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Engineering, 2010, 2, 337-343 doi:10.4236/eng.2010.25044 Published Online May 2010 (http://www.SciRP.org/journal/eng) Copyright © 2010 SciRes. ENG 337 Enhancement of Available Transfer Capability with Facts Device in the Competitive Power Market Bairavan Veerayan Manikandan1, Sathiasamuel Charles Raja2, Paramasivam Venkatesh2 1Mepco Schlenk Engineering College, Sivakasi, India 2Thiagarajar College of Engineering, Madurai, India E-mail: bvmani73@yahoo.com, {charlesrajas, pveee}@tce.edu Received December 21, 2009; revised February 9, 2010; accepted February 12, 2010 Abstract In order to facilitate the electricity market operation and trade in the restructured environment, ample trans- mission capability should be provided to satisfy the demand of increasing power transactions. The conflict of this requirement and the restrictions on the transmission expansion in the restructured electrical market has motivated the development of methodologies to enhance the Available Transfer Capability (ATC) of the ex- isting transmission grids. The insertion of FACTS devices in electrical systems seems to be a promising strategy to enhance ATC. In this paper, the viability and technical merits of boosting ATC using Thyristor Controlled Series Compensator (TCSC) is being analyzed. The work has been carried out on IEEE 30 bus and IEEE 118 bus systems. Bilateral and multilateral transactions are considered. Particle Swarm Optimiza- tion (PSO) algorithm and Genetic Algorithm (GA) are employed to obtain the optimal settings of TCSC. Keywords: Available Transfer Capability, Flexible AC Transmission Systems, Particle Swarm Optimization, Genetic Algorithm, Power Transfer Distribution Factors, Thyristor Controlled Series Compensator 1. Introduction Deregulation of the electric industry throughout the world aims at creating competitive markets to trade elec- tricity, which generates a host of new technical chal- lenges to market participants and power system re- searchers. For transmission networks, one of the major consequences of the non-discriminatory open-access requirement is a substantial increase of power transfers, which demand adequate available transfer capability [1] to ensure all economic transactions. Researchers have proposed various methods to evaluate ATC [2-4]. Suffi- cient ATC should be guaranteed to support free market trading and maintain an economical and secure operation over a wide range of system conditions. However, tight restrictions on the construction of new facilities due to the increasingly difficult economic, environmental, and social problems, have led to a much more intensive shared use of the existing transmission facilities by utili- ties and independent power producers (IPPs). These concerns have motivated the development of strategies and methodologies to boost the ATC of the existing transmission networks. Aimed at this problem, various ATC enhancement ap- proaches have been proposed, where adjusting terminal voltage of generators and taps changing of onload tap changer (OLTC), particularly rescheduling generator outputs, are considered as major control measures for ATC boosting. On the other hand, it is highly recognized that, with the capability of flexible power-flow control and rapid action, flexible ac transmission systems (FACTS) technology has a wide spectrum of impacts on the way the transmission system operates, in particular with respect to thermal, voltage, and stability constraints [5]. ATC values are always limited ultimately by heavily loaded circuits and/or nodes with relatively low voltage, with the increase of system loading. FACTS concept makes it possible to use circuit reactance, voltage mag- nitude, and phase angle as controls to redistribute line flow and regulate nodal voltage, thereby mitigating the critical situation. In addition, partly due to the physical constraints on circuit impedance and phase angle of nodal voltage, most high-voltage transmission lines are operating far below their thermal rating [6]. By the con- trol of line reactance and voltage phase angle, FACTS technology enables line loading to increase flexibly, in some cases, all the way up to thermal limits. Therefore, theoretically it can offer an effective and promising al- ternative to conventional methods for ATC enhancement. B. V. MANIKANDAN ET AL. 338 Undoubtedly, it is very important and imperative to carry out studies