Improvement of Voltage Stability Based on Static and Dynamic Criteria

Transcription

1 16th NATIONAL POWER SYSTEMS CONFERENCE, 15th-17th DECEMBER, Improvement of Voltage Stability Based on Static and Dynamic Criteria M. V. Reddy, Student Member, IEEE, Yemula Pradeep, Student Member, IEEE, V. S. K. Murthy Balijepalli, Student Member, IEEE, and S. A. Khaparde, Senior Member, IEEE, C. V. Dobaria Abstract This paper aims to reduce the voltage instability problem that occurs due to contingencies in the system by location of reactive compensation devices. The exercise is carried out in two stages comprising static and dynamic studies. Under first stage, contingency ranking is used to identify severe contingencies, and their effects on the steady state voltage profile is quantified by an index called contingency severity index (CSI) which ultimately determines the location of shunt capacitor. The application of index known as voltage stability margin index (VSMI) is used, which can simulate the voltage stability margin in real-time environment and it is used for validation studies. In the second stage, based on the criteria defined by NERC, the severity of voltage instability is quantified using severity index. The dynamic voltage profile is improved by locating static var compensator (SVC) as per the severity index. It is observed that system is stable in steady state, but dynamic simulation results show that it is not be stable in dynamic state. The concept of electrical distance for dynamic analysis is also used to further optimize the location. The entire methodology is applied to improve the voltage stability of standard 39 bus New England system. The results of steady state analysis, dynamic analysis and improvement of voltages after installing reactive support device and application of VSMI are presented in this paper. Index Terms Reactive power compensation, Static voltage stability, Dynamic voltage stability, Contingency severity index, Voltage Stability Margin Index, Electrical distance. I. INTRODUCTION RESTRUCTURING of power industry has led to stressing of power system equipment and requiring power systems to operate at critical loading levels. The operation of power system world wide is moving towards increasing stress levels on account of increase in demand, aging generation units and transmission infrastructure. The system is subjected to contingencies which lead the system to further stressed levels to the extent of collapse. These all problems cause instability of power system and are a threat to reliable and secure power delivery. During contingency the system may experience severe voltage dip, low voltage, voltage instability or complete voltage collapse. Reference [1] gives IEEE definitions for voltage instability and collapse. During past few decades, power industries all over the world have witnessed voltage instability related system failures [2]. The static security of the system is improved by locating reactive support devices considering different criterias. Mostly M. V. Reddy, Yemula Pradeep, V. S. K. Murthy Balijepalli, S. A. Khaparde, C. V. Dobariya are with the Department of Electrical Engineering, Indian Institute of Technology Bombay. ( mvreddy@iitb.ac.in, ypradeep@iitb.ac.in, vsk@ee.iitb.ac.in, sak@ee.iitb.ac.in, chandv@ee.iitb.ac.in) steady state based approach is available in literature [3] [11]. In reference [12] Static Var compensator device is located based on single contingency voltage sensitivity index. In this paper, contingency severity index is used for locating the SVC device under steady state stability. In reference [13], buses which have more reactive power deficiency or voltage dip are chosen for dynamic VAR support [14]. Under dynamic voltage stability, NERC criteria is used [15]. For steady state stability, contingency ranking is carried out using performance index of voltage. The effect of severe contingencies on bus voltage profile is assessed using contingency severity index values. With the increased loading of transmission lines the voltage stability problem is very critical issue. Generally, PV curve analysis is widely used for analyzing voltage stability issues. But it is time consuming process. So, to analyze voltage stability issues, voltage stability margin index [16] has been adopted. Similarly for dynamic voltage profile, severity index and electrical distance calculations are carried out for locating SVC device to stabilize system from transient voltage collapse. This entire premise has been tested on New England 39 bus system [17]. The rest of the paper is organized as follows. Section II describes the methodology for steady state voltage stability and dynamic voltage stability improvement. Section III explains about the mathematical formulation used for both steady state and dynamic voltage studies. Section IV presents the obtained numerical results on the New England 39 bus test system. Finally, section V concludes the paper. II. METHODOLOGY FOR VOLTAGE STABILITY IMPROVEMENT The methodology begins with presenting the criteria for static and dynamic voltage stability assessment adopted in this study. The base case loading levels for the system to be studied are taken close to the rated capacities of the equipment in the network. Under steady state conditions the following criteria are considered. The changes in the voltage levels under post contingency conditions are limited to the range of 0.95 p.u to 1.05 p.u. The list of possible contingencies included in the study should be sufficiently significant to affect the level of voltage security of the system. The probabilities associated with these contingencies are considered. Provision for assigning higher priority for voltage stability improvement to any chosen section of the system is also provided in the methodology. For dynamic conditions, NERC has defined certain criteria on which the current practices for assessment of transient

