Journal of Power and Energy Engineering, 2015, 3, 342-347
Published Online April 2015 in SciRes. http://www.scirp.org/journal/jpee
http://dx.doi.org/10.4236/jpee.2015.34046
How to cite this paper: Dong, W.C., Zhang, J., Huang, J.J. and Li, S.H. (2015) Dynamic Economic Dispatch for Wind Power
System Considering System Security and Spinning Reserve. Journal of Power and Energy Engineering, 3, 342-347.
http://dx.doi.org/10.4236/jpee.2015.34046
Dynamic Economic Dispatch for Wind
Power System Considering System
Security and Spinning Reserve
Wangchao Dong, Jing Zhang, Jiejie Huang, Shenghu Li
School of Electric Engineering and Automation, Hefei University of Technology, Hefei, China
Received Dec emb er 2014
Abstract
In this paper, dynamic economic dispatch model is proposed for power systems with bulk wind
power inte gration . The wind turbine generators are assumed to partially undertake the spinning
reserve for the thermal generator. A double-layer optimization model is proposed. The outer layer
use the diffe renti al evolution to search for the power output of thermal generators, and the inner
layer use the primal-dual interior point method to solve the OPF of the established output state.
Finally, the impact of spinning reserve with wind power on power system operating is validated.
Keywords
Spinning Reserve, Wind Power, Dynamic Economic Dispatch (DED), Different i al Evolution Method,
Interior Point Method
1. Introduction
The wind power is a kind of clean and sustainable energy source. However, considering the stochastic and in-
termittent properties, bulk integration of wind farms to the power systems may yield various problems to secu-
rity and stability. To guarantee the reliability of power supply, reserve capacity as much as installed capacity of
the wind power is necessary, which limited the development of wind power. At the mean time, there is a new
challenge brought by randomness of wind power. It is difficult for existing wind speed forecasting technology to
meet the reliability and accuracy requirement for traditional power generation plan.
To reduce the effects of wind power instability, many researches were proposed in the field of prediction ac-
curacy of wind speed and spinning reserve of wind power. Reference [1]-[3] proposed advanced prediction me-
thod, which the root mean square error of wind power prediction is between 10% and 20%. Reference [4] dis-
cussed the traditional calculation of reserve capacity which is easy to application. But it is not optimal consider-
ing economy and reliability. Reference [5] apply the optimization algorithm to calculate the optimal spinning
reserve required and balance the reliability and economy of generators’ outage, prediction deviation of load and
wind power. Reference [6] [7] considered the spinning reserve cost and set the objective function as minimum
total cost of generation and operation. Reference [8] [9] calculated the reserve capacity by using the reliability

W. C. Dong et al.
343
requirement of probability distributions of load and wind power prediction error. But it is not safe and economic
for thermal power unit to supply spinning reserve considering the energy cost, efficiency, and the ramp speed.
The article applied the spinning reserve model for wind farm to reducing the capacity demand of system secu-
rity. Based on spinning reserve model, the wind power system optimal scheduling considering wind turbines
was established. The calculating result was compared with that reserve model ignored. Interior point nested dif-
ferential evolution method was applied to solve the dynamic economic dispatch considering security con-
straint s.
2. Wind Farm Spinning Reserve Model
2.1. Wind Farm Output Optimal Control Strategy
A new optimal method to achieve complementary spare between multiple wind farms is presented which can
meet the requirement of high dimensions and multitasking scheduling. The method is expressed as follows:
out out
,
11
max
DT
jt
jt
PP
= =
=
∑∑
(1)
out set
,,
11
TT
jt jt
tt
PP
= =
<
∑∑
(2)
out pre
,,
0
jt jt
PP<<
(3)
where D is number of wind farms;
out
,jt
P
is real-time sampling output of wind farm j at hour t;
pre
,jt
P
and
pre
,jt
P
represent the given and predictive value of wind farm j at hour t.
2.2. Reserve Capacity Calculation
Normal distribution and Laplace distribution are applied to establish the distribution
( )
df wp
Pe
of wind power
predictive error ewp ,t.
( )( )( )
, 12
~
wp tTwpwpwp
efeaf eage= +
(4)
where,
( )
wp
fe
and
( )
wp
ge
represent the density functions of Normal distribution and Laplace distribution;
a1 and a2 meet the following requirement.
12
12
36
1
w
a ak
aa
+=

