Value of security: modeling time-dependent phenomena and weather ...

IEEE TRANSACTIONS ON POWER SYSTEMS, VOL. 17, NO. 3, AUGUST 2002

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Value of Security: Modeling Time-Dependent Phenomena and Weather Conditions Mario A. Rios, Member, IEEE, Daniel S. Kirschen, Senior Member, IEEE, Dilan Jayaweera, Dusko P. Nedic, and Ron N. Allan

Abstract—Deterministic security criteria provide a degree of security that may be insufficient under some operating conditions and excessive for others. To determine an appropriate level of security, one should perform a probabilistic cost/benefit analysis that balances the cost of the security margin against its benefits, i.e., the expected societal cost of the avoided outages. This paper shows how a previously published method based on Monte Carlo simulation can be enhanced to take into account time-dependent phenomena (TDP) such a cascade tripping of elements due to overloads, malfunction of the protection system, and potential power system instabilities. In addition, the importance of using failure rates that reflect the weather conditions is discussed. Studies based on the South-Western part of the transmission network of England and Wales demonstrate the validity of the models that have been developed. Index Terms—Power system operation, power system security, probabilistic models, weather modeling.

I. INTRODUCTION

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OWER systems are always operated with a significant security margin to ensure that the transmission network is capable of withstanding unpredictable events such as line and generator outages. If the security margin is determined using deterministic criteria, the resulting degree of security may or may not be optimal depending on the operating conditions. Instead of following fixed security standards for the operation of the power system, a cost/benefit analysis should be performed. While the cost of security is reflected directly and deterministically in the payments made to the generators, the benefit is related to the consequences of stochastic events and is therefore considerably more complex to evaluate. When exposed to the same disturbances under the same conditions, a more secure dispatch leads to smaller voluntary or involuntary load disconnections and requires fewer emergency actions than a less secure dispatch. The avoided societal costs of the load disconnection and the avoided cost of the emergency actions constitute the benefit of the more secure dispatch. Since unscheduled outages in power systems are stochastic phenomena, computing their cost requires a probabilistic approach. While probabilistic methods have been used extensively in power system planning, they have so far not been widely applied in the operational timeframe. Manuscript received January 11, 2000; revised March 26, 2000. This work was supported by the U.K. Engineering and Physical Sciences Research Council under Grant GR/K80310, and the National Grid Company. The authors are with the University of Manchester Institute of Science and Technology, Manchester, U.K. Publisher Item Identifier 10.1109/TPWRS.2002.800872.

Operators are less comfortable with uncertainty and prefer security [1] deterministic criteria, e.g., preventive or where the cost of a single outage is zero. However, as [2] shows, competition may force utilities to accept more risks. In order to manage this increased exposure to risk, the use of probabilistic techniques becomes essential. Analyses of reports of major disturbances [3]–[5] shows that these incidents are usually caused by combinations of failures that are deemed not probable ac). Determincording to traditional security criteria (e.g., istic contingency analysis is therefore ineffective in such cases. One of the advantages of adopting a probabilistic approach to security is that the Monte Carlo simulation has the ability to look beyond the probable contingencies and take into account rare but significant events. Rather than checking that the system could survive a limited set of contingencies, the proposed approach uses Monte Carlo simulation to calculate the Value of Security (VaS), which is defined as the expected cost of outages. This cost can vary significantly depending on the margin of security adopted by the operator. The simulation starts from the state of the power system as it is expected to be operated over the next day or the next few hours and subjects it to random events such as faults on lines, transformers, and cables, as well as outages of generators and compensation equipment. The ability of the system to sustain these disturbances is modeled using a quasi-steady state computation that takes into consideration the actions that the operator would be expected to take [6], [7]. Most of the time, the operator only needs to redispatch the generation or adjust the reactive control variables to remove constraint violations. In some cases, the only way the operator can avert a system collapse is by shedding some load. While such load-sheddings do not usually involve a direct cost to the utility, they have a very large social cost that must be taken into consideration in our cost/benefit analysis. In some relatively rare but important instances, the disturbance is so large that no corrective action (not even large amounts of load-sheddings) could prevent a collapse of the entire system. Such events are fortunately rare but must be taken into consideration because of their enormous social cost. Since this approach is intended to be used in the operational time frame, the initial conditions are known much more accurately than for planning studies. On the other hand, the fidelity requirements are much higher. Consequently, complex time-dependent phenomena (TDP), such as cascading outages, sympathetic trippings, and transient instabilities, must be modeled if the computed VaS is to be meaningful.

