New criteria for Voltage Stability evaluation in interconnected power system

Transcription

1 New criteria for Stability evaluation in interconnected power system Lavanya Neerugattu Dr.G.S Raju MTech Student, Dept.Of EEE Former Director IT, BHU Visiting Professor VNR Vignana Jyothi Institute of Engineering & Technology, Bachupally, Hyderabad. Abstract---The voltage instability is a serious issue in the modern power systems with rapid voltage droop due to stressed system with increased loading. Many techniques have been given to predict the voltage collapse and maintain the voltage stability of a power system. The stability index (VSI) is a feature for solving voltage stability problems. In this paper, a new index is proposed and the performance of the new index with other indices is discussed. The effectiveness of the proposed method is demonstrated through numerical studies on IEEE 3 bus system, using several scenarios of load increase. The process known as continuation load flow is used. The proposed voltage stability index is based on the difference between the present bus voltage level and the voltage at the nose point where the Jacobian becomes singular for the same load condition. A stable system may suffer voltage collapse when a contingency occurs. This paper analyses these cases. A new sensitivity factor between reactive power injection and improvement to the voltage stability margin is discussed. Keywords- voltage stability, continuation load flow, voltage stability index, nose point. I. INTRODUCTION ROBLEMS related to voltage stability in power systems are one of the major concerns in power system operation and future planning. stability is the ability of a power system to maintain acceptable voltages at all buses in the system under normal condition and after being subject to a disturbance [1], [5] and [9]. A power system is said to have voltage instability when a disturbance causes a progressive and uncontrollable decrease in voltage level. During the last several decades, voltage stability problem has been given more attention primarily due to a number of blackouts that occurred in many developed countries. Some well-known examples of voltage stability incidents were reported in France, Belgium, Sweden, USA, and Japan [], [3]. As Electrical Energy systems become more complex and heavily loaded, along with economical and environmental constraints, voltage instability becomes an increasingly serious problem, when systems operate close to their limits. instability is essentially a local phenomenon; however its consequences may have widespread cascaded impact. The study of voltage stability has been analyzed under different approaches that can be basically classified into dynamic and static analysis. The static voltage stability methods use steady state model for the analysis, such as power flow model or a linearized dynamic model. The dynamic analysis implies the use of a P model characterized by nonlinear differential and algebraic equations which include generator dynamics, OLTC transformers, SVC, etc, through transient stability simulations [4]. Although stability studies, in general, require a dynamic model of the power system, in this paper analysis of voltage behaviour has been approached using both static and dynamic techniques, which have been widely used for voltage stability analysis [1]. An accurate knowledge of how close the actual system s operating point is from the voltage stability limit (nose point) which is a measure of the voltage stability margin is crucial to operators. Therefore, to find voltage stability indices have become an important task for many stability studies. These indices provide reliable information about proximity to system voltage instability. The voltage stability index proposed here and its comparison with existing methods will be highlighted in this paper, through results obtained from simulating on IEEE 3 bus system. II. VOLTAGE STABILITY INDICES The status of voltage stability in a power system can be known through voltage stability indices. These indices can reveal the critical bus of a power system in an interconnected network or evaluate the voltage stability margins of a system. The indices used to examine the system stability are briefly described in this section. 1) L-index: Kessel et al. [5] developed a voltage stability index based on the solution of the power flow equations. The L index is a quantitative measure for the estimation of the distance of the actual state of the system to the stability limit. The L index describes the stability of the complete system and is given by: L = max j αl L j = max j αl 1 F ji i αg V i V j (1) Where F ji is matrix giving relationship between generator and load bus voltage. L j is a local indicator that identifies the buses where collapse may occur. The L index varies in the range between (no load) and 1 (voltage collapse). For a given operating condition, using the load-flow results, the voltage-stability L index is computed. 1

