RELIABILITY ASSESSMENT OF DISTRIBUTION NETWORS USING SEQUENTIAL MONTE CARLO SIMULATION

RELIABILITY ASSESSMENT OF DISTRIBUTION NETWORS USING SEQUENTIAL MONTE CARLO SIMULATION Srete Nikolovski *, Predrag Maric *, Ivan Mravak ** *Faculty of Electrical Engineering, K. Trpimira 2B, 31 Osijek, Croatia E-mail: srete@etfos.hr, pmaric@etfos.hr **HEP -Croatian National Grid Company, Grada Vukovara 37, 1 Zagreb, Croatia E-mail: Ivan.Mravak.@hep.hr INTRODUCTION This paper presents a Monte Carlo simulation approach to reliability evaluation of one distribution system. Stochastic model of distribution system components with Weibull distribution and Markov model of components are used. A set of system related reliability indices were calculated using sequential Monte Carlo simulation. The analysis was performed for a planned new 2 kv distribution network dedicated for supplying new highway road V-C. Monte-Carlo simulation was performed with full use of power restoration switches and full network load flow analysis. Load transfer was also considered to alleviate the overloading of distribution lines and transformers. SEQUENTIAL MONTE CARLO SIMULATION A sequential Monte Carlo simulation attempts to model system behavior precisely as it occurs in reality as a sequence of random events that build upon each other as the system progress through time. Some system contingences are modeled by probability distributions and can randomly occur at any point of time in the simulation. Other contingencies are conditional since their probability of occurrence depends upon prior events and the present state of the system. Sequential Monte Carlo simulation is implemented by dividing the simulation time period into small slices. Starting at first, each time slice is simulated in sequence to identify new contingences (such as faults) and respond to prior unresolved contingencies. Simulation accuracy increases as time slices become smaller, but the expense of increasing computation time. To model one year with a one-hour, time resolution requires 876 time slices. The probability of a contingency occurring during a time slice is equal to the probability of its having occurred at the end of time slice minus the probability of its having occurred at the beginning of the time slice. This is approximately equal to the value of the probability density function at the beginning of the time slice multiplied by the time slice duration. The equations are as follows: P(t) = F(t+ t) F(t) (1) P(t) t f(t) (2) P(t) = probability of occurrence in the time slice bounded by t and t F(t) = probability distribution function f(t) = probability density function t = duration of time slice Some probability distribution functions, like exponential distribution are stationary and do not vary in time. These events will have same likelihood of occurring in each time slice, equal to the rate of occurrence multiplied by the time slice duration. Other types of events are nonstationary and have probability functions that vary with time and must be individually computed for each time slice. Components models and parameters Sequential Monte Carlo simulation requires generation of artificial operating/restoration histories of the network components. In distribution system these components are overhead lines, cables, transformers, disconnect switches, fuses and breakers. Overhead lines, cables and transformers can be generally represented by two-state Markov model shown in Figure 2. State number 1 indicates that the component is in the operating up state and the state number 2 indicates that the component is in inoperable down state. 1 λ 2 A µ A Figure 1. A sequential Monte Carlo simulation divides the simulation into small slices. Figure 2. State space diagram of component

The time during the component remains in state number 1 is called the time to failure (TTF) or failure time (FT). The time during the component is in state number 2 is called the restoration time and can be either the time to repair (TTR) or the time to replace (TTR). The process of transiting from the up state to a down state is the failure process. Transition from up state to a down state can be caused by the failure of any components or by removal of components for maintenance. On Figure 3. is shown operating/restoration history of a component. Load point and system reliability indices The average values and the probability distributions of theese indices can be calculated from the load point operating /restoration histories. The three basic load point reliabilty indices are the average failure rate, the average repair rate, and the average annual unavailability or average outage time U. The average values of the three basic load point indicies for load point j can be calculated from the load point up-down operating history using