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IEEE TRANSACTIONS ON POWER SYSTEMS, VOL. 17, NO. 3, AUGUST 2002

Fig. 1. Processing done for each trial of the basic Monte Carlo simulation used for calculating the VaS.

This paper presents models for representing these TDP in the VaS computation. It also shows how the system can be analyzed taking these phenomena into account. In addition, the probabilities used to generate the random events must reflect not only the intrinsic characteristics of the equipment involved, but also external factors such as weather conditions. These external factors can have a significant effect on the probability of faults and hence on the expected cost of outages for a particular operating dispatch. This paper presents a method for adjusting failure rates under given weather conditions. Finally, the paper compares the results of the VaS for a base case (without TDP and weather effects), a case considering TDP and a case including weather effects. These studies are carried out on the South-Western part of the National Grid System in England and Wales. II. CALCULATING THE VALUE OF SECURITY The VaS of an operational plan is defined as the expected cost of unplanned outages. This quantity consists primarily of the social cost of load-sheddings. It also includes a much smaller component that reflects the cost of the corrective actions (e.g., generation redispatch) needed to remove constraints. A large number of trials is required to calculate the expected VaS using Monte Carlo simulation. In each trial of this simulation, random outages are applied to a known state of the system that results from the implementation of the operational plan. Fig. 1 details the four parts of the processing done for each trial: 1) generation of the disturbance; 2) computation of an equilibrium point; 3) correction of constraint violations; 4) evaluation of the cost of this trial.

The initial system state given by the network topology, load demand, and generation schedule is modified by random disturbances (outages of lines, transformers, busbars, compensation equipment, and generation plant). After restoring the generation-load balance if necessary, the new equilibrium point of the system is calculated using a power flow. If the power flow diverges, this is taken to indicate that the occurrence of this contingency state would result in voltage stability problems. The acceptability of this approach has been demonstrated in [8]. It is also important to keep in mind that the objective of this work is not to measure the exact point at which a voltage collapse might occur. Instead, it is to model the detection by a system operator of the onset of such a problem and the simulation of the corrective actions that he or she might take. Since most operators do not currently have sophisticated voltage security assessment tools at their disposal, highly accurate calculations are therefore not necessary. Based on conversations with experienced operators, a heuristic technique has therefore been developed to determine how much load is likely to be shed to save the system from a perceived problem. It is assumed that the operator’s response to an impending collapse would be to shed load in 5% blocks in the area of the largest mismatch. This load-shedding is repeated until convergence of the power flow is achieved. If convergence cannot be achieved by shedding load in the worst affected area, the load disconnections are extended to neighboring areas where they proceed again in blocks of 5% of the area load. If convergence has not been achieved after 100 load-shedding steps, the system is deemed to have collapsed. When the system has reached an equilibrium point (i.e., convergence of the power flow has been achieved), the resulting state of the system may exhibit violations of normal operating limits. Corrective actions must be taken to bring the system back within acceptable limits. Examples of possible corrective actions include redispatching generation, changing voltage setpoints, and tap ratios. Load is not shed to remove violations of operating limits if these violations cannot be corrected using normal controls. A fuzzy expert system with embedded power flow and linear sensitivity analysis [6] determines the extent and location of these corrective actions. The social cost of the load-sheddings and the actual costs of the corrective actions are computed and tallied. Tests have confirmed that the actual cost of the corrective actions is much smaller than the social cost of outages. III. TIME-DEPENDENT PHENOMENA (TDP) Most power systems are operated with a sufficient security margin that a single random outage will usually not cause such a serious disturbance. Two or more independent random outages could trigger a collapse if they take place within an interval of time sufficiently short that operators do not have the time to react appropriately. Analyses of major disturbances [3]–[5], [9]–[11] strongly suggest that a single random event occasionally triggers a sequence of events that leads to a serious disturbance. This sequence of events usually involves one or more of the following phenomena: 1) cascade tripping of transmission elements due to thermal overload;

