SIMULATION METHOD FOR RELIABILITY ASSESSMENT OF ELECTRICAL DISTRIBUTION SYSTEMS

SIMULATION METHOD FOR RELIABILITY ASSESSMENT OF ELECTRICAL DISTRIBUTION SYSTEMS Johan Setréus, Lina Bertling, Shima Mousavi Gargari KTH, School of Electrical Engineering, Stockholm, Sweden johan.setreus@ee.kth.se Abstract -This paper describes a simulation method for reliability assessment of electrical distribution systems. The method has been implemented in the reliability assessment tool RADPOW which now is able to perform both analytical and simulation evaluations. The implemented method is validated by comparing results from application studies made for an electrical distribution system in the Stockholm area. The studies includes both simulation and analytical approach and the use of two different computer tools; that are the in house tool RADPOW, and the commercial tool NEPLAN. The simulation approach is beneficial for solving complex reliability models that could be difficult to solve analytical, e.g for resulting in distribution functions for reliability indices. One application area for such reliability models are for reliability centered asset management (RCAM), where the maintenance effort is optimized based on its contribution to the overall system reliability. This approach is being developed at KTH, and the simulation approach presented in this paper aims to provide a tool to perform applications studies according with the RCAM approach. Keywords; Simulation, Electrical distribution system, reliability indices, RADPOW, NEPLAN, RCAM INTRODUCTION A central part in the planning of distribution systems, which becomes even more important in today's de-regulated electrical power system, is preventive maintenance (PM). This is the planned and scheduled maintenance that aims to postpone or reduce failures of a system. Electrical distribution system operators (DSO) have changed their organization and the pressure to reduce operational and maintenance costs is already being felt. The driving forces are changing from technical factors to economic and business factors and cost-effective PM is required. Consequently, there is an interest from DSOs to incorporate strategies for costeffective maintenance. Reliability Centred Maintenance (RCM) is such a strategy where maintenance of system components is related to the improvement in system reliability. The RCM method has been further developed in the reliability-centred asset management method (RCAM) [2] to provide a quantitative relationship between PM of assets and the total cost of maintenance [1]. In the search of the best possible asset management strategy for electrical distribution system it is essential to know the importance of the involved components. Each component is assigned performance indices that correspond for the overall reliability of supply. The indices can be used for prioritization of components; one example is to determine where maintenance actions will have the greatest effect. One way to perform such analysis is to evaluate the amount of interruptions a certain component causes the system. A simulation approach of this 1

kind of analysis enables us to develop models with a deeper level of detail for larger systems in a more straightforward manner compared to the analytical approach. This paper presents an implemented method for performing Monte Carlo simulations on a power system in order to evaluate the system reliability with a numerical measurement. This method can then easily be extended to be used for prioritization of components. RELIABILITY EVALUATION Methodologies Reliability evaluation of electrical distribution systems could be presented in quantitative measures given by average values for load points and the overall system. Table I shows on general indices. Table I - Reliability indices for electrical distribution systems. Load point level System level Failure frequency, λ (f/yr) SAIFI (int/yr.cust) Failure Duration, r (h/yr) SAIDI (h/yr.cust) Unavailability, U (h/yr) CAIDI (h/int) Energy not supplied (kwh/yr) AENS (kwh/yr.cust) To obtain reliability indices, two fundamental methodologies can be applied to the system with its interconnected components. These methods can be categorized as the analytical approach and the simulation approach. The analytical approach solves the problem directly with mathematical formulas, whereas the simulation approach uses numerical methods. Two special types of numerical methods are Simulation and the Monte Carlo method which uses random experiments on the system to evaluate the reliability indices. The Monte Carlo method, generally referred as Monte Carlo Simulation (MCS) is used in this paper to perform the simulation approach. The reliability assessment tool RADPOW The reliability computer program RADPOW was developed by Lina Bertling and Ying He at the Department of Electrical Engineering, KTH, as a part of their PhD projects during the years 1997-2002[2]. The name RADPOW is an abbreviation for Reliability Assessment of Distribution Power Systems, and as the name reveals, the program is developed for analysis of electrical distribution systems. For this purpose there already exist a number of computer programs, developed both for commercial and research use, but each having their advantages and disadvantages. RADPOW was developed for use in development of research methods for two applications areas; that are for RCAM and automatization. The first application aims to investigate how the reliability could be impacted by reducing the frequency of failures and the latter instead by reducing the outage time. The first version of RADPOW, referred to as RADPOW_1999, is based on analytical methods described in [4], [5] and [6]. The analytical evaluation in RADPOW is performed by a load-point-driven technique, which deduces all possible failure events for each load point and evaluates the effect of these for each load point. The deducted results is the minimal cut set of first and second order and the additional active failures for each load point. An additional active failure is a failure mode that occurs when an active failure of an item causes the interruption of other items in the system [2]. The minimal cut sets for the load points includes the components which upon failure cause an interruption of the load point. The 2

