THERE has been a growing interest in the optimal operation

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1 648 IEEE TRANSACTIONS ON POWER SYSTEMS, VOL. 22, NO. 2, MAY 2007 A New Optimal Routing Algorithm for Loss Minimization and Voltage Stability Improvement in Radial Power Systems Joong-Rin Shin, Member, IEEE, Byung-Seop Kim, Jong-Bae Park, Member, IEEE, and Kwang Y. Lee, Fellow, IEEE Abstract This paper presents an optimal routing algorithm (ORA) for minimizing power loss and at the same time maximizing the voltage stability in radial power systems. In the proposed ORA, a voltage stability index (VSI) for real-time assessment is introduced based on the conventional critical transmission path framework. In addition, the algorithm can automatically detect the critical transmission paths that will result in voltage collapse when additional real or reactive loads are added. To implement effective ORA, an improved branch exchange (IBE) method has been developed based on a loss calculation index and tie-branch power flows that is suited for real-time applications. The proposed algorithm has been tested in the IEEE 32- and 69-bus systems as well as in a large-scale Korea Electric Power Company 148-bus system to show its effectiveness and efficiency. Index Terms Branch exchange, combinatorial optimization, loss minimization, optimal routing algorithm (ORA), radial power system, voltage stability index (VSI). I. INTRODUCTION THERE has been a growing interest in the optimal operation of radial networks during the past decades, particularly in the area of distribution system automation for improved economy as well as security. Therefore, modifying the topological structures of the radial power systems from time to time, by changing the open/close states of the sectionalizing and tie switches to transfer loads from one transmission path to another, can significantly improve the operation conditions of power systems. When the loads are efficiently rescheduled by a suitable routing algorithm, power loss along the transmission paths can be reduced. The purpose of this paper is to develop an optimal routing algorithm (ORA), which not only minimizes the power loss but also, at the same time, enhances the voltage stability of the radial power system. Along this line, several analytical techniques for real-world applications have recently been proposed Manuscript received December 16, 2004; revised September 5, This work was supported by MOCIE under the IERC program. Paper no. TPWRS J.-R. Shin and J.-B. Park are with the Department of Electrical Engineering, Konkuk University, Seoul , Korea ( jrshin@konkuk.ac.kr; jbaepark@konkuk.ac.kr). B.-S. Kim is with the LS Industrial Systems Co. Ltd. (formerly LGIS), Anyang-Shi, Kyongki-Do , Korea ( bskim3@lsis.biz). K. Y. Lee is with the Department of Electrical Engineering, The Pennsylvania State University, University Park, PA USA ( kwanglee@psu.edu). Color versions of Figs. 6, 7, and 9 are available online at ieee.org. Digital Object Identifier /TPWRS to assess the risk of voltage instability in radial power systems [1], [2], [15]. The voltage stability is a very important issue in power system operation and planning since voltage instability may lead to voltage collapse and possibly the total system blackout [3]. The voltage instability can occur when a power system is heavily loaded in transmission lines and/or lacks in local reactive power sources [5], [6]. Although the voltage stability problem is in its nature a dynamic one, a great deal of the research work has been devoted to the static methods in real-time applications. A Thevenin equivalent circuit framework is applied by Lachs and others [5] to study voltage collapse phenomenon at a load bus, and the intimate relationship between voltage stability and power loss has been tackled in [4]. The voltage stability problem can be considered as a non-issue in distribution systems. However, in modern distribution systems, as they become more complex and large, the issue can be one of the critical problems. This issue is addressed in references [1], [2], [4], and [7]. In this paper, a new ORA is developed not only to reduce the power loss but also to improve the voltage stability in radial power systems. In addition, the proposed algorithm can efficiently perform the rapid assessment of the voltage stability margin and show the critical transmission path (CTP) when the open/close states of the sectionalizing and tie switches are changed. The problem has been formulated as a combinatorial optimization problem where its objective is the maximization of a newly