Energy and Power Engineering, 2013, 5, 46-51
doi:10.4236/epe.2013.53B010 Published Online May 2013 (http://www.scirp.org/journal/epe)
Equivalent Substitution Based Method for Calculation of
Best Installed Capacity of Pumped Storage Power Station
Jinming Li, Tao Yu, Huaizhi Wang
College of Electric Power, South China University of Technology, Guangzhou, Guangdong Province, China
Received 2013
ABSTRACT
This paper proposes a novel method to calculate the best installed capacity of pumped storage power station. First, we
choose the day with maximum load as the typical day for every month and simulate the system running in two cases of
whether the pumped storage power station is put into operation. The difference of the total coal consumption between
the two cases is the peak load shifting benefit. Furthermore, we build load model and power generation model to calcu-
late the benefit of emergency use and frequency modulation, which are the major projects of dynamic benefits. At last,
on the premise of ensuring the system requirements, the developed method employs the maximum benefit of the unit
capacity as the objective function to get the best installed capacity of pumped storage power station by simulations.
Tests on a provincial power grid have shown that the developed method which combines of load characteristics, electric
structure and other factors can get the best installed capacity of pumped storage power station easily and has a certain
guiding significance for the planning and construction of the pumped storage power station.
Keywords: Static Benefits; Dynamic Benefits; Pumped Storage Power Station; Best Installed Capacity
1. Introduction
With the sustainable and rapid development of china
economy, the electric power demand is also increasing
rapidly, which make the fluctuation of load and peak
valley load increasing year by year. Thermal power
plants are the major producer of electricity in China，but
the output regulating scope of most thermal power plants
is less than 50% and cannot meet the demand of the load
variation. The pumped storage power station is built to
solve this problem. When the power system is in low
load condition, the pumped storage units begin pumping
water from the reservoir in downriver to the reservoir in
upstream and release the water when the load begin to
increase, in this time ,the pumped storage units work in
the condition of generating[1,2 ]. In this way, the pumped
storage units can store energy. The pumped storage power
station is not affected by factors such as fuel, flood etc.,
and the regulating scope of pumped storage units is the
double of its rating [3,4]. At this point, pumped storage
units show great superiority comparing with other normal
power supplies. Therefore, in the region with greatly
fluctuating load but lacking of shift peak load capacity,
building pumped storage power station is the best meas-
ure to mitigate the difficulty of peak regulation and lack
of peak power.
In addition, pumped storage power station has good
dynamic function, such as frequency modulation, phase
modulation, spare, black start etc., which make it be a very
effective tool and mean to ensure the security, economy
and stability of power grid.
It involves many factors to determine the reasonable
proportion of pumped stor age power station in the power
system, including the current situation of energy develop-
ment and utilization, the electric structure, the distribution
of power station, the load characteristic, the pumping
power that power system can provide, the development
condition and the investment and operation cost of all
kinds of power plant. This paper employs the maximum
benefit of the unit capacity as the objective function to
get the best installed capacity of pumped storage power
station by simulations [5]. Tests on a provincial power
grid have shown the effectiveness of the method.
2. Static Benefits
The static benefits of pumped storage power station con-
tain two parts, the one is cap acity benefit and the othe r is
shift peak and valley benefits. Pumped storage power
station can undertake th e work of system working capac-
ity and spare capacity effectively, which can reduce the
installed capacity of thermal power station and save sys-
tem investment and operation cost. The resulting eco-
nomic benefits are called capacity benefits. After the
pumped storage power station is put into operation, the
system fuel consumption will increase due to the pump-