number of different overlapping failures events in a minimal cut set is called the order of the cut set. The output reliability results are the load point indices and the system indices evaluated from these. In order to adopt the simulation approach for RADPOW, a master thesis project was initiated in the year of 2006, which resulted in the RADPOW_2006 version [7]. RADPOW_2006 is thereby an extension of RADPOW_1999 by introducing an additional method for simulation. Fig. 1 illustrates the overall picture of the two evaluation methods used in RADPOW. System Data Network Model Assign each LPs the events that lead to failure for that LP Analytical method Simulation method Calculate the reliability indices for each LP with formulas Make a large number of random experiments to see how these affect LPs reliability Calculate the reliability for the system Fig. 1. Flowchart for the analytical and simulation method used in RADPOW. Simulation method implemented in RADPOW In order to make a simulation analysis on a power distribution system, the components involved in the system needs to be studied. As the system consists of several interconnected components, each having a probability to fail, one has to deduce how a specific component affects the system and its load points, given the status of the component. In this simulation method, each component has been assigned an integer defining the present status of the component. Three different component states are used: 0. The component is functioning. 1. The component suffers an active failure. 2. The component is being repaired or replaced. At first state the component is functioning, but have already been donated a time to failure (TTF), which will affect the component in the future. When the TTF has been reached, the component suffers an active failure and needs to be disconnected in order to begin the restoration of the component. It is assumed that this time, in state 1, is static for the component type and the length are referred to as SW. At the last component state the component is repaired, or, if possible, replaced during the static time interval REP. Only active failures have been considered, and hence each component follows the sequence 0-1-2-0-1.., if it is assumed that all components are functioning from the beginning. The simulation method developed for RADPOW uses an event-driven approach, which means that all failure events are treated separately to deduce the effect of the failure on the whole system by identifying the affected load points [2]. This means when a component fails, the 3

method has to deduce which load points that are affected, and this is achieved by the already deduced minimal cut sets and the additional active failures for each load point. Depending on the component state of a failed component, it affects the load point differently. If a component is in state 1 it affects all the load points having this component included in its minimal cut sets of first order or in the additional active failures. On the other hand, if the component is in state 2, it only affects the load points having this component in its minimal cut sets. For the second order failures, both state 1 and 2 for each of the two components will affect the load points having these components in its minimal cut sets of second order. The Monte Carlo Simulation (MCS) method used for RADPOW is referred to as time sequence simulation [5]. The implemented algorithm is presented in Fig. 2. The algorithm proceeds the following steps, as numbered in figure: 1. The input data consist of the number of samples N, simulation time Tstop, component reliability data for the system, the minimal cut set vectors, normally open paths and the additional active failure vectors for each load point (LP). n = 0. 2. All components are set to be functioning, which means state 0. The total time, Ttot, LPs number of failures and outage times are reset. A time to failure (TTF) is generated in years for each component using the exponential random generator, given the component data as input. 3. Jump to the next event; that is the event with the shortest time. During this interval the system is stable. Count up the total time. 4. Check how the LPs were affected during the interval and with the current states of the components. Use the minimal cut sets and the additional active failure vectors for this purpose. 5. If a LP is affected, check if there are any alternative paths, still functioning, that can be used by closing a normally open disconnector. If this is possible count up the outage time for the LP with the switching time for the disconnector. If a normally open path does not exist, add the total interval length to the outage time for the LP. Then check if the LP was down the interval before and if not increase the number of failures for this LP. 6. At the event, the present component is changing its component state to a new one, depending on its previous. The state for the component follows the sequence 0,1,2,0,1..., and hence it is easy to determine the next state. 7. a) If the component were in state 2 in the interval, it is now functioning, and hence its new state is set to 0. A new random TTF for the component is generated. 7. b) If the component were in state 0, its new state is set to 1. The time for isolating the component, the switching time, is set to the present static value from the input data. 7. c) If the component were in state 1, its new state is set to 2. The time for repair or replacement of the component, is set to the present static value from the input data. It has been assumed that the component always is replaced if this option is available. 8. If the time for simulation, Tstop, is reached, stop the current simulation and save the outage data for each LP. If not, proceed at step 3. 9. If the current number of simulated samples, n, equals the predetermined samples, N, the total simulation phase is finished. If not, restart from step 2 and count up n by one. 10. Evaluate the data from all samples, with the system indices and its standard deviations as results. 4

