**
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.

*Summary*

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

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

The
final chapter provides the conclusive considerations.

*Keywords*

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