin max
h,t and QOh,t are the minimal and maximal total discharges of
linear hydropower production function can be fitted with a two- hydropower plant h in the t th hour, respectively (m3/s).
variable quadratic polynomial based on the actual operating data
[43,44]: (4) Turbine discharge constraints:
( )
phh,t = fh vavg
h,t , qph,t (14) QPmin max
h,t ⩽qph,t ⩽QPh,t (22)

( )/
vavg
h,t = vh,t + vh,t− 1 2 (15) where QPmin max
h,t and QPh,t are the minimal and maximal turbine discharges
of hydropower plant h in the t th hour, respectively (m3/s).
avg
where vh,t is the average reservoir storage volume of hydropower plant h
in the t th hour (104 m3); vh,t is the reservoir storage volume of hydro­ (5) Power output constraints:
power plant h at the end of hour t (104 m3); qph,t is the turbine discharge min
PHh,t max
⩽phh,t ⩽PHh,t (23)
of hydropower plant h in the t th hour (m3/s).

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J. Zhang et al. Energy Conversion and Management 249 (2021) 114867

mission congestion. In this study, wind and solar power are prioritized
for accommodation.
⎧
⎪
⎪ cwind ⩽LCh
⎨ h
csolar
h ⩽LCh (25)
⎪
⎪
⎩ phh,t + pwh,t + psh,t ⩽LCh

where LCh is the maximal capacity of the existing transmission line

channel of hydropower plant h (MW).

2.3.3. Linearization method for hydropower production functions

The model is difficult to solve because of the nonlinear hydropower
production function. Based on the recently proposed PARallelogram
interpolation method [38], the linear programming formulations for the
nonlinear hydropower production function are proposed in this section.
Finally, the original nonlinear model was transformed into a linear
programming (LP) model which can be solved by the Gurobi solver
effectively. For convenience, take the function ph = f(vavg , qp) as an
Fig. 7. Example of 4 × 4 non-orthogonal meshes (m = 4, n = 4).
example below; In this method, the hydropower production function
will be discretized into a non-orthogonal mesh defined by parallelo­
where PHmin max
h,t , PHh,t are the minimal and maximal power outputs of grams ( QP
̂ m,n , V
̂ n ), as shown in Fig. 7; ( QP
̂ m,n , V
̂ n ) are sampling points; n
hydropower plant h in the t th hour, respectively (MW).
and m are indices n ∈ {1, 2, …, N}, m ∈ {1, 2, …, M}; PH ̂ m,n are the hy­
(6) Initial and terminal reservoir storage volume constraints:
{ dropower output with the ( QP m,n , Vn ) as input, PH m,n = f( V
̂ ̂ ̂ ̂ n , QP
̂ m,n );
vh,0 = Vhbeg V max min
and V are the minimal and maximal reservoir storage volumes,
(24)
vh,T = Vhend respectively; QPmax and QPmin are the minimal and maximal turbine
flow, respectively; ΔQP is the discrete gradient of the turbine flow on the
beg
where Vh and Vhend are the initial and terminal reservoir storage vol­ V axis, as shown in Fig. 7. All the previously presented parameters
avg
umes of hydropower plant h in the t th hour, respectively (104m3). represent are constants. vin and qpim,n are non-negative auxiliary var­
iables used by vavg and qp, respectively. Accordingly, the hydropower
3. Power transmission capacity constraints production function ph = f(vavg , qp) can be transformed into the
following linear constraints.
The follow equations set the upper limits for the capacity of wind and max
̂ n = V min + (n − 1) V − V min
solar power plants and the upper limits for the combined power output V , n ∈ {1, 2, …, N} (26)
N− 1
of hydro-wind-solar power planta respectively to prevent power trans­

Fig. 8. Location of the study area.

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J. Zhang et al. Energy Conversion and Management 249 (2021) 114867

Fig. 9. The operational performance of Beipan RBCEC in the PCM + PCDE mode. (a) presents the daily electricity generation of Beipan RBCEC in the whole year; (b)
and (c) show the hourly power output of hydro-wind-solar power in the week 6 and week 42 respectively.

