J. Electrical Systems x-x (2010): x-xx. Regular paper

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1 JBV Subrahmanyam Radhakrishna.C J. Electrical Systems x-x (2010): x-xx Regular paper A novel approach for Optimal Capacitor location and sizing in Unbalanced Radial Distribution Network for loss minimization A novel approach for investigating the problem of both choosing the optimal location and size of shunt capacitors in three-phase unbalanced radial distribution network (URDN) for loss minimization has been presented in this paper. There are two parts in the main objective function formulated: One, the cost related to capacitor purchase, capacitor installation and the other, cost of energy loss. This paper addresses the problem of choosing optimal locations and sizes for shunt capacitors in unbalanced radial distribution network with two algorithms:one,the capacitor placement node identification algorithm for selecting the best locations of capacitor placement, and another the variational technique algorithm for the sizing of capacitors, as per the standard size availability of capacitors. The objective function used in this paper aims at maximizing the net savings in the unbalanced radial distribution network by optimal capacitor placement and sizing. The results obtained with the proposed methodology for 25-bus and IEEE 37- bus Unbalanced Radial Distribution networks demonstrate its applicability. Keywords: Capacitor location, unbalanced radial distribution networks, power loss index (PLI), capacitor size. 1. Nomenclature URDN Unbalanced Radial Distribution Network V abc abc p, V q Voltage at p th bus and q th bus of phases a,b and c abc Y Admittance matrix a0 Q q, a IL q, b0 q c0 q Q, Q Rated value of shunt capacitors at phase a, b and c at bus q b IL q and c IL q Load models represented by the equivalent injected currents at Phase a,b and c at bus q LS a,ls b c,ls Power loss in the branch of phases a,b and c LP a,lp b c,lp Active Power loss in the branch of phases a,b and c LQ a,lq b c,lq Reactive Power loss in the branch of phases a,b and c K E Energy Cost (Rs/kWh) T Time Period ( hrs) TLP Total active power loss before capacitor placement TLP i Total active power loss after capacitor placement α Depreciation factor K I Installation cost (Rs. / location) K C Cost of the capacitor (Rs./kVAr) u (j) Capacitor bank rating max V q Maximum voltage magnitude at bus q max I Maximum current magnitude of branch P, Q Total active and reactive load of branch Corresponding author : JBV Subrahmanyam EEE Dept.,TRR Engineering College,Hyderabad,AP,India, jbvsjnm@gmail.com Copyright JES 2009 on-line : journal.esrgroups.org/jes

2 P max, Q max Q C PLI Rs. Source Maximum active and reactive powers of branch Reactive power injection Power Loss Index Indian currency Rupees 2. Introduction In an electrical utility distribution system, reactive currents produce power losses and result in increased ratings of distribution system components. Shunt capacitors are commonly used in distribution systems for reactive power compensation to improve voltage profile along the feeders, reduce power losses, and to increase the maximum power flow through lines, cables and transformers. These benefits depend greatly on how capacitors are placed in the distribution system. The general capacitor placement problem is how to determine the optimal locations and sizes to install capacitors at the buses of radial distribution systems [1-3]. Salama and Chikhani [4] developed a method for the control of reactive power in distribution systems at an end load for fixed load and varying load conditions, giving generalized equations for calculating the peak power and energy loss reductions, the optimum locations and rating of the capacitors. Genetic Algorithm has been used by Sundhararajan and Pahwa [5] for obtaining the optimum values of shunt capacitors. They have treated the capacitors as constant reactive power load. T.S.Abdul et al. [6] have proposed a heuristic technique, which brings about the identification of the sensitive nodes that have a very large impact on reducing the losses in the distribution systems. A systematic method of optimally locating and determining size of shunt capacitors for reactive power compensation on distribution feeders by taking into account the mutual coupling effect among phase conductors was developed by C.S.Chen et al.[7]. Lu and Hsu [8] have investigated the problem of reactive power and voltage control in a distribution substation. S.K. Goswami et al. [9] have developed heuristic rules for determination of the most sensitive capacitor location in a feeder segment. Using these rules, a technique was developed to identify a number of probable capacitor locations in a distribution network. A practical and easy way to implement solution technique for the capacitor placement problem based on a graph search method was proposed by J.C. Carlise and El-Keib[10]. G.Levitin et al. [11] formulated the capacitor allocation problem as complicated combinational problem and solved using Genetic Algorithm. Chiang et. al [12] has used the method of simulated annealing to obtain the optimum values of shunt capacitors for radial distribution networks. Genetic algorithm based solution is capable of determining a near global solution with lesser computational burden than the simulated annealing method hence H. Kim and S.K You [13] have used genetic algorithm for obtaining the optimum values of shunt capacitor bank. They have treated the capacitors as constant reactive power loads. These solutions mainly utilize the positive sequence network model and the associated power flows in formulating the problem. Hence, the results do not directly apply for systems containing feeders with missing phases, unevenly loaded feeders or shunt capacitors on single or double phase feeders in unbalanced distribution systems. This paper presents a novel approach to determine the best locations for capacitor placement and the optimal sizing of the capacitor bank in unbalanced radial distribution networks. The objective function formulated includes the energy cost, capacitor installation cost and purchase cost, so that the objective function is to be maximized for the net saving. In the proposed method, two algorithms are proposed for the optimal placement and sizing of shunt capacitors in the unbalanced radial distribution networks. The efficacy of the 2

