Composite Criteria based Network Contingency Ranking using Fuzzy Logic Approach

Transcription

1 INDIAN INSTITUTE OF TECHNOLOGY, KHARAGPUR, DECEMBER -9, Composite Criteria based Network Contingency Ranking using Fuzzy Logic Approach K.Visakha D.Thukaram Lawrence Jenkins Abstract -- Electric power systems are exposed to various contingencies. Network contingencies often contribute to overloading of network branches, unsatisfactory voltages and also leading to voltage collapse. To maintain security against voltage collapse, it is desirable to estimate the effect of contingencies on the voltage stability. This paper presents a new approach using fuzzy logic to evaluate the degree of severity of the considered contingency and to eliminating masking effect in the technique. The proposed approach, in addition to real power loadings and bus voltage violations, voltage stability indices at the load buses are also used as the post-contingent quantities to evaluate the network contingency ranking. Keywords -- Contingency ranking, power system security, voltage stability, fuzzy logic. I. INTRODUCTION In the present day power system planning and operation considerable interest is being shown in contingency analysis. Contingency screening and ranking is one of the important components of on-line system security assessment. The objective of contingency screening and ranking is to quickly and accurately select a short list of critical contingencies from a large list of potential contingencies and rank them according to their severity. Suitable preventive control actions can be implemented considering contingencies that are likely to affect the power system performance. Most of the contingency ranking methods, generally, ranks the contingencies in an approximate order of severity with respect to a scalar performance index (PI), which quantifies the system stress []-[]. The common disadvantages of several PI-based ranking methods is the masking phenomenon, which is defined as the ranking of a contingency, yielding a number of high loading but not violations equally with a contingency, which produces a single, overloaded line. In the reported literature for contingency ranking, some fast approximate methods such as DC load flow or P-Q iteration methods are employed to estimate post contingency quantities (line flows, bus voltages) for each contingency case. Based on these estimated quantities, a performance index (PI) is computed for each contingency and all the contingencies are ranked according to the values of the performance indices. It has been pointed out that two separate ranking lists are required for real power flow problems and K.Visakha,D.Thukaram*, Lawrence Jenkins * Corresponding Author, dtram@ee.iisc.ernet.in Department of Electrical Engineering, Indian Institute of Science, Bangalore- voltage profile problems, respectively, since the contingencies causing line overloads do not necessarily cause bus voltage violations and vice versa. Thus, two performance indices, which give measures for line overloads and for bus voltage violations respectively, are needed for real power and voltage contingency rankings []. However, with increased loading of existing power transmission systems, the problem of voltage stability and voltage collapse, has also become a major concern in power system planning and operation. It has been observed that voltage magnitudes do not give a good indicator of proximity to a voltage stability limit and voltage collapse [,]. In the proposed approach, in addition to real power loadings and bus voltage violations, voltage stability indices at the load buses are also used as the post-contingent quantities to evaluate the network composite contingency ranking. Since the human experts play an important role in security evaluation, an approach based on fuzzy set theory is proposed in this paper. The post-contingent quantities are expressed in fuzzy set notation and the heuristic rules employed by system operators in contingency ranking are compiled to reach the overall system severity index. The proposed method has been tested on typical practical systems and results for a -bus equivalent EHV power system network are presented to illustrate the proposed approach. II. VOLTAGE STABILITY INDEX (L-index) COMPUTATION Consider a system where n is the total number of buses with, g, g number of generator buses, and g+ n, remaining (n-g) buses. For a given system operating condition, using the load flow (state estimation) results, the voltage stability L-index is computed as [], V g i L j = Fji () i= V j Where j = g+ n and all the terms within the sigma on the RHS of equation () are complex quantities. The values of F ji are obtained from the network Y-bus matrix. For a given operating condition I G YGG YGL VG = I L Y Y () LL V L Where I G, I L and V G, VL represent complex current and voltage vectors at the generator nodes and load nodes.