+=

(5)
And
w
k
is peak data of wind power output deviation. The article consider that wind power predictive error
,wpt
e
and the reserve requirement of wind power output error are drawn from the same distribution.
( )( )
reserve
twpt wp
fe fe=
(6)
where,
( )
reserve
t wp
fe
is density function of reserve requirement and
( )
t wp
fe
is density function of predictive.
And reserve capacity can be determined by preassigned credibility
α
.
( )
d
t
t
R
t wp
Rfe
ξα
+
−>
∫
(7)
where,
α
is the lower confidence bound;
t
R
+
and
t
R
−
represent upper and lower bound of reserve capacity.
3. DED for Wind Power System
During researching the DED of wind power system, making wind power scheduling should be the first step
which means that we should consider the wind farm power output first.

W. C. Dong et al.
344
3.1. Objective Function
( ) ( ) ( )( )
1
N
Gii i
i
CPtU tFt
=
=
∑
(8)
where,
( )
i
Ft
is the generation cost of generator i at hour t;
( )
i
Ut
is operating state of generator i at hour t; 1
represent running state and 0 represent stopping state; T is the total time for scheduling cycle; N is number of
generators.
()( )( )
( )
2
ii iiii
Fta bPtcPt =++
(9)
where,
i
a
,
i
b
,
i
c
are coefficients of cost function;
( )
i
Pt
is active power output of generator i at hour t.
3.2. Constraint
3.2.1. Constraints of Wind Farm
( )
maxWWWW
PNKP t=
(10)
( )
max
0WW Pt P≤≤
(11)
()( )
dn
1
W WW
PtPt P−− ≤
(12)
()()
up
1
WW W
Pt PtP − −≤
(13)
( )()
dn max
=1
min %,1
N
WWR ii
i
PPPt Pt γ

= −− 



∑
(14)
()( )
min
1
min %,1
N
WupWR ii
i
PPPtP t β
=

= −− 



∑
(15)
where,
maxW
P
represent the maximum available output of wind farm at hour t;
( )
w
Pt
is maximum available
output of wind turbine at hour t; Kw is effective coefficient; Nw is number of wind turbines for wind farm.
( )
maxi
Pt
and
( )
mini
Pt
represent the maximum and minimum output of generator i at hour t.
% γ
and
% β
are the limitation of change rates.
3.2.2. Constraints of Conventional Unit
( )( )( )( )( )
min maxGii Gi Gii
PtU tPtPtUt≤≤
(16)
( )()
{ }
min min60
max ,1
iGi Giidown
P tPPtrT=−− ⋅
(17)
( )()
{ }
maxmaxup 60
min ,1
iGi Gii
PtPPtr T−+⋅
(18)
( )
( )
()( )
( )
10
on on
i iii
XtTUtUt−−−≥
(19)
( )
( )
( )()
( )
10
off off
iii i
Xt TUt Ut−− −≥
(20)
( )()()()
up
11
iiiii
U tU tPtPtP−−−≤


(21)
( )()()( )
down
11
iiii i
U tU tPtPtP−−− ≤


(22)
where, Pimax and Pimi n represent the output limitation of generator i; Pidown and Piup represent the ramp rate limita-
tion; Xion(t) and Xioff(t) represent the cumulative time of running and outage for generator i at hour t. Tion and Tioff
represent the minimum bound of running and outage cumulative time.

