# Impact of Transformer Topology on Short-Circuit Analysis in Distribution Systems with Inverter-Based Distributed Generations

^{1}

^{2}

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## Abstract

**:**

## 1. Introduction

- A detailed approach that can conduct fault analyses with IBDGs is presented while considering the interconnection transformer topology that can impact the symmetric components of fault currents. This thorough approach helps engineers or researchers to study any types of distribution systems with SBDGs or IBDGs.
- Different fault behaviors caused by various transformer topologies are studied, including D-Yg, Yg-D, Yg-D-Yg, D-D-Yg, and Y-D-Yg.
- The transformer grounding impact on the zero-sequence fault current contributions of DERs and the total fault current are analyzed.
- Ultimately, this study can give insights on how to practically design a transformer topology and its grounding in distribution systems.

## 2. Materials and Methods

_{2}represents a distributed generator (DG), which can be an SBDG or an IBDG in this work, while [27] tested an SBDG only.

## 3. Impact of Interconnection Transformer Topology on Fault Current Contribution

## 4. Investigation of Fault Behaviors of the IBDG

#### 4.1. Short-Circuit Analysis of the SBDG-Based System

_{f}is the total fault current, and ${V}_{G1}^{\left(1\right)}$ and ${V}_{G2}^{\left(1\right)}$ are the positive-sequence voltage sources of G1 and G2, respectively. The symmetrical components of the fault current from bus 1 to bus 2 can be calculated based on the current division rule, thus yielding ${\mathrm{I}}_{12}^{\left(0\right)}=2.0742\angle -{59.96}^{\xb0}\text{}pu$ and ${\mathrm{I}}_{12}^{\left(1\right)}={\mathrm{I}}_{12}^{\left(2\right)}=1.0590\angle -{59.96}^{\xb0}\text{}pu$, where ${\mathrm{I}}_{12}^{\left(1\right)}$, ${\mathrm{I}}_{12}^{\left(2\right)}$, and ${\mathrm{I}}_{12}^{\left(0\right)}$ are the positive-, negative-, and zero-sequence fault currents from bus 1 to 2, respectively. Similarly, the positive-, negative-, and zero-sequence fault currents from bus 3 to 2, which are denoted by ${\mathrm{I}}_{32}^{\left(1\right)}$, ${\mathrm{I}}_{32}^{\left(2\right)}$, and ${\mathrm{I}}_{32}^{\left(0\right)}$, respectively, can be computed, yielding ${\mathrm{I}}_{32}^{\left(0\right)}=0.4251\angle -{60.00}^{\xb0}\text{}pu$ and ${\mathrm{I}}_{32}^{\left(1\right)}={\mathrm{I}}_{32}^{\left(2\right)}=1.4403\angle -{59.97}^{\xb0}\text{}pu$. All these results are represented in Figure 3.

#### 4.2. Short-Circuit Analysis of the IBDG-Based System

#### 4.2.1. Decomposition and Short-Circuit Analysis: Voltage Source

_{f}is the total fault current, and ${V}_{G1}^{\left(1\right)}$ and ${V}_{G2}^{\left(1\right)}$ are the positive-sequence voltage sources of G1 and G2, respectively. The symmetrical components of the fault current from bus 1 to bus 2 can be calculated based on the current division rule, thus yielding ${\mathrm{I}}_{12}^{\left(0\right)}=1.0781\angle -{59.96}^{\xb0}pu$ and ${\mathrm{I}}_{12}^{\left(1\right)}={\mathrm{I}}_{12}^{\left(2\right)}=1.2619\angle -{59.97}^{\xb0}pu$, where ${\mathrm{I}}_{12}^{\left(1\right)}$, ${\mathrm{I}}_{12}^{\left(2\right)}$, and ${\mathrm{I}}_{12}^{\left(0\right)}$ are the positive-, negative-, and zero-sequence fault currents from bus 1 to 2, respectively.