on exploitation of FACTS technology to en- hance the ATC [7]. In this paper, ATC is calculated using ACPTDF in Combined Economic Emission Dispatch (CEED) envi- ronment [8,9] and an attempt is made to enhance Avail- able Transfer Capability using TCSC i.e. Thyristor con- trolled series compensator [10,11]. TCSC is connected in series with the line conductors to compensate for the inductive reactance of the line. Both bilateral and multi- lateral transactions are considered. Population based, cooperative and competitive stochastic search algorithms are very popular in the recent years in the research arena of computational intelligence. Some well established search algorithms such as PSO [12,13] and GA [14,15] are successfully implemented to solve simple and com- plex problems efficiently and effectively. Population based search approach in GA is motivated by evolution as seen in nature. PSO, on the other hand, is motivated from the simulation of social behavior. The optimal set- tings of TCSC are obtained using PSO and GA. The re- sults are illustrated on both IEEE 30 bus and IEEE 118 bus systems. 2. Available Transfer Capability Available Transfer Capability (ATC) is a measure of the transfer capability remaining in the physical transmission network for further commercial activity over and above the already committed uses [1]. ATC can be expressed as: sCommitmentonTransmissiExistingTTCATC (1) where, Total Transfer Capability (TTC) is defined as the amount of electric power that can be transferred over the interconnected transmission network or particular path or interface in a reliable manner while meeting all of a spe- cific set of defined pre and post contingency conditions. ATC at base case, between bus m and bus n using line flow limit (thermal limit) criterion is mathematically formulated using ACPTDF (or) PTDF as , min, mnij mnL A TCTij N (2) where Tij,mn denotes the transfer limit values for each line in the system. It is given by max 0 , , , max 0 , , ;0 (infinite) ;0 () ;0 ij ij ij mn ij mn ij mnij mn ij ij ij mn ij mn PP PTDF PTDF TPTD PP PTDF PTDF , F (3) where max ij P is the MW power limit of a line between bus i and j. o ij P is the base case power flow in line between bus i and j. PTDFij,mn is the power transfer distribution factor for the line between bus i and j when a transaction is taking place between bus m and n. NL is the total number of lines. The optimal settings of generators under CEED envi- ronment are considered as a base case power flow. 2.1. CEED Problem Formulation Optimization of CEED problem has been mathematically formulated and is given by the following equation: 1 (,) Ng i i minfFC EC (4) where φ is the optimal cost of generation (US$/h) and Ng represents the number of generators connected in the network. The cost is optimized within the following constraints: The power system constraint is given as follows Ng ildgi PPP 1 (5) where Pd is the total load of the system and Pl is the transmission losses of the system. The power flow equation of the power network ,gv 0 (6) The inequality constraint on real power generation of each generator i maxmin gigigi PPP (7) where min g i P and max g i P are minimum and maximum value of real power allowed at generator i respectively. The inequality constraint on voltage of each PQ bus maxmin iii VVV (8) where and are minimum and maximum voltage at bus i respectively. min i Vmax i V Power limit on transmission line max p qpq M VAf MVAf (9) where max p q M VAf is the maximum rating of transmission line connected between buses p and q. Total fuel cost of generation FC (US$/h) in terms of control variables of generator powers can expressed as, Ng iigiigii cPbPaFC 1 2 (10) where Pgi is the real power output of an ith generator and ai , bi , ci are the fuel cost curve coefficients. Copyright © 2010 SciRes. ENG B. V. MANIKANDAN ET AL.339 Total emission of generation EC (lb/h) can be ex- pressed as, Ng iigiigii PPEC 1 2 (11) where αi , βi and γi are emission coefficients. The bi-objective optimization problem (4) is converted into single optimization problem by introducing price penalty factor, h , which blends fuel cost with emission, () M inimizeFCh EC (12) CEED optimization problem is solved using evolu- tionary programming and more information is also available in the papers [8,9]. In most of the developing countries, the restructuring process of power industry is in the infant stage. Still the structure is