J. M. LI ET AL. 47
ing power of the pumped storage units. On the other hand,
because the pumped storage units can replace thermal
power unit to be the variable load plant and improve the
operating conditions of thermal power unit. In this way,
it can reduce the auxiliary power rate and the coal con-
sumption rate of the thermal power unit, the difference
value between the two cases is the pumped storage power
station's shift peak and valley benefits. The calcu lation of
capacity benefit calculation is relatively simple, but cal-
culating shift peak and valley benefits is a complicated
problem which involves many factors.
In this paper, we choose the day with maximum load
as the typical day for every month and simulate the sys-
tem running in two cases of whether the pumped storage
power station is put into operation. The forecast of
pumped storage power station 24 point output curve in
the typical day bases on the data of historical average,
and in consideration of the development of installed ca-
pacity and load level, we revise the curve proportion ally.
The 24 point output curve of power from other areas de-
pends on the fixed power energy of the agreement. Spe-
cific steps to calculate the Static benefits are shown as
follows:
1) Determine the output curve of the other units in the
area except pumped storage unit. With the considering o f
load and emergency reserves, deduct pumped storage
power station output and power from other areas from
the load curve in the typical day (when the pumped stor-
age power station is on pumping state, its output is a
negative value).
2) Sort the units in the power grid. According to the
principle of energy-saving power generation dispatching,
clean energy unit such as hydropower unit, nuclear reac-
tors are arranged to put into operation first, and how to
decide the priorities of thermal power units depend on
the unit coal consumption rate.
3) Unit Commitment (UC). The priority listin g method
is used to solve the UC problem. The method initially
arranges the generating units based on lowest operational
cost characteristics. The predetermined order is then used
for UC such that the system load is satisfied [6,7].
4) Calculate shift peak and valley benefits of pumped
storage power station. Add the coal consumption of all
units in two cases respectively to get the total coal con-
sumption of the system, then we can obtain the shift peak
and valley benefits in the typical day by calculating the
difference between the two cases. So it is easy to figure
up the shift peak and valley benefits for month and year
with monthly unbalanced coefficient and seasonal un-
balanced coefficient.
3. Dynamic Benefits
Dynamic benefits of pumped storage unit include several
aspects, and in the simulation of system operation, they
are related to each other. At present, quantitative evalua-
tion algorithms for dynamic benefits usually adopt partial
summation model method; its main idea is dividing
pumped storage power station capacity into several parts
according to the function it undertakes. Then put forward
quantitative calculation formula for every part respec-
tively, and calculate the dynamic benefit, the total dy-
namic benefit of pumped storage power station is the
sum of all parts [8].
This paper adopts equivalent replacement method that
is widely used in the engineering economics. The first
step is calculating the basic program, namely studying
the system reliability index and annual cost when the
studied station provides dynamic benefit service; The
second step consider alternative program, namely calcu-
lating the annual co st that is needed to keep the reliability
index being same with the basic program when the stud-
ied station doesn’t provide dynamic benefit service.
Comparing with th e basic program, the excess part of the
annual cost in alternative program is the benefit annual
value. This paper focuses on two important items in dy-
namic benefit: emergency reserves benefit and frequency
modulat i on benefit.
3.1. Emergency Reserves Benefit
Starting with the overall system, this paper builds a pumped
storage power station accident emergency reserves benefit
evaluation model to analysis emergency reserves benefit
of pumped storage unit by dynamic simulating of system
accident pattern analysis and accident reflection of all
kinds of units after in the process of system accident. The
emergency reserves benefit evaluation model includes
two child models, the one is load model and the other is
the power generation model.
Load model. The load model is based on historical load
data of power system and the development of social eco-
nomic characteristics in the future. The load mode con-
sists of three parts: the annu al peak load, the annual load
curve, the typical daily load curve. The load on the ith
moment in the typical day can be calculated as follow:
max m
=
mt hmt
LL LL

 (1)
where max is the annual peak load, m and hmt are
the annual load curve (seasonal unbalanced coefficient)
and the typical daily load curve, respectively.
LL L
Power generation model. Power generation model in-
cludes the analysis of system accident pattern and unit
response capability model. For simplicity, we count the
amount of power failure which need the pumped storage
unit response quickly and employ a quadratic fitting
method to evaluate the emergency capacity and accident
probability over the years. In addition, we assume that
load regulation speed of thermal power plants and gas-
powered plants are 2% and 7% of its rated capacity per

