Optimum Siting and Sizing of Distributed Generations in Radial and Networked Systems

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1 This article was downloaded by: [Iran University of Science &] On: 06 May 2012, At: 01:58 Publisher: Taylor & Francis Informa Ltd Registered in England and Wales Registered Number: Registered office: Mortimer House, Mortimer Street, London W1T 3JH, UK Electric Power Components and Systems Publication details, including instructions for authors and subscription information: Optimum Siting and Sizing of Distributed Generations in Radial and Networked Systems R. K. Singh a & S. K. Goswami b a Department of Electrical Engineering, Government Polytechnic, Faizabad, U.P., India b Department of Electrical Engineering, Jadavpur University, Kolkata, India Available online: 16 Jan 2009 To cite this article: R. K. Singh & S. K. Goswami (2009): Optimum Siting and Sizing of Distributed Generations in Radial and Networked Systems, Electric Power Components and Systems, 37:2, To link to this article: PLEASE SCROLL DOWN FOR ARTICLE Full terms and conditions of use: This article may be used for research, teaching, and private study purposes. Any substantial or systematic reproduction, redistribution, reselling, loan, sub-licensing, systematic supply, or distribution in any form to anyone is expressly forbidden. The publisher does not give any warranty express or implied or make any representation that the contents will be complete or accurate or up to date. The accuracy of any instructions, formulae, and drug doses should be independently verified with primary sources. The publisher shall not be liable for any loss, actions, claims, proceedings, demand, or costs or damages whatsoever or howsoever caused arising directly or indirectly in connection with or arising out of the use of this material.

2 Electric Power Components and Systems, 37: , 2009 Copyright Taylor & Francis Group, LLC ISSN: print/ online DOI: / Optimum Siting and Sizing of Distributed Generations in Radial and Networked Systems R. K. SINGH 1 and S. K. GOSWAMI 2 1 Department of Electrical Engineering, Government Polytechnic, Faizabad (U.P.), India 2 Department of Electrical Engineering, Jadavpur University, Kolkata, India 1. Introduction Abstract This article presents a genetic algorithm-based method to determine optimal location and size of the distributed generations to be placed in radial, as well as networked, systems with an objective to minimize the power loss. Several simulation studies have been conducted on radial feeders, as well as networked systems, considering single-distributed generation and multiple-distributed generations separately to minimize the power loss of the system subjected to no voltage violation at any of the buses. Simulation results are given, and the results are compared with the results of Wang and Hashem Nehrir [ Analytical approaches for optimal placement of distributed generation sources in power systems, IEEE Trans. Power Syst., Vol. 19, No. 4, pp , November 2004] and Gozel et al. [ placement and sizing of distributed generation on radial feeder with different static load model, Proc. of IEEE International Conference on Future Power Systems (EPS 2005), pp. 1 6, Amsterdam, The Netherlands, November 2005] to verify the proposed method. Keywords genetic algorithm, distributed generation, optimal location, optimal size, power loss, distribution networks As the result of deregulation, the electric power system worldwide is undergoing major structural changes from the present centralized generating systems. Distributed generations (s) are generating sources that serve customers on-site or provide support to distribution network, which is connected to the grid at distribution level voltages. s are considered as small power generators that complement central power stations by providing incremental capacity to power systems [1, 2]. The proper placement of s in power systems has many advantages in terms of reducing losses and on-peak operating costs, improving voltage profiles, eliminating construction of new transmission lines, and improving system reliability, integrity, and efficiency [2]. The design of engineering instruments should be optimized using an effective optimization technique in order to ensure the best allocation of limited financial resources. In electric power systems, most of the electrical energy losses occur in the distribution Received 7 February 2008; accepted 1 August Address correspondence to S. K. Goswami, Department of Electrical Engineering, Jadavpur University, Kolkata, West Bengal, India. skgoswani_ju@yahoo.co.in 127