⎧
QPmin
n = QPmin + ΔQP × (n − 1) (27) M− 1⎪
⎨̂
∑ PH m+1,1 − ̂
PH m,1
ph = ̂
PH 1,1 + ⋅qpim,1
QPmax
n = QPmax − ΔQP × (N − n) (28) ⎪ ̂ ̂
m ⎩ QP m+1,1 − QP m,1

max
− QPmin ⎡⎛ ⎞ ⎤⎫
̂ m,n = QPmin + (m − 1) QPn
QP n
, m ∈ {1, 2, …, M}, n ∈ {1, 2, …, N} ∑
N− 1 ̂ ̂ ̂ ̂
⎪
⎬
n
M− 1 PH
⎢⎜ m+1,n − PH m,n PH m+1,n− 1 − PH m,n− 1 ⎟ ⎥
+ ⎣⎝ − ⎠⋅qpim,n ⎦
(29) n=2
̂ m+1,n − QP
QP ̂ m,n QP ̂ m+1,n− 1 − QP
̂ m,n− 1 ⎪
⎭

∑
N− 1
⎛ ⎞
̂1 +
vavg ⩾ V viavg (30) ∑
N− 1 ̂ ̂
⎝ PH 1,n+1 − PH 1,n avg ⎠
n
n=1 + ⋅vin
n=1
̂ n+1 −
V ̂n
V
viavg ̂ ̂
1 ⩽V 2 − V 1 (31) (37)

̂ n+2 − V̂ n+1 avg

viavg
V
(32) 3. Case study
n+1 ⩽ ⋅vi , n ∈ {1, 2, …, N − 2}
̂ n+1 − V
V ̂n n
⎛ ⎞ 3.1. Study area
∑
M− 1 ∑
N− 1
⎜ QP ̂ 1,n
̂ 1,n+1 − QP ⎟
̂ 1,1 +
qp = QP qpim,1 + ⎝ avg
⋅vin ⎠ (33) The Beipan river basin (BRB) with abundant clean energy resources
̂ n+1 − V
V ̂n
m=1 n=1 is located in Guizhou Province of China. Four cascade hydropower
plants with a total installed capacity of 2663.5 MW have been built in
̂ m+1,1 − QP
qpim,1 ⩽ QP ̂ m,1 , m ∈ {1, 2, …, M − 1} (34) the main stream of the BRB, as shown in Fig. 8. The basic information of
the hydropower plants is presented in the Table A1. Moreover, the clean
̂ m+1,n+1 − QP
QP ̂ m,n+1 hydroelectricity of the BRB hydropower base is transmitted to the
qpim,n+1 ⩽ ⋅viavg
n ,m ∈ {1, 2, …, M − 1}, Guangdong province through the Xingan DC tie-line. The government is
̂ ̂
V n+1 − V n (35)
currently building the Beipan RBCEC by integrating utility-scale wind
n ∈ {1, 2, …, N − 2} and solar power into the BRB hydropower base; then, the wind and solar
power plants complementarily operating with the existing hydropower
qpim,n+1 ⩽qpim,n , m ∈ {1, 2, …, M − 1}, n ∈ {1, 2, …, N − 2} (36) plants serve as a hybrid power source to accomplish the complementary

9
J. Zhang et al. Energy Conversion and Management 249 (2021) 114867

Fig. 10. The operational performance of Beipan RBCEC in the PSM + PCDE mode. (a) presents the daily electricity generation of Beipan RBCEC in the whole year; (b)
and (c) show the hourly power output of hydro-wind-solar power and the peak-shaving performance in the typical week 8 and week 35 respectively.

generation scheme, whose electricity will be bundled together and

transmitted to the Guangdong power grid through the existing Xingan
DC tie-line. Therefore, in order to achieve the efficient utilization of the
clean energy resources and the full exploitation of hydropower flexi­
bility, we determine the effective complementary operation mode and
the corresponding optimal capacity configuration (integration poten­
tial) of new energy for the Beipan RBCEC with the method framework
proposed in this paper.

