1. Abstract

Summarize the application of genetic algorithms (GAs) to solve optimization problems in electrical networks (e.g., power flow optimization, loss minimization, network reconfiguration). Highlight key methods, MATLAB tools, and results (e.g., cost reduction, improved efficiency).

2. Introduction

• Objective: Optimize electrical network performance (e.g., reduce losses, enhance voltage stability, minimize operational costs).
• Challenges: Non-linear constraints, discrete variables (e.g., switch status), and large-scale systems.
• Why GAs?: Ability to handle non-convex, multi-modal, and mixed-integer problems.
• Applications:
  • Optimal Power Flow (OPF).
  • Distributed generation placement.
  • Network reconfiguration for loss minimization.
• Tools: MATLAB’s Global Optimization Toolbox, Power Systems Toolbox, and custom scripts.

3. Theoretical Background

3.1 Genetic Algorithms

• Key Steps:
  1. Initialization: Random population generation.
  2. Fitness Evaluation: Objective function (e.g., power loss, cost).
  3. Selection: Roulette wheel, tournament selection.
  4. Crossover: Blend, single-point, or uniform crossover.
  5. Mutation: Bit-flip, Gaussian perturbation.
  6. Termination: Convergence criteria or generation limits.

3.2 Electrical Network Optimization Problems

1. Optimal Power Flow (OPF):
   • Minimize generation cost or losses while satisfying power balance and constraints.
2. Network Reconfiguration:
   • Optimize switch status to reduce losses or balance loads.
3. Capacitor Placement:
   • Optimize capacitor sizing/location for voltage stability.

4. Methodology

4.1 GA Workflow for Electrical Networks

1. Problem Encoding:
   • Represent variables (e.g., generator outputs, switch status) as chromosomes.
2. Fitness Function:
   • Combine objectives (e.g., losses, voltage deviation) with penalties for constraints.
3. Constraint Handling:
   • Penalty functions or repair mechanisms for voltage limits, line capacities.

4.2 Case Study 1: Optimal Power Flow (OPF)

MATLAB Implementation

% Define OPF problem: Minimize fuel cost with generation limits  
nGenerators = 3;  
costCoeff = [0.1 5 50; 0.2 6 60]; % Quadratic cost coefficients [a, b, c]  

% GA Parameters  
options = optimoptions('ga', 'PopulationSize', 50, 'MaxGenerations', 100);  

% Bounds for generator outputs (Pmin, Pmax)  
lb = [50 100 150];  
ub = [200 300 400];  

% Fitness function: Total cost  
fitnessFcn = @(P) sum(costCoeff(:,1).*P.^2 + costCoeff(:,2).*P + costCoeff(:,3));  

% Constraints: Power balance (sum(P) = Load)  
Load = 800;  
Aeq = ones(1, nGenerators);  
beq = Load;  

% Run GA  
[P_opt, cost_opt] = ga(fitnessFcn, nGenerators, [], [], Aeq, beq, lb, ub, [], options);  
disp(['Optimal generation: ', num2str(P_opt), ' | Cost: $', num2str(cost_opt)]);

Results

• Compare GA results with traditional methods (e.g., interior-point).
• Plot convergence of fitness function over generations.