2 NATIONAL POWER SYSTEMS CONFERENCE, NPSC [ Y GG ],[ GL ] LL Y are corresponding partitioned portions of network Y-bus matrix. Rearranging the above equation () we get, V Z F I = Y,[ Y ] and [ ] I L G K LL GL Y GG Where [ F ] = -[ Y ] LL [ ] elements of [ F ] matrix. V L G () Y. F ji are the complex For stability, the index L j must not be violated (maximum limit=) for any of the nodes j. Hence, the global indicator L describing the stability of the complete subsystem is given by L= maximum of L j for all j (load buses). An L-index value away from and close to indicates an improved system security. While the different methods give a general picture of the proximity of the system voltage collapse, the L- index gives a scalar number to each load bus. Among the various indices for voltage stability and voltage collapse prediction, the L- index gives fairly consistent results. The advantage of this method lies in the simplicity of the numerical calculation and expresiveness of the results. The L- indices for given load conditions are computed for all load buses and the maximum of the L-indices gives the proximity of the system to voltage collapse. III.FUZZY REPRESENTATION OF POST- CONTINGENT QUANTITIES The post-contingent quantities must first be expressed in fuzzy set notation before they can be processed by the fuzzy reasoning rules. A. Line Loadings Each post-contingent percentage line loading is divided into four categories using fuzzy set notations: Lightly Loaded, -%(LL), Normally Loaded, -%(NL), Fully loaded, -%(FL), Over Loaded, above %(OL). Fig. shows the correspondence between line loading and the four linguistic variables, which shows the ranges of loadings, as ratio of actual flow to its rated MVA loading, covered by linguistic variables. The output membership functions to evaluate the severity of a post -contingent quantity are also divided into four categories using fuzzy set notations: Less Severe (LS), Below Severe (BS), Above Severe (AS) and More Severe (MS) as shown in Fig.. Fig.. Severity Membership Functions for Line Loadings The fuzzy rules, which are used for evaluation of severity indices of post -contingent quantities of line loadings, are IF Line Loading is LL then severity is LS IF Line Loading is ML then severity is BS IF Line Loading is FL then severity is AS IF Line Loading is OL then severity is MS After obtaining the severity indices of all the lines the Overall Severity Index (OSI LL ) of the line loading for a particular line outage is obtained using the following expression. OSI LL = w SI Where w = Weighting coefficient for a severity index, SI = Severity Index of a Post - Contingent Quantity The weighting coefficients used for the severity indices are w =. for LS =. for BS =. for AS =. for MS The effect of these weighting coefficients is that the overall severity index is first dominated by fourth category of severity index (MS) next by third, second and first category of severity index respectively. Thus the overall severity index reflects the actual severity of the system for a contingency. B. Voltage Profiles Fig.. Line Loadings and the corresponding linguistic variables In this case each post-contingent bus voltage profile is divided three categories using fuzzy set notations: Low Voltage, below.9pu (LV), Normal Voltage,.9-.pu (NV) and Over Voltage, above.pu (OV). Fig. shows the correspondence between bus voltages (in per unit) and the four linguistic variables, which shows ranges of bus voltages covered by linguistic variables.

