A Dynamic and Heuristic Phase Balancing Method for LV Feeders

Abstract

Due to the single-phase loads and their stochastic behavior, the current in the distribution feeders is not balanced. In addition, the single-phase loads are located in different positions along the LV feeders. So the amount of the unbalanced load and its location affect the feeder losses. An unbalanced load causes the feeder losses and the voltage drop. Because of time-varying behavior of the single-phase loads, phase balancing is a dynamic and combinatorial problem. In this research, a heuristic and dynamic solution for the phase balancing of the LV feeders is proposed. In this method, it is supposed that the loads’ tie could be connected to all phases through a three-phase switch. The aim of the proposed method is to make the feeder conditions as balanced as possible. The amount and the location of single-phase loads are considered in the proposed phase balancing method. Since the proposed method needs no communication interface or no remote controller, it is inexpensive, simple, practical, and robust. Applying this method provides a distributed and dynamic phase balancing control. In addition, the feasibility of reducing the used switches is investigated. The ability of the proposed method in the phase balancing of the LV feeders is approved by carrying out some simulations.

Improved Genetic Algorithm for Phase-Balancing in Three-Phase Distribution Networks: A Master-Slave Optimization Approach

“…Remark 3. Note that expression (12) presents the connection of the master and slave stages because the slave stage is necessary to determine the objective function value of each phase configuration for the loads provided by the proposed improved CBGA.…”

“…The remaining steps involve the evaluation of the objective function (12) to select which among the individuals y s i and y s j has the opportunity to replace the current population, considering the case where the objective function is better than the worst individual in the population and is different from all the other ones (diversity criteria).…”

“…As indicated by existing literature, the problem of phase balancing has been solved using multiple optimization approaches, including the classical Chu and Beasley genetic algorithms [12][13][14][15]; tabu search algorithm [16,17]; ant colony optimization [18,19]; immune optimization algorithm [20]; branch and bound and convex methods [4,21]; bat optimization algorithm [22]; vortex search algorithm [2]; particle swarm optimization methods [8,23,24]; differential evolution algorithm [25]; and simulated annealing optimization method [26]. The main characteristics of these approaches are the hybridization of metaheuristic discrete optimization methods (with binary and integer codifications) with three-phase power flow methods, which are typically based on sweep iterative backward/forward power flow methods, and the minimization of the amount of power loss for a particular load condition, which typically corresponds to the peak load condition.…”

“…Improved CBGA for solving the phase-balancing problem in threephase unbalanced distribution networks.Data: Define the three-phase grid under study. Define the maximum number of iterations s max ; Make s = 1; Define the size of the initial population p s ; Generate the initial population X s fulfilling the diversity criteria; for i ≤ p s do Select the individual x s i of the population; Evaluate it using the three-phase successive approximation power flow method in Algorithm 1; Determine its objective function value using(12), i.e., f 1 x s i Order the population in the ascending form of the objective function value; Select the worst individual of the population, i.e., x s worst ; for s ≤ s max do Generate the mutation probability ρ between 0 and 1; if ρ ≤ 1 2 then Select two individuals randomly from the initial population, i.e., x s i and x s j ; Apply the recombination criteria; Apply the multi-point mutation criteria to generate the offspring y s i and y s j ; Evaluate the objective function values f 1 y s i and f 1 y s j ; if f 1 y s i ≤ f 1 y s j then Assign as the winner the individual y s i ; if f 1 y s i ≤ f 1 (x s worst ) then Verify the diversity criteria and include the winner individual y i in the current population by replacing x s worst by y s i ; Order the population in the ascending form of the objective function value; else Assign as the winner the individual y s j ; if f 1 y s j ≤ f 1 (x s worst ) then Verify the diversity criteria and include the winner individual y j in the current population by replacing x s worst by y s j ; Order the population in the ascending form of the objective function value; else Select an arbitrary individual x s i from the population and make µ s = x s i ; Define the current radius of the hyper-ellipse r s ; Define the number of individuals that will generate 20% of the population size p s ; Create the neighborhood C s i (y) using (14); Revise the upper and lower bounds for each individual i in C s i (y) using (17); Evaluate the objective function for each individual i in C s i (y) using Algorithm 1; Define the winning individual in C s i (y) as the individual with the lower objective function value and term it as C s best ; if C s best ≤ f 1 (x s worst ) then Verify the diversity criteria and include the winning individual C s best in the current population by replacing x s worst with C s best ; Order the population in the ascending form of the objective function value;…”

An Improved Crow Search Algorithm Applied to the Phase Swapping Problem in Asymmetric Distribution Systems

“…In the specialized literature, the balance phase problem, with the minimizing power losses approach, has been solved using different optimization methods, including the Chu and Beasley genetic algorithms [8,16,[21][22][23][24], particle swarm optimization [9], mixedinteger convex optimization [25], bat optimization algorithm [26], differential evolution algorithm [27], simulated annealing optimizer [28], and vortex search algorithm [15], among others.…”