3.2. Input data

The basic information data of the hydropower plants, and the hourly
runoff data covering from 1980 to 2019 were collected from the Guizhou
Power Grid Company. After statistical analysis, the hourly runoff series
of a normal representative year (2017) is selected as the input data of the
model (First, the average annual runoff of the 40-year actual runoff data
set is calculated; then, the year with the smallest difference from the
average annual runoff is selected as the normal representative year Fig. 11. Water level process of GZ reservoir throughout the whole year.
(2017) to represent the universal scenario for the system operation). The
historical operating data in 2017 of the wind and solar power plants that
energy and the power generation results under the two modes can be
has been commissioned in the Beipan RBCEC was provided by the
calculated. In this section, based on the calculated results, the opera­
Guizhou Power Grid Company. The hourly load data series of the
tional performance of PCM + PCDE and PSMP + PCDE modes and their
receiving-end power grid in 2017 was provided by the China Southern
impacts on the operation of the hydropower plants are first analyzed
Power Grid Company.
(4.1.1); then, the effective complementary operation mode and the
Moreover, the original multi-period (8760) nonlinear model was
corresponding optimal capacity configuration of wind and solar power is
transformed into an LP model with the help of the linearization methods
determined for Beipan RBCEC (4.1.2).
presented in Section 2.3.3. The LP model was written with Pyomo in
Python3.6 and solved with Gurobi9.1. Finally, the model was imple­
4.1.1. Performance of the energy-power coupled complementary operation
mented on a laptop containing an Intel (R) Core (TM) i7-9750H CPU
modes
with 2.60 GHz and 16 GB RAM.
It is evident in Fig. 9 and Fig. 10 that the daily electricity generation
of new energy fluctuates sharply, especially in the dry season (Jan-May).
4. Results
Nevertheless, the energy-power coupled complementary operation
modes proposed in this paper can fully tap the hydropower flexibility to
4.1. Effective complementary operation mode and optimal capacity of
compensate for the high variability in new energy power generation.
new energy
Specifically, when Beipan RBCEC operates in the PCM + PCDE mode
(Fig. 9), hydropower plants can effectively smooth out the fluctuations
By plugging the two energy-power coupled complementary opera­
in both the daily electricity generation (for a week horizon) and the
tion modes (PCM + PCDE and PSMP + PCDE) in the proposed model
hourly output of new energy (for a day horizon). In the PSM + PCDE
framework respectively, the optimal capacity configuration of new

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J. Zhang et al. Energy Conversion and Management 249 (2021) 114867

Table 1 Table 3
Electricity generation results of GZ (MWh). Optimal capacity of new energy that can be integrated into each hydropower
Jan-May Jun-Sep Oct-Dec Annual
plant (MW).
hydropower plant PCM + PCDE PSM + PCDE
PSM + PCDE 679,068 1,203,107 428,631 2,310,806
PCM + PCDE 705,763 1,192,594 429,338 2,327,695 wind solar wind solar
Reference 652,320 1,271,087 429,492 2,352,899
SNP 18 13 184 0
GZ 0 100 97 900
MMW 0 286 64 14
Table 2 DQ 758 82 255 751
Total 776 481 600 1665
Annual electricity generation for PCM + PCDE and PSM + PCDE modes (MWh).
PCM + PCDE PSM + PCDE

