A Comprehensive Approach for Bulk Power System Reliability Assessment

PAPER D: #44 1 A Comprehensive Approach for Bulk Power System Reliability Assessment Fang Yang, Student Member, EEE, A. P. Sakis Meliopoulos, Fellow, EEE, George J. Cokkinides, Member, EEE, and George K. Stefopoulos, Student Member, EEE Abstract This paper proposes a comprehensive approach for bulk power system reliability assessment. Specifically, a framework of security-constrained adequacy evaluation (SCAE) based on analytical techniques is developed to assess the ability of a bulk power system to supply electric load while satisfying security constraints. This approach encompasses three main steps: (a) critical contingency selection, (b) effects analysis, and (c) reliability index computation. Based on an advanced singlephase quadratized power flow, a state linearization approach is developed to improve contingency selection accuracy, and a nondivergent optimal quadratized power flow (NDOQPF) algorithm is proposed to perform contingency effects analysis realistically and efficiently while assuring the convergence of power flow solution. The NDOQPF algorithm is also capable of solving the RTO/SO operational model in the deregulated environment. n addition, a breaker-oriented system network model is developed, based on which the SCAE framework can include the effects of protection system hidden failures on bulk power system reliability as well. The comprehensive approach is demonstrated with EEE reliability test systems. ndex Terms Bulk power system reliability assessment, contingency selection, effects analysis, reliability index, protection system hidden failure, security-constrained adequacy evaluation, single-phase quadratized power flow model.. NTRODUCTON N bulk power system planning and operating procedures, reliability assessment aims to assure reliable and acceptable electricity service to customers[1~4]. With the increase in the complexity of modern power systems and the movement toward power industry deregulation, system models and algorithms of traditional reliability assessment techniques become obsolete as they suffer from the lack of realistic system modeling and slow convergence (even nonconvergence) when the system is heavily stressed. n addition, recent research shows that protection system hidden failures may lead to cascading tripping events and are recognized as a contributing factor in power system disturbances [5~7]. Since protection systems are generally assumed to be perfect when considering bulk power system reliability, the effects of hidden failures in protection systems have not been considered in the current reliability assessment practice. This work was supported in part by the Power System Engineering Research Center (PSERC). Authors are with the Georgia nstitute of Technology, Atlanta, GA 3332, USA. The obective of this study is to advance bulk power system reliability assessment techniques to allow more realistic system modeling and efficient reliability assessment. For this purpose, a framework of security-constrained adequacy evaluation (SCAE) based on analytical techniques is proposed, which includes three main steps: (a) critical contingency selection, (b) effects analysis, and (c) reliability index computation. An advanced single-phase quadratized power flow (SPQPF) model is applied as a basis for the first two steps. Based on the SPQPF model, a state linearization approach is developed to improve contingency selection accuracy, and a non-divergent optimal quadratized power flow (NDOQPF) algorithm is proposed to perform contingency effects analysis realistically and efficiently while assuring the convergence of power flow solution. The NDOQPF algorithm is applicable in both regulated and deregulated operational models. n addition, a breaker-oriented system network model is developed such that the effects of protection system hidden failures can be included in the reliability assessment in the SCAE framework. The proposed comprehensive approach is demonstrated with EEE reliability test systems.. METHODOLOGY The overall computational algorithm of the proposed SCAE methodology for bulk power system reliability assessment is shown in Figure 1. First of all, feasible contingencies up to a certain level are defined. Then a contingency enumeration and selection is applied to enumerate and rank contingencies in each level according to their impact on system operation. The most critical contingencies are then subected to contingency effects analysis. n contingency effects analysis, two options are available in branches A and B: the network solution with remedial actions and the market simulation, which provide the means to perform effects analysis in the regulated or deregulated environment. The results of contingency effects analysis are stored and processed to calculate reliability indices that indicate system reliability levels in a quantitative way. The formulation of SPQPF, maor steps in the SCAE framework, and the evaluation of protection system hidden failures are described in following sections. A. Single-Phase Quadratized Power Flow [8] Traditional power flow models usually suffer from the lack of ability to model complex component characteristics and 978-1-4244-219-9/7/$25. 27 EEE 1587 PowerTech 27