the following formulae : N j λ j = (3) ΣTuj Figure 3. Component operating/repair history The parameters TTF, and TTR are random variables and may have different probability distributions. The probability distributions most often used to simulate these times are Exponential, Gamma, Weibull, Normal and Lognormal. In Figure 4. is shown Weibull distribution used in DIgSILENT software. Fuses and breakers are used to automatically isolate failed components or failed areas from healthy areas. They can exist in either operating or failed states which can be described in terms of their probabilities. From Weibull distribution for appropriate parameters exponential distribution can be done. N j µ j = (4) T T U j = (5) T + T uj Where T and uj T are the respective summations of all the up times T U and all the down times T d and N j is the number of failures during the total sampled years. In order to determine the probability distributions of the load point frequency, the period k of this index are calculated for each sample year. The number of years m(k) in which load point outage frequency equals k is counted. The probability distribution p(k) of the load point failure frequency can be calculated using m( k) p ( k) = M k =,1, 2... (6) where M is total sample years. Figure 4. Weibull distribution Determination of load point failures Component failures may affect one or more load points. The most difficult problem in the simulation is to find the load points affected by the failure of a component and to determine their operating/restoration histories, which are dependent on the network configuration, the system protection and the maintenance philosophy. In order to create a structured approach, the distribution system can be broken down into general segements. A complex radial distribution system can be divided into the combination of main feeder ( a feeder that is connected to a transformer station) and subfeeders. The probability distribution of load point unavailability can becalculated in a similar manner. To caclulate the probability distribution of outage duration, the failure number n(i), with outage duration between i-1 and i is counted. The probability distribution p(i) is : n( i) p ( i) = i =,1,2... (7) N where N is total failures in sampled years. The system indices can be calculated from the basic load point indices as system indices are basically weighted averages of the load point values. Well known and usually used system indices are : total number of customer int erruptions = total number of customers total = number of total number of customer int erruptions affected customers

sum of customer int erruptions durations = total number of customers sum of customer int erruptions durations = total number of customer int eruptions customer hours of available service = customer hours demanded = Expected energy not supplied. RELIABILITY ASSESSMENT OF DISTRIBUTION NETWORK FOR CORRIDOR V-C. Customers on new corridor V-C are supplied from 2 kv and 1 kv cable network connected to HEP Prijenos d.d. (Croatian power transmission network) at six 11/x kv transformer stations that are: B.,,, Osijek1, Djakovo and ci. Each 11/x kv transformer station supplies its own distribution network (i.e. determined number of customers) which may or may not be interconnected with the rest of the system. Each distribution network is a segment of system dedicated for supplying a new corridor V-C. If the fault occurs in a 11/x kv transformer station, the main idea of automated switching equipment is to automatically switch its 2 kv or 1 kv distribution network (segment of system) on the closest 11/x kv transformer station which works properly. Customers on the corridor V-C can be independently supplied from the rest of belonging system segment interconnecting with customers on corridor that are supplied from another system segment. Reliability assessment is performed for the main (base) system state (when all 11/x kv transformer stations work properly and their distribution sub networks are interconnected) and for N-1 states during outages of 11/x kv stations. Before Monte Carlo simulation starts, load flow analysis has to be performed. These simulations have been performed using DigSilent Power Factory 13 software. System reliability indices for the base system state are shown in table 1. TABLE 1. Reliability system indices for main system state 4.33 4.88 1.12 8.17.99 89.46 1.82 Comment of results; it can be expected that each customer will be unsupplied 4.33 times per year and the total time of interruptions in a year will be 4.88 hours which means that average duration per interruption will be 1.12 hours. Customers that will suffer power interruptions will be average 8.17 times per year unsupplied. Total amount of electrical energy that would not be delivered