3 128 R. K. Singh and S. K. Goswami systems. The genetic algorithm (GA) can be used as a tool for the design of a new distribution system and for the resizing of an existing one [3]. Most of the literature has considered power losses of the system as an objective function to be minimized [4 7] for locating the site for installation. The power losses of the systems depend on location, as well as size. It is found that as penetration increases, losses start to decrease and reach to a minimum value. If penetration level still increases, losses begin to increase marginally also. If penetration levels increase enough, the losses can be even higher than without a connected [8]. A 2/3 rule was described in [9] to place on a radial feeder with uniformly distributed loads. This method cannot be extended to a feeder with other types of loads or to networked systems. An analytical method has been described to optimally place in radial, as well as networked, systems [10]. A genetic tabu search algorithm has been described for optimal allocation in distribution networks [11]. Methods presented in [10, 11] determined only the location of, whereas, losses depend on both location and size [12]. A method was suggested in [13] for optimal placement and sizing of single source using an analytical approach, but its application is restricted to radial feeders only. This article presents a GA-based approach for optimal placement, as well as optimal sizing, of single and multiple s with real power support. The proposed method works well for both radial and networked systems. Using this method, simulation on radial feeders with different load patterns (increasing, centralized, and uniform) on IEEE 6-bus and 30-bus test systems shows the effectiveness and validity of the proposed method in determining the optimal bus and optimal size. The simulation studies are carried out with the single case and multiple s case separately. The aim of this article is to suggest methodology for proper location and sizing of s. Hence, some of the issues related to placement such as voltage rise phenomenon in a radial system and increase of fault level and its impact on protective gears economic, geographical, and environmental considerations have not been taken into account. 2. Formulation of the Problem Consider a network with n nodes. Let the set of equations, q D 0; (1) represent the power flow equation, where q D 0 contains 2n equations expressing the power and Var injections at the n nodes in terms of appropriate complex line impedances, node voltages, and angles. The power balance equations depict that the sum of power flows active and reactive injected into a node, minus the power flows extracted from the node, has to be zero. In our application, is considered as negative loads at buses; therefore, the power balance equation has been modified. Since is injecting only real power, there is no change in reactive power balance equations. The sum of all nodes injections of power in the network represents losses. In this article, loss minimization has been used as a performance index, and the GA has been used as a tool to optimize the performance index [14, 15]. The following conditions have been incorporated with the algorithm to obtain the desired result.

4 Siting and Sizing of Distributed Generators 129 (i) Any size between zero and maximum can be randomly generated using Eq. (8) in the initial population and, subsequently, in the next generation population, by genetic operation. (ii) Any bus location except the slack bus can be randomly generated using Eq. (7) in the initial population and, subsequently, in the next generation population, by genetic operation. For the loss minimization case, the performance index f is given by f D nx P i : (2) id1 Clearly, the sum of all node injections of power in the network represents the losses. The formulation of the problem may be summarized as Minimize f D nx P i (3) subject to q D 0, and voltage at all buses within the specified limits, i.e., where id1 P Gi C P i P Di D 0; (4) Q Gi Q Di D 0; (5) V min V V max ; (6) P Gi and Q Gi are the real and reactive generated power at Bus i, respectively; P i is the real power injected by at Bus i; P Di and Q Di are the real and reactive loads at Bus i, respectively; and V max and V min are the maximum and minimum allowable voltage at buses, respectively; for the base case, without (P D 0). 3. Placement of on Radial Feeders To simplify the analysis, only overhead transmission lines with uniformly distributed parameters are considered; that is, resistance and inductance per unit length are the same along the feeder, while capacitance and conductance per unit length are neglected. The load along the feeders is assumed to be static. The real and reactive power consumed by the load is supplied directly by external generation at Bus 1. Hence, Bus 1 has been considered the slack bus. 4. GAs for Placement and Sizing of Distributed Generators In a -enhanced feeder, the optimization is not straightforward, as in the case of a conventional feeder due to the presence of additional generators. The power losses of systems depend on both location and size. We produce a simple GAbased method to solve for optimal position and optimal size of simultaneously.