devised voltage stability index (VSI), which basically is inspired by a conventional approach based on the voltage phasor approach [7]. Additionally, in the proposed ORA, the conventional branch exchange method has been improved to reduce the computational burden. An improved branch exchange (IBE) method is based on a loss calculation index (LCI) and a tie branch power flow (TBP) when assessing the impact of a branch exchange on power loss in an analytical manner. To find an initial tree during the initialization phase of the ORA, a genetic algorithm (GA) [12] is used to overcome the local optimum traps existing in the conventional branch exchange method. The proposed algorithm has been evaluated in the IEEE 32-bus and IEEE 69-bus systems [10], [11] and in the 148-bus system of the Korea Electric Power Corporation (KEPCO) [14] to demonstrate its favorable performance. II. PROBLEM FORMULATION Traditionally, the network reconfiguration problem in a radial power system is to find a configuration that has the minimum /$ IEEE

2 SHIN et al.: NEW ORA FOR LOSS MINIMIZATION AND VOLTAGE STABILITY IMPROVEMENT 649 power loss while the system constraints are satisfied [11]. However, in this paper, the optimal routing problem is formulated as a network reconfiguration problem that can result in both the loss minimization and the voltage stability enhancement. The basic network for an optimal routing problem starts from a simple radial network with series impedances at branch of, constant demands at bus of, and complex line flow at branch of as shown in Fig. 1, where is the bus voltage phasor at bus. Due to a large number of switching combinations during the branch exchange processes, the optimal routing problem is usually characterized as a combinatorial optimization problem. The first goal of the combinatorial optimization problem is to minimize the power loss in the radial power system. The real power loss function,, and the constraint for a radial network configuration,, can be, respectively, described as follows: where (1a) (1b) Fig. 1. One-line diagram of a radial network. Fig. 2. Two-bus radial power system. where is the total number of feasible network configurations. The solution for a configuration with minimum power loss can be found through the repeated iterations in this combinatorial optimization problem. However, this paper introduces an additional goal of improving voltage stability while minimizing the power loss. This goal can be achieved by maximizing a VSI as follows: such that (2) is the voltage phasor and magnitude at bus, where is the number of load buses except the supply bus, is the number of total buses. Additionally, is defined to have the value of one, if a loop network [10] that includes both bus and can be composed in a network configuration; otherwise, it becomes zero. The first term in (1b) is the condition for not having any loop when all load buses are supplied power from the source, and the second term is for not having any isolated bus. The third term in (1b) is for detecting any non-radial network configuration with isolated loop network(s) whose values of the first and second term in (1b) are both zero. All possible cases illustrating the constraint (1b) are presented in Appendix A. The usual network reconfiguration problem is to find a configuration that reduces the power loss function (1a) while satisfying the radial constraint (1b). For a given configuration, there is more than one configuration that can reduce the power loss. The following defines the set of such configurations: where equality constraint of power balance equations; apparent power and its limit at bus. The VSI will be developed in Section III. III. VOLTAGE STABILITY INDEX FOR RADIAL POWER SYSTEMS A. Critical Transmission Path A radial transmission path with buses incurs line loss due to real and reactive loads (see Fig. 1). The loads at intermediate buses cause voltage drops along the paths. The key idea of the critical transmission path (CTP) is to project the voltage drop phasor at bus into the voltage phasor of the supply bus [7]. Therefore, the CTP can be defined as a series of buses with declining voltage magnitude, and the critical bus (e.g., the end bus in the CTP) can face with voltage collapse when additional real or reactive loadings are required. In this paper, this idea of CTP has been partially adopted for voltage stability assessment in a general radial network system. B. Derivation of Voltage Stability Index The VSI is derived from a sample power system with two buses as shown in Fig. 2, which can be expanded to an -bus power system.

