20 Allocating The Costs Of Reactive Power Purchased

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IEEE TRANSACTIONS ON POWER SYSTEMS, VOL. 19, NO. 1, FEBRUARY 2004

Allocating the Costs of Reactive Power Purchased in an Ancillary Service Market by Modified Y-Bus Matrix Method Wen-Chen Chu, Member, IEEE, Bin-Kwie Chen, Member, IEEE, and Chung-Hsien Liao

Abstract—In an open accessed transmission system, the costs of each ancillary service will be unbundled. This paper proposes a straightforward method of allocating the costs of reactive power purchased by contract or from a bidding market. This method uses basic circuit theory and partitions the Y-bus matrix to decompose the voltage of the load buses with a view to calculating the reactive power sharing. This method is derived from the system equations without such assumptions as the proportional flow or lossless transmission line. Index Terms—Ancillary service, cost allocation, reactive power.

I. INTRODUCTION

L

IBERALIZATION is the major trend in the power industry reform throughout the world. The transmission system is open to access by all power market participants, with the independent system operator (ISO) in charge of system dispatch and operation. To keep the system running normally, some ancillary services either purchased by contract or from a bidding market are needed. Certainly, the costs of these services should be shared by the users, and how to fairly allocate the costs becomes an important issue. The reactive power is confined to mainly local consumption, which will motivate the market to determine the actual value of each supply. A fair and adequate method for allocating the costs may help the market participants make appropriate and efficient investments of reactive power sources, which include static capacitors, flexible ac transmission system (FACTS) devices, and synchronous condensers. All of these can offer system operators more tools and can strengthen the system security. While focusing on the part of reactive power consumed by the loads, this paper tries to develop a scheme to allocate the costs of reactive power supplied by generators, synchronous condensers, or capacitors. So far, the methods of allocating real power and reactive power cost may fall into three categories. The first is the tracing of the electricity flow [1]–[3]. By calculating the upstream distribution matrix, this approach can deduce the real or reactive power from individual generators received by each load. Next is the approach to ascertaining the contributions of generators to the power flow [4], [5]. It simplifies the power system to state graphs and then uses recursive equations to solve Manuscript received June 19, 2003. This work was supported by the National Science Council under Grant NSC 91-2213-E-036-025. W.-C. Chu and B.-K. Chen are with the Department of Electrical Engineering, Tatung University, Taipei 10451, Taiwan, R.O.C.. C.-H. Liao is with Tatung Company, Taipei 10451, Taiwan, R.O.C. Digital Object Identifier 10.1109/TPWRS.2003.821425

the real and reactive power that each generator contributes to individual loads. The third is graph theory [6]–[8]. Contribution factors are calculated to determine the real or reactive power that each generator contributes to individual lines and loads. These methods have made some contributions to the modern power industry for system operation security, consumers’ pricing, and investment signals. However, in this paper, we would like to make a trial from a different perspective and with a different approach to develop an alternative methodology for users’ selection. This paper mainly discusses the allocation of the reactive power cost. However, it will not be concerned about the aspect of the real power because bilateral transactions of the real power will take place after the liberalization of the power industry as effective power transactions will be performed by fixed buyers and fixed sellers. Hence, the source and direction of the real power are already fixed, at least in the artificial assumption. By contrast, the reactive power is the result of the power system dispatching and does not exist in the bilateral transaction. The reactive power can be supplied by the synchronal generator, synchronal motor, and capacitor, so the cost certainly varies with suppliers and locations. Besides, the reactive power cannot transmit far off and will result in the loads with equal demand of reactive power; as a result of the different sources, the cost naturally varies. According to the fairness principle, it is necessary to identify the reactive power sources of every load and calculate the cost. Therefore, this paper mainly discusses the allocation of the cost of the reactive power. As for the matter of line losses, including real and reactive power, they are indeed to be shared by the users. The reactive power on load buses is the demand of consumers and the reactive power of line losses arises from the use of transmission lines, although both have the same physical properties. The authors would like to treat the part of line loss allocation as a separate topic under transmission use charge. Only the reactive power of load demand is the focus of this paper. The allocation method proposed in this paper is based on one basic principle of circuit theory, which states that every load bus voltage is contributed by all source voltages in the circuit. Therefore, this paper will deduce the relationship function of the load voltage (VL) and the generator voltage (VG), namely , to find out the quantity of the voltage component made up of all load voltages. Then it will use the voltage of each load voltage and load current known component from the results of the power flow analysis to obtain the reactive power that each load acquires from individual generators.