2 16th NATIONAL POWER SYSTEMS CONFERENCE, 15th-17th DECEMBER, voltage dip/sag are derived. In this study, severity index used to quantify voltage limit violations under the above criteria is adopted. Severity index is derived from the transient voltage response observed at all the buses. The mathematical background is further explained in section III. In the case of multiple reactive support devices, their locations have to consider the overlap effects of var support in the near by buses. The rest of the section presents the methodology for steady state voltage and dynamic voltage stability assessment used to address the above criteria. A. Methodology for Steady State Stability Improvement Initially A.C load flow study has been carried out using N-R method to get steady state voltage profile under base case. Initial list of contingencies for further study are prepared. Then multiple load flows are carried out, by incorporating one contingency at a time. From this information voltage performance index is calculated by substituting the post outage voltage magnitude into the equation (1). Voltage performance index can be penalized when voltage drop is more than maximum allowed voltage deviation from the nominal voltage. Based on PIV values, a list of severe contingencies is prepared. Contingency severity index (CSI) for each bus is calculated for each contingency. The bus which has highest CSI is most suitable for locating reactive support device. To confirm the location of the devices, a continuous load flow based constant powerfactor changing load at a given bus incorporating VSMI index are carried out. After placing reactive support device at the identified location, again A.C load flow study has been carried out for both base case and contingency case. The above procedure is explained through block diagram which is shown in Fig. 1. Fig. 1. Outline of work done: Steady-state. B. Methodology for Dynamic Voltage Stability Improvement For the same system considered in the steady state case, dynamic simulation has done by adding exciter data and generator data. The transient voltage profiles of each bus are calculated for a severe contingency. From these voltage profiles, dynamic severity index calculation has been done. According to NERC (N-1) contingency criteria, the buses which have voltage dip more than 0.25 p.u during the transient period, following a fault in the system are considered as severe buses. To reduce the number of locations for reactive support devices, concept of electrical distance is used. The bus which has high severity index and high electrical distance with respect to line, is most suitable location for reactive support device. After placing reactive support device, again dynamic simulation has been carried out. The above procedure is explained through block diagram which is shown in Fig. 2. Fig. 2. Outline of work done: Dynamic study. III. MATHEMATICAL FORMULATION A. Steady State Voltage Stability The idea of the approach presented in this section is to identify a bus that is most sensitive for large list of single contingencies. This section will describe the definition and calculation of the contingency severity index (CSI). To find out, severe contingencies contingency ranking has been done. This contingency ranking is based on the values of performance index of voltage(piv). According to [18], the voltage performance index is defined as P I v = N i=1 ω m 2n ( ) V i V i sp 2n V i lim (1) Where V i = Voltage magnitude at busbar i, V i sp = Specified or rated voltage magnitude at busbar i, V i lim = Voltage deviation limit above which voltage deviations are unacceptable. n = Exponent of P I v function (n = 1 for second order P I v ), ω m = Real non-negative weighting factor. ω m is used for assigning higher priorities to a section of buses in the network. The contingency severity index(csi) for bus j is defined as the sum of sensitives at node j to all considered single contingencies and expressed as CSI j = m P i U ij W ij (2) i=1

3 16th NATIONAL POWER SYSTEMS CONFERENCE, 15th-17th DECEMBER, Where m is the total number of contingencies considered, U is the participation matrix, W is the ratio matrix, and P is the contingency probability array matrix. According to CSI values, corresponding buses are ranked. The bus which has high value of CSI will be more sensitive for security system margin. The bus with the largest value of CSI is normally considered as the best location for SVC device. The same has been validated by using VSMI [19] based continuous load flow. In the continuous load flow module of VSMI, the load flows is run by changing the loads at sensitive buses and the essence of index is captured. Here, VSMI is defined as V SMI = θ rmax θ θ rmax (3) Where θ rmax is maximum angular difference between sending end and receiving end voltages and θ is the angular difference between sending and receiving end buses. The VSMI value indicates how close the angle θ is from θ rmax. Therefore a higher value of VSMI implies that θ is