R. N. Allen, R. Billinton, I. Sjarief, L. Gloel, and K. S. So, 'A Reliability ... Richard D. christie received his B.S. and M.E. degrees from Rensselaer in. 1973 and ...
IEEE Transactions on Power Delivery, Vol. 11, No. 4, October 1996
Distribution System Reliability Assessment Using Hierarchical Markov Modeling R.E. Brown*
R. D. Christie*
S. S. Venkata*
*Departmentof Electrical Engineering University of Washington, Box 352500 Seattle, WA 98195-2500
Abstract-Distribution system reliability assessment is concerned with power availability and power quality at each customer’s service entrance. This paper presents a new method, termed Hierarchical Markov Modeling (HMM), which can perform predictive distribution system reliability assessment. HMM is unique in that it decomposes the reliability model based on system topology, integrated protection systems, and individual protection devices. This structure, which easily accommodates the effects of backup protection, fault isolation, and load restoration, is compared to simpler reliability models. HMM is then used to assess the reliability of an existing utility distribution system and to explore the reliability impact of several design improvement options. I. INTRODUCTION Reliability concepts can be applied to virtually any engineered system. In its broadest sense, reliability is a measure of performance. This measure can be used to help systems meet performance criteria, to help quantify coniparisons between various options, and to help make economic decisions. The ultimate goal of reliability analysis is to help answer questions like “is the Jystem reliable enough?” “which scheme will fail less?” and “where can the next dollar be best spent to improve the system? ’’ When applied to power systems, reliability can be divided into the two basic aspects: system adequacy and system security [1,2]. Adequacy relates to the capacity of the system in relation to energy demanded and security relates to the dynamic response of the system to disturbances (such
96 WM 112-3 PWRD A paper recommended and approved by the IEEE Transmission and Distribution Committee of the IEEE Power Engineering Society for presentation at the 1996 IEEE/PES Winter Meeting, January 2125, 1996, Baltimore, MD. Manuscript submitted July 31, 1995; made available for printing November 13, 1995.
Snohomish County PUD #1 P.O. Box 1107 Everett, WA 98206
as faults). As such, system adequacy deals primarily with generation facilities or composite generation and transmission facilities. Since distribution systems are seldom loaded near their limits, system adequacy is of relatively small concern and reliability emphasis is on system security. Reliability assessment methods fall into two classes: simulation and analytical. Simulation is the most flexible method but suffers in computation time and uncertainty of precision. It has been successfully applied to generation systems , composite generation and transmission systeims [4,5], and substation reliability evaluation . Analytical methods can be further clivided into network modeling and Markov modeling. Network modeling has been the most popular technique for distribution system reliability analysis from the first EPRI program  to programs recently developed and used by major utilities [S-lO]. This popularity stems from Ihe simplicity of the method and the natural similarities between the network model and the distribution system topology. Unfortunately, network modeling cannot easily handle tiependent events such as fault isolation, load restoration, and complex protection systems. It is for this reason that research efforts on analytical reliability assessment techniques for distribution systems are shifting towards the more powerful method of Markov modeling. When a system can be described by a set of discriete states, and the probability of moving to a new state is oidy dependent upon the current state, the system can be described by a Markov model. Since distribution systems contain a large number of possible states, many simplifying assumptions must be made to limit the Markov model to a manageable size. Markov modeling has been successfully applied to transmission systems 1111 and distribution systems . The authors have developed a new analytical method for distribution system reliability assessment. This method is able to analyze the sustained interruption profile of a systlem without makiig limiting assumptions concerning switching systems, protection syste:ms, or individual component beh,avior. This method, called Hierarchical Markov Modeling, decomposes the reliability problem into three levels according to system topology, protection system behavior, :md
protection device behavior.
0 1996 IEEE
In order to determine the reliability of a distribution system, it is necessary to examine the interruption profiles of each customer. If the expected interruption frequencies and durations are known for each customer, basic reliability indices can be computed. Unfortunately, it is not practicable to look at each individual customer and directly determine these values. This is due to complex interdependencies between switching action and protection system behavior. What is needed is a method which can decompose the problem, address each issue separately, and combine the results to obtain customer interruption information. A technique termed Hierarchical Markov Modeling has been developed which addresses these issues. HMM creates a primary model based on system topology, secondary models based on integrated protection systems, and tertiary models based upon individual protection devices. Once the tertiary models have been solved, the secondary models can be solved. Solving the secondary models, in turn,allows the primary model to be solved and all of the customer interruption information to be computed. To illustrate HMM, the example distribution system seen in Figure 1 will be used. This system is characterized by two normally closed switches (Sl,S2), one normally open switch (S3), a breaker (Bl), three fuses (Fl,F2,F3), and three customers (Cl,C2,C3).
