Ph.D. Thesis

Minea Skok, The Evolutionary Algorithm for the Dynamic Planning of Distribution Networks, Ph.D. Thesis, University of Zagreb, Faculty of Electrical Engineering and Computing, Departement of Power Systems, Zagreb, Croatia, February, 2005.



The doctoral dissertation proposes a new method based on the evolutionary algorithms aimed at dynamic planning of distribution networks of a number of spatially closed structures for an uncertain future. Based on the results of the planning, robust decisions are being made regarding the optimum capacities and locations of new HV/MV substations, the size of the new transformers within the existing HV/MV substations and the routes of new conduits. The used evolutionary algorithm operators enable the structuring of the whole supply area into the given structure with minimum investment, maintenance costs, costs of power and energy losses and the costs of energy not supplied by a unique optimisation procedure. The model of the problem includes the existing network, uncertainty of input data and parameters, distributed generation, permissible voltage drop in regular and outage conditions, calculation of power and energy losses, verification of cable and transformer thermal limits and reliability indices in the distribution network. The procedure is based on a number of computer provided variant solutions, additionally evaluated by the planner, which are applicable to mid-term and long-term planning of distribution networks.

This doctoral dissertation is divided into eight parts.

The introductory chapter explains the role and importance of medium voltage distribution networks planning in urban areas. A brief description of the main features of the problem highlights the aim and the scientific contribution of this dissertation.

Part 1, upon defining the major concepts used in the thesis, provides a definition of medium voltage distribution networks planning and a division of planning into the functional groups. There is a detailed description of the features and the importance of mid-term and long-term planning of network reinforcement and build up (development) in urban areas, as well as of other relevant issues such as uncertainty of data and criteria for plan evaluation.

Part 2 provides a detailed review of representative studies and commercial programme packages dealing with the distribution network planning. The methods division is performed on the basis of the used problem model and optimisation techniques taking into account the used simplifications (goal function linearisation), consideration of time component (static, pseudo-dynamic and dynamic procedures), layout of the distribution network, geographic model of the area and the model of uncertain data.

Part 3 starts with a description of features of liberalisation in the electric power industry. The focus is put on describing the course of adjustment to the stated processes in the Republic of Croatia, i.e. the examination of jurisdiction and liabilities of a electricity distribution utility and the distribution system operator in market conditions. There follows a definition of new sources of influence in planning procedures due to re-regulation of natural monopolies with a special reference to the, world-wide used, models of rate (tariffs) regulation in distribution industry. The last section is entirely dedicated to the distributed generation – the technologies used in distributed generation and their impact to the distribution network. Part 3 closes with a review of the existing methods dealing with the problem of planning the distribution networks with distributed generation.

Part 4 presents two models of uncertain data – fuzzy sets and probability models. The first section, dealing with fuzzy sets, defines the operations with fuzzy numbers (fuzzy arithmetic). Apart from that, there is a description of the use of, hereby applied, fuzzy numbers in modelling of uncertain demand in MV/LV substations, uncertain generation in the distributed sources, uncertain expected values of parameters used in the calculation of supply unavailability and the prices uncertainty. The following section describes the probability models. There is a detailed description of the so-called hybrid of the probability and fuzzy model which is used for modelling indices and data used in calculations of supply unavailability in distribution networks. There follows a description and classification of available approaches for fuzzy numbers ranking for the purpose of comparing variant solutions in the optimisation procedure (i.e. evolutionary algorithms). Part 4 ends with a formalisation of the robustness concept and investment hedging in the procedure of planning the distribution network for uncertain future.

Part 5 is dedicated to the physical characteristics of the distribution networks. Upon a brief description of the basic structures of distribution networks, there follows an analysis of the features of the so called „pure“ spatially closed layouts, to which, in view of the aim of this study, the structure of distribution network strives in the u horizon year of the planning. Further, there is a description of a method of calculating power flows with fuzzy demands and generation in distributed sources. One of the sections in Part 5 deals specifically with methods of determining the optimum reconfiguration of distribution feeders for loss minimization in the spatially closed distribution networks. There is also a description of the approximate algorithm based on the heuristic rules and the technique of branch exchange used in the dissertation. The last section, upon the introductory definition of reliability indices, gives a detailed description of the existing approaches used in evaluation of supply unavailability (especially in planning procedures). This chapter closes with a review of methods for calculation of reliability indices. There is also a description of the two approximate algorithms which are used in this dissertation – one intended for the calculation in „pure“ spatially closed distribution networks, and the other, more general one, intended for calculations in spatially closed distribution networks which are not “pure” loop or linked structured.

Part 6 opens with a review of the basic terms of biological evolution and genetics. Upon a brief description of the features and the basic steps of two proposed evolutionary algorithms – primary (master) aimed at static planning and secondary (slave) aimed at dynamic planning of distribution networks- there follows a description of the algorithms outlines, selection operators, recombination and mutation operators. There is a description of the procedures of initial population creation, performance (fitness) estimation, and penalties used in the performance evaluation of illegal solutions. The last section in this chapter provides the description of the characteristics of the artificial immune system and the evolutionary algorithm with an implanted immune operator for static planning of distribution networks of „pure“ spatially closed layouts.

Upon briefly describing the flow of proposed method when applied to the planning of real distribution networks, Part 7 provides a test of applicability of the evolutionary algorithm in solving the two real problems of planning the complex distribution network in urban area of the city of Zagreb.

The final chapter provides the conclusive considerations.


power system, primary distribution. open-loop structured network, planning, dynamic model, uncertainty, fuzzy sets,  evolutionary algorithm