3 650 IEEE TRANSACTIONS ON POWER SYSTEMS, VOL. 22, NO. 2, MAY 2007 where the equivalent power injection and the impedance are defined by Fig. 3. Voltage phasor diagram of a power system with two buses. From the two-bus power system, the power flow equation and its Jacobian matrix can be derived as follows: (3a) (3b) where and imply, respectively, the real and imaginary parts of the bus admittance matrix. If we consider bus 1 as the slack bus, the condition of the singularity can be derived from the determinant of the Jacobian matrix. Since the Jacobian matrix contains state information of a network, a critical operating point can be defined from its singularity condition where denotes the determinant. The singularity condition (4) yields the following compact form, which is derived in [7] or. This condition can be satisfied by where is the direct-axis component of the voltage drop projected onto as illustrated in the phasor diagram of the two-bus system shown in Fig. 3. The voltage drop phasor in Fig. 3 can be also expressed in a rectangular form as follows: The voltage drop phasor can be expressed as a product of the impedance and the current in the line, where the current is due to the voltage phasor and injected power, as follows: From (7) and (8), the projected direct axis component can be replaced by the real part of (8). Therefore, the voltage stability condition (6) for the two-bus system becomes (4) (5) (6) (7) (8) The equivalent impedance in (10) is derived in Appendix B, while a similar approach can be found in [16]. Here, and imply the power loss and power load of branch along the CTP. Note that when the VSI approaches zero, the power transfer on the critical transmission path becomes unstable, resulting in the voltage collapse. IV. IMPROVED BRANCH EXCHANGE METHOD The branch exchange operation was first introduced to represent a switching option by closing a single tie switch and opening a single sectionalizing switch to preserve the radial property of feeders [9]. Recently, Baran and Wu [10] have developed an effective loss reduction formula. However, their method requires a relatively long computation time in identifying the branches to be exchanged. Using the load flow analysis, it calculates the change in the loss for each selected switching set in a loop network, at each search level. Therefore, in this paper, an improved branch exchange (IBE) method for the ORA has been developed to overcome the inherent dimensionality problem as well as the aforementioned calculation burden. A. Tie Branch Power Equation The main purpose of a tie branch power (TBP) flow equation is to directly calculate the power flow change along the closed tie branch without the iterative load flow analysis. For this formulation, we introduce a loop network with a tie branch as shown in Fig. 4(a) [10]. By closing a single switch on a tie branch and opening a single sectionalizing switch on an adjacent branch, a load on one side of the tie branch is transferred from L-side to R-side due to the branch exchange. Then, a new power flow,, along the closed tie branch, say,, will be enacted as illustrated in Fig. 4(b). The TBP of the closed tie branch satisfies the following condition: (11) By grouping the real and imaginary parts and omitting the common term in the real power flow and reactive power flow in (11), the following set of real and reactive power flow equations are obtained: (9) where is taken as the reference phasor. By extending the voltage stability condition (9) to an -bus system, the VSI for an -bus system is now defined as follows: (10) (12a) (12b)

4 SHIN et al.: NEW ORA FOR LOSS MINIMIZATION AND VOLTAGE STABILITY IMPROVEMENT 651 where voltage is assumed to be fixed to 1.0 p.u. in all buses of the loop network, and and, respectively, denote the power loss due to real power flow and reactive power flow in branch. Power loss changes when a BE takes place. Suppose a BE takes place between branches and, and divide a loop network with L-side and R-side as illustrated in Fig. 4(a); then the power loss decreases in branches in L-side but increases in R-side. Therefore, the power loss in a branch can be determined as follows: (16a) (16b) Fig. 4. Loop network associated with tie branch (t). (a) Before branch exchange between branches (k) and (t). (b) After branch exchange between branches (k) and (t). The equations in (12) are in the