2 ) Modal analysis: Gao et al. [6] proposed a method that computes the smallest Eigen value and associated eigenvectors of the reduced Jacobian matrix of the power system based on the steady state system model. The Eigen values are associated with the modes of voltage and reactive power variation. If all the Eigen values are positive, the system is considered to be voltage stable. If one of the Eigen values is negative or zero, the system is considered to be voltage unstable. A zero Eigen value of the reduced Jacobian matrix means that the system is on the border of voltage instability. The corresponding system Jacobian matrix becomes singular. The potential voltage collapse situation of a stable system can be predicted through the evaluation of the minimum positive Eigen values. The magnitude of minimum Eigen value provides a measure to know how close the system is to voltage collapse. By using the bus participation factor, the weakest bus can be determined, which is the greatest contributing factor for a system to reach voltage collapse situation. The reduced Jacobian matrix is as given below Δ Q = J R Δ V J R = [J 4 - J 3 J 1-1 J ] () Δ V= J R -1 Δ Q Bus participation factors: J R = ξ Λ η P ki = ξ ki η ik (3) Where J R = Reduced Jacobian matrix K = bus number i = Eigen value number ξ = right Eigen vector matrix of J R Λ = diagonal Eigen value matrix of J R η = left Eigen vector matrix of J R The most vulnerable bus K is that for which P ki is maximum. 3) The Proposed Method: In this study, margin method is employed as indicator to solve the stability problem. Where the margin is minimum that bus is considered as weak bus and the voltage margin is a measure to know how close the system is to voltage collapse. margin of a bus is computed using the equivalent system representation at that bus. to bus R of voltage E R through an equivalent reactance X as shown in Fig.1. From the equivalent system, P R = E s E R X Q R = E s E R cos δ E R sin δ (4) Where P R, Q R load connected to bus R X E S is the infinite bus voltage and X is equivalent reactance Take P R, Q R equations for evaluating the margin, Put E R =V at maximum loading point (nose point). dq = E s cos δ V = dv X (5) V = E S cos δ (6) Q = V X = V L = X Q (4Q +P ) Q (4Q +P ) Margin = E R - V L Where V L is voltage at bus R at nose point E R is the present bus voltage 4) P-V and Q-V curves: The P-V curves are the commonly used graphs for predicting voltage security. They are used to determine the loading margin of a power system. The power system load is gradually increased and, at each increment, it is necessary to recomputed power flows until the nose of the PV curve is reached. The margin between the voltage at collapse point and the current operating voltage is used as voltage stability criterion [7]. (7) (8) (9) Fig.1: Equivalent system at Bus K The system external to bus R supplying a load of P R +jq R is represented by an infinite bus of voltage E S <δ S connected PV curve of a load bus in the power system Fig.: With Q-V curve, it is possible for the operators, to know is the conditional reactive power that can be supplied by the

3 weakest bus before reaching minimum voltage limit. The reactive power margin is the MVAR distance from the operating point to the bottom of the Q-V curve. The Q-V curve can be used as an index for voltage instability. The point where dq/dv is zero is the point of voltage stability limit [3]. Fig.5: PV curve of load bus in IEEE 3 bus system Fig.3: QV curve of a load bus in the power system III. TEST RESULTS AND DISCUSSION The voltage stability analysis is performed on IEEE 3 bus system. This system has 6 generator buses, 4 load buses. This system is simulated by using Newton Raphson Load flow method. The voltage stability margin can be calculated with P-V curve. This shows the bus voltage levels as the loading factor k increases. The loading factor is 1 for base case and is gradually increased, in all generator and load buses of the system, until maximum loading point is reached, maintaining constant power factor for each load. As the power system load is gradually increased, the voltages at the buses decrease. b) Comparison of three methods with results: The table 1 shows that Values of L-index, Eigen values and margin of the IEEE 3 bus system at the weak bus by increasing the loading factor k. It is clear that critical voltage, Eigen values, margins gradually decrease and the L-index increases up to nose point. Table.1: stability indices are computed at bus Fig.4: Single line diagram for IEEE 3 bus system a) Continuation load flow method: After simulating the IEEE3 bus system, load flow is conducted for the base case to obtain the bus voltages. By observing Bus voltages the weakest bus is identified as Bus. For confirming that this is the most vulnerable bus to initiate voltage collapse of the system, the methods i.e., Eigen value, L- index and voltage margin methods are used. For finding the nose point of the system (more loadability at this bus) Continuation load flow method [8] is used. The analysis shows that the L-index for bus is the highest and the participation factor for the lowest Eigen value is highest for bus. This confirms that bus is the critical bus. 6 Loading factor K V(pu) Power P L (MW) Eigen values L-index margin Fig.6: Stability indicator L and its relation to the critical voltage 3

4 (pu) sensitivity index(δvm/ ΔQ) Bus participations Figure: 6 shows that bus exhibits the highest L j index, which indicates that it is the most vulnerable bus in the system. The L-index and the voltage at bus (critical bus) are plotted as a function of loading factor. Table.: Continuation load flow with shunt capacitor at bus S.NO. Loading factor K V(pu) Power PL(MW) Eigen values L-index margin chart of Bus participations Bus Fig.7: Bus participation factors in the least stable mode for critical operating case. At the critical operating point, the smallest Eigen value is.381. This value is considered the least stable mode for the critical operating point and is used to determine the bus participation factors. Figure shows the bus participation factors calculated by using equation (3) for the least stable mode for the critical operating point. The critical bus of this system is bus because this bus has the highest participation factor. c) Reactive Power Compensation to improve stability margin: d) Sensitivity Index: Fig.9. shows the Sensitivity of margin to Reactive power injection. Sensitivity Index S i = VM Q (1) Where ΔVM = Increase in margin ΔQ = Change in reactive power injection Adding shunt capacitor at the vulnerable bus will improve the voltage margin. The MVAR value of Shunt capacitor can be obtained by definition given below: MVAR = V X c (1) sensitivity curve Where X c = 1 ω c Capacitor C = 1 (πf X c ) Fig.8: Improvement of stability margin (11) PV curve with shunt capacitor PV curve without shunt capacitor Load factor K (pu) Fig.9: sensitivity curve When the voltage reaches to collapse point, the sensitivity is more at that point. e) Contingency case: Stable operating systems can suffer voltage instability under contingencies. Fig.1. shows two cases where the system remains stable and unstable after it suffers a contingency of generation trip out and a line outage. When the load is 1.5 times the base load, the system which is stable before contingency experiences voltage instability after the contingency. When the load factor is 1.3. stability is maintained both before and after contingency. 4

