# Modeling methodology and fault simulation of distribution networks integrated with inverter-based DG

- Longchang Wang
^{1}, - Houlei Gao
^{1}Email author and - Guibin Zou
^{1}

**2**:31

https://doi.org/10.1186/s41601-017-0058-9

© The Author(s) 2017

**Received: **23 January 2017

**Accepted: **29 June 2017

**Published: **15 August 2017

## Abstract

The increasing penetration of inverter-based distributed generations (DGs) significantly affects the fault characteristics of distribution networks. Fault analysis is a keystone for suitable protection scheme design. This paper presents the modelling methodology for distribution networks with inverter-based DGs and performs fault simulation based on the model. Firstly, a single inverter-based DG model based on the cascaded control structure is developed. Secondly, a simulation model of distribution network with two inverter-based DGs is established. Then, different fault simulations are performed based on the Real Time Digital Simulator (RTDS). Theoretical analyses are conducted to justify the simulation results, including the equivalent circuit of distribution networks with inverter-based DGs and the solution method for loop currents.

## Keywords

## 1 Introduction

In recent years, different kinds of distributed generation (DG) are being connected in distribution networks, such as wind generation and photovoltaic (PV) generation. A great number of power electronic devices are connected to distribution networks due to the integration of inverter-based DGs. Therefore, compared with traditional distribution network, planning and design, control and protection, simulation and analysis for distribution networks with inverter-based DGs are more complicated. This has motivated a considerable number of studies [1–5].

Simulation model plays an important role in the research of power system. As a real-time simulation tool designed for power system, Real-Time Digital Simulator (RTDS) are widely used for power system simulation and analysis [6–9]. One important advantage of RTDS is that it can interface electrical and control signal with physical devices and achieve hardware-in-loop simulation. Thus, the simulation models based on RTDS can be used to test real equipments.

Fault characteristics of distribution networks with DGs are quite different from traditional distribution networks. How to model DG under fault conditions is a prerequisite for fault analysis of the distribution networks with DGs. Researchers have put forward different equivalent models of inverter-based DG to analyze their fault characteristics, such as the current source with a parallel changeable impedance [10], the voltage source with a series changeable impedance [11], and the current source controlled by positive sequence voltage at common coupling point (PCC) [12]. In the previous researches, their simulation models contain only one DG. However, in reality, there may be several DGs placed in different locations.

In this paper, single inverter-based DG is modeled firstly based on RTDS. Then, a simulation model for a distribution network with two inverter-based DGs is developed. After that, fault simulations are performed using the simulation model and the results are analyzed briefly. Theoretical analyses are conducted to justify the correctness of simulation results and the effectiveness of control strategy for inverters under fault conditions. A brief summary is presented in the end.

## 2 Modeling of inverter-based DG

As one kind of green energy, PV generation has been widely integrated in power supply systems. Since PV generation output direct current, there must be inverters to connect it to AC grid. Therefore, PV is chosen as an example to introduce the modeling process of inverter-based DG in this study.

The commonly used constant P-Q control strategy based on dq synchronous reference frame is adopted in this study. Two different control modes are designed for different operation conditions. Under the normal conditions, DGs only have the active power output. However, during fault conditions, DGs provide extra reactive power support to mitigate the voltage sag at the PCC [13].

If we set *P*
^{∗} and *Q*
^{∗} as the active and reactive power reference, the corresponding current reference *i*
_{d}
^{∗} and *i*
_{q}
^{∗} under dq synchronous reference frame can be calculated according to (3).

where *u*
_{1} is the amplitude of positive sequence voltage (p.u.) at PCC, *i*
_{d0}
^{∗} is current reference of d-axis before the fault.

## 3 Modeling of distribution networks with inverter-based DGs

In Fig. 3, the DG1 and DG2 represent the two single-stage grid-connected PV systems. The TB, K1 to K4, Kdg1 and Kdg2 are circuit breakers at different locations. The feeders in the network adopt PI model. To simulate different fault conditions, four fault locations, f_{1} to f_{4}, are set at the middle of L_{1} to L_{4}, respectively. Load1 and load2 are inductive loads modeled by series resistance and inductor.