Hydro 7,543,410 7,507,563 PCDE mode can fully tap the hydropower flexibility to compensate for
Wind 1,391,602 983,676 the high variability of new energy’s hourly power output (power) and
Solar 580,041 2,031,995 daily electricity generation (energy). However, in the two energy-power
Total 9,515,053 10,523,234 coupled complementary operation modes, the utilization level of clean
energy resources in Beipan RBCEC is different. Table 2 shows that the
mode (Fig. 10), the fluctuation of daily electricity generation of wind total annual electricity generation of Beipan RBCEC in the PSM + PCDE
and solar power plants can also be effectively mitigated by hydropower mode is 10,523,234 MWh, which is 10.6% higher than that in PCM +
plants; the hourly combined output of the Beipan RBCEC can also fully PCDE mode (9,515,053 MWh). Furthermore, compared with the PCM +
respond to the peak load demands of the receiving-end power grid; the PCDE mode, the PSM + PCDE mode can increase the new energy power
peak-valley difference of the residual load decreases by 29% on average, generation of Beipan RBCEC from 1,971,643 MWh to 3,015,671 MWh,
which will greatly relieve the peak regulation pressure on the receiving- representing an increase of 53.0%. This indicates that the PSM + PCDE
end power grid. The above results indicate that, in both the PCM + PCDE mode can achieve a higher utilization level of clean energy resources in
and PSM + PCDE mode, the flexible hydropower system can simulta­ the Beipan RBCEC compared with the PCM + PCDE mode. In terms of
neously compensate for the high variability of new energy’s hourly the operation of the controlling reservoir (GZ), the annual average
power output (power) and daily electricity generation (energy), which fluctuation range of the hourly forebay water level for GZ reservoir in
will reduce the need for system flexibility from the power supply side the PCM + PCDE and the PSM + PCDE are 0.016 m and 0.018 m
and promote the efficient accommodation of utility-scale new energy in respectively. This indicates that although the PSM + PCDE mode can
Beipan RBCEC. integrate more new energy than the PCM + PCDE mode, it will not cause
Additionally, the energy-power coupled complementary operation a significant increase in fluctuations the reservoir water level compared
modes will affect the long-term operation of the existing hydropower the PCM + PCDE mode.
stations. Because GZ reservoir is the controlling reservoir of the Beipan The above results indicate that PSM + PCDE mode can integrate
River cascade hydropower system, a comparative analysis of the long- more new energy resources than the PCM + PCDE mode; moreover, the
term operation of GZ hydropower plant is carried out. The reference more integration of new energy in the PSM + PCDE mode will not
water level of GZ reservoir in the Fig. 11 (black solid line) is calculated significantly deepen the impacts on the operation of the controlling
by an optimization model which does not consider new energy inte­ reservoir, compared with the PCM + PCDE mode. Therefore, it is rec­
gration and the complementary operation modes; the objective of the ommended that Beipan RBCEC adopt the PSM + PCDE mode. In this
optimization model is to only maximize the hydropower power gener­ case, the total optimal capacity of wind and solar power that can be
ation. In other words, the reference water level can achieve the integrated into the Beipan RBCEC are 600 MW and 1665 MW, respec­
maximum power generation of the hydropower system. As is indicated tively (Table 3); the capacity ratio of hydropower, wind power, and solar
in Fig. 11, during the dry season (Jan-May), the water levels corre­ power in Beipan RBCEC is 54.0%: 12.2%: 33.8%, accounting for 71.3%,
sponding to PSM + PCDE and PCM + PCDE modes are lower than the 9.4%, 19.3% of the total annual electricity generation.
reference water level and finally drop to the dead water level (691 m) at
the end of the dry season. By contrast, the lowest water level of the 4.2. Operation analysis of the clean energy corridor in different typical
reference process is 696.71 m, which is higher than the dead water level. years
Moreover, during the dry season (Jan-May), the hydropower generation
in PSM + PCDE and the PCM + PCDE modes is greater than the reference In this section, based on the effective energy-power coupled com­
value, as shown in Table 1. The above results indicate that in order to plementary operation mode (PSM + PCDE) and the corresponding
compensate the variability of wind and solar power generation, the large optimal capacity configuration of new energy determined in the section
hydropower station GZ will by discharge more water to increase the 4.1.2, the complementary operation of Beipan RBCEC in other three
electricity generation during the dry season. However, for the whole typical years is simulated under the condition of giving priority to the
year, the annual power generation of GZ in the PSM + PCDE and the accommodation of wind and solar power. The three typical years include
PCM + PCDE modes are 2,310,806 MWh and 2,327,695 MWh, respec­ the dry year (1989), normal year (2015), and wet year (1997), corre­
tively, which are less than the reference value of 2,352,899 MWh sponding to 90%, 60% and 10% of inflow frequencies respectively.
(Table 1). This is mainly because more water of GZ reservoir is dis­ Because the hourly output of the unit megawatt wind and solar power
charged for power generation during the dry season to compensate for plants in the three typical years is not available, we calculated the hourly
the variability of wind and solar power; then during the flood season output of new energy based on the physical models [45,46] with the
(Jun-Sep) with abundant water inflow, the reservoir water level of GZ hourly meteorological data (wind speed, the solar radiation intensity
hydropower plant in the PSM + PCDE and PCM + PCDE modes will be and environmental temperature) as input. The hourly meteorological
lower than the reference process (Fig. 11), resulting in a greater decrease data can be extracted from the ERA5 reanalysis dataset, created by the
of hydropower generation during the flood season (Table 1). ECMWF [47,48].