3 proposed method is tested with the 25-bus and IEEE 37-bus unbalanced test distribution networks. 3. Modeling of components In a three phase unbalanced load flow of distribution system each individual component is mathematically represented by a model that approximates its behaviors. The network components include the distribution lines, shunt capacitors, cogeneration and transformers. In the power flow calculation, components are modeled by their equivalent circuits in terms of inductance, capacitance, resistance and injected current. 3.1 Distribution Line In general, the voltage at p th bus V p, and at q th bus, V q, are related by abc abc abc abc V = V I Y q p abc Where Y is the admittance matrix represented by aa ab ac Y Y Y abc ba bb bc Y = Y Y Y ca cb cc Y Y Y Shunt capacitance is also taken into consideration and the current injections at bus number k are expressed in terms of variables in the above. 3.2 Shunt Capacitors Shunt capacitors, which act as sources of reactive power, are often placed at strategic locations throughout distribution networks. Shunt capacitors are represented by their a0 b0 c0 equivalent injected currents. Let Q q, Qq and Q q be the rated value of shunt capacitors at phase a, b and c at bus q. The injected currents are a0 jq q * a V IC a q b0 jq b q ICq = * c V b IC q c0 jq q * V c 3.3 Transformers Copper loss and core loss (which is a function of the voltage on the secondary side of the transformer), winding connections, the phase shifting between primary and secondary windings and the off-nominal tapping are incorporated into transformer models. Transformer coreloss functions are represented in per unit of the system. Several different types of transformer connections are considered. 3

4 3.4 Load models Load models are represented by the equivalent injected currents, a IL q, b IL q and c IL q.the voltage dependency of loads is considered, which is a combination of constant power, constant current and constant impedance models. In addition, both grounded and ungrounded loads are considered. 3.5 Loss calculations For distribution line, the power loss in the branch of the feeder can be written as: a a a a a a a LS p ( ) q ( qp) LP jlq V I V I + b b b b b b b LS = LP + jlq = Vp ( I ) Vq ( Iqp ) c c c LS LP + jlq c c c c Vp ( I ) Vq ( I qp ) 3.6 Unbalanced Three phase load flow Since the determination of capacitor placement and size utilizes the unbalanced load flow solution, the later plays important role in the overall study. Voltage magnitude and angle at each bus for each phase can be exactly calculated as detailed network component modeling has been considered in the unbalanced load flow The following features are taken in to account in the load flow studies of unbalanced radial distribution networks. Sparse matrix techniques and data storage techniques are incorporated. Accurate modeling of network components (including shunt capacitance, series admittance, shunt capacitors, transformers, and voltage dependent load models) has been considered. No divergent cases have been encountered. Only a few iterations are required for each power flow study. 4. Problem Formulation The objective function of the present work is to determine the optimal size of the capacitors. The problem may be stated as, n i Max KE T [ TLP TLP ] α [ KI number of capacitor nodes KC u(j)] + (1) j = 1 Subjected to Voltage constraint Voltage magnitude at each node must lie with their permissible ranges to maintain power quality. min max V V V (2) q q q Current constraint Current magnitude of each branch (feeder, laterals, and switches) must lie with their permissible ranges. max I I (3) Power source limit constraint 4