to the loads is 89.46 MWh which equals 1.82 MWh per customer. Load flow analysis for this system stage shows good results. There are no voltage limits violations and problems and there are no overloaded lines and transformers. Customers located on the future V-C corridor have possibility of redundant 2 kv power supplying (SCADA system gives possibility of automated inter-connection with customers on corridor that are supplied from another system segment), so their reliability indices are better than reliability indices of the rest of old distribution system. N-1 reliability assessment For N-1 system states, reliability indices will be calculated for all system states when one component is out in the case when the one of 11/x kv transformer stations is out of service. Selected 11/x kv transformer station is assumed to be permanently unavailable one year. Reliability assessment will be performed for two cases. The first case is when the automated interconnection of all loads (TS 1/.4 kv) on corridor V-C is performed, when one of 11/x kv transformer station is unavailable. The second case is when that interconnection will not be done. Reliability indices for both of cases are shown in further tables. TABLE 2. Reliability indices for n-1 system states in case when all customers on corridor V-C are interconnected n-1 TABLE 3. Reliability indices for n-1 system states in case when all customers on corridor V-C are not interconnected. n-1 4.76 8.97 5.39 1.13.99 19.31 2.23 B. 4.38 8.25 5.34 1.22.99 97.7 1.98 4.43 8.42 5.33 1.21.99 98.19 2. Osijek 1 4.58 8.67 5.32 1.16.99 98.51 2. Djakovo 4.36 8.23 5.32 1.22.99 96.57 1.97 ci 4.48 8.44 5.5 1.23.99 1.81 2.6 8.24 2.18 13.57 1.64.99 289.4 5.9 B. 4.92 18.55 7.44 1.515.99 126.25 2.57 7.68 2.92 12.213 1.587.99 253.56 5.18 Osijek 1 6.7 19.82 9.1 1.48.99 225.69 4.61 Djakovo 6.93 24.25 11.3 1.64.99 226.22 4.62 ci 8.82 21.61 14.4 1.63.99 297.15 6.6 Reliability indices of distribution system when all customers on corridor V-C are interconnected are similar to reliability indices of main-base system case but reliability indices when all customers on corridor are not interconnected are approximately two times worse. That legitimate existing of automated interconnection of all customers using SCADA system on corridor V-C when one of 11/x kv transformer station is permanently unavailable.

Transformer stations 11/x kv and ci are on the opposite edges of analyzed distribution system and when those transformer stations are permanently unavailable reliability indices are much worse than reliability indices if some of other 11/x kv transformer stations are permanently unavailable. Comparison between reliability indices, here Energy Not Supplied, in the case when interconnection between all customers on V-C corridor exist and when this interconnection does not exist is shown in Figure 4. [MWh/a] 35 3 25 2 15 1 5 Figure 4. Comparison between in the case when interconnection exist red diagram and when does not exist- blue diagram. N-2 reliability assessment Comparison between reliability indices, for N-2 system states and N-1 system states when all customers on corridor V- C are interconnected and when they are not is shown in Figure 5 and 6. [MWh/a] 2 15 1 5 Figure 5. Comparison between for n-2 system states - red diagram and n-1 system states when interconnection exist blue diagram. [MWh/a] 35 3 25 2 15 1 5 For N-2 system states, reliability indices will be calculated for all system states in the case of coincidence of any two components when all two combinations of 11/x kv transformer stations are out of service. For selected 11/x kv transformer stations are assumed to be one year permanently unavailable. Reliability assessment will be performed in case of automated interconnection of all customers on corridor V-C when two of 11/x kv transformer stations are unavailable. Results of this reliability assessment are partly shown in table 4 (15 cases of coincidence of two 11/x kv stations out of service). Figure 6. Comparison between for n-2 system states - red diagram and n-1 system states when interconnection does not exist blue diagram. Results of each sequential Monte Carlo simulation are different because each simulation generates different random events. When Monte Carlo simulation is used, software enables us to change start and stop time, number of runs, maximal errors and confidence interval, as it is presented on Figure 7. TABLE 4. Reliability indices for n-2 system states when all customers on corridor V-C are interconnected. n-2 & B. 4.85 8.49 5.77 1.19.99 113.15 2.31 & 4.93 8.96 5.52 1.19.99 17.96 2.2 & 4.7 8.54 5.97 1.27.99 112.61 2.3 & 5.1 8.77 6.13 1.23.99 113.8 2.32 & 4.41 8.14 5.73 1.3.99 14.15 2.13 Djakovo Djakovo & 8.82 16.3 8.54.98.99 171.32 3.5 Figure 7. Dialog box for Monte Carlo simulation.

