Improved Genetic Algorithm for Phase-Balancing in Three-Phase Distribution Networks: A Master-Slave Optimization Approach
14 May 2021-Vol. 9, Iss: 6, pp 67
TL;DR: Numerical results from a modified version of the IEEE 37-node test feeder demonstrate that it is possible to reduce the annual operative costs of the network by approximately 20% by using optimal load balancing and that the improved version ofThe CBGA is at least three times faster than the classical CBGA.
Abstract: This paper addresses the phase-balancing problem in three-phase power grids with the radial configuration from the perspective of master–slave optimization. The master stage corresponds to an improved version of the Chu and Beasley genetic algorithm, which is based on the multi-point mutation operator and the generation of solutions using a Gaussian normal distribution based on the exploration and exploitation schemes of the vortex search algorithm. The master stage is entrusted with determining the configuration of the phases by using an integer codification. In the slave stage, a power flow for imbalanced distribution grids based on the three-phase version of the successive approximation method was used to determine the costs of daily energy losses. The objective of the optimization model is to minimize the annual operative costs of the network by considering the daily active and reactive power curves. Numerical results from a modified version of the IEEE 37-node test feeder demonstrate that it is possible to reduce the annual operative costs of the network by approximately 20% by using optimal load balancing. In addition, numerical results demonstrated that the improved version of the CBGA is at least three times faster than the classical CBGA, this was obtained in the peak load case for a test feeder composed of 15 nodes; also, the improved version of the CBGA was nineteen times faster than the vortex search algorithm. Other comparisons with the sine–cosine algorithm and the black hole optimizer confirmed the efficiency of the proposed optimization method regarding running time and objective function values.
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TL;DR: The problem of optimal phase-balancing in three-phase asymmetric distribution networks is addressed in this research from the point of view of combinatorial optimization using a master–slave optimization approach using the improved sine cosine algorithm (ISCA).
Abstract: The problem of optimal phase-balancing in three-phase asymmetric distribution networks is addressed in this research from the point of view of combinatorial optimization using a master–slave optimization approach. The master stage employs an improved sine cosine algorithm (ISCA), which is entrusted with determining the load reconfiguration at each node. The slave stage evaluates the energy losses for each set of load connections provided by the master stage by implementing the triangular-based power flow method. The mathematical model that was solved using the ISCA is designed to minimize the annual operating costs of the three-phase network. These costs include the annual costs of the energy losses, considering daily active and reactive power curves, as well as the costs of the working groups tasked with the implementation of the phase-balancing plan at each node. The peak load scenario was evaluated for a 15-bus test system to demonstrate the effectiveness of the proposed ISCA in reducing the power loss (18.66%) compared with optimization methods such as genetic algorithm (18.64%), the classical sine cosine algorithm (18.42%), black-hole optimizer (18.38%), and vortex search algorithm (18.59%). The IEEE 37-bus system was employed to determine the annual total costs of the network before and after implementing the phase-balancing plan provided by the proposed ISCA. The annual operative costs were reduced by about 13% with respect to the benchmark case, with investments between USD 2100 and USD 2200 in phase-balancing activities developed by the working groups. In addition, the positive effects of implementing the phase-balancing plan were evidenced in the voltage performance of the IEEE 37-bus system by improving the voltage regulation with a maximum of 4% in the whole network from an initial regulation of 6.30%. All numerical validations were performed in the MATLAB programming environment.
10 citations
TL;DR: In this article, the problem of optimal load redistribution in electrical three-phase medium-voltage grids is addressed from the point of view of mixed-integer convex optimization, where the objective function is defined as the l1-norm which is a convex function.