#### 4.2.2. Decomposition and Short-Circuit Analysis: Current Source

#### 4.2.3. Superposition

#### 4.3. Comparison of the SBDG and IBDG Cases

#### 4.4. Accuracy Test

## 5. Short-Circuit Analysis with Consideration of the Interconnection Transformer

#### 5.1. Case Study with Different Topologies of the Interconnection Transformer

#### 5.2. Case Study Analyses

## 6. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## Abbreviations

DER | Distributed energy resource |

SBDG | Synchronous-based distributed generation |

IBDG | Inverter-based distributed generation |

DG | Distributed generation |

SLG | Single-line-to-ground |

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**Figure 2.**Sequence network diagram of the test system with a synchronous machine-based distributed generation (SBDG). The numbers 1, 2, 3, 4, and 5 represent the bus indices.

**Figure 3.**Fault current contributions in the system with an SBDG: (

**a**) ampere unit and (

**b**) per unit (pu) configurations. The numbers 1, 2, 3, 4, and 5 represent the bus indices.

**Figure 4.**Test system with an IBDG: (

**a**) single-line diagram and (

**b**) sequence network diagram. The numbers 1, 2, 3, 4, and 5 represent the bus indices.

**Figure 5.**Sequence equivalent circuit for the voltage source. The numbers 1, 2, 3, 4, and 5 represent the bus indices.

**Figure 6.**Fault current contribution from the voltage source in the system with an IBDG. The numbers 1, 2, 3, 4, and 5 represent the bus indices.

**Figure 7.**Sequence equivalent circuit for the current source. The numbers 1, 2, 3, 4, and 5 represent the bus indices.

**Figure 8.**Fault current contribution of the current source in the system with an IBDG. The numbers 1, 2, 3, 4, and 5 represent the bus indices.

**Figure 9.**Total fault current contribution from both the voltage and current sources in the system with an IBDG: (

**a**) ampere unit and (

**b**) pu. The numbers 1, 2, 3, 4, and 5 represent the bus indices.

**Figure 10.**Sequence equivalent circuits of the system with a DG. The unit is pu. (

**a**) SBDG and (

**b**) IBDG. The numbers 1, 2, 3, 4, and 5 represent the bus indices.

**Figure 11.**Currents in the system in the ABC domain with a DG. The unit is pu. (

**a**) SBDG and (

**b**) IBDG.

**Figure 12.**Currents in the system in the ABC domain with a DG: (

**a**) SBDG and (

**b**) IBDG. The unit is ampere. The system with DGs in the ABC domain (amperes).

Previous Studies | Summary |
---|---|

[19] | Observed that the wind turbine controller may reduce the negative-sequence component of fault currents; injected negative-sequence currents |

[20] | Presented the method that changed the fault current phase angle to minimize the system fault current |

[21] | Quantified the fault current contributions due to IBDGs using steady-state and transient analyses |

[22] | Conducted fault analysis due to IBDGs under balanced conditions |

[23] | Considered IBDG’s voltage-dependent control modes for short-circuit analysis of radial and meshed networks |

[24] | Considered fault contributions from unbalanced IBDGs |

[25] | Improved computational speed for fault analysis with IBDGs |

**Table 2.**Bank connection types of a two-winding transformer. The symbols H and L denote the high- and low-voltage sides, respectively. The symbol N indicates a neutral line. The numbers 1, 2, and 0 represent the positive-, negative-, and zero-sequence networks, respectively.

