Advanced Materials Research ISSN: 1662-8985, Vols. 424-425, pp 693-696 doi:10.4028/www.scientific.net/AMR.424-425.693 © 2012 Trans Tech Publications, Switzerland

Online: 2012-01-03

Three layers optimization model for time-of-use and interruptible price based on fuel saving and emission reducing ZHAO Yinhui, TAN Zhongfu, SONG Yihang North China Electric Power University, Beijing 102206,China [email protected] Keywords: time-of-use price; interruptible price; fuel saving and emission reducing; optimization model

Abstract ： Based on fuel saving and emission reducing, this study establishes three layers optimization model for time-of-use and interruptible price. At first, a model to minimize total cost, including power purchase cost, emission cost and reserve cost was set up. Based on model 1, the time-of-use price optimization model was put forward afterwards. Finally, the three layers optimization model for time-of-use and interruptible price was established. 1

Introduction

Electric power industry assume huge responsibility to energy saving and emission reducing under the circumstances of energy crisis and environmental pressures. On the one hand, energy consumption should be decreased through optimized power generation dispatching schedule(ZHANG Xiaohua, et.al,2010). On the other hand, the use of electricity can be controlled by demand-side management(WANG Jiangbo, et. al, 2010). Considering the direction of energy conservation and time-of-use price integratedly, TAN Zhongfu(2009a) put forward an optimization model for designing peak-valley time-of-use power price of generation side and sale side. The risk for power supply company under demand-side time-of-use electricity price was analyzed by SONG Yihang(2010). TAN Zhongfu(2009b) put forward an optimization model that not only make power-supply companies and customers nondecreasing, but also solve the problem to the lack of incentive mechanism for actualizing interruptible price. 2

Optimization Models

2.1 Model 1 Generation cost of unit i at output git at period t : Fit ( g it ) = a1i + b1i g it + c1i g it2

(1)

Where, git is power output of unit i at period t , a1i , b1i , c1i are constants not less than 0. ( b1i + 2c1i g it ) means marginal cost of unit i at period t ，mostly it is marginal coal quantity.

σ t (bi + 2ci g it )∆Tt means coal cost consumed by unit i at period

t during ∆Tt , and

σ t means

coal price at period t . In the later, we can set ∆Tt =1, ∆Tt can be omitted. Bidding function

of unit i at period t : pit = λiσ t (bi + 2ci g it )

(2)

where λi is a constant, λi ≥ 1. emission function of unit i at period t : N it ( g it ) = a 2i + b2i g it + c 2i g it2

(3)

Where, a2i , b2i , c2i are constants not less than 0. Bidding function of unit i at period t : H it ( g it ) = γ (a 2i + b2i g it + c 2i g it2 ) Where, γ is emission environmental cost factor.

(4)

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Advanced Research on Engineering Materials, Energy, Management and Control

As ISO, its purpose is to minimize purchasing cost, includes purchasing electric energy and environment penalty, within 24 hours,as follows: MinW = ∑ ∑ u it [ g it max{Pit ( g it ) | u it = 1, i = 1,2, … , n} t i ( P1 ) (r ) (r ) (r) (r ) (r ) (r ) + H it ( g it ) + p it ( g it ) g it + p it ( g it ) g it ]

∑u

s.t.

it

g it = Dt

(5)

i

(r )

u it g i min ≤ g it + g it ≤ u it g i max

(6)

(r )

0 ≤ g it ≤ g it − g i min

(7)

g it − gi ,t −1 ≤ ∆g i

(8)

∑| u

it

− u i ,t −1 |≤ M i

(9)

t

t +Tion

∏u

if uit - uit -1 =1，then

uit =0 or 1

ij

=1

(10)

j =t

t +Tioff

if uit -1 - uit =1，then

∏ (1 − u

ij

) =1

j =t

p

(r )

p

(r)

(r)

( g it )= θ i （ bi +2 ci g it ） ，θ i  0

(11)

( g it )= θ i （ bi +2 ci g it ） ，θ i  0

(12)

it (r )

(r )

(r )

it

∑u

it

g it ≥ ΦDt

(13)

∑u

it

g it ≥ ΦDt

(14)

(r)

i

i

(r)

