Applied Computational Intelligence and Soft Computing

Volume 2016, Article ID 6928080, 8 pages

http://dx.doi.org/10.1155/2016/6928080

## A Dynamic and Heuristic Phase Balancing Method for LV Feeders

^{1}Department of Engineering, Shahrekord University, Shahrekord 34141-88186, Iran^{2}Department of Electrical and Electronic Engineering, Shiraz University of Technology, Shiraz 71555-313, Iran^{3}Department of Electrical Engineering, Islamic Azad University, Zarghan Branch, Zarghan, Iran

Received 10 November 2015; Revised 31 March 2016; Accepted 13 April 2016

Academic Editor: Christian W. Dawson

Copyright © 2016 Samad Taghipour Boroujeni et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

#### 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.

#### 1. Introduction

Nowadays, fossil fuels, the main source of our world energy, have been diminished day by day. In addition, the environmental pollution and the global warming concerns cause the increase in the importance of energy saving and loss reduction. So a lot of researches have been devoted to enhancing the efficiency of the energy converter machines. The most popular shape of energy, electrical energy, is mainly produced in the power plants, transmitted through the electrical networks, and consumed in the load points. Therefore, the electrical network efficiency has a greater role in the energy saving and loss reduction. Electrical networks include transmission and distribution systems. As the transmission voltage is higher than the distribution voltage, the distribution system losses are greater.

The phase balancing results in benefits such as loss reduction, voltage profile improvement, and system reliability enhancement. At LV feeders, single-phase loads make unbalanced conditions and increase losses in the LV feeders. These loads are distributed along the feeder and have different and stochastic behaviors. All of these aspects of the single-phase loads make distribution phase balancing more difficult and complicated. In fact phase balancing is a dynamic combinatorial problem.

The distribution load balancing has been considered in many researches. These researches can be divided into two main groups. The first group deals with the network reconfiguration through some switches [1–12]. These methods try to distribute the power demanded by one geographical zone among different feeders equally. In the second group, it is desired to distribute the power of one feeder among its different phases, equally. In addition, against profound and strong researches on load balancing [1–12], there are few papers on phase balancing [13–15]. In [13, 14], medium voltage phase balancing is addressed by choosing the best connection for the transformer nodes.

Traditionally, phase balancing is done at periodical intervals, manually, after some field measurements by the utilities [15, 16], which is mentioned here as the Static phase balancing (SPB). Although the SPB is a stable method, due to the stochastic and time-varying characteristics of the single-phase loads, it is not an efficient method in the loss reduction. On the other hand, the dynamic phase balancing (DPB) is a more effective method in the loss reduction. However, the DPB method is an expensive method and enough attention should be paid to its instability [16]. The DPB of the LV feeders is addressed in [15, 16] using a central remote controller and communication system.

DPB can be implemented easily in the distribution network equipped with an automated system [15, 16]. Although advances in power electronic devices, microcontroller processors, and communication systems make it easy to apply automation systems in the distribution networks, in many countries it needs a long time to have such systems, completely.

Since single-phase loads in LV networks are distributed along the feeder, their location is an important and effective parameter on the feeder losses, as well as their amount. In comparison with an unbalanced load in the first sections of LV feeder, the same unbalanced load in the end points of the considered feeder results in more losses. The impact of single-phase load locations is not considered in [15, 16]. In addition, the proposed methods in [15, 16] need an automated system with fuzzy or neural remote controllers, which make DPB system expensive and complicated.

In this research a heuristic and dynamic solution for phase balancing of LV feeders is proposed. In this method, it is supposed that customers’ ties are switchable between different phases through a three-phase switch. The three-phase switches are controlled by some distributed local controllers. These local controllers only need locally measured signals without any information about the other loads and branches which are far from the controller installing point. Therefore, the communication interface can be avoided. The proposed method tries to make the current in each section of the LV feeder as balanced as possible. In the proposed method amount and location of single-phase loads are considered inherently. Although some three-phase switches are used in the proposed method, it is inexpensive, simple, and practical. In some cases it may happen that the benefit of the loss reduction cannot overcome the cost of the installed switches. Therefore, a trade-off between the loss reduction and the number of the used switches should be done. So the Genetic Algorithm is applied to find the optimum number of switches as well as their locations. The proposed method does not need any remote controller and communication interface. So it is a fault tolerant method which provides a distributed and dynamic phase balancing control.

Hereafter phase balancing problem is represented in Section 2. The proposed algorithm is described in Section 3. In addition, the feasibility of reducing the number of the switches is investigated in Section 4. Simulation results are reported in Section 5. These results show the ability and the efficiency of the proposed method in phase balancing of the LV feeders.

#### 2. Problem Definition

For the sake of simplicity, loads are modeled as the constant currents in 4-wire, 3-phase distribution systems. Also KCL law is used to obtain branches current instead of the forward-backward load flow method. These assumptions’ consideration does not have effect on the generality of the phase balancing problem. Total loss of a LV feeder is as follows:where contains phases , , and and the neutral wire, and are the current and the resistance of the phase “” of the branch “,” respectively, and “” is number of the feeder branches.

In the presented paper, the radial LV feeder is studied as a graph. In the graph theory, the nodes are connected via some branches. Some concepts and definitions of the graph theory which are used in this research are as follows.

*(i) Branch*. A line section which connects two nodes together is defined as the branch. A branch contains at least two-wire branch (1-phase and 1-neutral wire).

*(ii) Main Node*. Main node is the nearest node of the LV feeder to the transformer. It is located at the beginning of the feeder. This node connects LV and MV networks together.

*(iii) End Node*. The end nodes are the deepest nodes in the feeder. From these nodes no branch is initiated.

*(iv) Node Path*. In a radial graph each node can be connected to the main node only in one path, called here the node path. The node path is a sequence of branches or nodes, which connect the considered node to the main node.

*(v) Upstream and Downstream Nodes*. Considering two nodes ( and ) of a branch, the node that is nearer to the main node is the upstream node of the other one. Similarly the latter one is the downstream node of the former. In other words, node is upstream to node (or node is downstream to node ), if the path sequence of node is a subset of the path sequence of node . Since the LV feeder graph is considered radial, each node has only one upstream node, except the main node. In addition, except the end nodes that have no downstream node, the other nodes have at least one downstream node.

*(vi) Node Ranking*. The criterion for the ranking is the position of nodes in the node paths. In the other words, the rank of an upstream node is more than the rank of its downstream nodes. In the node ranking, different nodes could have the same rank.

*(vii) Upstream and Downstream Branches*. Each node is connected to other nodes through some branches. For each node, the upstream branch is the branch which connects the considered node to its upstream node (or other nodes with a higher rank). Similarly the downstream branch is defined as the branch which connects the considered node to one of the downstream nodes (or other nodes with lower rank). Since the LV feeder graph is radial, each node has only one upstream branch except the main node that has no upstream branch. In addition, except end nodes that have no downstream branches, other nodes have at least one downstream branch.

*(viii) Subgraph*. A subgraph is a continuous graph whose nodes/branches are subsets of the main graph nodes/branches.

*(ix) An Example*. In order to make the above definitions more clear, an example is presented. Figure 1(a) shows a small radial LV feeder with 12 nodes and 11 branches. Node “” is the main node and nodes are the end nodes. The path of node “” is . The upstream and downstream nodes of node “” are “” and “,” respectively. Branch “” is the upstream branch of node “” and its downstream branches are . The nodes ranking are as follows: , , , , , and . Also the path of node “," shown in Figure 1(b), is a subgraph of the feeder graph of Figure 1(a).