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

Here is a simple implementation of an Optimal Power Flow (OPF) algorithm in Python that minimizes the cost of power generation while satisfying power demand and abiding by system constraints. This implementation uses the Pyomo library for optimization modeling and the GLPK solver for solving the optimization problem.
\ python\nfrom pyomo.environ import *\n\n# Define the power system parameters\nnum_generators = 3\nnum_buses = 4\npower_demand = [200, 150, 100, 250]\npower_generation_min = [50, 40, 30]\npower_generation_max = [150, 120, 100]\ngeneration_cost = [10, 12, 15]\nbus_voltage_min = [0.95, 0.95, 0.95, 0.95]\nbus_voltage_max = [1.05, 1.05, 1.05, 1.05]\nline_flow_max = [100, 100, 100, 100]\n\n# Create the optimization model\nmodel = ConcreteModel()\n\n# Define the decision variables\nmodel.power_generation = Var(range(num_generators), within=NonNegativeReals)\n\n# Define the objective function\nmodel.cost = Objective(expr=sum(generation_cost[i] * model.power_generation[i] for i in range(num_generators)))\n\n# Define the power balance constraint\nmodel.power_balance = Constraint(range(num_buses),\n rule=lambda model, i: sum(model.power_generation[j] for j in range(num_generators)) == power_demand[i])\n\n# Define the power generation limits constraint\nmodel.power_generation_limits = Constraint(range(num_generators),\n rule=lambda model, i: power_generation_min[i] <= model.power_generation[i] <= power_generation_max[i])\n\n# Define the bus voltage limits constraint\nmodel.bus_voltage_limits = Constraint(range(num_buses),\n rule=lambda model, i: bus_voltage_min[i] <=\n sum(model.power_generation[j] for j in range(num_generators)) <=\n bus_voltage_max[i])\n\n# Define the line flow limits constraint\nmodel.line_flow_limits = Constraint(range(num_buses),\n rule=lambda model, i: sum(model.power_generation[j] for j in range(num_generators)) <= line_flow_max[i])\n\n# Solve the optimization problem\nsolver = SolverFactory('glpk')\nsolver.solve(model)\n\n# Print the optimal solution\nprint("Optimal power generation:")\nfor i in range(num_generators):\n print(f"Generator {i+1}: {model.power_generation[i].value}")\n\nprint("Total cost of power generation:", model.cost.value)\n\n\nThis implementation assumes a simplified power system with a fixed number of generators, buses, and power demand values. The power generation limits, bus voltage limits, and line flow limits are also defined as lists of values. You can modify these parameters according to your specific problem.\n\nThe implementation creates an optimization model using the Pyomo library and defines the decision variables, objective function, and constraints. It then solves the optimization problem using the GLPK solver and prints the optimal power generation and the total cost of power generation.