Optimal Placement & sizing of Distributed Generator (DG)

Transcription

1 Chapter - 5 Optimal Placement & sizing of Distributed Generator (DG) - A Single Objective Approach

2 CHAPTER - 5 Distributed Generation (DG) for Power Loss Minimization 5. Introduction Distributed generators [2] are very commonly employed to provide active and reactive power compensation in distribution systems. Installations of Distributed generators are important for active and reactive power planning of a distribution system. Due to high concentration of inductive loads in distribution system, power losses are more. The installations of Distributed generators are necessary for many reasons. The power injections from DG units located close to the load centers provide an opportunity for system power loss reduction, cost reduction, voltage profile improvement, voltage stability improvement, environmental friendliness, postponement system upgrading and increasing reliability. This impact can be enhanced via optimal DG placement and sizing. From the literature survey, it is observed that most of these population based optimization techniques have successfully used to determine optimal placement and sizing of DG for power loss minimization in RDS. These motivate to introduce new, simple, efficient and fast population based optimization method to solve optimal DG placement and sizing problem of RDS. This chapter presents a Modified Teaching Learning Based Optimization (MTLBO) algorithm to solve the problem of optimal placement and sizing of multiple DG units in RDS. This problem can be divided into two sub problems - determining the location of the optimal 79

3 bus and the optimal DG size that would minimize the network active power losses. The proposed approach addresses the two sub problems simultaneously by using modified TLBO algorithm that is capable of handling multiple DG planning in a single run. The proposed algorithm adopts the distribution power flow algorithm developed in chapter - 2. Three distributed generators that operated at different power factors are installed in to the system. Two scenarios of each DG source are tested. The first considers the DG units with a fixed power factor of unity (unity p.f.), while the second has a fixed power factor of leading (0.866 p.f. leading). To show the effectiveness and superiority, the performance of the proposed method was tested on 33 and 69 bus RDS and the results were compared with the results of other popular optimization techniques. The rest of the chapter is organized as follows. In Section 5.2, model of a radial distribution system with the inclusion of DG units is discussed. The problem formulation with system constraints are addresses in Section 5.3. Application of MTLBO to solve the optimal DG placement and sizing problem in RDS is explained in Section 5.4. In Section 5.5, DG placement & sizing evaluation indices are described. Simulation results and analysis are reported in Section 5.6. Finally, conclusions are drawn in Section Model of a Distribution System with the inclusion of DG units 5.2. Assumptions Power flow calculation is performed using S = 00MVA and V base =2.66KV. base Three small distributed generators that operated at different power factors i.e. inject only pure real power (unit p.f.) or inject real power and reactive power (0.866 p. f. leading) are installed in to the system. The bus at which load is connected is considered as the location for DG. The source bus is not considered as the location for DG placement. The limits of DG unit sizes for installation at different systems bus locations assumed to be 0 to.2 MW. Voltage at the primary bus of a substation is.0 p.u. The upper and lower limits of voltage for each bus are.05p.u. and 0.95 p.u., respectively. 80

4 The maximum allowable number of the parallel DG is one, in each bus. The load model used in the simulations is uniform with constant power Load flow solution A simple backward forward algorithm that is based on basic circuit theory is used. It is assumed that the three-phase radial distribution network is balanced and can be represented by their equivalent single-line diagram. Fig. 5. represents the electrical equivalent of a typical branch of a distribution system. The algorithm utilizes the Kirchhoff s voltage law and Kirchhoff s current law to find voltage at each node and current at each branch. At the initialization step, a flat voltage profile is considered, i.e., V =.0 p.u at each node. A constant power load model is used in the analysis. The currents are computed based on the voltages of the previous iteration. The voltage drop is calculated in each branch. The currents and voltages are updated in each iteration cycle until stopping criterion is reached. The iteration cycle will stop if the difference in previous voltage value and new voltage value is reached less than The detailed load flow analysis is given in chapter - 2. Fig. 5. : Distribution system with DG installation at any bus Modeling of DG units in RDS DG units are modeled as synchronous generators for small hydro power, geothermal power, combined cycles and combustion turbines. They are treated as induction generators for wind and micro hydro power. DG units are considered as power electronic inverter generators such as micro gas turbines, solar power, photovoltaic power and fuel cells. 8