RIOS et al.: VALUE OF SECURITY: MODELING TIME-DEPENDENT PHENOMENA

2) sympathetic tripping of power system components following a fault (i.e., the unnecessary tripping of branches or injectors due to a malfunction in the protection system); 3) transient instability. A rigorous analysis of such sequences of events would require a time-domain simulation of their evolution. Such a simulation requires so much computing time that it is currently incompatible with the large number of trials that is required for a Monte Carlo simulation. A modeling of these TDPs that is sufficiently accurate, yet simple enough to be incorporated in the VaS calculation, has been developed. A. Modeling of Cascade Tripping When a set of parallel or quasi-parallel lines is heavily loaded a fault and subsequent tripping of one of these lines may cause overloads on the other lines. Unless corrective action is taken promptly by the operator, overload protection relays on these lines or faults due to sagging may cause cascade tripping of one or more remaining lines. This characteristic is modeled in the computation of the VaS by assuming that the overloaded lines are tripped in % of the situations encountered [12], where is the probability that the operator is unable to eliminate the overloads before the protection operates. B. Modeling of Sympathetic Tripping It has been observed in a large proportion of blackouts that protection system failures contribute to the degradation process. Failed or improperly set protection can make a bad situation worse. A study of significant disturbances (reported by NERC for the period 1984–1988) indicates that protective relays were involved in 75% of major disturbances [3], [4]. The concepts of hidden failure and vulnerability region (VR) are very useful for modeling protection system malfunction [3], [4]. A hidden failure in a protection system is a permanent defect that will cause a relay or a relay system to remove incorrectly and inappropriately circuit elements as a direct consequence of another switching event (the initial disturbance). Therefore, hidden failures play an important role in extending the disturbance. Each hidden failure has a region of vulnerability associated with it. If an abnormal event occurs inside this VR, the hidden failure may cause the relay to incorrectly remove the circuit element, thereby creating a larger abnormal state in which additional hidden failures may be exposed. This paper proposes a probabilistic method which includes these phenomena in the VaS computation. It associates the following characteristics with each transmission element: 1) a probability ( ) associated with the malfunction of the element’s protection system when a failure occurs in its VR (conditional probability); 2) a VR that defines the portion of the system where a fault may provoke the tripping of the element. A simple definition of the VR based upon the reach settings of distance relay units is used [3], [4]. For example, the VR associated with the relay at the A-end of line A–B in Fig. 2, consists of the union of four VRs.

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Fig. 2. VR of line A–B.

Type 1—Reverse local bus VR: The line relays at bus B are prevented from tripping by the directional feature of the relays at bus A. The VR extends from the local bus (A) up to half of the line as determined by the setting of the relays at bus B. Type 2—Remote bus VR: the VR is beyond the remote bus (B) and has a reach of half of the line protected by the relay. Type 3—Zone 2 VR: the VR is beyond bus B and has a reach of 20% of the line protected by the relay. This VR reflects the problems that occur when the timer of the zone 2 distance relay at bus A fails closed. Type 4—Zone 3 VR: the VR is similar to type 3 except that the reach of the region is 1.2 times the longest line connected behind the remote bus (B). This VR reflects the problems that occur when the timer of the zone 3 distance relay at bus A fails closed. When a fault occurs on a line, transformer, or busbar, its potential effect on protection malfunction is evaluated for each element that has the original faulted element in its VR. For example, suppose that a fault occurs on line 7–8 of Fig. 2. Since this line is in the VR of the relay at A of line A–B, a Monte Carlo trial will indicate whether or not line A–B is tripped by sympathy. The probability used in this Monte Carlo trial is the value . C. Modeling the Loss of Stability of Generating Units The disconnection of one or more generating units because of loss of synchronism will usually seriously degrade the operating state of a power system. Such a disconnection results from a line fault, a generator failure, or a cascading event in the transmission system. Probabilistic modeling of transient stability is a very complex problem because of all the parameters that have to be taken into consideration. Some very interesting modeling and analysis work has been done in this area [13], [14]. While the time, type, and location of the fault are independent events, the critical clearing time depends on the type and the location of the fault. Assessing the transient stability of the system therefore requires the consideration of conditional probabilities of stability. Billinton and Aboreshaid [13] define the probability of stability ) as follows: due to a fault on line ( (1) where