4.1.2. Effective complementary operation mode and optimal capacity of 4.2.1. Performance of the PSM + PCDE mode
new energy As is indicated in Fig. 12, although the power generation of new
The above results indicate that, both the PCM + PCDE and PSM + energy and the runoff are greatly different in the dry, normal, and wet

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J. Zhang et al. Energy Conversion and Management 249 (2021) 114867

Fig. 12. Operation results of Beipan RBCEC in different typical years.

Fig. 13. The water level processes of the GZ reservoir in the three typical years.

typical years, the hydropower system can effectively compensate for the
high variability in hourly power output and daily electricity generation
of new energy. Specifically, hydropower plants can effectively smooth
out the fluctuations in the daily electricity generation of new energy Fig. 14. Annual electricity generation of hydro/wind/solar in the three
every week (Fig. 12(a–c)); and the hourly combined output of the Beipan typical years.
RBCEC can fully respond to the peak load demands of the receiving-end
power grid (Fig. 12 (d–f)). This will greatly promote the large-scale to the different situations in the dry, normal, and wet typical years.
accommodation of utility-scale new energy. The results indicate that Additionally, Beipan RBCEC has the best peak-shaving performance
the operation mode and the corresponding optimal capacity configura­ in the dry year, with an average reduction of 29% in the peak-valley
tion of new energy determined in the section 4.1.2 can be well adapted difference of the residual load. However, in the wet year, the average

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J. Zhang et al. Energy Conversion and Management 249 (2021) 114867

inflow causes the reservoir water level to reach the upper limit prema­
turely; then, the regulation ability of hydropower plant will decrease,
thereby reducing the peak regulation performance.

4.2.2. Power generation of Beipan RBCEC in the three typical years

The annual total electricity generation of Beipan RBCEC in the dry,
normal, and wet typical years are 8,344,288 MWh, 10,902,323 MWh
and 13,631,624 MWh, respectively. The annual electricity generation of
Fig. 15. Annual spilled water in the three typical years. hydro/wind/solar is shown in the Fig. 14. The reference value (Black
dotted line) in the Fig. 14 is the theoretical maximum power generation
reduction of the load peak-valley difference is 23%, smaller than that in of hydropower which can be calculated with an optimization model; the
the dry year and the normal year (25%). The water level processes of the optimization model does not consider the new energy integration and
GZ reservoir in the three typical years are shown in the Fig. 13. In the dry the complementary operation modes, as mentioned in the Section 4.1.1.
year, the water level of GZ reservoir does not reach the upper and lower Fig. 14 shows that there is a certain degree of complementarity
limits throughout the whole year; the hydropower plant will have among the annual power generation of the hydropower and the new
enough reservoir regulation ability to compensate for the variability of energy in Beipan RBCEC; the larger the annual hydropower generation
new energy. Therefore, Beipan RBCEC has the best peak-shaving per­ is, the smaller the annual electricity generation of new energy will be,
formance in the dry year. By contrast, for the wet year, the excessive and vice versa. The complementarity of hydro-wind-solar electricity

Fig. 16. Daily electricity generation of Beipan RBCEC in the power-based complementary operation modes.

Fig. 17. Daily electricity demand of receiving-end power grid and daily electricity generation of Beipan RBCEC in two typical weeks; residual electricity demand is
equal to the daily electricity demand minus the daily electricity generation.