1. Input data n = n +1 2. All components are functioning. Generate time to failure for each component 0 TTF3 TTF10 TTF8 TTF1 Ttot = 0 Stop time years Current time 3. Jump to the next event Ttot = Ttot + t 0 TTF3 TTF10 TTF8 TTF1 Ttot = Ttot + t t Current time years 4. How are the LPs affected during the time interval and with the current component status? 5. If LP is affected: 1.Add a failure to LP (if functioning before). 2.Add the outage time t or switching time for disconnector to LP 1. Check if any components with status 1 are included in the additional active failures of the LP. 2. Check if any components with status 1 or 2 are included in the minimal cut sets of first and second order of the LP. Check if there is any open paths that can be closed with disconnectors. 6.Update the component status after the interval. Produce a new time for component, depending on next status 0, 1 or 2. 0 1 2 7a. New TTF is generated 7b. SW-time from data 0 7c. Rep-time from data TTF3 TTF10 TTF8 TTF1 SW3 Current time years no 8. Ttot > Tstop? yes no 9. n == N? yes 10. Evaluate the outages for each load point and each iteration Fig. 2. The overall algorithm used in the simulation method in RADPOW. The output results consist of the load point and system indices, shown in Table I, for each simulation sample. Statistical data are then evaluated for all the samples, with the mean values and variances of the samples. The chosen simulation time in a simulation analysis of a power system depends on the complexity of the system and the required accuracy of the output results. In this method the total simulation time consists of the chosen number of simulation samples and the sample time in years. In order to determine these input parameters, one has to see how the output results converge for the specific system with different sample lengths in years. These parameters depend on the size of the system and the reliability data for the components; the smaller probabilities for the components to fail, the longer sample times are needed to comprehend the system behaviour. Rare events with high impacts can have a huge effect on simulations. If some events happen very occasionally, but each having a large impact on the system, a large number of samples or a long sample time is needed for the simulation. 5

Approximations and simplifications in method The following simplifications have been adopted in the implemented simulation method: Passive faults are not included in the method. Temporary and transient failures are not considered. Outages caused by maintenance followed by an overlapping failure are not considered. The none functioning of breakers, the stuck probability, is not considered. The function of fuses is not implemented in the method. The switching time for the normally open disconnector has been set to one hour. Besides these limits in the method, only failure modes of first and second order have been considered, as the minimal cut sets does not include failure modes of higher order. The reliability assessment tool NEPLAN NEPLAN is an electric power system analyzer which has been developed by BCP group in Switzerland. This software package is used mainly for transmission and distribution systems analyses. NEPLAN reliability software can be used to provide not only the reliability indices for both individual load points and the overall power systems, but also it can be used to provide the cost of unreliability. NEPLAN is based on Markov process and enumeration techniques. The most important input data required for reliability evaluation in NEPLAN are the failure rate, repair time and switching time of the components. In the evaluation method in NEPLAN all the possible failure combinations are created according to the predefined failure criteria deduced by the program. Then the effect analysis of each failure mode is assessed and the corrective action with main emphasis on alleviating the abnormality of a system will be performed. If it is not possible to return the system to its normal state after an interruption, the program applies the remedial action i.e. load curtailment. System states which result in load curtailment will contribute to the failure frequency and the outage duration for the load points and these indices are then used in the reliability calculation of the system indices [9]. CASE STUDY The Birka case system An urban electrical distribution system in the Stockholm city area, referred to as the Birka system, has been used for the application studies presented in this paper. This system has previously been analysed in e.g. [2][3]. The system studied is based on the Birka Nät 220/110 kv Bredäng station and 33/11 kv Liljeholmen station, connected via two parallel 110 kv cables. The system model of this part of the network, that is used for analysis, was first presented by [2] in a maintenance and reliability study using the RCAM approach. The model used for analysis is shown in Fig. 3. The most significant simplification, in this model, is that the double busbar arrangements have been simplified to a single bus representation. To compensate for this redundancy loss, the repair time of busbars has been reduced to the effective switching time it takes to switch off one of the busbars in the double arrangement. Other simplifications made on the model from the one presented in [2], are (i) breakers are considered to be ideal with no stuck probability and (ii) the component outages only depends on the active failure rate. The customers are presented as two 33 kv load points, station Högalid (HD) and subway (SL), and one 11 kv load point (LH11). There are 32 identical feeders outgoing from Liljeholmen. In the model these feeders has been modelled as one average 11 kv feeder with a total of 447 customers. HD supplies a total of 23400 customers. 6