quadratic form and the TBP solutions can be found as the roots of the real and reactive power flow equations as where and are real and reactive power flow in branch, and are the ATBP computed by (14), and and are, respectively, the L-side and R-side shown in Fig. 4(a). Here, and mean estimated power loss due to the BE. For an arbitrary branch exchange between tie branch and an adjacent branch, the changes of real part loss and reactive part loss in any branch are described as follows: where (13) (17) where and are defined in (15), which are, respectively, the power loss due to real power flow and reactive power flow in branch before the BE. Therefore, the total real power changes due to a BE between tie branch and an adjacent branch in a loop network can be evaluated in both L-side and R-side as follows: (18a) Equation (13) gives an explicit solution of TBP once the voltage is given. In this paper, we will use the approximate TBP (ATBP) by substituting with an approximate voltage in (13), where the approximate voltage is the voltage obtained by the load flow calculation in the previous search level. Implicit forms of the ATBP can be expressed as follows: (14) This ATBP equation can be effectively used to find the branch power in lieu of iterative load flow calculations during branch exchanges in a loop network system. This reduces the computational requirement drastically. B. Loss Calculation Index To find the optimum branch in a loop, it is required to estimate the change in the loss for each branch exchange. First consider the real power loss (1a) in its simplified form (15) and the loss calculation index is defined by (18b) (19) Finally, the updated power flow covering all branches can be calculated as follows: (20a) (20b) C. Selection of Optimal Branch via Loss Calculation Index Module The optimal branch to be exchanged can be found by the proposed loss calculation index (LCI) module, which is summarized in the following steps. Step a) Perform a BE between branch and an adjacent branch for a loop network. Step b) Calculate by (14).

5 652 IEEE TRANSACTIONS ON POWER SYSTEMS, VOL. 22, NO. 2, MAY 2007 TABLE I SUMMARY OF TEST SYSTEMS Fig. 5. Solution procedure of the optimal routing algorithm. Fig. 6. VSI curve of the 69-bus system. Step c) Calculate, and by (18) and (19). Step d) Go to step a); repeat for all adjacent branches for all loop networks. Step e) Determine the branch with the highest as a tentative optimum loop network. Step f) Update power flow in all branches in the current optimum loop network by (20). Step g) If all branches in the tentative optimum loop satisfy the network constraints of (1b), select the loop as the best candidate to perform the BE; otherwise, go to step e) for a new tentative optimum loop with the next highest. V. SOLUTION PROCEDURE The solution procedure for the optimal routing problem is described in Fig. 5. The procedure starts from the condition whether or not the initial network is satisfied by the constraint (1b). If it is not a radial network where all demand buses are connected, then an initial radial network is constructed by using a GA [12]. On the other hand, if it is already a radial network where all demand buses are connected, then it starts directly from the second step and perform the loss calculation index module to find the optimum branch, as described in Section IV-C. Then a branch exchange is performed for the optimum branch and state vector is renewed by a load flow. In this paper, the Distflow method [11] is adopted as a load flow analysis tool. It then calculates the network parameters, i.e., power loss, power load, and bus voltages,, and along the critical transmission path. Finally, two conditions are checked in sequence: the loss minimization criterion and the voltage stability improvement. The procedure will be repeated until no improvement is made on both the loss minimization and the voltage stability. VI. CASE STUDIES AND DISCUSSIONS The proposed optimal routing algorithm is tested on the IEEE 32-bus and IEEE 69-bus radial power systems [10], [11] and on the 148-bus power system [14] of the KEPCO. The ULTC and shunt capacitor actions are blocked, and the loads are considered as constant power loads. The algorithm is implemented in a Pentium 400-MHz IBM-compatible PC. The following standard units are used in all tables and figures: second (sec.), per unit (p.u.), kw, and