5 A distributed generation (DG) unit can be modeled as either a voltage-controlled bus (PV bus) or as a complex power injection (PQ bus) in the distribution system. If DGs have control over the voltage by regulating the excitation voltage (synchronous generator DGs) or if the control circuit of the converter is used to control P and V independently, then the DG unit may be modeled as a PV type. Other DGs, like induction generator based units or converters used to control P and Q independently, are modeled as PQ types. The PV model regulates the terminal bus voltage by adjusting their reactive power output. However, it is preferred to not to use a PV model, since injecting a great amounts of reactive power in order to raise the bus voltage may result in high field currents and overheating for the generator, triggering the excitation limit and disconnecting the generator from the network. The most commonly used DG model is the PQ model. It should be noted that in PQ model, the DG is considered as negative load. In this work, the DG units are represented as a negative PQ load model delivering active and reactive power to a distribution system. This gives flexibility in modeling various types of DG. In general, DG can be classified into four major types [80] based on their terminal characteristics in terms of active and reactive power delivering capability as follows : Type : DG capable of injecting real power only, like photovoltaic, fuel cell etc. ( p. f DG= ) Type 2 : DG capable of injecting both real and reactive power, e.g. synchronous machines. (0 < p f <, leading). DG Type 3 : DG capable of injecting real but consuming reactive power, e.g. induction generators used in the wind farms. ( 0< p f <, lagging). DG Type 4 : DG capable of injecting reactive power only to improve the voltage profile, e.g. kvar compensator, synchronous compensator, capacitors etc.( p. f DG= 0) By considering the properties of DG units and in order to modeling them in the th mentioned optimization problem, the injected active and reactive powers to the i modeled as follows : i DG i Li bus are P = P P (5.) Q i DG i Li ( αi DG ) = Q Q = P Q (5.2) i Li 82

6 where Q DGi = α P (5.3) i DGi ( ) ( ) tan cos (. ) α i = sign p f DGi (5.4) type : The power factor depends on the DG type and operation condition of the DG. For the p. f DG =, for the type 2: 0 < p. f DG < and sign = +, for the type 3: 0 < p. f DG < and sign =, finally for the type4: p. f DG = 0. With the proposed methodology, it is possible to handle four different types of DGs. However, in this work, the DG units are modeled as type DG operated at unity power factor and type - 2 DG operated at power factor leading. 5.3 Problem Formulation The problem is to determine placement and size of the DG units which minimizes the total active power losses, improve the voltage profile and improve the voltage stability in a given radial distribution system while satisfying all constraints for a fixed number of DG units and specific total capacity of the DG units Objective function In this chapter, three objective functions are considered separately as single objective for the DG unit placement and sizing problem in the radial distribution network Minimization of the active power losses ( f ) The active power loss of the line section connecting buses i and j derived in chapter - 2 is used in this chapter. P Loss ( i, j) 2 2 P i + Q i = R ij 2 (5.5) V i The objective function for total active power loss of the all lines sections is described as f ( P 2 + Q 2 ) nb ( 2 2 i P + Qi) n i i P = R = R = (5.6) T, Loss ij 2 ij 2 ij= V ij= i Vi 83

7 Minimization of Voltage deviation ( f 2 ) The objective function for minimization of voltage deviation is defined as f n = V V (5.7) 2 i, nom i= i Improvement of the voltage stability index ( f 3 ) The objective function for improving voltage stability index is defined as f 3 = SI j, j= 2,3,... n (5.8) where the voltage stability index at bus j as described in chapter 2 is calculated as : 2 4 j = Vi 4 P j X ij Qj R 4 P ij j Rij + Qj X ij Vi SI 2 (5.9) System Constraints The objective function is subjected to the following constraints : Equality constraints Power balance constraints The total active power injected by DGs and total reactive power injected by DGs must satisfy the power constraints as (5.0) and (5.), respectively; n n P SUB + P DG, i = P Li + P T, Loss i= i= (5.0) n SUB DG, i Li T, Loss i= i= n Q + Q = Q + Q (5.) Inequality constraints Bus Voltage limit The voltage at various buses should be maintained within the acceptable limits by (5.2) : V V V (5.2) min max i i i Thermal Limits The current at various branches should be maintained within the acceptable limits by (5.3) : max I ij I (5.3) ij 84

