Logically constrained optimal power flow: Solver-based mixed-integer nonlinear programming model

Abstract

There is increasing evidence of the shortage of solver-based models for solving logically-constrained AC optimal power flow problem (LCOPF). Although in the literature the heuristic-based models have been widely used to handle the LCOPF problems with logical terms such as conditional statements, logical-and, logical-or, etc., their requirement of several trials and adjustments plagues finding a trustworthy solution. On the other hand, a welldefined solver-based model is of much interest in practice, due to rapidity and precision in finding an optimal solution. To remedy this shortcoming, in this paper we provide a solver-friendly procedure to recast the logical constraints to solver-based mixed-integer nonlinear programming (MINLP) terms. We specifically investigate the recasting of logical constraints into the terms of the objective function, so it facilitates the pre-solving and probing techniques of commercial solvers and consequently results in a higher computational efficiency. By applying this recast method to the problem, two sub-power-and sub-function-based MINLP models, namely SP-MINLP and SF-MINLP, respectively, are proposed. Results not only show the superiority of the proposed models in finding a better optimal solution, compared to the existing approaches in the literature, but also the effectiveness and computational tractability in solving large-scale power systems under different configurations.

A Demand-Side Management-Based Model for G&TEP Problem Considering FSC Allocation

“…, , (24). It is worth mentioning that the main reason of linearizing the nonlinear terms is that the existing commercial solvers guarantee finding the global solution of the MILP models, while, more often than not, even for a very well-defined solver-friendly mixed integer nonlinear nonconvex programming model, there is no guarantee for finding the global solution [25].…”

Matching of Local Load with On-Site PV Production in a Grid-Connected Residential Building

“…The resulting model is a mixed-integer nonlinear programming (MINLP) model and the existing solution approaches or commercial solvers cannot guarantee finding the global solution, although a high-quality solution might be obtained [21]. To this end, the MINLP model was reformulated into a mixed-integer linear programming (MILP) model that could be effectively embedded into an HEMS.…”

Optimal power flow problem considering multiple-fuel options and disjoint operating zones: A solver-friendly MINLP model

“…In [19], a Shuffle Frog Leaping Algorithm (SFLA) and Simulated Annealing (SA) approach was proposed to address the difficulties of solving the OPF problem with non-smooth and non-convex generator fuel cost, while in [20], the hybrid model of the same problem was studied via an efficient evolutionary algorithm that works based on sensitivity and heuristic approach principles. Unlike the above studies, the authors in [21] performed an effective mixed-integer nonlinear model to solve the OPF problems at the presence of VPEs and POZs. In this work, the authors recast the logic terms in a way that the existing commercial solvers can handle them.…”

“…The aforementioned recently published and in-press works in this area reveals 1) the necessity and importance of considering the multiple fuel options in OPF problems, and 2) the lack of a model that can be solved via commercial solvers. However, neither the solver-based model in [21] nor the heuristic-based approaches did not handle two logic constraints, POZs and MFOs, simultaneously. The main obstacle in considering more than one logic constraint simultaneously is the overlapped areas in which both the logic constraints are active.…”