PAPER D: #44 2 slow convergence. To improve accuracy and efficiency in contingency selection and effects analysis, a single-phase quadratized power flow (SPQPF) model is applied in the proposed SCAE methodology. The SPQPF model is set up based on the application of the Kirchhoff s current law at each bus, with the intention that most of power flow equations are linear in bulk power systems. Also, system states are expressed in Cartesian coordinates (bus voltage real and imaginary parts) that can avoid trigonometric terms and make power flow equations less complex. Moreover, since Newton s method is ideally suitable to solve quadratic equations, all power flow equations are quadratized, which are achieved by introducing additional state variables. All these considerations in the formulation of the quadratized power flow model can effectively reduce nonlinearity and complexity in the power flow model and provide superior performance in two aspects: (a) faster convergence and (b) ability to model complex load characteristics in the quadratized form. Figure 1. Overall computational algorithm of SCAE methodology for bulk power system reliability assessment. B. Contingency Enumeration and Selection All feasible contingencies are enumerated according to different outage levels. Contingency selection is then applied to each level to identify critical contingencies that may lead to system unreliability, such as system loss of load. Traditional contingency selection based on performance index (P) linearization methods is prone to misranking due to the highly nonlinear nature of the traditional power flow model. n this work, a state linearization approach [9] is applied to reduce the error introduced by the P linearization. n this approach, the contingency ranking problem is reformulated using the SPQPF model that has milder nonlinearities (by construction), and an indirect differentiation procedure is used to yield higher order sensitivity terms in calculating the P of postcontingency situation as shown in Equation (1). Specifically, instead of linearizing performance index directly as in the traditional contingency selection methods, the system state variables are linearized with respect to the contingency control variable, the performance index of post-contingency is then calculated using the linearized post-contingency system state variables, which includes higher-order terms in Taylor s series and provides traces of indices with curvature, which can follow the highly nonlinear variations of the original performance indices to some extent. Results of the state linearization approach have shown promising results in improving contingency ranking accuracy [1~12]. The change in performance index ( J ) from pre-contingency to postcontingency is then used for contingency ranking. After contingency ranking, the most critical contingencies are subected to the effects analysis. post dx J J ( x ( uc 1), uc) du post o dx pre o J J x u 1, c uc J x, uc 1. (1) duc where J performance index pre J pre-contingency performance index post J post-contingency performance index x system state variable x pre-contingency state variable u contingency control variable c Note that the value of contingency control variable u c is one (1.) for the pre-contingency condition and changes to zero () for the post-contingency case. C. Effects Analysis Based on NDOQPF Algorithm A non-divergent optimal quadratized power flow algorithm[13,14] is presented for effects analysis to simulate the system response to the most critical contingencies, including maor controls and operational practices. Consider a system and let vectors x and u represent the system state variables and control variables of remedial actions (RAs) such as unit real/reactive generation adustments, switched capacitors/ reactors, transformer tap/phase shift adustments, and the last RA would be used is load shedding. Assug a given operating state vector x and control variable vector u and considering a general system bus k as shown in Figure 2, unless x and u represent a power flow solution, a mismatch value exists at bus k equal to mk _ r. mk _ i Assume that a fictitious current source ( mk _ r ) is mk _ i placed at bus k and let the output of the current source be equal to the mismatch value mk _ r, the Kirchhoff s mk _ i current law is then satisfied at bus k. Similar fictitious sources/mismatches can be assumed for other SPQPF equations such that x and u represent the current operating condition of the system. The actual operating condition can be obtained by gradually driving the output of the fictitious 1588

PAPER D: #44 3 sources/mismatches to zero. This transition can be achieved along a traectory that maintains feasibility and optimality. Mathematically, above procedure is formulated as a constrained optimization problem. n r Minimize J m i u i1 Subect to G( x, u, m) V ~ P Q 1 ~ V V 1,, 1,, l g g u P g Q g u P Q g g u 1,, 1,, 1,, b ged g pv m m 1,, n, (2) where penalty coefficient for mismatches m mismatch value of the i th SPQPF equation i th weight coefficient of the remedial action u th amount of the remedial action adustment n number of SPQPF equations r number of total control variables G ( x, u, m) SPQPF equations x, u, m state, control, mismatch variable vectors respectively b number of buses l number of circuit branches g number of generators participating economic dispatch ed g number of PV generators pv r solution that may include load shedding. n the deregulated environment, power market participants submit their energy bids to the SO/RTO, and the SO/RTO deteres the least expensive dispatch of generation