Probabilistic evaluation of distribution power transformers reliability indices considering load transfers and mobile unit substations

Abstract This paper proposes a new and practical probabilistic method for calculating reliability indices and costs associated with distribution substations that share spare transformers of a same group. Based on Monte Carlo simulation, the proposed algorithm considers the chronological representation of failure occurrences, and enhances previous methods by modeling emergency actions, such as transferring load to neighboring feeders and connecting a mobile unit substation to ensure electricity supply to customers during the replacement of failed transformers. Thus, spare transformer requirements with new acquisitions to replenish the stock or even to expand the system are probabilistically assessed. All waiting times associated to these actions can be duly represented by any probability distribution, including the usual exponential model. A more accurate calculation of reliability indices and costs associated with the interruption of consumers is achieved. The corresponding computational algorithm is used in several numerical applications, considering a class of transformers of a Brazilian electricity utility. The results of these applications are deeply discussed to demonstrate the practical relevance of the proposed method.

[1]  Dirk P. Kroese,et al.  Simulation and the Monte Carlo method , 1981, Wiley series in probability and mathematical statistics.

[2]  Wlad Mielczarski,et al.  Management of inventory to reduce outages in supply feeder , 1995, Proceedings 1995 International Conference on Energy Management and Power Delivery EMPD '95.

[3]  Roy Billinton,et al.  Reliability evaluation of power systems , 1984 .

[4]  D.O. Koval,et al.  Development of probabilistic models for computing optimal distribution substation spare transformers , 2005, IEEE Transactions on Industry Applications.

[5]  Akshay Kumar Saha,et al.  Transformer risk modelling by stochastic augmentation of reliability-centred maintenance , 2015 .

[6]  G.A. Hamoud.  Use of mobile unit transformers in high voltage load stations , 2008, 2008 IEEE Power and Energy Society General Meeting - Conversion and Delivery of Electrical Energy in the 21st Century.

[7]  Vladica Mijailovic.  Probabilistic model for planning keeping of power transformer spare components with general repair time distribution , 2013 .

[8]  Magdy M. A. Salama,et al.  Asset management techniques for transformers , 2010 .

[9]  Gomaa Hamoud.  Assessment of spare transformer requirements for distribution stations , 2011, 2011 IEEE Power and Energy Society General Meeting.

[10]  Vladica Mijailovic,et al.  Method for determining optimal power transformers exploitation strategy , 2012 .

[11]  Nanang Hariyanto,et al.  The use of Markov chain method to determine spare transformer number with 3-criteria parameters , 2016, 2016 International Conference on Probabilistic Methods Applied to Power Systems (PMAPS).

[12]  Nigel Slack,et al.  Operations management , 1994 .

[13]  João Guilherme de C. Costa,et al.  Evaluation of spare transformer requirements for distribution substations via chronological Monte Carlo simulation , 2017, 2017 IEEE Manchester PowerTech.

[14]  Roy Billinton,et al.  Reliability evaluation of engineering systems : concepts and techniques , 1992 .

[15]  Cynthia Yiu,et al.  One Markov model for spare analysis of distribution power transformers , 2016, 2017 IEEE Power & Energy Society General Meeting.

[16]  J.M. Nahman,et al.  Probability Models for Optimal Sparing of Distribution Network Transformers , 2009, IEEE Transactions on Power Delivery.

[17]  Wenyuan Li,et al.  Risk Assessment Of Power Systems: Models, Methods, and Applications , 2004 .

[18]  G. Hamoud.  Cost/Benefit Analysis for Use of Mobile Unit Substations in Customer Delivery Systems , 2006, 2006 IEEE Power Engineering Society General Meeting.

[19]  A.M.L. da Silva,et al.  Probabilistic Methodologies for Determining the Optimal Number of Substation Spare Transformers , 2010, IEEE Transactions on Power Systems.

[20]  Armando Martins Leite da Silva,et al.  Probabilistic Method for Optimizing the Number and Timing of Substation Spare Transformers , 2015, IEEE Transactions on Power Systems.

[21]  G. A. Hamoud.  Use of Markov Models in Assessing Spare Transformer Requirements for Distribution Stations , 2012, IEEE Transactions on Power Systems.

[22]  Athanasios Papoulis,et al.  Probability, Random Variables and Stochastic Processes , 1965 .

[23]  Cynthia Yiu,et al.  Use of Mobile Unit Substations in redundant customer delivery systems , 2014, 2014 IEEE PES General Meeting | Conference & Exposition.

[24]  E. Vaahedi,et al.  Determining number and timing of substation spare transformers using a probabilistic cost analysis approach , 1999 .

[25]  Armando M. Leite da Silva,et al.  Spare transformers optimization using Monte Carlo simulation and metaheuristic techniques , 2015, 2015 18th International Conference on Intelligent System Application to Power Systems (ISAP).