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

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.

Due to the increase of intermittent renewable energy sources, it is becoming more important to consider renewable generation forecast error when solving the optimal power flow (OPF) problem. The stochastic OPF, which uses multiple forecast scenarios, generally leads to a lower cost compared to the standard deterministic OPF, which uses a single forecast. However, the stochastic OPF is computationally more demanding than the deterministic OPF. Both cost savings and computation times further increase when storage units or ramp-constrained generators are included, as they require solving a multi-period OPF problem. Our contribution is a hybrid method approaching the cost performance of the stochastic OPF while maintaining a computational burden close to the deterministic OPF. The method combines elements from both the stochastic and the deterministic OPF, and relies on Benders Cuts to interface them. Using a receding horizon approach over one year, we find that, based on eleven test cases, one version of our hybrid method leads to at least 70% of the cost improvement of the stochastic OPF, while the computation time increase is at most 40% of the stochastic OPF time increase. Furthermore, the computational advantage of our method increases with the system size. Two different versions of the method allow favoring of either the computational improvement or the cost improvement. We also identify directions for further improvement. Finally, our method can be used for more general problems in which one wishes to combine two models with different levels of complexity.

Since conventional optimal power flow (OPF) algorithms are limited and too slow for operational planning, power system operation and planning engineers have been seeking efficient OPF algorithms for three decades. The interior point method is one of the most efficient algorithms. In this paper, an improved quadratic interior point (IQIP) method is used to solve comprehensive OPF problems with a variety of objective functions, including economic dispatch, VAr planning and loss minimization. The IQIP method features a general starting point (rather than selected good point as in the general interior point method) and fast convergence. Consequently, the OPF package described in this paper offers huge improvements in speed, accuracy and convergence in solving multi-objective and multi-constraint optimization problems. It will be a very useful tool for the power industry.

In recent decades, the energy market around the world has been reshaped to accommodate the high penetration of renewable energy resources. Although renewable energy sources have brought various benefits, including low operation cost of wind and solar PV power plants, and reducing the environmental risks associated with the conventional power resources, they have imposed a wide range of difficulties in power system planning and operation. Naturally, classical optimal power flow (OPF) is a nonlinear problem. Integrating renewable energy resources with conventional thermal power generators escalates the difficulty of the OPF problem due to the uncertain and intermittent nature of these resources. To address the complexity associated with the process of the integration of renewable energy resources into the classical electric power systems, two probability distribution functions (Weibull and lognormal) are used to forecast the voltaic power output of wind and solar photovoltaic, respectively. Optimal power flow, including renewable energy, is formulated as a single-objective and multi-objective problem in which many objective functions are considered, such as minimizing the fuel cost, emission, real power loss, and voltage deviation. Real power generation, bus voltage, load tap changers ratios, and shunt compensators values are optimized under various power systems’ constraints. This paper aims to solve the OPF problem and examines the effect of renewable energy resources on the above-mentioned objective functions. A combined model of wind integrated IEEE 30-bus system, solar PV integrated IEEE 30-bus system, and hybrid wind and solar PV integrated IEEE 30-bus system is performed using the equilibrium optimizer technique (EO) and other five heuristic search methods. A comparison of simulation and statistical results of EO with other optimization techniques showed that EO is more effective and superior and provides the lowest optimization value in term of electric power generation, real power loss, emission index and voltage deviation.

The aim of the research work is to propose an integrated optimization technique, established with the integration of the invasive weed optimization (IWO) and Powell’s pattern search (PPS) method. The IWO algorithm has been undertaken as a global search technique, which is inspired from the specific ecological behavior of weeds and has the ability to adapt to the changing environment. The local search PPS method is based upon a conjugate-based search and having excellent exploitation search capability, which helps to improve the solution obtained from IWO technique. The proposed technique is applied to solve optimal power flow (OPF) problem with the flexible AC transmission system devices. The OPF problem is a nonlinear, non-convex optimization problem and consists of continuous and discrete decision variables. The three objective functions comprise total fuel cost, pollutant emission and system transmission loss which are minimized sequentially. The proposed technique is tested on four standard IEEE test systems, and results are compared with the reported results in the literature and found promising. The results illustrate that the proposed technique performs better as compared to IWO technique in terms of the quality of solution and convergence characteristics. Further, t test is performed to validate the statistical performance of the proposed integrated optimization technique.

A new hybrid decomposition-based multiobjective evolutionary algorithm is proposed for optimal power flow (OPF) including wind and solar generation uncertainty. This study recommends a novel constraint-handling method, which adaptively adds the penalty function and eliminates the parameter dependency on penalty function evaluation. The summation-based sorting and improved diversified selection methods are utilized to enhance the diversity of multiobjective optimization algorithms. The OPF problem is modeled as a multiobjective optimization problem with four objectives such as minimizing (i) total fuel cost (TC) including the cost of renewable energy source (RES), (ii) total emission (TE), (iii) active power loss (APL), and (iv) voltage magnitude deviation (VMD). The impact of RESs such as wind and solar energy sources on integration is considered in optimal power flow cost analysis. The costs of RESs are considered in the OPF problem to minimize the overall cost so that the impact of intermittence and uncertainty of renewable sources is studied in terms of cost and operation wise. The uncertainty of wind and solar energy sources is described using probability distribution functions (PDFs) such as Weibull and lognormal distributions. The efficiency of the algorithm is tested on IEEE 30-, IEEE 57-, and IEEE 118-bus systems for all possible conditions of renewable sources using Monte Carlo simulations.

In an effort to quantify and manage uncertainties inside power systems with penetration of renewable energy, uncertainty costs have been defined and different uncertainty cost functions have been calculated for different types of generators and electric vehicles. This article seeks to use the uncertainty cost formulation to propose algorithms and solve the problem of optimal power flow extended to controllable renewable systems and controllable loads. In a previous study, the first and second derivatives of the uncertainty cost functions were calculated and now an analytical and heuristic algorithm of optimal power flow are used. To corroborate the analytical solution, the optimal power flow was solved by means of metaheuristic algorithms. Finally, it was found that analytical algorithms have a much higher performance than metaheuristic methods, especially as the number of decision variables in an optimization problem grows.

Here, a new approach is proposed for solving the optimal power flow (OPF) problem in transmission networks using a Gradient Bald Eagle Search Algorithm (GBES) with a Local Escaping Operator (LEO). The method takes into account uncertainty of the renewable energy sources (wind energy and photovoltaic systems) and Vehicle‐to‐Grid (V2G) in the stochastic OPF problem. To improve the efficiency of the proposed technique and enhance its local exploitation capability, the LEO method's selection features are utilized. Monte Carlo methods are employed to estimate the generation costs of the renewable sources and PEVs and study their feasibility. The uncertainty of the renewable sources and PEVs is represented by Weibull, lognormal, and normal probability distribution functions (PDFs). The GBES approach is experimentally compared with well‐known meta‐heuristics using twenty‐three different test functions, and the results indicate its superiority over BES and other recently developed algorithms. Furthermore, the proposed method's effectiveness is evaluated using IEEE 30‐bus test system under various scenarios, and the simulation results demonstrate that it can effectively address OPF issues considering renewable energy sources and V2G, providing superior optimal solutions compared to other algorithms.

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.

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.

Modified JAYA algorithm for optimal power flow incorporating renewable energy sources considering the cost, emission, power loss and voltage profile improvement

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.

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, 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.