Abstract: The problem of the optimal load redistribution in electrical three-phase medium-voltage grids is addressed in this research from the point of view of mixed-integer convex optimization. The mathematical formulation of the load redistribution problem is developed in terminals of the distribution node by accumulating all active and reactive power loads per phase. These loads are used to propose an objective function in terms of minimization of the average unbalanced (asymmetry) grade of the network with respect to the ideal mean consumption per-phase. The objective function is defined as the l1-norm which is a convex function. As the constraints consider the binary nature of the decision variable, each node is conformed by a 3×3 matrix where each row and column have to sum 1, and two equations associated with the load redistribution at each phase for each of the network nodes. Numerical results demonstrate the efficiency of the proposed mixed-integer convex model to equilibrate the power consumption per phase in regards with the ideal value in three different test feeders, which are composed of 4, 15, and 37 buses, respectively.
10 citations
TL;DR: Numerical results on the 8-, 25-, and 37-node test systems show the efficiency of the proposed approach when compared to the classical version of the crow search algorithm, the Chu and Beasley genetic algorithm, and the vortex search algorithm.
Abstract: This paper discusses the power loss minimization problem in asymmetric distribution systems (ADS) based on phase swapping. This problem is presented using a mixed-integer nonlinear programming model, which is resolved by applying a master–slave methodology. The master stage consists of an improved version of the crow search algorithm. This stage is based on the generation of candidate solutions using a normal Gaussian probability distribution. The master stage is responsible for providing the connection settings for the system loads using integer coding. The slave stage uses a power flow for ADSs based on the three-phase version of the iterative sweep method, which is used to determine the network power losses for each load connection supplied by the master stage. Numerical results on the 8-, 25-, and 37-node test systems show the efficiency of the proposed approach when compared to the classical version of the crow search algorithm, the Chu and Beasley genetic algorithm, and the vortex search algorithm. All simulations were obtained using MATLAB and validated in the DigSILENT power system analysis software.
8 citations
TL;DR: The numerical results in three radial test feeders demonstrated the effectiveness of the proposed MIQC model as compared to metaheuristic optimizers such as the genetic algorithm, black hole optimizer, sine–cosine algorithm, and vortex search algorithm.
Abstract: With this study, we address the optimal phase balancing problem in three-phase networks with asymmetric loads in reference to a mixed-integer quadratic convex (MIQC) model. The objective function considers the minimization of the sum of the square currents through the distribution lines multiplied by the average resistance value of the line. As constraints are considered for the active and reactive power redistribution in all the nodes considering a 3×3 binary decision variable having six possible combinations, the branch and nodal current relations are related to an extended upper-triangular matrix. The solution offered by the proposed MIQC model is evaluated using the triangular-based three-phase power flow method in order to determine the final steady state of the network with respect to the number of power loss upon the application of the phase balancing approach. The numerical results in three radial test feeders composed of 8, 15, and 25 nodes demonstrated the effectiveness of the proposed MIQC model as compared to metaheuristic optimizers such as the genetic algorithm, black hole optimizer, sine–cosine algorithm, and vortex search algorithm. All simulations were carried out in MATLAB 2020a using the CVX tool and the Gurobi solver.
7 citations
TL;DR: In this article , the problem of optimal phase swapping in asymmetric distribution grids through the application of hurricane-based optimization algorithm (HOA) is solved by using a master-slave optimization procedure.
Abstract: This article addresses the problem of optimal phase-swapping in asymmetric distribution grids through the application of hurricane-based optimization algorithm (HOA). The exact mixed-integer nonlinear programming (MINLP) model is solved by using a master–slave optimization procedure. The master stage is entrusted with the definition of load connection at each stage by using an integer codification that ensures that, per node, only one from the possible six-load connections is assigned. In the slave stage, the load connection set provided by the master stage is applied with the backward/forward power flow method in its matricial form to determine the amount of grid power losses. The computational performance of the HOA was tested in three literature test feeders composed of 8, 25, and 37 nodes. Numerical results show the effectiveness of the proposed master–slave optimization approach when compared with the classical Chu and Beasley genetic algorithm (CBGA) and the discrete vortex search algorithm (DVSA). The reductions reached with HOA were 24.34%, 4.16%, and 19.25% for the 8-, 28-, and 37-bus systems; this confirms the literature reports in the first two test feeders and improves the best current solution of the IEEE 37-bus grid. All simulations are carried out in the MATLAB programming environment.
