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EVOLUTIONARY PROGRAMMING BASED OPTIMAL REACTIVE POWER PLANNING FOR VOLTAGE STABILITY IMPROVEMENT AND LOSS MINIMIZATION IN POWER SYSTEM
I. Musirin∗ and T.K.A. Rahman∗
References
[1] proposed an improved methodof operational and investment planning, utilizing a simplegenetic algorithm (SGA) combined with the successive lin-ear programming method. The ﬂexibility, robustness andeasy modiﬁcation of SGA were highlighted, which impliedthat the proposed technique was a promising approach forRPP.The application of EP in the RPP optimization wasreported as a reliable technique in minimizing the totalloss and voltage proﬁle in power systems as highlighted in[9, 10]. Lee and Yang [10] performed a comparative studybetween the three EC techniques namely the EP, ES andGA with the linear programming method in solving theRPP. Results obtained from the proposed EC techniquesshowed better performance over the linear programmingmethod in terms of total cost and power loss minimizationwhile hard limits were satisﬁed.This paper presents the application of EP- based opti-mization technique for implementing RPP in power system.Three RPP techniques were implemented to achieve thistask, which are optimal RPD, optimal TTCS and optimalcombination of RPD and TTCS. This study addressed twoobjective functions for the optimization process, which arevoltage stability improvement and total loss minimization.1The proposed technique was tested on the IEEE 30-bus re-liability test system (RTS). Comparative studies were per-formed on those three techniques, and it was revealed thatthe optimal combination of RPD and TTCS with voltagestability improvement as objective function has advantageover the others—in terms of loss minimization and voltageproﬁle improvement.2. Problem FormulationIn operation planning and real-time control, the mainobjective of the optimal RPP is to determine the optimalvalues of reactive power to be dispatched by the generatorsand/or TTCS values to improve voltage stability conditionor minimize total loss in the system.2.1 Voltage Stability Improvement as ObjectiveFunctionIn this study, the objective is to improve the voltage stabil-ity condition when the system is subjected to reactive loadvariations, particularly for the heavily loaded case. Theline voltage stability index derived by Musirin and Rah-man [11], termed as Fast Voltage Stability Index (FVSI ),was used as the ﬁtness function. It is used to assess thevoltage stability condition of the system. The mathemat-ical equation for FVSI was formulated from a line modelas shown in Fig. 1.Figure 1. Line model.The receiving end voltage can be represented inquadratic form as:V 22 −RXsin δ + cos δV1V2 +X+R2XQ2 = 0 (1)where δ = δ1 − δ2.The voltage stability index can be written as [11, 12]FV SIij =4Z2ijQjV 2i Xij(2)where Zij = line impedance, Xij is the line reactance, Qjis the reactive power at the receiving end and Vi is sendingend voltage. FVSI values for each line in the system werecomputed to indicate the voltage stability condition of thelines in the system. FVSI value closed to unity indicatesthat the line and hence the whole system is closed to itsvoltage stability limit.2.2 Loss Minimization as Objective FunctionIn this study, the objective function of RPP is to minimizethe active power in the transmission network, which canbe described as follows:min fP =k∈NEPkLoss (V, θ)=k∈NEk=(i,j)gkV 2i + V 2j − 2ViVj cos θijs.t.hQi =QGi − QDi (3)− Vij∈NiVj (Gij sin θij − Bij cos θij)=0 i ∈ NP QVi min ≤ Vi ≤ Vi max i ∈ NBQGi min ≤ QGi ≤ QGi max i ∈ {NP V , ns}where ns is the slack (reference) bus number, Qiand Qj arethe reactive power on the sending and receiving buses, QGis the generated reactive power, Vi and Vj are the voltagemagnitude at the sending and receiving buses.Equation (3) can be simpliﬁed to a generalized objec-tive function as:min fQ =k∈NEOkLoss (V, θ) +k∈NVlimλ (Vi − Vj)2+k∈NVlimλ (QGi − QGi lim)2s.t. hQi = QGi − QDi − Vik∈NEVj(Gij sin θij− Bij cos θij) = 0 i ∈ NP Q (4)where Vi lim =⎧⎨⎩Vi max, if Vi > Vi maxVi min, if Vi < Vi minQGi lim =⎧⎨⎩QGi max, if QGi > QGi maxQGi min, if QGi < QGi min3. Evolutionary ProgrammingEP is an optimization technique based on the natural se-lection. It involves random number generation, statisticalevaluation, ﬁtness calculation, mutation and new gener-ation which are bred by mode of selection [13]. In thisstudy, the EP optimization technique was implementedin the optimal RPD, TTCS, and optimal combination ofRPD and TTCS within two objective functions. The EP isimplemented according to the operators explained in thissection.23.1 InitializationInitially a series of random numbers, xi, are generatedusing uniformly distributed random generators, wherefor optimal RPDxi = [Qg1i, Qg2i, Qg3i, . . . , Qgki]for optimal TTCSxi = [T1j, T2i, . . . , Tni]and for optimal combination of RPD and TTCSxi = [Qg2i, Qg5i, Qg8i, Qg11i, Qg13i, T1i, T2i, T3i, T4i](5)i = 1, 2, 3, 4, 5, . . . , m, where m is the control variable;k = 1, 2, 3, . . . , k, where k is the generator number; n is thetransformer number. The random numbers should followthe following inequality constraints.Qming2 ≤ Qg2 ≤ Qmaxg2 , Qming5 ≤ Qg5 ≤ Qmaxg5 , Qming8 ≤ Qg8≤ Qmaxg8 , Qming11 ≤ Qg11 ≤ Qmaxg11 , Qming13 ≤ Qg13 ≤ Qmaxg13 ,Tmin1 ≤ T1 ≤ Tmax1 , Tmin2 ≤ T2 ≤ Tmax2 , Tmin3 ≤ T3≤ Tmax3 , Tmin2 ≤ T4 ≤ Tmax4The ﬁtness for voltage stability improvement as objectivefunction is FVSI, whereas the ﬁtness for total loss mini-mization as the objective function is the total power loss inthe system. Some initial conditions were considered duringthe initialization process, i.e.,V(m) ≥ V _set (6)FV SI ≤ FV SI_set (7)loss ≤ loss_set (8)V_set, FVSI_set and loss_set are the values computedfrom the load program at a selected loading conditionbefore any of RPP techniques is performed.3.2 MutationMutation is performed on the random number, xi, toproduce oﬀspring. The mutation process is implementedbased on the following equation.xi+m,j = xi,j + N0, β(xj max − xj min)fifmax(9)wherexi+m,j = mutated parents (oﬀspring)xi,j = parentsN = Gaussian random variable with mean μand variance γ2β = mutation scale, 0 < β < 1xj max = maximum random number for everyvariablexj min = minimum random number for everyvariablefi = ﬁtness for the ith random numberfmax = maximum ﬁtnessThe mutation scale, β, is adjusted to achieve better con-vergence.3.3 SelectionThe oﬀspring produced from the mutation process werecombined with the parents to undergo a selection processto identify the candidates who can be transcribed intothe next generation. In this study, priority selectionwas employed, whereby the populations were sorted inascending order according to their ﬁtness values. The ﬁrsthalf of the populations would be transcribed to the nextgeneration [13].3.4 Stopping CriterionThe convergence criterion is deﬁned by the diﬀerence be-tween the maximum ﬁtness and minimum ﬁtness ≤ 0.0001,i.e.,fitness max − fitnessmin ≤ 0.0001 (10)The generation process will be repeated until the conver-gence criterion is met.4. Implementation of EP-based RPP TechniqueThe IEEE 30-bus reliability test system was used as the testsystem for implementing the proposed RPP. This systemhas 6 generator buses, 24 load buses, 41 inter-connectedlines and 4 transformer tap changers. Five generators wereassigned as the control variable for minimizing the totalloss in the system in the optimization of RPD. On theother hand, the four transformer taps were considered asthe control variable in the optimization of TTCS. There-fore, for the optimal combination of RPD and TTCS; ninecontrol variables are required. The optimization of RPD,TTCS and combination of RPD and TTCS was imple-mented separately. The following procedures were imple-mented to develop an evolutionary programme for the RPPprocedures:1. Set the RPP constraints, i.e., FVSI ≤ FVSI_set andVm(bus) ≥ V_set for voltage stability improvement as3objective function whereas total loss ≤ loss_set andVm(bus) ≥ V_set for loss minimization as objectivefunction.2. Generate random number for the 1st generation,x1, x2, x3, x4, x5,. . . , x9 (ﬁve control variables for RPD,four control variables for TTCS and nine controlvariables for the combination of RPD and TTCS orRPP).3. Check for constraints violations. Go to step 2 ifconstraints violated, otherwise go to step 4.4. Fill in population pool.5. If pool is full, go to step 6, otherwise go to step 2.6. Determine xi min and xi max.7. Assign x1, x2, x3, x4, x5, . . . , x9 as the control variablesin the system data.8. Calculate the ﬁtness values by the running load ﬂowprogramme to evaluate FVSI or total loss.9. Determine FVSI_min, FVSI_max, FVSI_avg andFVSI_sum for voltage stability improvement as ob-jective function and loss_min, loss_max, loss_avgand loss_sum for loss minimization as objective func-tion (for statistical evaluation).10. Mutate the parents (generate oﬀsprings).11. Recalculate ﬁtness using the oﬀsprings (run load ﬂowto re-evaluate FVSI or total loss).12. Combine the parents and oﬀspring.13. Perform selection by ranking process.14. Transcribe new generations.15. If solution is not converged, repeat steps 6–14, other-wise go to step 16.16. Stop.4.1 Optimal RPDThe injected reactive powers on the generator buses weretaken as the control variables to improve the voltage sta-bility condition (indicated by FVSI reduction) or to min-imize total loss in the system. In the proposed technique,EP was used to determine the optimum reactive power tobe dispatched by the participating generator buses. In thedeveloped EP for RPD optimization, the random numberrepresented the injected reactive power of the generatorbuses in the system. Five variables namely x1, x2, x3, x4and x5 were used to represent the reactive power to beinjected to generators 2, 5, 8, 11 and 13. The ﬁnal resultsobtained from the EP would be the optimal reactive powerto be dispatched by the generators to improve voltagestability condition or minimize total loss in the system.4.2 Optimal TTCSFor the case of optimizing TTCS, random numbers namelyx1, x2, x3 and x4 generated from the initialization processrepresent the TTCS values, i.e., T1, T2, T3 and T4. In thiscase, similar constraints as that in the optimal RPD wereimposed. The optimized x1, x2, x3 