5 The total loads of a certain partial network should not exceed the capacity limit of the corresponding power source. max P P (4) Q max Q (5) Where K E =Energy Cost (3.0 Rs/kWh) T = Time Period (8760 hrs) TLP = Total active power loss before capacitor placement TLP i = Total active power loss after capacitor placement α = Depreciation factor (0.2) K I =Installation cost (Rs.50,000 / location) K C =cost of the capacitor (Rs.200/kVAr) U( j )= Capacitor bank rating 5. Algorithm for capacitor placement node identification The algorithm for identifying the capacitor placement nodes best suitable for capacitor location is: 1. Read the given data of unbalanced radial distribution network. 2. Perform the unbalanced load flows and calculate the base case total active power loss. 3. By compensating the reactive power injections (Q C ) at each node (except source node) in all the phases, run the unbalanced load flows and calculate the active power losses in each case. 4. Calculate the power loss reduction and power loss indices using the PLI eqn. (6) 5. Select the capacitor placement nodes whose PLI > Tolerance obtained by experimentation 6. Stop. 6. Variational Technique Algorithm for obtaining the optimal Capacitor size Step 1: Read the system data and the capacitor placement nodes for capacitor location. Step 2: Set capacitor placement node place as k Step 3: Install a capacitor at bus k with size varying in integer steps of the standard size of capacitors. Perform the Unbalanced power flow and Select Q c at k bus that has the highest cost saving using the Eqn. (1) without violating the constraints. Step 4: Repeat step 3 for m buses chosen for placing new capacitors. Step 5: Adjust the first capacitor (i=1) in integer steps while keeping others fixed. Select Q c for the first one that has the maximum cost saving with out violating the constraints. Repeat for i=2, m. Step 6: Repeat step 5 if the maximum saving still increases without violating the constraints. Step 7: Stop 5

6 7. Capacitor placement node identification algorithm applied for 25-bus unbalanced radial distribution system The proposed capacitor placement node identification method for capacitor location is explained with the 25- bus system whose line and load data are given in Appendix (A).After performing the load flows, the base case total active power loss obtained is KW.After compensating the reactive power injection at each node in all the phases equal to the local reactive load at that particular node, perform the load flows and record the total active power loss and loss reduction in each case. Table-1 shows the results for 25- bus system. Table-1 power loss reductions for 25-bus URDN compensating Qc at Node no. Total Active Power loss after compensating Qc at each node (in all the phases)(kw) Loss reduction(kw) The power loss indices (PLI) are calculated as ( Loss. reduction[ i] Min. reduction ) PLI[] i = (6) ( Max. reduction Min. reduction ) The PLI was used to select the capacitor placement locations for placing the capacitor in the distribution feeders. The determination of these capacitor placement locations basically helps reduce the search space for the optimization procedure. The PLI is a systematic procedure to select those locations which have maximum impact on the system real power losses, with respect to the nodal reactive power. The power loss indices (PLI) obtained for 25-bus system are given in table-2 6

7 Table-2 power loss indices for 25-bus URDN Node no. Power loss Index(PLI) The most suitable nodes for the capacitor placement are chosen based on the condition that PLI to be greater than a PLI tolerance value that lies between 0 and 1. The tolerance value for a chosen system is selected by experimenting with different values of PLI in descending order of the PLI limits. The best out of the tolerance values gives the highest net profit, satisfying the system constraints. Fig.1 plot between nodes and PLI for 25 bus URDN 7