5 130 R. K. Singh and S. K. Goswami The GA effectively implements the survival of the fittest strategy using the principles of Darwinian natural selection and biological-inspired operations. The GA typically starts with a randomly generated initial population of individuals and iteratively transforms the initial population into a new generation of the population using two genetic operators mutation and crossover. The individuals are probabilistically selected to participate in the genetic operation based on their fitness measures. The iterative transformation of the population is executed inside the main generational loop of the run of GA. After the termination criterion is satisfied, the single best individual in the population produced during the run is harvested and designated as the result of the run. If the run is successful, the result may be the solution to the problem. In our application, the initial population vector is randomly generated using Eqs. (7) and (8): _location D round.2 C rand.number_of _buses 2//; (7) _size D.rand maximum size/; (8) where round is a round-off function that rounds non-integer values toward the nearest integers to generate only integer bus location, and rand is a function that randomly generates any number between 0 and 1. In this way, any size up to the maximum and any bus except the slack bus can be randomly generated. Each population of the initial population vector consists of size and corresponding bus location. Now, the generated size is reinforced in the network at the corresponding generated bus location for each population, and then the voltage profile of the buses are determined. If the voltages at the buses are within specified limits, the population is a survived population; otherwise, the population is not fit for placement and is rejected. A survived population vector is created that contains all survived populations selected from the initial population vector. The performance index is determined for each survived population of the survived population vector. The population that determines the optimal performance index is the optimal population. The survived population vector is further used to generate the next generation population using two genetic operators crossover and mutation. The above-mentioned steps are repeated to obtain the best results. 5. The Proposed Algorithm In order to determine the best location and size of the unit for the distribution network, the following algorithm has been suggested considering the appropriate voltage levels. The major steps of the proposed algorithm are as follows. Step 1. Create an initial population vector by randomly generating location and size. Each population of the initial population vector consists of size and corresponding bus location. Step 2. Apply each population of the initial population vector on the network; that is, the size generated in the population is reinforced in the network at the corresponding generated bus location. Step 3. Check for the voltage violation at all buses for each population applied on the network. Step 4. If the voltage is within specified limits ( 5%) for all buses, the population is a survived population of the survived population vector. Step 5. Calculate the losses for each population of the survived population vector. The population for which loss is minimum is the optimal population.

6 Siting and Sizing of Distributed Generators 131 Step 6. If the convergence criterion is satisfied, stop and display the results; otherwise go to Step 7. Step 7. Apply the survived population vector from the initial population vector to generate the next generation population using two genetic operators crossover and mutation and repeat Step 3 to Step 6. The general flowchart of the solution algorithms is shown in Figure 1. The proposed method is first applied for single placement and then it is extended for multiple placements. 6. Simulation Results The proposed method is applied on several standard test systems for both radial and networked systems (see Figures 2 and 3), considering single and multiple s separately. The simulation results of single placement are compared with the results of [10, 13] One Placement Scenario In this scenario, one single plant with suitable capacity is considered for placement Radial Feeders with Time-invariant Loads and. The results of the simulation of an 11-bus system are compared with the results of [10], whereas, the results of a 13-bus system are compared with the results of [13]. Eleven-bus radial feeder The method is tested on an 11-bus radial feeder with a time-invariant load simulated under three different loading conditions. (1) Increasing distributed loads: Three case studies are performed. Case 1.1: The system is simulated with a fixed size of 3.3 MW, and the optimal bus location, as shown in Figure 4, is Bus 8. Case 1.2: The different capacities (up to the maximum of 3.3 MW) are applied on Bus 8, and the optimal size, as depicted in Figure 5, is 2.8 MW. Case 1.3: All possible combinations of location and corresponding size (up to the maximum size of 3.3 MW) are checked. The optimal bus location and optimal size are Bus 9 and 2.6 MW, respectively, as shown in Figure 6. (2) Centrally distributed loads: Two case studies have been conducted. Case 2.1: The system is simulated with a fixed size of 2.6 MW, and the optimal bus location, as shown in Figure 7, is Bus 6. Case 2.2: All possible combinations of location and corresponding size (up to the maximum size of 2.6 MW) are checked. The optimal bus location and optimal size are Bus 7 and 2.0 MW, respectively, as shown in Figure 8. (3) Uniformly distributed loads: Two case studies performed. Case 3.1: Different sizes (up to the maximum of 5.5 MW) are applied on Bus 6; the loss varies with size, as shown in Figure 9. The size in the range of 4.6 MW to 5.5 MW is chosen to be placed on Bus 6 (Figure 9). Any other size beyond this range is not fit for placement at Bus 6, as voltage violation occurs at the buses; therefore, size 4.6 MW is the optimal size at Bus 6.