Where, θ i , θ i are bidding factors for upper and down reserve; Φ ∈ (0,1), Φ ∈ (0,1) are reserve factor for upper and down reserve, Ti ,on continuous operation time of unit i at least; Ti ,off continuous taking off time of unit i at least; ∆g i maximum ramping output of unit i during1 hour； M i maximum times of unit i on-off during 24 hours. 0-1 Variable uit =1 means producing of unit

i at period t is purchased, uit =0 means producing of unit i at period t is not purchased； n is total number of units； gi min means lower limit of git ; g i max means upper limit of git ; D t means load demand at period t. there are two classes of variables, one is continuous variable git , the other is discrete variable uit . Purchasing Cost :

W * = ∑∑ u it* [ g it* max{Pit ( g it* ) | u it* = 1, i = 1,2, … , n} + H it ( g it* ) t

i

(r )

*( r )

*( r )

+ p it ( g it ) g it

(15) (r )

*( r )

*( r )

+ p it ( g it ) g it ]

Total generation fuel cost: F * = ∑∑ [u it* Fit ( g it* ) + u it* (1 − u i*,t −1 ) Fsit* ] t

(16)

i

Where, Fsit is start-up cost function of unit i at period t , here we can suppose it as a constant. Total emission : N * = ∑∑ u it* N it ( g it* ) t

(17)

i

* * Supply company revenue: V = p p ∑ Dt − W

t

(18)

Advanced Materials Research Vols. 424-425

*( r )

695

*( r )

u*i ,t −1 , u *it , g *it , g it , g it are optimum solution from the model (P1), F*sit is from u*i ,t −1 , u *it , g *it . 2.2 Model 2 Consume-price elasticity factor for load system: eij = ( ∫ ∆Di dt / ∫ Di dt ) /( ∆p j / p j ) ∆Ti

∆Ti

(19)

Where, ∫ ∆Di dt , ∆p j means increment of electricity consuming and price at period i, j; ∆Ti

∫

∆Ti

Di dt , p j means electricity consuming and price at period i, j. Suppose ∆Ti =1，we have:

eij = (∆Di / Di ) /( ∆p j / p j )

(20)

We can find, as i = j , eij 0. Consume-price elasticity matrix for load system: E = {eij } . let: ∆pi = pi - p p . Since ∆Ti =1，we have Di = qi / ∆Ti = qi , qi(0) = Di0 , hence 0 0   ∆p1 / p p  …  D1   D10  q1( 0)     D  D   (0) 0   ∆p 2 / p p  …  2  =  20  +  0 q 2 E   … … … …          (0)   0 … q 24  D24   D30   0  ∆p 24 / p p 

(21)

Where, qi( 0) , qi means electricity quantity before and after TOU at period i, p p , pi means electricity price before and after TOU. Hence, we can have: Dt = Dt ( ∆p1 , ∆p 2 ,…, ∆p24 ) (22) Suppose ∆pt as follows:

∆pt = α p p , t ∈ T f ; ∆pt = 0, t ∈ Tp ; ∆pt = β p p , t ∈ Tg . So we can have Dt = Dt (α , β ) . Where, α , β is varying rate at peak, valley period respectively; T f , Tp , Tg are time sets of peak, shoulder, valley respectively. We get optimization model about TOU： MinW = ∑∑ u it [ g it max{Pit ( g it ) | u it = 1, i = 1,2, … , n} t i ( P2 ) (r ) (r ) (r ) (r ) (r) (r ) + H it ( g it ) + p it ( g it ) g it + p it ( g it ) g it ]

s.t.

(5)-(12) ∑ uit g it = Dt (∆p1 , ∆p 2 ,…, ∆p 24 )

(23)

i

∑( p

p

t

+ ∆pt ) Dt / ∑ Dt ≤ p p

∑∑ [u F ( g ) + u (1 − u ∑∑ u N ( g ) ≤N it

t

it

it

it

i ,t −1

) Fsit ] ≤ F *

*

t

t

p

(25)

i

it

∑(p

(24)

t

it

it

(26)

i

+ ∆p t ) Dt − ∑∑ u it [ g it max{Pit ( g it ) | u it = 1} + γN it ( g it )] ≥ V * t

(27)

i

Variables of the model (P2) are α , β , uit , g it . After solving the model (P2), we can have purchasing cost W ** , Generation fuel cost F ** Emission N ** and Supply company revenue V ** .From the above calculation results, we can find that TOU can bring benefits to generation units, consumers, electricity suppliers.