vertically inte- grated but they purchase power from Independent Power Producers (IPP) to meet the growing demand. Hence, the regional transmission operator is responsible for the re- dispatch of generator power by considering the physical limits of the system and emissions standards. Also, there are some power markets which support both bilateral transactions based on ATC and centralized dispatch based on bids. In these markets, assured firm transactions are implemented first and then they will follow central- ized dispatch mechanism with the remaining transfer capacity. Therefore the proposed CEED based ATC cal- culation and enhancement method can be well suited for such cases described above. 2.2. ACPTDF Formulation The AC power transfer distribution factors proposed for calculation of ATC [4] were used to find various trans- mission system quantities for a change in MW transac- tion at different operating conditions. Consider a bilateral transaction tk between a seller bus m and buyer bus n. Line l carries the part of the trans- acted power and is connected between buses i and j. For a change in real power, transaction among the above buyer and seller by ∆tk MW, if the change in a transmis- sion line quantity q1 is ∆q1 , power transfer distribution factors can be defined as, k l mnij t q PTDF , (13) The transmission quantity ql can be either real power flow from bus i to j (Pij ) (or) real power flow from bus j to bus i (Pji ). The above factors have been proposed to compute at a base case load flow with results using sen- sitivity properties of NRLF Jacobian. Consider full Jaco- bian in polar coordinates [JT], defined to include all the buses except slack (including ∆Q-∆V equations also for PV buses). Q P J Q P V QQ V PP VT 1 1 (14) In a base case load flow, if only one of the kth bilateral transactions is changed by ∆tk MW, only the following two entries in the mismatch vector on RHS of (14) will be non zero. k itP k jtP (15) With the above mismatch vector elements, the change in voltage angle and magnitude at all buses can be com- puted from (14) & (15) and, hence, the new voltage pro- file can be calculated. These can be utilized to compute all the transmission quantities ql and hence the corre- sponding changes in these quantities ∆ql from the base case. Once the ∆ql for all the lines corresponding to a change in transaction ∆tk is known, PTDFs can be ob- tained from (13). 3. Overview of PSO and GA 3.1 Particle Swarm Optimization The PSO is a population-based optimization method first proposed by Kennedy and Eberhart [12]. PSO technique finds the optimal solution using a population of particles. PSO is developed through simulation of bird flocking in two-dimensional space. The position of each agent is represented in X-Y plane with position(,) x y SS ) , Vx (ve- locity along X-axis), and Vy (velocity along Y-axis). Modification of the agent position is realized by the po- sition and velocity information. Bird flocking optimizes a certain objective function. Each agent knows its best value so far, called ‘Pbest’, which contains the informa- tion on position and velocities. This information is the analogy of personal experience of each agent. Moreover, each agent knows the best value so far in the group, ‘Gbest’ among all ‘Pbest’. This information is the analogy of knowledge, how the other neighbouring agents have performed. Each agent tries to modify its position by considering current positions (, x y SS, current velocities (,) x Y VV , the individual intelligence (Pbest), and the group intelligence (Gbest). The following equations are utilized, in computing the position and velocities, in the X-Y plane: 1 11 22 () () i kk ii best k best i VWVCrandPS Crand GS k i (16) 1kkk iii SSV 1 (17) where, 1k i V is the velocity of ith individual at (1) th K Copyright © 2010 SciRes. ENG B. V. MANIKANDAN ET AL. 340 iteration, is the velocity of ith individual at kth itera- tion, W is the inertia weight, C1, C2 are the positive constants having values (0,2.5), rand1, rand2 are the ran- dom numbers selected between 0 and 1, is the best position of the ith individual, Gbest is the best position among the individuals (group best) and Si k is the position of ith individual at kth iteration. The acceleration coeffi- cients C1, and C2 control how far a particle will move in a single iteration. Typically, these are both set to a value of 2.5. k i V i best P The velocity of each particle is