Transformer Bank Connection | Positive/Negative Sequence | Zero Sequence |
---|---|---|

Same as above | ||

Same as above | ||

Same as above | ||

Same as above | ||

Same as above | ||

Same as above | ||

Same as above |

Transformer Bank Connection | Positive/Negative Sequence | Zero Sequence |
---|---|---|

Same as above | ||

Same as above |

Transformer Type | Topology | Fault Current Behavior in the Zero-Sequence Network |
---|---|---|

Two-winding transformer | D-Yg | |

Yg-D | ||

Three-winding transformer | Y-D-Yg | |

D-D-Yg | ||

Yg-D-Yg |

Sequence | Impedance of G1 | Impedance of T1 | Impedance of Line | Secondary Impedance of T2 | Primary Impedance of T2 | Tertiary Impedance of T2 | Impedance of G2 |
---|---|---|---|---|---|---|---|

Positive (symbol) | $\mathrm{j}0.2\text{}\left({X}_{G1}^{\left(1\right)}\right)$ | $\mathrm{j}0.1375\text{}\left({X}_{T1}^{\left(1\right)}\right)$ | $\mathrm{j}0.0907\text{}\left({X}_{L}^{\left(1\right)}\right)$ | $-\mathrm{j}0.0083\text{}\left({X}_{T2S}^{\left(1\right)}\right)$ | $\mathrm{j}0.0450\text{}\left({X}_{T2P}^{\left(1\right)}\right)$ | $\mathrm{j}0.1950\text{}\left({X}_{T2T}^{\left(1\right)}\right)$ | $\mathrm{j}0.03\text{}\left({X}_{G2}^{\left(1\right)}\right)$ |

Negative (symbol) | $\mathrm{j}0.2\text{}\left({X}_{G1}^{\left(2\right)}\right)$ | $\mathrm{j}0.1375\text{}\left({X}_{T1}^{\left(2\right)}\right)$ | $\mathrm{j}0.0907\text{}\left({X}_{L}^{\left(2\right)}\right)$ | $-\mathrm{j}0.0083\text{}\left({X}_{T2S}^{\left(2\right)}\right)$ | $\mathrm{j}0.0450\text{}\left({X}_{T2P}^{\left(2\right)}\right)$ | $\mathrm{j}0.1950\text{}\left({X}_{T2T}^{\left(2\right)}\right)$ | $\mathrm{j}0.03\text{}\left({X}_{G2}^{\left(2\right)}\right)$ |

Zero (symbol) | $\mathrm{j}0.2\text{}\left({X}_{G1}^{\left(0\right)}\right)$ | $\mathrm{j}0.1375\text{}\left({X}_{T1}^{\left(0\right)}\right)$ | $\mathrm{j}0.3062\text{}\left({X}_{L}^{\left(0\right)}\right)$ | $-\mathrm{j}0.0083\text{}\left({X}_{T2S}^{\left(0\right)}\right)$ | $\mathrm{j}0.0450\text{}\left({X}_{T2P}^{\left(0\right)}\right)$ | $\mathrm{j}0.1950\text{}\left({X}_{T2T}^{\left(0\right)}\right)$ | $\mathrm{j}0.04\text{}\left({X}_{G2}^{\left(0\right)}\right)$ |

Sequence | Impedance of G1 | Impedance of T1 | Impedance of Line | Secondary Impedance of T2 | Primary Impedance of T2 | Tertiary Impedance of T2 | Norton Impedance of G2 |
---|---|---|---|---|---|---|---|

Positive (symbol) | $\mathrm{j}0.2\text{}\left({X}_{G1}^{\left(1\right)}\right)$ | $\mathrm{j}0.1375\text{}\left({X}_{T1}^{\left(1\right)}\right)$ | $\mathrm{j}0.0907\text{}\left({X}_{L}^{\left(1\right)}\right)$ | $-\mathrm{j}0.0083\text{}\left({X}_{T2S}^{\left(1\right)}\right)$ | $\mathrm{j}0.0450\text{}\left({X}_{T2P}^{\left(1\right)}\right)$ | $\mathrm{j}0.1950\text{}\left({X}_{T2T}^{\left(1\right)}\right)$ | $\mathrm{10,000}\text{}\left({Z}_{G2}^{\left(1\right)}\right)$ |