8 Fig.1 shows power loss index plot for the 25 bus URDN. From experimentation, the best value of PLI tolerance obtained is 0.4 and hence nodes 9,12,14 and 15 are identified as the most sensitive and best capacitor placement nodes for the capacitor placement for maximum net saving(table-3). Table-3 Selection of capacitor placement nodes in 25-bus URDN Tolerance Node numbers Total capacitor size(kvar) Net Saving (Rs) ,34, ,12,14, ,54, ,10,11,12,13,14,15, ,30, Results Example 1: 25-bus system The proposed algorithm is tested on the 25-bus unbalanced radial distribution network shown in Fig.2.The line and load data are given in Appendix A. The voltages before and after compensation are shown in table.4. The total active power losses, minimum voltages and summary of test results for the 25 bus URDN before and after compensation are given in table.5. From the results, the size of the capacitor banks obtained at buses 9, 12, 14 and 15 are 450, 300, 300 and 450 kvar respectively. It has been observed that the total active power losses are reduced from kw to kw and the minimum voltages in phases a, b and c are improved from , and p.u to0.9355, and p.u respectively after installing the capacitor banks. Table 4 Voltage profile for the 25bus URDN Bus No. before Compensation After Compensation Va (p.u) Vb (p.u) Vc (p.u) Va (p.u) Vb (p.u) Vc (p.u)

9 Fig. 2 Single line diagram of 25-bus URDN 9

10 Table -5 Summary of phase wise test results for the 25 bus URDN Description Capacitor placed at node Before Compensation After Compensation a b c a b c 3 x 50 3 x x 50 2 x 50 2 x 50 2 x 50 3 x 50 3 x 50 3 x 50 2 x 50 2 x 50 3 x 50 Minimum Voltage Voltage regulation (%) Improvement of Voltage regulation (%) Active Power Loss (kw) Total Active Power Loss reduction (%) Reactive Power Loss (kvar) Total Reactive Power Loss reduction (%) Total Demand (kw) Total Released Demand (kw) Total Reactive Power Demand (kvar) Total Released Reactive Power Demand (kvar) Total Feeder demand (kva) Total Released Feeder demand (kva) Net Saving (Rs./annum) - 11, 54, 738 Example:2 IEEE 37-bus system The proposed algorithm is tested on IEEE 37 bus unbalanced radial distribution network shown in Fig. 3. The line and load data are taken from Radial Distribution test feeders [14]. The capacitor bank considered here is delta connected. After compensating the reactive power injection at each node in all the phases load flows are performed and the total active power loss, loss reduction and power loss indices obtained in each case are shows in table 6. 10

11 Fig. 3 Single line diagram of IEEE 37-bus URDN Table-6 Power loss reductions and power loss indices for 37-bus URDN Total Active Loss compensating Qc Power loss after Reduction (KW) PLI at Node no. compensating Qc at each node (in all the phases)(kw)

12 Fig. 4 Plot between nodes and PLI for 37 bus URDN Fig. 4 shows power loss index plot for 37 bus URDN. From experimentation the best value of PLI tolerance obtained is 0.6 and hence nodes 2, 10, 11, 33 and 37 are identified as the most sensitive and best capacitor placement nodes for the capacitor placement for maximum net saving.(table-7) 12

13 Table-7 Selection of capacitor placement in IEEE 37-bus URDN for capacitor placement Tolerance Node Total capacitor Net Saving (Rs) numbers size(kvar) ,65, ,72, ,41,610 The voltages before and after compensation are given in Table.8. The total active power losses, minimum voltages and summary of test results for the 37 bus URDN before and after compensation are given in Table.9. From the results, the size of the capacitor banks obtained at buses 2, 10, 11, 33 and 37 are 300, 150, 150, 300, 150 kvar respectively. It has been observed that the total active power losses are reduced from kw to kw and the minimum voltages in phases a, b and c are improved from , and p.u to , and p.u respectively after installing the capacitor banks. Table 8 Voltage profile for IEEE 37bus URDN Bus No. before Compensation After Compensation Va Vb Vc(p.u) Va (p.u) Vb (p.u) Vc (p.u) (p.u) (p.u)

14 Table -9 Summary of phase wise test results for 37 bus URDN Before Compensation After Compensation Description a b c a b c Capacitor placed at node x 50-1 x 50 2 x 50 1 x 50 2 x 50-1 x 50 2 x 50 1 x 50 2 x 50-1 x 50 2 x 50 1 x 50 Minimum Voltage Voltage regulation (%) Improvement of Voltage regulation (%) Active Power Loss (kw) Total Active Power Loss reduction (%) Reactive Power Loss (kvar) Total Reactive Power Loss reduction (%) Total Demand (kw) Total Released Demand (kw) Total Reactive Power Demand (kvar) Total Released Reactive Power Demand (kvar) Total Feeder demand (kva) Total Released Feeder demand (kva) Net Saving (Rs./annum) - 3,72,739 14