7 132 R. K. Singh and S. K. Goswami Figure 1. Flow chart of proposed method.

8 Siting and Sizing of Distributed Generators 133 Figure 2. A radial feeder with uniformly distributed loads [10]. Case 3.2: All possible combinations of location and corresponding size (up to the maximum of 5.5 MW) are checked. The optimal bus location and optimal size are Bus 8 and 3.9 MW, respectively, as shown in Figure 10. The system architecture is the same when loads are centrally distributed or increasingly distributed. The line parameter,, and load sizes are given in Appendix A. Table 1 depicts the comparison of results of the simulation study and that of [10]. The results show the real power losses of the system without and with a of given capacity at optimal location under all three loading conditions. It can be seen that the optimal location determined in the results of the simulation and [10] is the same, while the system losses are almost similar. The proposed method optimizes location as well as size of. The results of the simulation when the size is also optimized are shown in Table 2. It can be seen that when location, as well as size, are optimized together, the system losses are reduced too much; the location of also changes from the case where only the location is optimized. Figure 4 shows the variation of losses at buses with a given size of 3.3 MW under the increasingly distributed loading profile. The optimal location is Bus 8 under this condition; therefore, the results of the simulation and [10] are similar. When the size at Bus 8 is optimized, the optimal size is 2.8 MW, as depicted in Figure 5. Figure 6 shows the results of simulation when location and size is optimized; therefore, the optimal location and optimal size of are Bus 9 and 2.6 MW, respectively. Figure 3. A 6-bus networked power system studied [10].

9 134 R. K. Singh and S. K. Goswami Figure 4. Power losses of radial feeder with increasing loads and 3.3-MW (Case 1.1). Figure 5. Variation of losses with size at Bus 8 for increasing loads (Case 1.2). Figure 6. Variation of losses with size at Bus 9 for increasing loads (Case 1.2).

10 Siting and Sizing of Distributed Generators 135 Figure 7. Power losses of the radial feeder with centralized loads and 2.6-MW (Case 2.1). Figure 8. Power losses of radial feeder with centralized loads and 2.0-MW (Case 2.2). Figure 9. Variation of losses with size at Bus 6 for uniform loads (Case 3.1).

11 136 R. K. Singh and S. K. Goswami Figure 10. Power losses on radial feeder with uniform loads and 3.9-MW (Case 3.2). Line loading Table 1 Simulation results of case studies with time-invariant loads and on 11-bus radial feeder (without considering size) bus (simulation) place [10] Total power losses (MW) (simulation) Without With Total power losses (MW) [10] Without With Increasing Central Uniform Table 2 Simulation results of case studies with time-invariant loads and single on 11-bus radial feeder (with optimizing size) Line loading bus size (MW) penetration % of load (allowable) Total power losses (MW) Without With Increasing Central Uniform