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probability of stability for a given fault of type at location of line ; probability of a fault of type ; probability of a fault at location . It is assumed that any of four fault types can occur on any of the portions of the line. Off-line computations are necessary to obtain the set of prob, , , and . In the Monte Carlo simuabilities lation used for the VaS calculation, random sampling using the determines whether a fault provokes set of probabilities instability in the system. If a stability problem is simulated, it is necessary to determine the affected generators. Off-line stability studies can be used to determine the VRs associated with the stability of each generator. Thus, if a fault on line provokes instability and this line is in the VR of a generator, then this generator is disconnected. One might argue that the proposed method requires the knowledge of a number of parameters that are difficult to obtain. The techniques described in [15] could prove very useful for the estimation of these parameters. While it is clear that uncertainty on the value of these parameters may affect the accuracy of the absolute VaS, one should keep in mind that this value is used primarily for comparison purposes. Reference [7] describes a technique for efficiently comparing two or more operating scenarios on the basis of the VaS. This technique is based on correlated sampling and considerably reduces the effect of the errors on the parameters by comparing the scenarios using the same sets of random contingencies. D. Incorporating TDP in the VaS Calculation Fig. 3 illustrates the changes that have to be made to the basic Monte Carlo simulation to incorporate the effect of TDP in each trial. As discussed above, random outages can be accompanied by sympathetic trippings of transmission lines due to protection malfunctions and by the disconnection of generators because of transient instability. On the basis of the models described above, these additional outages are simulated in a probabilistic manner, i.e., on the basis of the selection of random numbers. When the system has reached an equilibrium point (i.e., convergence of the power flow has been achieved), a series of cascade tripping events may occur because some lines may be overloaded. In this case, a new power flow computation is required. If these cascade outages are severe, the power flow may diverge and load is again shed until a new equilibrium point is reached. IV. WEATHER EFFECT Weather conditions are fairly predictable over the operational time scale. Hence, the weather need not be regarded as a random variable, and the effects of predicted weather patterns can be reflected in the probabilities of different random events occurring in the power systems. As stated in [16], failure rates of some components, such as overhead transmission lines, depend on the weather conditions to which they are exposed. The weather conditions that affect the performance of the transmission lines could vary from one region to another and could be different from one season to another. Lightning, wind speed, and precipitations have the most

Fig. 3. Processing done for each trial of the Monte Carlo simulation when modeling the TDP.

significant effect on the reliability of the system. In addition, the severity of the weather scenario is determined by the intensity of the constituent aspects. Therefore, the actual number of severity levels needed to represent weather aspects depends not only on the available data but also on an appreciation of the intensity of the individual constituent factors and their impact on the transmission network. For the VaS computation, five weather states have been defined: 1) normal weather; 2) thunderstorm; 3) freezing rain/wet snow; 4) high winds; and 5) dry spell followed by fog. Alternatively, a simpler definition of weather states would define only two possible states: 1) adverse weather and 2) normal (or nonadverse) weather. The weather state can be specified on a regional basis in order to model different weather conditions within the system. The proportion of failures of network element n occurring in each weather state is [17] (2) where proportion of failures for component ; average failure rate of component ;

in weather state

RIOS et al.: VALUE OF SECURITY: MODELING TIME-DEPENDENT PHENOMENA

failure rate of component n in weather state ; duration of the weather state ; equal to the sum of all weather state durations. is usually not available for each individual component. Only an average value ( ) for each class of components (e.g., lines at 400 kV) can be obtained from the data collected for most is computed from (3) as systems. Therefore, a particular

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TABLE I SUMMARY OF TEST RESULTS

(3) Hence, the average failure rate is adjusted by the factor to obtain a weather dependent failure rate. This adjustment is only applied to overhead lines since they are the only type of component whose performance is significantly affected by the weather. Each region that a line crosses may have a different . weather condition and thus a different adjustment factor The failure rate of the line is therefore adjusted by a factor that depends on the length of the line and the weather in each region (4) where number of regions that the line crosses; length of the line in region ; total length of the line. V. TEST RESULTS The concepts described in this paper have been tested using a model representing the South-Western region of the transmission system of England and Wales [18]. This system has 53 buses, 107 branches, and 21 generators. The probability of failures for transmission equipment and generating units have been calculated on the basis of published reliability data [19], [20]. Two scenarios were studied. 1) Oil Scenario: an oil-fired power station on the south coast of England generates. The normal operating cost for this scenario is £183 195. 2) No-Oil Scenario: the oil-fired station does not generate and its output is replaced by extra generation at a large power plant near London, U.K. This scenario is normally considered as less secure than the other one but its normal operating cost is only £178 124. The Monte Carlo simulation was deemed to have converged when a degree of confidence of 95% was achieved for a confidence interval of 5% of the VaS. A minimum of 20 000 trials was set to avoid premature convergence. In most cases the simulation stopped after this minimum number of trials and took about 4 min of CPU time on a SUN Enterprise 450. Table I gives the estimated value of the outage costs (in £1000) and the estimated standard deviation ( ) for both scenarios. The simulations were repeated five times for each case and the value shown in Table I represents the average of these five simulations. The last column shows the number of cascade, sympathetic, or transient instability trippings that occurred in all the trials done for both cases. The effect of each of these phenomena has been studied separately. Since the data required to calculate the probability of transient instability or sympathetic tripping may be