15 9.0 Conclusion In this paper a novel approach has been presented for optimal capacitor placement and sizing to improve the voltage profile and minimize the power losses in unbalanced radial distribution networks. The proposed method to determine suitable capacitor placement nodes for capacitor location is based on power loss indices in unbalanced radial distribution networks. Capacitor-sizing problem for loss minimization using variational technique algorithm has also been presented. Results obtained demonstrate the applicability and efficacy of the proposed method for capacitor placement and sizing in the 25-bus and IEEE 37 bus unbalanced radial distribution networks. Appendix A Base kv: 4.16, Base MVA: 30 Table A1 Load data and line connectivity of 25-bus unbalanced system branch Sending Receiving Conductor Length, Receiving end load in kva End End type ft A phase B phase C phase j j j j j j j j j j j j j j j j j j j j j j j j j j j j j j j j j j j j j j j j j j j j j j j j j j j ` j j j j j j j j j j j j j j j35 Type a 1 b Impedance in ohms/mile a b c j j j j j j c j j j

16 a j j j b j j j c j j j a j j j b j j j c j j j References [1] J. J. Grainger and S. H. Lee, Optimum size and location of shunt capacitors for reduction of losses on distribution feeders, IEEE Trans. on Power Apparatus and Systems, Vol. PAS-100, pp , March, [2] M. Baran, F. Wu, "Optimal capacitor placement on radial distribution system", IEEE Trans. on Power Delivery, Vol. 4, No. 1, pp , January, 1989 [3] H. Chiang, "Optimal capacitor placements in distribution system: Part I, Part II", IEEE Trans. on Power Delivery, Vol. 5, No. 2, pp , January, [4] M.M.A.Salama, A.Y.Chikhani, A simple network approach to the VAR controlled problem for radial distribution systems, IEEE Trans. on Power Delivery, Vol.8, No.3, 1993, pp [5] S.Sundharrajan and A.Pahwa, Optimal selection of capacitors for radial distribution systems using a genetic algorithm, IEEE Trans. on Power Systems. Vol.9, August 1994, pp [6] T.S.Abdul-Salam, A.Y.Chikhani, R.Hackam, A new technique for loss reduction using compensating capacitors applied to distribution systems with varying load condition, IEEE Trans. on Power Delivery, Vol.9, No.2, 1994, pp [7] C.S.Chen, C.T. Hsu, Y.H.Yan, Optimal distribution feeder capacitor placement considering mutual coupling effect of conductors, IEEE Trans. on Power Delivery, Vol.10, No.2, Apr 1995, pp [8] F.C.Lu, Y.Y.Hsu, Reactive power / Voltage control in a distribution sub-station using dynamic programming, IEE Proc-C, Vol.142, No.6, Nov.1995, pp [9] S.K.Goswami, T.Ghose, S.K.Basu, An approximate method for capacitor placement in distribution system using heuristics and greedy search technique, Electric Power System Research, Vol.51, 1999, pp [10] J.C.Carlise, A.A.El-Keib, A graph search algorithm for optimal placement of fixed and switched capacitors on radial distribution systems, IEEE Trans. on Power Delivery, Vol.15, No.1, Jan. 2000, pp [11] G.Levitin, A.Kalyuzhny, A.Shenkaman, Optimal capacitor allocation in distribution systems using genetic algorithm and a fast energy loss computation technique, IEEE Trans. on Power Delivery, Vol.15, No.2, Apr. 2000, pp [12] [12] H-D. Chiang, J-C. Wang, J. Tong and G. Darling, Optimal Capacitor placement in Large-Scale Unbalanced Distribution System: System Modeling and A new Formulation, IEEE Trans. on Power systems, vol.10, No. 1, Feb 1995, pp [13] [13] H. Kim, S-K. You, Voltage Profile Improvement by capacitor Placement and control in unbalanced distribution Systems using GA, IEEE power Engineering Society Summer Meeting, 1999, Vol. 2, pp [14] [14] Radial Distribution test feeders