modified according to (16) and the minimum and maximum velocity of each variable in each particle is set within the limits of Vmin and Vmax respectively. The position is modified according to (17). The inertia weight factor ‘W’ is modified using (18) to enable quick convergence. iter iter WW W max minmax max )( ) ) W 11 and 22 and (18) where Wmax is the initial value of inertia weight equal to 0.9, Wmin is the final value of inertia weight equal to 0.4, iter is the current iteration number and itermax is the maximum iteration number. Small values of w result in more rapid convergence usually on a suboptimal position, while a too large value may prevent divergence. The PSO system combines two models: A so- cial-only model and the cognition-only model. These models are represented by the velocity update, shown in (16). The second term in the velocity update equation is associated with cognition since it only takes into account the particle’s own ex- periences. The third term in the velocity update equation represents the social interac- tion between the particles. It suggests that individuals ignore their own experience and adjust their behavior according to the successful beliefs of individual in the neighborhood. ( i k best i C rPS ( k best i CrG S 3.2. Genetic Algorithm GAs has been extensively used in power system optimi- zation problems. GAs are search algorithms based on the mechanics of natural selection and natural genetics. GAs are different from other optimization methods. GAs search from a population of points, not from a single point. GAs can therefore discover a globally optimal point. GAs can deal with non-smooth, non-continuous and non-differentiable functions that are the real-life op- timization problems. GAs use probabilistic transition rules to select generations, not deterministic rules, so they can search a complicated and uncertain area to find the global optimum. However, to make GAs more prac- ticable, the problems of memory and computing time arising from the coding of large number of variables in real life systems need to be solved. The steps involved in simple GA are Initial population generation, Fitness evaluation, Selection, Crossover and Mutation. In this work, Real Coded Genetic Algorithm (RCGA) with specialized crossover operator called Simulated Binary crossover (SBX) and polynomial mutation is em- ployed. Simulated Binary Crossover creates children solutions in proportion to the difference in parent solu- tions. The following steps are followed to create two children solutions from two parents: Choose a random number ,[0,1] i u Calculate qi as given in the below equation 1 1 1 1 (2 ),0.5 1, 2(1 ) c ii qi c i uu otherwise u (19) where, qi is the spread factor and is defined as the ratio of the absolute difference in offspring values to that of the parents. c is the crossover index. Then compute the offspring & as, (1, 1)t i x(2,1)t i x (1,1)(1, )(2,) (2,1)(1, )(2, ) 0.5 (1)(1) 0.5 (1)(1) tt iqiiqi tt iqiiq xx xx t i t ii x x (20) Newly generated offspring undergo polynomial muta- tion operation. Like in the SBX operator, the probability distribution can also be a polynomial function, instead of a normal distribution. The new offspring (1, 1)t i y is de- termined as follows, (1, 1)(1,1)() ttUL ii ii yx xx i (21) where and are the upper and lower limit values. The parameter U i xL i x i is calculated from the polynomial probability distribution. 1/( 1) 1/( 1) () 0.5(1)(1) (2 )1,0.5 12(1),0.5 m m m ii im ii P and rif rifr r (22) where m is the mutation index. In this operator the shape of the probability distribution is directly controlled by the external parameter m and distribution is not dy- namically changed with generations. Newly generated individuals replace their parents and forms the parents for the next generation. The iterative procedure can be terminated when any one of the following criteria is met i.e., an acceptable solution has been reached, a state with no further improvement in solution is reached, control Copyright © 2010 SciRes. ENG B. V. MANIKANDAN ET AL.341 variables has converged to a stable state or a pre-defined number of iterations have been completed. 