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Performance Evaluation of Optimal Power Flow by Using Interior Point Method Wah Wah Lwin, Pyone Lai Swe, Zaw Htet Myint Abstract— Optimal power flow, which is characterized as a difficult optimization problem, involves the optimization of an objective function that can take various forms, for example, minimization of total production cost, and minimization of total loss in transmission networks, subject to a set of physical and operating constraints such as generation and load balance, bus voltage limits, power flow equations, and active and reactive power limits . The application of interior point method by using matlab interior point solver (MIPS) in matpower to optimal power flow can also reduce the power losses considerably and can improve the voltage profile of the power systems. The IEEE 14 bus system is used to compare the performance of the mentioned method and power system optimization techniques. For the implementation of the system Matpower4.1 software package and Matlab optimization toolbox packages are employed. Index Terms— Optimal Power Flow, Matlab Interior Point Solver (MIPS), Karush-Kuhn-Tucker (KKT) conditions, IEEE test system. I. INTRODUCTION The goal of OPF is to find the optimal settings of a given power system network that optimize the system objective functions such as total generation cost, system loss, bus voltage deviation, emission of generating units, number of control actions, and load shedding while satisfying its power flow equations, system security, and equipment operating limits. Different control variables, some of which are generators’ real power outputs and voltages, transformer tap changing settings, phase shifters, switched capacitors, and reactors, are manipulated to achieve an optimal network setting based on the problem formulation. According to the selected objective functions, and constraints, there are different mathematical formulations for the OPF problem. They can be broadly classified as follows (1) Linear problem in which objectives and constraints are given in linear forms with continuous control variables. (2) Nonlinear problem where either objectives or constraints or both combined are nonlinear with continuous control variables. (3) Mixed - integer linear problems when control variables are both discrete and continuous. Wah Wah lwin, Department of Electrical Power Engineering, Mandalay Technological University (e-mail: [email protected]). Mandalay , Myanmar , Phone/ Mobile No:+9533224233 Pyone Lai Swe, Department of Electrical Power Engineering, Mandalay Technological University, Mandalay , Myanmar, Phone/ Mobile No.+95402590310 Zaw Htet Myint, , Department of Electrical Power Engineering, Mandalay Technological University, Mandalay , Myanmar, Phone/ Mobile No+95402679802. Various techniques were developed to solve the OPF problem. The algorithms may be classified into two groups: (1) conventional optimization methods, (2) intelligence search methods. II. SOLUTION METHODS OF OPF The problem of Optimal Power Flow is the allocation of given load amongst the generating units in operation so that the overall cost of generation is minimum. In OPF, the entire set of equality and inequality constraints, all the necessary and sufficient conditions of control parameters etc. must be satisfied thoroughly. The OPF is important for operating and planning engineers. The objective function can take various forms such as fuel cost, transmission losses, and reactive sources allocation. The objective function of interest in this paper is designated as the minimization of the total production cost of scheduled generating units. Such a minimization problem is most used as it reflects current economic dispatch practice and importantly, cost related aspect is always ranked high among operational requirement in power systems. Various techniques have been proposed to solve the OPF problem for example, non-linear programming, quadratic programming , linear programming, and interior point methods Among these, the interior point method has been of recent interest and will be employed as a major tool to solve the OPF problem in this paper .