Flujo de potencia óptimo para redes radiales y enmalladas empleando programación semidefinida

Abstract

Este artículo presenta una formulación convexa para el problema de flujo de potencia óptimo (Optimal Power Flow-OPF) en sistemas de potencia radiales y enmallados, a través de un modelo matemático basado en programación semidefinida (Semidefinite Programming-SDP), el cual trasforma el modelo cuadrático no convexo del OPF en un modelo convexo relajado, que puede ser solucionado de forma mucho más eficiente. El modelo es implementado en MATLAB usando el paquete de optimización convexa CVX. Los resultados obtenidos son comparados con el modelo no lineal del problema implementado en GAMS y MATPOWER usando cuatro sistemas típicos de la literatura especializada, dos de tipo radial y dos enmallado. Las soluciones encontradas por esta aproximación convexa, son muy cercanas a las respuestas presentadas en la literatura especializada para el modelo no lineal. Este tipo de aproximación permite obtener soluciones de muy buena calidad, muy cercanas a la solución óptima del problema en tiempos computacionales menores y susceptibles de aplicarse en problemas de operación y control en tiempo real.

Economic Dispatch of Renewable Generators and BESS in DC Microgrids Using Second-Order Cone Optimization

“…Due to that, they use the non-linear non-convex model for the economic dispatch problem [6]. This implies that is possible to find a better configuration by using convex optimization formulations, which permits arriving at the global optimum of problem [20,21]. In [8], a convex optimization formulation based on semidefinite programming (SDP) to operate BESSs and renewable power generation in DCMGs was developed.…”

On the Matricial Formulation of Iterative Sweep Power Flow for Radial and Meshed Distribution Networks with Guarantee of Convergence

“…To determine the behavior of electrical networks under well-defined voltage conditions, power flow methodologies are used, which facilitate the calculation of the voltage profiles at all the nodes of the network for a particular load condition [7,8]. The main challenge in the power-flow analysis of distribution networks is the constant power loads that produce nonlinear relationships between the voltages and powers [9,10], which makes the use of numerical methods for solving the power-flow problem necessary [11]. A typical tendency in the power-flow analysis of electrical distribution networks is the use of graph-based methods to address the power-flow problem based on the radial structure of the grid [12,13].…”

“…Other approaches have also been presented in specialized literature in relation to linear and convex approximations for power-flow solutions in distribution networks. In [11], a convex approximation for a power-flow analysis of radial and meshed distribution networks was presented while considering a semidefinite programming approximation by using a rectangular representation of the power-balance equations. In [8], a second-order cone programming approximation was described while considering branch variables related to currents and powers in all the lines.…”

“…where Z dd is defined as A T d YA d −1 , and b = +Z dd A T d YA s V s . It should be noted that to solve expression (11), an iterative procedure is required, as this expression has a recursive structure. For this purpose, let us to add an iterative counter t that starts from the initial point t = 0 (i.e., V 0 d is perfectly known), which allows the rewriting of (11) as presented below:…”

A Mixed-Integer Quadratic Formulation of the Phase-Balancing Problem in Residential Microgrids

“…It is possible to obtain a convex relaxation of it by using a linear representation of the power flow problem in three-phase networks [19]. For this representation, a linearization is applied to the relation between voltages and powers, allowing the rewriting of them as a set of complex affine functions [20]. We recur to the integer convex optimization theory regarding the binary variables that model the phase-balancing problem.…”