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J. Zhang et al. Energy Conversion and Management 249 (2021) 114867

Fig. 18. Sensitivity of the optimal integrated capacity of new energy to the expansion of the existing power transmission channels and the control index of the PSM
+ PCDE mode.

generation can help alleviate the transmission congestion for Beipan electricity demand falls (day 6 – day 7 in week 4 and 52), the daily
RBCEC; The simulated results show that the new energy curtailment electricity generation of Beipan RBCEC increases; when the daily elec­
caused by the transmission congestion in the dry, normal, and wet tricity demand rises (day 1 – day 2 in week 52), the daily electricity
typical years are only 60 MWh, 141 MWh and 49 MWh, respectively, generation of Beipan RBCEC decreases; the reverse fluctuation between
which is a satisfactory result. the daily electricity generation and electricity demand in the PSM mode
Fig. 14 also shows that the deviation of the annual hydropower will aggravate the fluctuations in the residual electricity demand
generation (blue solid line) from its reference value (black dotted line) (Fig. 17), which will increase the regulation pressure on the receiving-
increases with the annual inflow. Compared with the reference value, end power grid in terms of restoring the daily energy balance between
the annual hydropower generation is reduced by 0.03%, 0.59% and supply and demand.
7.37% respectively in dry year, normal year, and wet year. This indicates More importantly, the receiving-end power grid (Guangdong power
that compensating for the wind and solar power will cause hydropower grid) of Beipan RBCEC is vigorously developing new energy industry to
system loss more energy in the wet year. As already mentioned in the alleviate the power shortage and optimize the energy mix; Guangdong
Section 4.2.1, excessive inflow in the wet year will decrease the power grid with increasing shares of new energy requires more flexi­
reservoir-storage regulation ability of the hydropower plants; the inte­ bility to balance electricity supply and demand at different timescales.
gration of new energy will also put additional regulation pressure on the The above results show that, in the power-based complementary oper­
hydropower system; finally, the wet year will see much more spilled ation modes, the daily electric energy transmitted from Guizhou Beipan
water (Fig. 15) and energy loss of the hydropower, compared with the RBCEC fluctuates sharply, which will exert serious impacts on the daily
dry and normal years. energy balance between supply and demand in Guangdong power grid
and limit the large-scale and safe accommodation of new energy. By
contrast, the energy-power coupled complementary operation modes
4.3. Comparative analysis of the simulated results for different operation can fully tap the hydropower flexibility to compensate for the high
modes variability in both power output and daily electricity generation of wind
and solar energy (Fig. 9 and Fig. 10); this will facilitate the effective
In this section, the operational performances of power-based com­ accommodation of utility-scale new energy in Beipan RBCEC.
plementary operation modes (PCM and PSM) and the energy-power
coupled complementary operation modes are compared and analyzed.
As mentioned in the Section 1.2, increasing the share of new energy in 4.4. Sensitivity analysis
the power systems poses a challenge in terms of the variability in both
the power output (MW) and the daily electricity generation (MWh). As As indicated in the Section 4.1.2, it’s suggested that Beipan RBCEC
shown in the Fig. 16, the daily electricity generation fluctuates sharply adopts the PSM + PCDE mode, which can achieve more new energy
in the power-based complementary operation modes (PCM and PSM) integration. In this section, the sensitivities of the optimal capacity of
throughout the whole year. new energy to some key factors are analyzed, including: (i) the capacity
The weekly maximum fluctuation range (WMFR) and weekly expansion rate (CER) of the existing power transmission channels; (ii)
average volatility (WAV) are selected as the fluctuation indexes of daily the control index value for the PSM + PCDE mode (MAFR: the maximum
electricity generation. Overall, the annual average (maximal) WMFR allowable fluctuation range of daily electricity generation for a week
and WAV reach 10,292 MWh (23,178 MWh) and 14% (34%) respec­ horizon, MWh). The results of PSM + PCDE in the Section 4.1.2 are set as
tively in the PSM mode, and in the PCM mode, they increase to 19,117 the base case. The influence of expanding the power transmission
MWh (45750 MWh) and 28% (84%), respectively. By contrast, in the channel and changing the control index of the PSM + PCDE mode on the
energy-power coupled complementary operation modes (PSM + PCDE integrational potential of new energy is shown in Fig. 18.
and PCM + PCDE), Beipan RBCEC can provide constant daily electricity Obviously, expanding the power transmission channel of Beipan
generation to the receiving-end power grid every week, that is, WMFR RBCEC and relaxing the index requirements of the PSM + PCDE mode (i.
and WAV are 0 MWh and 0% respectively Fig. 9 and Fig. 10. e., increasing the MAFR) will increase the optimal capacity of new en­
Moreover, Fig. 17 shows the daily electricity demand of receiving- ergy that can be integrated into the existing hydropower system, as
end power grid and daily electricity generation of Beipan RBCEC in shown in the CER-MAFR-sensitive zone of the Fig. 18. Furthermore,
the PSM and PSM + PCDE modes for two typical weeks (week 4 and when the CER is greater than 50%, the optimal capacity of new energy
week 52). As indicated in the Fig. 17, Beipan RBCEC can provide con­ will not change significantly with the expansion of power transmission
stant daily electricity generation throughout the week in the energy- channels; however, once the MAFR is increased at this time, the optimal
power coupled mode of PSM + PCDE, which will not put additional integrated capacity of new energy is still going to increase, as shown in
daily electricity regulation pressure on the receiving-end power grid. the MAFR-sensitive zone of the Fig. 18. Note that 50% is a rough cut-off
However, in the power-based PSM mode, the daily electric energy point, because the CFR change step for the sensitivity analysis in this
transmitted from Beipan RBCEC fluctuates sharply; when the daily paper is set at 10%.