[3] III. INTERIOR POINT METHODS The Interior Point Methods (IPM’s) have been used in the past two decades to solve OPF problems and many investigations and algorithms have been developed in this sense. Initially, the IPM’s were used in the form of barrier methods and later thanks to the multiple investigations developed in this area such as the ellipsoid method and the projective scaling method. These algorithms have grown in popularity due to their performance in big dimensions problems. The interior point (IP) technique was purposed by N.K.Karmarkar. It can solve a large-scale linear programming problem by moving through the interior, rather than the boundary as in the simplex method, of the feasible region to find an optimal solution. The IP method was originally proposed to solve linear programming problems; however, later it was implemented to efficiently handle quadratic programming problems.[4] The interior point technique starts by determining an initial solution using Mehrotra’s algorithm, which is used to locate a feasible or near-feasible solution. There are then two procedures to be performed in an iterative manner until the 1 optimal solution has been found. The former is the determination of a search direction for each variable in the search space by a Newton’s method. The latter is the determination of a step length normally assigned a value as close to unity as possible to accelerate solution convergence while strictly maintaining primal and dual feasibility. A calculated solution in each iteration will be checked for optimality by the Karush-Kuhn-Tucker (KKT) conditions, which consist of primal feasibility, dual feasibility and complementary slackness.[5] Currently the IPM’s are being applied extensively to Power Systems Optimization due to their mathematical features over other methods, the Primal Dual IPM is one of the IPM’s has been applied to solve optimization problems in Power Systems.[6]-[7] IV. CONCEPT OF OPTIMAL POWER FLOW The main objective of an OPF problem is to determine the optimal setting of control variables in a power system network to optimize an objective function while respecting a set of physical and operating constraints such as generation and load balance, bus voltage limits, power flow equations, and active and reactive power limits. Generally, an OPF Problem can be formulated as NG (P i 1 Gi N N Pi (V , ) Vi ViYij cos( i j ij ) N Qi (V , ) Vi ViYij sin( i j ij ) (9) j 1 Nonlinear equations (8) and (9) can be linearized by the Taylor’s expansion using P(V , ) J 11 J 12 Q(V , ) J J V 21 22 (10) Transmission loss ( PL ) given in the Equation (7) can be directly calculated from the power flow. C. Inequality Constraints The inequality restrictions are the power limits in the branches of the system. These inequalities are represented as follow: (11) h f (, Vm ) Ff (, Vm ) Fmax 0 (12) h t (, Vm ) Ft (, Vm ) Fmax 0 D. Variables limits The variables have upper and lower limits determined by (13) which represent the operational limits of the system, in terms of the buses voltage limits and the generators power limits. vim, min v im v im, max , i 1,...., n b h(u , x) 0 (3) pig, min pig pig, max , i 1,...., n g (13) q ig, min q ig q ig, max , i 1,...., n g ref i ref , ref vector of control variables vector of state variables Objective function set of equality constraints set of inequality constraints VI. INTERIOR POINT METHOD WITH MIPS SOLVER Matpower includes a new primal-dual interior point solver called MIPS, for Matlab Interior Point Solver.[1] Some details on the primal-dual interior point algorithm used by MIPS are as follow: V. FORMULATION OF OPF As has been discussed, the objective function considered in this paper is to minimize the total production cost of scheduled generating units. OPF formulation consists of three main components: objective function, equality constraints, and inequality constraints. A. Objective Function A. Problem Formulation and Lagrangian Min f ( X ) (14) G( X ) 0 (15) (16) (17) x Subject to H(X ) 0 l AX u Ng i 1 (8) j 1 (2) MinFT ( i P i PGi i ) (7) i 1 Subject to g (u, x) 0 2 Gi (6) ) ( PDi ) PL 0 (1) u : x : f (u,x) : g (u,x) : h (u,x) : (5) Q Gi QDi Q(V , , t ) 0 MinimizeF (u, x) Where; (4) Where Ng : number of generators in the system α i , β i , γ i : fuel cost coefficient of the generator at bus i PGi PGi PDi P(V , , t ) 0 : real power generation at bus i B. Equality Constraints The equality restrictions are the power balance equations in every bus of the system. And the injections of