An Approach for Formation of Voltage Control Areas based on Voltage Stability Criterion

Transcription

1 16th NATIONAL POWER SYSTEMS CONFERENCE, 15th-17th DECEMBER, An Approach for Formation of Voltage Control Areas d on Voltage Stability Criterion Dushyant Juneja, Student Member, IEEE, Manish Prasad, and M. K. Verma Abstract This paper presents a new approach for formation of voltage control areas (s) d on voltage stability criterion. The formation of s has been done d on individual critical loading factor (maximum loadability) of various buses in the geographically compact region. The with lowest range of maximum loading factor of buses has been considered as the most critical area requiring attention, to reduce chances of voltage failures. Case studies have been performed on IEEE 14-bus system and a practical 75-bus Indian system representing Uttar Pradesh and Uttarakhand Power Corporation Network. The s have also been formed using an existing approach. The superiority of proposed approach over existing approach has been established on two test systems in voltage stability assessment. Index Terms Voltage control area, Voltage stability, Maximum loadability, Jacobian sensitivities. W I. INTRODUCTION ITH continuous increase in power demand, and due to limited transmission expansion, modern power system networks are being operated under heavily stressed conditions. This has imposed the threat of maintaining the required bus voltages, and thus the systems have been facing voltage instability problem [1]. There have been numerous methods to access the voltage stability, such as voltage stability indices [2], [3]. The structural weakness of the power system, due to weak transmission boundaries between different groups of buses, has also been considered a reason of system instability [4]. These groups of buses, located in geographically compact region, have similar voltage changes for any outside disturbance. The bus clusters so formed are called voltage control areas (s) [5]. Due to weak transmission boundaries, loss of voltage controls within a voltage control area may result into voltage collapse in that area since the voltage controls in other voltage control areas may have relatively less impact in controlling the voltages. Critical areas requiring attention may be identified, and each of the remaining areas may be reduced to equivalent nodes by a network reduction technique. This reduced representation of power system may be helpful in fast voltage stability analysis. Voltage control areas have been determined by eliminating smaller off-diagonal elements of normalized Q-V Jacobian in D. Juneja( juneja.dushyant@ieee.org) and M. Prasad are students at the Institute of Technology, Banaras Hindu University, Varanasi, India M. K. Verma ( mkverma.eee@itbhu.ac.in, Mobile: ) is with the Department of Electrical Engineering, Institute of Technology, Banaras Hindu University, Varanasi, India, In order to consider the effect of Q- and P-V coupling, which are very much valid under highly stressed conditions, this algorithm has been applied to full load flow Jacobian instead of decoupled Q-V Jacobian in 6. The method requires proper selection of threshold ( ) for elimination of smaller off-diagonal elements, which is a difficult task since smaller value of puts almost all the buses in one cluster, whereas a larger value may make each bus a separate voltage control area. A V-Q curve minima d -selection algorithm has been proposed in 7. The buses having almost identical V-Q curve minima and reactive reserve basin (the set of generators hitting their Q-limits while reaching minima point) have been clubbed together to form voltage control areas near nose point. A comparison of areas so formed with those obtained using Jacobian sensitivities for different - values has been utilized to determine optimum threshold value 7. However, the voltage control areas formed by Jacobian sensitivities [5], [6] are not valid for change in system operating conditions and topology of the network, as it may result in large change in the elements of Jacobian. An entropy d determination of voltage control areas under different operating conditions has been suggested in 8. This work did not consider the effect of change in network topology due to contingencies. Formation of voltage control areas under contingencies using an electrical distance concept and V-Q sensitivities of power flow Jacobian