Optimal Locating and Sizing of TCPST for Congestion Management in Deregulated Electricity Markets

Transcription

1 Optimal Locating and Sizing of TCPST for Congestion Management in Deregulated Electricity Markets M. Joorabian Shahid Chamran University, Ahwaz, Iran M. Saniei Shahid Chamran University, Ahwaz, Iran H. Sepahvand Shahid Chamran University, Ahwaz, Iran Abstract-Congestion and overloads in transmission lines always is one of the basic problems in the power system operation. Some of the consequences of this problem in the restructured power system are sudden price increasing in some areas, increase in market power and reduction in the competition in the market. FACTS devices as an efficient, powerful and economical means can have a key role in transmission line congestion management. Locating and parameters setting of the FACTS devices is very important to achieve the desired objectives. In this paper, TCPST has been used in the congestion management. For optimal setting of TCPST and determining the appropriate location for the management and reduction of the transmission lines congestion in the restructured environment, a method based on the locational marginal price (LMP) and optimal power flow (OPF) in combination with TCPST is used. This method is applied on IEEE 14 and 30 bus systems. Simulation results show the effect of TCPST appropriate locating on the reduction of the total restructured power system costs. Index Terms--Congestion management, FACTS devices, LMP, OPF, TCPST I. ITRODUCTIO Electricity industry restructuring in recent years has created a competition environment in the power and thus the electricity prices reduction, the power network efficiency Increasing and improving the service quality. Due to technical limitations of the existing power transmission, electricity market in many cases has deviation from a full competitive system. The most important limitation is the congestion in the transmission system, restricting the competition environment. After the energy market implementation in the restructured power system, and determination of each producer's share of, in some situations, the network constraints such as transmission line power flow limit are violated. Application of appropriate strategies to resolve the congestion problem is known as the congestion management and is one of the main responsibilities of the independent system operator (ISO). Three forms of congestion management schemes including the price area based, optimal power flow based, and available transfer capability based have been presented in [1]. A comprehensive bibliographical survey on various congestion management schemes has been presented in [2]. FACTS devices are recently employing to help the power system operator in the congestion management. Advances in the power electronics technology have made these devices more economically. Also, the increasing of the power system loading and the deregulation in the power electricity market, have made a good motivation in use of the power flow controllers. This paper deals with the optimal locating and sizing of a TCPST, for congestion management in competitive power markets. The location of FACTS devices can be based on static or dynamic performance of the system. The sensitivity factor methods are generally used to find the best location to enhance the static performance of the system. In [3], a sensitivity based approach for the optimal location of thyristor controlled series capacitor (TCSC) and thyristor controlled phase angle regulator (TCPAR) was proposed for the congestion management. In [4] a Congestion-Based system expansion planning method, suitable for the Chinese power market, was introduced. Also, they have proposed an Optimal Plan Selection method based on LMP (locational marginal price). An optimization-based methodology for placement of Flexible AC Transmission Systems (FACTS) devices was investigated in [5] in order to relieve congestion in the transmission lines. In [6] a methodology and the corresponding software tools for Power Transfer Distribution Factors (PTDF) and Available Transfer Capacity (ATC) evaluation have been presented. The impact of phase shifters on locational prices was analyzed in Paper [7], and presented that phase shifter could be used to mitigate or reduce transmission congestion by redirecting line flows, reduce the cost of power dispatch by adjusting LMPs, and enhance market competition. In [8], by using the real power