Figure 2. Primary M d k Model ~
This restores power to C1 and corresponds to State la. This state will be sustained until the system is either switched back to State 0, or is further switched to State lb, where C3 is restored through back feeding. State lb is attained by opening 52 and closing S3. In the primary model, states are determined exclusively by sectionalizing switch positions and not by the status of protection devices. The sectionalizing switches determine the system topology while the protection system determines how the system will respond to contingencies while in a certain topology. To accommodate the effects of the protection system, each state in the primary Markov model has its own associated secondary Markov model.
Figure 1. Example System
This system is normally fed from a single substation (shown by the heavy vertical line to the left), but can be back fed from a second substation (shown by the heavy vertical line to the right) if needed.
2. I Primary Markov Adodels (System Topology)
HMM begins by creating a primary model based on system topology. A generic primary model is seen in Figure 2. This model has a normal operating state (State 0), and additional states corresponding to various switching actions. In Figure 2, p’s represent repair rates, and 0’s represent switching rates. The normal operating state of the example system, State 0, corresponds the switch positions shown in Figure 1. Imagine a fault occurs at the position indicated. This causes B1 to trip and all customers to be interrupted. The system can then isolate the fault by opening S1 and resetting B1.
2.2 Secondary Markov Models (Protection Systems)
To model the protection system behavior of each primary model state, secondary models are be created. These models have a base state of all protective devices in a closed position. For example, State 0 of fhe example system primary model will have a secondary model associated with it. The base state of this model will correspond to B1, Fl, F2, and F3 being closed. A secondary model can transition out of its base state by a protection device opening (such as B1, F1, F2, or F3). Since all protection device events are assumed to be mutually exclusive (a good assumption in non-storm conditions), the opened device must close before another protection device can open. A secondary model characterized by N protective devices (PD-1 through PD-N) can be seen in Figure 3 (A’S represent failure rates and p’s represent repair rates) In the secondary model, protection devices can be either open or closed, and are characterized by a failure rate and a repair rate. This is accurate, but over-simplified. Although a protective device has a net failure rate, many separate events can cause the device to open . For example, B1 of the example system is supposed to trip if a fault occurs on the main feeder. B1 can also false trip, trip to backup a failed Euse, trip because of a miscoordinated fuse, etc. To accom-
1 I Protective Devices Closed
Figure 3. Secondruy Markov Model
modate these multiple failure modes, each protection device has an associated tertiary Markov model. 2.3 Tertiary Markov Models (Protection Devices)
To accommodate the complex behavior of individual protection devices, a tertiary model is developed. This model has a base state for when the device is closed, and an additional states corresponding to specific causes of tripping. Examples of these causes include primary tripping, backup tripping, maintenance, and false tripping. A generic tertiary model can be seen in Figure 4 (1’s represent failure rates and p’s represent repair rates).
