Optimal Procurement Of Var

Optimal Procurement of VAR Ancillary Service in the Electricity Market Considering Voltage Security E. E. El-Araby

Naoto Yorino

Yoshifumi Zoka

Department of Artificial Complex Systems Engineering Hiroshima University Higashi Hiroshima, Japan Abstract— This paper presents a competitive bidding scheme for procuring VAR service in the electricity market with the consideration of voltage security in normal and postcontingency states. To determine the most beneficial VAR contracts that satisfy the required level of system security and ensure adequate payment of VAR service, an optimization problem that simultaneously minimizes the total payment of the procured VAR and operating costs in all transition states while maintaining a set of physical constraints including voltage security margin is developed. The global solution of the proposed formulation is obtained using a hybrid genetic algorithms/successive linear programming (GA/SLP) method.

I.

INTRODUCTION

In recent years, the electric power systems worldwide have been moving from the traditional regulated and monopoly structure toward an open-access competitive market environment. In this new paradigm, the independent system operator "ISO" is responsible for the system dispatch and operation. In order to maintain the system reliability and security, the ISO is required for the procurement of some essential ancillary services [1]. The reactive power service is one of the ancillary services that must be in place to support energy transfer in a secure manner. The management and procurement of this service vary widely for each deregulated market. In the U.S., the North American Electric Reliability Council identifies that only the synchronous generator is entitled to provide VAR as an ancillary service, and is eligible for financial compensation. This also is true for the UK and Australian markets. The Australian market recognizes also the VAR from synchronous condensers as an ancillary service. The main aspects of the procurement of VAR in most electricity markets are as follows: (1) The ISO usually procures VAR on long-term contract basis. (2) In many markets, a minimum obligatory of VAR from generators is defined. This obligation is often expressed as a power factor capability range, usually with no payment.

0-7803-8834-8/05/$20.00 ©2005 IEEE.

(3) Most of the existing markets emphasize the recovery of the generator opportunity costs in their procurement of VAR service. (4) Different payment structures are currently used, where there is no standard methodology by which the ISO pay resources for VAR. A detailed review of the VAR management and payment schemes in different markets is given in [2]. Several published papers have recognized that the current practice of the VAR procurement has relied on the heuristics and operators' judgments for many transmission operators [3,4]. These papers revealed that it is essential to procure VAR service in a competitive manner in order to incentive the market's participants to provide VAR service and ensure an adequate payment that guarantees the economic efficiency of this service. Although the fact that the voltage collapse is closely related to the deficiencies of the reactive-power supports and this situation threatens the system security, the voltage security problem has been rarely considered in the previous researches that dealt with the VAR service in a competition based market environment [5]. Since the ISO seeks those VAR suppliers that simultaneously minimize its total payment and meet the required VAR in the normal and emergency states, it is very effective to develop a VAR procurement competitive method that takes into consideration the voltage stability in the normal and contingency states in order to avoid the likely extra VAR payment and ensure the system security in the emergency states. This paper focuses on the provision of the VAR service from generators and synchronous condensers in a competitive market-based environment, where the successful participants in this market will get a long-term contract with ISO to provide the required VAR whenever called upon. The reactive power procured in this VAR market is considered to be adequate in maintaining voltage security in all transition states, where the voltage stability margin is explicitly treated in the proposed method. The objective function is to minimize simultaneously the sum of the total payment of VAR service and operating costs

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in normal and contingency states to guarantee the economic efficiency of this service. The total payment of VAR service includes the payment of the extra reactive capacity beyond the generators VAR obligations and the lost of the opportunity costs. The operating costs include power loss cost in the normal state and control costs in the emergency states. II.

VAR MARKET SCHEME

MVAR

The possible VAR market scheme presented in this paper considers only the generators and synchronous condensers since they are only eligible for VAR ancillary service. A key physical constraint in the provision of the VAR by a generator is its generation capability constraint. It represents the hard physical limitation of a generator's capability for the simultaneous production of real and reactive power. A typical generation capability curve is shown in Fig. 1. As we have mentioned in the introduction, many existing transmission operators obligate the generators to provide a certain amount of VAR, which is usually within a specified range of power factor. According to a NERC planning standard guideline [1], reactive capability within 0.9 lagging and 0.95 leading should be available.