12 Siting and Sizing of Distributed Generators 137 Table 3 Simulation results of case studies with static loads and on 13-bus radial feeder Results of simulation Results of [13] Load profile location capacity of 100% of load Power losses (MW) location capacity of 80% of load Power losses (MW) Power losses without (MW) capacity of 100% of load location capacity of 80% of load location Increasing Central Uniform Under the centralized loading profile, the system is simulated with a given size of 2.6 MW; the optimal location for this is Bus 6, as seen in Figure 7. Figure 8 depicts the results of simulation when the location and size are optimized together; therefore, the optimal location and optimal size of are Bus 7 and 2.0 MW, respectively. Under the uniformly distributed loading profile, the system is simulated with a given size of 5.5 MW, and the optimal location for this is Bus 6; therefore, results are similar to that determined in [10]. In fact, Bus 6 is the only survived location for the size of 5.5 MW, as the placement of this at other buses violates the voltage limits at the buses. The size in the range of 4.6 MW to 5.5 MW are chosen to be placed on Bus 6 (Figure 9). Any other size beyond this range is not fit for placement at Bus 6, as voltage violation occurs at the buses; therefore, a size of 4.6 MW is optimal at Bus 6. Figure 10 depicts the results of the simulation when the location and size are optimized together; therefore, the optimal location and optimal size of are Bus 8 and 3.9 MW, respectively. Placement on some of the buses is not shown in the results, as the voltage violation occurs when placement is considered for these buses. Hence, under the increasingly distributed load profile, Buses 7, 8, and 9 (Figure 4) are considered for placement. Buses 5, 6, 7, 8, 9, 10, and 11 (Figure 8) are considered for placement under the centrally distributed load profile, while Buses 7, 8, and 9 (Figure 10) are suitable for placement under the uniformly distributed loading condition. Thirteen-bus radial feeder This system is also simulated using the proposed method; the parameters of the system, load, and size are given in Table D1 of Appendix D [13]. The results of the simulation are given in Table 3. It is observed that the results of the simulation and [13] are similar Networked Systems Case 4: 6-bus system. The proposed method was applied on a 25-kv IEEE 6-bus system, which can be considered as a sub-transmission/distribution system. The parameters of this system are given in Appendix B. All possible combinations of location and corresponding size (up to the maximum size of 5 MW) are checked. The optimal location and optimal size are Bus 3 and 5 MW, respectively. Figure 11 depicts the system losses with 5-MW at different bus locations. It is noted from the figure that loss is also at its minimum when is placed at Bus 3 with a size of 5 MW,

13 138 R. K. Singh and S. K. Goswami Figure 11. Power losses of an IEEE 6-bus test system (Figure 3) with a 5-MW (Case 4). indicating that results obtained from the proposed GA is the same as the results reported in [10]. Case 5: 30-bus system. The proposed method was also tested on the slightly modified IEEE 30-bus test system, which can be considered a meshed transmission/sub-transmission system [10]. The system has 30 buses (mainly 132- and 33-kv buses) and 41 lines. This system bus data is given in Appendix C. All possible combinations of location and corresponding size (up to the maximum size of 15 MW) are checked. The total power loss of the system reaches the minimum value when is located at Bus 5 with a size of 15 MW, as reported in [10]. The optimal bus determined by the method proposed in this article is also Bus 5 (as shown in Figure 12). In this system also, some of the buses have not been shown as the candidates for placement, as the voltage violation occurs when placement is considered for these buses. In the results (Figure 12), Buses 2, 5, 7, 8, 9, 11, 26, 27, 29, and 30 have been considered for placement Multiple Placement Scenario In this scenario, a maximum of four s with appropriate sizes are considered for placement at a time. The method is tested on the 11-bus radial system and on an IEEE 6-bus test system. These are the same systems that are simulated under one scenario. The results of simulation for the 11-bus radial feeder and 6-bus networked system are shown in Tables 4 and 5, respectively. It is observed that for a smaller penetration level of the single placement has more impact on losses, and for a higher penetration level of, the dispersed placements have more impact on losses. In the case of the 6-bus system, three- placement is found to be more suitable than four- placement in terms of reducing losses. It can be seen in Tables 2, 4, and 5 that dispersed placement of s invites more penetration, which improves the objective of reducing losses with satisfying the voltage constraints.

