2011 The International Conference on Advanced Power System Automation and Protection

*Corresponding author (email: ysj427@163.com) APAP2011 www.apap2011.org

Analysis of Integrated Wind Power Cost Based on Dynamic Economic Dispatch

YANG ShengJie1, YAO JianGang1, SUN Qian1, Xiao ZhiYuan2

1 Hunan University, Changsha 410082, China; 2 Changsha Electric Power Bureau, Changsha 410015, China;

Abstract As smart grid developing in China, renewable energy gains more and more attention, and a few large farms of power plant are building. Considering wind power’s instability and fluctuation, large-scale integration of it has considerable impact on the electric network and generates a series of additional costs. In this paper, we characterize the stochastic wind power via probability distribution function(pdf) and cumulative distribution function(cdf), analyze the integrated cost of wind power in the context of Dynamic Economic Dispatch DED .Numerical examples are provided for a test system. We also give suggestions to wind power’s price setting in china.

Keywords dynamic economic dispatch, wind power, evolutionary algorithm

1 Introduction

Dynamic Economic dispatch (DED) problem is the conventional way to save energy in electric production, which concerns mainly the fuel cost of thermal plant[1-3]. But as the development of distri-bute generation (DG), the grid accept energy from less concentration and miner capability source. Wind power is one of the important sources. Because it’s natural, clean, no mission, wind power gains its priority in power generation. On the other hand , wind is unstable and stochastic, so it generates impact on the grid. In year 2000, the capacity of wind generators is 344.3MW. Until the end of 2010, this capacity has reached 35000MW. The growth rate of wind power (WP) is amazing and meaningful.

Some researchers have considered the relation of WP. The im-pact of real time pricing on the usage of wind generation is ana-lyzed on Electricity Reliability Council of Texas (ERCOT) sys-tem[4-5]. In this paper, we consider the wind power’s effect on the system cost comparing with the conventional DED. According to the research, wind power’s property can be described as Weibull distribution [6]. This paper uses the cdf and pdf to calculate the ex-pectation of wind power’s output. An evolutionary algorithm is applied to the numerical tests and converges quickly. The result shows that the wind power can considerably reduce the cost.

2 Problem description

EDE problem can be formulated as follows. Objective function:

,1 1

min ( )T N

i i tt i

F C P� �

��� (1)

2, , ,( )i i t i i t i i t iC P a P b P c� � � (2)

Power balance constraint without WP:

,1

N

t i ti

L P�

�� (3)

Power balance constraint with WP:

,1

N

t i t ti

L P W�

� �� (4)

Capacity constraint: min max

,i i t iP P P� � (5)

Ramping constraints:

, , 1i i t i t iDR P P UR�� � � (6)

Where iDR and iUR are the maximum decreasing and in-creasing ramp rates for unit i.

___________________________________ 978-1-4244-9621-1/11/$26.00 ©2011 IEEE

2011 The International Conference on Advanced Power System Automation and Protection

3 Wind power’s stochastic property

The wind’s stochastic property is key to forecast WP. And a wide research has developed in the field. Now the widely accepted model is two parameters Weibull distribution. We use the model in [7,8], the wind speed’s cdf of the Weibull distribution is de-picted as follows:

( : , ) 1 exp , ( 0)k

vvF v c k vc

� � � � � �� � �� �� � �

(7)

Where v is the wind speed, and c>0 and k>0 are respectively the scale factor and shape factor.. And the pdf of V is

1

( ) expk k

Vk v vf vc c c

� � � � �� � � � �� � � �� � �

(8)

For a generic wind turbine, some researchers use a simplified mode to characterize the relation between the WP and wind speed:

� �

0 ( )( )

( ) / ( )

in out

r r out

in r r in in r

v v or v vW w v v v

v v w v v v v v

� ���� � ��� � � � ��

(9)

Where W is the wind power, rw is the conversion system’s rated

power, inv is the cut-in speed, outv is the cut-out speed. So we gain the expectation of wind power described in (9).