active and reactive power and are calculated through the power flow equations. X min X X max The approach taken involves converting the ni inequality constraints into equality constraints using a barrier function and vector of positive slack variables Z. ni min f ( X ) ln( Zm) X m 1 Subject to G ( X ) 0 H(X ) Z 0 Z 0 (18) (19) (20) 2 As the parameter of perturbation approaches zero, the solution to this problem approaches that of the original problem. For a given value of the Lagrangian for this equality constrained problem is ni (21) L ( X , Z , , ) f ( X ) T G ( X ) T ( H ( X ) Z ) ln( Zm) m1 Taking the partial derivatives with respect to each of the variables yields: LXX X GX H X ( Z (e (H ( X ) Z H X X ))) LX T T T LZ ( X , Z , , ) e [Z ] L ( X , Z , , ) G T ( X ) T L ( X , Z , , ) H ( X ) Z T T H X [ Z ] 1 (e H ( X )) H X [ Z ] 1 [ Z ] LX T (23) X Z F F ( X , Z , , ) T Where; (26) (28) Z Z Z e Z Z e Z (29) Z (e Z ) 1 Solving the 4th row of (28) for ΔZ yields H X X Z H ( X ) Z (30) Z H ( X ) Z H X X Then, substituting (29) and (30) into the 1st row of (28) results in T T LXX X G X H X ( Z (e Z )) LX T T 1 T T T T T T Combining (31) and the 3rd row of (28) results in a system of equations of reduced size: M G X T X N (32) G X 0 G ( X ) The Newton update can then be computed in the following 3 steps: 1. Compute ΔX and Δλ from (32). 2. Compute ΔZ from (30). 3. Compute Δμ from (29). In order to maintain strict feasibility of the trial solution, the algorithm truncates the Newton step by scaling the primal and dual variables by αp and αd, respectively, where these scale factors are computed as follows: Zm ,1 Zm m ,1 d min min m 0 m (33) Zm 0 This set of equations can be simplified and reduced to a smaller set of equations by solving explicitly for Δμ in terms of ΔZ and for ΔZ in terms of ΔX. Taking the 2nd row of (28) and solving for Δμ we get T M f XX G XX ( ) H XX ( ) H X [ Z ] 1 [ ]H X (27) T X LX Z Z e G( X ) T T H ( X ) Z LXX X G X H X LX (31) T P min min C. Newton Step The first order optimality conditions are solved using Newton's method. The Newton update step can be written as follows: HX [Z ] 0 0 T MX G X N T T f X T GX T H X T LX [ ]Z e Z e F ( X , Z , , ) G( X ) G( X ) T T H (X ) Z H ( X ) Z T T N f X G X H X H X [ Z ] 1 (e H ( X )) where GX [ ] 0 0 0 I 0 T T (25) 0 T N LX H X [Z ] 1 (e H ( X )) 0 LXX 0 G X H X T ( LXX H X [ Z ] 1 [ ]H X )X G X T Z 0 F 1 T H X [ Z ] 1 [ Z ] H X [ Z ] 1 [ ]H X X LX (22) B. First Order Optimality Conditions The first order optimality (Karush-Kuhn-Tucker) conditions for this problem are satisfied when the partial derivatives of the Lagrangian above are all set to zero: (24) F ( X , Z , , ) 0 FZ 1 T T LXX ( X , Z , , ) f XX G XX ( ) H XX ( ) X T M LXX H X [ Z ] 1 [ ]H X 1 And the Hessian of the Lagrangian with respect to X is given by F T L X G X H X H X [ Z ] e H X [ Z ] H ( X ) T LX ( X , Z , , ) f X T G X T H X 1 T XX (34) Resulting in the variable updates below. X X P X (35) Z Z P Z (36) d (37) (38) d In MIPS, ξ is set to 0.99995. MIPS uses the following rule to update γ at each iteration, after updating Z and μ: ZT (39) ni In MIPS, σ is set to 0.1. VII. APPILCATION OF INTERIOR POINT METHOD TO IEEE14 BUS SYSTEM The one line diagram of IEEE 14 bus system is shown in Figure 1. The system data is taken from MATPOWER. MATPOWER is a package of Matlab m-files for solving power flow and optimal power flow problems. It is intended as a simulation tool for researchers and educators which will be easy to use and modify. The line data, bus data and generation data are given in matrix forms, respectively. The data is on 100 MVA base. A. Single Line Diagram As shown in single line diagram, the generation power is largest at Bus 1 and thus it is taken as slack bus. The 3 remaining generator buses are taken as voltage control buses. There are four voltage control buses and ten load buses. According to the data, four transformers and three reactive power compensations are also placed in single line diagram. The buses of IEEE14 bus system are interconnected to form a network. There are 20 interconnected lines. The single line diagram of IEEE14 bus system is described in Figure 1. 