difficult to obtain, the computations have been done for a range of values of these probabilities ( value in the first column where applicable). These results show that, in all cases, the security cost of the Oil scenario is lower than the cost for the No-Oil scenario. However, since the energy cost of the Oil scenario is about £5000 higher, choosing the best scenario is not always obvious, except for the cases with high security costs (e.g., bad weather and high probability of sympathetic tripping). In those cases, the Oil scenario is clearly the cheapest on a total cost basis. Modeling of cascade trippings and transient instability does not have a measurable effect for the scenarios considered and relatively few such events were simulated. This is not very surprising because the system used for these tests consists of relatively short lines with high thermal ratings. On the other hand, the results show that hidden failures and the consequent sympathetic tripping have a significant effect on the outage costs. The possibility of such phenomena should therefore be taken into consideration when deciding on the desired level of security in a power system. Utilities should therefore collect data that will make possible a more accurate estimation of the probability of transient instability and sympathetic tripping. Finally, a comparison of the first and last lines of Table I shows that the weather model that has been developed is able to quantify the effect that adverse weather conditions have on the security of the system. VI. CONCLUSIONS This paper has discussed the modeling of TDP, such as cascade and sympathetic tripping, transient stability, and weather effect in the computation of the VaS in power systems. Studies carried out show that sympathetic trippings and weather conditions have the most significant impact on the load interruption costs and that this effect depends on the operating scenarios under consideration. Method and models for taking these phenomena into consideration in a Monte Carlo simulation have been described. Incorporating these effects in the calculation of the VaS makes possible a more accurate cost/benefit analysis. The results presented show that these phenomena can have a significant influence on the scenario that the operator should adopt to achieve an optimal balance between cost and security. More