3 INDIAN INSTITUTE OF TECHNOLOGY, KHARAGPUR, DECEMBER -9, Each post-contingent voltage stability index is divided into five categories using fuzzy set notations: Very Low Index, -.(VLI), Low Index,.-.(LI), Medium Index,.-.(MI), High Index,.-. (HI) and Very High Index,. above (VHI). Fig. shows the correspondence between voltage stability L-index and the four linguistic variables, which shows ranges of voltage stability L-index covered by a linguistic variable. Fig.. Voltage Profiles and the corresponding linguistic variables The output membership functions used to evaluate the severity of a post -contingent quantity are also divided into three categories using fuzzy set notations: Below Severe (BS), Above Severe (AS) and MS (More Severe) and are shown in Fig.. Fig. Voltage Stability Index and the corresponding linguistic variables The output membership functions to evaluate the severity of a post -contingent quantity are also divided into five categories using fuzzy set notations: Very Less Severe (VLS), Less Severe (LS), Below Severe(BS), Above Severe(AS) and More Severe(MS) and are shown in Fig.. Fig. Severity Membership Functions for Voltage Profiles The fuzzy rules, which are used for evaluation of severity indices of, post -contingent quantities of voltage profiles are IF Voltage Profile is NV then severity is BS IF Voltage Profile is OV then severity is AS IF Voltage Profile is LV then severity is MS After obtaining the severity indices of all the voltage profiles the Overall Severity Index (OSI VP ) of the bus voltage profiles for a particular line outage is obtained using the following expression. OSI VP = w SI The weighting coefficients used for the severity indices are w =. for BS =. for AS =. for MS C. Voltage Stability Indices Fig. Severity Membership Functions for Voltage Stability Index The fuzzy rules, which are used for evaluation of severity indices of, post -contingent quantities of line loadings are IF Voltage Stability Index is VLI then severity is VLS IF Voltage Stability Index is LI then severity is LS IF Voltage Stability Index is MI then severity is BS IF Voltage Stability Index is HI then severity is AS IF Voltage Stability Index is VHI then severity is MS After obtaining the severity indices of all the voltage stability indices the Overall Severity Index (OSI VSI ) of the bus voltage

4 NATIONAL POWER SYSTEMS CONFERENCE, NPSC stability index for a particular line outage is obtained using the following expression. OSI VSI = w SI The weighting coefficients used for the severity indices are w =. for VLS =. for LS =. for BS =. for AS =. for MS IV. PROPOSED FUZZY LOGIC APPROACH FOR CONTINGENCY RANKING The membership function for each post-contingent quantity of line flows, bus voltages and voltage stability index is established and with these membership functions at hand, the overall severity index for the contingency is computed as follows. Each post-contingent quantity is described by a linguistic variable and the associated membership function. Now, to reach a possible overall severity index for line loading, voltage profiles and voltage stability index the fuzzy inference system shown in Fig. is used. loadings are obtained the Overall Severity Index (OSI LL ) of the line loadings for a particular line outage is obtained using the following expression. OSI LL = w SI Similarly the severity indices and overall severity index for the bus voltages and voltage stability indices are obtained by using the respective fuzzy rules. The network composite overall severity index (NCOSI) is obtained by adding the three overall severity indices as shown in Fig.. When the overall severity index for each contingency in the contingency list has been figured out, the overall severity indices for those contingency cases with a severity index exceeding a pre-specified value are listed out and ranked according to the network composite overall severity index. V. TEST SYSTEM STUDIES AND RESULTS The approach is applied on a practical system of -bus equivalent EHV power system network shown in Fig.9.The system has generator buses and other buses. The load is represented at kv side of kv / kv at number of buses. Input FUZZY INFERENCE SYSTEM Output Fig.. Fuzzy Inference System (FIS) The inputs are line loading, voltage profiles and voltage stability indices and the outputs are severity indices, which are evaluated using the fuzzy rules. The approach for evaluating the overall severity index for line loading is as follows. If the percentage line loading of a line is then the severity index, which is evaluated using the above fuzzy rules, is..similarly the severity indices for all other line Line Loading OSI LL FIS Voltage Profiles Voltage Stability Index FIS FIS OSI VP Fig.. Parallel operated fuzzy Inference Systems OSI VSI NCOSI 9 9 Fig. 9 - Equivalent EHV Power System Network

