Economic Dispatch for Power Generation System Incorporating Wind and Photovoltaic Power

Jie Meng1, a, Geng-yin Li1, b and Shi-jun Cheng1, c

School of Electrical and Electronic Engineering (North China Electric Power University),

Beijing 102206, China

aforevernew88@163.com, bligyls@sina.com, clchengshijun111@163.com

Keywords: wind and photovoltaic power; economic dispatch; interruptible load; spinning reserve

Abstract: With the higher penetrations of wind and photovoltaic power in system, the randomness

of its outputs adds amounts of uncertainty to system generation planning and scheduling. This paper

formulates a day-ahead power economic dispatch model based on the uncertainty information of

wind and photovoltaic power prediction obtained by prediction interval of power with a certain

probability. The costs of spinning reserve and interruptible load regarded as spinning reserve are

also taken into consideration. The proposed model is solved by Cplex. Finally, the simulation

example of system composed of 10-units proves the validity of the model.

Introduction

With the emergence of energy crisis and the excessive increase of the consumption, wind and

photovoltaic power generation have a rapid development. The operation of large-scale wind,

photovoltaic stations connected to grid has become the future trend. However, the randomness of

wind and solar make its output difficult to predict, which also make traditional economic dispatch

method not applicable[1-2]

. Therefore, it is of great practical significance for system optimal

operation to make research on dispatch and operation with consideration of large-scale wind power

and photovoltaic power connected to grid [4-6]

.

Because of the low accuracy of wind and photovoltaic power prediction, system cannot use the

information directly for getting a better scheme, which needs to reflect uncertain prediction

information in schedule model. The optimal dispatch model is based on interval prediction

information of wind and photovoltaic power with a certain probability. In addition, this paper adds

the cost of spinning reserve and interruptible load regarded as spinning reserve to reflect the impact

of randomness of wind and photovoltaic power on the grid and backup demand scheduling. The

proposed model is solved by Cplex after being linear processed. Finally, the simulation example of

system composed of 10-units proves the validity of the model.

Analysis on system uncertainty

Studies have shown that wind power prediction error can be descripted by normal distribution. That

is 2~ (0, )ww PP N , f

wP and wP represent predicted wind power output and actual wind power output.

The probability density function and distribution functions are as follows: 2 2( ) /21

( )2

( ) ( )

fw w Pw

w

w

P P

w

P

f

w ww

P

f P e

P PF P

(1)

The power output of PV depends on the solar radiation considered to obey Beta distribution in a

certain period, and the probability density function of PV output power is shown as follows:

1 1( )( ) ( ) (1 )

( ) ( )

pv pv

pv pv

m m

P Pf P

P P

(2)

Applied Mechanics and Materials Vol. 441 (2014) pp 263-267Online available since 2013/Dec/04 at www.scientific.net© (2014) Trans Tech Publications, Switzerlanddoi:10.4028/www.scientific.net/AMM.441.263

All rights reserved. No part of contents of this paper may be reproduced or transmitted in any form or by any means without the written permission of TTP,www.ttp.net. (ID: 130.15.241.167, Queen's University, Kingston, Canada-24/08/14,14:28:04)

pvP is actual power output of PV system; mP is the maximum power output of PV system; ,

are distribution parameters.

These two random variables can be equivalent to one random variable z w pvP P P

Assuming the two variables are mutually independent, the probability density function can be

obtained by convolution. The probability distribution function is expressed as:

0( ) ( )

zP

z z zF P f p dp (3)

Thus, according to the requirements of economy and reliability, the upper and lower limits of

wind-PV power prediction interval zP , zP can be calculated by choosing a certain probability.

The day-ahead dispatch model based on prediction interval

Objective Function. The interruptible load is taken as scheduled backup resource considered into

the generation scheduling in this paper. The costs of conventional thermal power generation and the

positive and negative spinning reserve as well as cost of interruptible load purchased by grid are

considered in objective function.

The objective function is formatted as follows:

, , , 1 , ,

1 1

min { [ ( ) (1 ) ( , )] }gNT

u d

i t i i t i t si ri i t i t IL

t i

F U C P U C C R R C

(4)

2

, , ,( )i i t i i i t i i tC P a b P c P (5)

, , , , , ,( , )u d u u d d

ri i t i t i t i t i t i tC R R k R k R (6)

, ,IL IL t IL tC P k (7)

,i tU is the binary variable that is equal to l if unit i is online in period t. ,( )i i tC P is the production

cost of unit i in period t,,i tP is the output of unit i in period t . siC , , ,( , )u d

ri i t i tC R R are the startup cost

and spinning reserve cost of unit i in period t . , ,,u d

i t i tR R are the positive and negative spinning

reserve in period t . ,IL tP , ILC are interruptible load and its cost in period t .

Constraints. 1) Power balance constraints

, , , , ,

1

gN

f f

i t i t w t pv t L t

i

U P P P P

(8)

Where:,

f

w tP ,,

f

pv tP are the predicted power outputs of wind and PV power system in period t;

,L tP is the load demand in period t.

2) Power output constraints and ramping response rate constraints of thermal units

, ,min , , ,maxi t i i t i t iU P P U P (9)

, , 1

ramp

i t i t iP P P (10)

,maxiP ,,miniP are the maximum and minimum power output of unit i ; ramp

iP is the ramping limit

(up/down) of unit i .

264 Machinery Electronics and Control Engineering III

3) Minimum up and down times constraints

, 1 , , 1,( )( ) 0i t i t i t on iU U T MUT (11)

, , 1 , 1,( )( ) 0i t i t i t off iU U T MDT (12)

Where:, 1,i t onT

,, 1,i t offT

are the continuous up and down times in period 1t , and iMUT , iMDT

are the minimum up time and minimum down time.