14 Line loading Table 4 Simulation results of case studies with time-invariant loads and multiple s on 11-bus radial feeder (with optimizing size) injection (MW) penetration % of load (allowable) location 1 size 1 location 2 size 2 location 3 size 3 location 4 size 4 Increasing Central Uniform Losses (MW) Siting and Sizing of Distributed Generators 139

15 location Table 5 Simulation results of case studies with an IEEE 6-bus test system and multiple s (with optimizing size) Single placement size (MW) Losses (MW) penetration % of load (allowable) penetration (MW) penetration % of load (allowable) location 1 Multiple placement size 1 location 2 size 2 location 3 size Losses (MW) 140 R. K. Singh and S. K. Goswami

16 Siting and Sizing of Distributed Generators 141 Figure 12. Power losses of an IEEE 30-bus test system with a 15 MW (Case 5). Comparison Table 6 Simulation results of maximum voltage drop with and without Without 11-bus radial feeder with centralized load With of MW capacity Single Multiple Without 6-bus networked system With of MW capacity Single Multiple Maximum voltage drop (per unit) 6.3. Voltage Profile Improvement of the Buses The simulation results for voltage variations at the buses are shown in Table 6. It can be observed that the presence of in radial and networked systems improves the voltage profiles of the buses. The dispersed placements of s have more impact in terms of voltage profile improvement in the case of a radial feeder, whereas, for networked systems, single placement shows better voltage profiles of the buses. 7. Conclusions This study presents a GA-based approach to obtain optimal location and size of s in radial, as well as networked, systems with single and multiple s separately, in order to minimize the total power loss of the system. Several case studies have been conducted, and the results of the single case are compared with the results of the

17 142 R. K. Singh and S. K. Goswami literature to check the validity of the proposed method. Both the results are similar when the size is not optimized. When size optimization is also considered, the simulation results are even better than the results reported in the literature. It is observed that the dispersed placement is more suitable in the case of a high penetration level of, and it invites more penetration, which improves the objective of reducing losses with satisfying the voltage constraints. References 1. International Energy Agency (IEA), Distributed generation in liberalized electricity markets, Technical Report, pp , Gautam, D., and Mithulananthan, N., placement in deregulated electricity market, EPSR, Vol. 77, No. 2, pp , October Carrano, E. G., Soars, L. A. E., Takahashi, R. H. C., Saldanha, R. R., and Neto, O. M., Electric distribution network multiobjective design using a problem-specific genetic algorithm, IEEE Trans. Power Delivery, Vol. 21, No. 2, pp , April Kim, K.-H., Lee, Y.-J., and You, S.-K., Dispersed generation placement using fuzzy-ga in distribution systems, Proc. IEEE Power Eng. Soc. Summer Mtg., Vol. 3, pp , July Hadjsaid, N., Canard, J. F., and Duman, F., Dispersed generation impact on distribution network, IEEE Comput. Appl. Power, Vol. 12, pp , April Griffin, T., Tomsovic, K., Secrest, D., and Law, A., Placement of dispersed generation systems for reduced losses, Proceedings of the IEEE 33rd Annual Hawaii International Conference on Systems Sciences, Vol. 4, pp. 1 9, Nehrir, M. H., Wang, C., and Gerez, V., Impact of wind power distributed generation on distribution systems, Proceedings of the 17th International Conference on Electricity Distribution (CIRED), Barcelona, Spain, May Mendez Quezada, V. H., Abbad, J. R., and San Roman, T. G., Assessment of energy distribution losses for increasing penetration of distributed generation, IEEE Trans. Power Syst., Vol. 21, No. 2, pp , May Willis, H. L., Analytical methods and rules of thumb for modeling -distribution interaction, Proc. IEEE Power Eng. Soc. Summer Mtg., Vol. 3, pp , July Wang, C., and Hashem Nehrir, M., Analytical approaches for optimal placement of distributed generation sources in power systems, IEEE Trans. Power Syst., Vol. 19, No. 4, pp , November Gandomkar, M., Vakilian, M., and Ehsan, M., A genetic-based tabu search algorithms for optimal allocation in distribution networks, Elect. Power Compon. Syst., Vol. 33, pp , Rau, N. S., and Wan, Y.-H., Optimum location of resources in distribution planning, IEEE Trans. Power Syst., Vol. 9, pp , November Gozel, T., Hocaoglu, M. K., Eminoglu, U., and Balikci, A., placement and sizing of distributed generation on radial feeder with different static load model, Proceedings of the IEEE International Conference on Future Power Systems (EPS 2005), pp. 1 6, Amsterdam, The Netherlands, November Sarmistha, S. C., Genetic programming an approach to smart machine, J. Institution Engineers, Vol. 86, pp , December Goldberg, D. E., Genetic Algorithms in Search, Optimization and Machine Learning, Boston, MA: Addison Wesley, 1989.