while satisfying customers demand and system reliability requirements [15, 16]. f transmission congestion occurs, energy bids and other remedial actions are appropriately selected to relieve congestion. Mathematically, such SO/RTO operational procedure is formulated as a constrained optimization problem. The obective is to imize the overall system cost in terms of generator bids while satisfying system constraints. The formulated constrained optimization problem in the deregulated environment is no different from that in the regulated environment. Therefore, the proposed NDOQPF algorithm is capable of efficiently solving such the generic SO/RTO operational model as well. D. Effects of Protection System Hidden Failures on Bulk Power System Reliability To take into account the performance of protection systems in reliability assessment, the system network model based on the breaker-oriented substation model is developed [17,18]. An example of breaker-oriented substation model is shown in Figure 3, which includes maor protection system components such as transducers (CT and VT), relays, and circuit breakers. Each component may suffer from hidden failures depending on its inherent mechanism. For example, transducers may not provide outputs that faithfully represent the primary outage or current due to the saturation, a relay may fail to detect the system status correctly and trip the intact system components as a result of an outdated setting, and any failures in the trip mechanism of a circuit breaker, such as the open circuit of trip coils or the circuit breaker plates fail to separate because of welding, will lead to circuit breaker fail to trip. Bus A CB1 TC1 Protection System 1 CB6 L1 F1 CT1 CT2 VT R1 L4 Figure 2. A general bus k in a power system with a fictitious current source. CB2 CB5 The mismatch variable v is reduced gradually from 1 to during the solution procedure. Given v in each step, the solution of the above optimization problem provides new control settings. These controls are implemented in the system and the power flow solution is updated. Any violated operating constraints are included in the set of active constraints. A nonzero value of mismatch variable indicates that the algorithm has not converged yet. The procedure is repeated until no mismatch and no constraint violation exist. The proposed algorithm achieves power flow non-divergence by introducing fictitious sources/mismatches that are driven to zero as the solution progresses. Therefore, the NDOQPF algorithm guarantees convergence if a solution exists; if a solution does not exist, the algorithm provides a sub-optimal L2 CB3 TC3 CT3 Bus B L3 CB4 Protection System 2 Figure 3. A breaker-and-a-half bus arrangement substation model Nowadays, various types of intelligent electronic devices (EDs) in power system substations are able to provide more redundant, accurate, and real time system data and make the system real time monitoring and analysis technologies possible. Such technologies can be used to perform real-time validation and verification for transducer outputs and relay CT4 TC4 R2 1589

PAPER D: #44 4 settings by means such as the substation level state estimation and real time system modeling. Therefore, the advanced system monitoring and analysis capability can detect hidden failures existing in transducers and relays considerably. However, such techniques do not detect the circuit breaker s ability to trip. Hidden failures in the circuit breaker trip mechanisms will remain uncovered until circuit breakers fail to open during disturbances. n this work, the consideration of protection system hidden failures concentrates on hidden failures in the circuit breaker trip mechanism (CBTM). The example substation shown in Figure 3 has six circuit breakers, each CBTM can cycle between normal and hidden failure statuses. This process can be modeled as a two-state Markov process. We assume that the occurrences of such hidden failures are independent with their own failure and repair rates. Two-state Markov models for the six CBTMs (CBTM1 to CBTM6) are shown in Figure 4, in which and represent failure and repair rates of each CBTM, CBTM1 1 1 CBTM2 CBTM3 CBTM4 CBTM5 CBTM6 2 2 3 3 4 4 Figure 4. Two-state Markov models of CBTMs 5 5 6 6 The probabilities of normal and hidden failure statuses of each CBTM are given in following expressions: p ( t) exp( ( ) t), q ( t) 1 p ( t) exp( ( ) t). (3) Hidden failures in CBTMs can cause the trip of intact equipment following system disturbances, which reduces the system reliability level. n this section, an approach of hidden failure effects analysis is proposed to obtain possible hidden failure outages following any initial faults. This approach is illustrated with the following example. We assume that the trip mechanism of circuit breaker 2 (CB2) in the example substation has hidden failure that can cause CB2 fail to open. f an initial fault F1 occurs on transmission line L1, circuit breakers 1 and 2 should open to isolate the faulty circuit L1 accordingly. Since CB2 fail to open due to its hidden failure, circuit breaker 3 (CB3) that is adacent to CB2 will open and cause the outage of intact component transmission line L2. Such effects analysis procedure can be repeated for all other possible initial faults. The hidden failure effects analysis procedure can be performed for all substations in the system. E. Reliability ndex Computation Reliability indices are computed