has been suggested in 9. However, this method is d on the assumption of P-V and Q- decoupling, which may not be valid under highly stressed conditions. Group of coherent buses have been formed in 10 using generator branch reactive power flow sensitivities to reactive power injection at load buses. The buses having similar generator branch sensitivity values within a reasonable limit of 5% have been clubbed to form voltage control areas. However, generator branch sensitivities are not expected to remain same for change in operating condition or network topology. Voltage control areas have been formed d on Jacobian sensitivities together with voltage variations under contingencies [11]. However, formation of voltage control areas has been done at the case operating point and V-Q curve minima have been used for selection of threshold only, for elimination of weaker off-diagonal elements of Jacobian. Voltage control areas have been formed using bus participation factors corresponding to zero eigen value at the nose point of P-V curve [12]. However, eigen analysis is a linear analysis and may not always be suitable at the nose point of P-V curve. This paper proposes formation of voltage control areas d on maximum loadability of different buses. The s

2 16th NATIONAL POWER SYSTEMS CONFERENCE, 15th-17th DECEMBER, so formed represent bus clusters having similar voltage stability problem. The s have been formed for IEEE 14- bus system and a practical 75-bus Indian system representing Uttar Pradesh and Uttarakhand Power Corporation Network. II. METHODOLOGY The proposed algorithm computes s d on the maximum loadability of individual buses to a unidirectional load increment proportional to case loadings. The algorithm is as follows: 1) For computing maximum loadability at bus i (λ i,max ) in an N bus system, run a continuation power flow [13] defining power directions as follows: (1 + λ j ), j = i P Dj = P Dj Q Dj = Q Dj P Dj, j i (1 + λ j ), j = i Q Dj, j i for j = 1,,N P Gj = P Gj (1 + λ j ) for j = 1,, N G where, P Dj = Real power demand at bus-j P Dj = Real power demand at bus-j at the case operating point Q Dj = Reactive power demand at bus-j Q Dj = Reactive power demand at bus-j at the case operating point λ j = Loading factor at bus-j P Gj = Real power generation at bus-j P Gj = Real power generation at bus-j at the case operating point N G = of generators buses present in the system 2) Club the load buses in geographically compact region having closer maximum loading factor (λ i,max ). Put the buses with zero loads in the clusters of load buses having geographical proximity to such buses. The bus clusters so formed represent voltage control areas for the system. III. CASE STUDIES The proposed method of formation of voltage control areas have been applied to IEEE 14-bus system (shown in figure-1) and a practical 75-bus Indian system (shown in figure-2) representing Uttar Pradesh and Uttarakhand Power corporation Network. IEEE 14-bus system has 5 generators with 20 transmission lines (including 2 transformers), and one phase shifting transformer. Loads have been connected to 11 buses. The practical 75 bus Indian system has 15 generators on buses 1-15, and 98 transmission lines including 24 transformers. Loads have been connected to 41 buses in this system. There are 19 buses having neither generator nor load connected. These buses simply provide junction to lines connected. A. IEEE 14 Bus System The maximum loadability (λ i,max )of load buses were computed using algorithm presented in Section-II with the help of continuation power flow d software package UWPFLOW [14]. The maximum loading factor of load buses has been shown in Table-I. The voltage control areas were formed clubbing load buses in geographically compact region with closer range of maximum loadability, and buses with zero loads having geographical closeness to group of buses with closer maximum loadability. The voltage control areas formed by the proposed approach together with range of maximum loading factor of load buses present in different areas have in shown in Table-II. The voltage control areas formed by the proposed approach are also shown in figure-1. The s were also formed using an existing approach [11] considering elimination of weaker off-diagonal elements of different sub-matrices of Newton Raphson Load Flow (NRLF) Jacobian up to a threshold α decided by similar V-Q curve minima and