Q1*

Region III ( Q1 to Q1* & Q 2 to Q*2 ): In this region the generator will reduce its real power output and consequently its lost revenue will be recovered by the ISO.

FP

Q*2 Q2 Qmd2

Based on the classification of the above regions, a bidding scheme that allows the ISO to procure VAR service from generators and synchronous condensers in competitive manner is introduced. This bidding method mainly relies on the generator VAR payment function. According to the defined above regions, a typical VAR payment function is depicted in Fig. 2. The mathematical formulation of this function is given by the following equation:

Lagging pf

Psch Q md2

Qmd1 Q1 Q* MVAR 1

Figure 2. Payment Structure

Q1 Q md1

Q*2

paper, we assume that the generator will provide its VAR service as described in the following regions: Region I ( Q md2 to Q md1 ): The reactive power produced in this region is obligatory with no payment. Region II ( Q md1 to Q1 & Q md2 to Q 2 ): This region represents the extra reactive VAR provided by generator beyond it obligatory without rescheduling its real power output. A generator in this region is expecting a payment from the ISO for its VAR service.

Leading pf

MW

FP = -µ1Qg1 - µ 2 Qg2 + µ3Qg3+ µ 4 Qg4

Q2

Figure 1. Generator Capability Curve

The principle of the proportional obligations that compel the generators to provide VAR service in proportion to their active power output is exploited here to develop the proposed market structure [4]. According to this principle, the generator VAR within a pre-specified range of power factor is mandatory with no payment. The VAR of a generator beyond the mandatory is considered solely as an ancillary service that the generator offers and should be compensated for providing it. Therefore, the VAR that the generator offers and expected to be recovered is divided into two parts. The first part is the VAR injection or absorption that the generator provides beyond its mandatory without rescheduling its real power output and the second part is the lost of opportunity cost incurred as a result of reducing its real power output. For instant, consider the power schedule of the generator is given by Psch as shown in Fig. 1. In this

(1)

where the coefficients µ1 , µ 2 , µ3 and µ 4 are the offer prices that the generators provide for each region discussed before and Qg1 , Qg2 , Qg3 and Qg4 are the corresponding provided VAR amount respectively. Note that the generator supplied VAR amount that will be recovered in each region must satisfy the following constraints: Lead pf Q 2 − Q md2 ≤ Qg1 ≤ 0 , Q*2 − Q 2 ≤ Qg2 ≤ 0 Lag pf 0 ≤ Qg3 ≤ Q1 − Q md1 , 0 ≤ Qg4 ≤

Q1*

− Q1

(2) (3)

Therefore, in order to run the market, the generators are also required to make available information on Q1 , Q1* , Q 2 and Q*2 as shown in Fig. 1. The objective of the ISO in the above market structure is to determine the most beneficial reactive power contracts that satisfy a minimum total payment of the procured VAR while maintaining the system security in normal and credible contingencies. Therefore, the main contribution of this paper is to develop a mathematical formulation that allows the ISO

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to use the above bidding scheme in achieving simultaneously the required level of the system security and the minimization of its total payment. The basic idea behind this mathematical formulation starts from the fact that the system reactive power reserves have a profound impact in avoiding voltage instability, which usually tends to occur from lack of reactive power supplies in heavily stressed conditions. Recently, we have recognized the importance of the inclusion of voltage stability in the conventional VAR planning problem [6,7]. The main objective of that work is to provide a tool for the utilities of the vertically integrated power systems that enables them to determine a minimum investment cost of new FACTS devices that suppose to be used to keep voltage security in multi transition states. This idea has been modified in the present work to procure the VAR ancillary service in the electricity market with taken into consideration the voltage security in normal and contingency states. However, the situation in the market is different in two main aspects. The first one is that the FACTS devices are not considered as an ancillary service in the current electricity markets. Therefore, the investment of new FACTS is excluded in the present work, where the generators and synchronous condensers are merely the main providers of the VAR service. The second aspect is that the VAR service is procured in a competitive market-based environment, which is not the case in the vertically integrated systems. In order to satisfy the main objective of the ISO in obtaining the required VAR service in minimum payment, it is necessary to employ the procured VAR efficiently in the system operation. Consequently, the following base case and contingency states subproblems are assumed to achieve the ISO main goal. III.