line flow performance index in normal and contingency conditions for bilateral trading and using a way to maximize the social welfare, the best location of a thyristor controlled phase shifter was proposed. in [9], mixed integer linear programming (MILP) was used to develop a method for the optimal placement of TCPSTs in large-scale power systems based on a dc load flow model. In [10] an algorithm considering the pool model and bilateral transaction matrix for enhancement of power system loadability with optimal location of thyristor controlled phase angle regulators (TCPAR) was proposed. In [11], congestion problem in the bilateral electricity markets was solved using

2 redispatch method with considering FACTS devices in the network. The FACTS devices considered include the thyristor controlled series capacitor (TCSC) and the thyristor controlled phase angle regulator (TCPAR). In [12], a method was proposed to evaluate the optimal placement of the Thyristor Controlled Phase Shifter Transformers. This paper presents a new method for the proper location of series FACTS devices for congestion management in the deregulated electricity markets. The proposed method is based on LMPs calculated by the optimal power flow (OPF) problem formulation. An OPF formulation has been used for TCPST optimal setting. In this method, the total cost used in the OPF formulation, are including TGC (total cost), TCC (total congestion cost) and TCPST investment cost. A pool type of market is considered in this paper. The proposed method is applicable to any type of FACTS devices; however, here it is used to locate TCPST. This method is applied on IEEE 14 and 30 bus systems. II. FACTS DEVICE STATIC MODEL AD ITS COST FUCTIO A. TCPST Static Model Fig. 1 shows a simple transmission line represented by its lumped π equivalent parameters connected between bus-i and bus-j. Let complex voltages at bus-i and bus-j are V i δ i and V j δ j respectively. The real and reactive power flow from bus-i to bus-j can be written as P ij = V 2 i G ij V i V j G ij cos δ ij + B ij sin δ ij (1) 2 Q ij = V i B ij + B sh V i V j G ij sin δ ij B ij cos δ ij (2) where δ ij = δ i δ j. Similarly, the real and reactive power flow from bus-j to bus-i is P ji = V 2 j G ij V i V j G ij cos δ ij B ij sin δ ij (3) 2 Q ji = V j B ij + B sh + V i V j G ij sin δ ij + B ij cos δ ij (4) Fig. 1. Model of transmission line. The static model of a TCPST and transmission line between bus-i and bus-j is shown in Fig. 2. The real and reactive power flow equations with TCPST are P s ij = V 2 i T 2 G ij V i V j T G ij cos(δ ij + φ) + B ij sin(δ ij + φ) (5) Q s ij = V 2 i T 2 B ij + B sh V i V j T G ij sin(δ ij + φ) (6) B ij cos(δ ij + φ) P s ji = V 2 j T 2 G ij V i V j T G ij cos(δ ij + φ) B ij sin(δ ij + φ) (7) Q s ji = V 2 j T 2 B ij + B sh + V i V j T G ij sin(δ ij + φ) + (8) B ij cos(δ ij + φ) where T = secφ. Fig. 2. Equivalent circuit of TCPST. Fig. 3. Injection model of TCPST. Based on circuit theory, the injection equivalent model of Fig. 3 can be obtained. The injected active and reactive power at bus-i and bus-j of a line having a phase shifter are P is = V 2 i K 2 G ij V i V j K G ij cos δ ij + B ij sin δ ij (9) Q is = V 2 i K 2 B ij V i V j K G ij cos δ ij + B ij sin δ ij (10) P js = V i V j K G ij sin δ ij + B ij cos δ ij (11) Q js = V i V j K G ij cos δ ij B ij sin δ ij (12) where K = tan φ B. TCPST Cost Function The cost of a TCPST is more related to the operating voltage and the current rating of the circuit concerned. Thus, once the TCPST is installed, the cost is fixed and the cost function can be expressed as follows [13]: C TCPST = d. P max + IC (US$) (13) where d is a positive constant representing the capital cost and IC is the installation costs of the TCPST. P max is the thermal limit of the transmission line where TCPST is to be installed [13]. III. OPTIMAL PLACEMET OF TCPST C. OPF Formulation OPF tool has been used normally in a pool based deregulated power markets to calculate dispatch and load schedules, and to manage congestion in the system. The generally accepted objective function in this environment is the maximization of social welfare. In this paper, the cost of FACTS devices is included to the social welfare maximization problem which can be expressed as: Min P G G i=1 C Gi P G D j =1 B Dj P D + COST(FACTS) (14) where G and D are the number of generators and loads respectively, C Gi (P G ) is the bid curve of ith generator, and B Dj P D is the benefit curve for the jth demand. subject to

