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

Mahdi Pourakbari-Kasmaei, Matti Lehtonen, Mahmud Fotuhi-Firuzabad, Mousa Marzband, José Roberto Sanches Mantovani

Research output: Contribution to journalArticlepeer-review

31 Citations (Scopus)
21 Downloads (Pure)


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.
Original languageEnglish
Pages (from-to)45-55
Number of pages11
JournalInternational Journal of Electrical Power & Energy Systems
Early online date21 May 2019
Publication statusPublished - 1 Dec 2019


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