on the basis of identifying the set of contingencies that satisfy a specific failure criterion and the transition rates from any contingency inside the set to a contingency outside the set. Three different classes of reliability indices, including probability, frequency, and duration indices, are computed.. APPROACH DEMONSTRATON n this section, the EEE 24-bus reliability test system and its derivation, the circuit breaker-oriented 24-substation reliability test system, are used to demonstrate advanced techniques developed in the proposed comprehensive approach for bulk power system reliability assessment. The EEE 24-bus reliability test system [19] was developed by the EEE reliability subcommittee for testing various reliability analysis methods. This system is used to test the system state linearization approach and the non-divergent optimal quadratized power flow algorithm. n addition, the hidden failure effects analysis method for evaluating the impact of protection system hidden failures on bulk power system reliability is demonstrated with the circuit breaker-oriented 24-substation reliability test system, which is derived from the EEE 24-bus reliability test system by converting each bus in the original system to a substation with a specific bus arrangement. A. State Linearization Approach To demonstrate the effectiveness of the state linearization approach for critical contingency selection and ranking, the first-level contingencies of the EEE 24-bus reliability test system are ranked using three different contingency selection and ranking methods in terms of the current-based circuit loading index. The three methods include (1) the full power flow solution method, (2) the traditional performance index linearization method, and (3) the proposed system state linearization method. The full power flow solution method calculates the exact performance index changes resulting from contingencies and provides a complete accurate ranking of the contingencies, which is used as the standard to verify the performance of other two methods. The second method is the traditional performance index linearization method that predicts the linear approximation of the exact performance index change. The third method is the proposed state linearization method that predicts the nonlinearity of performance index changes to a certain extent by including higher-order terms in Taylor s series. Based on the three methods, changes in the circuit loading index are computed for the first-level contingencies resulting from independent transmission circuit outages, based on which these contingencies are ranked. Part of ranking results is provided in Table 1, which demonstrates that the proposed state linearization method can reduce misranking significantly in critical contingency selection and ranking compared to the traditional performance index linearization technique. B. Non-Divergent Optimal Quadratized Power Flow Algorithm Based on the results of contingency selection and ranking, the non-divergent optimal quadratized power flow (NDOQPF) algorithm is applied to the most critical contingencies for their effects analysis. Part of the contingency effects analysis results for first-level contingencies resulting from independent circuit outages is listed in Table 2. For each contingency, the 159

PAPER D: #44 5 result shows if it causes any operating constraint violations; when constraint violations occur, the result shows if load shedding is required to maintain normal system operation; whenever load shedding is necessary, the corresponding contingency is recorded as a system failure state and make a contribution to system unreliability. Table 2 shows that six contingencies cause constraint violations and require load shedding for the system to operate normally. They represent system failure states. The remaining contingencies may cause constraint violations, but remedial actions without load shedding can maintain normal system operation. Such evaluation results reflect the ability of the NDOQPF algorithm to simulate contingencies in a realistic manner to capture the system response including all maor controls and adustments. Regarding the second-level or higher-level contingencies, using the traditional power flow algorithm to conduct the effects analysis may produce non-convergence because of the severe impact of high-level contingencies on system operation. This non-convergence problem can be solved using the NDOQPF algorithm. For example, consider a second-level contingency that involves the outages of two circuits C3-9 (first level) and C15-24 (second level). The traditional power flow under this second-level contingency diverges, while the NDOQPF algorithm converges and provides a list of remedial actions. For illustrative purposes, the effects analysis procedure and results of this contingency are detailed below. Table 1: Contingency ranking based on three methods. Outage Circuit Exact Ranking P Linearization Ranking State Linearization Ranking C6-1 1 33 1 C15-24 2 14 5 C3-24 3 1 4 C14-16 4 31 2 C16-17 5 32 3 C2-6 6 1 9 C2-23 7 2 6 C12-23 8 4 7 C16-19 9 13 13 C15-21 1 3 8 Table 2: SCAE of First Level ndependent Contingencies for EEE 24-Bus RTS (C: Circuit G: Generator) Rank No. Outage Component Constraint Violations (Yes/No) RAs w/o load shedding (Yes/No) Load Shedding (Yes/No) 1 C6-1 Yes Yes Yes 2 C15-24 Yes Yes Yes 3 C3-24 Yes Yes Yes 4 C16-17 Yes Yes Yes 5 C2-6 Yes Yes Yes 6 C13-23 Yes Yes