farther away from the θ rmax. B. Dynamic Voltage Stability In this section, we addresses the contingency assessment based on NERC (N-1) contingency criteria [20]. So, severity index values are calculated based on this criteria. Power system abnormal state during contingency is reflected by voltage dip. Thus a severity index, SI v is used to quantify voltage limit violation. Let D = {V (t) t [t cl, t f ]} for V 0 V dev D such that V 0 V dev V 0 V (t) V (t) D Where V dev is the maximum voltage deviation and V 0 is the nominal voltage. The severity index is given by the equation IV. CASE STUDY: NEW ENGLAND 39 BUS SYSTEM The New England IEEE 39 bus test transmission network is used to illustrate the effectiveness of the dynamic and steady-state methods. The system data of this network is available in [17], which consists of 10 generators, 39 buses, and 46 branches. In this study, transient two-axis model for synchronous generator is used together with excitation control. SVC is used as reactive power device. Loads are modeled as combination of constant impedance, current and power. Steady state AC load flow calculations have been done using MATPOWER [22] tool. For calculating performance index of voltage and contingency ranking MiPower [23] software is used. Contingency severity index is calculated using MSExcel. For calculating severity index, electrical distance and a continuous load flow based VSMI, MATLAB software is used. Dynamic simulation has been done using multi machine transient stability tool [24]. Here results of steady state voltage stability and dynamic voltage stability have shown in different cases. Case A, represents steady state voltage stability improvement. Case B, represents short term voltage collapse and improvement of dynamic voltage profile after placing SVC device. Case A: For steady state stability, reactive support device is placed based on CSI values. From the contingency ranking, the decisive contingencies from a large list of contingencies are ranked according to values of performance index of voltages (PIV). Based on PIV values, and outages are the most severe contingencies and are shown in Table I outage is also considered for calculation of contingency severity index. Since it the outage for which the system becomes unstable in dynamic case. The voltage response of buses under contingency is shown in Fig. 5. From the contingency severity index, 15 th bus is more sensitive to reactive power injection which is shown in Fig. 3. { V0 V SI v = dev /V 0 if V 0 V dev /V otherwise Based on severity index values, a set of severe buses can be found. To reduce the number of locations for reactive power injection, electrical distance concept has been introduced [21]. Electrical distance between bus and line is defined as a i jk = (z ji z ki )y j k + z ji y sh j k (4) Fig. 3. Contingency severity index values for different buses. Where z ji, z ki are the impedance matrix elements, y j k is the admittance of a branch j k and yj k sh is the shunt admittance of a line j k. Electrical distance represents the propagation of voltage variation following reactive power injection at a bus. The magnitude of the a i jk parameter provides a measure of the electrical distance between bus i and one point at the beginning of the line j-k. While placing SVC at buses, the type of reactive power compensation required has been investigated, and it is found that SVC at bus no.15 is working as a capacitor and supplies reactive power for Before placing SVC, the voltage profile in the range of 0.92 p.u to 1.06 p.u. But, After placing SVC, the voltage magnitude of a bus is within the limits. The voltage response of buses under contingency is shown in Fig. 4.

4 16th NATIONAL POWER SYSTEMS CONFERENCE, 15th-17th DECEMBER, TABLE I CONTINGENCY RANKING From Bus To Bus PIV Rank A. System Validation Using Voltage Stability Margin Index A base case for the 39-bus system was taken and the active load at bus 15, 16 are increased considering one bus at a time maintaining power factor constant, in steps from the base case. Based on the bus voltages and angles the VSMI index for each bus is calculated. The range of Index is from 0 to 1. If the index reaches 0 then it indicates the corresponding bus Margin in view of voltage stability is approaching Zero. This can be observed from the graphs. The VSMI values of bus no.16 is obtained by increase the loads incrementally. After placing SVC device, the VSMI is increased means it increases the stability margin. So, the VSMI for bus no.16 under base case is shown in Fig. 6. Fig. 6. Base case VSMI values of a 16 th bus If line line outage occurs, then the effect of this contingency on VSMI values is shown in Fig. 7. From the figure, reactive power device improved the VSMI values for each increment in load. Fig. 4. Voltage profiles at 15 th bus with and without reactive support. Fig. 7. Contingency case VSMI values of a 16 th bus Fig. 5. Voltage profiles at 16 th bus with and without reactive support. Case B: A three phase fault occurred at the end of line near bus 16 at t=0.1 sec. The fault was cleared after 6 cycles by tripping the line After fault clearing, generator excitation voltage shoots up, to provide reactive power support. But some generators reach its excitation limit lately. This leads to significant voltage drop and generators may go out of synchronism. Finally short-term voltage collapse occurred. The bus voltage response due to line contingency is shown in Fig. 8.

