Energy and Power Engineering, 2013, 5, 1011-1015
doi:10.4236/epe.2013.54B193 Published Online July 2013 (
Optimal Spinning Reserve for Power System with Wind
Longlong Li, Dongmei Zhao
School of Electrical and Electronic Engineering, North China Electric Power University, Beijing, China
Received March, 2013
This paper presents an evolutionary stochastic production simulation to solve the optimal spinning reserve configuration
problem in power system with wind integrated. Equivalent load curve is generated with considering the wind power
forecasting deviation and generation scheduling of hydropower plant in different water periods. The equivalent load
duration curve (ELDC), redrawn from equivalent load curve is the core of stochastic production simulation which fo-
cuses on random outage of generator and load fluc tuation. The optimal spin ning reserve model is estab lished ar ound the
reliability index Expected Energy Not Served (ENNS). The optimal scheduling of spinning reserve is reached while the
cost of purchasing spinning reserve is equal to the outage loss. At last, results of the optimal spinning reserve model
tested in Hainan power grid help redu ce the costs of spinning reserve configuration.
Keywords: Spinning Reserve; Wind Farm; Stochastic Production Simulation
1. Introduction
With the rapid development of the domestic wind power
in recent years, the installed capacity of China's wind
power had reached 62.364 GW, accounting for 1/4 of the
world's installed capacity, and China had occupied the
most wind power status of the world [1]. Due to the ran-
domness and intermittency of wind power, random out-
age of generator and load fluctuation, grid must be in-
stalled with certain operating reserve capacity.
Power system must configure some additional spin-
ning reserve to compensate the fluctuation of w ind pow er.
The system reserve can be divided into primary reserve
(instantaneous reserve), secondary reserve (spinning re-
serve) and third reserve (long-term reserve) in [2-4]. [5-6]
analyze the impacts of large-scale wind farm integrated
on power system peaking regulation by simulating the
annual timing load curve and wind power output. [7-8]
present a definition and computation approach for costs
analysis of spinning reserve and benefit assessment. But
its study objects contain only conventional units. Con-
sidering load forecasting error and wind power output
deviation, [9] establishes a model for determining reserve
capacity requirement.
This paper establishes the model for determining the
optimal spinning reserve by analyzing the deviation of
wind power prediction and the operation of hydropower
in different water periods, and using the stochastic pro-
duction simulation technology considering random out-
age of generator and load fluctuation. Finally, give an
example to verify the feasibility of this method.
2. Wind Power Forecasting
There is a direct relationship between output power and
wind speed of wind turbines, so power prediction prob-
lem can be transformed into the wind speed prediction
problem. First of all, smooth the historical observation
data of wind speed to establish the time series ARMA (p,
q) model [10], and get the wind speed forecasting model
after model identification, setting order and parameter
estimation. The general relationship between wind power
and wind speed is like this:
33 33
cut incut out
wcut in
ncutin ncutin
vv orvv
vv vv
The prediction deviation is inevitable. Wind power
forecast deviation is approximately in line with the nor-
mal distribution. Through the statistical history predic-
tion deviation da ta of wind power, calculate the mean
and variance 2
of deviation data, which can establish
*The National High Technology Research and Development of China
863 Program (2012AA050201).
Copyright © 2013 SciRes. EPE
L. L. LI, D. M. ZHAO
the probability dens ity function of wind power prediction
deviation. Draw wind power output belt considering pre-
diction devi ation as shown be l ow ( Figure 1).
Select the two edge curves as wind power output
curves, and calculate system spinning reserve under these
two extreme scenarios. The larger of the results is opti-
mal spinning reserve.
3. Optimal Spinning Reserve Model
In the context of market-oriented reforms, the develop-
ment of reserve decisions need to take into account both
reliability and economy, that meet the reliability re-
quirements of operation, and as much as possible to fol-
low the principle of comprehensive economic benefit at
the same time. Benefit is reduction of Expected Energy
Not Served (ENNS) after the configuration of spinning
reserve; Cost is measured by the opportunity cost of giv-
ing up generating or reserve quotation. The difference
can be defined as the comprehensive economic benefit of
spinnin g re serve [11].
Take the maximum comprehensive economic benefits
of purchasing spinning reserve as the objective function,
and establish the optimal reserve model.
The objective function:
max()=* E-*R
Finally, complete content and organizational editing
before formatting. Please take note of the following items
when proofreading spelling and grammar:
In the equation, C is outage cost which Power Grid
Corporation provides; E
is the changed amount of
Expected Energy Not Served (ENNS) after the configu-
ration of spinning reserve; n is the total number of units;
is reserve quotation of unit i; i is reserve capacity
of unit i; A is the comprehensive economic benefits after
purchasing spinning reserve.
Mainly consider the following constraints:
1) Grid must configure certain spinn ing reserve.
=-X 0
Figure 1. Wind power output belt.
In the inequality, is rated capacity of unit i.
2) Reserve capacity of each unit cannot exceed the
maximum it can provide.
In the inequality, ma x,i is the maximum reserve ca-
pacity which unit i can provide.
3) The speed of providing reserve must meet the
ramping rate.
In the inequality, ,amp i is the ramping rating of unit i;
the time category of spinning reserve working is 10 min-
4. The Operation of Hydropower in Differ-
ent Water Periods
Hydropower energy compared with conventional thermal
power, has obvious advantages, low cost, and is also a
kind of clean energy source. Most hydropower equip-
ment is simple, and easy to operate. Hydropower unit
start-stop quickly, and can track the load flexibly. In the
generating scheduling of power system, according to the
changes of regional hydropower, its scheduling scheme
is more flexible.