Parameters of main components

Components | Parameters |
---|---|

Main source | Voltage magnitude: 10.5 kV Positive impedance: 1∠80 |

Transmission line L | Positive impedance: (0.270 + j0.335) Ω/km Length: 5 km, 4 km, 4 km,5 km, respectively |

Loads | Load1: 1MVA, power factor is 0.9 Load2: 4MVA, power factor is 0.9 |

## 4 Fault simulation and calculation

Based on the proposed simulation model in Section 3, large numbers of fault simulations are performed at different locations of the system model. The typical simulation results for three-phase faults and phase-to-phase faults at location f_{4} are presented in this section.

### 4.1 Three-phase fault

_{4}. The current waveforms flowing through each line are shown in Fig. 4. The output current and voltage waveforms of the main source and two DGs are shown in Fig. 5.

From Fig. 5, it can be seen that the current supplied by main source increased greatly, while current supplied by DGs increased slightly under the fault condition, which means that the control strategy for inverter-based DGs can effectively limit the output current of DG.

### 4.2 Phase-to-phase fault (A-B)

_{4}. The current waveforms flowing through each line are shown in Fig. 6. The output current and voltage waveforms of the main source and two DGs are shown in Fig. 7.

From Fig. 7, it can be observed that the current of main source has the traditional fault characteristics, such as current of phase A and B increased greatly and the output current became unsymmetrical. However, fault current characteristics of DGs are obvious different. The output current increased slightly and maintained symmetrical under the A-B fault condition.

### 4.3 Current and voltage phasor calculation

In order to present the fault characteristics clearly, current and voltage phasors (steady state components under fault condition) are calculated based on one-cycle Fourier algorithm. The calculation results of the current of phase A flowing through line L_{2}, L_{3}, L_{4} and the voltage of phase A at PCC (M and N) are presented in this subsection.

_{4}, calculation results are as follows:

Equation (5) show that due to the fault current injections from DG1 and DG2, the magnitude of \( {\dot{I}}_{{\mathrm{L}}_3\mathrm{A}} \) is greater than that of \( {\dot{I}}_{{\mathrm{L}}_2\mathrm{A}} \), while the magnitude of \( {\dot{I}}_{{\mathrm{L}}_4\mathrm{A}} \) is greater than that of \( {\dot{I}}_{{\mathrm{L}}_3\mathrm{A}} \). The phase angle differences among \( {\dot{I}}_{{\mathrm{L}}_2\mathrm{A}} \), \( {\dot{I}}_{{\mathrm{L}}_3\mathrm{A}} \) and \( {\dot{I}}_{{\mathrm{L}}_4\mathrm{A}} \) are quite small. The magnitude of \( {\dot{V}}_{MA} \) is greater than that of \( {\dot{V}}_{NA} \), and \( {\dot{V}}_{MA} \) leads \( {\dot{V}}_{NA} \) in phase angle.

_{4}, calculation results are as follows:

It can be seen from (6) that the calculation results show the similar characteristics as the above three-phase fault results.

## 5 Theoretical verification

In this section, the theoretical derivations and calculations are presented to verify the simulation results.

### 5.1 Fault equivalent circuit

where *u*
_{1} is the amplitude of positive sequence voltage at PCC and f(*u*
_{1}) is a nonlinear function. For a given value of *u*
_{1}, f(*u*
_{1}) can be calculated according to (4).

*I*

_{dg , d}and

*I*

_{dg , q}can be calculated from (4), and then \( {I}_{\mathrm{dg},\mathrm{f}}=\sqrt{{I_{\mathrm{dg},\mathrm{d}}}^2+{I_{\mathrm{dg},\mathrm{q}}}^2} \). Let Δ

*θ*be the phase angle difference between \( {\dot{U}}_{pcc} \) and \( {\dot{I}}_{\mathrm{dg},\mathrm{f}} \), which equals to the power factor angle of PV,

*φ*. Considering (3), the angle

*φ*can be derived from the output active and reactive power:

In this paper, the fault equivalent model under A-B fault at location f_{4} is taken as an example. There are positive and negative sequence components under A-B fault. The positive network contains main source and two PVs, but the negative network has no source because the main source and PV only output positive sequence voltage and current.