3 Power balance equation: P i θ, V P Gi + P Di = 0 Q i θ, V Q Gi + Q Di = 0 If TCPST is located in line between buses i and j, the power balance equations at nodes i and j are given by P i θ, V P Gi + P Di + P is = 0 Q i θ, V Q Gi + Q Di + Q is = 0 P j θ, V P Gj + P Dj + P js = 0 Q j θ, V Q Gj + Q Dj + Q js = 0 Apparent line flow limit: max S ij θ, V S ij Power limit: P min max Gi P Gi P Gi Q min max Gi Q Gi Q Gi Bus voltage and angle limits: V min max i V i V i θ min max i θ i θ i TCPST angle limit: φ min φ φ max For any node j For any node j where G and D are the number of generators and loads min respectively, C Gi (P G ) is the bid curve of ith generator, P Gi and P max Gi are minimum and maximum active power min max limits of generating unit at bus i, Q Gi and Q Gi are minimum and maximum reactive power limits min max of generating unit at bus i, V i and V i are minimum and maximum voltage limits at bus i, S ij is the apparent power max flow in transmission line connecting nodes i and j, and S ij is its maximum limit, P Gi and Q Gi are the active and reactive power at node i, P Di and Q Di are the active and reactive power load at node i, P i and Q i are the net active and reactive power injection at node i, φ min and φ max are the minimum and maximum limits of TCPST reactance, and is the number of nodes in the system. D. Solution Technique The augmented objective function of the above OPF problem augmenting all the constraints is expressed as G D L = i=1 C Gi P G j =1 B Dj P D + COST FACTS + i=1 λ Pi P i P Gi + P Di + P is + i=1 λ Qi Q i Q Gi + Q Di + Q is + L max μ Lij S ij S ij + G μ min PGi P min Gi P Gi ij =1 i=1 + G max μ max i=1 PGi P Gi P Gi + G μ min i=1 QGi Q min Gi Q Gi + G max μ max i=1 QGi Q Gi Q Gi + i=1 μ min Vi V min i V i + max μ max i=1 Vi V i V i + μ φ min φ min φ + μ φ max φ max φ (15) where, λ P and λ Q are the Lagrange multipliers associated with the equality constraints (power balance equations) and μ L μ PG min μ PG max μ QG min μ QG max μ Vi min μ Vi max μ φ m in μ φ max are the Lagrange multipliers associated with the inequality constraints (line flow limit, generator real and reactive power limits, bus voltage limits and TCPST angle limits, respectively). The solution of the OPF gives the values of these multipliers along with the dispatch result. Each multiplier in (15) has economic significance. The important one is the Lagrange multiplier λ P associated with the real power balance equations. It is the real power spot price or nodal price or LMP and can be used for pricing energy in electricity markets [14]. IV. PROPOSED METHOD The main goal of this paper is to find the optimal location and parameter setting of TCPST in order to minimize total cost objective function. The objective function is defined by: Cost = TGC + TCC + C TCPST (16) Where C TCPST is Cost Function of TCPST,TGC is Generation Cost and TCC is Congestion Cost. To find the total congestion cost, first an OPF is performed. Using the results of this OPF, flow of each line and LMPs are calculated. Then, total congestion cost can be computed as follows: TCC = L ij =1 ρ ij P ij (17) Where P ij,is power flow of line ij, L is the number of transmission lines and λ ij is: ρ ij = LMP i LMP j (18) Then, ranking of lines for TCPST location is based on the CCCs, as defined below, in descending order of magnitude to form a priority list. CCC ij = CC ij (19) TCC Where CC ij = ρ ij P ij is the congestion cost of line ij. The number of lines to be considered for priority list depends on the size of the system. Finally, for each line in the priority list, OPF can be run with TCPST placed in that line and the total cost can be computed. Calculation procedure of the proposed method is summarized in the following steps: Step 1: Run the base case OPF to calculate the LMP at all the buses and the power flow across all the line sections. Step 2: Calculate congestion cost contribution of individual lines (using Eqs. (17) (19)) using LMP values and power flows calculated in Step 1 and arrange in descending order of magnitude to form priority table. Step 3: For each line in the priority list, run OPF with TCPST in that line and calculate the total cost given by eq. (16). Step 4: The best location of TCPST is the one where by placing TCPST gives the minimum total cost. If the best location is between two generator buses, then the next best location is selected. The procedure is illustrated in Fig. 4.

