An improved particle swarm optimization method to optimal reactive power flow problems

Summary This paper presents a creature-inspired stud krill herd (SKH) algorithm consisting of stud selection and crossover operators, which are augmented in the krill herd algorithm to solve the optimal power flow (OPF) problems in a power system. Due to the nonlinear and nonconvex nature of the OPF problem, it is quite difficult to find optimal solution using conventional optimization algorithms. Here in SKH, a stud-selection operator is introduced in the krill herd algorithm to further enhance the quality of the solution, and crossover operator is embedded to avoid premature convergence. To investigate the performance, the proposed SKH algorithm has been demonstrated on the OPF problems of IEEE 30-bus, Algerian 59-bus, and IEEE 118-bus systems considering various objective functions such as total production cost, L-index, power loss, and emission pollution to be minimized. The OPF results have been compared with those obtained with other methods, and it has been found that SKH algorithm is successful in providing better quality solutions in reasonable execution times.

The optimal power flow (OPF) problem is a well-known non-convex optimization problem that aims to minimize the cost of electric power generation subject to consumer demand, the physics of power flow, and technological constraints. To find an optimal solution to this problem, local search techniques such as interior point methods are typically used. However, due to the non-convex nature of the problem, these methods are likely to result in a sub-optimal solution. The goal of this paper is to characterize the worst-case performance of local search on the OPF problem. To accomplish this, we formulate the OPF problem as a canonical quadratically-constrained quadratic program (QCQP). Then, we study the problem of finding the worst-case local minimum of this QCQP, which is non-convex and hard to solve in general. We find a relaxation of this problem into a semidefinite program (SDP) and show that it is exact for certain cases. Using some test cases which are known to have multiple local minima, we demonstrate the effectiveness of the proposed relaxation to bound the worst-case local minimum. We compare the obtained upper bound on local minima to the lower bound provided by the standard SDP relaxation of the OPF problem to understand how much SDP outperforms local search for a given problem.

The optimal power flow (OPF) problem minimizes the operating cost of an electric power system. Applications of convex relaxation techniques to the non-convex OPF problem have been of recent interest, including work using the Lasserre hierarchy of "moment" relaxations to globally solve many OPF problems. By preprocessing the network model to eliminate low-impedance lines, this paper demonstrates the capability of the moment relaxations to globally solve large OPF problems that minimize active power losses for portions of several European power systems. Large problems with more general objective functions have thus far been computationally intractable for current formulations of the moment relaxations. To overcome this limitation, this paper proposes the combination of an objective function penalization with the moment relaxations. This combination yields feasible points with objective function values that are close to the global optimum of several large OPF problems. Compared to an existing penalization method, the combination of penalization and the moment relaxations eliminates the need to specify one of the penalty parameters and solves a broader class of problems.

Recent years have witnessed the success of employing convex relaxations of the AC optimal power flow (OPF) problem to find global or near-global optimal solutions. The majority of the effort has focused on solving problem formulations where variables live in continuous spaces. Our focus here is in the extension of these results to the co-optimization of network topology and the OPF problem. We employ binary variables to model topology reconfiguration in the standard semidefinite programming (SDP) formulation of the OPF problem. This makes the problem non-convex, not only because the variables are binary, but also because of the presence of bilinear products between the binary and other continuous variables. Our proposed convex relaxation to this problem incorporates the bilinear terms in a novel way that improves over the commonly used McCormick approximation. We also address the exponential complexity associated with the discrete variables by partitioning the network graph in a way that minimizes the impact on the optimal value of the relaxation. As a result, the problem is broken down into several parallel mixed-integer problems, reducing the overall computational complexity. Simulations in the IEEE 118-bus test case demonstrate that our approach converges to solutions which are very close to the lower bound of the mixed-integer OPF problem.

For operating electrical power networks, the Optimal Power Flow (OPF) problem plays a central role. The problem is nonconvex and NP hard. Therefore, designing efficient solution algorithms is crucial, though their global optimality is not guaranteed. Existing semi-definite programming relaxation based approaches are restricted to OPF problems for which zero duality holds, whereas for non-convex problems there is a lack of solution methods of provable performance. In this paper, an efficient novel method to address the general nonconvex OPF problem is investigated. The proposed method is based on alternating direction method of multipliers combined with sequential convex approximations. The global OPF problem is decomposed into smaller problems associated to each bus of the network, the solutions of which are coordinated via a light communication protocol. Therefore, the proposed method is highly scalable. The convergence properties of the proposed algorithm are mathematically and numerically substantiated.

In this paper, a new method to incorporating FACTS devices in optimal power flow (OPF) problem is presented. This method can provide an enhanced economic solution with the use of controllable FACTS devices. Two types of FACTS devices, thyristor controlled series compensators (TCSC) and thyristor controlled phase shifters (TCPS), are considered in this method. The specified power flow control constraints due to the use of FACTS devices are included in the OPF problem. The proposed method decomposes the solution of such modified OPF problem into two subproblems' iteration. The first subproblem is a power flow control problem and the second subproblem is a conventional OPF problem. The two subproblems are solved iteratively until convergence. Case studies are presented to show the effectiveness of the proposed method.