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CHU et al.: REACTIVE POWER PURCHASED IN AN ANCILLARY SERVICE MARKET BY MODIFIED MATRIX METHOD

After that, it will further calculate the reactive power cost obtained from different sources if the reactive power is acquired by bidding on the liberalized power market. II. METHODOLOGY OF MODIFIED Y-BUS MATRIX The proposed methodology begins with the system node equation. For the convenience of explanation, it is assumed that the power system has a total number of buses, generators, and loads, among which bus no. are generation buses are load buses. Therefore, the Y bus of and bus no. dimension can be divided into four submatrixes as shown in (1)

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] matrix, so the original matrix [ ] is elements in the [ . With the equivalent admittances of replaced by matrix loads being represented, the load buses will have no injection current, thus reducing the sub-matrix [IL] to [0]. Hence, (2) is changed as shown: (4) Equation (4) on the lower half part of the matrix is used to arrive at: (5) And then the relationship functions can be obtained as follows:

..

..

.

(6)

. and

..

..

.

(7) .

In (7), it is assumed that (8)

.. .

.. .

and (7) can be rewritten as (9)

(1) .. .

.. .

The voltage of each load bus consisting of the voltages contributed by individual generators is expanded as shown in the following equation:

Equation (1) can be briefly represented as the following (2): (10) (2) The main goal is to deduce the load bus voltages as a function . The conof the generator bus voltage, namely, cept is based on the superposition of circuit theory, which states that each load voltage consists of individual source voltages in the circuit. However, it is required that all of the loads must be represented as admittances in the circuit if the theory is applied, but the loads in the form of injection current are derived from apparent power for performing power flow analysis. Therefore, the load must be transformed from the injection current into the equivalent admittance and the Y bus matrix must then be modified. The load can be transformed into the equivalent admittance by using the bus voltage known from the results of power flow analysis. Meanwhile, one thing that has to be emphasized here is that the power flow program should be executed to obtain the values of voltage, real power, and reactive power on each bus of the system studied before applying the proposed methodology. The relevant equation is as follows: (3) is the apparent power of load on bus j, is the where is the resultant equivalent admittance of load on bus j, and voltage of bus j of power flow analysis. We use (3) to calculate of every load and then modify the the equivalent admittance submatrix [ ] in the original Y bus matrix. The modification to the diagonal is executed by adding the corresponding

and it is assumed that (11) where is the voltage contribution that load acquires from generator . Equation (10) may also be expressed as (12) With (12), it can be recognized that the voltage contribution of each load bus received from individual generators is . The reactive power contribution that load acquires from generator is as follows: Im

(13)

where is the load current which is to divide the power of the load by known load bus voltage and take the conjugate of the complex number on load bus . On finding the reactive power contribution that load obtains from generator , one may assume that the bidding price of the reactive power of generator in the ancillary services market is . Then the cost that load has to pay generator i is (14) where ator , and market.

is the reactive power cost that load pays generis the bidding price of generator in the ancillary

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Fig. 2.

Five-bus sample system.

TABLE I ALLOCATING REACTIVE POWER BY THE PROPORTIONAL SHARING METHOD

TABLE II ALLOCATING REACTIVE POWER BY THE PROPOSED METHOD Fig. 1.

Flowchart for calculating reactive power cost.

By summing up the reactive power costs that each load pays the generators, one can find the reactive power cost that should be allocated to each load. The reactive power cost that load should pay is (15) where is the reactive power cost that load should be allocated. All of the procedures of the computation mentioned above can be demonstrated as a flowchart illustrated in Fig. 1. III. COMPARISON AND DISCUSSIONS In order to explain the proposed method in more depth, a five-bus sample system is created to demonstrate the allocation of reactive power for each load bus. A comparison with the proportional sharing method is also made to present the features of this method. The five-bus sample system is shown in Fig. 2. The computed power flow is also indicated in this figure.