kvar. Table I shows a brief summary of the test systems. However, due to space limitation, not all the results will be presented. A. Voltage Stability Index Assessment Fig. 6 shows the VSI curve of the CTP in the IEEE 69-bus system. The CTP is constructed by the proposed optimal routing algorithm (ORP) and is composed of buses 0, 1, 2, 2e, 3, 4, 5, 6, 7, 8, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, and 54. The loadings of all buses are simultaneously increased by the same ratio of S/S-base where S-base is the initial apparent load in each load bus. When S/S-base is 3.07, the critical voltage of was detected at bus 54, the end bus in the CTP, with the VSI of Table II illustrates the results of the CTP of the 148-bus KEPCO system, which are obtained by the proposed ORP. In the table, the buses along the CTP are ordered in descending magnitudes of the bus voltages. The final VSI is given, along with the complex power load,, and the complex power loss,, along the CTP and the critical voltage,, which is the voltage of the last load bus (Bus 138) in the CTP. B. Results of the Improved Branch Exchange Method Table III shows the obtained results from the TBP equation when real power loadings are sequentially increased. Case 1 is the results obtained by the load flow analysis, which is considered as the base case for comparison. Case 2 is the results obtained from the TBP (13). In this case, we observe that the computed TBP is exact (i.e., all error rates are 0% in comparison

6 SHIN et al.: NEW ORA FOR LOSS MINIMIZATION AND VOLTAGE STABILITY IMPROVEMENT 653 TABLE II RESULTS OF THE CTP OF THE KEPCO 148-BUS SYSTEM TABLE III EXAMINATIONS OF THE TBP EQUATION FOR THE 69-BUS SYSTEM TABLE IV COMPARISONS OF CONVERGENCE PROBABILITIES TABLE V COMPARISONS OF AVERAGE COMPUTATION TIME with Case 1). Case 3 is the results obtained when the approximate voltage is used in computing the TBP, i.e., ATBP (14). In this case, errors at the voltage levels higher than 0.9 are negligible (e.g., 0.147% at the voltage level when the loading is ten times of the base loading). These results show that the ATBP (14) can practically replace the conventional load flow analysis and can drastically reduce the computation time. In Case 4, the voltage magnitude is assumed constant, in which case the error rates are relatively large compared to Case 3. Table IV shows the comparison between the proposed IBE method and Baran and Wu s method [10] in terms of the convergence probabilities in constructing an initial radial network. The results are based on the average from 100 trials. An initial radial network is determined through a random creation in Baran and Wu s method; on the other hand, a GA method [12] is used in the proposed IBE method. It is evident that GA performs much better than the random selection in constructing the initial radial network. Table V shows the comparison of the computation time between the proposed IBE method and Baran and Wu s method [10]. For the proposed IBE, the average computation time does not include the GA computation time, which was used only once to obtain an initial topology. Here, the initial topologies for 32-, 69-, and 148-bus test systems are the same ones originated from [10], [13], and [14]. It should be noted that the number of load flow calculations is much less for the proposed IBE method compared to Baran and Wu s method, because the TBP equation replaces the load flow. The number of iterations, on the other hand, only doubles for the IBE method compared to Baran and Wu s method. C. Main Results of the Optimal Routing Algorithm Table VI provides comparisons between the proposed IBE method and other conventional studies to show the reliability of the proposed algorithm in the three test systems. For the 32-bus test system [10], the proposed IBE provides the same optimal result with Baran and Wu s [10], Gomes, and other methods described in [17] in terms of tie-branch configurations. For the 69-bus system, the comparison is limited to the