4) Spinning reserve constraints

, , , ,

1

%gN

u f

i t i t IL t L t z z

i

U R P u P P P

(13)

, , , , , ,max

u

i t i t i t i t i t iU P U R U P (14)

, ,

u ramp

i t i t iR U P (15)

, , ,

1

%gN

d f

i t i t L t z z

i

U R d P P P

(16)

, , , , , ,min

d

i t i t i t i t i t iU P U R U P (17)

, ,

d ramp

i t i t iR U P (18)

Where: ,

u

i tR , ,

d

i tR are the spinning reserve of unit i in period t. , ,

f f f

z w t pv tP P P ,is the combined

predicted power output of wind and PV power system. zP , zP

are the upper and lower limits of

wind-PV power prediction interval.

The example and analysis

The system that includes ten conventional thermal units, a wind farm and a photovoltaic power

system is analyzed in this paper. One day taken as scheduling period is divided into 24 hourly

periods. The rated power of wind and PV system are both 150MW. The prediction error standard

deviations of power output obtained from wind and PV system are both 10% of the predicted

power. The positive and negative spinning reserve requirements are set to 10% and 1%of the load

demand. The price of spinning reserve provided by conventional units is 12$/WM. The

characteristics of thermal units are based on the case studies presented in [7] with a total capacity of

1950MW.The predicted power output of wind,PV system and load demand are showed in Figure

1.The dispatch model should be linearized before using CPLEX to solve.

Applied Mechanics and Materials Vol. 441 265

load wind forecast output pv forecast output joint forecast output of wind and pv

ou

tpu

t/W

M

time / h

Fig.1 The predicted power output and load demand

The power output of thermal units over the 24-h scheduling period without consideration of

interruptible load can be seen in Fig.2.Unit 4, unit 8 and unit 9 bear large load and operate in each

scheduling period due to the better operation economy of them. While the other units are at

different start-stop states according to the actual load and constraint conditions in different times.

Fig.2 The generation scheduling without consideration of interruptible load

When interruptible load is introduced to demand side as spinning reserve, it can reduce the

increases of expensive spinning reserve in peak load. It is assumed that the maximum interruptible

load the user side can offer is 5% of load demand and its compensation coefficient is 13$/MW. The

unit commitment situations considering interruptible load are showed in Table 1.

Table 1 The units commitment situation considering interruptible load

time unit states time unit states time unit states time unit states

1 0001000110 7 1011000110 13 1011000110 19 1011000110

2 0001000110 8 1011000110 14 1011000110 20 1011000110

3 0001000110 9 1011000110 15 1011000110 21 1011000110

4 0011000110 10 1011000110 16 1011000110 22 1011000110

5 0011000110 11 1011000110 17 1011000110 23 1111011110

6 1011000110 12 1011000110 18 1011000110 24 0101011110

By contrast, the introduction of interruptible load can avoid unit 5 and unit 10 with high cost

operating in the period 8-12 and 23-24. It indicates that compensating interruptible load can avoid

starting units because of lacking spinning reserve. By comparing the costs in Table 2, when

interruptible load is seen as spinning reserve, it increases the corresponding compensation costs.

266 Machinery Electronics and Control Engineering III

Meanwhile the total costs, startup costs and reserve costs are reduced, which is conducive to

optimizing the allocation of resources.

Table 2 The contrast of costs after considering interruptible load

Summary

Considering the uncertainty of wind and photovoltaic power prediction, the economic dispatch

model based on power interval prediction is built in this paper. Meanwhile, the spinning reserve

cost is introduced. The interruptible load can be seen as spinning reserve to improve the economy of

system operation. The example results showed that introducing the interval prediction information

of wind and photovoltaic power with a certain confidence probability into power generation plan

can reduce the impact of its volatility on the system scheduling. The consideration of spinning

reserve costs and interruptible load costs optimizes unit commitment strategy and reduces the

spinning reserve capacity to some extent. Finally, it proves the reasonability of proposed model

which can provide methodological guidance to formulate dispatch scheme.

References

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dynamic economic dispatch in wind power integrated system[J].Automation of Electric Power

Systems ,Vol. 30(2006), p. 22-26.

[3] Ruey-Hsun Liang. A fuzzy optimization approach for generation scheduling with wind and

solar energy systems [J]. IEEE Transactions on Power Systems, Vol. 22 (2007), p. 1665-1674.

[4] Xiong Hu, Xiang Tieyuan, Chen Hongkun. Research of fuzzy chance constrained unit

commitment containing large-scale intermittent power[J]. Proceedings of the CSEE, Vol. 33

(2013),p.36-44.

[5] Jiang Yuewen, Chen Chong,Wen Buying. Particle swarm research of stochastic simulation for

unit commitment in wind farms integrated power system [J].Transactions of China

electrotechnical society, Vol. 26 (2007), p. 37-41.

[6] Tao Li. Price-based unit commitment: a case of Lagrangian relaxation versus mixed integer

programming [J].IEEE Transactions on. Power Systems, Vol. 20 (2005), p. 2015-2025.

Cases Fuel

costs($)

Startup

costs($)

Reserve

costs($)

Interruptible load

costs($)

Total

costs($)

Without interruptible

load 312754.45 9160.00 56029.20 0 377943.65

Including

interruptible load 312334.90 8270.00 55031.88 1080 376716.78

Applied Mechanics and Materials Vol. 441 267

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