0 0 0
spent in their associated primary model state to obtain annual values. Consider the seconday model corresponding to State 0 of the example system. C1 will be interrupted in the state corresponding to B1 tripping and the state corresponding 1.0 F1 tripping. If B1 is tripped HB, hdyr in State 0 and F1 is tripped HFI hr/yr in State 0, and the primary model shows that the system will be in State 0 Do hr/yr, then C1 can expect D,(HB, +HFl)hr/yr of interruption time due to State 0. After the annual customer interruption information is known for each primary state, the values for each state cam be totaled. This results in an annual interruption frequency and duration value for each customer. This customer interruption frequency and duration knowledge can then be directly used to compute any related reliability index. 2.4 Implementation of M
Distribution system reliability assessment using HMIM has been implemented in a software application named DSRADS (Distribution System Reliability Assessment and Design System). This Windows based program obtains system topological data from an existing utility data base and assigns user-specified default values to all component reliabnlity data. The program then allows for customization of all data. Reliability results can then be obtained on a system level, a feeder level, a customer level, or for any user specified set of customers. Results can be displayed numerically or graphically. DS-RADS has been used to analyze an existing utility distribution system and to explore the reliability impact of several design improvement options on this system. 111. ANALYSIS AND RESULTS The reliability assessment method developed in Section 2 has been applied to the Woods Creek area of Snohomish County in Washington Sitate. The Woods Creek substation supplies power to a rural *areain Snohomish via four feeders (1808, 1809, 1810, and 1811). The northern half of this system can be seen in Figure 5 and the southem half of the system can be seen in Figure 6. These four feeders ar~eequipped with fuses and reclosers to interrupt faults and have manual disconnect switches and automatic sectionalizers to isolate faults. In addition, normally open tie switches exist which can transfer loads to the altemate sources of Three Lakes, Sultan, and West Monroe Substations. 3. I Reliability Data
Before a reliability analysis can be performed, reliablility characteristics must assigned to each component on the
system. The reliability data used in this analysis were cb-
tained from historical utility data and previously published data 1141. A summary of this data is presented in Table 1 (overhead line data, though used for the entire system, was selected based on historical data from feeders 1808 and 1809). h refers to the component’s failure rate and is measured in failures per year. MTTR refers to the component’s mean-time-to-repair and is measured in hours. PSS refers to the component’s probability of successful switching if the component is required to switch in a given situation. Table 1. Comoonent Reliabilitv Data
Breaker Fuse Manual Switch Automated Switch
0.0060 0.0023 0.0001 0.0001
4.0 1.1 2.0 2.0
In addition to the values given in Table 1, all manual switches are assumed to take an average time of 1 hour to switch and all automated switches are assumed to switch instantaneously. 3.2 Levels of Reliabilify Modeling
Reliability indices have been computed for the Woods Creek system based on 5 levels of reliability modeling. The highest level, Level 5, models all of_ the effects of protection _ _ - - ~ - -__- -_--- __ f
I\ I ! I ! I
devices and sectionalizing switches. A summary of the different levels of reliability modeling examined in this paper is: Does not model any protection device or switch effects. Any fault causes an entire feeder to black out until the fault is repaired. Level 2: Models primary protection device behavior only. Level 3: Level 2 + fault isolation through normally closed sectionalizing switches. Level 4: Level 3 + back feeding k o u g h normally open tie switches. Level 5: Level 4 +backup protection. Level 1:
The SAIDI values computed for each level of reliability modeling can be seen in Table 2. The historical SAIDI, computed from 1994 outage reports, is also included. SAID1 is given for the entire system and for each of the four individual feeders. (SAIDI, or System Average Interruption Duration Index, refers to the number of hours per year that a customer can expect to be without power). Level 5 SAID1 values are higher than Level 4 results and lower than Levels 1-3 results. Level 4 SAIDI values are lower because all protection devices are considered to trip when they are supposed to. Though a tripping failure may be infrequent, its effect on the system may be large because the backup device will interrupt a much larger part of the system. Level 3 shows an increase in SAID1 values because customers downstream of the fault cannot be restored by back feeding. Level 2 shows a further increase from Level 3 results because it does not allow for the isolation of a fault and the subsequent restoration of upstream customers. Level 1 yields by far the worst SAIDI values. The main reason is that Level 1 does not model the primary tripping effects of protection devices. This results in a feeder blackout if any
I i I
I I I
I I NO. Switch +N.C. Switch
_ ~ _ Feeder _ Boundary Figure 5. Northern Half of Woods Creek
Figure 6. Southern Halfof Woods Creek
19133 fault occurs on it. Table 2. SAIDI Values (hrs/year)
The SAIFI values computed for Levels 1-5 can be seen in Table 3. (SAIFI, or System Average Interruption Frequency Index, refers to the number of interruptions per year that a customer can expect). The effects Levels 1-5 on SAIFI values is similar to their effects of SAIDI values. Level 4 SAIFI values decrease from Level 5 results because all protection devices are considered to trip when they are supposed to. Level 2 and Level 3 SATFI values are the same as Level 5 results because, though certain customers will experience shorter intermption times, their interruption frequencies remain identical. Level 1, again, yields the worst index values. Table 3. SAIFI Values (iterruptiondyear) Total 1808 1809 1810 1811
Level 5 Level 3
Level 2 Level 1
* Information not available Since Level 5 reliability modeling includes more effects than lower levels of reliability modeling, and because its computed SAIDI and SAIFI values were close to historically computed values, it was used to explore design improvement option on feeders 1808 and 1809.