7 654 IEEE TRANSACTIONS ON POWER SYSTEMS, VOL. 22, NO. 2, MAY 2007 TABLE VI COMPARISONS OF THE BE METHODS Fig. 8. Detected CTP in the final of the 148-bus system. Fig. 9. Comparisons of voltage profiles of the 148-bus system before/after BE. Fig. 7. Optimal routing process of the 148-bus system. Jasmon s approach [13] due to the lack of information. The similar situation is happened for the 148-bus KEPCO distribution system [14]. However, the contribution of our research will be that better solutions are obtained than the published ones in [13] and [14], although we cannot guarantee that the obtained solutions are global for the 69- and 148-bus systems. In the 69-bus system, the IBE method gives one tie branch, 58(46, 47), different from the Jasmon s [13], resulting in lower power loss. In the 148-bus system, three tie branches, 34(25, 34), 113(104, 113), and 159(105, 113), are different from the Jeon et al. s [14], resulting in greater reduction in power loss. This table shows that the proposed IBE method is compatible with other existing methods, with improved power loss minimization. However, it should also be noted that the IBE method not only improves the power loss minimization but also improves the voltage stability. Fig. 7 illustrates the convergence characteristics of the VSI and power loss in the KEPCO 148-bus system. In the 148-bus system, the VSI increased from to , resulting from the application of the proposed ORA (i.e., VSI is improved by 38.11%, while the power loss is decreased by 61.19%). Fig. 8 shows the result obtained in the final step of the 148-bus system, which is considered as the optimal solution for the reconfiguration of the system. In the initial network topology, the detected CTP by GA was composed of buses 0, 1, 2, 5, 9, 13, 20, 29, 39, 51, 61, 78, 67, 57, 46, 56, 66, 77, 87, 98, 108, 115, 122, 129, and 138. In the figure, bold lines mean the detected CTP in the final iteration, and dotted lines imply open tie switches. As shown in the figure, we can see that the CTP is successfully connected in a radial topology. Fig. 9 shows that voltage profiles in the 148-bus system are improved in all buses after the optimal routing process due to the improved voltage stability. We have considered the power loss minimization as the primary objective with voltage stability as the secondary, as can be seen in Fig. 5. The VSI provides distribution network operators with information on the voltage stability margin and critical transmission path. Our approach can provide direct and useful information on critical voltage stability problems by considering the voltage stability index. For example, in a critical situation, we can employ the network configuration with better

8 SHIN et al.: NEW ORA FOR LOSS MINIMIZATION AND VOLTAGE STABILITY IMPROVEMENT 655 voltage stability margin while sacrificing the power loss minimization. The following example shows the trade-off between the power loss and the voltage stability index in the IEEE 32-bus test system [10]: solution with the loss minimization as the primary objective: [kw], [p.u.], tie branches (7, 9, 14, 32, 37) as described in Table VI; solution with voltage stability as the primary objective: [kw], [p.u.], tie branches (7, 9, 14, 32, 28). This example shows that the VSI can be improved by 3% at the expense of increased power loss of 0.31%. VII. CONCLUSION This paper has proposed a new optimal routing algorithm to minimize power loss and at the same time to maximize the voltage stability in radial power systems. The main features of this paper can be summarized as follows. An effective VSI has been developed to assess the voltage stability, which is well suited for frequent switching options. As shown in the case studies, the voltage stability of a radial system can be rapidly assessed by the proposed VSI. Furthermore, information of all buses along the CTP and the critical bus can be automatically detected during the BE process. Therefore, operators can prepare a preventive action scheme in a sudden contingency or disturbance environment that may lead to the voltage collapse in a regional distribution system. The algorithm can perform both dual and single optimization based on the priority of operational conditions. For example, in an ill-conditioned distribution system, operators can employ the network configuration based on the VSI only, or dual optimization with both VSI and loss minimization. On the other hand (i.e., in a well-conditioned system), it may be sufficient only to consider the loss minimization objective function. Operators can use lookup tables focused on the ill-conditioned system environments, which could provide them with operational information to improve the voltage stability while sacrificing the loss