In flood period, in order to make full use of water re-
sources, prioritize the full hydropower units and assume
base load. Hydropower units output can be considered as
a straight line, in the bottom of the load curve as shown
in the Figure 2 below.
In drought period, due to the limited water resources, it
is necessary to give full play to the ability of tracking
load flexibly, and arrange hydropower unit in the peak
load period, play the role of “peaking”. According to the
hydropower plant runoff and the reservoir storage, cal-
culate the generated energy each hydropower plant can
produce in the scheduling period.
iiiib ijid
 
v (6)
Figure 2. Hydropower units assume baseload.
Copyright © 2013 SciRes. EPE
L. L. LI, D. M. ZHAO 1013
In the equation, i
n is generating efficiency of hy-
dropower plant i; k is coefficient of output; i is the
reservoir height; i is the percentage of water storage
capacity; ,ib is the initial water reservoir; ,ij
is water
flow of reservoir i in the period j; ,id is the amount of
water in the reservoir at the end of the scheduling.
v v
Sort the load of each study period in descending order,
and the maximum load is Pm satisfying the following
im H
k is the peaking point as shown in the following Figure
5. Stochastic Production Simulation
Choose the biggest wind power output as an example.
Due to the balance of system active power, we know this:
ii i
iLi i
ii iiii
 
 
 (8)
Put the wind power output and hydropower output to
the right side of the equal sign, and superimposed with
the actual load as the equivalent load.
P is the output of hydropower unit i; iH is the num-
ber of hydropower units; W is the number of wind tur-
bines; i
P is the load in study period; is the output
of wind turbine i.
Random outage of generator and load fluctuation may
also case the active power imbalance in addition to the
randomness and intermittency of wind power. Stochastic
production simulation can deduce Expected Energy Not
Served (ENNS) on the basis of considering all the above
uncertain factors. The details are as follows:
1) Redrawn the equivalent load curve above into the
original load duration curve0()
x. And point (x0,00
means the duration when the equivalent load equals or
greater than x0.
2) Assume the unit i fails. The forced outage rate of
unit i is qi. Amend the original load duration curve by
considering random outages of unit i.
()()( )
fxpf xqf xP
p is the normal operation probability of unit i.
We can get the equivalent load duration curve (ELDC)
x after considering random outages of all the ther-
mal power units, as shown in Figure 4.
3) In Figure 4, due to the definition of Expected En-
ergy Not Served (ENNS) and the meaning of the equiva-
lent load duration curve (ELDC), we can get this:
xdx (10)
X is the maximum load in the study period.
P is the
rated capacity of all the units.
6. Numerical Example
Take the Hainan power grid for example object. The
system consists of eight coal units, 12 units of gas tur-
bines, three hydropower plants and four wind farms, spe-
cific parameters as shown in the following table. Without
loss of generality, select the upper edge curve of wind
power output belt, with the hydropower units working in
the dry season and the power grid operating in large
mode. The outage cost C = 4 yuan / kWh.
Select July 12, 2012 as a typical day in the research
period. The power generation load of the typical day is
shown in following Figu r e 5.
Figure 3. Peaking position.
Figure 4. The equivalent load duration curve (ELDC).
Figure 5. The power generation load of the typical day.
Copyright © 2013 SciRes. EPE
L. L. LI, D. M. ZHAO
By calculation, the generated energy of three hydro-
power plants in the research period is shown in the fol-
lowing Table 1.
Hydropower units in the dry season are mainly re-
sponsible for peaking. Peaking position is shown below
(Figure 6). The maximum load after peaking is
Redrawn the equivalent load curve peaked above into
the equivalent load duration curve (ELDC) ()
x as
shown in the following Figure 7.
We can get the results shown in the following Figure
8 by solving the optimal spinning reserve model.
In the figure, abscissa is spinning reserve capacity, and
ordinate is the comprehensive economic benefits. With
the increase in spinning reserve capacity, the comprehen-
sive economic benefits are also increasing. When spin-
ning reserve capacity increases to a certain value, the
comprehensive economic benefits to maximize reach the
maximum. Now the cost of purchasing spinning reserve
is equal to the outage loss. The optimal spinning reserve
capacity is 373MW. However, the spinning reserve ca-
pacity of Hainan power gr id in July 12 , 2012 is 457 MW.
This model reduces the cost of power grid in spinning
reserve configuration under the premise of meeting the
operational reliability.
7. Conclusions
This paper shows how stochastic production simulation
can be applied to solve the optimal spinning reserve
problem which determines the spinning reserve require-
ments in power system with wind integrated. This model
helps a power system overcome the randomness and in-
termittency of wind power, random outage of generator
Table 1. The generated energy of three hydropower plants.
hydropower rated capacity total power
1 4*60 840.6
2 2*40 393.3
3 4*20 176.1
Figure 6. Peaking position of the typical day.
Figure 7. The equivalent load duration curve (ELDC) of the
typical day.
Figure 8. The relationship between comprehensive eco-
nomic benefits and spinning reserve capaci ty.
and load fluctuation. Results tested in Hainan power grid
reduce the cost of spinning reserve configuration without
affecting operational reliability.
The main contributions of this paper include 1) intro-
ducing a efficient method to forecast wind power output,
2) developing a model on the optimal spinning reserve, 3)
propose a convenient approach to solve the operation
problem of hydropower in different water period, 4)
formulating the stochastic production simulation.
The mat lab program developed in this paper has been
able to solve the optimal spinning reserve model. Expect
to apply software copyright and supply service to power
companies in the future.
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