J. M. LI ET AL.
48
random fluctuations of load into the model. Take the
China Southern Grid as an example, the load fluctuate
about 150MW when the frequency fluctuate 0.03 Hz. For
simplicity, we assume that the typical daily load fluctua-
tion meet the standard normal distribution, so the prob-
ability of load fluctuation within 150MW can be calcu-
lated as
 (2) = 0.9772. Probability of load fluctuation
amplitude is shown in Figure 2.
minute, respectively. Then remove the capacity of full
load units from total unit-operating capacity of system
and the remaining capacity is the resp on se capacity in th e
system.
This paper adopt the lacking electricity caused by ac-
cident in the year as the reliability index and the flow-
chart of the method for emergency reserves benefit evalua-
tion is depicted in Figure 1, where

and 0

are reli-
able index of alternative program and basic program.
3.2. Frequency Modulation Benefit
Frequency modulation benefit consists of load reserve
benefit and load tracking benefit. According to the re-
search achievement of Prof. A. Ferreira from Electrical
Power Research Institute of America, load reserve bene-
fit and load tracking benefit are approximately the same,
so this paper only calculate load reserve benefit and Fre-
quency modulation benefit is double of load reserve
benefit.
The basic evaluation process of Frequency modulation
benefit is similar to that of emergency reserves benefit,
the only one difference between them is the load model
and power generation model they adopt. Load reserve
capacity adjustment of Pumped storage power station is
usually due to the imbalance of system instant power
caused by unscheduled increasing load and random fluc-
tuations of load. Hence, it is necessary to do a detailed
simulation analysis of random fluctuations of load when
evaluate the load reserve benefit.
The load model in the evaluation of load reserve bene-
fit is a 24-point typical daily load curve. On that basis,
then add short-term unscheduled increasing load and Figure 1. Flowchart of emergency reserves benefit evaluation.
2
()
15

6
()
15
10 ()
15
14 ()
15
18 ()
15

22
()
15

26
()
15

(2)

2
()
15


6
()
15


10
()
15


14
()
15


18
()
15


22
()
15


26
()
15


(2)
Figure 2. Flowchart of Probability of load fluctuation amplitude.

J. M. LI ET AL. 49
On the promise that pumped storage power station
have enough capacity to undertake the task of shift peak
and valley and emergency reserve, pumped storage units
make use of spare capacity and the remaining power for
emergency reserve to provide load reserve to system.
During low load period, pumped storage units work as a
water pump and it wi ll increase the load o f system. In this
state, it can’t be frequency modulation unit and frequency
modulation is undertaken squarely by other kinds of units,
these would often be thermal power unit. Therefore, the
evaluation of load reserve benefit should be divided into
rest time and power generation time.
The flowchart of the method for frequency modulation
benefit evaluation is depicted in Figure 3, wher e

and
0

are reliable index of alternative program and basic
program.
4. Example Analysis
Increase the installed capacity of pumped storage power
station according to the unit capacity of pumped storage
unit in studied area in the case that load characteristic is
known. Then evaluate the total benefit of every scheme,
respectively. The capacity that correspond maximum
benefit of unit capacity would be the best installed ca-
pacity of pumped storage power station. For simplified
calculation, we assume that pumped storage units make
full use of their capacity. Thus, in the premise of satisfy-
ing the requirement of dynamic task, including emer-
gency reserve, load reserve, load tracking etc., all of the
Figure 3. Flowchart of Freque ncy modulati on benefit evalua-
tion.
remain capacity is put into pumping during low load pe-
riod, and output in peak time is set be 75 percent of the
pumping power in valley time [9].
In order to test the algorithm, summer and winter
typical day of a provincial power grid in normal rainfall
year day are selected to be the research subjects. Every
planning scheme with different installed capacity is
simulated detailed Based on the present status of power
system, the main principles for the test is:
1) Basing on the installed capacity of every kind of
power sets and the historical d ata of th eir output per year,
the result of simulation for units except pumped storage
units should be consistent with realities as far as possible.
2) The electric structure of this power grid is relatively
complex, and all of the factors should be considered, in-
cluding nuclear power, thermal power, hydropower, pneu-
moelectric and power from other areas.
3) The main power sources for peaking in the simula-
tion are thermal power and pneumoelectric. In order to
reduce wasted water for peak modulation, hydropower
doesn’t join peak-regulation in the summer and peak-
shaving depth in the winter is set to be 50%. Moreover,
nuclear power doesn’t join peak-regulation all over the
year.
4) The alternative power is thermal power when the
pumped storage power station is removed from power sys-
tem. All benefits are converted into standard coal equiva-
lent.
The max imum load, mi nimum load and peak-vale dif-
ference are shown in Table 1. The load curves of sum-
mer typical day and winter typical day are given in Fig-
ure 4.
Table1. Load of two typical day load curves (MW).
Typical
day Maximum Load Minimum Load peak-vale difference
Summer 87000 43514 43486
Winter 25800 14500 11300
048 1216 20 24
0
2
4
6
8x 104
Time (h)
Load (MW)
Winter
Summer
Figure 4. Load curves of summer typical day and winter
typical day.