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Advanced Research on Engineering Materials, Energy, Management and Control

2.3 Model 3 MinW =

( P3 )

∑∑u

it

(r)

(r )

t

(r)

(r )

i

(r )

+ p it ( g it ) g it ] +

s.t.

(r)

[ g it max{ Pit ( g it ) | u it = 1} + H it ( g it ) + p it ( g it ) g it 24

∑[p t =1

(r ) dt

(r )

(r )

(r)

(r )

(r )

∆ D t ( p dt ) + p dt ∆ D t （ p dt ）]

(5)-(12), (23)-(24)

∑u

it

g it + ∆D t ≥ G t

(28)

∑u

it

g it + ∆D t ≥ G t

(29)

(r )

(r )

(r)

i

[∆D

i (r ) t

(r ) t

(r )

(r)

(r )

/ Dt ] /[ p dt /( p p + ∆pt )] =| ett |

(30)

(r )

= η p dt | ett | Dt /( p p + ∆pt )

(31)

∆D t = η p dt | ett | Dt /( p p + ∆pt )

(32)

∑∑ [u

Fit ( g it ) + u it (1 − u i ,t −1 ) Fsit ] ≤ F **

(33)

N it ( g it ) ≤ N **

(34)

∆D

(r )

t

t

∑(p

(r )

it

i

∑∑ u t

(r )

it

i

p

+ ∆p t ) Dt −∑∑ u it [ g it max{Pit ( g it ) | u it = 1} + γN it ( g it )] ≥ V ** t

(35)

i

***( r )

Where， η ≥ 1, η ≥ 1. With the optimum solutions u it*** , u i*,*t*−1 , g it*** , g it ***( r )

p dt

***( r )

, g it

***( r )

, p dt

,

gotten form solving the model( P3 ), we can calculate purchasing cost W *** , generation fuel

cost F *** , emission N *** , supply company revenue V *** . Then the effect of further optimization can be calculated as follow: ∆W *** = W *** − W * , ∆F *** = F *** − F * , ∆N *** = N *** − N * .

3.

Conclusion

A three layers optimization model for time-of-use and interruptible price is established in this paper. The model fully consider the benefits of power generators, power supply company and environment, which maximize the social effect. In addition, the comparison between different shows the further effect as the time-of-use price and interruptible price was considered progressively.

4.

References

[1] ZHANG Xiaohua, ZHAO Jinquan, CHEN Xingying. (2010) Multi-objective Unit Commitment Fuzzy Modeling and Optimization for Energy-saving and Emission Reduction. Proceedings of the CSEE, 30[22]: 71-76. [2] WANG Jiangbo, LIANG Rongshan, TIAN Kuo. (2010) International Experience of Demand-side Management Security System and Enlightenment to China. East China Electric Power, 38[10], 1491-1494. [3] TAN Zhong-fu, CHEN Guang-juan, ZHAO Jian-bao. (2009a) Optimization Model for Designing Peak-valley Time-of-use Power Price of Generation Side and Sale Side at the Direction of Energy Conservation Dispatch. Proceedings of the CSEE, 29[01]: 55-62. [4] SONG Yihang, TAN Zhongfu, YU Chao. (2010) Analysis Model on the Impact of Demand-Side TOU Electricity Price on Purchasing and Selling Risk for Power Supply Company. Transactions of China Electrotechnical Society, 25[11], 183-190. [5] TAN Zhongfu, XIE Pinjie, WANG Mianbin. (2009b) The Optimal Design of Integrating Interruptible Price With Peak-Valley Time-of-Use Power Price Based on Improving Electricity Efficiency. Transactions of China Electrotechnical Society, 24[9], 161-168.

Advanced Research on Engineering Materials, Energy, Management and Control 10.4028/www.scientific.net/AMR.424-425

Three Layers Optimization Model for Time-of-Use and Interruptible Price Based on Fuel Saving and Emission Reducing 10.4028/www.scientific.net/AMR.424-425.693