Optimal Power Flow (OPF) Algorithm for Cost Minimization in Power Generation

Here is an example implementation of an Optimal Power Flow (OPF) algorithm that minimizes the cost of power generation while satisfying power demand and abiding by system constraints. This algorithm uses the MATLAB Optimization Toolbox to solve the OPF problem.
\ matlab\nfunction [x, fval] = opf_algorithm(demand, costs, constraints)\n % demand: vector of power demand at each bus\n % costs: matrix of generation costs at each generator\n % constraints: matrix of system constraints (e.g., maximum generator capacity)\n \n % Number of buses and generators\n num_buses = length(demand);\n num_gens = size(costs, 1);\n\n % Define optimization problem\n f = costs(:); % Objective function coefficients\n Aeq = ones(1, num_gens); % Equality constraint matrix\n beq = sum(demand); % Total power demand constraint\n lb = zeros(num_gens, 1); % Lower bounds for generator outputs\n ub = constraints(:, 2); % Upper bounds for generator outputs\n\n % Solve OPF problem\n options = optimoptions('linprog', 'Algorithm', 'interior-point', 'Display', 'off');\n [x, fval] = linprog(f, [], [], Aeq, beq, lb, ub, options);\n\n % Reshape solution to matrix form\n x = reshape(x, [], num_buses)';\nend\n\n\nTo use this algorithm, you can define the power demand, generation costs, and system constraints as inputs to the opf_algorithm function. The power demand is a vector of the power demand at each bus, the generation costs is a matrix where each row represents the cost coefficients for a generator, and the system constraints is a matrix where each row represents the constraints for a generator (e.g., maximum capacity).\n\nHere is an example usage of the algorithm:\n\nmatlab\ndemand = [100; 150; 200]; % Power demand at each bus\ncosts = [10, 20, 30; 15, 25, 35]; % Generation costs for each generator\nconstraints = [100, 200; 150, 250]; % Constraints for each generator\n\n[x, fval] = opf_algorithm(demand, costs, constraints);\ndisp('Optimal generator outputs:');\ndisp(x);\ndisp('Minimum cost of power generation:');\ndisp(fval);\n\n\nThis will solve the OPF problem using the given power demand, generation costs, and system constraints, and output the optimal generator outputs and the minimum cost of power generation.