Where.

\( {\dot{E}}_{\mathrm{s}} \): Voltage of the main source;

*Z*
_{s}: Equivalent PSI of the main source;

*Z*
_{L1}, *Z*
_{L2}, *Z*
_{L3}: PSI of L_{1}, L_{2}, L_{3}, respectively;

*Z*
_{L41}: PSI of the line from fault point to busbar N;

*Z*
_{L42}: PSI of the line from fault point to the end of L_{4};

*Z*
_{Load1}: Equivalent PSI of the load1;

*Z*
_{Load2}: Equivalent PSI of the load2.

where *Z*
_{tem1} = *Z*
_{L1} + *Z*
_{Load1}, *k* = *Z*
_{tem1}/(*Z*
_{s} + *Z*
_{tem1}), *Z*
_{2 ∑ 1} = (*Z*
_{s}
*Z*
_{tem1})/(*Z*
_{s} + *Z*
_{tem1}) + *Z*
_{L2} + *Z*
_{L3} + *Z*
_{L41}, *Z*
_{2 ∑ 2} = *Z*
_{L42} + *Z*
_{Load2}.

In Fig. 10(b), the equivalent impedance Z_{2} and Z_{3} are expressed as:

*Z*
_{2} = *Z*
_{L3}, *Z*
_{3} = *Z*
_{L41} + (Z_{2∑} ⋅ Z_{2 ∑ 2})/(Z_{2∑} + Z_{2 ∑ 2}).

### 5.2 Solving method

Especially, there are four nonlinear equations related to f(*u*
_{m1}) and f(*u*
_{n1}). The Newton-Raphson algorithm is used to solve the equation group in (13).

During every iteration, the amplitude and phase angle of full-voltage at position M and N need to be calculated. Then *I*
_{dg1 , f} can be calculated according to (4) and *θ*
_{dg1} can be calculated according to (8) and (9). *I*
_{dg2 , f}and *θ*
_{dg2} can be derived in the same way.

### 5.3 Comparisons with simulation results

Comparison between simulation and theoretical results for three-phase fault at f_{4}

Phasors | Simulation results | Theoretical results | Absolute errors | Relative errors/% | |
---|---|---|---|---|---|

\( {\dot{I}}_{{\mathrm{L}}_2\mathrm{A}} \) | Amp. | 1.515 | 1.512 | 0.003 | 0.200 |

Ang. | −78.4 | −82.8 | 4.4 | 2.458 | |

\( {\dot{I}}_{{\mathrm{L}}_3\mathrm{A}} \) | Amp. | 1.603 | 1.610 | 0.008 | 0.473 |

Ang. | −80.7 | −82.8 | 2.1 | 1.210 | |

\( {\dot{I}}_{{\mathrm{L}}_4\mathrm{A}} \) | Amp. | 1.838 | 1.758 | 0.080 | 4.354 |

Ang. | −82.4 | −87.3 | 4.9 | 2.689 | |

\( {\dot{V}}_{MA} \) | Amp. | 4.902 | 4.659 | 0.243 | 4.961 |

Ang. | −31.9 | −33.5 | 1.6 | 0.928 | |

\( {\dot{V}}_{NA} \) | Amp. | 2.051 | 1.891 | 0.160 | 7.803 |

Ang. | −33.1 | −36.1 | 3.0 | 1.675 |

Comparison between simulation and theoretical results for A-B fault at f_{4}

Phasors | Simulation result | Theoretical result | Absolute error | Relative error/% | |
---|---|---|---|---|---|

\( {\dot{I}}_{{\mathrm{L}}_2\mathrm{A}} \) | Amp. | 1.331 | 1.340 | 0.009 | 0.676 |

