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Canadian Journal of Electrical and Computer Engineering Revue canadienne de génie électrique et informatique Spring 2012 V olume 37, Number 2 Printemps 2012 Volume 37, Numéro 2 IEEE CANADA http://ieee.ca/journal

Optimal Capacitor Placement and Sizing in Distribution Systems with Harmonics Consideration Using a Hybrid Method Based on Simulated Annealing and Generic Algorithm

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This paper presents a hybrid algorithm formed by combining the simulated annealing and genetic algorithm (SA-GA) for solving the optimal capacitor placement problem in distribution systems. The objective is to minimize the energy losses in the system while taking the capacitor installation costs into consideration. The capacitor cost is a step-like and, therefore, a non-differentiable function. Load variations, load constraints, operational constraints and constraints on capacitor types and sizes will be all considered in the problem formulation. Models of the distribution system at the fundamental frequency and at harmonic frequencies are established in order to include the non-linear loads into the problem formulation. Nonlinear loads are included to make sure that the resulting harmonic distortion levels are within the acceptable limits. The solution algorithm is implemented into a software package in MATLAB and tested on a 30-bus distribution system containing a loop. Simulation results signify the robustness of the developed SA-GA in finding the optimal locations and ratings of shunt capacitors.

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Page 1: Optimal Capacitor Placement and Sizing in Distribution Systems with Harmonics Consideration Using a Hybrid Method Based on Simulated Annealing and Generic Algorithm

Canadian Journal of Electrical and Computer Engineering

Revue

canadienne de génie électrique et informatique

Spring 2012 Volume 37, Number 2

Printemps 2012 Volume 37, Numéro 2

IEEE CANADA

http://ieee.ca/journal

Page 2: Optimal Capacitor Placement and Sizing in Distribution Systems with Harmonics Consideration Using a Hybrid Method Based on Simulated Annealing and Generic Algorithm

Canadian

Journal of Electrical and Computer Engineering

Spring 2012, Volume 37, Number 2 / Printemps 2012, Volume 37, Numéro 2

Table of Contents / Table des matières

1 Message from the Editors

2 Time-frequency single-phase power components measurements for harmonics and inter-harmonics distortion based on

Wavelet Packet transform; Part I: Mathematical formulation

Mohamed E. El-Hawary and Walid G. Morsi

11 Time-frequency single-phase power components measurements for harmonics and inter-harmonics distortion based on

Wavelet Packet transform; Part II: Case studies and results

Mohamed E. El-Hawary and Walid G. Morsi

18 A global optimization technique for microwave imaging of the inhomogeneous and dispersive breast

Abas Sabouni, Sima Noghanian and Stephen Pistorius

29 Fast block motion estimation based on sorting of prediction vectors

S.M.R. Soroushmehr, S. Samavi and Shahram Shirani

37 Separation of Core Losses in Distribution Transformers Using Experimental Methods

Juan Carlos Olivares-Galvan, Rafael Escarela-Perez, Eduardo Campero Littlewood, Francisco de Leon and Carlos Aviles Cruz

49 Optimal Capacitor Placement and Sizing in Distribution Systems with Harmonics Consideration Using a Hybrid Method

Based on Simulated Annealing and Generic Algorithm

M.Rashidi, A.Pedram, M.Bahmani

56 A photonic crystal technology compatible with integrated circuit technologies

Khadijeh Bayat, Mahdi Farrokh Baroughi, Sujeet K. Chaudhuri and Safieddin Safavi-Naeini

68 Graphical display of tactile sensing data with application in minimally invasive surgery

Javad Dargahi, Siamak Najarian, and Reza Ramezanifard

77 Test bus assignment, sizing, and partitioning for system-on-chip

Haidar M. Harmanani and Rachel Sawan

87 Improved Tomlinson-Harashima precoding for the downlink of multi-user MIMO systems

Jia Liu and Witold A. Krzymien

Journal canadien

de génie

électrique et informatique

Page 3: Optimal Capacitor Placement and Sizing in Distribution Systems with Harmonics Consideration Using a Hybrid Method Based on Simulated Annealing and Generic Algorithm

Can. J. Elect. Comput. Eng., Vol. 37, No. 2, Spring 2012

Optimal Capacitor Placement and Sizing in Distribution Systems with Harmonics

Consideration Using a Hybrid Method Based on Simulated Annealing and Generic Algorithm

Mehran Rashidi*, Ahmad Pedram and Mohammad Bahmani

This paper presents a hybrid algorithm formed by combining the simulated annealing and genetic algorithm (SA-GA) for solving the optimal capacitor placement problem in distribution systems. The objective is to minimize the energy losses in the system while taking the capacitor installation costs into consideration. The capacitor cost is a step-like and, therefore, a non-differentiable function. Load variations, load constraints, operational constraints and constraints on capacitor types and sizes will be all considered in the problem formulation. Models of the distribution system at the fundamental frequency and at harmonic frequencies are established in order to include the non-linear loads into the problem formulation. Nonlinear loads are included to make sure that the resulting harmonic distortion levels are within the acceptable limits. The solution algorithm is implemented into a software package in MATLAB and tested on a 30-bus distribution system containing a loop. Simulation results signify the robustness of the developed SA-GA in finding the optimal locations and ratings of shunt capacitors.