( )( ) ( ) ( )

1 1, ,( )

exp

outr

in r

vvin r

V r Vr inv v v v

k kinr rk k

r in

kout

r k

v v wE W f v dv w f v dvv v

vw c vv v k k c k c

vwc

� �

�� �

�

� � � � ��� � � � �� � �� �� �

� �� �

� �

� �

(10)

4 Evolutionary algorithm (EA)

As systems and models are becoming more and more complex, the problem with high dimension and lots of constraints is hard to get the global optimal point. EA develops quickly in recently years. Though EA still does not gain strict support from mathe-matic view, it actually performs well in global optimization. EA simulates the evolution and learning of natural world which is the main difference with other algorithms. The process of EA can be in general described as follows:

Figure 1 Flow chart of EA

The formulation (1) – (6) can be depicted simply as: min ( )f X (11)

Subject to: ( ) 0 , {1,2, , }ih i n� �X � (12)

( ) 0 , {1,2, , }jg j m� �X � (13)

We get the basic idea from [9,10]. The key features of EA us-ing here are described as follows:

(a) Encoding Each individual represents a potential solution encoded in

some way. We use the real-valued technique to code the gene-rators’ output during a day. A 24-dimension vector

1 2 24( , , , )i i ix x x� represents unit i ’s supply schedule.

(b) Mutation When the offspring is created, the Gaussian mutation is a

widely accepted method.

max minmin max

' min(max( ( , ), ), )10ij ijx P PN x P P�

� (14)

Where max min( , ( ) /10)ijN x P P� indicates the normal dis-

tribution with mean ijx and standard deviation

max min( ) /10P P�

(c) Penalty function How to deal with the constraint is critical to the algorithm. The

fitness of the individual can be calculated in the following way: 1( ) ( ) ( )

t

F f GT

� � �X X X (15)

Where2 2( ) (max( ( ),0)) ( )j iG g h� �� �X X X (16)

And � is the solution space of the optimization problem. 1/ tT is the penalty factor when the individual violate the con-straints. Like the simulated annealing algorithm (SA),

2011 The International Conference on Advanced Power System Automation and Protection

1 0.99t tT T� � ensures the temperature decreases as slow as possible, also ensures searching the solution globally.

5 Simulation

We use thermal units’ cost data lists in Table 1, which is from [11]. Then assume the ramping rate of each unit. The expectation of WP output is similar to the data in [12] and shown in figure 2 and the forecasted 24-hour load curve is shown in figure 3.

Table 1 Fuel cost coefficients and capacity limits

Unit ia ib ic minP maxP1 100 200 10 0.05 0.52 120 150 10 0.05 0.63 40 180 20 0.05 14 60 100 10 0.05 1.25 40 180 20 0.05 16 100 150 10 0.05 0.6

2 4 6 8 10 12 14 16 18 20 22 240.05

0.055

0.06

0.065

0.07

0.075

0.08

hour

win

d po

wer

out

put(p

.u.)

Figure 2 The expectation of wind power output.

Here we focus on two cases according to that WP is consi-dered or not. The dispatch schedules of thermal units are listed in Table 2 and Table 3 using EA described above. And their total costs are 13579.307$ and 13245.306$ respectively. The saved fuel cost is 334.001$. The environment cost is also decreased considerably though not included here.

2 4 6 8 10 12 14 16 18 20 22 240

0.5

1

1.5

2

2.5

3

3.5

4

load

/p.u

.