reactive reserve basin (the set of reactive power sources hitting their Q-limit while reaching V-Q curve minima). The s formed by this existing approach along with range of maximum loadability of different load buses present in s have been shown in Table-III. It is observed from tables II and III that s formed by the proposed approach gives much closer range of maximum loadability of load buses present in them compared to s formed by the existing approach suggested in [11]. All the areas (except area-5 where no load bus is present) formed by the existing method have much larger range of maximum loading factor of load buses present in them. It is also observed from Table-II that -1 formed by proposed approach represents the most critical area due to lowest range of maximum loadability of load buses present in it. TABLE I MAXIMUM LOADING FACTOR FOR LOAD BUSES IN IEEE 14 BUS SYSTEM Bus Maximum Loadng Factor ((λ i,max )

3 16th NATIONAL POWER SYSTEMS CONFERENCE, 15th-17th DECEMBER, TABLE II S FORMED BY THE PROPOSED APPROACH - IEEE 14 BUS SYSTEM TABLE III s FORMED BY AN EXISTING METHOD [11] (IEEE 14-BUS SYSTEM) loading factor (λ i,max ) of load buses present in the 1. 3,4,7,8,9,10,13, , , loading factor (λ i,max ) of load buses present in the 1. 1,2, , ,9,10, ,12,13, No load bus present Figure-1. IEEE 14-bus system with s formed by proposed method B. Practical 75-Bus Indian system The maximum loadability (λ i,max )of load buses were computed using algorithm presented in Section-II with the help of continuation power flow d software package UWPFLOW [14]. The maximum loading factor of load buses has been shown in Table-IV. The voltage control areas were formed clubbing load buses in geographically compact region with closer range of maximum loadability, and buses with zero loads having geographical closeness to group of buses with closer maximum loadability. Geographically distant buses having closer maximum loadability were not considered for formation of s. The voltage control areas formed by the proposed approach together with range of maximum loading factor of load buses present in different areas have been shown in Table-V. The voltage control areas formed by the proposed approach are also shown in figure-2. TABLE IV MAXIMUM LOADING FACTOR FOR LOAD BUSES IN 75-BUS SYSTEM Bus Maximum Loading factor (λ i,max ) The s were also formed using an existing approach [11] considering elimination of weaker off-diagonal elements of different sub-matrices of Newton Raphson Load Flow (NRLF) Jacobian up to a threshold α decided by similar V-Q curve minima and reactive reserve basin (the set of reactive power sources hitting their Q-limit while reaching V-Q curve minima). The s formed by this existing approach along with range of maximum loadability of different load buses

4 16th NATIONAL POWER SYSTEMS CONFERENCE, 15th-17th DECEMBER, present in s have been shown in Table-VI. It is observed from tables V and VI that s formed by the proposed approach gives much closer range of maximum loadability of load buses present in them compared to s formed by the existing approach suggested in [11]. Areas 3, 4 & 5 formed by the existing method have wide range of maximum loadability of load buses present in them. It is also observed from Table- V that -1 formed by proposed approach represents the most critical area due to lowest range of maximum loadability of load buses present in it. TABLE V S FORMED BY THE PROPOSED APPROACH - 75-BUS SYSTEM loading factor (λ i,max ) of load buses present in the ,52,27,26,22,25,60, 14,43,57,59, ,69,36,19,20,64,66, ,40,11,48, ,62, ,21,29,30, ,24,28,4,10,34,8, ,17,23,35,9,41,12, , ,74,44,45,55,15, ,39,5,6,7,31,33, ,3,18, , , TABLE VI s FORMED BY AN EXISTING METHOD [11] (75-BUS SYSTEM) IV. CONCLUSION loading factor (λ i,max ) of load buses present in the 1. 30,29,75,65,21,53, ,12,35,17,1,42,13, ,74,9 3. 