switches. The reliability clf this option was analyzed by DSRADS and is recorded as; Case A in Table 4. If reliability needs to be further improved, it is possible to automate the switches on feeders 1808 and 1811. This will speed up fault isolation and load restoration and should result in higher reliability. The reliability of this automated switching option has been analyzed and is recorded as Case B. Adding the tie switch and disconnect switch improved the total system SAIDI by 5.1% and the feeder 1808 SAD11 by 15.7%. The other feediers were not affected. Automating the switching action further improved the total syste:m SAIDI to a total of 10.9% and the feeder 1808 SAIDI to' a total of 27.4%. A 17% improvement is also seen on feedler 1811. In an effort to improve the reliability of feeder 1809, a new tie switch is added which can connect feeder 1809 with a substation that is being considered to be built south of Woods Creek. In addition, a new disconnect switch is added. These additions, shown ini bold, can be seen in Figure 6. Initially, these switches are treated as manual switches. The reliability of this option has been analyzed by DSRADS and recorded as Case C in Table 4. If reliability needs to be further improved, it is possible to automate the switches on feeder 1809. This will speed up fault isolation and load restoration and should result in higher reliability. The reliability of this aullomated switching option has been analyzed and recorded as Case D. Adding the tie switch and disconnect switch improved the total substation area SAID1 by 6.2% and the feeder 1809 SAIDI by 16%. Automating the switching action further improved the total system SAIDI to a total of 9.4% and the feeder 1809 SAIDI to a total of 25.3%. Table 4. SAIDI Values -/year)
3.3 Effect of System Design Improvements
The Woods Creek area does not receive desirably high electric service reliability when compared to other service areas of Snohomish county. Within the Woods Creek area customers fed from feeders 1808 and 1809 experience particularly low reliability. With this in mind, several design option are studied with the objective of improving the reliability of Woods Creek in general and feeders 1808 and 1809 in particular. In an effort to improve the reliability of feeder 1808, a new tie switch is added which can connect feeder 1808 with feeder 1811. In addition, a new disconnect switch is added. These additions, shown in bold, can be seen in Figure 5. Initially, these switches are assumed to be manual
5 7 System
w 0 3 V
Figure 7. S u m m a q of Result;.
Two additional cases were examined. Case E includes the system improvements of Cases A and C. Case F includes the system improvements of Cases B and D. Cases E and F, recorded in Table 4, correspond to system SAID1 improvements of 11.2% and 20.3% respectively. A bar chart summarizing Table 4 is shown in Figure 7. IV. CONCLUSIONS This paper has presented a new analytical technique for distribution system reliability analysis. This method, termed Hierarchical Markov Modeling, includes the effects of multiple failure modes, fault isolation, and load restoration by creating Markov models based on system topology, integrated protection systems, and individual protection devices. This model produces more accurate results when compared to models which do not include one or more of the following effects: primary protection, backup protection, fault isolation, and load restoration. Hierarchical Markov Modeling has been implemented in a Windows-based software application named DS-RADS. Accuracy and usefulness have been examined by applying DS-RADS to an existing utility distribution system. Accuracy has been tested by comparing results to historical data. Usefulness has been demonstrated by identifying poor apeas of reliability and examining the reliability impact of several design improvement options. DS-RADS is a complete and useful analysis tool, but improvements can be made. First, its reliability analysis can be expanded to include other power quality issues in addition to mutually exclusive sustained interruptions. Possibilities include momentary interruptions, voltage sag during faults, and ubiquitous failures during storms. Second, the analysis can move beyond basic reliability indices and measure reliability in terms of incurred customer costs.