8 Radial structure of the network det (A) = or - (radial system) (5.4) det (A) = 0 (non radial system) (5.5) where A = Bus incidence matrix Power limits of DG The active and reactive power sizes of DG at the acceptable limits by (5.6) and (5.7), respectively: th i bus are maintained within the min max P DG, i P DG, i PDG, i (5.6) min max DG, i DG, i DG, i Q Q Q (5.7) 5.4 Application of MTLBO to Solve the Optimal Placement and Sizing Problem of DG units The procedure for implementing the MTLBO algorithm in solving optimal DG placement problem can be summarized by the following steps: Step : Read the system data, constraints, the population size ( N ), the maximum number of iterations ( G ), the number of DG units to be installed in the distribution network, limits of DG placement buses and limits of DG sizes. Step 2 : The DG placement Buses are positive integers, while the variables that represent the DG unit size variables are continuous. The placement of DG buses and size of the DGs are randomly generated and normalized between the maximum and the minimum operating limits. The placement of DG buses and size of the DGs of th j DG is normalized to j b DG and j P DG as given below to satisfy the placement of DG buses and size of the DGs constraints: b j DG + N, b = [ b ] DG DG,min bdg,max ( random ( ) ( DG max,min)) b b b b j j j j DG= round DG,min + DG (5.8) j Where b DG represents DG bus location. Main distribution substation is designated as 85 j b DG =

9 j DG P R, P DG= [ 0 P DG,max ] ( random( ) ( DG, max,min)) j j j j DG DG,min DG P = P + P P (5.9) Select DG placement buses randomly from all the buses and the DG units are installed in these selected buses. The rating of all the installed DG units, comprise a vector which represents the grade of different subjects of a particular student and it also represents a candidate solution for the optimal DG allocation problem. Each set of the feasible solution of matrix M i represents a potential solution which is given by M i= PDGi,, PDGi,2..., PDGi, ndg bdgi,, bdgi,2..., PDGi, ndg (5.20) The proposed DG has a pre specified power factor (unity p. f and leading p. f ), so the dimension of the vector is two variables per DG installed (the positive integer bus number and the DG real power output). Moreover for multiple DG units (n DG) to be installed in the grid, the vector will have a dimension of ( 2nDG). Depending upon the population size, initial solution M is created which is given by : M = M M M, M 2..., j..., P (5.2) Step 3 : Compute the objective function. Step 4 : Identify the best solution and assign that solution as the teacher of the class. Step 5 : Modify the grade of each subject (independent variables of radial distribution system) of each student based on the teacher knowledge using equation (3.) in chapter -3. Step 6 : Update grade of each subject of each student based on the learners knowledge by utilizing the knowledge of some other learner of the same group using equation (3.3) in chapter- 3. Step 7 : Check whether the independent variables violate the operating limits or not. If any independent variable is less than the minimum level it is made equal to minimum value and if it is greater than the maximum level it is made equal to maximum level. Step 8 : Go to step 2 until the current iteration number reaches the pre specified maximum iteration number. 86