IIII.... IntroductionIntroductionIntroductionIntroduction The application of shunt capacitors in distribution systems has always been an important subject to distribution engineers. It is a well-known fact that the major portion of the power losses occurs at the distribution level. The cumulative data gathered for the whole utility industry indicate that about 60% of the capacitors are applied to the distribution feeders, 30% to the substation buses and the remaining 10% to transmission system [1]. Shunt capacitors have been widely installed by utilities to provide reactive power compensation to improve service quality via voltage regulation, to improve the efficiency of power distribution via real power and energy reduction and to achieve deferral of construction, if possible, via system capacity release. The economic benefits which can be derived from capacitor installation can be summarized as [2]: 1. Released generation capacity. 2. Released transmission capacity. 3. Released distribution substation capacity. 4. Reduced energy losses. 5. Reduced voltage drop (Improved voltage regulation). 6. Reduced capacity of feeder and associated apparatus. 7. Postponement or elimination of capital expenditure due to system improvements and/or expansions. 8. Revenue increase due to voltage improvements. The extent of these benefits depends on how the capacitors are placed on the system. Due to this, optimization of the capacitor placement problem becomes of a great necessity. Recently, the growing need for distribution automation and control has generated interest in the capacitor placement problem. In fact, capacitor placement is regarded as a function with outstanding importance associated with distribution automation. The general capacitor placement problem is defined as the problem of how to determine the location, type, number and size of capacitors to be installed in the system [3].

The objective is to minimize the energy losses while considering the capacitor installation costs. In other words, the revenue savings resulting from the energy loss reductions are weighed against the installation cost of capacitors [3]. The goal is to achieve the optimal or maximum value while satisfying the system constraints. The decision variables of the capacitor placement are discrete i.e. the solution is a set of integers and therefore, capacitor placement problem is classified as a combinatorial problem. The problem of finding optimal solutions to such a problem is therefore known as combinatorial optimization. Nowadays the levels of harmonic voltages and currents on distribution systems are becoming a serious problem. Harmonics can cause a lot of operational problems. Some of these problems include the following [4]: l. Capacitor bank failure from dielectric breakdown or reactive power overload. 2. Interference with ripple control and power-line carrier systems. 3. Excessive losses in and heating of induction and synchronous machines. 4. Overvoltages and excessive currents on the system from resonance to harmonic currents or voltages on the network. 5. Dielectric instability of insulated cables due to harmonic overvoltages. 6. Inductive interference with telecommunication systems. 7. Errors in induction watt-hour meters. 8. Signal interference and relay malfunction, specifically in solid-state and microprocessor controlled systems. 9. Interference with large motor controllers and power plant excitation systems.

Loads that do not draw a sinusoidal current from a sinusoidal voltage source are said to be nonlinear, that is the relationship between voltage and current at every instant of time is not constant. Examples of nonlinear loads include rectifiers, welders, inverters, arc furnaces, frequency converters and voltage controllers. Nonlinear loads are one of the major sources of power system harmonics. They generate excessive harmonic currents that can result in unacceptable voltage distortion levels [5]. The degree to which a power system is affected by harmonics depends on the *Mehran Rashidi is with the Department of Electrical Engineering,

Islamic Azad University, Bandar-Abbas Branch, Iran. E-mail: [email protected]

Page 4: Optimal Capacitor Placement and Sizing in Distribution Systems with Harmonics Consideration Using a Hybrid Method Based on Simulated Annealing and Generic Algorithm

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processing; adaptive signal processing; signal processing for communica-tions; VLSI signal processing; computer arithmetic / Traitement du signal: numérique, multi-taux, multi-dimensionnel, adaptatif, adapté aux communica-tions, adapté au VLSI; arithmétique des ordinateurs

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tion and error correction coding / Communication; traitement du signal pour les communications, modulation et correction d’erreurs en codage

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Dr. John Salmon, University of Alberta, Edmonton E-mail / Courriel: [email protected] • Power electronics; variable-speed drives / Électronique de puissance;

entraînements à vitesse variable

Dr. Vijay K. Sood, Concordia University, Montreal E-mail / Courriel: [email protected] • Power systems (HVDC and FACTS); power electronics / Systèmes de

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Page 5: Optimal Capacitor Placement and Sizing in Distribution Systems with Harmonics Consideration Using a Hybrid Method Based on Simulated Annealing and Generic Algorithm

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