4 START OPF without FACTS Congestion YES form priority table (n line is selected) i = 1 O Place FACTS on ith Line of table priority OPF with FACTS Compute Cost and Store the Values i = i+1 YES i n STOP Fig. 4. Proposed procedure of choosing economical placement of FACTS O Among 20 lines in IEEE 14-bus system, we selected 6 more important lines (lines 1, 2, 3, 4, 5, and 7) that have larger congestion cost contribution as candidates for placement of TCPST. By locating TCPST in the selected lines and running the optimization program, proper locations of TCPST subjected to the objective function is obtained. Table II gives the priority list of locations for TCPST based on the proposed method. The best location for installing TCPST in order to relieve congestion and reduction in total cost is the line 2. Comparing Table II with the results of the optimal power flow without TCPST given in Table I reveals that the total costs obtained by locating of TCPST are considerably less than those in the base case. Also, the LMP values for all buses, and the active power flows for all lines and the active power for all generators with and without TCPST are shown in Fig.5 and Fig.6 and Fig.7 respectively. As can be seen, with presence of TCPST, the system buses LMPs are approximately close to each other and the congestion of line 1-2 has got released and the generators with less cost has more, thus it reduces the expenses of the. TABLE II PRIORITY TABLE BASED O OPF WITH TCPST FOR IEEE 14-BUS SYSTEM BY PROPOSED METHOD Priority number TCPST location congestion Saving ($/h) cost ($/h) cost ($/h) 1 2(1-5) (1-2) (2-5) (4-5) (2-4) (2-3) V. CASE STUDIES AD DISCUSSIOS The proposed method for the optimal placement of the TCPST for congestion management has been implemented on modified IEEE 14 bus and IEEE 30-bus test systems. The network and load data for these systems are taken from [15]. Line limits for these systems is taken from Refs. [16,17], respectively. A. IEEE 14-Bus Test System There are 20 line sections in IEEE 14-bus system. Line flow limits for IEEE 14-bus system has been shown in the appendix. The priority list for IEEE 14-bus system is formed with six candidate lines. Table I shows total congestion cost, total cost, total cost, and overloaded lines for IEEE 14-bus test system. As can be seen, the line 1 is being congested. The total cost without TCPST (base case) is ($/h). TABLE I RESULTS BASED O OPF WITHOUT TCPST FOR IEEE 14-BUS SYSTEM Congested Line number cost ($/h) Congestion 1 (1-2) Fig. 5.The LMP values, with and without TCPST for IEEE 14-bus system Fig. 6.The active power flow values, with and without TCPST for IEEE 14-bus system

5 Also, the LMP values for all buses, and the active power flows for all lines and the active power for all generators with and without TCPST, are shown in Fig.8 and Fig.9 and Fig.10 respectively. As can be seen, with presence of TCPST, the system buses LMPs are approximately close to each other and the congestion of line 1-2 has got released. Therefore, with regard to the TCPST, the limitations resulted from the line capacity constraints such as lines congestion, cost, congestion cost, and buses LMP will be resolved. Fig. 7.The active power s, with and without TCPST for IEEE 14-bus system B. IEEE 30-Bus Test System IEEE 30-bus system has 41 line sections. The line flow limit is set to 100 MVA. The priority list for IEEE 30-bus system is formed with ten candidate lines. Table III shows total congestion cost, total cost, total cost and overloaded lines for IEEE 30-bus test system. As can be seen, the line 1 is being congested. The total cost without TCPST (base case) is 10515($/h). Among 41 lines in IEEE 30-bus system, we selected 10 more important lines that have larger congestion cost contribution as candidates for placement of TCPST. By locating TCPST in the selected lines and running the optimization program, proper locations of TCPST subjected to the objective function is obtained. Table IV gives the priority list of locations for TCPST based on the proposed method. The best location for installing TCPST in order to relieve congestion and reduction in total cost is the line 1. Comparing Table IV with the results of the optimal power flow without TCPST given in Table III reveals that the total costs obtained by locating of TCPST are considerably less than those in the base case. Fig. 8.The LMP values, with