Yes 7 C12-23 Yes Yes No 8 C16-19 Yes Yes No 9 C15-21 Yes Yes No 1 C15-16 Yes Yes No The first-level outage of circuit C3-9 does not cause any constraint violations. The solution after the first-level outage, represented with x (the vector of system state variables) and u (the vector of system control variables), is used as the base case for the second-level outage of C15-24. Under the operating point ( x, u ), after the first-level outage and given the additional outage of circuit C15-24, the mismatch vector m is calculated first. The artificial control variable v is then gradually reduced as follows: v : 1..667.333.. Note that when v is 1., the mismatch vector is m, and the operating point is x andu, the system does not have any constraint violations. n the progress of the solution, the optimization problem shown in Equation (2) is formulated at each step of the control variable v if constraint violations exist and solved using the linear programg technique. The procedure is repeated until variable v reaches zero. During the solution procedure, maor active constraints include the following two inequality constraints: V, V. 3 V 3 24 V 24 Such violated constraints cannot be eliated completely by the available remedial actions (excluding load shedding). Therefore, to maintain the normal system operating conditions, load shedding is applied, and 63% of the system load at bus 3 is tripped as a result. Load shedding _ bus3 113.82MW 23. 4MVAR. Corresponding to this load change, the reduction in the total amounts of system real power and reactive power outputs are as follows: P 16. 91MW, Q 23. 4MW. The solution of this second-level contingency illustrates the maor advantage of the NDOQPF algorithm in achieving the non-divergent solution when the system is overstressed by multi-level contingencies. C. Protection System Hidden Failure Effects Analysis The effects of protection system hidden failures on bulk power system reliability are evaluated using a circuit breakeroriented, 24-substation reliability test system, which is mostly derived from the original EEE 24-bus reliability test system. The approach used to develop the circuit breaker-oriented system is to replace each node (bus) of the original system with a substation that has specific bus arrangement (e.g., ring, breaker and a half, and so on). The bus arrangement at each node and the location of each circuit breaker become the explicit part of the network model. Based on the circuit breaker-oriented system model, the effects analysis of the circuit breaker trip mechanism (CBTM) hidden failure is performed for each substation. After the contingencies resulting from CBTM hidden failures for all substations are obtained and consolidated, the securityconstrained adequacy evaluation approach is applied to 1591

PAPER D: #44 6 evaluate contingencies resulting from independent, commonmode, and hidden failure outages. The reliability evaluation result of first-level contingencies resulting from transmission circuit outages shows that six contingencies that result from independent outages, four contingencies that result from the common-mode outages, and forty-seven contingencies that result from hidden failure outages lead to system unreliability. Therefore, most of contingencies that lead to system failures are contingencies resulting from hidden failure outages because of intact system component outages following initial system faults, which exacerbate an already stressed system. Part of these contingencies is provided in Table 3. Table 3: List of contingencies leading to system unreliability. Contingency Type Contingency Outage Component Number ndependent 1 C6-1 outage 2 C15-24 3 C3-24 4 C16-17 5 C2-6 Common-mode 6 C19-2A,B outage 7 C2-23A,B Hidden failure 8 C3-9,C3-24 outage 9 C2-4,C4-9 1 C5-1,C1-5 11 C6-1,C2-6 12 C8-1,C8-9 13 C6-1,C5-1 14 C11-14,C14-16 The reliability indices of probability, frequency, and duration of such system loss-of-load events are calculated for both situations with and without the consideration of contingencies resulting from hidden failure outages. All these results are shown in Table 4, which indicate that hidden failures in protection systems can downgrade the system reliability level considerably. Table 4: Comparison of reliability indices with and without contingencies resulting from hidden failure outages. Reliability ndex W/O Hidden Failure Outages With Hidden Failure Outages Probability 6.976e-4 8.93e-4 Frequency(/yr).261.384 Duration(hrs) 23.428 2.32 V. CONCLUSONS A comprehensive security-constrained adequacy evaluation (SCAE) methodology based on analytical techniques is proposed for bulk power system reliability assessment. Advanced techniques are developed to improve contingency selection and effects analysis performance. This work also investigates the effects of protection system hidden failures on bulk power system reliability. The advanced techniques in the proposed methodology are demonstrated with EEE reliability test systems. REFERENCES [1] R. Billinton and W. Li, Reliability Assessment of Electric Power Systems Using Monte Carlo Methods, Plenum Press, 1994. [2] R. Billinton and R. N. Allan, Reliability Evaluation of Power Systems, Plenum Press, 1996. [3] J. Endrenyi, Reliability Modeling in Electric Power System, John Wiley & Sons Ltd., 1978. [4] A. P. Meliopoulos, R. Kovacs, N. J. Balu, M. Lauby, N. D. Reppen, M. P. Bhavarau, and R. 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