and x4 obtained fromthe EP are the new values for TTCS to improve voltagestability condition or to minimize total loss in the system.4.3 Optimal Combination of RPD and TTCSThe RPD and TTCS were combined together for improvingthe voltage stability condition or minimizing total lossin the system. The control variables are the injectedreactive powers and the TTCS. Nine variables were used torepresent ﬁve generated reactive powers on the generatorbuses and four transformer setting values.5. Results and DiscussionThe results for the three RPP techniques are represented inthree separate sections for each objective function, becausethese procedures were implemented one at a time. Bus3 was subjected to the variation of loading conditions.Comparisons of results were performed to identify the mostsuitable RPP technique for improving the voltage stabilitycondition or loss minimization.5.1 Voltage Stability Improvement as ObjectiveFunctionIn this study, voltage stability analyses were initially con-ducted prior to the implementation of the RPP so that themaximum stability point can be estimated. The applica-tion of FVSI as the ﬁtness function in the voltage stabilityimprovement as the objective has yielded to voltage sta-bility improvement in the system. The implementation ofRPP has improved the voltage stability condition indicatedby the reduction in FVSI values and at the same time thevoltage at the loaded bus was increased to an acceptablelimit. Total loss was also computed during this process.5.1.1 Optimal RPD for Voltage StabilityImprovementTest was conducted with reactive power loading at bus 3varied. The results for the optimal RPD when bus 3 wasreactively loaded are tabulated in Table 1. The reactivepower loading was increased up to 175 MVAr where thevoltage has dropped to 0.8816 pu.From the table, it is observed that the FVSI value atevery loading condition with the implementation of RPD(post-RPD) is lower than that before its implementationnoted as pre-RPD. This implies that the voltage stabilitycondition has been improved. At the same time, voltageproﬁles are also improved and total losses are reduced.At Qd3 = 175 MVAr, EP has identiﬁed that the optimumreactive power to be dispatched by the generator buses areQg2 = 42.18 MVAr, Qg5 = 39.89 MVAr, Qg8 = 56.74 MVAr,Qg11 = 23.15 MVAr and Qg13 = 22.55 MVAr. The imple-mentation of RPD with voltage stability improvement asobjective function has improved the FVSI value from0.4442 to 0.4440 whereas the total loss is reduced from27.14 to 10.59 MW. The voltage at this bus is increasedfrom 0.8816 to 0.9310 pu.4Table 1Results for RPD When Bus 3 Was Reactively Loaded: IEEE 30-Bus RTS (Objective Function = Voltage StabilityImprovement)Loading Analysis FVSI Total Evolution Computation Qg2 Qg5 Qg8 Qg11 Qg13 VmConditions Loss Number Time (MVAr) (MVAr) (MVAr) (MVAr) (MVAr) (pu)(MVAr) (MW) (s)Qd3 = 50 Pre-RPD 0.2597 18.53 35.17 35.67 55.06 18.9 15.68 0.9937Post-RPD 0.1774 4.81 5 37.42 29.85 37.27 50.90 13.11 3.10 1.0347Qd3 = 125 Pre-RPD 0.3408 22.32 55.06 37.37 59.95 26.05 22.25 0.9285Post-RPD 0.3254 7.59 5 71.36 49.36 38.21 51.21 7.65 13.36 0.9685Qd3 = 175 Pre-RPD 0.4442 27.14 58.46 44.41 67.98 26.53 29.41 0.8816Post-RPD 0.4440 10.59 5 289.48 42.18 39.89 56.74 23.15 22.55 0.9310Table 2Results for TTCS When Bus 3 Was Reactively Loaded: IEEE 30-Bus RTS (Objective Function = Voltage StabilityImprovement)Loading Conditions Analysis FVSI Total Loss Evolution Computation T1 T2 T3 T4 Vm (pu)(MVAr) (MW) Number Time (s)Qd3 = 50 Pre-TTCS 0.2597 18.53 0.9937Post-TTCS 0.1824 18.57 7 78.780 0.950 1.270 1.060 0.930 0.9963Qd3 = 125 Pre-TTCS 0.3408 22.33 0.9285Post-TTCS 0.2817 21.95 4 29.330 0.950 1.270 1.060 0.940 0.9352Qd3 = 175 Pre-TTCS 0.4442 27.14 0.8816Post-TTCS 0.4062 27.32 7 197.630 0.922 0.836 1.236 1.044 0.89515.1.2 Optimal TTCS for Voltage StabilityImprovementIn this study, TTCSs are the control variables to be op-timized. Similar loading conditions as those utilized forthe RPD were used to test the developed technique forvoltage stability improvement. The reactive power loadingat bus 3 was increased gradually and the optimum valuesof TTCS of T1, T2, T3 and T4 were determined to improvethe voltage stability condition of the system.The results for the EP optimization technique whenbus 3 is reactively loaded taking FVSI as the ﬁtness aretabulated in Table 2. T1, T2, T3 and T4 are the optimizedTTCS values identiﬁed to improve the voltage stabilitycondition. Changing the TTCS to the optimum valuesdetermined by EP has improved the voltage stability con-dition. The voltage proﬁle at bus 3 has also been improvedwith the optimized TTCS. It can be seen from the resultswhen Qd3 = 175 MVAr, the implementation of TTCS opti-mization technique with voltage stability improvement asobjective function has improved the voltage stability con-dition indicated by the reduction in the FVSI value from0.4442 to 0.4062. However, the total loss is increased from27.14 to 27.32 MW. This is because the introduction of newTTCS values has altered the properties of the participatinglines. In addition, the voltage has been improved from0.8816 to 0.8951 pu.5.1.3 Optimal Combination of RPD and TTCS forVoltage Stability ImprovementFurther study has been conducted in the implementationof RPP by employing optimal RPD and TTCS concur-rently for voltage stability improvement. EP was used todetermine the optimal reactive power to be dispatched bythe generators and optimal setting of the transformer tapchanger. The ﬁve variables (i.e., Qg2, Qg5, Qg8, Qg11 andQg13) required in the RPD were combined with the fourvariables (i.e., T1, T2, T3 and T4). Similar loading condi-tions were used to test the developed technique for voltagestability improvement by optimizing the TTCS and RPDusing the EP. The results for the optimal combinationof RPD and TTCS optimization process when bus 3 wasreactively loaded are tabulated in Table 3.From the table, the values of T1, T2, T3, T4, Qg2,Qg5, Qg8, Qg11 and Qg13 are the optimized TTCS andreactive power dispatch identiﬁed by the EP to improvethe voltage stability condition at the respective loadingcondition. It is observed that the voltage stability conditionof the system was improved. The voltage proﬁles wereincreased from their original values and the total lossesin the system were reduced. For instance, optimizing theTTCS and RPD has signiﬁcantly improved the voltagestability condition indicated by the reduction of FVSIvalue from 0.4442 to 0.4424 at Qd3 = 175 MVAr. Total5Table 3Results for RPP When Bus 3 Was Reactively Loaded: IEEE 30-Bus RTS (Objective Function = Voltage StabilityImprovement)Loading Analysis FVSI Total Evolution Computation T1 T2 T3 T4 Qg2 Qg5 Qg8 Qg11 Qg13 VmConditions Loss Number Time (s) (MVAr) (MVAr) (MVAr) (MVAr) (MVAr) (pu)(MVAr) (MW)Qd3 = 50 Pre-RPP 0.2597 18.53 35.17 35.67 55.06 18.90 15.68 0.9937Post-RPP 0.1624 5.12 9 86.34 0.99 0.97 1.00 0.95 34.98 6.05 18.20 16.34 20.65 1.0150Qd3 = 125 Pre-RPP 0.3408 22.33 55.06 37.37 59.95 26.05 22.25 0.9285Post-RPP 0.3331 8.81 12 192.97 0.99 1.18 1.11 0.89 49.15 36.83 56.91 10.84 7.96 0.9662Qd3 = 175 Pre-RPP 0.4442 27.14 58.46 44.41 67.98 26.53 29.41 0.8816Post-RPP 0.4424 11.22 11 101.83 1.05 0.99 0.91 1.05 48.28 36.16 59.81 23.38 23.23 0.9313Table 4Results for RPD When Bus 3 Was Reactively Loaded: IEEE 30-Bus RTS (Objective Function = Loss Minimization)Loading Analysis FVSI Total Evolution Computation Qg2 Qg5 Qg8 Qg11 Qg13 Vm (pu)Conditions Loss Number Time (s) (MVAr) (MVAr) (MVAr) (MVAr) (MVAr)(MVAr) (MW)Qd3 = 50 Pre-RPD 0.2597 18.53 35.17 35.67 55.06 18.90 15.68 0.9937Post-RPD 0.2062 5.04 5 34.73 7.60 31.53 27.84 9.03 11.40 1.0132Qd3 = 125 Pre-RPD 0.3408 22.33 55.06 37.37 59.95 26.05 22.25 0.9285Post-RPD 0.3450 7.71 6 33.22 34.26 27.49 56.14 9.82 12.94 0.9625Qd3 = 175 Pre-RPD 0.4442 27.14 58.46 44.41 67.98 26.53 29.41 0.8816Post-RPD 0.5308 12.67 5 26.17 34.26 27.49 56.14 9.82 12.94 0.9012losses are also reduced from 27.14 to 11.22 MW whereasthe voltage is also improved from 0.8816 to 0.9313 pu.5.2 Loss Minimization as Objective FunctionThe optimization process was repeated for the RPD,TTCS, and combination of RPD and TTCS with totalloss minimization as the objective function. In this study,the total loss lower than the loss_set and voltage at theloaded bus higher than V_set were assigned as the con-straints for the initialization. The loss_set and V_setare the total loss and voltage at the loaded bus before thereactive power planning RPP is implemented. EP opti-mization technique was conducted at the similar loadingconditions as those implemented in the RPP when FVSIwas taken as the ﬁtness function. The implementation ofRPP has minimized the total losses and the voltage at theloaded bus was increased. FVSI was also computed oncethe total loss has been minimized. This is to monitor theeﬀect of loss minimization on voltage stability condition inthe system.5.2.1 Results for Optimal RPD in Loss MinimizationThe results for optimal RPD identiﬁed by the EP withloss minimization as the objective function when bus 3 wassubjected to load variations are tabulated in Table 4.The total losses, FVSI values, and voltage bus varia-tion were recorded as the loading condition was graduallyincreased. From the table, the values of Qg2, Qg5, Qg8, Qg11and Qg13 are the optimized reactive powers need to bedispatched by the generator buses to minimize the totallosses in the system. Total losses with optimum RPD arelower than that before the optimization, which implies thatthe total losses for the system have been minimized. Thevoltage at bus 3 is increased with the implementation ofoptimal RPD. However, the value of FVSI is increased. Itcan be seen for the case of Qd3 = 175 MVAr; the total lossesare reduced from 27.14 to 12.67 MW. However, the FVSIvalue is increased from 0.4442 to 0.5308. This implies thathaving total loss minimization as objective function forRPD has not improved the voltage stability condition ofthe system as the FVSI value is increased. The optimumRPD has also improved the voltage at bus 3 from 0.8816to 0.9012 pu.5.2.2 Optimal TTCS for Loss MinimizationThe proposed EP optimization technique with total lossminimization as the objective function was further appliedto optimize the TTCS. This technique is tested on