W. C. Dong et al.
345
3.2.3. Constraints of System Security
( )( )( )
loss
11
ND
LGi Wj
jj
PtP tPtP
= =
=++
∑∑
(23)
( )
1
cossin 0
nb
GmLmmkmkmkmkmk
k
PP V VGB θθ
=
−−+ =
∑
(24)
( )
1
sincos0
nb
GmLmmk mkmkmkmk
k
QQV VGB θθ
=
−−− =
∑
(25)
min maxm mm
θ θθ ≤≤
(26)
min maxmmm
V VV≤≤
(27)
22
maxmk mk
SS≤
(28)
where,
( )
L
Pt
is total load at hour t; Ploss is power net loss; nb is the number of branches; m and k are heading
node number of branch; Vk and θk are node voltage; Smk is branch power; Smkmax is branch power limitation.
3.2.4. Constraints of Wind Spinning Reserve
Cons traints of wind power spinning reserve consist of wind farm output optimal method and reserve capacity
calculation which can be described by Equations (1)-(6).
4. Solution Method
Differential Evolution algorithm is a randomized parallel search algorithm while interior-point method is suita-
ble for solving convex optimization problem. The paper apply interior-point nested differential evolution me-
thod to solve the dynamic economic dispatch problem. The steps are as follow.
Step 1. Set related coefficients of differential evolution algorithm;
Step 2. Initial group, each individual can be regard as a solution to the DED problem which consist with pow-
er output of thermal generators in the scheduling cycle; and initial group can calculate as follow.
()
minmax min
itis ii
P PrPP = +⋅−
(29)
where, rs is a [0,1] uniform distribution random number.
Step 3. Using interior-point method to solve the OPF for each single individual.
( ) () ( ) ( )
1
min
N
i ti
i
GFFPth EPt
=

= +⋅

∑
(30)
Step 4. Evaluate the fitness value of each individual.
1
T
t
TC GF
=
=∑
(31)
Step 5. Set the iteration number k + 1;
Step 6. Variation, generate variate individual.
( )
G GGG
ik lm
vP FP P=+−
(32)
where,
n
k
P
,
n
l
P
and
n
m
P
are random selected individuals different from each other; F is zoom factor;
Step 7. Crossover, generate temp individual from original group and variate group uin.
()( )
()( )
,
,
rand or rand ;
rand and rand .
n
ij R n
in
ij R
vj Cjni
uPj Cjni
≤=

=>≠


(33)
where,
( )
rand j
is random number between [0,1]; and CR is corssover probability;
Step 8. Using interior-point method to solve OPF with
n
i
u
to be the initial value, and evaluate the fitness.

W. C. Dong et al.
346
Step 9. Select the next generation according to the greedy method.
( )()
( )()
1
nn n
iii
n
inn n
iii
uTCuTCP
PPTCuTCP
+
<

=≥


(34)
Step 10. Loop over all these individuals and k = k + 1. If k is less than iteration limitation, turn to step5;
Step 11. Output the optimal solution in group.
5. Numerical Examples
Text on the IEEE-RTS24 buses system with two wind farms of 200 MW connected in node 8 and 17. Parame-
ters of generators and load are shown in [10] [11]. Wind speed data adopts from the Royal Netherlands Meteo-
rological Institute (KNMI) history data in 24 hours [12]. Spinning reserve cost coefficient is set to 20$/MWh
[13]. Assume that base load is allocated to 22 and 23 nodes in the context of priority scheduling wind power. As
for differential evolution algorithm, population size set to 20, maximum evolution is 10, zoom factor is 0.75 and
crossover probability factor is set to 1.
The paper analyses the influence of spinning reserve constraint to dynamic economic dispatch by separate the
problem to six situations.
a. No wind power connected;
b. Ignoring spinning reserve constraint with wind power connected;
c. Considering system spinning reserve constraint with wind power connected;
d. Ignoring spinning reserve constraint with limited wind power connected
e. Considering system spinning reserve constraint with limited wind power connected;
f. Considering spinning reserve constraint of wind farms and system with limited wind power connected;
Calculation results of single time continuous optimization with OPF nested DE applied are shown as follow
(Tables 1 and 2).
6. Conclusions
The paper proposed the DED model considering constraints of security and spinning reserve. Differential evolu-
tion algorithm and interior-point method are employed to analyses the influence of wind farm spinning reserve
to power system operating scheduling.
1) After considering security and system spinning reserve constraints, the economic dispatch cost increases
which better conforms to the wind power system actual operating rule.
Table 1. Result of OPF nested DE method.
Soluti on Fu e l Cost (106 $) Reserv e Cost (106 $) Total Cost (106 $)
a 0 2.1372 0 2.1372
1 2.2075 0 2.2075
b 0 1.8487 0 1.8487
1 1.9358 0 1.9358
c 0 1.8446 0 .1306 1 .9752
1 1.9193 0.1086 2 .0279
d 0 1.8768 0 1.8768
1 1.9490 0 1.9490
e 0 1.8710 0 .1234 1 .9944
1 1.9460 0.1054 2 .0514
f 0 1.8456 0.1 126 1.9582
1 1.9196 0.0944 2 .0140