5 16th NATIONAL POWER SYSTEMS CONFERENCE, 15th-17th DECEMBER, Fig. 8. Bus voltage response due to line contingency Fig. 10. Electrical distance distance between bus and line For the same contingency steady state response is within the limits from Fig. 5. The result showed that although the system may have post disturbance equilibrium in steady-state but it is actually unstable in transient frame. This dynamic simulation has done using a multi- machine transient stability tool [24]. From the severity index and electrical distance values bus no.16 and 17 are the suitable locations for a contingency So, After placing reactive support device at bus no.16, the dynamic voltage profile has been improved which is shown Fig. 11. The bus voltage response is shown in Fig. 8, due to line contingency shows short term system collapse around t=1.2 sec. So, basically voltage response after t=1.2 sec does not mean anything as the system has already become unstable. The voltage response after t=1.2 sec is just to show that the system has become unstable. To improve voltage profile during dynamic state, installation of reactive support device is necessary. Before installation, severity index for each bus has calculated. From severity index values, a set of severe buses has been prepared which is shown in Fig. 9. Fig. 11. Bus voltage response due to line contingency with SVC Fig. 9. Severity index of buses due to line contingency To reduce the number of locations for reactive support devices, electrical distance is used. It is highly possible that buses in close electrical neighborhood of most sensitive buses are also very sensitive. Thus the values of electrical distances between line and each bus is shown in Fig. 10. This reduction in number of locations reducing the complexity of problem. Another significant advantage is that it avoids small installations at electrically adjacent and likewise sensitive buses. V. CONCLUSION A comprehensive analysis of both steady state and dynamic voltage instability phenomenon under contingency conditions are carried out. For finding severe contingencies, contingency ranking is used. Contingency severity index, VSMI and electrical distance concepts are used to locate reactive support devices under steady state. The response of system voltage to a disturbance and system behavior during a voltage collapse situation can be considered as dynamic power system phenomena. However as far as reactive long term planning is concerned, a steady state analysis has been shown to be generally adequate for providing an indicator of the margin from current operating point to voltage collapse point and for determining the location and MVar rating of any necessary reactive power source. Dynamic analysis is separately used to design the controls for system reactive support. Even though, under voltage load shedding, can improve the dynamic response. but it can take more time to operate, in that time short term voltage collapse may occur. From the results obtained during this research, it is observed that only steady state analysis cannot guarantee the short-term stability because sometimes system may seem stable in long-term but it may not stable in short-term.

6 16th NATIONAL POWER SYSTEMS CONFERENCE, 15th-17th DECEMBER, REFERENCES [1] IEEE/CIGRE Joint Task Force on Stability Terms and Definitions, Definition and classification of power system stability, IEEE Trans. Power Syst., vol. 19, no. 2, pp , May [2] G. S. Vassell, Northeast Blackout of 1965, IEEE Power Engineering Reviw, vol. 11, pp. 4 8, Jan [3] W. D. Rosehart, C. A. Canizares, and V. H. Quintana, Effect of detailed power system models in traditional and voltage-stability constrained optimal power-flow problems, IEEE Trans. Power Systems, vol. 18, no. 1, pp , Feb [4] B. B. Chakrabarti, D. Chattopadhyay, and C. Kumble, Voltage stability constrained var planning-a case study for new zealand, in Proc Large Engineering Systems Conf. Power Engineering, pp [5] J. R. S. Mantovani and A. V. Garcia, A heuristic method for reactive power planning, IEEE Trans. Power Systems, vol. 11, no. 1, pp , Feb [6] K. Aoki, M. Fan, and A. Nishikori, Optimal var planning by approximation method for recursive mixed-integer linear programming, IEEE Trans. Power Systems, vol. 3, no. 4, pp , Nov [7] M. Randhawa, B. Sapkota, V. Vittal, S. Kolluri, and S. Mondal, Voltage stability assessment for a large power systems, in Proc IEEE Power and Energy Society General Meeting. [8] G. K. Morison, B. Gao, and P. Kundur, Voltage stability analysis using static and dynamic