minimization target. Additionally, the IBE method is proposed to reduce calculation time. The IBE method is based on the loss calculation index. The index can be used as an effective measure to assess the variation of power loss without solving the iterative load flow during the BEs in a loop network. For estimation of the new tie-branch power flow resulting from load transfer during the BEs, the newly derived TBP equation is used with reasonable accuracy. The ORA also has adopted the GA as a global search algorithm to search for an initial radial network. As shown in numerical experiments, it is assured that this hybrid method is very effective in large-scale systems. APPENDIX Fig. 10. Four networks to illustrate the concept of (1b). are supplied power from the source (i.e., node 0). Although the topology of Case B is in a radial form, one load bus (i.e., node 4) is not supplied power from the source. The other two cases (i.e., Cases C and D) have loop networks, where all load buses are supplied power in Case C, while three load buses are isolated in Case D. We will verify (1b) numerically for each case. 1) Case A: Since and Note that all the values of (for ) become 1 since all nodes have at least one connection with other nodes. Therefore, the second term in (1b) becomes This case has to be checked additionally with the third term in (1b) because both the first and second term are equal to zero. Since all values of are zero, the third term in (1b) becomes and thus,. Therefore, we can start the optimal routing process with this kind of initial topology. 2) Case B: Since and Moreover Therefore,, which means that this topology violates the constraint (1b). 3) Case C: Since and A. Example Illustrating Constraint (1b) To illustrate the constraint (1b), consider the following 4 cases in Fig. 10. Case A is the only radial network where all load buses

9 656 IEEE TRANSACTIONS ON POWER SYSTEMS, VOL. 22, NO. 2, MAY 2007 In Fig. 12, we can define the following variables: Fig. 11. Simple network of a critical transmission path. (B1a) (B1b) (B1c) Fig. 12. Equivalent network of the driving point. Combining (B1c) and (B1b) yields Moreover (B2) In general, the sending end voltage at the first stage is fixed to a constant value ( [p.u.]), and we can finally derive the equivalent impedance of the simple network as follows: Therefore,, which means that this topology also violates the constraint (1b). 4) Case D: Since and (B3) Moreover This case also has to be checked with the third term in (1b). Since, the third term becomes Thus,. The example illustrates that all terms in (1b) need to be checked that there is no loop and no buses are isolated. B. Derivation of Equivalent Impedance in (10) If a CTP in a radial system is composed of constant power demands as illustrated in Fig. 11, each branch causes line power losses. In Fig. 11, denote line power loss, and mean the injected power flow in the first sending end. From Fig. 11, we can define the equivalent network of the current driving point as shown in Fig. 12. REFERENCES [1] P. Ju and X. Y. Zhou, Dynamic equivalents of distribution systems for voltage stability studies, Proc. Inst. Elect. Eng., Gen., Transm., Distrib., vol. 148, no. 1, pp , Jan [2] R. Lind and D. Karlsson, Distribution system modelling for voltage stability studies, IEEE Trans. Power Syst., vol. 11, no. 4, pp , Nov [3] J. R. Shin, B. S. Kim, M. S. Chae, and S. A. Sebo, Improvement of the precise P-V curve considering the effects of voltage dependent load models and transmission losses for voltage stability analysis, Proc. Inst. Elect. Eng., Gen., Transm., Distrib., vol. 149, no. 4, pp , Jul [4] B. Venkatesh, G. Sadasivam, and M. A. Khan, A new optimal reactive power scheduling method for loss minimization and voltage stability margin maximization using successive multi-objective fuzzy LP technique, IEEE Trans. Power Syst., vol. 15, no. 2, pp , May [5] W. R. Lachs and D. Sutanto, Different types of voltage instability, IEEE Trans. Power Syst., vol. 9, no. 2, pp , May [6] P. Kundur, Power System Stability and Control. New York: McGraw- Hill, [7] F. Gubina and B. Strmcnik, Voltage collapse proximity index determination using voltage phasors approach, IEEE Trans. Power Syst., vol. 10, no. 2, pp , May [8] A. M. Chebbo, M. R. Irving, and M. J. H. Sterling, Voltage collapse proximity indicator: Behavior and implications, Proc. Inst. Elect. Eng., C, vol. 