Mathematical Problems in Engineering

Volume 2016, Article ID 9404951, 10 pages

http://dx.doi.org/10.1155/2016/9404951

## Integrated Power Flow and Short Circuit Calculation Method for Distribution Network with Inverter Based Distributed Generation

^{1}School of Automation and Information Engineering, Xi’an University of Technology, Xi’an, Shaanxi 710048, China^{2}Xi’an Hailian Petrochemical Technologies Co., Ltd., Xi’an, Shaanxi 710065, China

Received 27 January 2016; Revised 27 May 2016; Accepted 30 May 2016

Academic Editor: Yan-Wu Wang

Copyright © 2016 Shan Yang and Xiangqian Tong. 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

Power flow calculation and short circuit calculation are the basis of theoretical research for distribution network with inverter based distributed generation. The similarity of equivalent model for inverter based distributed generation during normal and fault conditions of distribution network and the differences between power flow and short circuit calculation are analyzed in this paper. Then an integrated power flow and short circuit calculation method for distribution network with inverter based distributed generation is proposed. The proposed method let the inverter based distributed generation be equivalent to bus, which makes it suitable to calculate the power flow of distribution network with a current limited inverter based distributed generation. And the low voltage ride through capability of inverter based distributed generation can be considered as well in this paper. Finally, some tests of power flow and short circuit current calculation are performed on a 33-bus distribution network. The calculated results from the proposed method in this paper are contrasted with those by the traditional method and the simulation method, whose results have verified the effectiveness of the integrated method suggested in this paper.

#### 1. Introduction

The reserved finiteness and destruction of environment by fossil energy have made the application of distributed generation (DG) widespread gradually [1]. The grid-connected DG in distribution network can reduce the loss of fossil energy and network lines and improve the utilization of energy and the reliability of customers. However, DG also brings some unfavorable effects at the same time. For example, in normal operation condition of distribution network, the electrical states of distribution network will be changed due to the random power output from DG. And the changed installed position and installed capacity of DG may bring some unfavorable effects on voltage and loss. In fault operation condition of distribution network, the magnitude and direction of short circuit current flowing through the line could be changed too, and the misoperation and failure action of traditional 3-sectional current protection could happen [2, 3]. Power flow and short circuit calculation are the basis of analyzing the normal and fault conditions of distribution network, respectively. Therefore, it is important to study the power flow and short circuit calculation for research of distribution network with DG.

The DGs in distribution network are mainly divided into generator based DG and inverter based DG, of which the inverter based DG is applied in distribution network widely, such as photovoltaic (PV), permanent magnet synchronous generator (PMSG), and energy storage system (ESS). Therefore, it is significant to study the power flow and short circuit calculation methods for distribution network with inverter based DGs. As the research focus in this paper, the DG mentioned below without additional instruction referred to is expressed as inverter based DG.

Both in power flow and in short circuit calculation, the research at present mainly consists of building equivalent model of inverter based DG and putting forward corresponding calculation method. Being unlike generator based DG, the output characteristic of inverter based DG is mainly dominated by its control unit. In power flow calculation, the equivalent models of DGs under different control are different. In constant power control, the DG should be equivalent to bus while in constant voltage control, the DG should be equivalent to PV bus if the reactive power output from DG is within limit. If the reactive power output from DG is beyond the limit, the DG should be equivalent to bus [4, 5]. Therefore, the equivalent model of inverter based DG is mainly modeled as bus or PV bus. And for calculation method, back/forward sweep method and Newton method are generally used the same as traditional power flow calculation [6–8].

In short circuit calculation, the present fault equivalent models of inverter based DG have had the following three forms. At the assumption of constant active and reactive power output from DG during a fault, DG should be equivalent to constant power model [9]. According to the current limiting characteristic of inverter, DG should enter current limiting status during a fault. As a result, DG can be equivalent to constant current source approximately [10, 11]. The fault equivalent model of inverter based DG is decided by judging the current limiting status of DG. The DG entering the current limiting status is equivalent to constant current model. Conversely, the DG is equivalent to constant power model [12, 13]. As far as short circuit calculation method is concerned, the superposition theorem, which calculates the normal component and fault component of distribution network, respectively, and superposes them [14], is usually adopted.

From the researches introduced above, it can be seen that, in power flow calculation, the equivalent model of inverter based DG is processed ideally. The current limiting status of inverter based DG has not been considered. For example, DG may enter into the current limiting status when the voltage stability of distribution network is analyzed with power flow calculation for the loads increasing too much. In this case, the control objectives of inverter cannot be maintained. Hence, if the inverter based DG is still modeled as or PV bus, the impact of DG on power flow cannot be correctly included. Similarly, in short circuit calculation, DG may enter into the current limiting status as well for the decreased voltage at point of common coupling (PCC) during a fault. At this moment, the inverter based DG should be equivalent to current source, which has been mentioned in some researches already. But the current source models proposed in those researches are ideally for the simplified analysis of current output regulation. In addition, a lot of inverter based DGs have been configured with Low Voltage Ride Through (LVRT) control at present [15]. Therefore, the fault equivalent model of inverter based DG under LVRT control should be studied.

In this paper, the equivalent model of inverter based DG in normal and fault operation conditions of distribution network and the difference between power flow and short circuit calculation are analyzed at first. Then, an integrated power flow and short circuit calculation method of distribution network with inverter based DG is proposed according to the similarities between equivalent models of inverter based DG in normal and fault operation conditions. Finally, the proposed method is verified in an example. It is convenient to use the integrated calculation method to calculate power flow or short circuit current in practical engineering.

#### 2. Equivalent Model of Inverter Based DG

The output characteristics of inverter based DG during normal and fault operation conditions of distribution network are associated with the control strategy of inverter. The dual-loop control is usually adopted, which outer loop control targets are usually constant active and reactive power or constant DC voltage and reactive power. The output signals from outer loop are reference signals of inner ring, which mainly adopt decoupled control [16, 17]. The control principle of inverter with current limiting function, which orients -axis to grid voltage vector, is shown in Figure 1.