Negative (symbol) | $\mathrm{j}0.2\text{}\left({X}_{G1}^{\left(2\right)}\right)$ | $\mathrm{j}0.1375\text{}\left({X}_{T1}^{\left(2\right)}\right)$ | $\mathrm{j}0.0907\text{}\left({X}_{L}^{\left(2\right)}\right)$ | $-\mathrm{j}0.0083\text{}\left({X}_{T2S}^{\left(2\right)}\right)$ | $\mathrm{j}0.0450\text{}\left({X}_{T2P}^{\left(2\right)}\right)$ | $\mathrm{j}0.1950\text{}\left({X}_{T2T}^{\left(2\right)}\right)$ | $\mathrm{10,000}\text{}\left({Z}_{G2}^{\left(2\right)}\right)$ |

Zero (symbol) | $\mathrm{j}0.2\text{}\left({X}_{G1}^{\left(0\right)}\right)$ | $\mathrm{j}0.1375\text{}\left({X}_{T1}^{\left(0\right)}\right)$ | $\mathrm{j}0.3062\text{}\left({X}_{L}^{\left(0\right)}\right)$ | $-\mathrm{j}0.0083\text{}\left({X}_{T2S}^{\left(0\right)}\right)$ | $\mathrm{j}0.0450\text{}\left({X}_{T2P}^{\left(0\right)}\right)$ | $\mathrm{j}0.1950\text{}\left({X}_{T2T}^{\left(0\right)}\right)$ | $\mathrm{10,000}\text{}\left({Z}_{G2}^{\left(0\right)}\right)$ |

Bus No. | V_{a} | V_{b} | V_{c} | 3V_{0} | V_{0} | V_{1} | V_{2} | |||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|

Magnitude (Mag) (pu) | Phase Angle (°) | Mag (pu) | Phase Angle (°) | Mag (pu) | Phase Angle (°) | Mag (pu) | Phase Angle (°) | Mag (pu) | Phase Angle (°) | Mag (pu) | Phase Angle (°) | Mag (pu) | Phase Angle (°) | |

1 | 0.7105 | −11.89 | 0.6201 | −92.03 | 1.0199 | 131.31 | 0.0000 | 0 | 0.0000 | 0 | 0.7565 | 8.73 | 0.2664 | −101.35 |

2 | 0.0000 | 0 | 0.9438 | −55.75 | 0.9439 | 153.05 | 0.4695 | −131.35 | 0.1565 | −131.35 | 0.6061 | 48.65 | 0.4496 | −131.35 |

3 | 0.1239 | 92.61 | 0.9890 | −48.01 | 0.9343 | 155.03 | 0.2890 | −131.36 | 0.0963 | −131.36 | 0.6409 | 56.36 | 0.4496 | −131.35 |

4 | 0.2477 | 92.61 | 1.0504 | −41.06 | 0.9259 | 157.05 | 0.1086 | −131.38 | 0.0362 | −131.38 | 0.6860 | 63.16 | 0.4496 | −131.36 |

5 | 0.2797 | 96.30 | 1.0783 | −39.86 | 0.9317 | 159.39 | 0.1135 | −131.38 | 0.0378 | −131.38 | 0.7067 | 65.65 | 0.4496 | −131.36 |

From | To | I_{a} | I_{b} | I_{c} | 3I_{0} | I_{0} | I_{1} | I_{2} | |||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|

Bus No. | Bus No. | Mag (pu) | Phase Angle (°) | Mag (pu) | Phase Angle (°) | Mag (pu) | Phase Angle (°) | Mag (pu) | Phase Angle (°) | Mag (pu) | Phase Angle (°) | Mag (pu) | Phase Angle (°) | Mag (pu) | Phase Angle (°) |

1 | 2 | 3.6084 | −56.54 | 1.1375 | 97.35 | 0.8107 | −27.30 | 3.4142 | −41.31 | 1.1381 | −41.31 | 1.3860 | −84.44 | 1.3321 | −41.32 |