W. C. Dong et al.
347
Table 2. Result of single time continuous optimal.
Soluti on Fuel Cost (10 6 $) Reserv e Cos t (10 6 $) Tota l cos t (10 6 $)
a 0 2.1372 0 2.1372
1 2.2378 0 2.2378
b 0 1 .8487 0 1.8487
1 1.9410 0 1.9410
c 0 1.8446 0.1306 1 .9752
1 1.9227 0.1038 2.0 265
d 0 1 .8768 0 1.8768
1 1.9640 0 1.9640
e 0 1.8710 0.1234 1 .9944
1 1.9547 0.0973 2.0 520
f 0 1.8456 0.1204 1.9 660
1 1.9293 0.0929 2.0 222
2) Compared to the largest output mode, it will decrease the system spinning reserve cost to limit the output
of wind farms and employ the wind farm spinning reserve.
3) It will reduce the abandon volume of wind, save system reserve capacity and increase the efficiency of the
system operating while considering wind farm spinning reserve.
References
[1] Lei, Y., Wang, W., Hua, Y., et al. (2002) Wind Power Value Analysis on Power System. Power System Technology,
26, 10-14.
[2] Wang, J., Wan g, X. and Wu, Y. (2005) Operating Reserve Model in Power Market. IEEE Transactions on Power Sys-
tem, 20, 223-229. http://dx.doi.org/10.1109/TPWRS.2004.841232
[3] Wang, D., Chen, Z., Tu , M., et al. (2012) Reserve Capacity Calculation Considering Large Scale Wind Power. Auto-
mation of Electric Power System, 36, 24-28.
[4] Jin, H., Xion g, X. and Wu, Y. (2012) Sho rt -Term Load Forecasting Method Based on Similarity Principle. Automation
of Electric Power System, 25, 45-48.
[5] Lee, T. (2007) Optimal Spinning Reserve for Wind Thermal Power System Using EIPSO. IEEE Transactions on Pow-
er System, 22, 1612-1621. http://dx.doi.org/10.1109/TPWRS.2007.907519
[6] Hans, B. and Jose, A. (2008) Statistical Analysis of Wind Power Forecast Error. IEEE Transactions on Power System,
23, 983-991. http://dx.doi.org/10.1109/TPWRS.2008.922526
[7] Yao, Y. and Yu, J. (2011) Wind Power System Multi-Objective Hybrid Optimal Scheduling. Automation of Electric
Power System, 35, 118-12 4.
[8] Ortega, M. and Kirscher, D. (20 09 ) Estimating the Spinning Reserve Requirements in Systems with Significant Wind
Power Generation Penetration. IEEE Transactions on Power System, 24, 114-124.
http://dx.doi.org/10.1109/TPWRS.2008.2004745
[9] Sun, C., Zhou, H. and Zhang, Y. (2012) Dynamic Environment Economic Based on Differential Evolution Algorithm.
Computing Science, 11, 208-211.
[10] Basu, M. (2011 ) Economic Environmental Dispatch Using Multi-Objective Differential Evolution. Applied Soft Com-
puting, 11, 2845-2853. http://dx.doi.org/10.1016/j.asoc.2010.11.014
[11] Basu, M. (2008) Dynamic Economic Emission Dispatch Using Non-Dominated Sorting Genetic Algorithm-II. Elec-
trical Power and Energy Systems, 30, 140-149. http://dx.doi.org/10.1016/j.ijepes.2007.06.009
[12] KNMI Hydra Project (20 13) Wind Climate Assessment of the Netherlands. http://dcr.rpi.edu/commdesign/class1.html
[13] Wei, Z., Sun, H., Gu, H., et al. (2012) Wind Power System Dynamic Economic Dispatch Considering Risk Reserve
Constraints. Proceedings of the CSEE, 32, 47-55.