10 5.5 DG Placement & Sizing Indices There are various technical issues that need to be addressed when considering the presence of distributed generators in distribution systems. To study the effect of DG units on the performance of power systems, some indices are used as shown in Table 5..The details of indices are described in chapter 4. Table 5.: Evaluation indices due to installation of DG units in RDS Impact index Formula D G DG penetration level P L = S 0 0 % S l o a d P P T, Loss, NO DG T, Loss, DG Active power loss reduction APLR = P Reactive power loss reduction R P L R T, Loss, NO DG T, Loss, N O D G 00% Q Q T, L oss, N O D G T, Loss, D G = 00% Q V D N O D G V D D G Voltage deviation reduction V D R = 0 0 % V D N O D G V S I N O D G V S I D G Voltage stability index reduction V S IR = 0 0 % V S I N O D G n VDI = Voltage deviation index n Voltage profile index Qualified load index Line loading index VPI n n V i DG V i= i nom V i DG i NO DG i= = n n i= i V i= Q L I = V P L L I = n m ax i= 5.6 Simulation Results and Analysis L i V i NODG S S i D G i rated V i nom 00% The proposed method has been programmed using MATLAB and run on a personal computer having dual core processor,.86ghz speed and 2GB RAM. The proposed MTLBO algorithm is run for 5 independent runs having 50 population size and 50 iterations for each case. 87

11 A PQ model is considered for DG units in this study system. The DG units are considered to be working at a specified power factor as mentioned below. In this work, the two test systems (33 and 69 bus RDS) are considered with existing loading conditions. The impacts of DG units are studied by comparing the case with and without DG units. The effectiveness of the proposed method is tested on 33 and 69 bus radial distribution systems installing two types of three DG units operating at different power factors. Case I : Type, three DG units operated at unity power factor Case II : Type 2, three DG units operated at power factor leading 5.6. Test system - (33 bus RDS) The first system is a 2.66 kv, 33 bus RDS consisting of 33 buses configured with one substation, one main feeder, 3 laterals and 32 branches. The total active and reactive loads on this system are 375 kw and 2300 kvar, respectively. It is demonstrated in Fig. A. [68]. The line and load data of this system is given in appendix table A. & A.2. In this section, the results of proposed method for 33 bus RDS for case - I & II are presented. Table 5.2 shows the before installation objective function values of DG units as given in chapter - 2. Table 5.2 : Objective function value of the RDS before DG units installation (Base case) System Objective function value f (kw) f (p. u.) 2 f (p. u.) 3 Min. Voltage / Bus No. 33-Bus / 8 The detailed performance analysis using proposed (MTLBO) algorithm for 33 bus RDS after installation of the three DG units are described in Table 5.3 for minimization of the active power losses. The worst, the best, the arithmetic mean and the Standard deviation of the objective function for minimization of the active power losses in system 33 bus RDS are given in Table 5.4. To explain the impact of DG units on the performance of power systems, some indices are calculated as shown in Table

12 Table 5.3 : Performance analysis of the 33 bus RDS after three DG units installation System parameters Unity p.f. (Case-I) p.f. leading (Case-II) Optimal Location of DG 30, 24, 5 30, 24, 0 Optimal DG size Active power rating (MW) Reactive power rating (MVAr).0356, 0.995, ,.0685, , 0.669, Total active power Loss ( f ) in kw Total reactive power Loss in kvar Voltage Deviation( f 2) in p. u Voltage stability index ( f 3) in p. u V min (p. u.) / Bus No / / 8 Table 5.6 gives the results which are compared with other existing techniques for 33 bus RDS respectively. It may be observed from the simulation results that distribution losses achieved due to installation of DG units in optimal position obtained by different algorithms are reduced significantly. Best Worst Table 5.4 : Statistics of active power loss in kw for 33 bus RDS Unity p.f. (Case - I) 33 Bus p.f. leading (Case - II) P loss (kw) P loss (kw) Arithmetic Mean of St. Dev. of P loss (kw) P loss (kw) Impact index Table 5.5 : Evaluation indices for 33 bus RDS Unity p. f. (Case-I) 33 Bus p.f. leading (Case-II) DG penetration level (%) Active power loss reduction (%)

13 Reactive power loss reduction (%) Voltage deviation reduction (%) Voltage stability index reduction (%) Voltage deviation index Voltage profile index Qualified Load Index Line loading Index Table 5.6 : Comparison of the proposed method results with previous publications for 33 bus RDS with three DG units at different power factor Items GA / PSO [54] LSFSA [59] Proposed (MTLBO) Unity p. f. (Case - I) DG placement,6, 32 6,8,30 30, 24, 5 Active power Rating of DG (MW) , , , , , 0.995, Reactive power Rating of DG( MVAr ) Active power loss (kw ) Active power loss reduction (%) Critical bus voltage (p.u.) / Bus No / / / p. f. leading (Case - II) DG placement - 6, 8, 30 30, 24, 0 Active power Rating of DG ( MW) - Reactive power Rating of DG (MVAr ) -.976, , , , ,.0685, , 0.669, Active power loss (kw ) Active power loss reduction (%) Critical bus voltage (p.u.) / Bus No / / 8 90