5 V (pu) V (pu) Fig.1: PV curves with & without Contingency Table.3: Continuation load flow at contingency case at Bus8 and line 15-3 S. NO Loading factor K Voltag e V(pu) Power PL(M W) PV curve with contingency Eigen values L-index PV curve without contingency Loading factor K margin This shows that a voltage stable system under normal conditions can become unstable under contingency condition. IV. SUPERIOURTY OF THE PROPOSED METHOD 1. The margin computation at each bus is done using the locally available signals V, P, Q at that bus only. All the existing methods used to study voltage stability require complete data of the network.. The system operator can readily use this method to evaluate the vulnerability of each bus for voltage collapse using online data which is available to him. 3. The voltage margin computed by this method will provide the system operator with useful information about how much load can be added to the bus before the system suffers voltage instability. 4. Unlike other methods using the Eigen value of the system Jacobian or the L-index which compares the present bus voltage with the open circuit voltage to arrive at the voltage stability index, the proposed method gives the magnitude of the bus voltage at which the system looses the voltage stability. f) Time domain analysis:.8.7 case1.6.5 case time (sec) V. CONCLUSION This paper presents a study and analysis of the performance of the system static voltage collapse indices. All the other indices applied to IEEE 3 bus system gave similar results. The study indicated that the bus of IEEE 3 bus system is identified as the weakest bus in the system. Sensitivity Index of margin to Reactive power injection, is calculated. The authors conclude that the proposed method to calculate voltage margin is faster and more elegant. Fig.11. shows the voltage at bus as a function of time following a contingency for the two cases of system loading mentioned above. Fig.11: Time domain analysis for contingency cases For this time domain analysis[1], the following assumptions are made, 1. All P and Q are kept constant at load bus.. Except slack bus, all other generators have blocked their governors. 3. All electrical transients are neglected. 4. Generator bus voltages are held constant. ACKNOWLEDGEMENT The authors gratefully thank Dr.M.Ramamoorty, Distinguished Professor, for his continuous guidance and involvement in the project. The first author is fortunate to work under him, who is an inspiring creative researcher par excellence. We are with feelings from the bottom of hearts express our indebtedness. It is a rewarding experience and we look forward in future also seeking his help and to share his ideas to sincerely try to implement. The first author is happy to record her sincere thanks for the encouragement and support extended by Dr.K.Anuradha, Head of the EEE Department and Prof.C.D.Naidu, Principal of the Institute. 5

6 REFERENCES [1] P.Kundur Power System Stability and Control McGraw-Hill, New York, 1994 [] Stability of Power Systems: Concepts, Analytical Tools and Industry Experience, IEEE Committee Vol.IEEE/PES 93TH358-- PWR 199. [3] K. Takahashi and Y. Nomura The Power System Failure on July 3 rd 1987 in Tokyo CIGRE SC-37 Meeting 37.87(JP) 7(E) [4] J.C. Chow, R. Fischl and H. Yan On the Evaluation of Collapse Criteria IEEE Trans., PWRS-5, pp. 61-6, May 199 [5] P.Kessel, H.Glavitsch Estimating the Stability of a Power System IEEE, Transactions on Power Delivery, Vol.PWRD-1, N3, July 1986 [6] B.Gao, G.K.Morison, P.Kundur Stability Evaluation Using Modal Analysis IEEE, Transactions on Power Systems, Vol.7, N4, November 199 [7] Editor/Coordinator: Claudio Canizares Stability Assessment: Concepts, Practices and Tools IEEE/PES Power System Stability Subcommittee Special Publication, August. [8] V. Ajjarapu and C. Christy, "The continuation power flow: A tool for steady state voltage stability analysis", IEEE Trans. on Power Systems, vol. 7,11. 1, February 199, pp [9] C. W. Taylor, Power system voltage stability, McGraw Hill, NY, [1] Transient electromechanical process in electrical systems book by Prof. V. A. Venikov, MEI, MIR publications