A. Sankarakrishnan and R. Billinton, ‘Sequential Monte Carlo Simulation for Composite Power System Reliability Analysis with Time Varying Loads,’ IEEE/PES 1995 Winter Meeting, New York, N. Y., IEEE, 1995.  R. Billinton and A Smkarakrishnan, ‘Adequacy Assessment of Composite Power Systems with HVDC Links Using Monte Carlo Simulation,’ IZ5EYPE.S I994 WinlerMeeting,New York, N. Y., IEEE, 1994.  R. Billinton and G. Lian, ‘Monte Carlo Approach to Substation Reliability Evaluation,’ IEE Proceedings-C, Vol. 140, No. 2, March 1993, pp. 147-152.  EPRI Report EL2018, Development of Distribution Reliability and Risk Analysis Models, Aug. 1981. (Report prepared by Westinghouse 
Corp.) S. R. Gilligan, ‘A Method for Estimating the Reliability of Distribution
Circuits,’ IEEE Transactions on Power Delivery, Vol. 7, No. 2, April 1992, pp. 694-698.  G. Kjolle and Kjell Sand, ‘RELRAD - An Analytical Approach €or Distribution System Reliability Assessment,’ LEEE Transacrions on PowerDelivery, Vol. 7, No. 2, April 1992, pp. 809-814. [IO] Yuan-Yih Hsu, Li-Ming Chen, Jiann-Liang Chen, et al., ‘Application of a Microcomputer-Based Database Management System to Distribution System Reliability Evaluation,’ LEEE Transactions on Power Deliveiy, Vol. 5, NO. 1, Jan. 1990, pp. 343-350. [ I l l J. A. Buzacott and G. J. Anders, ‘Reliability Evaluation of Systems With After Fault Switching,’ LEEX Transactions on Power Systems, Vol. 2, NO.3, Aug. 1987, pp. 601-607.  T. Gonen, Electric Power Distribution System Engineering, McGraw Hill, 1986.  M. M. Adibi and D. P. Milanicz, ‘Protective System Issues During Restoration’ zE,CEPES 1995 WinferMeeling,New York, N. Y., IEEE, 1995.  R. N. Allen, R. Billinton, I. Sjarief, L. Gloel, and K. S. So, ‘A Reliability Test System for Educational Purposes - Basic Distribution System Data and Results,’ IEEE Transactions on Power Systems, Vol. 6, No. 2, May 1991.
VII. BIOGRAPHIES Richard E. Brown received his B.S.E.E. from the University of Washington in 1991. While working as a consulting engineer, he returned to the UW and received his M.S.E.E in 1993. Mr. Brown is presently a Ph.D. candidate, is a member of Eta Kappa Nu and is the current PES student chapter president.
Suryasish Gupta received his B.S.E.E. from Jadavpur University (India) in 1994. He is currently working on his M.S.E.E. at the University of Washington.
The authors would like to express their appreciation to Snohomish County PUD #1 for financial support during this research effort. Special thanks to Iggy Castro, John White, and others for useful feedback in the development process.
Richard D. christie received his B.S. and M.E. degrees from Rensselaer in 1973 and 1974 respectively. After service in the U.S. Navy nuclear power program and employment at Leeds & Northrop he obtained his Ph.D. from Camegie-Mellon in 1989. Dr. Christie is presently an assistant professor at the University of Washington.
VI.REFERENCES [l] L. Goel and R. Billinton, ‘Utilization of Interrupted Energy Assessment Rates to Evaluate Reliability Worth in Electrical Power Systems,’ E E E Transactions on Power Systems, Vol. 8, No. 3, Aug. 1993, pp. 929-936.  R. Billinton, J. Oteng-Adji, and R. Ghajar, ‘Comparison of Two Alternate Methods to Establish an Interrupted Energy Assessment Rate,” D E E Transactions on Power Systems, Vol. 2, No. 3, Aug. 1987, pp. 75 1-757.  R. N. Allan and J. R. Ochoa, ‘Modeling and Assessment of Station Originated Outages for Composite Systems Reliability Evaluation,’ lEEE Transactions on Power Systems, Vol. 3, No. 1, Feb. 1988, pp. 158-165.
SubrahmanyamS. Venkata received his Ph.1). h m the University of South Carolina, Columbia in 1971. He is presently at the University of Washington where he is a Professor of Electrical Engineering and Director of the Electric Energy Industrial Consortium. Dr. Venkata is a member of Tau Beta Pi, Sigma Xi, Eta Kappa Nu, and several IEEE committees and subcommittees. He has published and presented more than 120 papers and is co-author of “Introduction to Electric Energy Devices” (Prentice-Hall, 1987). He is a registered professional engineer. Robert W. Fletcher received his M.S. degree from the University of Washington in 1994. He is the principal long range planner and R&D engineer at Snohimish County PUD #l. He is a member of Eta Kappa Nu and is a registered professional engineer.