139, no. 3, pp , May [9] S. Civanlar, J. J. Grainger, and S. H. Lee, Distribution feeder reconfiguration for loss reduction, IEEE Trans. Power Del., vol. 3, no. 3, pp , Jul [10] M. E. Baran and F. Wu, Network reconfiguration in distribution systems for loss reduction and load balancing, IEEE Trans. Power Del., vol. 4, no. 2, pp , Apr [11] M. E. Baran and F. Wu, Optimal sizing of capacitors placed on a radial distribution system, IEEE Trans. Power Del., vol. 4, no. 1, pp , Jan [12] B. S. Kim, J. R. Shin, J. B. Park, M. S. Chae, and S. A. Sebo, Genetic algorithm based approach to the optimal reactive power dispatch considering the voltage dependency of loads, Eng. Intell. Syst. Elect. Eng. Commun., vol. 10, no. 4, pp , Dec [13] G. B. Jasmon, Network reconfiguration for load balancing in distribution networks, Proc. Inst. Elect. Eng., Gen., Transm., Distrib., vol. 146, no. 6, pp , Nov

10 SHIN et al.: NEW ORA FOR LOSS MINIMIZATION AND VOLTAGE STABILITY IMPROVEMENT 657 [14] Y. J. Jeon, J. C. Kim, J.-O. Kim, J. R. Shin, and K. Y. Lee, An efficient simulated annealing algorithm for network reconfiguration in large-scale distribution systems, IEEE Trans. Power Del., vol. 17, no. 4, pp , Oct [15] M. A. Kashem, V. Ganapathy, and G. B. Jasmon, Network reconfiguration for enhancement of voltage stability in distribution networks, Proc. Inst. Elect. Eng., Gen., Transm., Distrib., vol. 147, no. 3, pp , May [16] G. B. Jasmon and L. H. C. C. Lee, Contingency ranking technique incorporating voltage stability criterion, Proc. Inst. Elect. Eng., C, vol. 140, no. 2, pp , Mar [17] F. V. Gomes, S. Carneiro, Jr., J. L. R. Pereira, M. P. Vinagre, P. A. N. Garcia, and L. R. Araujo, A new heuristic reconfiguration algorithm for large distribution systems, IEEE Trans. Power Syst., vol. 20, no. 3, pp , Aug Joong-Rin Shin (M 90) received the B.S., M.S., and Ph.D. degrees from Seoul National University, Seoul, Korea, in 1977, 1984, and 1989, respectively. Since 1990, he has been with Konkuk University, Seoul, where he is currently a Professor of electrical engineering. From 1977 to 1990, he was an Engineer at the Korea Electric Power Corporation (KEPCO). His major research fields include power system analysis, planning, reliability evaluation, and power system engineering tools. Byung-Seop Kim received the B.S., M.S., and Ph.D. degrees from Konkuk University, Seoul, Korea, in 1994, 1998, and 2002, respectively. Currently, he works as a Senior Research Engineer in the Central R{&}D Center, LS Industrial Systems Co., Ltd. (formerly LG Industrial Systems Co., Ltd.), Kyongki-Do, Korea, where he is developing power application programs for energy management system (EMS) and supervisory control and data acquisition (SCADA) system. His research interests are power system analysis, optimization, power market analysis, and common information model (CIM) in IEC and economic studies. Jong-Bae Park (M 98) received the B.S., M.S., and Ph.D. degrees from Seoul National University, Seoul, Korea, in 1987, 1989, and 1998, respectively. From 1989 to 1998, he worked as a Researcher at the Korea Electric Power Corporation (KEPCO), and from 1998 to 2001, he was an Assistant Professor at Anyang University, Anyang City, Korea. Currently, he is an Assistant Professor at Konkuk University, Seoul, and with Electric Power Research Institute (EPRI) as a Visiting Scholar since His research interests are power system planning, optimization, Kwang Y. Lee (F 01) received the B.Sc. degree in electrical engineering from Seoul National University, Seoul, Korea, in 1964 and the M.S. degree in electrical engineering from North Dakota State University, Fargo, in He received the Ph.D. degree in system science from Michigan State University, East Lansing, in Currently, he is a Professor of electrical engineering at The Pennsylvania State University (Penn State), University Park. He was also on the faculties of Michigan State University, Oregon State University, and University of Houston, Houston, TX. He is currently Director of the Power Systems Control Laboratory at Penn State. His interests are power systems control, operation and planning, and intelligent system applications to power systems and power plant control. Dr. Lee is an Associate Editor of IEEE TRANSACTIONS ON NEURAL NETWORKS, Editor of IEEE TRANSACTIONS ON NEURAL NETWORKS, and a registered Professional Engineer.