J. M. LI ET AL.
50
The operation period of pumped storage power station
is set to be 50 years. Investment of pumped storage unit
is 3500yuan per capacity. The annual operation cost is
0.5 percent of investment expenses. Spinning reserve of
system is 4.2 percent of maximum load [10]. One part of
it is emergency reserve which is about 3 percent of maxi-
mum load and the remaining capacity is load reserve
which is about 1.2 percent of maximum load. Prices of
standard coal and nature gas are 900 yuan per ton, 3yuan
per cubic meter, respectively.
Simulation results for different installed capacity of
umped storage power station are shown in Table 2. The
comparison of annual total cost, fuel cost, annual fixed
running cost between alternative program and basic pro-
gram is given in Figure 5. The results of this experiment
lead to several conclusions:
1) There is a linear relationship between fixed running
cost and installed capacity of pumped storage power sta-
tion, as well as investment annual value and installed
capacity of pumped storage power station. The variable
running cost show little changes with the increase of in-
stalled capacity of pumped storage power station. So it
can be ignored compared with fixed running cost and
investment annual value.
Table 2. Simulation results for different installed capacity.
Installed
capacity Investment annual value Fixed running cost Variable running costCoal consumption Load rate of thermal plantGas consumption Annual fuel costs Total benefit
MW Million yuan Million yuan Million yuanMillion ton -- Billion cubic
meter Billion yuan Million yuan
0 0 0 0 58.40 62.50% 3.51 63.00 0
4200 294 90.3 2.3 57.50 67.30% 3.51 62.17 831
4800 354 103.2 2.6 57.35 68.00% 3.51 62.03 969
5400 414 116.1 3 57.19 69.20% 3.51 61.89 1117
6000 474 129 3.3 57.02 70.50% 3.51 61.72 1279
6600 534 141.9 3.6 56.82 71.90% 3.51 61.54 1464
7200 594 154.8 3.9 56.66 74.30% 3.51 61.40 1608
7800 654 167.7 4.3 56.56 75.40% 3.51 61.31 1696
8400 714 180.6 4.6 56.51 76.60% 3.51 61.24 1763
9000 774 193.5 4.9 56.42 77.60% 3.51 61.18 1822
9600 834 206.4 5.2 56.38 78.40% 3.51 61.13 1875
10200 894 219.3 5.6 56.33 79.20% 3.51 61.08 1922
10800 954 232.2 5.9 56.29 79.70% 3.51 61.05 1958
11400 1014 245.1 6.2 56.26 79.90% 3.51 61.01 1994
12000 1074 258 6.6 56.23 80.10% 3.51 60.98 2023
12600 1134 270.9 6.9 56.19 80.20% 3.51 60.95 2051
13200 1194 283.8 7.2 56.17 80.20% 3.51 60.93 2075
0200040006000800010000 12000 14000
0
500
1000
1500
2000
2500
Instal l ed capacity(MW)
Co st(million y uan )
Investment annual value
Fixed running cost
Variable running cost
Total benefit
Figure 5. Cost comparison between alternative program and basic program.