thesimilar loading condition as used in the previous tests.Bus 3 was subjected to reactive load variation. Theresults for the EP-based optimization of TTCS when bus3 was subjected to reactive load variation with total lossesminimization as the objective function are tabulated inTable 5.From the table, the values for T1, T2, T3 and T4are the optimised TTCS values to minimize the totallosses. The implementation of EP for optimizing the TTCS6Table 5Results for TTCS Optimization When Bus 3 Was Reactively Loaded: IEEE 30-Bus RTS (Objective Function = LossMinimization)Loading Conditions Analysis FVSI Total Loss Evolution Computation T1 T2 T3 T4 Vm (pu)(MVAr) (MW) Number Time (s)Qd3 = 50 Pre-TTCS 0.2597 18.53 0.9937Post-TTCS 0.4715 18.31 91 659.97 1.21 1.05 1.30 1.06 1.0125Qd3 = 125 Pre-TTCS 0.3408 22.33 0.9285Post-TTCS 0.6480 20.84 13 404.74 1.28 1.09 1.35 1.07 0.9648Qd3 = 175 Pre-TTCS 0.4442 27.14 0.8816Post-TTCS 0.8000 24.28 21 84.46 1.26 1.26 1.49 0.99 0.9298Table 6Results for RPP When Bus 3 Was Reactively Loaded: IEEE 30-Bus RTS (Objective Function = Loss Minimization)Loading Analysis FVSI Total Evolution Computation T1 T2 T3 T4 Qg2 Qg5 Qg8 Qg11 Qg13 VmConditions Loss Number Time (s) (MVAr) (MVAr) (MVAr) (MVAr) (MVAr) (pu)(MVAr) (MW)Qd3 = 50 Pre-RPP 0.2597 18.53 35.17 35.67 55.06 18.9 15.68 0.9937Post-RPP 0.2094 4.74 13 227.18 0.84 0.86 0.91 0.79 23.94 35.59 53.89 1.18 21.46 1.0422Qd3 = 125 Pre-RPP 0.3408 22.33 55.06 37.37 59.95 26.05 22.25 0.9285Post-RPP 0.4256 7.52 14 69.24 0.84 0.86 0.92 0.80 24.32 35.91 54.55 1.45 21.71 0.9665Qd3 = 175 Pre-RPP 0.4442 27.14 58.46 44.41 67.98 26.53 29.41 0.8816Post-RPP 0.6053 12.30 16 105.66 0.84 0.86 0.92 0.80 24.33 35.91 54.55 1.45 21.71 0.9058Note: RPP = RPD + TTCSwith the total loss minimization as objective function hasminimized the total losses in the system and has improvedthe voltage at bus 3. However, the FVSI value has beenincreased, which implies the voltage stability condition ofthe system has been reduced. It can be observed that whenQd3 = 175 MVAr, the implementation of TTCS and totalloss minimization as objective function has reduced thevoltage stability condition of the system in which the FVSIvalue has been increased from 0.4442 to 0.8000. However,the total loss is reduced from 27.14 to 24.28 MW and thevoltage at bus 3 is increased from 0.8816 to 0.9298 pu.5.2.3 Results for Optimal Combination of RPD andTTCS in Loss MinimizationEvolutionary Programming optimization technique wasfurther developed to determine optimal combination ofRPD and TTCS with total loss minimization as the ob-jective function. Similar loading conditions as previoustests were used to assess the proposed technique. In thisstudy, the random numbers generated in the EP algorithmrepresent the actual injected reactive powers and TTCSnamely Qg2, Qg5, Qg8, Qg11, Qg13, T1, T2, T3 and T4. Theresults for optimum RPD and TTCS identiﬁed by the EPwith loss minimization as the objective function when bus3 was reactively loaded are tabulated in Table 6.From the table, the values for T1, T2, T3 and T4are the optimized TTCS values whereas the values forQg2, Qg5, Qg8, Qg11 and Qg13 are the optimized reactivepowers need to be injected to generators 2, 5, 8, 11 and13 for minimizing the total loss. With the optimum RPDand TTCS, it can be seen that the total loss were re-duced whereas the voltage proﬁle is signiﬁcantly increasedfor each loading condition. However, the implementationof RPD and TTCS with total loss as the objective func-tion has reduced the voltage stability condition indicatedby the increment in FVSI values. For example, whenQd3 = 175 MVAr, the total losses in the system is reducedfrom 27.14 to 12.30 MW. Voltage stability condition isreduced, indicated by the increase in FVSI value from0.4442 to 0.6053.5.3 Comparison of RPP TechniquesThe results obtained from the proposed RPP techniquesnamely RPD, TTCS, and combined RPD and TTCS withvoltage stability improvement, as the objective function,are compared to those obtained when loss minimizationis taken as the objective function. The comparison ismade in terms of voltage stability improvement, totalloss minimization, computation time, voltage proﬁle, andmaximum voltage at other load buses.The results obtained from the RPD, TTCS, and thecombination of RPD and TTCS for each objective functionare compared for each participating bus. Table 7 shows theresults when the three techniques were implemented on thesystem with reactive power loading at bus 3 is increased to175 MVAr.The application of voltage stability improvement asthe objective function in the RPD technique has improved7Table 7Results for Comparative Studies between Voltage Stability Improvement and Total Loss Minimization as Two SeparateObjective Function When Qd3 = 175 MVArRPP techniques Pre-RPP RPD TTCS RPD + TTCSObjective function VSI TLM VSI TLM VSI TLMFVSI 0.4442 0.4440 0.5308 0.4062 0.8000 0.4424 0.6053Total loss (MW) 27.14 10.59 12.67 27.32 24.28 11.22 12.30Evolution number 5 5 7 21 11 16Computation time (s) 289.48 26.17 197.63 84.44 101.83 105.66Bus voltage, Vm (pu) 0.8816 0.9310 0.9017 0.8951 0.9298 0.9313 0.9058Maximum voltage at other load buses (pu) 1.06 1.10 1.06 1.06 1.06 1.06 1.06Note: RPP = reactive power planning RPD = reactive power dispatchTTCS = transformer tap changer setting VSI = voltage stability improvementTLM = total loss minimizationthe voltage stability condition indicated by the reductionin FVSI value from 0.4442 to 0.4440. It has also reducedthe total loss in the system from 27.14 to 10.59 MW. Whentotal loss minimization is taken as the objective functionin the optimization of RPD, the total loss is reduced to12.67 MW. However, the FVSI is increased from 0.4442to 0.5308. Thus, value having voltage stability improve-ment as the objective function in the optimization of RPDhas improved both the voltage stability condition and alsominimized the total loss in the system. The voltage proﬁleobtained when voltage stability improvement was used asthe objective function is better than that when total lossminimization was used as the objective function. The ap-plication of total loss minimization as objective functionhas minimized the total loss in the system; however, thevoltage stability condition of the system was weak, indi-cated by the increase in the FVSI value. Therefore, theapplication of voltage stability improvement as the objec-tive function gives better results than those obtained whentotal loss minimization is used as the objective function inoptimizing the RPD.In optimizing the TTCS, the application of voltagestability improvement as objective function has reducedthe FVSI value from 0.4442 to 0.4062 but it has beenincreased to 0.8000 with the total loss minimization asthe objective function. The total loss reduction resultedfrom the total loss minimization as objective function isbetter than that in the voltage stability improvement asobjective function. Voltage proﬁle is increased when bothobjective functions were used to optimize the TTCS. Fromthe table, it is also observed that when EP was used to op-timize RPD and TTCS together, the application of voltagestability improvement as the objective function has givenbetter results in terms of voltage stability improvement,total loss minimization, and voltage improvement. Thisdemonstrates that the application of voltage stability im-provement as objective function is better in all the threeproposed RPP techniques. The optimal combination ofRPD and TTCS with voltage stability improvement as theobjective function outperformed optimal TTCS and opti-mal RPD in terms of voltage stability improvement andvoltage proﬁle increment. The total loss in the system hasbeen reduced to 11.22 MW whereas the voltage is increasedfrom 0.8816 to 0.9313 pu. It is observed that, with totalloss minimization as the objective function, the reductionin total loss is higher than that given by voltage stabilityimprovement as the objective function. The overall resultsshow that optimizing the combination of RPD and TTCSwith voltage stability improvement as the objective func-tion is the most suitable RPP technique as this techniquecould improve voltage stability condition and minimizetotal losses in the system.6. ConclusionA study on RPP using optimal RPD, optimal TTCS andoptimal combination of RPD and TTCS for voltage stabil-ity improvement and total loss minimization in a systemwas presented. EP was employed as the optimization ap-proach in determining the optimum values for the controlvariables in the optimal RPD, optimal TTCS, and opti-mal combination of RPD and TTCS for both objectivefunctions in a power system. Results showed that theoptimal combination of RPD and TTCS gave the bestresults in terms of voltage stability improvement, totalloss minimization, fast computation, and voltage proﬁleimprovement over other techniques. Therefore, the pro-posed technique is possible to be implemented practicallywhich could achieve voltage stability improvement and lossminimization in a power system.References[1] K.Y. Lee, X. Bai, & Y.M. Park, Optimization method forreactive power planning by using a modiﬁed simple geneticalgorithm, IEEE Transaction on Power Systems, 10 (4), 1995,1843–1850.
[2] H.N. Ng, M.M.A. Salama, & A.Y. Chikhani, Classiﬁcation ofcapacitor allocation techniques, IEEE Transaction on PowerSystems, 15 (1), 2000, 387–392.
[3] K. Iba, Reactive power optimization by genetic algorithm,IEEE Transaction on Power Systems, 9 (2), 1994, 685–692.8
[4] M.H. Haque, Optimal locations of shunt FACTs devices in longtransmission lines, IEE Proceedings – Generation Transmissionand Distribution, 147 (4), 2000, 218–222.
[5] W.N. Abdullah, H. Saibon, A.M.M. Zain, & K.L. Lo, Geneticalgorithm for optimal reactive power dispatch, IEEE EnergyManagement and Power Delivery Conference, 1, 1998, 160–164.
[6] Q.H. Wu & J.T. Ma, Genetic search for optimal reactivepower dispatch of power systems, Proc. IEEE Int. ControlConference, 1994, 717–722.
[7] Y. Liu, L. Ma & J. Zhang, Reactive power optimisation byGA/SA/TS combined algorithms, Journal of Electrical Powerand Energy Systems, 24, 2002, 765–769.
[8] Q.H. Wu & J.T. Ma, Power system optimal reactive powerdispatch using evolutionary programming, IEEE Transactionon Power Systems, 10 (3), 1995, 1243–1249.