After a huge number of simulations, the mean value of reliability indices are approaching very close to the expected mean value, even if the simulated time period is changed. On Figure 8 is shown how indices (for n-2 system state) becomes very close to 5, after a huge number of simulations with different simulated time period. [4] DIgSILENT software Power Factory 13 Manuals, 24, Digsilent GmbH, Gomaringen, Germany [5] R. Bilinton, G. Lian, 1993 Station Reliability Evaluation Using Monte Carlo Approach IEEE Transactions on Power Delivery, Vol. 8, No. 3. BIOGRAPHIES Figure 8. after 2 simulations with different simulated time period. Different colors of graphs means different simulated time period. CONCLUSION In this paper Sequential Monte Carlo simulation is used for reliability analysis of 2 kv distribution network for new planned corridor V-C road power supply. All system components are modeled with Weibull distribution for two state Markov model of component. Two main switching states are considered in reliability indices calculation: The first case is when the automated interconnection of all loads (TS 1/.4 kv) on corridor V-C is performed and the second case is when that interconnection is not done. System reliability indices:,,, 1/Ca),,, are calculated for all system states in the case of N-1 or N-2 fault coincidence, when one or any two combinations of 11/x kv supply transformer stations are out of service. This type of analysis can help in the process of construction, building and maintaining this distribution network of corridor V-C road. REFERENCES [1] R. Billinton, P. Wang, 1999, "Teaching Distribution System Reliability Evaluation Using Monte Carlo Simulation", IEEE Transactions on Power Systems, Vol.14, No.2. [2] R. Billinton, P. Wang, 1998, "Distribution System Reliability Cost/Worth Analysis Using Analytical and Sequential Simulation Techiniques", IEEE Transactions on Power Systems, Vol.13, No.4. [3] R.E. Brown, 22, Electric Power Distribution Reliability, Marcel Decker, Inc, New York, USA Srete Nikolovski was born in Belgrade on 1. October, 1954. He obtained his B.Sc. degree in 1978 and Master of Science degree (M.Sc) in 1989, both in the field of Electrical Engineering, from the Faculty of Electrical Engineering, University of Belgrade. He received his PhD degree from the Faculty of Electrical Engineering and Computing, University of Zagreb, Croatia in 1993. He was appointed Assistant Professor in 1996. Currently he is Associate Professor on the Power System Engineering Department at the Faculty of Electrical Engineering, University of Osijek, Croatia. He is IEEE senior member. His main interest is in power system modeling, simulation and analysis, especially in reliability assessment of power system and power system protection. Predrag Mari was born on 11 December 1979 in Osijek,. He obtained diploma degree in 24 in field of Electrical Power Engineering from the faculty of Electrical Engineering, University of Osijek. His graduation thesis awarded two prizes: Hrvoje Po ar of Croatian Energy Association as specially noticed thesis in field of power engineering, and a prize from Croatian Power Company HEP for the best graduation thesis in the field of power engineering. Currently he works as research assistant in the Power System Engineering Department at the Faculty of Electrical Engineering, University of Osijek. His main interest is modeling, simulation and analysis of transient phenomena in power systems and power system protection Ivan Mravak was born on 23. February 1954 in Vukovar. He obtained diploma degree in 1979 from the Technical faculty in Novi Sad and Master of Science degree (MSc) in 1993, both in the field of Electrical Power Engineering. He worked in Kombinat Borovo factory until the1988, after he left and became the technical manager in HEP Elektra Distribution in Vukovar. From 1993 he became coordinator for building in HEP Direction for distribution. From 1997 he worked as manager of the sector for technical activities in HEP Distribution. In 24 he became a General Manager of HEP- Croatian National Grid Company. His main interest is in reliability analysis of distribution system, management of production, transmission and distribution of electric energy.