J. M. LI ET AL. 51
2) When installed capacity of pumped storage power
station is less than 7200 MW, the benefits are obvious.
The benefit will increase about 166.7 thousand tons of
standard coal for every 600MW increase, about 150 mil-
lion yuan when converted into economic benefit. The
growth begins lower with the increase of installed capac-
ity of pumped storage power station. When installed ca-
pacity is in the scope of 7200 MW to 9600 MW, the
benefit will increase about 88.9 thousand tons of standard
coal for every 600 MW increase, about 80 million yuan
when converted into economic benefit. The benefit will
be very low when the installed capacity continues to in-
crease for there is only 24.4 thousand tons of standard
coal increase for every 600 MW increases, about 22 mil-
lion yuan when converted into economic benefit.
3) When the growth of benefit is higher than that of
annual running cost (less than 7200 MW), we can in-
crease the installed capacity appropriately. And with the
increase of installed capacity of pumped storage power
station, growth of benefit slows significantly. Therefore,
it can be concluded that the best installed capacity of
pumped storage power station is 7200 MW.
5. Conclusions
The rapid development of economy exacerbates the power
peaking contradiction. Power programming should adjust
in time as the load ch ang es. So how to determine th e best
installed capacity become more and more important to
power system. This paper choose the day with maximum
load as the typical day for every month and simulate the
system running in two cases of whether the pumped
storage power station is put into operation. Then build
load model and power generation model to calculate the
benefit of emergency use and frequency modulation,
which are the major projects of dynamic benefits. The
developed method employs the maximum benefit of the
unit capacity as the objective function to get the best in-
stalled capacity of pumped storage power station by
simulations. Tests on a provincial power grid have shown
that the developed method has a meaningful guideline in
practice.
REFERENCES
[1] H. L. Zhang, D. M. Xie, J. Y. Liu, et al., “Optimized
Control of the Startup and Shutdown of Peaking Units,”
Journal of Engineering for Thermal Energy and Power,
Vol. 20, No. 5, 2005, pp. 300-303.
[2] X. M. Yu, X. G. Xiong, Y. W. Wu, et al., “Discussion on
Optimal Mode for Peaking Units Expansion Planning and
Its Application,” Electric Power, Vol. 36, No.1, 2003, pp.
48-51.
[3] J. Barton and D. Infield, “Energy Storage and Its Use
with Intermittent Renewable Energy,” IEEE Transaction.
Energy Conversion, Vol. 19, No. 2, 2004, pp. 441-448.
doi：10.1109/TEC.2003.822305
[4] W. Leonhard and E. Grobe, “Sustainable Electrical En-
ergy Supply with Wind and Pumped Storage: A Realistic
long-term Strategy or Utopia,” Proceedings IEEE Power
Engineering Society General Meeting, 2004, pp. 1221-
1225.
[5] Anonymous, “Pumped-storage Project Updates,” Interna-
tional Journal of Hydropower Dams, Vol. 9, No. 5, 2002,
pp. 104-109.
[6] R. M. Burns and C. A. Gibson, “Optimization of Priority
Lists for a Unit Commitment Program,” in Proceeding
IEEE Power Engineering Society Summer Meeting, 1975.
[7] Narayana Prasad Padhy, “Unit Commitment—A Biblio-
graphical Survey,” IEEE Transaction Power System, Vol.
19, No. 2, 2004, pp. 1196-1205.
doi:10.1109/TPWRS.2003.821611
[8] H. K. Song, Y. D. Tang, G. Q. Tang, et al., “Analy-
sis of Power Generation Enterprise Bidding Strategies
Considering Demand Side Bidding,” Electric Power
Automation Equipment, Vol. 27, No. 6, 2007, pp. 47-50.
[9] K. Aoki, M. Itoh, K. Nara. and M. Kanezashi, “Optimal
Long-term Unit Commitment In Large Scale Systems In-
cluding Fuel Constrained Thermal And Pumped Storage
Hydro,” IEEE Transaction Power System, Vol. 4, No. 3,
1989, pp.1065-1073. doi:10.1109/59.32600
[10] K. Aoki, M. Itoh, T. Satoh, et al., “Optimal Long-term
Unit Commitment in Large Scale Systems Including Fuel
Constrained Thermal and Pumped-storage Hydro,” IEEE
Transaction on Power Systems, Vol. 4, No. 3, 1989, pp.
1065-1073. doi:10.1109/59.32600