13 14 12 11 10 G1 G5 6 1 C 9 C G4 8 C. Generator Data The generator data for IEEE14 bus system is shown in Table II. There are five generator buses in the system. Among them Bus one is operates as slack bus and remaining buses are voltage control buses. Bus 1 exhibits the largest generating capacity and bus 2 exhibits the second largest generating capacity. The powers are also shown with per unit values based on 100 MVA. The maximum generating capacity of remaining buses are set as 100 pu. The maximum and minimum reactive powers are also shown in column 4 and 5. They are the reactive power constrained of the system. The status shown in column 8 are set as 1 for all generator. This means that all generators are operating. Table II. Generator Data for IEEE14 Bus System 7 5 Q 4 bus 2 G3 G2 Figure 1. Single Line Diagram for IEEE14 Bus System B. Bus Data The bus data for IEEE14 bus system is shown in Table I. In bus type identification, bus type 3 stands for slack bus, 2 for voltage control bus and 1 stands for load bus. P d and Qd are the demand or load power at the corresponding buses. The demand powers are given in per unit with 100 MVA base. According to data, Bus 3 exhibits the largest load in terms of both real and reactive power. Gs and Bs are the shunt conductance and susceptance at the buses. These values are set as zero except Bus 9 where the bus susceptance is assigned as 19 p.u. The next column is area data and it is to be use for interconnected system. In IEEE14 bus system all buses are assigned as area 1 and thus the buses are located at the same area. Voltage magnitude and angle at each bus are denoted by Vm and Va in the table. Base kV is not defined in this system. Zone is also assigned as 1. The last two columns describe maximum and minimum voltages at the buses. Table I. Bus Data for IEEE14 Bus System Bu s-i t y p e s a r e a Pd Qd s Vm 1 3 0 0 0 0 1 2 2 22 13 0 0 3 2 94 19 0 4 1 48 -4 5 1 7.6 6 2 7 1 8 2 Va ba se K V 1.1 0 1 1 0 1 0 0 1.6 0 11 7.5 0 0 G B 0 0 zo ne V V max min 0 1 1.1 0.9 -5 0 1 1.1 0.9 1 -13 0 1 1.1 0.9 1 1 -10 0 1 1.1 0.9 0 1 1 -9 0 1 1.1 0.9 0 0 1 1.1 -14 0 1 1.1 0.9 0 0 1 1.1 -13 0 1 1.1 0.9 0 9 1 30 17 0 0 1 9 1 1.1 -13 0 1 1.1 0.9 1 1.1 -15 0 1 1.1 0.9 10 1 9 5.8 0 0 1 1.1 -15 0 1 1.1 0.9 11 1 3.5 1.8 0 0 1 1.1 -15 0 1 1.1 0.9 12 1 6.1 1.6 0 0 1 1.1 -15 0 1 1.1 0.9 13 1 14 5.8 0 0 1 1.1 -15 0 1 1.1 0.9 14 1 15 5 0 0 1 1 -16 0 1 1.1 0.9 max Qmin -16.9 10 0 stat us 1.06 100 1 332.4 0 Vg P 1 2 40 42.4 50 -40 1.05 100 1 140 0 3 0 23.4 40 0 1.01 100 1 100 0 6 0 12.2 24 -6 1.07 100 1 100 0 8 0 17.4 24 -6 1.09 100 1 100 0 C 3 Qg mbase Pg 232 .4 Pmax min D. Branch Data There are 20 interconnected lines in IEEE14 bus system and the data for each line is described in Table III. The first two column show the from bus and to bus as fbus and tbus respectively. The next three columns describe the resistance, reactance and susceptance of the respective line. The three rates are also mentioned as A, B and C. The ratio in column 8 describe the voltage ratio between the two buses. According to this ratio data, the transformers are placed between buses 4 and 7, 4 and 9 and 5 and 6 in single line diagram. The angle in column 9 is set as 0 for all buses. The status in column 10 describe all buses are sound and in operation. Table III. Branch Data for IEEE14 Bus System C ra tio an g st at us 0 0 0 1 0 0 0 0 1 0 0 0 0 1 9900 0 0 0 0 1 9900 0 0 0 0 1 0.0128 9900 0 0 0 0 1 0 9900 0 0 0 0 1 0.2091 0 9900 0 0 1 0 1 0 0.5562 0 9900 0 0 0 1 0 0.252 0 9900 0 0 1 0. 9 0 1 11 0.095 0.1989 0 9900 0 0 0 0 1 12 0.1229 0.2558 0 9900 0 0 0 0 1 6 13 0.0662 0.1303 0 9900 0 0 0 0 1 7 8 0 0.1762 0 9900 0 0 0 0 1 7 9 0 0.11 0 9900 0 0 0 0 1 9 10 0.0318 0.0845 0 9900 0 0 0 0 1 9 14 0.1271 0.2704 0 9900 0 0 0 0 1 10 11 0.0821 0.1921 0 9900 0 0 0 0 1 12 13 0.2209 0.1999 0 9900 0 0 0 0 1 13 14 0.1709 0.348 0 9900 0 0 0 0 1 F bu s Tb r X b rate A 1 2 0.0194 0.0592 0.0528 9900 0 1 5 0.054 0.223 0.0492 9900 2 3 0.047 0.198 0.0438 9900 2 4 0.0581 0.1763 0.034 2 5 0.057 0.1739 0.0346 3 4 0.067 0.171 4 5 0.0134 0.0421 4 7 0 4 9 5 6 6 6 us B 4 E. Generator Cost Function The generator cost function for IEEE14 bus system is shown in Table IV. Table IV. Generator Cost Function for IEEE14 Bus System No 1 2 3 4 5 Bus 1 2 3 6 8 c2 0.04 0.25 0.01 0.01 0.01 c1 20 20 40 40 40 c0 0 0 0 0 0 VIII. CONSTRAINTS FOR INTERIOR POINT METHOD In optimal power flow study with interior point method, the constraints are important data. Three constraints can be observed in IEEE14 bus system. Thus the