and without TCPST for IEEE 30-bus system Fig. 9.The active power flow values, with and without TCPST for IEEE 30-bus system TABLE III RESULTS BASED O OPF WITHOUT TCPST FOR IEEE 30-BUS SYSTEM Congested Line number Congestion 1 (1-2) TABLE IV PRIORITY TABLE BASED O OPF WITH TCPST FOR IEEE 30-BUS SYSTEM BY PROPOSED METHOD Priority number TCPST location cost ($/h) congestio n cost ($/h) Saving($ /h) 1 1(1-2) (3-4) (1-3) (2-4) (4-6) (2-6) (2-5) (6-7) (4-12) (12-15) Fig. 10.The active power s, with and without TCPST for IEEE 30-bus system VI. COCLUSIOS In this paper, an LMP based method has been proposed for optimal location of TCPST to manage congestion in the electricity markets. An OPF formulation has been used for TCPST optimal setting. In this method, the total cost used in the OPF formulation, are including TGC (total

6 cost), TCC (total congestion cost) and TCPST investment cost. A pool type of market was considered in this paper. Since FACTS devices are very expensive and their capital risk is very high in the restructured power industry, economical consideration of these devices is more important than ever. The proposed method was tested on IEEE 14 and 30 bus system and validated through comparison of obtained social welfare with and without TCPST. The results presented in this paper show that for reduction transmission congestion costs and control of the lines power flow, TCPST is a good candidate. Moreover, according to the obtained results, the proposed method in this paper can reliably be used for TSCS locating and analyzing its economical consideration. REFERECES [1] R.D. Christie, B.F. Wollenberg and I. Wangstien, Transmission management in the deregulated environment, in Proc. IEEE, vol. 88, o. 2, Feb. 2000, pp [2] Ashwani Kumar, S.C. Srivastava, and S.. Singh, Congestion management in competitive power markets-a bibliographical survey, International Journal of Electric Power System and Research vol. 76, pp , July 2005 [3] S.. Singh and A. K. David, Optimal location of FACTS devices for congestion management, Electr. Power Syst. Res., vol. 58, pp , June [4] KF. Song, M. R. Irving, "Congestion-Based Transmission System Expansion Planning in Developing Chinese Power Market, UPEC 2007 [5] M. Gitizadeh, A modified simulated annealing approach to congestion alleviation in a power system using FACTS devices, UPEC2010, 31st Aug - 3rd Sept 2010 [6] Constantin Barbulescu, Stefan Kilyeni, Dan Petru Cristian, Dan Jigoria- Oprea, Congestion management using open power market environment electricity trading, UPEC2010, 31st Aug - 3rd Sept [7] Bo Lu, Zuyi Li, Mohammad Shahidehpour. "Impact of Phase Shifters on Locational Prices" Special Issue, ASCE Journal of Energy Engineering, Vol. 131, o. 1, pp , April [8] A. Kazemi, R. Sharifi, Optimal Location of Thyristor Controlled Phase Shifter in Restructured Power Systems By Congestion Management, Industrial Technology, ICIT IEEE International Conference on, Dec [9] F. G. M. Lima, F. D. Galiana, I. Kockar, J. Munoz, "Phase Shifter Placement in Large Scale Systems via Mixed Integer Linear Programming", IEEE Trans. on Power Systems, Vol. 18, o. 3, August [10] A. Kumar, S. Parida, S.C. Srivastava and S.. Singh, "Enhancement of power system loadability with optimal location of TCPAR in competitive electricity market using MILP", International conference on power systems, ICPS2004, Katmandu, epal, [11] You Shi, Kennedy Mwanza, Le Anh Tuan, Valuation of FACTS for Managing Congestion in Bilateral Contract Markets, Power Engineering Society General Meeting, IEEE, June 2007 [12] M. Zeraatzade, I. Kockar, Yong-Hua song, Minimizing Balancing Market Congestion Re-dispatch Costs by Optimal Placements of FACTS Devices, Power Tech, 2007 IEEE Lausanne 1-5 July 2007 [13] E. J. Oliveira, J. W. M. Lima, and K. C. Almeida, "Allocation of FACTS devices in hydrothermal system," IEEE Trans. Power Systems, vol. 15, pp , February [14] F.L. Alvarado, Controlling Power Systems with Price Signals, Decision Support Syst., vol. 40, 2005, pp [15] Power System Test Case Achieves, Retrieved 10 December From [16] V.C. Ramesh, X. Li, A fuzzy multiobjective approach to contingency constrained OPF, IEEE Trans. Power Syst. 12 (3) (1997) [17] R. D. Zimerman, C. E. Murillo-Sanchez, and D. Gam, MATPOWR A MATLAB Power System Simulation Package, Version 3, available at: APPEDIX Line flow limits for IEEE 14-bus system Line From/To Buses MVA