B. Post-Contingeny State Subproblems For the contingency states, the corrective control actions are assumed based on the reactive power controls and load shedding to guarantee the system security. The objective function is to minimize the total amount of the control costs while satisfying, for each contingency state, the nominal load operating point constraints set and the collapse point constraints set. The formulation of this problem is stated as: Minimize FC (p(0) ,p(k) ,s(k) ,Q(0) ,Q(k) )

∑ µ sl s(k) +∑ µ pi p(k) -p(0) +∑ µ qj Q(k) -Q(0) }

={

i

l

(4)

subject to

 

 ≤ H b(0) (x b(0) ,pb(0) ,Qb(0) ,λb(0) ) ≤ H b(0)   Qg1 + Qg2 + Q md2 ≤ Qb(0) ≤ Qg3 + Qg4 + Q md1  

(7)

j

subject to (k) (k) (k) (k) (k) G (k) b (x b ,p b ,s b ,Q b ,λb ) ≤ 0

(k) (k) (k) (k) (k) G (k) c (x c ,p c ,sc ,Qc ,λc ) ≤ 0

Minimize FA (x b(0) ,pb(0) ,Qb(0) ,λb(0) )

Gb(0) (x b(0) ,pb(0) ,Qb(0) ,λb(0) ) = 0

(6)

where the subscripts b and c indicate the nominal load operating point and collapse point. FA is the power loss cost. The superscript (0) refers to the base case subproblem. x is the state variables vector. Q is the generator VAR output. p is the control variables vector excluding Q. λ is the load parameter value. Note that the equality constraints at the point of collapse stand for the conditions of the saddle node bifurcations, which are useful in identifying λ .

OPERATION SUBPROBLEMS

A. Base Case Subproblem To ensure an adequate payment for the VAR service, the procured VAR must be utilized efficiently in the base case. Choosing a proper objective function to be minimized in the operation can effectively satisfy this need. In this paper, the cost of the power loss is selected as the main objective function in the base case subproblem. To maintain voltage stability margin requirement, two sets of constraints have been included in the formulation. The first set represents the equality and inequality constraints at the nominal load operating point and the second set represents the equality and inequality constraints at the point of collapse. This problem is formulated as

H b(0)

  (0) (0) (0) (0) H c(0) ≤ H c(0) (x (0)  c ,pc ,Qc ,λc ) ≤ H c Qg1 + Qg2 + Q md2 ≤ Qc(0) ≤ Qg3 + Qg4 + Q md1  

(0) (0) (0) Gc(0) (x (0) c ,pc ,Qc ,λc ) = 0

(8)

(k) where G (k) b and G c are similar to the constraints (5) and (6) respectively except that the superscript k refers to post-

contingency state and the load shedding s is included. µ sl , µ pi and µ qj are unit control cost coefficients of s, p and Q

respectively. Note that the inclusion of the load shedding in each subproblem described above will guarantee the feasibility of the problem during the computation process. However, since the control costs of load shedding are much higher than the other controls, they will be the final option among the controls. C. Overall Problem Formulation To guarantee the economic efficiency of the VAR service, we simultaneously minimize the total payment of procured VAR and operating costs in normal and contingency states as follows Minimize

(5)

F=

m

∑ Fpj + FA + ∑ j

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k =1

FC(k) , m =number of contingencies

subject to Generators constraints (2) and (3) Base case constraints (5) and (6) Post-contingency states constraints (8) IV.

(9)

SOLUTION ALGORITHM

An optimization technique based on a hybrid GA/SLP for finding a global optimal solution of (9) is presented in this section [7]. The computational procedures of the proposed method are summarized in Fig.2. The algorithm starts from a random initial population, where its individuals are indicated in Fig. 3 by indv1, indv2.,……., indvn1,. Each individual in the population represents a candidate solution, i.e., a pattern of generators VAR service. For instant, assume individual 1 (indv.1) represents a candidate pattern of generators VAR service. This candidate pattern is used as a common candidate for the base case and all contingency states under investigation. The SLP is used to solve the optimization problems (4-6) and (7-8) individually. According to the optimization results, the fitness of indv.1 is

opportunity offer price of the synchronous condensers is zero in this table. Based on submitted offers, the solution algorithm presented in section IV is executed. The most three sever contingencies are selected for the simulation. The minimum bus voltage limit and the desired voltage stability margin for each contingency are assumed to be 0.9 and 0.25 respectively. The results of the optimal VAR procured beyond generators mandatory in this examination are given in Table. 2. TABLE I.