3,18,68,71,26,27,24, ,10,51, ,44,45,73,55,63,4, ,56,54,43,14,34, ,50,16,2, ,32,33,39,62,5,6,7, ,25,60,70, ,20,66,64,11,40, , ,58, ,37, A new method for formation of voltage control areas d on clustering of buses with closer maximum loadability has been presented in this paper. The traditional methods of s formation are best suited for voltage control under normal loadings, whereas, s formed by the proposed method are more suitable for voltage stability assessment. The having lowest range of maximum loadability of buses present in it has been considered as most critical area prone to voltage collapse. Case studies performed on two test systems establish superiority of proposed approach over an existing approach in voltage stability assessment. Voltage control areas formed by the proposed method may be reduced to equivalent nodes by some network reduction technique. Reduced network may be quite useful in on-line voltage stability studies. Further research is required in fast prediction of maximum loadability of buses for on-line formation of voltage control areas under different operating conditions. Figure bus Indian system with s formed by proposed method V. REFERENCES [1] IEEE / CIGRE Joint Task Force on Stability Terms and Definitions, Definition and classification of power system stability, IEEE Transactions on Power Systems, Vol. 19, No. 3, pp , August [2] F. Milano, An Open Source Power System Analysis Toolbox, IEEE Transactions on Power Systems, Vol. 20, No. 3, pp , August [3] C. A. Cañizares, "Voltage Stability Indices, Chapter 4, Voltage Stability Assessment: Concepts, Practices and Tools, IEEE-PES Power Systems Stability Subcommittee Special Publication, August [4] M. A. Pai, P. W. Sauer, B. Lesieutre, and R. K. Ranjan, Structural stability in power systems, EPRI Final Report, TR , April [5] R. A. Schlueter, I. Hu, M. W. Chang, J. C. Lo, and A. Costi, Methods for determining proximity to voltage collapse, IEEE Transactions on Power System, Vol. 6, No. 1, pp , February [6] Lie, T., Schlueter, R.A., Rusche, P.A., and Rhoades, R., Method of identifying weak transmission network stability boundaries, IEEE

5 16th NATIONAL POWER SYSTEMS CONFERENCE, 15th-17th DECEMBER, Transactions on Power Systems, Vol. 8, No. 1, pp , February [7] R. A. Schlueter, A voltage stability security assessment method, IEEE Transactions on Power Systems, 1998, Vol. 13, No. 4, pp , November 1998 [8] S. K. Joshi and S. C. Srivastava: Determination of voltage control area using entropy concept, Proceedings IEE Japan International Conference Power and Energy, Naguya, Japan, pp , August 2-4, [9] H. Liu, A. Bose and V. Venkatasubramanian, A fast voltage security assessment method using adaptive bounding, IEEE Transactions on Power Systems, Vol. 15, No. 3, pp , August [10] C. A. Aumuller and T. K. Saha, Determination of power system coherent bus groups by novel sensitivity-d method for voltage stability assessment, IEEE Transactions on Power Systems, Vol. 18, No. 3, pp , August [11] M. K. Verma and S. C. Srivastava, Approach to determine voltage control areas considering impact of contingencies, IEE Proceedings, Part-C, Generation, Transmission and Distribution, Vol. 152, No. 3, pp , May [12] K. Morison, X. Wang, A. Moshref, A. Edris, Identification of voltage control areas and reactive power reserve; An advancement in on-line voltage security assessment, IEEE PES General meeting - Conversion and Delivery of Electrical Energy in the 21st Century, Pittsburg (Canada), pp. 1 7, July 20-24, [13] V. Ajjarapu and C. Christy, The Continuation power flow: a tool for steady state voltage stability analysis, IEEE Transactions on Power Systems, Vol. 7, No. 1, pp , February [14] UWPFLOW software: Continuation and direct methods to locate fold bifurcations in AC/DC/FACTS power systems, available at VI. BIOGRAPHIES Dushyant Juneja (B 1988, M 2010) received B. Tech. degree in Electrical Engineering from the Institute of Technology, Banaras Hindu University, Varanasi (India) in His special fields of interest include voltage stability studies and nonlinear control. Manish Prasad (B 1987) received B. Tech. degree in Electrical Engineering from the Institute of Technology, Banaras Hindu University, Varanasi (India) in His interests include power system analysis and voltage control. M. K. Verma (B 1965) received B. Sc. (Eng.) degree in Electrical Engineering from Regional Engineering College, (presently National Institute of Technology), Rourkela (India) in 1989, M. Sc. (Eng.) degree from Bihar Institute of Technology (presently Birsa Institute of Technology), Sindri (India) in 1994 and Ph.D. degree from Indian Institute of Technology, Kanpur (India) in Presently, he is Associate Professor in the Department of Electrical Engineering, Institute of Technology, Banaras Hindu University, Varanasi (India). His research interests include voltage stability studies, application of FACTS controllers, operation and control of modern power systems and power quality.