[10] performed a comparative studybetween the three EC techniques namely the EP, ES andGA with the linear programming method in solving theRPP. Results obtained from the proposed EC techniquesshowed better performance over the linear programmingmethod in terms of total cost and power loss minimizationwhile hard limits were satisﬁed.This paper presents the application of EP- based opti-mization technique for implementing RPP in power system.Three RPP techniques were implemented to achieve thistask, which are optimal RPD, optimal TTCS and optimalcombination of RPD and TTCS. This study addressed twoobjective functions for the optimization process, which arevoltage stability improvement and total loss minimization.1The proposed technique was tested on the IEEE 30-bus re-liability test system (RTS). Comparative studies were per-formed on those three techniques, and it was revealed thatthe optimal combination of RPD and TTCS with voltagestability improvement as objective function has advantageover the others—in terms of loss minimization and voltageproﬁle improvement.2. Problem FormulationIn operation planning and real-time control, the mainobjective of the optimal RPP is to determine the optimalvalues of reactive power to be dispatched by the generatorsand/or TTCS values to improve voltage stability conditionor minimize total loss in the system.2.1 Voltage Stability Improvement as ObjectiveFunctionIn this study, the objective is to improve the voltage stabil-ity condition when the system is subjected to reactive loadvariations, particularly for the heavily loaded case. Theline voltage stability index derived by Musirin and Rah-man
[11], termed as Fast Voltage Stability Index (FVSI ),was used as the ﬁtness function. It is used to assess thevoltage stability condition of the system. The mathemat-ical equation for FVSI was formulated from a line modelas shown in Fig. 1.Figure 1. Line model.The receiving end voltage can be represented inquadratic form as:V 22 −RXsin δ + cos δV1V2 +X+R2XQ2 = 0 (1)where δ = δ1 − δ2.The voltage stability index can be written as [11, 12]FV SIij =4Z2ijQjV 2i Xij(2)where Zij = line impedance, Xij is the line reactance, Qjis the reactive power at the receiving end and Vi is sendingend voltage. FVSI values for each line in the system werecomputed to indicate the voltage stability condition of thelines in the system. FVSI value closed to unity indicatesthat the line and hence the whole system is closed to itsvoltage stability limit.2.2 Loss Minimization as Objective FunctionIn this study, the objective function of RPP is to minimizethe active power in the transmission network, which canbe described as follows:min fP =k∈NEPkLoss (V, θ)=k∈NEk=(i,j)gkV 2i + V 2j − 2ViVj cos θijs.t.hQi =QGi − QDi (3)− Vij∈NiVj (Gij sin θij − Bij cos θij)=0 i ∈ NP QVi min ≤ Vi ≤ Vi max i ∈ NBQGi min ≤ QGi ≤ QGi max i ∈ {NP V , ns}where ns is the slack (reference) bus number, Qiand Qj arethe reactive power on the sending and receiving buses, QGis the generated reactive power, Vi and Vj are the voltagemagnitude at the sending and receiving buses.Equation (3) can be simpliﬁed to a generalized objec-tive function as:min fQ =k∈NEOkLoss (V, θ) +k∈NVlimλ (Vi − Vj)2+k∈NVlimλ (QGi − QGi lim)2s.t. hQi = QGi − QDi − Vik∈NEVj(Gij sin θij− Bij cos θij) = 0 i ∈ NP Q (4)where Vi lim =⎧⎨⎩Vi max, if Vi > Vi maxVi min, if Vi < Vi minQGi lim =⎧⎨⎩QGi max, if QGi > QGi maxQGi min, if QGi < QGi min3. Evolutionary ProgrammingEP is an optimization technique based on the natural se-lection. It involves random number generation, statisticalevaluation, ﬁtness calculation, mutation and new gener-ation which are bred by mode of selection [13]. In thisstudy, the EP optimization technique was implementedin the optimal RPD, TTCS, and optimal combination ofRPD and TTCS within two objective functions. The EP isimplemented according to the operators explained in thissection.23.1 InitializationInitially a series of random numbers, xi, are generatedusing uniformly distributed random generators, wherefor optimal RPDxi = [Qg1i, Qg2i, Qg3i, . . . , Qgki]for optimal TTCSxi = [T1j, T2i, . . . , Tni]and for optimal combination of RPD and TTCSxi = [Qg2i, Qg5i, Qg8i, Qg11i, Qg13i, T1i, T2i, T3i, T4i](5)i = 1, 2, 3, 4, 5, . . . , m, where m is the control variable;k = 1, 2, 3, . . . , k, where k is the generator number; n is thetransformer number. The random numbers should followthe following inequality constraints.Qming2 ≤ Qg2 ≤ Qmaxg2 , Qming5 ≤ Qg5 ≤ Qmaxg5 , Qming8 ≤ Qg8≤ Qmaxg8 , Qming11 ≤ Qg11 ≤ Qmaxg11 , Qming13 ≤ Qg13 ≤ Qmaxg13 ,Tmin1 ≤ T1 ≤ Tmax1 , Tmin2 ≤ T2 ≤ Tmax2 , Tmin3 ≤ T3≤ Tmax3 , Tmin2 ≤ T4 ≤ Tmax4The ﬁtness for voltage stability improvement as objectivefunction is FVSI, whereas the ﬁtness for total loss mini-mization as the objective function is the total power loss inthe system. Some initial conditions were considered duringthe initialization process, i.e.,V(m) ≥ V _set (6)FV SI ≤ FV SI_set (7)loss ≤ loss_set (8)V_set, FVSI_set and loss_set are the values computedfrom the load program at a selected loading conditionbefore any of RPP techniques is performed.3.2 MutationMutation is performed on the random number, xi, toproduce oﬀspring. The mutation process is implementedbased on the following equation.xi+m,j = xi,j + N0, β(xj max − xj min)fifmax(9)wherexi+m,j = mutated parents (oﬀspring)xi,j = parentsN = Gaussian random variable with mean μand variance γ2β = mutation scale, 0 < β < 1xj max = maximum random number for everyvariablexj min = minimum random number for everyvariablefi = ﬁtness for the ith random numberfmax = maximum ﬁtnessThe mutation scale, β, is adjusted to achieve better con-vergence.3.3 SelectionThe oﬀspring produced from the mutation process werecombined with the parents to undergo a selection processto identify the candidates who can be transcribed intothe next generation. In this study, priority selectionwas employed, whereby the populations were sorted inascending order according to their ﬁtness values. The ﬁrsthalf of the populations would be transcribed to the nextgeneration [13].3.4 Stopping CriterionThe convergence criterion is deﬁned by the diﬀerence be-tween the maximum ﬁtness and minimum ﬁtness ≤ 0.0001,i.e.,fitness max − fitnessmin ≤ 0.0001 (10)The generation process will be repeated until the conver-gence criterion is met.4. Implementation of EP-based RPP TechniqueThe IEEE 30-bus reliability test system was used as the testsystem for implementing the proposed RPP. This systemhas 6 generator buses, 24 load buses, 41 inter-connectedlines and 4 transformer tap changers. Five generators wereassigned as the control variable for minimizing the totalloss in the system in the optimization of RPD. On theother hand, the four transformer taps were considered asthe control variable in the optimization of TTCS. There-fore, for the optimal combination of RPD and TTCS; ninecontrol variables are required. The optimization of RPD,TTCS and combination of RPD and TTCS was imple-mented separately. The following procedures were imple-mented to develop an evolutionary programme for the RPPprocedures:1. Set the RPP constraints, i.e., FVSI ≤ FVSI_set andVm(bus) ≥ V_set for voltage stability improvement as3objective function whereas total loss ≤ loss_set andVm(bus) ≥ V_set for loss minimization as objectivefunction.2. Generate random number for the 1st generation,x1, x2, x3, x4, x5,. . . , x9 (ﬁve control variables for RPD,four control variables for TTCS and nine controlvariables for the combination of RPD and TTCS orRPP).3. Check for constraints violations. Go to step 2 ifconstraints violated, otherwise go to step 4.4. Fill in population pool.5. If pool is full, go to step 6, otherwise go to step 2.6. Determine xi min and xi max.7. Assign x1, x2, x3, x4, x5, . . . , x9 as the control variablesin the system data.8. Calculate the ﬁtness values by the running load ﬂowprogramme to evaluate FVSI or total loss.9. Determine FVSI_min, FVSI_max, FVSI_avg andFVSI_sum for voltage stability improvement as ob-jective function and loss_min, loss_max, loss_avgand loss_sum for loss minimization as objective func-tion (for statistical evaluation).10. Mutate the parents (generate oﬀsprings).11. Recalculate ﬁtness using the oﬀsprings (run load ﬂowto re-evaluate FVSI or total loss).12. Combine the parents and oﬀspring.13. Perform selection by ranking process.14. Transcribe new generations.15. If solution is not converged, repeat steps 6–14, other-wise go to step 16.16. Stop.4.1 Optimal RPDThe injected reactive powers on the generator buses weretaken as the control variables to improve the voltage sta-bility condition (indicated by FVSI reduction) or to min-imize total loss in the system. In the proposed technique,EP was used to determine the optimum reactive power tobe dispatched by the participating generator buses. In thedeveloped EP for RPD optimization, the random numberrepresented the injected reactive power of the generatorbuses in the system. Five variables namely x1, x2, x3, x4and x5 were used to represent the reactive power to beinjected to generators 2, 5, 8, 11 and 13. The ﬁnal resultsobtained from the EP would be the optimal reactive powerto be dispatched by the generators to improve voltagestability condition or minimize total loss in the system.4.2 Optimal TTCSFor the case of optimizing TTCS, random numbers namelyx1, x2, x3 and x4 generated from the initialization processrepresent the TTCS values, i.e., T1, T2, T3 and T4. In thiscase, similar constraints as that in the optimal RPD wereimposed. The optimized x1, x2, x3 and x4 obtained fromthe EP are the new values for TTCS to improve voltagestability condition or to minimize total loss in the system.4.3 Optimal Combination of RPD and TTCSThe RPD and TTCS were combined together for improvingthe voltage stability condition or minimizing total lossin the system. The control variables are the injectedreactive powers and the TTCS. Nine variables were used torepresent ﬁve generated reactive powers on the generatorbuses and four transformer setting values.5. Results and DiscussionThe results for the three RPP techniques are represented inthree separate sections for each objective function, becausethese procedures were implemented one at a time. Bus3 was subjected to the variation of loading conditions.Comparisons of results were performed to identify the mostsuitable RPP technique for improving the voltage stabilitycondition or loss minimization.5.1 Voltage Stability Improvement as ObjectiveFunctionIn this study, voltage stability analyses were initially con-ducted prior to the implementation of the RPP so that themaximum stability point can be estimated. The applica-tion of FVSI as the ﬁtness function in the voltage stabilityimprovement as the objective has yielded to voltage sta-bility improvement in the system. The implementation ofRPP has improved the voltage stability condition indicatedby the reduction in FVSI values and at the same time thevoltage at the loaded bus was increased to an acceptablelimit. Total loss was also computed during this process.5.1.1 Optimal RPD for Voltage StabilityImprovementTest was conducted with reactive power loading at bus 3varied. The results for the optimal RPD when bus 3 wasreactively loaded are tabulated in Table 1. The reactivepower loading was increased up to 175 MVAr where thevoltage has dropped to 0.8816 pu.From the table, it is observed that the FVSI value atevery loading condition with the implementation of RPD(post-RPD) is lower than that before its implementationnoted as pre-RPD. This implies that the voltage stabilitycondition has been improved. At the same time, voltageproﬁles are also