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

This paper proposes a solver-friendly model for disjoint, non-smooth, and nonconvex optimal power flow (OPF) problems. The conventional OPF problem is considered as a nonconvex and highly nonlinear problem for which finding a high-quality solution is a big challenge. However, considering practical logic-based constraints, namely multiple-fuel options (MFOs) and prohibited operating zones (POZs), jointly with the non-smooth terms such as valve point effect (VPE) results in even more difficulties in finding a near-optimal solution. In complex problems, the nonlinearity itself is not a big issue in finding the optimal solution, but the nonconvexity does matter and considering MFO, POZ, and VPE increase the degree of nonconvexity exponentially. Another primary concern in practice is related to the limitations of the existing commercial solvers in handling the original logic-based models. These solvers either fail or show intractability in solving the equivalent mixed integer nonlinear programming (MINLP) models. This paper aims at addressing the existing gaps in the literature, mainly handling the MFOs and POZs simultaneously in OPF problems by proposing a solver-friendly MINLP (SF-MINLP) model. In this regard, due to the actions that are done in the pre-solve step of the existing commercial MINLP solvers, the most adaptable model is obtained by melting the primary integer decision variables, associated with the feasible region, into the objective function. For the verification and didactical purposes, the proposed SF-MINLP model is applied to the IEEE 30-bus system under two different loading conditions, namely normal and increased, and details are provided. The model is also tested on the IEEE 118-bus system to reveal its effectiveness and applicability in larger-scale systems. Results show the effectiveness and tractability of the model in finding a high-quality solution with high computational efficiency

Experiments with hybrid Bernstein global optimization algorithm for the OPF problem in power systems

This paper presents an algorithm based on the Bernstein form of polynomials for solving the optimal power flow (OPF) problem in electrical power networks. The proposed algorithm combines local and global optimization methods and is therefore referred to as a `hybrid' Bernstein algorithm in the context of this work. The proposed algorithm is a branch-and-bound (B&B) procedure wherein a local search method is used to obtain a good upper bound on the global minimum at each branching node. Subsequently, the Bernstein form of polynomials is used to obtain a lower bound on the global minimum. The performance of the proposed algorithm is compared with the previously reported Bernstein algorithm to demonstrate its effi cacy in terms of the chosen performance metrics. Furthermore, the proposed algorithm is tested by solving the OPF problem for several benchmark IEEE power system examples and its performance is compared with generic global optimization solvers such as BARON and COUENNE. The test results demonstrate that the algorithm HBBB delivers satisfactory performance in terms of solution optimality.This research is supported by the National Research Foundation, Prime Ministers Office, Singapore, under its CREATE programme