2 | F | 3.9962 | −41.32 | 0.0000 | 0.00 | 0.0000 | 0.00 | 3.9962 | −41.32 | 1.3321 | −41.32 | 1.3321 | −41.32 | 1.3321 | −41.32 |

3 | 2 | 1.0779 | 20.18 | 1.1375 | −82.65 | 0.8107 | 152.70 | 0.5820 | −41.35 | 0.1940 | −41.35 | 1.0000 | 30.00 | 0.0000 | 48.64 |

4 | 3 | 1.0779 | 20.18 | 1.1375 | −82.65 | 0.8107 | 152.70 | 0.5820 | −41.35 | 0.1940 | −41.35 | 1.0000 | 30.00 | 0.0000 | 48.64 |

5 | 4 | 1.0001 | 30.00 | 1.0000 | −90.00 | 1.0000 | 150.00 | 0.0000 | 48.62 | 0.0000 | 48.62 | 1.0000 | 30.00 | 0.0000 | 48.64 |

**Table 9.**Accuracy test results between MATLAB code and PSCAD/EMTDC. Note that the magnitude of 0.0000 represents a very small number.

MATLAB Code(Frequency Domain) | PSCAD/EMTDC(Time Domain) | ||||||||||||

V_{0} | V_{1} | V_{2} | V_{0} | V_{1} | V_{2} | ||||||||

Voltage | Bus | Mag (pu) | Phase Angle (°) | Mag (pu) | Phase Angle (°) | Mag (pu) | Phase Angle (°) | Mag (pu) | Phase Angle (°) | Mag (pu) | Phase Angle (°) | Mag (pu) | Phase Angle (°) |

2 | 0.1565 | −131.35 | 0.6061 | 48.65 | 0.4496 | −131.35 | 0.1576 | −132.40 | 0.6067 | 48.41 | 0.4491 | −133.27 | |

3 | 0.0963 | −131.36 | 0.6409 | 56.36 | 0.4496 | −131.35 | 0.0971 | −130.96 | 0.6443 | 56.00 | 0.4493 | −131.29 | |

4 | 0.0362 | −131.38 | 0.6860 | 63.16 | 0.4496 | −131.35 | 0.0365 | −124.72 | 0.6912 | 62.67 | 0.4489 | −131.28 | |

MATLAB code(Frequency Domain) | PSCAD/EMTDC(Time Domain) | ||||||||||||

I_{0} | I_{1} | I_{2} | I_{0} | I_{1} | I_{2} | ||||||||

Current | Bus | Mag (pu) | Phase angle (°) | Mag (pu) | Phase angle (°) | Mag (pu) | Phase angle (°) | Mag (pu) | Phase angle (°) | Mag (pu) | Phase angle (°) | Mag (pu) | Phase angle (°) |

1→2(F) | 3.4142 | −41.31 | 1.3860 | −84.44 | 1.3321 | −41.32 | 3.4322 | −42.37 | 1.3841 | −84.36 | 1.3404 | −41.27 | |

3→2(F) | 0.5820 | −41.35 | 1.0000 | 30.00 | 0.0000 | 48.64 | 0.5847 | −34.71 | 0.9980 | 30.11 | 0.0015 | −41.36 | |

4→3 | 0.5820 | −41.35 | 1.0000 | 30.00 | 0.0000 | 48.64 | 0.5862 | −34.72 | 0.9942 | 30.50 | 0.0067 | −41.27 |

Bus Location | Fault Current Magnitude in MATLAB Code | Bus Location | Fault Current Magnitude in MATLAB Code |
---|---|---|---|

2 | 3.4142 | 3.4322 | 0.52 |

3 | 0.5820 | 0.5847 | 0.46 |

4 | 0.5820 | 0.5862 | 0.76 |

Transformer Bank Connection | Sequence Network |
---|---|

D-Yg | |

Yg-D | |

Y-D-Yg | |

D-D-Yg |

Bus No. | V_{a} | V_{b} | V_{c} | 3V_{0} | V_{0} | V_{1} | V_{2} | |||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|