improved and total losses are reduced.At Qd3 = 175 MVAr, EP has identiﬁed that the optimumreactive power to be dispatched by the generator buses areQg2 = 42.18 MVAr, Qg5 = 39.89 MVAr, Qg8 = 56.74 MVAr,Qg11 = 23.15 MVAr and Qg13 = 22.55 MVAr. The imple-mentation of RPD with voltage stability improvement asobjective function has improved the FVSI value from0.4442 to 0.4440 whereas the total loss is reduced from27.14 to 10.59 MW. The voltage at this bus is increasedfrom 0.8816 to 0.9310 pu.4Table 1Results for RPD When Bus 3 Was Reactively Loaded: IEEE 30-Bus RTS (Objective Function = Voltage StabilityImprovement)Loading Analysis FVSI Total Evolution Computation Qg2 Qg5 Qg8 Qg11 Qg13 VmConditions Loss Number Time (MVAr) (MVAr) (MVAr) (MVAr) (MVAr) (pu)(MVAr) (MW) (s)Qd3 = 50 Pre-RPD 0.2597 18.53 35.17 35.67 55.06 18.9 15.68 0.9937Post-RPD 0.1774 4.81 5 37.42 29.85 37.27 50.90 13.11 3.10 1.0347Qd3 = 125 Pre-RPD 0.3408 22.32 55.06 37.37 59.95 26.05 22.25 0.9285Post-RPD 0.3254 7.59 5 71.36 49.36 38.21 51.21 7.65 13.36 0.9685Qd3 = 175 Pre-RPD 0.4442 27.14 58.46 44.41 67.98 26.53 29.41 0.8816Post-RPD 0.4440 10.59 5 289.48 42.18 39.89 56.74 23.15 22.55 0.9310Table 2Results for TTCS When Bus 3 Was Reactively Loaded: IEEE 30-Bus RTS (Objective Function = Voltage StabilityImprovement)Loading Conditions Analysis FVSI Total Loss Evolution Computation T1 T2 T3 T4 Vm (pu)(MVAr) (MW) Number Time (s)Qd3 = 50 Pre-TTCS 0.2597 18.53 0.9937Post-TTCS 0.1824 18.57 7 78.780 0.950 1.270 1.060 0.930 0.9963Qd3 = 125 Pre-TTCS 0.3408 22.33 0.9285Post-TTCS 0.2817 21.95 4 29.330 0.950 1.270 1.060 0.940 0.9352Qd3 = 175 Pre-TTCS 0.4442 27.14 0.8816Post-TTCS 0.4062 27.32 7 197.630 0.922 0.836 1.236 1.044 0.89515.1.2 Optimal TTCS for Voltage StabilityImprovementIn this study, TTCSs are the control variables to be op-timized. Similar loading conditions as those utilized forthe RPD were used to test the developed technique forvoltage stability improvement. The reactive power loadingat bus 3 was increased gradually and the optimum valuesof TTCS of T1, T2, T3 and T4 were determined to improvethe voltage stability condition of the system.The results for the EP optimization technique whenbus 3 is reactively loaded taking FVSI as the ﬁtness aretabulated in Table 2. T1, T2, T3 and T4 are the optimizedTTCS values identiﬁed to improve the voltage stabilitycondition. Changing the TTCS to the optimum valuesdetermined by EP has improved the voltage stability con-dition. The voltage proﬁle at bus 3 has also been improvedwith the optimized TTCS. It can be seen from the resultswhen Qd3 = 175 MVAr, the implementation of TTCS opti-mization technique with voltage stability improvement asobjective function has improved the voltage stability con-dition indicated by the reduction in the FVSI value from0.4442 to 0.4062. However, the total loss is increased from27.14 to 27.32 MW. This is because the introduction of newTTCS values has altered the properties of the participatinglines. In addition, the voltage has been improved from0.8816 to 0.8951 pu.5.1.3 Optimal Combination of RPD and TTCS forVoltage Stability ImprovementFurther study has been conducted in the implementationof RPP by employing optimal RPD and TTCS concur-rently for voltage stability improvement. EP was used todetermine the optimal reactive power to be dispatched bythe generators and optimal setting of the transformer tapchanger. The ﬁve variables (i.e., Qg2, Qg5, Qg8, Qg11 andQg13) required in the RPD were combined with the fourvariables (i.e., T1, T2, T3 and T4). Similar loading condi-tions were used to test the developed technique for voltagestability improvement by optimizing the TTCS and RPDusing the EP. The results for the optimal combinationof RPD and TTCS optimization process when bus 3 wasreactively loaded are tabulated in Table 3.From the table, the values of T1, T2, T3, T4, Qg2,Qg5, Qg8, Qg11 and Qg13 are the optimized TTCS andreactive power dispatch identiﬁed by the EP to improvethe voltage stability condition at the respective loadingcondition. It is observed that the voltage stability conditionof the system was improved. The voltage proﬁles wereincreased from their original values and the total lossesin the system were reduced. For instance, optimizing theTTCS and RPD has signiﬁcantly improved the voltagestability condition indicated by the reduction of FVSIvalue from 0.4442 to 0.4424 at Qd3 = 175 MVAr. Total5Table 3Results for RPP When Bus 3 Was Reactively Loaded: IEEE 30-Bus RTS (Objective Function = Voltage StabilityImprovement)Loading Analysis FVSI Total Evolution Computation T1 T2 T3 T4 Qg2 Qg5 Qg8 Qg11 Qg13 VmConditions Loss Number Time (s) (MVAr) (MVAr) (MVAr) (MVAr) (MVAr) (pu)(MVAr) (MW)Qd3 = 50 Pre-RPP 0.2597 18.53 35.17 35.67 55.06 18.90 15.68 0.9937Post-RPP 0.1624 5.12 9 86.34 0.99 0.97 1.00 0.95 34.98 6.05 18.20 16.34 20.65 1.0150Qd3 = 125 Pre-RPP 0.3408 22.33 55.06 37.37 59.95 26.05 22.25 0.9285Post-RPP 0.3331 8.81 12 192.97 0.99 1.18 1.11 0.89 49.15 36.83 56.91 10.84 7.96 0.9662Qd3 = 175 Pre-RPP 0.4442 27.14 58.46 44.41 67.98 26.53 29.41 0.8816Post-RPP 0.4424 11.22 11 101.83 1.05 0.99 0.91 1.05 48.28 36.16 59.81 23.38 23.23 0.9313Table 4Results for RPD When Bus 3 Was Reactively Loaded: IEEE 30-Bus RTS (Objective Function = Loss Minimization)Loading Analysis FVSI Total Evolution Computation Qg2 Qg5 Qg8 Qg11 Qg13 Vm (pu)Conditions Loss Number Time (s) (MVAr) (MVAr) (MVAr) (MVAr) (MVAr)(MVAr) (MW)Qd3 = 50 Pre-RPD 0.2597 18.53 35.17 35.67 55.06 18.90 15.68 0.9937Post-RPD 0.2062 5.04 5 34.73 7.60 31.53 27.84 9.03 11.40 1.0132Qd3 = 125 Pre-RPD 0.3408 22.33 55.06 37.37 59.95 26.05 22.25 0.9285Post-RPD 0.3450 7.71 6 33.22 34.26 27.49 56.14 9.82 12.94 0.9625Qd3 = 175 Pre-RPD 0.4442 27.14 58.46 44.41 67.98 26.53 29.41 0.8816Post-RPD 0.5308 12.67 5 26.17 34.26 27.49 56.14 9.82 12.94 0.9012losses are also reduced from 27.14 to 11.22 MW whereasthe voltage is also improved from 0.8816 to 0.9313 pu.5.2 Loss Minimization as Objective FunctionThe optimization process was repeated for the RPD,TTCS, and combination of RPD and TTCS with totalloss minimization as the objective function. In this study,the total loss lower than the loss_set and voltage at theloaded bus higher than V_set were assigned as the con-straints for the initialization. The loss_set and V_setare the total loss and voltage at the loaded bus before thereactive power planning RPP is implemented. EP opti-mization technique was conducted at the similar loadingconditions as those implemented in the RPP when FVSIwas taken as the ﬁtness function. The implementation ofRPP has minimized the total losses and the voltage at theloaded bus was increased. FVSI was also computed oncethe total loss has been minimized. This is to monitor theeﬀect of loss minimization on voltage stability condition inthe system.5.2.1 Results for Optimal RPD in Loss MinimizationThe results for optimal RPD identiﬁed by the EP withloss minimization as the objective function when bus 3 wassubjected to load variations are tabulated in Table 4.The total losses, FVSI values, and voltage bus varia-tion were recorded as the loading condition was graduallyincreased. From the table, the values of Qg2, Qg5, Qg8, Qg11and Qg13 are the optimized reactive powers need to bedispatched by the generator buses to minimize the totallosses in the system. Total losses with optimum RPD arelower than that before the optimization, which implies thatthe total losses for the system have been minimized. Thevoltage at bus 3 is increased with the implementation ofoptimal RPD. However, the value of FVSI is increased. Itcan be seen for the case of Qd3 = 175 MVAr; the total lossesare reduced from 27.14 to 12.67 MW. However, the FVSIvalue is increased from 0.4442 to 0.5308. This implies thathaving total loss minimization as objective function forRPD has not improved the voltage stability condition ofthe system as the FVSI value is increased. The optimumRPD has also improved the voltage at bus 3 from 0.8816to 0.9012 pu.5.2.2 Optimal TTCS for Loss MinimizationThe proposed EP optimization technique with total lossminimization as the objective function was further appliedto optimize the TTCS. This technique is tested on thesimilar loading condition as used in the previous tests.Bus 3 was subjected to reactive load variation. Theresults for the EP-based optimization of TTCS when bus3 was subjected to reactive load variation with total lossesminimization as the objective function are tabulated inTable 5.From the table, the values for T1, T2, T3 and T4are the optimised TTCS values to minimize the totallosses. The implementation of EP for optimizing the TTCS6Table 5Results for TTCS Optimization When Bus 3 Was Reactively Loaded: IEEE 30-Bus RTS (Objective Function = LossMinimization)Loading Conditions Analysis FVSI Total Loss Evolution Computation T1 T2 T3 T4 Vm (pu)(MVAr) (MW) Number Time (s)Qd3 = 50 Pre-TTCS 0.2597 18.53 0.9937Post-TTCS 0.4715 18.31 91 659.97 1.21 1.05 1.30 1.06 1.0125Qd3 = 125 Pre-TTCS 0.3408 22.33 0.9285Post-TTCS 0.6480 20.84 13 404.74 1.28 1.09 1.35 1.07 0.9648Qd3 = 175 Pre-TTCS 0.4442 27.14 0.8816Post-TTCS 0.8000 24.28 21 84.46 1.26 1.26 1.49 0.99 0.9298Table 6Results for RPP When Bus 3 Was Reactively Loaded: IEEE 30-Bus RTS (Objective Function = Loss Minimization)Loading Analysis FVSI Total Evolution Computation T1 T2 T3 T4 Qg2 Qg5 Qg8 Qg11 Qg13 VmConditions Loss Number Time (s) (MVAr) (MVAr) (MVAr) (MVAr) (MVAr) (pu)(MVAr) (MW)Qd3 = 50 Pre-RPP 0.2597 18.53 35.17 35.67 55.06 18.9 15.68 0.9937Post-RPP 0.2094 4.74 13 227.18 0.84 0.86 0.91 0.79 23.94 35.59 53.89 1.18 21.46 1.0422Qd3 = 125 Pre-RPP 0.3408 22.33 55.06 37.37 59.95 26.05 22.25 0.9285Post-RPP 0.4256 7.52 14 69.24 0.84 0.86 0.92 0.80 24.32 35.91 54.55 1.45 21.71 0.9665Qd3 = 175 Pre-RPP 0.4442 27.14 58.46 44.41 67.98 26.53 29.41 0.8816Post-RPP 0.6053 12.30 16 105.66 0.84 0.86 0.92 0.80 24.33 35.91 54.55 1.45 21.71 0.9058Note: RPP = RPD + TTCSwith the total loss minimization as objective function hasminimized the total losses in the system and has improvedthe voltage at bus 3. However, the FVSI value has beenincreased, which implies the voltage stability condition ofthe system has been reduced. It can be observed that whenQd3 = 175 MVAr, the implementation of TTCS and totalloss minimization as objective function has reduced thevoltage stability condition of the system in which the FVSIvalue has been increased from 0.4442 to 0.8000. However,the total loss is reduced from 27.14 to 24.28 MW and thevoltage at bus 3 is increased from 0.8816 to 0.9298 pu.5.2.3 Results for Optimal Combination of RPD andTTCS in Loss MinimizationEvolutionary Programming optimization technique wasfurther developed to determine optimal combination ofRPD and TTCS with total loss minimization as the ob-jective function. Similar loading conditions as previoustests were used to assess the proposed technique. In thisstudy, the random numbers generated in the EP algorithmrepresent the actual injected reactive powers and TTCSnamely Qg2, Qg5, Qg8, Qg11, Qg13, T1, T2, T3 and T4. Theresults for optimum RPD and TTCS identiﬁed by the EPwith loss minimization as the objective function when bus3 was reactively loaded are tabulated in Table 6.From the table, the values for T1, T2, T3 and T4are the optimized TTCS values whereas the values forQg2, Qg5, Qg8, Qg11 and Qg13 are the optimized reactivepowers need to be injected to generators 2, 5, 8, 11 and13 for minimizing the total loss. With the optimum RPDand TTCS, it can be seen that the total loss were re-duced whereas the voltage proﬁle is signiﬁcantly increasedfor each loading condition. However, the implementationof RPD and TTCS with total loss as the objective