inputs files are also necessary for these constraints. The assigned constraints are reactive power constraints and capacity constraints at generator buses, and voltage constraints at all bus. A. Reactive Power Constraints The reactive power constraints are assigned at generator buses and these data are arranged in ‘qconstr’ input file as follow: % Bus no Qmax Qmin qconstr=[ 1 10 2 3 6 8 50 40 24 24 0 -4 0 0 -6 -6 B. Capacity Constraints The capacity constraints or real power constraints are assigned at generator buses and these data are arranged in ‘pconstr’ input file as follow: % Bus no Pmax Pmin pconstr=[ 1 2 3 6 8 332.4 140 100 100 100 0 0 0 0 0 C. Voltage Constraints The voltage constraints are assigned at all buses and these data are arranged in ‘vconstr’. The ‘vconstr’ for IEEE14 bus system are within +/- 6% at all buses. for optimization of general case and not intended only for power system optimization. The research and modeling of the power flow and OPF problems were done entirely using the MATPOWER toolbox version 4.1. The toolbox is capable of modeling complex networks, providing properties of buses, branches, generators, generator costs and loads. These quantities are all given in matrices that can be easily modified. The power flow cost problem is solved using the Newton-Raphson and Lambda iteration method, while the optimization problem has several different solvers. The majority of the produced code focused on building the corresponding matrices in the problems for MATPOWER to solve. In the simulation of interior point method for optimal power flow for IEEE14 bus system, the optimal point is reached within 0.3seconds. At the end of simulation, the total generation cost is obtained as 8081.53 $/hr and the total loss is 9.287 MW. Total transmission efficiency is 96.54 %. The resulting system summary is shown in Table V. Table V. OPF result with Interior Point Method for IEEE 14 Bus System How many? Buses 14 Generators Committed Gens Loads Fixed 5 System Summary How much? P (MW) Total Gen Capacity 772.4 On-line Capacity Generation 5 (actual) 11 Load 11 Fixed Q (MVAr) -52 to 148 772.4 -52 to 148 268.3 259 259 67.6 73.5 73.5 Dispatchable 0 Dispatchable -0.0 of -0.0 -0.0 Shunts 1 Shunt (inj) -0.0 20.7 Branches 20 9.29 39.16 Transformers 3 - 24.3 Inter-ties 0 Losses (I^2 * Z) Branch Charging (inj) Total Inter-tie Flow 0.0 0.0 Areas 1 According to the assigned parameters, the parameters operated at maximum and minimum values are also generated by the program. Table 6 shows these minimum and maximum operating points. The magnitudes as well as the location are also described in this table. Table VI. Result Data For Maximum and Minimun Values IX. PERFORMANCE EVALUATION OF IEEE 14 BUS SYSTEM The application of interior point method to IEEE14 bus system is carried out by matlab interior point solver (MIPS) in Matpower4.1 optimization toolbox. This software package in intended for optimization of power system thus it is suitable for this paper. In Matpower, ipm_opf_solver command is used for interior point method of optimal power flow. With Matlab software, interior point method can be executed using ipm command. But Matlab optimization toolbox is intended Voltage Magnitude Voltage Angle P Losses (I^2*R) Minimum Maximum 0.94p.u. @ bus 69 1.060 p.u. at bus 40 -28.26 deg @ bus 63 8.47 deg at bus 34 - 6.05 MW at line 43-47 5 Q Losses (I^2*X) Lambda P -0.0 $/MWh at bus 1 -0.0 $/MWh at bus 1 38.31MVAr at line 43-47 157.55$/MWh at bus 69 499.9 $/MWh at bus 69 Lambda Q At the bus data, the voltage magnitudes and angles, real and reactive power generation and demand and real and reactive power cost at each bus are described. The slack bus generates maximum real power with 194.33 MW and there is no reactive power generation at slack bus. At the generator of bus 6, there is only reactive power generation with 11.55 MVAR. The real and reactive power generation of each generators are within the assigned limits. The cost of real power is maximum at Bus 14 and it is minimum at Bus 1. With the interior point method, the bus voltage profile is very good at all bus. The minimum bus voltage is 1.014 pu at bus 4. The bus voltage magnitude is at upper limit for Bus 1, 6 and 8. All bus voltages are also within the assigned constraint values. The maximum bus voltage phase angle can be observed at bus 14 