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work is needed to quantify more accurately the probabilities of failure used in the proposed models. REFERENCES [1] B. Stott, O. Alsac, and A. J. Monticelli, “Security analysis and optimization,” Proc. IEEE, vol. 75, pp. 1623–1644, Dec. 1987. [2] The National Grid Company, “A review of transmission security standards,”, Coventry, U.K., 1994. [3] A. G. Phadke and J. S. Thorp, “Expose hidden failures to prevent cascading outages,” IEEE Comput. Appl. Power Syst., vol. 11, no. 3, pp. 20–23, 1996. [4] Tamronglak, S. H. Horowitz, A. G. Phadke, and J. S. Thorp, “Anatomy of power systems blackouts: Preventive relaying strategies,” IEEE Trans. Power Delivery, vol. 11, pp. 708–715, Apr. 1995. [5] M. J. Mackey and CIGRE WG 34.09, “Summary report on survey to establish protection performance during major disturbances,”, Electra Rep. 196, June 2001. [6] K. R. W. Bell, D. S. Kirschen, R. N. Allan, and P. Kelen, “Efficient Monte Carlo assessment of the value of security,” in Proc. 13th Power System Computation Conf., Trondheim, Norway, June 1999, pp. 81–87. [7] D. S. Kirschen, M. A. Rios, K. R. W. Bell, and R. N. Allan, “Selection of operation scenarios based on the value of security,” in Proc. 6th Int. Conf. Probabilistic Methods Applied to Power Systems, Madeira, Brazil, Sept. 2000, Paper PSP-003. [8] B. Gao, G. K. Morison, and P. Kundur, “Toward the development of a systematic approach for voltage stability assessment of a large-scale power systems,” IEEE Trans. Power Syst., vol. 1, pp. 1314–1319, Aug. 1996. [9] J. Corwin and W. Miles, “Impact assessment on the 1977 New York blackout,”, Washington, DC, Tech. Rep. U.S. DOE, July 1977. [10] E. Agneholm, “The restoration process following a major breakdown in a power system,” Chalmers University of Technology, Gothenburg, Sweden, Tech. Rep. 230L, May 1996. [11] WSCC Investigative Task, Salt Lake City, UT, “WSCC preliminary system disturbance report August 10, 1996,” WSCC, Tech. Rep. for the DOE, Aug. 1986. [12] A. Merlin and J. C. Dodu, “New probabilistic approach taking into account reliability and operation security in EHV power system planning at EdF,” IEEE Trans. Power Syst., vol. 1, pp. 175–181, Aug. 1986. [13] R. Billinton and S. Aboreshaid, “Security evaluation of composite power systems,” IEE Proc., Gener. Transm. and Distrib., vol. 142, no. 5, pp. 511–516, 1995. [14] J. D. McCalley, A. A. Fouad, V. Vittal, A. A. Irizarry-Rivera, B. L. Agrawal, and R. G. Farmer, “A risk-based security index for determining operating limits in stability-limited electric power systems,” IEEE Trans. Power Syst., vol. 12, pp. 1210–1219, Aug. 1997. [15] L. Wehenkel, Automatic Learning Techniques in Power Systems. Norwell, MA: Kluwer, 1998. [16] M. R. Bhuiyan and R. N. Allan, “Inclusion of weather in composite system reliability evaluation using sequential simulation,” IEE Proc., Gener. Transm. and Distrib., vol. 141, no. 6, pp. 575–584, 1994. [17] R. Billinton and R. N. Allan, Reliability Evaluation of Power Systems, 2nd ed. New York: Plenum, 1996. [18] N. T. Hawkins, “On-line reactive power management in electric power systems,” Ph.D. dissertation, University of London, London, U.K., 1996.

[19] R. Billinton, R. Ghajar, F. Filippeli, and R. Del Bianco, “Transmission equipment reliability using the Canadian Electrical Association information system,” in Proc. 2nd Int. Conf. Reliability of Transmission and Distribution Equipment, Mar. 1995, IEE Conf. Pub. 406, pp. 13–18. [20] Canadian Electricity Association (CEA), Montreal, QC, “Generation equipment status—Annual report 1995,” CEA, 1996.

Mario A. Rios (S’89–M’91) received the B.Sc. and M.Sc. degrees in electrical engineering from Andes University, Bogota, Colombia, in 1991 and 1992, respectively. He received the Ph.D. in electrical engineering from INPG-LEG, France, and Andes University. Currently, he is working at CONCOL, Bogota, Colombia, and the University of Andes. His interests include transient and dynamical stability studies of power systems, reliability and planning of power systems, as well as control and analysis of power systems. Dr. Rios is a member of the IEEE.

Daniel S. Kirschen (S’80–M’84–S’84–SM’93) received the electrical and mechanical engineer degree from the Free University of Brussels, Belgium, in 1979. He received the M.Sc. and Ph.D. degrees from the University of Wisconsin, Madison, in 1980 and 1985, respectively. Currently, he is a Reader at the University of Manchester Institute of Science and Technology, Manchester, U.K. His main areas of interest are power-system operation and economics. Dr. Kirschen is a Senior Member of the IEEE.

Dilan Jayaweera received the B.Sc. degree in electrical and electronic engineering from the University of Peradeniya, Sri Lanka, in 1995. He received the M.Sc. degree in electrical power engineering from the University of Manchester Institute of Science and Technology in 2000. Currently, he is working on his Ph.D. dissertation at University of Manchester Institute of Science and Technology.

Dusko P. Nedic received the B.Sc. degree in electrical engineering from the University of Novi Sad, Yugoslavia, in 1994. He received the M.Sc. degree in electrical engineering from the University of Belgrade in 1999. From 1996 to 2000, he was a research engineer at Elektrovojvodina, Novi Sad. He is currently working on his Ph.D. dissertation at the University of Manchester Institute of Science and Technology.

Ron N. Allan is Professor of Electrical Energy Systems at the University of Manchester Institute of Science and Technology. His research activity has focused on the development and application of concepts, as well as models and evaluation techniques for assessing power-system reliability. He has published many papers and has co-authored three textbooks, and has contributed to several others.