The system consists of the following types of components: 110 kv, 33 kv and 11 kv underground cables, 110 kv, 33 and 11 kv busbars, 110 kv, 33 kv and 11 kv breakers, 220/110 kv, 110/33 kv, 33/11 kv and 11/0.4 kv transformers. 220 kv BÄ c2 c8 c1 c3 c9 110 kv c5 c4 c11 c10 bus transformer breaker fuse c6 c12 cable supply point load point c14 33 kv c7 c13 c49 c51 c50 c53 c54 c16 c15 c20 c19 c24 c23 c36 c38 c37 c40 c43 c11 c41 c44 c56 c52 c57 c55 c17 c21 c25 c18 c22 c26 c46 c39 c42 c45 c47 c58 SL c27 11 kv c29 c28 c48 HD c30 c31 c32 c33 c34 c35 LH11 Fig. 3. The Birka system model used in the case study.[2][3] Reliability analysis of the Birka system In order to validate the simulation method, the results from the simulation method has been compared both to the analytical results in RADPOW and NEPLAN. For the simulation in RADPOW the sample time was set to 1000 years and the number of samples to 10000. This sample time is of course not realistic, but a lower value of this result in under estimations of both outage frequency and duration, because of the assumption that all components are functioning from the beginning and the relatively high component reliability. Table II presents a comparison of the average failure rates in the load points from the reliability analysis of the Birka system. Table II - The average failure rates per year for the load points in the Birka system, evaluated with three different methods. Load point RADPOW RADPOW NEPLAN ΔRADsim ΔRADsim λ [f/yr] Simulation Analytical -RADAna -NEP LH11 0.282 0.282 0.278 0 0.004 HD 0.059 0.059 0.057 0 0.002 SL 0.058 0.058 0.056 0 0.002 7

The failure rate is significant at the 11 kv level compared with the two 33 kv load points, the average failure rate for an 11 kv customer being about 0.28 failure/year. For the network with 32 identical load points as LH11, outgoing from Liljeholmen, this would imply about 9 failures per year. Table III presents a similar comparison for the average unavailability in the load points. Table III - The average unavailability in hours per year for the load points in the Birka system, evaluated with three different methods. Load point RADPOW RADPOW NEPLAN ΔRADsim ΔRADsim U [h/yr] Simulation Analytical -RADAna -NEP LH11 0.474 0.475 0.470 0.001 0.004 HD 0.099 0.100 0.098 0.001 0.001 SL 0.098 0.099 0.096 0.001 0.002 The results from these two load point indices clearly show the accuracy in results when performing a simulation with the implemented method. Only a slightly difference appears in the third decimal. The overall system indices for the Birka system are presented in Table IV. The results clearly show the impact of the large number of customers in HD, as SAIFI and SAIDI almost have the same values as the failure frequency and the unavailability respectively, in HD. Table IV - The system reliability indices for the Birka system, evaluated with the three different methods. System RADPOW RADPOW NEPLAN ΔRADsim ΔRADsim Indices Simulation Analytical -RADAna -NEP SAIFI [int/yr.cust] 0.063 0.063 0.062 0 0.001 SAIDI [h/yr.cust] 0.105 0.107 0.104 0.002 0.001 CAIDI [h/int] 1.671 1.683 1.703 0.012 0.032 AENS [kwh/yr.cust] 0.110 0.111 0.113 0.001 0.003 ASAI 0.99999 0.99999 0.99999 0 0 In order to illustrate the distribution of the samples in a performed simulation, a bar graph can be drawn in RADPOW for each system index. The distribution of the 10000 samples for SAIFI and the Birka system is shown in Fig. 4. 8