18 Siting and Sizing of Distributed Generators 143 Appendix A. Parameter of the System in Figure 2 [10] Table A1 Load at each bus (MW) Load type Uniformly distributed Centrally distributed Increasingly distributed size (MW) Uniformly Centrally Increasingly Line parameters (AWG ACSR 1/0): line spacing D 1.32 m (equal spacing assumed), R D 0:538, X L D 0:4626, bus voltage: 12.5 kv, line length between two neighboring buses: 2.5 km. Appendix B. Parameters of the System in Figure 3 [10] Table B1 Bus data Bus no. Voltage (p.u.) Bus power (MVA) 1 1:0 C j 0:0 Slack bus 2 4:0 j1:00 3 7:25 j 2:00 4 5:00 j1:25 5 jv 5 j :00 j1:50 Table B2 Line data From To Z serial (p.u.) Z shunt (p.u.) 1 2 0:2238 C j 0:5090 j 0: :2238 C j 0:5090 j 0: :2238 C j 0:5090 j 0: :2238 C j 0:5090 j 0: :2238 C j 0:5090 j 0: :2276 C j 0:2961 j 0: :2603 C 0:7382 j 0:0008

19 144 R. K. Singh and S. K. Goswami Appendix C. Bus Data of the IEEE 30-bus Test System [10] Table C1 Bus no. Type Load (p.u.) Rated bus voltage (kv) Bus voltage (p.u.) 1 Swing P -V 0:217 C j 0: P -Q 0:024 C j 0: P -Q 0:076 C j 0: P -V 0:0942 C j 0: P -Q P -Q 0:228 C j 0: P -V 0:3 C j 0: P -Q P -Q 0:058 C j 0: P -V P -Q 0:112 C j 0: P -V P -Q 0:062 C j 0: P -Q 0:082 C j 0: P -Q 0:035 C j 0: P -Q 0:09 C j 0: P -Q 0:032 C j 0: P -Q 0:095 C j 0: P -Q 0:022 C j 0: P -Q 0:175 C j 0: P -Q P -Q 0:032 C j 0: P -Q 0:087 C j 0: P -Q P -Q 0:035 C j 0: P -Q P -Q P -Q 0:024 C j 0: P -Q 0:106 C j 0:

20 Siting and Sizing of Distributed Generators 145 Appendix D. Parameters of 13-bus Radial Feeder [13] Table D1 Load at each bus (MW) Load profile Uniformly distributed Centrally distributed Increasing distributed size (MW) Total load (uniformly) Total load (centrally) Total load (increasingly) 3.9 MW 2.94 MW 3.51 MW Line parameters: R D 0:538 /km, X L D 0:4626 /km, R D 0:8608 p.u., X D 0:74016 p.u., line length between two buses: 2.5 km, bus voltage: 12.5 kv.