5 INDIAN INSTITUTE OF TECHNOLOGY, KHARAGPUR, DECEMBER -9, 9 A.- Line Outage Contingency The percentage line loadings, bus voltage profiles and voltage stability indices for the line outage, connected between buses and, the corresponding severity indices which are evaluated by using the respective Fuzzy Inference Systems (FIS) are shown in Tables I and II. TABLE I PERCENTAGE LINE LOADINGS AND CORRESPONDING SEVERITY INDICES Line Between buses Load No. 9 Percentage Line Loading Severity Index (SI LL ) TABLE II BUS VOLTAGES, VOLTAGE STABILITY INDICES AND THE CORRESPONDING SEVERITY INDICES Voltage Profile V (pu) Severity Index (SI VP ) Voltage Stability Index L-Index Severity Index (SI VSI ) The Overall Severity Index for the line loading, bus voltages and voltage stability indices are obtained by using the expression and are given by OSI LL = 9.; OSI VP =.; OSI VSI =. The composite Network Overall Severity Index is obtained by adding the above three Overall Severity Indices. NCOSI = OSI LL +OSI VP +OSI VSI = 9. B.- Line Outage Contingency The percentage line loading, bus voltage profiles and voltage stability indices for the line outage (connected between buses and ) and the corresponding severity indices, which are evaluated by using the respective Fuzzy Inference Systems (FIS), are also shown in Table III and IV. TABLE III PERCENTAGE LINE LOADING AND CORRESPONDING SEVERITY INDICES Line Between buses Percentage Line Loading Severity Index (SI LL )

6 NATIONAL POWER SYSTEMS CONFERENCE, NPSC Load No. 9 9 TABLE IV BUS VOLTAGES, VOLTAGE STABILITY INDICES AND THE CORRESPONDING SEVERITY INDICES Voltage Profile V (pu) Severity Index SI VP ) Voltage Stability Index L-Index Severity Index (SI VSI ) The Overall Severity Index for the line loading, bus voltages and voltage stability indices are given by OSI LL =.9; OSI VP = 9; OSI VSI = 9. The composite Network Overall Severity Index is given by CNOSI = OSI LL +OSI VP +OSI VSI =. The ranking of the five selected line outage contingency cases using the proposed approach is shown in Table V. TABLE V OVERALL SEVERITY INDICES AND RANKS Line OSI LL OSI VP OSI VSI Line NCOSI Rank The ranking can be easily verified from the Table VI, which shows the number of lines/buses under different category of severity. From the above Table VI it can be seen that the line - outage contingency has more number of lines/buses under the MS severity category. Thus it has got the rank.the proposed method of contingency ranking is able to distinguish clearly the actual severity of the system considering line loading, voltage profiles and voltage stability index from one contingency to other. Hence the proposed method eliminates problem of the masking effect. TABLE VI NUMBER OF LINE/BUSE UNDER DIFFERENT SEVERITY CATEGORIES Line outage between buses Number of Line Loading Voltage Profiles Voltage Stability Indices LS BS AS MS BS AS MS VLS LS BS AS MS. VI. CONCLUSIONS In this paper, in addition to real power loadings and bus voltages, the voltage stability indices at the load buses are also used as the post-contingent quantities to evaluate the network composite contingency ranking. These postcontingent quantities are expressed in fuzzy set notation. Then the heuristic rules employed in contingency ranking are compiled to reach the overall system severity index. The proposed contingency ranking method eliminates the masking effect effectively. The above-proposed fuzzy approach has been tested and results for a -bus Equivalent EHV Power System Network are presented. VII. REFERENCES [] F.D. Galiana. Bound estimates of the severity of line outages. IEEE Transactions on PAS 9;Vol.; -. [] T.S. Sidhu, L.Cui. Contingency screening for steady state security analysis by using FFT and ANNs. IEEE Transactions on Power Systems ; Vol.; -. [] G.C. Ejebe, B.F.Wollenberg, Automatic contingency selection. IEEE Transactions on PAS 99,Vol.9; 9-9. [] T.F. Halpin, R.Fischl, R.Fink. Analysis of automatic contingency selection algorithms. IEEE Transactions on PAS 9;Vol.; 9-9. [] Yuan Y.H, Kuo H.C. Fuzzy Set Based Contingency Ranking. IEEE Transactions on Power Systems 99; (); 9-9. [] Bansilal, Thukaram D, Parthasarathy K. Optimal reactive power dispatch algorithm for voltage stability improvement. Electrical Power and Energy Systems 99; (); -. [] Udupa A N, Thukaram D, Parthasarathy K. An expert fuzzy control approach to voltage stability enhancement. Electrical Power and Energy Systems 999; ;