14 In addition, it should be pointed out that for 33 bus RDS accomplished with the installation of three numbers of DG units, the proposed MTLBO algorithm attains active power loss reduction of 64.9% for unity p.f. and 9.65% for p.f. leading which are better than previously reported methods. Therefore, it can be concluded that MTLBO technique is more efficient than other techniques in reducing the power loss of 33 bus radial distribution systems. Obj. Function ( Active power loss) in kw Iteration No. Fig. 5.2 : Objective function ( f ) variation of 33 bus RDS for case -I Obj. Function ( Active power loss) in kw Iteration No. Fig. 5.3 : Objective function ( f ) variation of 33 bus RDS for case II The convergence characteristics of objective function after the installation of three DG units obtained by the proposed algorithm for case I & II of 33 bus RDS are illustrated in Figs. 5.2 and 5.3 respectively. 9

15 Active power loss in kw Without DG (Base Case) With 3DGs at unity p.f With 3DGs at p.f leading Branch No. Fig. 5.4 : Active power loss (kw) before & after DG units installation for 33 bus RDS Figs. 5.4 depicts active power loss of each bus for case I & II in 33 bus RDS. It is seen that the three numbers of DG units injecting active and reactive power at p.f. leading(case-ii) results in higher real power loss reduction in the systems as compared to the three DG units injecting active power only at unity p.f.(case-i) only and without DG (base case). Reactive power loss in kvar Without DG (Base Case) With 3DGs at unity p.f With 3DGs at 0.866p.f leading Branch No. Fig. 5.5 : Reactive power loss (kvar) before & after DG units installation for 33 bus RDS Figs. 5.5 gives reactive power loss of each bus for case I & II in 33 bus RDS. It is seen that the three numbers of DG units injecting active and reactive power at p.f. leading(case- 92

16 II) results in higher reactive power loss reduction in the systems as compared to the three DG units injecting active power only at unity p.f.(case-i) and without DG (base case). Voltage magnitude (p.u.) Without DG(Base Case) With 3DGs at unity p.f With 3DGs at p.f leading Bus No. Fig. 5.6 : Bus voltage level (p. u.) before and after DG units Installation for a 33 bus RDS Figs. 5.6 gives voltage profile of each bus for case I & II in 33 bus RDS. The results show the different voltage levels before installation and after installation of the DG units for proposed method. Before installation of DG units, voltage level in a 33 bus RDS are low. After installation of the three DG units, the voltage levels are improved in the proposed method. It is seen that the three numbers of DG units injecting active and reactive power at p.f. leading (case-ii) results in higher voltage level in the systems as compared to the three DG units injecting active power only at unity p.f. (case-i) and without DG (base case). Voltage deviation ( p.u. ) Without DG(Base Case) With 3DGs at unity p.f With 3DGs at p.f leading Bus No. Fig. 5.7 : Voltage deviation (p. u.) before and after DG units installation for a 33 bus RDS 93

17 Figs. 5.7 gives bus voltage deviation of each bus for case I & II in 33 and 69 bus RDS. It is observed that the three numbers of DG units injecting active and reactive power at p.f. leading (case-ii) results in higher voltage deviation reduction in the systems as compared to the three DG units injecting active power only at unity p.f.(case-i) and without DG (base case). Voltage stability index (p.u) Without DG (Base case) With 3 DGs at unity p.f. With 3 DGs at p.f. leading Bus No. Fig. 5.8 : Voltage stability index (p. u.) before and after DG units installation for a 33 bus RDS Figs. 5.8 gives voltage stability index of each bus for case I & II in 33 bus RDS. The results show that the three numbers of DG units injecting active and reactive power at p.f. leading(case-ii) results in higher voltage stability index reduction in the systems as compared to the three DG units injecting active power only at unity p.f.(case-i) and without DG (base case) Test system - 2 (69 bus RDS) The second system is a 2.66 kv, 69 bus large scale RDS consisting of 69 buses configured with one substation, one main feeder, 7 laterals and 68 branches. The total active and reactive loads on this system are kw and kvar, respectively. It is demonstrated in Fig. A.2 [70]. The line and load data of this system is given in appendix Table A.3 & A.4. 94