func-tion has reduced the voltage stability condition indicatedby the increment in FVSI values. For example, whenQd3 = 175 MVAr, the total losses in the system is reducedfrom 27.14 to 12.30 MW. Voltage stability condition isreduced, indicated by the increase in FVSI value from0.4442 to 0.6053.5.3 Comparison of RPP TechniquesThe results obtained from the proposed RPP techniquesnamely RPD, TTCS, and combined RPD and TTCS withvoltage stability improvement, as the objective function,are compared to those obtained when loss minimizationis taken as the objective function. The comparison ismade in terms of voltage stability improvement, totalloss minimization, computation time, voltage proﬁle, andmaximum voltage at other load buses.The results obtained from the RPD, TTCS, and thecombination of RPD and TTCS for each objective functionare compared for each participating bus. Table 7 shows theresults when the three techniques were implemented on thesystem with reactive power loading at bus 3 is increased to175 MVAr.The application of voltage stability improvement asthe objective function in the RPD technique has improved7Table 7Results for Comparative Studies between Voltage Stability Improvement and Total Loss Minimization as Two SeparateObjective Function When Qd3 = 175 MVArRPP techniques Pre-RPP RPD TTCS RPD + TTCSObjective function VSI TLM VSI TLM VSI TLMFVSI 0.4442 0.4440 0.5308 0.4062 0.8000 0.4424 0.6053Total loss (MW) 27.14 10.59 12.67 27.32 24.28 11.22 12.30Evolution number 5 5 7 21 11 16Computation time (s) 289.48 26.17 197.63 84.44 101.83 105.66Bus voltage, Vm (pu) 0.8816 0.9310 0.9017 0.8951 0.9298 0.9313 0.9058Maximum voltage at other load buses (pu) 1.06 1.10 1.06 1.06 1.06 1.06 1.06Note: RPP = reactive power planning RPD = reactive power dispatchTTCS = transformer tap changer setting VSI = voltage stability improvementTLM = total loss minimizationthe voltage stability condition indicated by the reductionin FVSI value from 0.4442 to 0.4440. It has also reducedthe total loss in the system from 27.14 to 10.59 MW. Whentotal loss minimization is taken as the objective functionin the optimization of RPD, the total loss is reduced to12.67 MW. However, the FVSI is increased from 0.4442to 0.5308. Thus, value having voltage stability improve-ment as the objective function in the optimization of RPDhas improved both the voltage stability condition and alsominimized the total loss in the system. The voltage proﬁleobtained when voltage stability improvement was used asthe objective function is better than that when total lossminimization was used as the objective function. The ap-plication of total loss minimization as objective functionhas minimized the total loss in the system; however, thevoltage stability condition of the system was weak, indi-cated by the increase in the FVSI value. Therefore, theapplication of voltage stability improvement as the objec-tive function gives better results than those obtained whentotal loss minimization is used as the objective function inoptimizing the RPD.In optimizing the TTCS, the application of voltagestability improvement as objective function has reducedthe FVSI value from 0.4442 to 0.4062 but it has beenincreased to 0.8000 with the total loss minimization asthe objective function. The total loss reduction resultedfrom the total loss minimization as objective function isbetter than that in the voltage stability improvement asobjective function. Voltage proﬁle is increased when bothobjective functions were used to optimize the TTCS. Fromthe table, it is also observed that when EP was used to op-timize RPD and TTCS together, the application of voltagestability improvement as the objective function has givenbetter results in terms of voltage stability improvement,total loss minimization, and voltage improvement. Thisdemonstrates that the application of voltage stability im-provement as objective function is better in all the threeproposed RPP techniques. The optimal combination ofRPD and TTCS with voltage stability improvement as theobjective function outperformed optimal TTCS and opti-mal RPD in terms of voltage stability improvement andvoltage proﬁle increment. The total loss in the system hasbeen reduced to 11.22 MW whereas the voltage is increasedfrom 0.8816 to 0.9313 pu. It is observed that, with totalloss minimization as the objective function, the reductionin total loss is higher than that given by voltage stabilityimprovement as the objective function. The overall resultsshow that optimizing the combination of RPD and TTCSwith voltage stability improvement as the objective func-tion is the most suitable RPP technique as this techniquecould improve voltage stability condition and minimizetotal losses in the system.6. ConclusionA study on RPP using optimal RPD, optimal TTCS andoptimal combination of RPD and TTCS for voltage stabil-ity improvement and total loss minimization in a systemwas presented. EP was employed as the optimization ap-proach in determining the optimum values for the controlvariables in the optimal RPD, optimal TTCS, and opti-mal combination of RPD and TTCS for both objectivefunctions in a power system. Results showed that theoptimal combination of RPD and TTCS gave the bestresults in terms of voltage stability improvement, totalloss minimization, fast computation, and voltage proﬁleimprovement over other techniques. Therefore, the pro-posed technique is possible to be implemented practicallywhich could achieve voltage stability improvement and lossminimization in a power system.References[1] K.Y. Lee, X. Bai, & Y.M. Park, Optimization method forreactive power planning by using a modiﬁed simple geneticalgorithm, IEEE Transaction on Power Systems, 10 (4), 1995,1843–1850.[2] H.N. Ng, M.M.A. Salama, & A.Y. Chikhani, Classiﬁcation ofcapacitor allocation techniques, IEEE Transaction on PowerSystems, 15 (1), 2000, 387–392.[3] K. Iba, Reactive power optimization by genetic algorithm,IEEE Transaction on Power Systems, 9 (2), 1994, 685–692.8[4] M.H. Haque, Optimal locations of shunt FACTs devices in longtransmission lines, IEE Proceedings – Generation Transmissionand Distribution, 147 (4), 2000, 218–222.[5] W.N. Abdullah, H. Saibon, A.M.M. Zain, & K.L. Lo, Geneticalgorithm for optimal reactive power dispatch, IEEE EnergyManagement and Power Delivery Conference, 1, 1998, 160–164.[6] Q.H. Wu & J.T. Ma, Genetic search for optimal reactivepower dispatch of power systems, Proc. IEEE Int. ControlConference, 1994, 717–722.[7] Y. Liu, L. Ma & J. Zhang, Reactive power optimisation byGA/SA/TS combined algorithms, Journal of Electrical Powerand Energy Systems, 24, 2002, 765–769.[8] Q.H. Wu & J.T. Ma, Power system optimal reactive powerdispatch using evolutionary programming, IEEE Transactionon Power Systems, 10 (3), 1995, 1243–1249.[9] K.Y. Lee & F.F. Yang, optimal reactive power planning usingevolutionary algorithms: A comparative study for evolutionaryprogramming, evolutionary strategy, genetic algorithm, andlinear programming, IEEE Transaction on Power Systems,13 (1), 1998, 101–108.[10] I. Musirin & T.K.A. Rahman, Estimating maximum load-ability for weak bus identiﬁcation using FVSI, IEEE PowerEngineering Review, 22, 2002, 50–52.[11] I. Musirin & T.K.A. Rahman, Estimation of maximum load-ability in power systems using fast voltage stability index,International Journal of Power and Energy Systems, 25 (3),2005, 181–189.
[13]. In thisstudy, the EP optimization technique was implementedin the optimal RPD, TTCS, and optimal combination ofRPD and TTCS within two objective functions. The EP isimplemented according to the operators explained in thissection.23.1 InitializationInitially a series of random numbers, xi, are generatedusing uniformly distributed random generators, wherefor optimal RPDxi = [Qg1i, Qg2i, Qg3i, . . . , Qgki]for optimal TTCSxi = [T1j, T2i, . . . , Tni]and for optimal combination of RPD and TTCSxi = [Qg2i, Qg5i, Qg8i, Qg11i, Qg13i, T1i, T2i, T3i, T4i](5)i = 1, 2, 3, 4, 5, . . . , m, where m is the control variable;k = 1, 2, 3, . . . , k, where k is the generator number; n is thetransformer number. The random numbers should followthe following inequality constraints.Qming2 ≤ Qg2 ≤ Qmaxg2 , Qming5 ≤ Qg5 ≤ Qmaxg5 , Qming8 ≤ Qg8≤ Qmaxg8 , Qming11 ≤ Qg11 ≤ Qmaxg11 , Qming13 ≤ Qg13 ≤ Qmaxg13 ,Tmin1 ≤ T1 ≤ Tmax1 , Tmin2 ≤ T2 ≤ Tmax2 , Tmin3 ≤ T3≤ Tmax3 , Tmin2 ≤ T4 ≤ Tmax4The ﬁtness for voltage stability improvement as objectivefunction is FVSI, whereas the ﬁtness for total loss mini-mization as the objective function is the total power loss inthe system. Some initial conditions were considered duringthe initialization process, i.e.,V(m) ≥ V _set (6)FV SI ≤ FV SI_set (7)loss ≤ loss_set (8)V_set, FVSI_set and loss_set are the values computedfrom the load program at a selected loading conditionbefore any of RPP techniques is performed.3.2 MutationMutation is performed on the random number, xi, toproduce oﬀspring. The mutation process is implementedbased on the following equation.xi+m,j = xi,j + N0, β(xj max − xj min)fifmax(9)wherexi+m,j = mutated parents (oﬀspring)xi,j = parentsN = Gaussian random variable with mean μand variance γ2β = mutation scale, 0 < β < 1xj max = maximum random number for everyvariablexj min = minimum random number for everyvariablefi = ﬁtness for the ith random numberfmax = maximum ﬁtnessThe mutation scale, β, is adjusted to achieve better con-vergence.3.3 SelectionThe oﬀspring produced from the mutation process werecombined with the parents to undergo a selection processto identify the candidates who can be transcribed intothe next generation. In this study, priority selectionwas employed, whereby the populations were sorted inascending order according to their ﬁtness values. The ﬁrsthalf of the populations would be transcribed to the nextgeneration [13].3.4 Stopping CriterionThe convergence criterion is deﬁned by the diﬀerence be-tween the maximum ﬁtness and minimum ﬁtness ≤ 0.0001,i.e.,fitness max − fitnessmin ≤ 0.0001 (10)The generation process will be repeated until the conver-gence criterion is met.4. Implementation of EP-based RPP TechniqueThe IEEE 30-bus reliability test system was used as the testsystem for implementing the proposed RPP. This systemhas 6 generator buses, 24 load buses, 41 inter-connectedlines and 4 transformer tap changers. Five generators wereassigned as the control variable for minimizing the totalloss in the system in the optimization of RPD. On theother hand, the four transformer taps were considered asthe control variable in the optimization of TTCS. There-fore, for the optimal combination of RPD and TTCS; ninecontrol variables are required. The optimization of RPD,TTCS and combination of RPD and TTCS was imple-mented separately. The following procedures were imple-mented to develop an evolutionary programme for the RPPprocedures:1. Set the RPP constraints, i.e., FVSI ≤ FVSI_set andVm(bus) ≥ V_set for voltage stability improvement as3objective function whereas total loss ≤ loss_set andVm(bus) ≥ V_set for loss minimization as objectivefunction.2. Generate random number for the 1st generation,x1, x2, x3, x4, x5,. . . , x9 (ﬁve control variables for RPD,four control variables for TTCS and nine controlvariables for the combination of RPD and TTCS orRPP).3. Check for constraints violations. Go to step 2 ifconstraints violated, otherwise go to step 4.4. Fill in population pool.5. If pool is full, go to step 6, otherwise go to step 2.6. Determine xi min and xi max.7. Assign x1, x2, x3, x4, x5, . . . , x9 as the control variablesin the system data.8. Calculate the ﬁtness values by the running load ﬂowprogramme to evaluate FVSI or total loss.9. Determine