hour

Figure 3 The forested 24-hour load curve

Table 2 Dynamic economic dispatch without wind power

hour Unit1 Unit2 Unit3 Unit 4 Unit 5 Unit 6

1 0.0500 0.2042 0.2377 0.8252 0.2377 0.2451 2 0.0500 0.2003 0.2260 0.8173 0.2260 0.2404 3 0.0500 0.1984 0.2201 0.8134 0.2201 0.2380 4 0.0500 0.1944 0.2083 0.8056 0.2083 0.2333 5 0.0500 0.1886 0.1907 0.7938 0.1907 0.2263 6 0.0500 0.1846 0.1789 0.7859 0.1789 0.2216 7 0.0500 0.1993 0.2230 0.8154 0.2230 0.2392 8 0.0500 0.2111 0.2583 0.8389 0.2583 0.2533 9 0.0500 0.2444 0.3583 0.9056 0.3583 0.2933 10 0.0977 0.2898 0.4943 0.9962 0.4943 0.3477 11 0.1430 0.3275 0.6075 1.0716 0.6075 0.3930 12 0.1725 0.3520 0.6811 1.1208 0.6811 0.4225 13 0.2072 0.3810 0.7680 1.1787 0.7680 0.4572 14 0.2236 0.3947 0.8090 1.2000 0.8090 0.4736 15 0.1998 0.3749 0.7496 1.1664 0.7496 0.4498 16 0.2093 0.3827 0.7732 1.1822 0.7732 0.4593 17 0.1777 0.3564 0.6943 1.1295 0.6943 0.4277 18 0.1398 0.3249 0.5996 1.0664 0.5996 0.3898 19 0.1019 0.2933 0.5048 1.0032 0.5048 0.3519 20 0.1072 0.2977 0.5180 1.0120 0.5180 0.3572 21 0.1156 0.3047 0.5390 1.0260 0.5390 0.3656 22 0.1398 0.3249 0.5996 1.0664 0.5996 0.3898 23 0.0904 0.2836 0.4759 0.9839 0.4759 0.3404 24 0.0500 0.2464 0.3642 0.9095 0.3642 0.2957

Table 3 Dynamic economic dispatch considering WP

hour Unit1 Unit2 Unit3 Unit 4 Unit 5 Unit 6

1 0.0500 0.1972 0.2166 0.8110 0.2166 0.2366 2 0.0500 0.1937 0.2060 0.8040 0.2060 0.2324 3 0.0500 0.1923 0.2019 0.8012 0.2019 0.2307 4 0.0500 0.1887 0.1910 0.7940 0.1910 0.2264 5 0.0500 0.1820 0.1710 0.7807 0.1710 0.2184 6 0.0500 0.1782 0.1595 0.7730 0.1595 0.2138 7 0.0500 0.1931 0.2042 0.8028 0.2042 0.2317 8 0.0500 0.2052 0.2407 0.8271 0.2407 0.2463 9 0.0500 0.2389 0.3416 0.8944 0.3416 0.2866 10 0.0920 0.2850 0.4801 0.9867 0.4801 0.3420 11 0.1377 0.3231 0.5943 1.0629 0.5943 0.3877 12 0.1669 0.3474 0.6672 1.1115 0.6672 0.4169 13 0.2014 0.3762 0.7535 1.1690 0.7535 0.4514 14 0.2168 0.3890 0.7919 1.1946 0.7919 0.4668 15 0.1935 0.3696 0.7338 1.1558 0.7338 0.4435 16 0.2028 0.3773 0.7569 1.1713 0.7569 0.4528 17 0.1707 0.3506 0.6767 1.1178 0.6767 0.4207 18 0.1324 0.3186 0.5809 1.0539 0.5809 0.3824 19 0.0939 0.2866 0.4848 0.9899 0.4848 0.3439 20 0.0994 0.2912 0.4985 0.9990 0.4985 0.3494 21 0.1081 0.2985 0.5204 1.0136 0.5204 0.3581 22 0.1321 0.3185 0.5804 1.0536 0.5804 0.3821

2011 The International Conference on Advanced Power System Automation and Protection

23 0.0828 0.2773 0.4569 0.9713 0.4569 0.3328 24 0.0500 0.2394 0.3433 0.8956 0.3433 0.2873

6 Conclusion

In this paper, the wind power’s effect on DED was analyzed. Considering wind’s unstable property, the output of wind genera-tor is also stochastic. We use the expectation of wind power on behalf of the actual value to optimize the integrated cost of the grid. The difference between cases with and without WP was obvious. The advantage of WP is analyzed in numerical form. In order to encourage the development of clean energy in China, the price of WP can be set approaching to the value of save fuel cost divided by supplied WP. In this way the profit of WP power may be paid back to the WP generator owners. Independent System Operator (ISO) can use some contracts or emission permission to find the potential profit from WP.

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