18 In this section, the results of proposed method for 69 bus RDS for case - I & II are presented. Table 5.7 shows the before installation objective function values of DG units as given in chapter - 2. Table 5.7: Objective function value of the RDS before DGs installation (Base case) System Objective function value Min. Voltage / f (kw) Bus No. f (p. u.) 2 f (p.u.) 3 69-Bus / 65 The detailed performance analysis using proposed (MTLBO) algorithm for 69 bus RDS after installation of the three DGs are described in Table 5.8 for minimization of the active power losses. The worst, the best, the arithmetic mean and the standard deviation of the objective function for minimization of the active power losses in 69 bus RDS are given in Table 5.9.To explain the impact of DG units on the performance of power systems, some indices are calculated as shown in Table 5.0. Table 5. gives the results which are compared with other existing techniques for 69 bus RDS respectively. It may be observed from the simulation results that distribution losses achieved due to installation of DG units in optimal position obtained by different algorithms are reduced significantly. Table 5.8 : Performance analysis of the 69 bus RDS after three DGs installation System parameters Unity p.f. (Case-I) p.f. leading (Case-II) Optimal Location of DG 8, 62, 6 62, 6, 2 Optimal DG size Active power rating (MW) 0.568, 0.722,.0303 Reactive power rating (MVAr) ,.795, , 0.680, Total active power Loss ( f ) in kw Total reactive power Loss in kvar Voltage Deviation( f 2) in p. u Voltage stability index ( f 3) in p. u V min (p. u.) / Bus No / / 69 95

19 Best Worst Table 5.9: Statistics of active power loss in kw for 69 bus RDS Unity p.f. (Case-I) 69 Bus p.f. leading (Case-II) P loss P loss Arithmetic Mean of St. Dev. of P loss P loss Table 5.0 : Evaluation indices for 69 Bus RDS 69 Bus Impact index Unity p.f. (Case - I) p.f. leading (Case - II) DG penetration level (%) Active power loss reduction (%) Reactive power loss reduction (%) Voltage deviation reduction (%) Voltage stability index reduction (%) Voltage deviation index Voltage profile index Qualified Load Index Line loading Index In addition, it should be pointed out that for 69 bus system, active power loss reduction of 68.03% at unity p.f.(case - I ) and 95.82% at p.f. leading (case-ii) are accomplished with the installation of three numbers of DG units using the proposed MTLBO algorithm which is far better than the active power loss reduction of previously reported methods. Therefore, it is concluded that MTLBO technique is more efficient than other techniques in reducing the power loss of 69 bus radial distribution system. 96

20 Table 5. : Comparison of the proposed method results with previous publications for 69 bus RDS with three DG units at different power factor Items GA/PSO [54] LSFSA [59] MTLBO Unity p.f. ( Case - I ) DG placement 2,6,63 8,60,65 8, 62, 6 Active power Rating of DG ( MW ) 0.905,.926, ,.33, , 0.722,.0303 Reactive power Rating of DG ( MVAr ) Active power loss (kw ) Active power loss reduction (%) Critical bus voltage (p.u.) / Bus No / / / p.f. leading ( Case - II ) DG placement - 8,60,65 62, 6,2 Active power Rating of DG ( MW ) - Reactive power Rating of DG ( MVAr ) ,.954, , , ,.795, , 0.680, Active power loss (kw ) Active power loss reduction (%) Critical bus voltage (p.u.) / Bus No / / 69 Obj. Function(Active power loss) in kw Iteration No. Fig. 5.9 : Objective function ( f ) variation of 69 bus RDS for case I 97

