Optimal power flow solution including the syncronous generator capability curve constraints with a convex relaxation method

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.

A method for quickly bounding the optimal objective value of an OPF problem using a semidefinite relaxation and a local solution

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.

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.

This paper proposes a convex optimization based distributed algorithm to solve the multi-period optimal gas- power flow (OGPF) problem in coupled energy distribution systems. At the gas distribution system side, the non- convex Weymouth gas flow equations are convexified as quadratic constraints. Then the optimal gas flow (OGF) subproblem is solved by an iterative second-order cone programming (SOCP) procedure, whose efficiency is two orders of magnitudes higher than traditional nonlinear methods. A convex quadratic program based initiation scheme is suggested, which helps to find a high-quality starting point. At the power distribution system side, convex relaxation is performed on the non-convex branch flow equations, and the optimal power flow (OPF) subproblem gives rise to an SOCP. Tightness is guaranteed by the radial topology. In the proposed distributed algorithm, the OGF problem and the OPF problem are solved independently, and coordinated by the alternating direction multiplier method (ADMM). Numerical results corroborate significant enhancements on computational robustness and efficiency compared with existing OGPF calculation methods.

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.

Although a significant amount of research has been directed to developing necessary and sufficient conditions for the optimal solutions of several engineering problems, there is little work on the development of a necessary and sufficient condition for optimal power flow (OPF) solutions. This paper seeks to develop the following: (1) a necessary and sufficient condition for a local OPF solution, and (2) a necessary and sufficient condition for an OPF Karush-Kuhn-Tucker (KKT) solution. The derived necessary and sufficient conditions were numerically verified on IEEE 30-, 57- and 118-bus systems. Computationally, the derived necessary and sufficient condition is also useful in assisting existing OPF methods to obtain OPF solutions instead of KKT solutions (i.e., KKT saddle points).

This study proposes an improved particle swarm optimization method to find optimal power flow by using the power transmission loss as an objective function. In the literature, PSO is a well — known intelligent search method to handle the solution of optimal power flow problem. A novel scheme which is called Improved PSO (IPSO) is defined by modifying the initialization step of PSO algorithm and choosing the load bus voltages, generator active and reactive powers, line flow capacities as penalty functions in the objective function. PSO and IPSO-based optimal power flow solutions are compared with each other on IEEE 118 and 300 bus systems. According to the test results, the power loss obtained by IPSO-based solution has less power loss than PSO-based solution. This proposed method can be used to obtain faster desirable solutions and better power loss results for the optimal power flow problem in case of power loss minimization.

Enhanced Genetic Algorithm based computation technique for multi-objective Optimal Power Flow solution

The optimal power flow (OPF) problem is one of the most popular and important issues that researchers need to solve in power systems. In this study, a modified weighted teaching-learning-based optimization (WTLBO) algorithm was designed and implemented for the OPF problem, regarding the teaching-learning-based optimization (TLBO) algorithm, which is one of the meta-heuristic algorithms. To demonstrate the effectiveness of TLBO and developed WTLBO algorithms in OPF solutions, six different single/multi-objective functions consisting of targets, such as fuel cost, total active power losses, and voltage deviation were tested on standard IEEE 30 and 57 bus systems. Multi-objective functions were transformed into a single objective function using the weighted sum method. Analysis results were compared with different optimization algorithms used in the literature. When the developed WTLBO algorithm is compared according to the single/multi-objective functions in OPF solutions, it has been proven that it performs better than the original TLBO algorithm and other algorithms in the literature. As a result of the analysis, according to the TLBO algorithm, in the IEEE 30 bus power system, in the proposed WTLBO algorithm, a decrease of 0.05% in the total fuel cost, 2.20% in active power losses, and 13.37% in voltage deviation are observed.

Optimal power flow using gravitational search algorithm

This paper presents the semismooth Newton-type algorithms for solving optimal power flow (OPF) problems. Considering that there exist plentiful bounded constraints in OPF, the paper treats general inequality constraints and bounded constraints separately. By introducing a diagonal matrix and the nonlinear complementarity function, the Karush-Kuhn-Tucker (KKT) system of the OPF is transformed equivalently to a system of nonsmooth bounded constrained equations. Comparing with the classical OPF methods and the nonlinear complementarity problem (NCP) method, this treatment has two remarkable advantages. First, it has a strong ability to handle the inequality constraints in OPF problems. Second, it reduces the number of dual variables in the KKT system. Based on the reformulated equations, the paper designs a projected semismooth Newton algorithm which has nice global and local convergence property. Furthermore, according to the weak-coupling property in power systems, the paper presents a decoupled semismooth Newton-type algorithm. The decoupled method solves the system of equations via solving two lower dimension problems. Therefore the method saves the computing cost in theory. Some standard IEEE systems are used to test the two algorithms, and numerical results show that the proposed algorithms are promising for solving OPF problems

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.

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.

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.