3 citations
References
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TL;DR: In this survey, the problem-solving paradigm of ACO is explicated and compared to traditional routing algorithms along the issues of routing information, routing overhead and adaptivity.
Abstract: Although an ant is a simple creature, collectively a colony of ants performs useful tasks such as finding the shortest path to a food source and sharing this information with other ants by depositing pheromone. In the field of ant colony optimization (ACO), models of collective intelligence of ants are transformed into useful optimization techniques that find applications in computer networking. In this survey, the problem-solving paradigm of ACO is explicated and compared to traditional routing algorithms along the issues of routing information, routing overhead and adaptivity. The contributions of this survey include 1) providing a comparison and critique of the state-of-the-art approaches for mitigating stagnation (a major problem in many ACO algorithms), 2) surveying and comparing three major research in applying ACO in routing and load-balancing, and 3) discussing new directions and identifying open problems. The approaches for mitigating stagnation discussed include: evaporation, aging, pheromone smoothing and limiting, privileged pheromone laying and pheromone-heuristic control. The survey on ACO in routing/load-balancing includes comparison and critique of ant-based control and its ramifications, AntNet and its extensions, as well as ASGA and SynthECA. Discussions on new directions include an ongoing work of the authors in applying multiple ant colony optimization in load-balancing.
503 citations
TL;DR: Modified plant growth simulation algorithm has been applied here successfully to minimize real power loss because it does not require barrier factors or cross over rates because the objectives and constraints are dealt separately.
165 citations
TL;DR: In this paper, simulated annealing is used to solve a power distribution phase balancing problem with its nonlinear effects, such as, voltage drops and energy losses, making the problem difficult to solve.
Abstract: Deregulation eliminates the boundary of the territory of the monopoly power industry. Competition forces utilities to improve power quality as well as to reduce investment and operation costs. Feeder imbalance describes a situation in which the voltages of a three-phase voltage source are not identical in magnitude, or the phase differences between them are not 120 electrical degrees, or both. It affects motors and other devices that depend upon a well-balanced three-phase voltage source. Phase balancing is to make the voltages balanced at each load point of the feeder. Phase swapping is a direct approach for phase balancing with the minimum cost. Phase balancing can enhance utilities' competitive capability by improving reliability, quality, and reducing costs. Therefore, phase balancing optimization is nowadays receiving more attention in the power industry, especially in today's deregulating environments. The nonlinear effects, such as, voltage drops and energy losses, make the problem difficult to solve. This paper introduces simulated annealing as an effective method to solve a power distribution phase balancing problem with its nonlinear effects.
112 citations
TL;DR: This study introduces the problem of minimizing average relative percentage of imbalance (ARPI) with sequence-dependent setup times in a parallel-machine environment and a mathematical model that minimizes ARPI is proposed.
74 citations
TL;DR: In this paper, the immune algorithm is proposed to derive the rephasing strategy arrangement of laterals and distribution transformers to enhance three-phase balancing of distribution systems, where the multi-objective function is formulated by considering the unbalance of phasing currents, the customer service interruption cost (CIC) and labour cost to perform the optimal rephases strategy.
Abstract: The immune algorithm (IA) is proposed to derive the rephasing strategy arrangement of laterals and distribution transformers to enhance three-phase balancing of distribution systems. The multi-objective function is formulated by considering the unbalance of phasing currents, the customer service interruption cost (CIC) and labour cost to perform the optimal rephasing strategy. For each feasible rephasing strategy, the number of customers affected with total interruption load demand and outage duration time are used to calculate the impact of system reliability because of rephasing engineering works. To demonstrate the effectiveness of the proposed methodology, a practical distribution feeder in Taipower with 271 customers is selected for computer simulation. By minimising the objective function subjected to the operation constraints, the rephasing strategy has been derived by selecting the laterals and distribution transformers for phasing adjustment. It is found that the neutral current of test feeder has been reduced to be less than the neutral overcurrent limit by executing the rephasing of laterals and distribution transformers.
62 citations