FVSI_min, FVSI_max, FVSI_avg andFVSI_sum for voltage stability improvement as ob-jective function and loss_min, loss_max, loss_avgand loss_sum for loss minimization as objective func-tion (for statistical evaluation).10. Mutate the parents (generate oﬀsprings).11. Recalculate ﬁtness using the oﬀsprings (run load ﬂowto re-evaluate FVSI or total loss).12. Combine the parents and oﬀspring.13. Perform selection by ranking process.14. Transcribe new generations.15. If solution is not converged, repeat steps 6–14, other-wise go to step 16.16. Stop.4.1 Optimal RPDThe injected reactive powers on the generator buses weretaken as the control variables to improve the voltage sta-bility condition (indicated by FVSI reduction) or to min-imize total loss in the system. In the proposed technique,EP was used to determine the optimum reactive power tobe dispatched by the participating generator buses. In thedeveloped EP for RPD optimization, the random numberrepresented the injected reactive power of the generatorbuses in the system. Five variables namely x1, x2, x3, x4and x5 were used to represent the reactive power to beinjected to generators 2, 5, 8, 11 and 13. The ﬁnal resultsobtained from the EP would be the optimal reactive powerto be dispatched by the generators to improve voltagestability condition or minimize total loss in the system.4.2 Optimal TTCSFor the case of optimizing TTCS, random numbers namelyx1, x2, x3 and x4 generated from the initialization processrepresent the TTCS values, i.e., T1, T2, T3 and T4. In thiscase, similar constraints as that in the optimal RPD wereimposed. The optimized x1, x2, x3 and x4 obtained fromthe EP are the new values for TTCS to improve voltagestability condition or to minimize total loss in the system.4.3 Optimal Combination of RPD and TTCSThe RPD and TTCS were combined together for improvingthe voltage stability condition or minimizing total lossin the system. The control variables are the injectedreactive powers and the TTCS. Nine variables were used torepresent ﬁve generated reactive powers on the generatorbuses and four transformer setting values.5. Results and DiscussionThe results for the three RPP techniques are represented inthree separate sections for each objective function, becausethese procedures were implemented one at a time. Bus3 was subjected to the variation of loading conditions.Comparisons of results were performed to identify the mostsuitable RPP technique for improving the voltage stabilitycondition or loss minimization.5.1 Voltage Stability Improvement as ObjectiveFunctionIn this study, voltage stability analyses were initially con-ducted prior to the implementation of the RPP so that themaximum stability point can be estimated. The applica-tion of FVSI as the ﬁtness function in the voltage stabilityimprovement as the objective has yielded to voltage sta-bility improvement in the system. The implementation ofRPP has improved the voltage stability condition indicatedby the reduction in FVSI values and at the same time thevoltage at the loaded bus was increased to an acceptablelimit. Total loss was also computed during this process.5.1.1 Optimal RPD for Voltage StabilityImprovementTest was conducted with reactive power loading at bus 3varied. The results for the optimal RPD when bus 3 wasreactively loaded are tabulated in Table 1. The reactivepower loading was increased up to 175 MVAr where thevoltage has dropped to 0.8816 pu.From the table, it is observed that the FVSI value atevery loading condition with the implementation of RPD(post-RPD) is lower than that before its implementationnoted as pre-RPD. This implies that the voltage stabilitycondition has been improved. At the same time, voltageproﬁles are also improved and total losses are reduced.At Qd3 = 175 MVAr, EP has identiﬁed that the optimumreactive power to be dispatched by the generator buses areQg2 = 42.18 MVAr, Qg5 = 39.89 MVAr, Qg8 = 56.74 MVAr,Qg11 = 23.15 MVAr and Qg13 = 22.55 MVAr. The imple-mentation of RPD with voltage stability improvement asobjective function has improved the FVSI value from0.4442 to 0.4440 whereas the total loss is reduced from27.14 to 10.59 MW. The voltage at this bus is increasedfrom 0.8816 to 0.9310 pu.4Table 1Results for RPD When Bus 3 Was Reactively Loaded: IEEE 30-Bus RTS (Objective Function = Voltage StabilityImprovement)Loading Analysis FVSI Total Evolution Computation Qg2 Qg5 Qg8 Qg11 Qg13 VmConditions Loss Number Time (MVAr) (MVAr) (MVAr) (MVAr) (MVAr) (pu)(MVAr) (MW) (s)Qd3 = 50 Pre-RPD 0.2597 18.53 35.17 35.67 55.06 18.9 15.68 0.9937Post-RPD 0.1774 4.81 5 37.42 29.85 37.27 50.90 13.11 3.10 1.0347Qd3 = 125 Pre-RPD 0.3408 22.32 55.06 37.37 59.95 26.05 22.25 0.9285Post-RPD 0.3254 7.59 5 71.36 49.36 38.21 51.21 7.65 13.36 0.9685Qd3 = 175 Pre-RPD 0.4442 27.14 58.46 44.41 67.98 26.53 29.41 0.8816Post-RPD 0.4440 10.59 5 289.48 42.18 39.89 56.74 23.15 22.55 0.9310Table 2Results for TTCS When Bus 3 Was Reactively Loaded: IEEE 30-Bus RTS (Objective Function = Voltage StabilityImprovement)Loading Conditions Analysis FVSI Total Loss Evolution Computation T1 T2 T3 T4 Vm (pu)(MVAr) (MW) Number Time (s)Qd3 = 50 Pre-TTCS 0.2597 18.53 0.9937Post-TTCS 0.1824 18.57 7 78.780 0.950 1.270 1.060 0.930 0.9963Qd3 = 125 Pre-TTCS 0.3408 22.33 0.9285Post-TTCS 0.2817 21.95 4 29.330 0.950 1.270 1.060 0.940 0.9352Qd3 = 175 Pre-TTCS 0.4442 27.14 0.8816Post-TTCS 0.4062 27.32 7 197.630 0.922 0.836 1.236 1.044 0.89515.1.2 Optimal TTCS for Voltage StabilityImprovementIn this study, TTCSs are the control variables to be op-timized. Similar loading conditions as those utilized forthe RPD were used to test the developed technique forvoltage stability improvement. The reactive power loadingat bus 3 was increased gradually and the optimum valuesof TTCS of T1, T2, T3 and T4 were determined to improvethe voltage stability condition of the system.The results for the EP optimization technique whenbus 3 is reactively loaded taking FVSI as the ﬁtness aretabulated in Table 2. T1, T2, T3 and T4 are the optimizedTTCS values identiﬁed to improve the voltage stabilitycondition. Changing the TTCS to the optimum valuesdetermined by EP has improved the voltage stability con-dition. The voltage proﬁle at bus 3 has also been improvedwith the optimized TTCS. It can be seen from the resultswhen Qd3 = 175 MVAr, the implementation of TTCS opti-mization technique with voltage stability improvement asobjective function has improved the voltage stability con-dition indicated by the reduction in the FVSI value from0.4442 to 0.4062. However, the total loss is increased from27.14 to 27.32 MW. This is because the introduction of newTTCS values has altered the properties of the participatinglines. In addition, the voltage has been improved from0.8816 to 0.8951 pu.5.1.3 Optimal Combination of RPD and TTCS forVoltage Stability ImprovementFurther study has been conducted in the implementationof RPP by employing optimal RPD and TTCS concur-rently for voltage stability improvement. EP was used todetermine the optimal reactive power to be dispatched bythe generators and optimal setting of the transformer tapchanger. The ﬁve variables (i.e., Qg2, Qg5, Qg8, Qg11 andQg13) required in the RPD were combined with the fourvariables (i.e., T1, T2, T3 and T4). Similar loading condi-tions were used to test the developed technique for voltagestability improvement by optimizing the TTCS and RPDusing the EP. The results for the optimal combinationof RPD and TTCS optimization process when bus 3 wasreactively loaded are tabulated in Table 3.From the table, the values of T1, T2, T3, T4, Qg2,Qg5, Qg8, Qg11 and Qg13 are the optimized TTCS andreactive power dispatch identiﬁed by the EP to improvethe voltage stability condition at the respective loadingcondition. It is observed that the voltage stability conditionof the system was improved. The voltage proﬁles wereincreased from their original values and the total lossesin the system were reduced. For instance, optimizing theTTCS and RPD has signiﬁcantly improved the voltagestability condition indicated by the reduction of FVSIvalue from 0.4442 to 0.4424 at Qd3 = 175 MVAr. Total5Table 3Results for RPP When Bus 3 Was Reactively Loaded: IEEE 30-Bus RTS (Objective Function = Voltage StabilityImprovement)Loading Analysis FVSI Total Evolution Computation T1 T2 T3 T4 Qg2 Qg5 Qg8 Qg11 Qg13 VmConditions Loss Number Time (s) (MVAr) (MVAr) (MVAr) (MVAr) (MVAr) (pu)(MVAr) (MW)Qd3 = 50 Pre-RPP 0.2597 18.53 35.17 35.67 55.06 18.90 15.68 0.9937Post-RPP 0.1624 5.12 9 86.34 0.99 0.97 1.00 0.95 34.98 6.05 18.20 16.34 20.65 1.0150Qd3 = 125 Pre-RPP 0.3408 22.33 55.06 37.37 59.95 26.05 22.25 0.9285Post-RPP 0.3331 8.81 12 192.97 0.99 1.18 1.11 0.89 49.15 36.83 56.91 10.84 7.96 0.9662Qd3 = 175 Pre-RPP 0.4442 27.14 58.46 44.41 67.98 26.53 29.41 0.8816Post-RPP 0.4424 11.22 11 101.83 1.05 0.99 0.91 1.05 48.28 36.16 59.81 23.38 23.23 0.9313Table 4Results for RPD When Bus 3 Was Reactively Loaded: IEEE 30-Bus RTS (Objective Function = Loss Minimization)Loading Analysis FVSI Total Evolution Computation Qg2 Qg5 Qg8 Qg11 Qg13 Vm (pu)Conditions Loss Number Time (s) (MVAr) (MVAr) (MVAr) (MVAr) (MVAr)(MVAr) (MW)Qd3 = 50 Pre-RPD 0.2597 18.53 35.17 35.67 55.06 18.90 15.68 0.9937Post-RPD 0.2062 5.04 5 34.73 7.60 31.53 27.84 9.03 11.40 1.0132Qd3 = 125 Pre-RPD 0.3408 22.33 55.06 37.37 59.95 26.05 22.25 0.9285Post-RPD 0.3450 7.71 6 33.22 34.26 27.49 56.14 9.82 12.94 0.9625Qd3 = 175 Pre-RPD 0.4442 27.14 58.46 44.41 67.98 26.53 29.41 0.8816Post-RPD 0.5308 12.67 5 26.17 34.26 27.49 56.14 9.82 12.94 0.9012losses are also reduced from 27.14 to 11.22 MW whereasthe voltage is also improved from 0.8816 to 0.9313 pu.5.2 Loss Minimization as Objective FunctionThe optimization process was repeated for the RPD,TTCS, and combination of RPD and TTCS with totalloss minimization as the objective function. In this study,the total loss lower than the loss_set and voltage at theloaded bus higher than V_set were assigned as the con-straints for the initialization. The loss_set and V_setare the total loss and voltage at the loaded bus before thereactive power planning RPP is implemented. EP opti-mization technique was conducted at the similar loadingconditions as those implemented in the RPP when FVSIwas taken as the ﬁtness function. The implementation ofRPP has minimized the total losses and the voltage at theloaded bus was increased. FVSI was also computed oncethe total loss has been minimized. This is to monitor theeﬀect of loss minimization on voltage stability condition inthe system.5.2.1 Results for Optimal RPD in Loss MinimizationThe results for optimal RPD identiﬁed by the EP withloss minimization as the objective function when bus 3 wassubjected to load variations are tabulated in Table 4.The total losses, FVSI values, and voltage bus varia-tion were recorded as the loading condition was graduallyincreased. From the table, the values of Qg2, Qg5, Qg8, Qg11and Qg13 are the optimized reactive powers need to bedispatched by the generator buses to minimize the totallosses in the system. Total losses with optimum RPD arelower than that before the optimization, which implies thatthe total losses for the system have been minimized. Thevoltage at bus 3 is increased with the implementation ofoptimal RPD. However, the value of FVSI is increased. Itcan be seen for the case of Qd3 = 175 MVAr; the total lossesare reduced from 27.14 to 12.67 MW. However, the FVSIvalue is increased from 0.4442 to 0.5308. This implies thathaving total loss minimization as objective function forRPD has not improved the voltage stability condition ofthe system as the FVSI value is increased. The optimumRPD has also improved the