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J. Zhang et al. Energy Conversion and Management 249 (2021) 114867

Some scholars have also analyzed the sensitivity of optimal capacity (1) Based on the comparative analysis of the calculated results in
of new energy that can be integrated into the hydro-wind-solar hybrid different modes, it is recommended that Beipan RBCEC adopt the
system to the installed capacity of the hydropower plant and the reser­ PSM + PCDE mode. The PSM + PCDE mode will increase the
voir storage; the results showed that the larger the installed capacity or annual wind and solar power generation by 53.0% and the annual
the reservoir storage is, the larger the optimal integrated capacity of new power generation of Beipan RBCEC by 10.6%, compared with the
energy will be [25,27]. PCM + PCDE mode. Correspondingly, in the PSM + PCDE mode
Based on the sensitivity analysis, it can be indicated that the actual and under the support of the existing power transmission chan­
integration potential of new energy in the RBCEC can be comprehen­ nels and the flexibility of hydropower plants, the optimal ca­
sively influenced by (i) the installed capacity of the hydropower plant, pacity of wind and solar power that can be integrated into the
(ii) the reservoir storage, (iii) the complementary operation modes, and Beipan RBCEC are 600 MW and 1665 MW, respectively.
(iv) the maximal capacity of power transmission channels. Furthermore, (2) Integrating new energy into the existing hydropower system will
the theoretical maximal integration potential of new energy will be change the inter-seasonal distribution of water and electricity of
affected by the first three factors; the actual deployment level of the the hydropower stations. During the dry season, the hydropower
theoretical maximum integration potential will be affected by the reservoirs will release more water to increase the hydropower
maximal capacity of power transmission channels. generation to compensate for the high variability of new energy,
which will result in a lower water level at the end of the dry
5. Discussion season; then, during the flood season with abundant inflow, the
hydropower plants will have a lower water head, thereby
In this section, several points for further improving the model are reducing the hydropower generation in the flood season.
discussed. (3) The effective operation mode and the corresponding optimal
First, like the previous studies [27,29,36], we constructed the model capacity configuration of new energy determined by the pro­
with the objective of maximizing the electricity generation of the clean posed method for Beipan RBCEC can be well adapted to the
energy. However, the economic feasibility of the deployment solution different situations in the dry, normal, and wet typical years.
for new energy is also important. Owing to the market price fluctuations Moreover, the ability of hydropower to compensate variable new
of wind turbines and PV panels and the changes in the governmental energy will be affected by runoff. Compared with the dry and
subsidy policy for renewable energy prices, determining reasonable normal years, the excessive inflow in the wet year will cause the
benefits and cost parameters can be challenging. Therefore, the pro­ reservoir water level to reach the upper limit prematurely, and
posed model can be extended with reliable economic indicators for this will decrease the reservoir-storage regulation ability of the
optimized results with technical and economic advantages. hydropower stations; as a result, wet year will see a decline in the
Second, because the currently highest temporal resolution data performance of the complementary operation mode and an in­
provided by power grid companies is hourly data, we built the optimi­ crease in the hydropower energy loss.
zation model at hourly resolution for an entire year in this paper. (4) The daily electricity generation fluctuates sharply in the power-