In this paper, we consider the Optimal Power Flow (OPF) problem which consists in determining the power production at each bus of an electric network by minimizing the production cost. Our contribution is an exact solution algorithm for the OPF problem. It consists in a spatial branch-and-bound algorithm based on a compact quadratically-constrained convex relaxation. It is computed by solving the semidefinite rank relaxation of OPF once at the root node of the algorithm. An important result is that the optimal value of our compact relaxation is equal to the rank relaxation value. Then, at every sub-nodes of our branch-and-bound, the lower bound is obtained by solving a quadratic convex problem instead of an SDP. Another contribution is that we add only O(n+m) variables that model the squares of the initial variables, where n is the number of buses in the power system and m the number of transmission lines, to construct our relaxation. Then, since the relations between the initial and auxiliary variables are non-convex, we relax them to get a quadratic convex relaxation. Finally, in our branch-and-bound algorithm, we only have to force a reduced number of equalities to prove global optimality. This quadratic convex relaxation approach is here tailored to the OPF problem, but it can address any application whose formulation is a quadratic optimization problem subject to quadratic equalities and ring constraints. Our first experiments on instances of the OPF problem show that our new algorithm Compact OPF (COPF) is more efficient than the standard solvers and other quadratic convex relaxation based methods we compare it with.

In this paper, we propose a predictor–corrector primal–dual approach for the doubly modified logarithmic barrier function ($$\hbox {M}^{2}\hbox {BF}$$) method in order to solve Optimal Reactive Power Flow (ORPF) problems. The $$\hbox {M}^{2}\hbox {BF}$$ is a modification of the Polyak’s modified logarithmic barrier function (MBF) and is also a particular element of a recent family of nonquadratic penalty functions for augmented Lagrangian methods for handling convex problems only with inequality constraints. We also propose a global convergence strategy to be inserted in the proposed algorithm, which is developed over weak assumptions concerning the primal Hessian matrix. The resulting predictor–corrector primal–dual $$\hbox {M}^{2}\hbox {BF}$$ approach is applied for solving ORPF problems involving power systems with 57, 89, 118, 200, 300, 1354, 2007 and 2869 buses. A comparison with two state-of-the-art methods is performed. Numerical results show that the proposed approach is competitive and capable of solving ORPF problems for small to large-scale power systems.

The AC optimal power flow (OPF) problem is essential for the schedule and operation of power systems. Convex relaxation methods have been studied and used extensively to obtain an optimal solution to the OPF problem. When the exactness of convex relaxations is not guaranteed, it is important to recover a feasible solution for the convex relaxation methods. This paper presents an alternative convex optimisation (ACP) approach that can efficiently recover a feasible solution from the result of second‐order cone programming (SOCP) relaxed OPF in mesh networks. The OPF problem is first formulated as a difference‐of‐convex programming (DCP) problem, then efficiently solved by a penalty convex concave procedure (CCP). By using the solution of a tightened SOCP OPF as an initial point, the proposed algorithm is able to find a global or near‐global optimal solution to the AC OPF problem. Numerical tests show that the proposed method outperforms those semi‐definite programming (SDP) and quadratically constrained quadratic programming (QCQP)–based algorithms.

This paper investigates potential of modified differential evolution (MDE) algorithm, to find solution for optimal power flow (OPF) problem of power system. The performance of the proposed MDE algorithm is experienced on the modified IEEE-30 bus test systems integrating flexible ac transmission systems (FACTS) devices, that is, thyristor controlled phase shifter (TCPS) and thyristor controlled series capacitor (TCSC) at preset locations. The OPF problem of the present work is formulated with five different objective functions viz. (a) fuel cost (with valve point effect) minimization, (b) power transmission losses minimization, (c) emission reduction (d) fuel cost (without valve point effect) minimization and (e) minimization of combined economic and environmental cost. The proposed implementation exploits MDE, resulting in a much shorter execution time while retaining the best possible solution of OPF problem.

A new hybrid evolutionary algorithm for multi-objective optimal power flow in an integrated WE, PV, and PEV power system

This paper presents a study based on versatile bio-inspired metaheuristic stud krill herd (SKH) algorithm to tackle the optimal power flow (OPF) problems in a power system network. SKH consists of stud selection and crossover operator that is incorporated into the original krill herd algorithm to improve the quality of the solution and especially to avoid being trapped in local optima. In order to investigate the performance, the proposed algorithm is demonstrated on the optimal power flow problems of IEEE 14-bus, IEEE 30-bus and IEEE 57-bus systems. The different objective functions considered are minimization of total production cost with and without valve point loading effect, minimization of active power loss, minimization of L-index and minimization of emission pollution. The OPF results obtained with the proposed approach are compared with the other evolutionary algorithms recently reported in the literature.

Optimal reactive power flow using multi-objective mathematical programming

This paper presents a multiobjective optimization methodology to find the optimal location for an optimal unified power flow controller (OUPFC) device. Moreover, the installation cost function of the OUPFC device is developed. The objective functions are the total fuel cost, power losses, and system loadability with and without the minimum cost of the OUPFC installation. The \varepsilon-constraint approach is implemented for the multiobjective mathematical programming formulation. The proposed algorithm is implemented in the IEEE 30- and 118-bus test systems. The solution procedure uses nonlinear programming to optimally locate the OUPFC incorporated in an optimal power flow problem considering these objective functions and improves the operation of the power system. The optimization problem is modeled in the general algebraic modeling system software using a MINOS solver. Furthermore, the results obtained by the OUPFC are compared to those of the phase shifting transformer (PST) and unified power flow controller (UPFC) devices. The performance and applicability of the OUPFC is highlighted compared to the PST and UPFC from an analytical and technical point of view.

With transportation electrification, the power systems and traffic systems are more and more interdependent on each other. To analysis this interdependence more concisely, an optimal traffic power flow problem is formulated with the help of alternating current (AC) optimal power flow and vehicle routing problem (VPR). These two problems are integrated into an unified time-space network (TSN), as a mixed integer programming problem. To solve the meso-scale level problems with multiple oriented destination pairs, the random permuted alternating direction method of multipliers is adopted to solve the formulated problem distributed. The case study is performed on the modified IEEE-30 and Sioux fall networks, and the results verify the effectiveness of the proposed scheme.