voltage at bus 3 from 0.8816to 0.9012 pu.5.2.2 Optimal TTCS for Loss MinimizationThe proposed EP optimization technique with total lossminimization as the objective function was further appliedto optimize the TTCS. This technique is tested on thesimilar loading condition as used in the previous tests.Bus 3 was subjected to reactive load variation. Theresults for the EP-based optimization of TTCS when bus3 was subjected to reactive load variation with total lossesminimization as the objective function are tabulated inTable 5.From the table, the values for T1, T2, T3 and T4are the optimised TTCS values to minimize the totallosses. The implementation of EP for optimizing the TTCS6Table 5Results for TTCS Optimization When Bus 3 Was Reactively Loaded: IEEE 30-Bus RTS (Objective Function = LossMinimization)Loading Conditions Analysis FVSI Total Loss Evolution Computation T1 T2 T3 T4 Vm (pu)(MVAr) (MW) Number Time (s)Qd3 = 50 Pre-TTCS 0.2597 18.53 0.9937Post-TTCS 0.4715 18.31 91 659.97 1.21 1.05 1.30 1.06 1.0125Qd3 = 125 Pre-TTCS 0.3408 22.33 0.9285Post-TTCS 0.6480 20.84 13 404.74 1.28 1.09 1.35 1.07 0.9648Qd3 = 175 Pre-TTCS 0.4442 27.14 0.8816Post-TTCS 0.8000 24.28 21 84.46 1.26 1.26 1.49 0.99 0.9298Table 6Results for RPP When Bus 3 Was Reactively Loaded: IEEE 30-Bus RTS (Objective Function = Loss Minimization)Loading Analysis FVSI Total Evolution Computation T1 T2 T3 T4 Qg2 Qg5 Qg8 Qg11 Qg13 VmConditions Loss Number Time (s) (MVAr) (MVAr) (MVAr) (MVAr) (MVAr) (pu)(MVAr) (MW)Qd3 = 50 Pre-RPP 0.2597 18.53 35.17 35.67 55.06 18.9 15.68 0.9937Post-RPP 0.2094 4.74 13 227.18 0.84 0.86 0.91 0.79 23.94 35.59 53.89 1.18 21.46 1.0422Qd3 = 125 Pre-RPP 0.3408 22.33 55.06 37.37 59.95 26.05 22.25 0.9285Post-RPP 0.4256 7.52 14 69.24 0.84 0.86 0.92 0.80 24.32 35.91 54.55 1.45 21.71 0.9665Qd3 = 175 Pre-RPP 0.4442 27.14 58.46 44.41 67.98 26.53 29.41 0.8816Post-RPP 0.6053 12.30 16 105.66 0.84 0.86 0.92 0.80 24.33 35.91 54.55 1.45 21.71 0.9058Note: RPP = RPD + TTCSwith the total loss minimization as objective function hasminimized the total losses in the system and has improvedthe voltage at bus 3. However, the FVSI value has beenincreased, which implies the voltage stability condition ofthe system has been reduced. It can be observed that whenQd3 = 175 MVAr, the implementation of TTCS and totalloss minimization as objective function has reduced thevoltage stability condition of the system in which the FVSIvalue has been increased from 0.4442 to 0.8000. However,the total loss is reduced from 27.14 to 24.28 MW and thevoltage at bus 3 is increased from 0.8816 to 0.9298 pu.5.2.3 Results for Optimal Combination of RPD andTTCS in Loss MinimizationEvolutionary Programming optimization technique wasfurther developed to determine optimal combination ofRPD and TTCS with total loss minimization as the ob-jective function. Similar loading conditions as previoustests were used to assess the proposed technique. In thisstudy, the random numbers generated in the EP algorithmrepresent the actual injected reactive powers and TTCSnamely Qg2, Qg5, Qg8, Qg11, Qg13, T1, T2, T3 and T4. Theresults for optimum RPD and TTCS identiﬁed by the EPwith loss minimization as the objective function when bus3 was reactively loaded are tabulated in Table 6.From the table, the values for T1, T2, T3 and T4are the optimized TTCS values whereas the values forQg2, Qg5, Qg8, Qg11 and Qg13 are the optimized reactivepowers need to be injected to generators 2, 5, 8, 11 and13 for minimizing the total loss. With the optimum RPDand TTCS, it can be seen that the total loss were re-duced whereas the voltage proﬁle is signiﬁcantly increasedfor each loading condition. However, the implementationof RPD and TTCS with total loss as the objective func-tion has reduced the voltage stability condition indicatedby the increment in FVSI values. For example, whenQd3 = 175 MVAr, the total losses in the system is reducedfrom 27.14 to 12.30 MW. Voltage stability condition isreduced, indicated by the increase in FVSI value from0.4442 to 0.6053.5.3 Comparison of RPP TechniquesThe results obtained from the proposed RPP techniquesnamely RPD, TTCS, and combined RPD and TTCS withvoltage stability improvement, as the objective function,are compared to those obtained when loss minimizationis taken as the objective function. The comparison ismade in terms of voltage stability improvement, totalloss minimization, computation time, voltage proﬁle, andmaximum voltage at other load buses.The results obtained from the RPD, TTCS, and thecombination of RPD and TTCS for each objective functionare compared for each participating bus. Table 7 shows theresults when the three techniques were implemented on thesystem with reactive power loading at bus 3 is increased to175 MVAr.The application of voltage stability improvement asthe objective function in the RPD technique has improved7Table 7Results for Comparative Studies between Voltage Stability Improvement and Total Loss Minimization as Two SeparateObjective Function When Qd3 = 175 MVArRPP techniques Pre-RPP RPD TTCS RPD + TTCSObjective function VSI TLM VSI TLM VSI TLMFVSI 0.4442 0.4440 0.5308 0.4062 0.8000 0.4424 0.6053Total loss (MW) 27.14 10.59 12.67 27.32 24.28 11.22 12.30Evolution number 5 5 7 21 11 16Computation time (s) 289.48 26.17 197.63 84.44 101.83 105.66Bus voltage, Vm (pu) 0.8816 0.9310 0.9017 0.8951 0.9298 0.9313 0.9058Maximum voltage at other load buses (pu) 1.06 1.10 1.06 1.06 1.06 1.06 1.06Note: RPP = reactive power planning RPD = reactive power dispatchTTCS = transformer tap changer setting VSI = voltage stability improvementTLM = total loss minimizationthe voltage stability condition indicated by the reductionin FVSI value from 0.4442 to 0.4440. It has also reducedthe total loss in the system from 27.14 to 10.59 MW. Whentotal loss minimization is taken as the objective functionin the optimization of RPD, the total loss is reduced to12.67 MW. However, the FVSI is increased from 0.4442to 0.5308. Thus, value having voltage stability improve-ment as the objective function in the optimization of RPDhas improved both the voltage stability condition and alsominimized the total loss in the system. The voltage proﬁleobtained when voltage stability improvement was used asthe objective function is better than that when total lossminimization was used as the objective function. The ap-plication of total loss minimization as objective functionhas minimized the total loss in the system; however, thevoltage stability condition of the system was weak, indi-cated by the increase in the FVSI value. Therefore, theapplication of voltage stability improvement as the objec-tive function gives better results than those obtained whentotal loss minimization is used as the objective function inoptimizing the RPD.In optimizing the TTCS, the application of voltagestability improvement as objective function has reducedthe FVSI value from 0.4442 to 0.4062 but it has beenincreased to 0.8000 with the total loss minimization asthe objective function. The total loss reduction resultedfrom the total loss minimization as objective function isbetter than that in the voltage stability improvement asobjective function. Voltage proﬁle is increased when bothobjective functions were used to optimize the TTCS. Fromthe table, it is also observed that when EP was used to op-timize RPD and TTCS together, the application of voltagestability improvement as the objective function has givenbetter results in terms of voltage stability improvement,total loss minimization, and voltage improvement. Thisdemonstrates that the application of voltage stability im-provement as objective function is better in all the threeproposed RPP techniques. The optimal combination ofRPD and TTCS with voltage stability improvement as theobjective function outperformed optimal TTCS and opti-mal RPD in terms of voltage stability improvement andvoltage proﬁle increment. The total loss in the system hasbeen reduced to 11.22 MW whereas the voltage is increasedfrom 0.8816 to 0.9313 pu. It is observed that, with totalloss minimization as the objective function, the reductionin total loss is higher than that given by voltage stabilityimprovement as the objective function. The overall resultsshow that optimizing the combination of RPD and TTCSwith voltage stability improvement as the objective func-tion is the most suitable RPP technique as this techniquecould improve voltage stability condition and minimizetotal losses in the system.6. ConclusionA study on RPP using optimal RPD, optimal TTCS andoptimal combination of RPD and TTCS for voltage stabil-ity improvement and total loss minimization in a systemwas presented. EP was employed as the optimization ap-proach in determining the optimum values for the controlvariables in the optimal RPD, optimal TTCS, and opti-mal combination of RPD and TTCS for both objectivefunctions in a power system. Results showed that theoptimal combination of RPD and TTCS gave the bestresults in terms of voltage stability improvement, totalloss minimization, fast computation, and voltage proﬁleimprovement over other techniques. Therefore, the pro-posed technique is possible to be implemented practicallywhich could achieve voltage stability improvement and lossminimization in a power system.References[1] K.Y. Lee, X. Bai, & Y.M. Park, Optimization method forreactive power planning by using a modiﬁed simple geneticalgorithm, IEEE Transaction on Power Systems, 10 (4), 1995,1843–1850.[2] H.N. Ng, M.M.A. Salama, & A.Y. Chikhani, Classiﬁcation ofcapacitor allocation techniques, IEEE Transaction on PowerSystems, 15 (1), 2000, 387–392.[3] K. Iba, Reactive power optimization by genetic algorithm,IEEE Transaction on Power Systems, 9 (2), 1994, 685–692.8[4] M.H. Haque, Optimal locations of shunt FACTs devices in longtransmission lines, IEE Proceedings – Generation Transmissionand Distribution, 147 (4), 2000, 218–222.[5] W.N. Abdullah, H. Saibon, A.M.M. Zain, & K.L. Lo, Geneticalgorithm for optimal reactive power dispatch, IEEE EnergyManagement and Power Delivery Conference, 1, 1998, 160–164.[6] Q.H. Wu & J.T. Ma, Genetic search for optimal reactivepower dispatch of power systems, Proc. IEEE Int. ControlConference, 1994, 717–722.[7] Y. Liu, L. Ma & J. Zhang, Reactive power optimisation byGA/SA/TS combined algorithms, Journal of Electrical Powerand Energy Systems, 24, 2002, 765–769.[8] Q.H. Wu & J.T. Ma, Power system optimal reactive powerdispatch using evolutionary programming, IEEE Transactionon Power Systems, 10 (3), 1995, 1243–1249.[9] K.Y. Lee & F.F. Yang, optimal reactive power planning usingevolutionary algorithms: A comparative study for evolutionaryprogramming, evolutionary strategy, genetic algorithm, andlinear programming, IEEE Transaction on Power Systems,13 (1), 1998, 101–108.[10] I. Musirin & T.K.A. Rahman, Estimating maximum load-ability for weak bus identiﬁcation using FVSI, IEEE PowerEngineering Review, 22, 2002, 50–52.[11] I. Musirin & T.K.A. Rahman, Estimation of maximum load-ability in power systems using fast voltage stability index,International Journal of Power and Energy Systems, 25 (3),2005, 181–189.[12] L.L. Lai, Intelligent system application in power engineering:Evolutionary programming and neural networks (John Wiley& Sons, 1998).[13] J.Z. Zhu & X.F. Xiong, Optimal reactive power control usinginterior point method, Electric Power Systems Research, 66,2003, 187–192.
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DOI:
10.2316/Journal.203.2009.1.203-3688
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(203) International Journal of Power and Energy Systems - 2009
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