However, once sub-hour or minute resolution data become available, based complementary operation modes, especially during the
the optimization model can be easily combined with these data to obtain dry seasons, which will aggravate the fluctuations in the residual
more reliable results [32]. daily electricity demand of the receiving-end power grid. By
Third, the integration potential of wind and solar power into a river contrast, Beipan RBCEC can provide constant daily electricity
basin clean energy corridor can be improved by coupling the existing generation every week in the energy-power coupled mode, which
cascade hydropower plants with other flexibility improvement mea­ will facilitate the efficient cross-reginal accommodation of utility-
sures, such as hydropower expansion [27], hydrogen production inte­ scale new energy in the RBCEC.
gration [49] or the construction of seasonal pumped hydropower (5) The actual potential of new energy integration into the existing
storage [50]. The proposed optimization model can be readily coupled hydropower plants can be influenced by many factors. The
with the above different component models to select the optimal flexi­ theoretical maximal integration potential of new energy will be
bility improvement measure for river basin clean energy corridors. affected by the installed hydropower capacity, reservoir storage,
Fourth, according to different situations, more energy-power and complementary operation modes; however, the actual
coupled complementary operation modes can be established and inte­ deployment level of the theoretical maximum integration po­
grated into the proposed method framework with pluggability in this tential will be affected by the maximal capacity of power trans­
paper. mission channels.

6. Conclusions The results and methods in this paper may provide a valuable tech­
nical approach for determining the effective complementary operation
In the context of carbon peak and carbon neutrality, integrating wind mode and the optimal capacity configuration of wind and solar power
and solar power into the existing large hydropower base to build the for large-scale hydro-wind-solar clean energy bases. Future work will
RBCEC is a promising way to reduce the demand for system flexibility in focus on the methods of remolding the functions of cascade hydropower
the power grids and promote the effective accommodation of utility- systems to fully tap and improve hydropower flexibility.
scale wind and solar power. This paper proposes for the first time a
universal method framework to determine the effective energy-power Declaration of Competing Interest
coupled complementary operation mode and the corresponding inte­
gration potential of new energy for RBCECs. The Beipan RBCEC under The authors declare that they have no known competing financial
construction in Guizhou province, China, is selected as a case study to interests or personal relationships that could have appeared to influence
verify the performance of the proposed method. Several primary con­ the work reported in this paper.
clusions can be drawn from this study:

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Acknowledgement case study of the world’s largest hydro-photovoltaic plant. Energy Converse
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The work was supported by the National Natural Science Foundation of hybrid renewable energy systems. Energy Convers Manage. 2019;199:112027.
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Table A1
Main basic characteristics of cascade hydropower plants of Beipan river basin.
Hydropower Installed capacity Normal water level Dead water level Reservoir characteristics Transmission Capacity of existing lines
plant (MW) (m) (m) (MW)

SNP 185.5 885 865 Daily regulation 190

GZ 1040 745 691 Incomplete multi-year 1040
regulation
MMY 558 585 580 Daily regulation 560
DQ 880 490 483 Daily regulation 880

photovoltaic for rural areas: A case study in Yogyakarta. Indonesia. Energy Rep.
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