Optimal power flow using a genetic algorithm and linear algebra [electronic resource] /

by Maust, Reid S.

Optimal Power Flow Using a Genetic Algorithm and Linear Algebra Reid S. Maust Artificial intelligence is used to help a hypothetical electric utility meet is electric load economically. The optimal power flow problem (OPF) problem is an optimization problem, in which the utility strives to minimize its costs while satisfying all of its constraints. A genetic algorithm (GA)—a specific type of artificial intelligence—is employed to perform this optimization. To speed convergence, some theory from linear algebra is incorporated into the algorithm. A GA provides several advantages over more traditional OPF algorithms. For instance, a GA does not constrain the shape of the generators’ cost curves and is flexible enough to incorporate control devices such as tap-changing transformers and static VAR compensators. In the literature, GA-based methods typically use the GA to find the real power and voltage magnitude at each generation bus. To enforce the inequality constraints on voltage magnitudes and angles, these algorithms must compute these quantities for all buses. This requires the solution of the load-flow equations, a set of nonlinear equations that provide real and reactive power in terms of voltage magnitude and angle. Solving for the voltage quantities is computationally intensive when performed repeatedly through the iterations of a method. In contrast, the GA-OPF method presented here reduces the number of load-flow solutions by having the GA find the voltage magnitude and angle at each bus. The real and reactive power are then found by direct substitution into the load-flow equations. To narrow the search for the optimal solution, a vector space is derived that contains all solutions meeting the inequality constraints. This speeds convergence of the algorithm by eliminating a large number of illegal solutions. The effectiveness of this method is demonstrated on three test systems—the Steinberg and Smith example, the IEEE 30-bus test system, and the IEEE 118-bus test system. For the first two examples, the GA-OPF algorithm finds an answer that agrees with published results. For the 118-bus system, the GA-OPF demonstrates its ability to enforce emission constraints and its potential to be used with larger systems. Thus, the GA-OPF algorithm is shown to be a valid tool to perform this optimization.