4. Thyristor Controlled Series Compensator A TCSC is a series-controlled capacitive reactance that can provide continuous control of power on the AC line over a wide range. It can be operated in both capacitive and inductive modes. In capacitive mode, it reduces the transfer reactance between the buses at which the line is connected, thus increasing the maximum power that can be transmitted and reducing the effective active and reac- tive power losses. From the system viewpoint, the prin- ciple of variable-series compensation is simply to in- crease the fundamental-frequency voltage across a fixed capacitor (FC) in a series-compensated line through ap- propriate variation of the firing angle, . This enhanced voltage changes the effective value of the series- capaci- tive reactance The basic conceptual TCSC module comprises a series capacitor, C, in parallel with a thyristor-controlled reac- tor, Ls as shown in Figure 1. However, a practical TCSC module also includes protective equipment normally installed with series capacitors. The model of a transmission line with a TCSC connec ted between bus–i and bus-j is shown in Figure 2. In this work, TCSC is modelled as a variable reactance whose value varies from –0.8 XL to +0.2 XL in order to avoid over compensation of the line. XL is the reactance of the line in which TCSC is connected. 5. Problem Formulation The aim of the optimization is to perform the best I line L S Figure 1. TCSC basic module. jB - Z ij = r ij + jx ij jB - Figure 2. Model of TCSC. utilization of thes. The objec-e existing transmission lin tive is to maximize the ATC i.e., uncommitted active transfer capacity of the prescribed interface, when a transaction is taking place between a seller bus (m) and buyer bus (n). It is represented as mn M aximizeATCp (23) where ATCmn is given by Equation (2). The optimization problem is solved subject to the following FACTS de- vice constraint (24) and power flow constraints (5-9). 0.8 0.2 LTCSC L X XXp (24) . Algorithm he basic steps involved in enhancing ATC values with ead the system input data. in CEED environ- m 3: Consider wheeling transactions (tk). ution fac- to ansactions as variables, line flow, real an e limiting element in the system buses i.e nt. ob- ta ncorporating TCSC out, th he simulation studies are carried out on Intel Pentium ork has been carried out on IEEE 30 bus and IE 6 T TCSC device using PSO and GA algorithm are given below: Step 1: R Step 2: Run a base case load flow ent and determine the optimal settings of generators [8,9]. Step Step 4: Compute AC power transfer distrib rs as per (13). Step 5: Take tr d reactive power limits of generators as constraints and compute the feasible wheeling transactions determine the ATC as per (2). Step 6: Find th ., that carry power close to thermal limit Step 7: Place TCSC in the limiting eleme Step 8: Run PSO algorithm and GA separately to in the settings of TCSC. Step 9: Calculate ATC after i Step 10 : Is any other transaction has to be carried en consider the next transaction and go to step 3, oth- erwise stop the procedure. 7. Results and Discussion T Dual Core, 2.40 GHZ system in MATLAB 7.3 environ- ment. The w EE 118 bus systems. For the ATC determination, gen- erators setting are obtained from CEED environment as explained by the authors in [8,9]. Thermal limit of each line is considered as a constraint and reactive power de- mand at load buses has been taken as constant. For run- ning the PSO algorithm, the initial population of indi- viduals are created by satisfying the constraints. For each individual in the population, the fitness function, velocity Copyright © 2010 SciRes. ENG B. V. MANIKANDAN ET AL. Copyright © 2010 SciRes. ENG 342 Table.1. ATC in MW – with and without TCSC using PSO. System Method Transaction between buses ATC Without TCSC (MW) ATC With TCSC (MW) Settings of TCSC (p.u.) Position of TCSC Execution time (sec) 2-28 22.970 26.553 0.0300 6-28 103.056707 5-23 23.901 23.935 0.1350 23-24 102.823764 IEEE 30 Bus ACPTDF 2-12 58.830 67.949 0.0895 22-24 103.232553 Table 2. ATC in MW – with and without TCSC using GA. System Method Transaction between buses ATC With- out TCSC (MW) ATC With TCSC (MW) Settings of TCSC (p.u.) Position of TCSC Execution time (sec) 2-28 22.970 26.1473 0.0277 6-28 108.071454 5-23 23.901 23.8743 0.1332 23-24 107.427641 IEEE 30 Bus ACPTDF 2-12 58.830 67.2674 0.0843 22-24 107.136452 updation and new population creation are done as ex- plained in Subsection 3.1.1. With GA, the TCSC settings, placement and execution time for the transaction (49-100) are 0.0148 p.u, line 81-80 and 146.347801 seconds respectively. Similarly, for the transaction (1-118), the values are 0.0229 p.u, line 75-118 and 145.778420 seconds respectively. The network and line datas for IEEE 30 bus system IEEE 118 bus system is taken from [16]. There are 6 generators and 41 lines in the IEEE 30 bus system. In IEEE 118 bus system, there are 13 generators and 99 lines. For each considered transaction, TCSC is placed in the most limiting line i.e., line flow close to thermal limit. Algorithms are run for 100 iterations. 