The results from adopting the proportional sharing method are listed in Table I, while those obtained from the proposed method for this paper are listed in Table II. There are several observations to be discussed below. 1) It is necessary to use the reactive power flow to calculate the share of reactive power consumed on load buses, because the real power and reactive power may have different directions. The power flow between bus 1 and bus 2 is a case in point. 2) If bus 1 and bus 3 are selected to demonstrate the proportional sharing calculation, there are 6.8 MVARs from generator 1 and 0.61 MVARs from generator 2. Total reactive power demand on bus 3 is four MVARs. And 3.64 MVARs are from G1 and 0.36 MVARs are from G2, if the sharing rate of 91% and 9% are used. But as can be

CHU et al.: REACTIVE POWER PURCHASED IN AN ANCILLARY SERVICE MARKET BY MODIFIED MATRIX METHOD

TABLE III ALLOCATION OF REACTIVE POWER OF IEEE 30-BUS SYSTEM WITHOUT ADDED CAPACITOR

observed from the figure, the exiting reactive power from bus 1 to bus 3 is 7.44 MVARs, though only 6.3 MVARs enter bus 3. The existing difference is the line losses. If the Q demand on bus 3 is proportionally shared in the way described previously, this approach implies that the line losses are also shared in the same proportion as is used at the entrance of bus 1. 3) From the figure, it can also be observed that the real power flow is larger than reactive power flow on each line due to the higher power factor of the loads. But the line reactance is much larger than line resistance, causing the reactive power loss to be higher than real power loss. It means that the loss percentage of reactive power is larger than that of real power. Therefore, ignoring the line losses or sharing the losses in the same proportion as that of the power flow is feasible for the real power part, though likely inappropriate for the reactive power part. 4) A comparison of the results of these two methods as shown in Table I and Table II reveals that there exist some similarities and differences. The consumed reactive power on bus 3 is mainly supplied by G1, while most of it on both bus 4 and bus 5 is obtained from G2. However, the corresponding amounts indicated in these two tables express some discrepancy. We believe that the differences are caused by the method adopted. The proposed method is based on voltage superposition, which will get the line flow with different directions for the contribution from individual generators. On the other hand, the proportional sharing method takes account of the net line flow.

IV. CASE STUDY The IEEE 30-bus system is taken as an example in this paper to illustrate the allocation of reactive power cost, using the proposed method described in the previous section.

ALLOCATION

OF

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TABLE IV REACTIVE POWER OF IEEE 30-BUS SYSTEM WITH ADDED CAPACITOR

Before the simulation experiment,part adjustment forthe IEEE 30-bus system will be made. That is to order the bus numbers and let bus 1 to bus 6 be generator buses and the others be load buses. The system input data of this IEEE 30-bus system are listed in Tables A.1 and A.2. As can be seen, there is line charging, which will supply the reactive power to this system. After the deregulation of the electric power industry, it is believed that the electric power transmission network is provided to all users under the open-access policy. But the line charging exists because of the physical characteristics of the transmission line rather than a specific generator or a specific reactive power source. The grid users have to pay for the use of transmission facilities and related operation and maintenance costs by way of the transmission service charge. The charge has covered the transmission providers’ costs and profits. The reactive power generated by line charging will not drive up any owner’s costs. On the other hand, how to determine the value and to participate in the bidding market is another problem, because the line charging phenomenon cannot be switched on or off like other reactive power sources. This paper prefers to take the view that the line charging and line loss arise from the property of transmission lines and are to be counted as the same matter as thetransmissionservice charge. Consequently, the line charging is not included in the cost allocation. The reactive power that each load obtains from each generator can be calculated with the IEEE 30-bus system and the results are shown in Table III. It can be seen that the reactive power consumed on each load bus is supplied by these six generators, with the quantity as listed in Table III. The sum of the reactive power on each load bus acquired from each generator is in conformity with its actual reactive power demand. If the selling prices of the generators are different, then the total amount of reactive power costs charged to the loads can be calculated with (15). Finally, if the reactive power is delivered from a synchronous condenser or a static capacitor, this method can still work functionally. It just treats this kind of bus as the generator bus, whose parameters are in the upper level submatrices in (2). In other words, the voltages and power on each bus have been determined by load-flow analysis. The voltages on buses of these sources will be directly used to calculate the

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TABLE A.1 LINE DATA OF IEEE 30-BUS SYSTEM

effect on each load bus by (10). In order to justify the impact of a reactive power source in this sample system, a static capacitor is addedtobus7andtheresultsarelistedin TableIV.With thiscapacitor of 10 MVAR included, the power flows and voltages of this system have been changed. The bus voltage contributions from each generator are also changed, reflecting in a change that can be seen as a reduced share on each load bus of the reactive power from the existing six generators (see Table IV). Obviously, the G7 represents the supply of reactive power from this capacitor, which takes over part of the role of other generators. This phenomenon is particularly obvious on bus 26, whose reactive power suppliers are shifted to G7 as bus 7 is close to bus 26. V. CONCLUSION Over the past ten years, the deregulation in the power industry has been carried out in many countries. The operation of the power system calls for the support of ancillary services that involve grid open access. How to fairly allocate the costs of these ancillary services becomes an important issue. This paper