approaches, IEEE Trans. Power Systems, vol. 8, no. 3, pp , Aug [9] H. H. Happ and K. A. Wirgau, Static and dynamic var compensation in system planning, IEEE Trans. Power Systems, vol. PAS-97, no. 5, pp , Sep./Oct [10] V. Ajjarapu, P. L. Lau, and S. Battula, An optimal reactive power planning strategy against voltage collapse, IEEE Trans. Power Systems, vol. 9, no. 2, pp , May [11] J. G. Singh, S. N. Singh, and S. C. Srivastava, An approach for optimal placement of static var compensators based on reactive power spot price, IEEE Trans. Power Systems, vol. 22, no. 4, pp , Nov [12] S. Sutha and N. N. Kamaraj, Optimal location of multi type facts devices for multiple contingencies using particle swarm optimization, IJEE Power Engineering, vol. 16, no. 1, pp , Jan [13] D. Mader, S. Kolluri, M. Chaturvedi, and A. Kumar, Planning and implementation of large synchronously switched shunt capacitor banks in the entergy system, in Proc IEEE Power Engineering Society Summer Meeting, vol. 4, pp [14] S. Kolluri, A. Kumar, K. Tinnium, and R. Daquila, Innovative approach for solving dynamic voltage stability problem on the entergy system, in Proc IEEE Power Engineering Society Summer Meeting, vol. 2, pp [15] Western Electricity Coordinating Council. NERC/WECC planning standards. [online] available: standingcommittees/pcc/rs/documents. [16] T. He, S. Kolluri, S. Mandal, F. Galvan, and P. Rastgoufard, Identification of weak locations in bulk transmission systems using voltage stability margin index, International Conference on Probabilistic Methods Applied to Power Systems, pp , Sept [17] J. Chow, power System Toolbox Version 2.0, Cherry Tree Scientific Software, Ontario, Canada, [18] G. C. Ejebe and B. F. Wollenberg, Automatic contingency selection, IEEE Trans. of Power Apparatus and systems, vol. PAS-98, no. 1, pp , Jan/Feb [19] Joe H. Chow, Felix F. Wu, and James A. Momoh, Applied mathematics for restructured electric power systems. Springer, [20] D. J. Shoup, J. J. Paserba, and C. W. Taylor, A survey of current practices for transient voltage dip/sag criteria related to power system stability, in Proc. IEEE Power Systems Conference and Exposition, vol. 2, pp , July [21] A. J. Conejo, J. Contreras, D. A. Lima, and A. Padilha-Feltrin, Z-bus transmission network cost allocation, IEEE Trans. Power Syst., vol. 22, no. 1, pp , Feb [22] MATPOWER: A matlab power system simulation package. [online] available: [23] MiPower: Computer Aided Power System Simulation Software. [online] available: [24] A Multi-machine Transient Stability Programme. [online] available: anil/download/transientstabilityprograms. M. V. Reddy has a Masters degree in the Department of Electrical Engineering at Indian Institute of Technology Bombay, India. His research interests include voltage stability, restructured power systems, power system simulation studies. He is a graduate student member of the IEEE Bombay section, and the IEEE power and energy society. Yemula Pradeep is currently working towards Ph.D. degree in Department of Electrical Engineering at Indian Institute of Technology Bombay, India. His research interests include IT applications in power systems and power systems restructuring issues. He is a graduate student member of the IEEE Bombay section, and the IEEE power and energy society. V. S. K. Murthy Balijepalli is currently a research scholar with the Department of Electrical Engineering, Indian Institute of Technology Bombay, India. He is a graduate student member of the IEEE Bombay section, and the IEEE power and energy society. His current research interests include Transmission System Expansion Planning, data mining application to power systems, smart grids and governing standards. Shrikrishna A. Khaparde (M 87-SM 91) is a Professor in the Department of Electrical Engineering, Indian Institute of Technology Bombay, India. He is a member of the Advisory Committee of Maharashtra Electricity Regulatory Commission (MERC). He is the editor of International Journal of Emerging Electric Power Systems (IJEEPS). He has co-authored books titled, Computational Methods for Large Sparse Power System Analysis: An Object Oriented Approach, and, Transformer Engineering: Design & Practice, published by Kluwer Academic Publishers and Marcel Dekker, respectively. His research areas include distributed generation and power system restructuring. C. V. Dobariya is a Project manager in the Department of Electrical Engineering, Indian Institute of Technology Bombay, India. His area of interest includes renewable energy and power system economics.