7.2. Multilateral Transaction The results for multilateral transaction using PSO are shown in Figure 4. For the multilateral transaction be- tween buses i.e., (2, 11) – (28, 26) considered in IEEE30 bus system, TCSC is placed in the line between buses 25-27 and its setting is 0.1044 p.u. The time taken for completing the execution is 102.810250 seconds. For the multilateral transaction between buses i.e., (25,59,46) – (89,100,103,111) considered in IEEE 118 bus system, TCSC is placed in the line between buses 100-103 and its setting is 0.0262 p.u. The execution time is 136. 225383 seconds. Three bilateral transactions and one multilateral trans- action are considered for IEEE 30 bus system. Two bi- lateral and one multilateral transaction are considered for IEEE 118 bus system. 7.1. Bilateral Transaction The position of TCSC, its settings from PSO algorithm and the ATC values before and after incorporating TCSC are shown in Table 1. The steps involved in simple GA i.e., initial population generation, fitness evaluation, se- lection, crossover and mutation are carried out for the considered transactions and the results are given in Ta- ble 2. The results for multilateral transaction using GA are shown in Figure 5. For the same multilateral transaction considered in IEEE30 bus system, TCSC is placed in the line between buses 25-27 and its setting is 0.1040 p.u. For the IEEE 118 bus system, two bilateral transac- tions between buses i.e., (49-100) and (1-118) are con- sidered. The results obtained with TCSC using PSO and GA are shown in Figure 3. For the PSO algorithm, the settings of TCSC are 0.0185 p.u for the transaction (49-100) and 0.0240 p.u for transaction (1-118). TCSC is placed in series with the limiting line 81-80 for transaction (49-100) and for the transaction (1-118), it is placed in the limiting line 75-118. The execution time is 139.047090 seconds for transaction (49-100) and 137.654722 for transaction (1-118). Figure 3. ATC results – using PSO and GA. B. V. MANIKANDAN ET AL.343 10.5709 11.3668 47.899 60.0918 0 10 20 30 40 50 60 70 ATCinMW IEEE30bus IEEE118bus MultilateralTransaction Withou t TC SC WithTCSC Figure 4. ATC for Multilateral transaction – PSO. 10.571 11.348 47.899 59.877 0 10 20 30 40 50 60 ATCinMW IE E E30Bus IEEE118bus MultilateralTransaction Without TC SC With TC SC Figure 5. ATC for Multilateral transaction – GA. The time taken for completing the execution is 103. 120562 seconds. For the same multilateral transaction in IEEE 118 bus system, TCSC is placed in the line be- tween buses 100-103 and its setting is 0.0254 p.u. The execution time is 134.927363 seconds. 8. Conclusions From the view point of operational planning, this paper evaluated the impact of FACTS device on ATC en- hancement. The results demonstrated that the use of FACTS devices, particularly the TCSC can boost the ATC substantially. The considerable difference between ATC values with and without TCSC justifies that the FACTS technology can offer an effective and promising solution to boost the usable power transfer capability, thereby improving transmission services of the competi- tive electricity market. On using PSO and GA for the above problem, it is found that, PSO algorithm is pro- viding very good enhanced result with minimum execu- tion time compared to GA. But for the multilateral transaction, the GA results are very much closer to PSO results in all aspects including settings of TCSC and execution time. Both algorithms predicted the same lim- iting line for bilateral and multilateral transactions con- sidered in IEEE test systems. 9. References [1] “ATC Definitions and Determination, a Frame Work for Determining Available Transfer Capabilities of the In- terconnected Transmission Networks for a Commercially Viable Electricity Market,” NERC Report, June 1996. [2] J. Weber, “Efficient Available Transfer Capability Analy- sis Using Linear Method,” PSERC Internet Seminar, Power World Corporation, Urbana, 2000. [3] A. Kumar and S. C. 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