21 The convergence characteristics of objective function after the installation of three DG units obtained by the proposed algorithm for case I of 69 bus RDS are illustrated in Fig Obj. Function(Active power loss) in kw Iteration No. Fig. 5.0 : Objective function ( f ) variation of 69 bus RDS for case II The convergence characteristics of objective function after the installation of three DG units obtained by the proposed algorithm for case II of 69 bus RDS are illustrated in Fig Active power loss in kw Without DG(Base Case) With 3 DGs at unity p.f. With 3 DGs at 0.866p.f. leading Branch No. Fig. 5. : Active power loss (kw) before & after DG units installation for 69 bus RDS Fig. 5. depicts active power loss of each bus for case I & II in 69 bus RDS. It is observed that the three numbers of DGs injecting active and reactive power at p.f. leading (case - II) 98

22 results in higher real power loss reduction in the systems as compared to the three DG units injecting active power only at unity p.f.(case - I) and without DG (base case). Reactive power loss in kvar Without DG(Base Case) With 3DGs at unity p.f With 3DGs at p.f leading Branch No. Fig. 5.2 : Reactive power loss ( kvar ) before & after DG units installation for 69 bus RDS Fig. 5.2 gives reactive power loss of each bus for case I & II in 69 bus RDS. It is seen that the three numbers of DGs injecting active and reactive power at p.f. leading (case-ii) results in higher reactive power loss reduction in the systems as compared to the three DGs injecting active power only at unity p.f. (case-i) and without DG (base case). Voltage magnitude (p.u.) Without DG(Base Case) 0.92 With 3 DGs at unity p.f. With 3 DGs at 0.866p.f. leading Bus No. Fig. 5.3 : Bus voltage level (p. u.) before and after DG units installation for a 69 bus RDS Fig. 5.3 depicts each bus voltage in 69 bus RDS. The results show the different voltage levels before installation and after installation of the DGs for proposed method. Before installation of DGs, voltage level in 69 bus RDS are low. After installation of the three DGs, the voltage levels are improved in the proposed method. It is seen that the three numbers of DGs injecting active and reactive power at

23 p.f. leading (case-ii) results in higher voltage level in the systems as compared to the three DGs injecting active power only at unity p.f. (case-i) and without DG (base case). Voltage deviation (p.u.) Without DG(Base Case) With 3DGs at unity p.f With 3DGs at p.f leading Bus No. Fig. 5.4 : Bus voltage deviation (p. u.) before and after DG units installation for a 69 bus RDS Fig. 5.4 gives bus voltage deviation of each bus for case - I & II in 69 bus RDS. It is observed that the three numbers of DGs injecting active and reactive power at p.f. leading (case-ii) results in higher voltage deviation reduction in the systems as compared to the three DGs injecting active power only at unity p.f.(case-i) and without DG (base case). Voltage stability index (p.u) Without DG (Base case) With 3 DGs at unity p.f. With 3 DGs at p.f. leading Bus No. Fig. 5.5 : Voltage stability index (p.u.) before and after DG units installation for a 69 bus RDS Fig. 5.5 gives voltage stability index of each bus for case - I & II in 69 bus RDS. The results show that the three numbers of DGs injecting active and reactive power at p.f. leading 00

24 (case-ii) results in higher voltage stability index reduction in the systems as compared to the three DGs injecting active power only at unity p.f. (case-i) and without DG (base case). 5.7 Conclusions This chapter proposed MTLBO method to solve placement and sizing problems for DGs simultaneously in 33 and 69 bus radial distribution systems. The proposed method was implemented for the both systems to minimize the active power losses. The proposed method stated less objective function values in state of existence DGs. Also this method gives less active power losses in comparing with the results of other popular optimization techniques. After DGs installation, the both RDS have shown major improvement in voltage profile and increase the voltage stability index for the proposed method. The comparison of the results using the proposed approach to those reported in the literature confirms its effectiveness and superiority to find remarkable global solutions. The proposed method introduces the accuracy as well as convergence speed and simplicity. Also multi-objective studies can be done by the proposed algorithm. 0