where the angle is – 14.274. The maximum voltage phase angle is also acceptable for system stability. There are 20 branches in IEEE14 bus system. In line data, real and reactive power flow and losses on the lines are described. Optimal line flow is intended for the minimum power loss on the line. According to line flow results, the maximum power flow can be observed at line 1-2 and minimum line flow can be observed at line 12-13. The maximum real power losses occurred at line 1-2 where the losses are 2.902 MW. At line 4-7, 4-9, 5-6, 7-8 and 7-9 the real power loss is zero. The reactive power losses are rather large compared to real power losses. The maximum reactive power loss occurred at line 1-2 and minimum reactive power losses can be observed at line 12-13. According to the result, the real power losses on the line is 9.287 MW and reactive power losses is 39.16 MVAR. These losses are smaller compared to other methods. According to simulation results of bus data, all bus voltages are within regulation limits. Thus interior point method can solve optimal problem as well as voltage regulation problem. In power generation, generator at bus 4 is operating at upper bound of real power and generator at bus 1 is operating at upper bound of reactive power. X. COMPARISON WITH OTHER POWER SYETEM OPTIMIZATION METHODS To examine the performance of the interior point method in OPF problem, the same case (IEEE14 bus system) is also solved by Newton-Raphson and Lambda Iteration methods which are used for power system optimization . The results for important data by each method are shown in table. Table VII. Comparison with Other Power System Optimization Methods SN 1 2 Parameter Generation Cost ($/h) Power Loss Linear Programming Lambda Newton- Iteration Raphson 8081.53 8498.72 9459.50 9.287 11.14 15.992 (MW) 3 4 5 6 7 Transmission Efficiency (%) Voltage Regulation (%) 96.54 % 95.88 %. 94.185 %. 6% 12.1 % 14 % Max Voltage 1.06 at buses (pu) Min. Voltage (pu) Max Voltage angle (deg) 1,6,8 1.014 at bus 4 - 14.274. 1.0 at bus1 1.0 at bus 1 0.879 at bus 0.860 at bus 14 -16.819 14 - 19.657 According to the results, solving interior point method with MIPS solver can provide the best performance in optimization as well as voltage profile. It can also handle all assigned constraints. In Newton-Raphson and Lambda Iteration methods, the constraints are not satisfied. XI. CONCLUSION This paper presented interior point method with matlab interior point solver to optimal power flow of IEEE 14 bus system. These interior point method captures both the voltage phase angles and magnitudes, which are coupled through equations for active and reactive power. Experimental comparisons with AC solutions on a variety of standard IEEE and MatPower benchmarks shows that the interior point method are highly accurate for active and reactive power, phase angles and voltage magnitudes. The interior point method can be efficiently used as a building block for optimization problems involving constraints on real and reactive power flow and voltage magnitudes. ACKNOWLEDGEMENTS The author wishes to express her deep gratitude to his Excellency, Minister Dr. Ko Ko Oo, Ministry of Science and Technology, for opening the Master of Engineering course at Mandalay Technological University. The author is very thankful to Dr. Myint Thein, Pro-Rector of Mandalay Technological University, for his in valuable permission and kind support in carrying out this research work. The author wishes to record her thanks to Dr. Khin Thuzar Soe, Associate Professor and Head, Department of Electrical Power Engineering, Mandalay Technological University, for his guidance, suggestions and necessary advice. The author is deeply indebted to her supervisor, Dr. Pyone Lai Swe, Lecture, Department of Electrical Power Engineering, Mandalay Technological University, for his careful guidance, necessary advice and encouragement. REFERENCES [1] Zimmerman, Ray D., Murillo-Sanchez, Carlos E. and Gan, Deqiang. MATPOWER A MATLAB Power System Simulation Package. PSERC. [Online] [Cited: 02 11, 2013.] http://www.pserc.cornell.edu/matpower [2] Zimmerman, Ray Daniel, Murillo-Sánchez, Carlos Edmundo and Thomas, Robert John. MATPOWER: steady-state operations, planning and analysis tools for power systems 6 research and education. 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