Mag (pu) | Phase Angle (°) | Mag (pu) | Phase Angle (°) | Mag (pu) | Phase Angle (°) | Mag (pu) | Phase Angle (°) | Mag (pu) | Phase Angle (°) | Mag (pu) | Phase Angle (°) | Mag (pu) | Phase Angle (°) | |

1 | 0.7161 | −11.09 | 1.0198 | 131.31 | 1.0198 | 131.31 | 0.0000 | 0 | 0.0000 | 0.00 | 0.7629 | 8.82 | 0.2598 | −101.35 |

2 | 0.0000 | 0 | 0.9525 | 154.99 | 0.9525 | 154.99 | 0.5358 | −131.35 | 0.1786 | −131.35 | 0.6170 | 48.65 | 0.4384 | −131.35 |

3 | 0.0907 | 120.00 | 0.9646 | 160.36 | 0.9646 | 160.36 | 0.5358 | −131.35 | 0.1786 | −131.35 | 0.6517 | 56.23 | 0.4384 | −131.35 |

4 | 0.1815 | 120.00 | 0.9850 | 165.56 | 0.9850 | 165.56 | 0.5358 | −131.35 | 0.1786 | −131.35 | 0.6966 | 62.94 | 0.4384 | −131.35 |

5 | 0.8455 | 132.41 | 0.5058 | −170.16 | 0.505 | −170.16 | 0.0000 | 0.00 | 0.0000 | 0.00 | 0.7800 | 101.45 | 0.4384 | −161.35 |

From | To | I_{a} | I_{b} | I_{c} | 3I_{0} | I_{0} | I_{1} | I_{2} | |||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|

Bus No. | Bus No. | Mag (pu) | Phase Angle (°) | Mag (pu) | Phase Angle (°) | Mag (pu) | Phase Angle (°) | Mag (pu) | Phase Angle (°) | Mag (pu) | Phase Angle (°) | Mag (pu) | Phase Angle (°) | Mag (pu) | Phase Angle (°) |

1 | 2 | 1.6383 | −65.13 | 2.6358 | 116.81 | 1.0000 | −60.00 | 0.0000 | 0.00 | 0.0000 | 0.00 | 1.3625 | −115.41 | 1.2990 | −11.35 |

2 | F | 3.8970 | −41.35 | 0.0000 | 0.00 | 0.0000 | 0.00 | 3.8970 | −41.35 | 1.2990 | −41.35 | 1.2990 | −41.35 | 1.2990 | −41.35 |

3 | 2 | 1.0001 | −150.00 | 1.0000 | 89.99 | 1.0000 | −30.00 | 0.0000 | 0.00 | 0.0000 | 0.00 | 1.0000 | −150.00 | 0.0000 | −131.35 |

4 | 3 | 1.0001 | −150.00 | 1.0000 | 89.99 | 1.0000 | −30.00 | 0.0000 | 0.00 | 0.0000 | 0.00 | 1.0000 | −150.00 | 0.0000 | −131.35 |

5 | 4 | 1.0001 | −150.00 | 1.0000 | 89.99 | 1.0000 | −30.00 | 0.0000 | 0.00 | 0.0000 | 0.00 | 1.0000 | −150.00 | 0.0000 | −131.35 |

Bus No. | V_{a} | V_{b} | V_{c} | 3V_{0} | V_{0} | V_{1} | V_{2} | |||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|

Mag (pu) | Phase Angle (°) | Mag (pu) | Phase Angle (°) | Mag (pu) | Phase Angle (°) | Mag (pu) | Phase Angle (°) | Mag (pu) | Phase Angle (°) | Mag (pu) | Phase Angle (°) | Mag (pu) | Phase Angle (°) | |