indv.2

base case

1

2

3

4

5

µ1 , µ 2

6.0, 0. 0

7.2, 12.5

5.0, 0.0

8.0, 11.5

6.0, 0.0

6.5, 14.0

µ3 , µ 4

8.0, 0. 0

7.0, 12.5

6.0, 0.0

8.5, 11.5

5.8, 0.0

7.8, 14.0

Qmd1, Qmd2 0.0, 0. 0

0.20, - 0.1

2.22, -1.4

0.0, 0.0

1.53, -0.50

2.5, 3.25

0.09, 0.09 1.94, 2.52

Q2 , Q*2

0.5, 0. 5

0.0, 0.0

0.75, 0.98 0.25, 0.25

6

-0.17, -0. 17 -0.12, -0.16 -0.08, - 0.08 -1.75, -2.28 -0.03, -0.03 -0.63, -0.81

TABLE II.

OPTIMAL VAR PROCUREMENT

1

2

3

4

5

Qg1 , Qg2

0.0, 0. 0

0.0, 0.0

0.0, 0.0

0.0, 0.0

0.0, 0.0

0.0, 0.0

Qg3 , Qg4

0.5, 0. 0

0.51, 0.0

0.25, 0.0

0.15, 0.0

0.09, 0.0

0.37, 0.0

Generator

6

ACKNOWLEDGMENT

indv.n1

The authors gratefully acknowledge the support from JSPS Postdoctoral Fellowship Program.

cont.

1. . . . .m

REFERENCES [1] [2]

evaluate. indv. evaluate. indv. evaluate. indv. store best individual in the solution set

[3]

GA operators next generation

[4]

Figure 3. A hybrid GA/SLP Solution Method

V.

Generator

Q1, Q1*

evaluated in terms of FP , FA and FC . The same computational procedures will be repeated for each individual in the population. Accordingly, the best individual and its associated generators VAR pattern are stored in a solution set. Then, genetic algorithm operators (reproduction, crossover, mutation) are applied to produce next generation. These procedures are repeated till a termination criterion is satisfied. Finally, the final solution is retrieved from the solution set.

indv.1

GENERATOR AND SYNCHRONOUS CONDENSERS OFFERS

[5]

TEST RESULTS

The proposed method has been applied to IEEE-57 bus system, where the original loads as well as generations have been increased uniformly by 50% to define the base case. The offer prices and reactive power capabilities for the VAR service providers that the ISO requires to run proposed market structure are given in Table. 1. Note that the

[6]

[7]

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NERC Planning Standards, North Amrican Electric Reliability Council.//www.nerc.com [online] Jin Zhong and Kankar Bhattacharya, “Reactive Power management in deregulated power systems- A review ,” in proc. IEEE Winter Meeting, Vol. 2, No. 2, pp. 294-300, 2002 Jin Zhong and Kankar Bhattacharya, “Toward a Competitive Market for Reactive Power ,” IEEE Transactions on Power Systems, Vol. 17, No. 4, pp. 1206-1215, November 2002. Shangyou Hao, “A Reactive Power Management Proposal for Transmission,” IEEE Transactions on Power Systems, Vol. 18, No. 4, pp. 1374-1381, November 2003. Deb Chattopadhyay et al, “A spot pricing mechanism for voltage stability, “ Electrical Power and Energy Systems, 25, No. 9, pp. 725734, November 2003. N. Yorino, E. E. El-Araby, H. Sasaki and S. Harada, “A new formulation for FACTS allocation for security enhancement against voltage collapse,” IEEE Transactions on Power Systems, Vol. 18, No. 1, pp. 3-10, February 2000 E. E. El-Araby, N. Yorino and H. Sasaki “ A two Level hybrid GA/SLP for FACTS allocation problem considering voltage security,” International Journal of Electrical Power & Energy Systems, Vol. 25, No. 4, pp. 259-338, May 2003.