SAIFI (int/yr.cust) Hits/interval 500 450 400 350 300 250 200 150 100 50 0.036 0.041 0.048 0.054 0.060 0.067 0.073 0.079 0.086 0.092 (int/yr.cust) Fig. 4. Distribution of 10000 samples of SAIFI performed by the MCS method in RADPOW_2006. DISCUSSION Computation time is an issue that usually is hold against simulations in order to get appropriate results that converges. The MCS described in this paper uses the most basic sample strategy referred to as simple sampling, which needs a relatively large number of samples to receive a sufficiently accurate result. There are techniques for reduction of calculation times without loss of precision, variance reduction techniques as stratified sampling and weighted sampling as examples, but still it is costly in terms of computation time. However, there are situations when analytical methods are not suitable to use because of the difficulties to model the problem analytical without making too large approximations. In these situations the simulation approach is an alternative. In a simulation approach there is also possible to extend the model to handle general distributions of component deterioration. If the failures in the simulation are saved in a log file, the MCS provides a deeper understanding e.g. how different second order failure events occurs or how the repair or replacement of components are dealt with when there are constraints in the work force. The MCS method can also easily be extended to be used for prioritization of components; one example is how to determine where the maintenance action will have the greatest effect. Taken further this prioritization can be used in the optimization of maintenance from a system reliability perspective, which is one of the major goals for asset management of electrical networks that is handled by RCAM. CONCLUSIONS The conclusion of this paper is that the implemented MCS method in RADPOW provides the same results as the analytical method in RADPOW and the NEPLAN software for a case system. The method can be used for reliability assessment of power distribution system and has a potential to be developed further to incorporate general life time distributions for the components in the system. Another aspect that can be developed in a more straightforward 9

manner is prioritization of components e.g. to determine where the maintenance actions will have the greatest effect. REFERENCES [1]: L. Bertling, R. N. Allan, R. Eriksson, A reliability-centred asset maintenance method for assessing the impact of maintenance in power distribution systems, TPWRS-00271-2003.R3, IEEE Transactions on Power Systems, 2003.. [2]: L. Bertling. Reliability Centred Maintenance for Electric Power Distribution Systems. Doctoral dissertation, Department of Electrical Engineering, KTH, Stockholm, Sweden, August 2002. ISBN: 91-7283-345-9. [3]: L. Bertling, R. Eriksson, R. N. Allan, "Relation between preventive maintenance and reliability cost-effective distribution system", IEEE PowerTech'01 Porto, September, 2001. [4] L. Bertling, Y. He, G. Andersson, R.N. Allan, "Modelling and evaluating the effect of automatic and remote control on the reliability of distribution systems", Proceedings of the 13th Power System Computational Conference (PSCC), Trondheim, 1999, Page no 884-890. [5] R. Billinton and R.N. Allan, Reliability Evaluation of Power Systems, New York, 2nd Edition, Plenum, 1996 [6] R. Billinton and R.N. Allan, Reliability Evaluation of Engineering Systems, New York, 2nd Edition, Plenum, 1992 [7] J. Setréus. Development of a simulation method for the reliability assessment program RADPOW. Master thesis. Department of Electrical Engineering, KTH, Stockholm, Sweden, June 2006. Triata: XR-E-ETK 2006:10. [8] S. Mousavi Gargari. Reliability assessment of complex power systems and the use of the NEPLAN tool. Master thesis. Department of Electrical Engineering, KTH, Stockholm, Sweden, June 2006. Triata: XR-E-ETK 2006:11. 10