UNIVERSITY OF CAPE TOWN FACULTY OF ENGINEERING AND BUILT ENVIRONMENT DEPARTMENT OF ELECTRICAL ENGINEERING Using Probability Density Functions to Analyze the EffectTown of External Threats on the Reliability of a South African Power Grid MILTON EDIMUCape of Supervisors: Prof. C. T. Gaunt & Dr. R. Herman Thesis submitted in fulfilment of the requirements for the degree of Doctor of Philosophy University In Electrical Engineering October 2013 Keywords-Bulk Power System, Reliability Analysis, Risk Modelling, Adverse Weather, Probability Distribution Functions The copyright of this thesis vests in the author. No quotation from it or information derived from it is to be published without full acknowledgementTown of the source. The thesis is to be used for private study or non- commercial research purposes only. Cape Published by the University ofof Cape Town (UCT) in terms of the non-exclusive license granted to UCT by the author. University DECLARATION I know the meaning of plagiarism and declare that all the work in the document, save for that which is properly acknowledged, is my own. The number of words in the main text of the thesis is less than 80,000. th Signature: Signature Removed Date: 10 October 2013 Page II ABSTRACT The implications of reliability based decisions are a vital component of the control and management of power systems. Network planners strive to achieve an optimum level of investments and reliability. Network operators on the other hand aim at mitigating the costs associated with low levels of reliability. Effective decision making requires the management of uncertainties in the process applied. Thus, the modelling of reliability inputs, methodology applied in assessing network reliability and the interpretation of the reliability outputs should be carefully considered in reliability analyses. This thesis applies probability density functions, as opposed to deterministic averages, to model component failures. The probabilistic models are derived from historical failure data that is usually confined to finite ranges. Thus, the Beta distribution which has the unique characteristic of being able to be rescaled to a different finite range is selected. The thesis presents a new reliability evaluation technique that is based on the sequential Monte Carlo simulation. The technique applies a time-dependent probabilistic modelling approach to network reliability parameters. The approach uses the Beta probability density functions to model stochastic network parameters while taking into account seasonal and time- of-day influences. While the modelling approach can be applied to different aspects such as intermittent power supply and system loading, it is applied in this thesis to model the failure and repair rates of network components. Unlike the conventional sequential Monte Carlo methods, the new technique does not require the derivation of an inverse translation function for the probability distribution applied. The conventional Monte Carlo technique simulates the up and down component states when building their chronological cycles. The new technique applied here focuses instead on simulating the down states of component chronological cycles. The simulation determines the number of down states, when they will occur and how long they will last before developing the chronological cycle. Page III Tests performed on a published network show that focussing on the down states significantly improves the computation times of a sequential Monte Carlo simulation. Also, the reliability results of the new sequential Monte Carlo technique are more dependent on the input failure models than on the number of simulation runs or the stopping criterion applied to a simulation and in this respect gives results different from present standard approaches. The thesis also applies the new approach on a real bulk power network. The bulk network is part of the South African power grid. Thus, the network threats considered and the corresponding failure data collected are typical of the real South African conditions. The thesis shows that probability density functions are superior to deterministic average values when modelling reliability parameters. Probability density functions reflect the variability in reliability parameters through their dispersion and skewness. The time-dependent probabilistic approach is applied in both planning and operational reliability analyses. The component failure models developed show that variability in network parameters is different for planning and operational reliability analyses. The thesis shows how the modelling approach is used to translate long-term failure models into operational (short-term) failure models. DigSilent and MATLAB software packages are used to perform network stability and reliability simulations in this thesis. The reliability simulation results of the time-dependent probabilistic approach show that the perception on a network’s reliability is significantly impacted on when probability distribution functions that account for the full range of parameter values are applied as inputs. The results also show that the application of the probabilistic models to network components must be considered in the context of either network planning or operation. Furthermore, the risk-based approach applied to the interpretation of reliability indices significantly influences the perception on the network’s reliability performance. The risk-based approach allows the uncertainty allowed in a network planning or operation decision to be quantified. Page IV ACKNOWLEDMENTS First and foremost, I would like to thank the almighty God for paving the road that has brought me this far. May you continue to shed your light in my life. Amen! My sincere gratitude goes to the University of Cape Town, particularly my supervisors Prof. C.T. Gaunt and Dr. R. Herman for availing me this opportunity. I appreciate all the guidance and advice provided. I promise to pass on the lessons learnt. The support staff in the Department of electrical Engineering: Marlene, Chris, Phillip, Nicole, Carol and Pierre. Thank you for all your efforts in making my stay at UCT a smooth one. A special thank you to the UCT Postgraduate funding office for the support rendered during the course of this thesis. I dedicate this thesis to my parents, Prof Adipala Ekwamu and the late Mrs. Theopista Nagujja Adipala. To my mother I miss you still. To my father, thank you for being my inspiration and showing me what it means to be a real man. I would like to thank my wife, Mrs. Pamela Alinda Edimu, for the unending support and encouragement. Thank you for always believing in me. To the rest of my family, I thank you for the prayers. I needed them. I would also like to thank all the old and new friends I have met during my stay in South Africa. It was an absolute pleasure meeting all of you and thank you for the many needed breaks from this research. For God and my country…! Page V TABLE OF CONTENTS DECLARATION ....................................................................................................................... II ABSTRACT ............................................................................................................................ III ACKNOWLEDMENTS .............................................................................................................. V 1. INTRODUCTION .............................................................................................................. 1 1.1 BACKGROUND .................................................................................................................. 1 1.2 NETWORK PLANNING AND OPERATION CHALLENGES .................................................... 3 1.3 REVIEW OF WORLD WIDE ENVIRONMENT INDUCED NETWORK OUTAGES .................... 5 1.4 HYPOTHESIS AND RESEARCH QUESTIONS ..................................................................... 10 1.5 OUTLINE OF THE THESIS ................................................................................................. 13 1.6 PUBLICATIONS SUBMITTED DURING COMPLETION OF THESIS ..................................... 15 2. ESTIMATING BULK NETWORK RELIABILITY .................................................................... 17 2.1 INTRODUCTION .............................................................................................................. 17 2.2 RELIABILITY OF A POWER NETWORK ............................................................................. 17 2.3 MEASURING NETWORK RELIABILITY .............................................................................. 19 2.4 USING PROBABILITY DENSITY FUNCTIONS (PDFs) IN RELIABILITY ANALYSIS ................. 31 2.5 THE BETA PDF ................................................................................................................. 36 2.6 SUMMARY ...................................................................................................................... 39 3. MODELLING EFFECTS OF EXTERNAL THREATS ON NETWORK COMPONENTS ................. 41 3.1 INTRODUCTION .............................................................................................................. 41 Page VI 3.2 VULNERABILITY OF BULK NETWORKS TO EXTERNAL THREATS ..................................... 42 3.3 APPROACHES APPLIED TO MODELLING NETWORK COMPONENT FAILURES ................ 53 3.4 ANALYZING SEASONAL AND TIME-DEPENDENCY OF NETWORK FAILURES ................... 67 3.5 SUMMARY .....................................................................................................................