Ang. | −112.5 | −104.0 | 8.5 | 4.743 | |

\( {\dot{I}}_{{\mathrm{L}}_3\mathrm{A}} \) | Amp. | 1.415 | 1.429 | 0.014 | 0.989 |

Ang. | −111.7 | −104.4 | 7.3 | 4.138 | |

\( {\dot{I}}_{{\mathrm{L}}_4\mathrm{A}} \) | Amp. | 1.623 | 1.609 | 0.014 | 0.863 |

Ang. | −112.0 | −107.3 | 4.7 | 2.578 | |

\( {\dot{V}}_{MA} \) | Amp. | 6.221 | 5.621 | 0.599 | 9.629 |

Ang. | −103.2 | −100.7 | 2.5 | 1.369 | |

\( {\dot{V}}_{NA} \) | Amp. | 4.629 | 4.354 | 0.276 | 5.962 |

Ang. | −124.2 | −125.3 | 1.1 | 0.637 |

It can be seen from Table 2 and Table 3 that the theoretical results are consistent with simulation results. The relative errors of most quantities are within 5%. All the absolute errors of phasor angles are within 5° under three-phase fault condition, and within 10° under A-B fault condition. The comparisons have shown the effectiveness of the simulations results.

## 6 Conclusions

To investigate the fault characteristics of distribution networks with inverter-based DGs, this paper proposes a complete simulation model for a typical distribution network integrated with PV generators based on the RTDS.

The comparisons between the simulation results and the theoretical analysis proved the feasibility of the proposed modeling methodology. Both the fault simulation waveforms and the phasor calculation results show that the output current of inverter-based DG increases slightly (less than 2 times of rated value) and maintains symmetrical under different fault conditions, which are quite different from that of traditional sources.

Moreover, using the proposed simulation model, RTDS can produce analogue voltage and current signals reflecting fault characteristics of distribution network with inverter-based DGs. Then these analogue signals can be used to test actual protection devices in a close- loop manner.

## Declarations

### Acknowledgments

This work was supported by Nation Natural Science Foundation of China (51377100) and the Key Scientific and Technological Project of State Grid Shandong Power Company (SGSDWF00YJJS1400563).

### Authors’ contributions

LW investigated the modeling methodology of distribution networks integrated with IBDGs, conducted the fault simulation and drafted the manuscript. HG proposed the equivalent circuit of distribution networks with IBDGs and the solution method for loop current. GZ verified the simulation model and analyzed the simulation results. All authors read and approved the final manuscript.

### Authors’ information

**Longchang Wang** was born in Shandong Province, China, in 1990. He received the B.S. degree in electrical engineering from Shandong University, Jinan, China, in 2014. He is now a Master candidate in the School of Electrical Engineering, Shandong University. His research interest is power system protection and control. E-mail:longchangw@126.com.

**Houlei Gao** (M’11) was born in Shandong Province, China, in 1963. He received the B.S. and M.S. degrees in electrical power engineering from Shandong University of Technology, Jinan, China, in 1983 and 1988, respectively, and the Ph.D. degree in electrical power system and automation from Tianjin University, Tianjin, China, in 1997. From 2004 to 2005, he worked as senior visiting scholar with the School of Electrical and Electronic Engineering, Queen’s University Belfast, U.K. He is currently a Professor at the School of Electrical Engineering, Shandong University, China. He has authored or coauthored more than 170 technical papers. His research interests include power system protection, fault location, smart substation and distributed generation. E-mail: houleig@sdu.edu.cn.

**Guibin Zou** (M’12) was born in Shandong Province, China, in 1971. He received the M.Sc. and Ph.D. degrees in the automation of electric power systems from Shandong University, Jinan, China, in 2000 and 2009, respectively. Currently, he is a Professor with the School of Electrical Engineering, Shandong University. His research areas include power system protection and control, power system simulation and modeling, digital substations, and wind power generation techniques.

### Competing interests

The authors declare that they have no competing interests.

**Open Access**This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.

## Authors’ Affiliations

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