TABLE A.2 POWER FLOW ANALYSIS RESULTS OF IEEE 30-BUS SYSTEM

focused on the reactive power part and developed a straightforward method based on the network theory. The proposed method can identify the source and can calculate the amount of the consumed reactive power on each load bus. The simulation results have also shown the conformity of reactive power supply and reception in a power system. The calculation results might bring about some differences from those based on other methods, but the allocation of reactive power costs is like the other topics stemming from deregulation, where different viewpoints and approaches may end up with different results. This paper would like to try to offer the solution by an alternative methodology. REFERENCES [1] J. Bialek, “Tracing the flow of electricity,” Proc. Inst. Elect. Eng., Gen., Transm. Dist., vol. 143, no. 4, pp. 313–320, July 1996. [2] J.Janusz Bialek, “Topological generation and load distribution factors for supplement charge allocation in transmission open access,” IEEE Trans. Power Syst., vol. 12, pp. 1185–1193, Aug. 1997. , “Allocation of transmission supplementary charge to real and re[3] active loads,” IEEE Trans. Power Syst., vol. 13, pp. 749–754, Aug. 1998. [4] D.Daniel Kirschen, R.Ron Allan, and G.Goran Strbac, “Contributions of individual generators to loads and flows,” IEEE Trans. Power Syst., vol. 12, pp. 52–60, Feb. 1997. [5] G.Goran Strbac, D.Daniel Kirschen, and S.Syed Ahmed, “Allocation transmission system usage on the basis of traceable contributions of generators and loads to flows,” IEEE Trans. Power Syst., vol. 13, pp. 527–532, May 1998. [6] F. F.Felix F. Wu, Y.Yixin Ni, and P.Ping Wei, “Power transfer allocation for open access using graph theory—fundamentals and applications in systems without loopflow,” IEEE Trans. Power Syst., vol. 15, pp. 923–929, Aug. 2000.

CHU et al.: REACTIVE POWER PURCHASED IN AN ANCILLARY SERVICE MARKET BY MODIFIED MATRIX METHOD

[7] P.Ping Wei, B.Bin Yuan, Y.Yixin Ni, and F. F.Felix F. Wu, “Power flow tracing for transmission open access,” in Proc. Elect. Utility Deregulation Restructuring Power Technol. Int. Conf., 2000, pp. 476–481. [8] F.Fubin Liu, Y.Yang Li, and G.Guoqing Tang, “A quick & practicable power flow tracing method on electric energy market part II: a new practicable method,” in Proc. IEEE Power Eng. Soc. Winter Meet., vol. 3, 2001, pp. 1238–1243.

Wen-Chen Chu (M’86) was born in Taipei, Taiwan, R.O.C., in 1952. He received the B.S. degree in electric engineering from Tatung Institute of Technology, Taipei, Taiwan, R.O.C., in 1976, and the M.S. and Ph.D. degrees from the University of Texas at Arlington in 1983 and 1986, respectively. Currently, he is a Professor at Tatung University. He was an Electrical Engineer with Fu-Hwa Engineering Company, Jedda, Saudi Arabia, and the Taiwan Power Company, Taipei, Taiwan, R.O.C., before attending graduate school. His research areas include cogeneration systems and power industry deregulation. Dr. Chu is a member of Tau Beta Pi.

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Bin-Kwie Chen (M’86) was born in Kaohsiung, Taiwan, R.O.C., on June 3, 1953. He received the B.S. degree from the National Cheng Kung University, Tainan, Taiwan, R.O.C., in 1976, and the M.S.E.E. and Ph.D. degrees from the University of Texas at Arlington in 1982 and 1986, respectively. Currently, he is teaching at Tatung University, Taipei, Taiwan, R.O.C. After finishing his compulsory military service in 1978, he was a Design Engineer with the Design and Construction Department of Taiwan Power Company, Taipei, Taiwan, R.O.C., where his duties and responsibilities include the design of power system, light system, MCC, substation, and control room arrangements for power plants. His main research interest includes exploiting computer methods for power system analysis in the areas of planning, operation, and control.

Chung-Hsien Liao was born in Taipei, Taiwan, R.O.C., in 1978. He received the B.S. and M.S. degrees in electrical engineering from Tatung University, Taipei, Taiwan, R.O.C., in 2000 and 2002, respectively. Currently, he is an Electrical Engineer with Tatung Company, Taipei, Taiwan, R.O.C.