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

Abstract 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.

[1]  K. Vaisakh,et al.  Adaptive PSODV algorithm for OPF with non-smooth cost functions and statistical analysis , 2011, Simul. Model. Pract. Theory.

[2]  Vincent W. S. Wong,et al.  Semidefinite Relaxation of Optimal Power Flow for AC–DC Grids , 2017, IEEE Transactions on Power Systems.

[3]  Javier Contreras,et al.  Carbon footprint allocation among consumers and transmission losses , 2017, 2017 IEEE International Conference on Environment and Electrical Engineering and 2017 IEEE Industrial and Commercial Power Systems Europe (EEEIC / I&CPS Europe).

[4]  Serhat Duman,et al.  Optimal power flow using gravitational search algorithm , 2012 .

[5]  Brian W. Kernighan,et al.  AMPL: A Modeling Language for Mathematical Programming , 1993 .

[6]  Bohn Stafleu van Loghum,et al.  Online … , 2002, LOG IN.

[7]  S. Surender Reddy,et al.  Efficiency Improvements in Meta-Heuristic Algorithms to Solve the Optimal Power Flow Problem , 2016 .

[8]  K. Vaisakh,et al.  Genetic evolving ant direction HDE for OPF with non-smooth cost functions and statistical analysis , 2011, Expert Syst. Appl..

[9]  Vincent W. S. Wong,et al.  Security-Constrained Unit Commitment for AC-DC Grids With Generation and Load Uncertainty , 2018, IEEE Transactions on Power Systems.

[10]  Taher Niknam,et al.  Reserve constrained dynamic optimal power flow subject to valve-point effects, prohibited zones and multi-fuel constraints , 2012 .

[11]  M. A. Abido,et al.  Optimal power flow using Teaching-Learning-Based Optimization technique , 2014 .

[12]  Taher Niknam,et al.  A new hybrid algorithm for optimal power flow considering prohibited zones and valve point effect , 2012 .

[13]  P. R. Bijwe,et al.  Efficiency improvements in meta-heuristic algorithms to solve the optimal power flow problem , 2016 .

[14]  G. L. Decker,et al.  Valve point loading of turbines , 1958, Electrical Engineering.

[15]  Sahand Ghavidel,et al.  A novel hybrid algorithm of imperialist competitive algorithm and teaching learning algorithm for optimal power flow problem with non-smooth cost functions , 2014, Eng. Appl. Artif. Intell..

[16]  Thang Trung Nguyen,et al.  A high performance social spider optimization algorithm for optimal power flow solution with single objective optimization , 2019, Energy.

[17]  Jorge Nocedal,et al.  Knitro: An Integrated Package for Nonlinear Optimization , 2006 .

[18]  Mahdi Pourakbari-Kasmaei,et al.  An effortless hybrid method to solve economic load dispatch problem in power systems , 2011 .

[19]  Ranjit Roy,et al.  Optimal power flow solution of power system incorporating stochastic wind power using Gbest guided artificial bee colony algorithm , 2015 .

[20]  M. Hadi Amini,et al.  Decomposition Methods for Distributed Optimal Power Flow: Panorama and Case Studies of the DC Model , 2018 .

[21]  Samir Sayah,et al.  Modified differential evolution algorithm for optimal power flow with non-smooth cost functions , 2008 .

[22]  Hany M. Hasanien,et al.  Optimal power flow solution in power systems using a novel Sine-Cosine algorithm , 2018, International Journal of Electrical Power & Energy Systems.

[23]  Javier Contreras,et al.  A demand power factor-based approach for finding the maximum loading point , 2017 .

[24]  M. Narimani,et al.  A novel approach to multi-objective optimal power flow by a new hybrid optimization algorithm considering generator constraints and multi-fuel type , 2013 .

[25]  S. Surender Reddy,et al.  Multi-Objective Optimal Power Flow Using Efficient Evolutionary Algorithm , 2017 .

[26]  Ruey-Hsun Liang,et al.  Multi-objective dynamic optimal power flow using improved artificial bee colony algorithm based on Pareto optimization: Multi-objective Dynamic Optimal Power Flow , 2016 .

[27]  Lei Ding,et al.  Double weighted particle swarm optimization to non-convex wind penetrated emission/economic dispatch and multiple fuel option systems , 2018 .

[28]  Mahdi Pourakbari-Kasmaei,et al.  An unequivocal normalization-based paradigm to solve dynamic economic and emission active-reactive OPF (optimal power flow) , 2014 .

[29]  Nima Amjady,et al.  Security constrained optimal power flow considering detailed generator model by a new robust differe , 2011 .

[30]  Mahdi Pourakbari-Kasmaei,et al.  Logically constrained optimal power flow: Solver-based mixed-integer nonlinear programming model , 2018 .

[31]  P. R. Bijwe,et al.  Efficiency improvements in metaheuristic algorithms to solve the optimal power flow problem , 2016 .

[32]  Al-Attar Ali Mohamed,et al.  Optimal power flow using moth swarm algorithm , 2017 .

[33]  H. R. E. H. Bouchekara,et al.  Optimal power flow with emission and non-smooth cost functions using backtracking search optimization algorithm , 2016 .

[34]  Mahdi Pourakbari-Kasmaei,et al.  Multi-area environmentally constrained active–reactive optimal power flow: a short-term tie line planning study , 2016 .