1 | 0.7090 | −12.10 | 0.6177 | −91.85 | 1.0198 | 131.31 | 0.0000 | 0.00 | 0.0000 | 0.00 | 0.7547 | 8.71 | 0.2681 | −101.35 |

2 | 0.0000 | 0.00 | 0.9415 | −55.23 | 0.9415 | 152.53 | 0.4516 | −131.35 | 0.1505 | −131.35 | 0.6030 | 48.65 | 0.6030 | 48.65 |

3 | 0.1352 | 88.16 | 0.9863 | −46.62 | 0.9276 | 153.61 | 0.2258 | −131.36 | 0.0753 | −131.36 | 0.6378 | 56.40 | 0.4525 | −131.35 |

4 | 0.2703 | 88.16 | 1.0512 | −38.92 | 0.9141 | 154.73 | 0.0001 | 138.66 | 0.0000 | 138.66 | 0.6830 | 63.23 | 0.4525 | −131.35 |

5 | 0.8432 | 134.05 | 1.1963 | −26.72 | 0.4871 | −171.95 | 0.0000 | 0.00 | 0.0000 | 0.00 | 0.7671 | 101.85 | 0.4525 | −161.35 |

From | To | I_{a} | I_{b} | I_{c} | 3I_{0} | I_{0} | I_{1} | I_{2} | |||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|

Bus No. | Bus No. | Mag (pu) | Phase Angle (°) | Mag (pu) | Phase Angle (°) | Mag (pu) | Phase Angle (°) | Mag (pu) | Phase Angle (°) | Mag (pu) | Phase Angle (°) | Mag (pu) | Phase Angle (°) | Mag (pu) | Phase Angle (°) |

1 | 2 | 1.7045 | −64.15 | 2.7028 | 117.38 | 1.0000 | −60.00 | 0.0000 | 0.00 | 0.0000 | 0.00 | 1.3927 | −114.22 | 1.3406 | −11.35 |

2 | F | 4.0218 | −41.35 | 0.0000 | 0.00 | 0.0000 | 0.00 | 4.0218 | −41.35 | 1.3406 | −41.35 | 1.3406 | −41.35 | 1.3406 | −41.35 |

3 | 2 | 1.1036 | −162.18 | 1.1769 | 99.02 | 0.7605 | −26.36 | 0.7374 | 138.66 | 0.2458 | 138.66 | 1.0000 | −150.00 | 0.0000 | −131.35 |

4 | 3 | 1.1036 | −162.18 | 1.1769 | 99.02 | 0.7605 | −26.36 | 0.7374 | 138.66 | 0.2458 | 138.66 | 1.0000 | −150.00 | 0.0000 | −131.35 |

5 | 4 | 1.0001 | −150.00 | 1.0000 | 89.99 | 1.0000 | −30.00 | 0.0000 | 0.00 | 0.0000 | 0.00 | 1.0000 | −150.00 | 0.0000 | −131.35 |

Bus No. | V_{a} | V_{b} | V_{c} | 3V_{0} | V_{0} | V_{1} | V_{2} | |||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|

Mag (pu) | Phase Angle (°) | Mag (pu) | Phase Angle (°) | Mag (pu) | Phase Angle (°) | Mag (pu) | Phase Angle (°) | Mag (pu) | Phase Angle (°) | Mag (pu) | Phase Angle (°) | Mag (pu) | Phase Angle (°) | |

1 | 0.7161 | −11.09 | 0.6289 | −92.69 | 1.0198 | 131.31 | 0.0000 | 0.00 | 0.0000 | 0.00 | 0.7629 | 8.82 | 0.2598 | −101.35 |

2 | 0.0000 | 0.00 | 0.9525 | −57.69 | 0.9525 | 154.99 | 0.5358 | −131.35 | 0.1786 | −131.35 | 0.6170 | 48.65 | 0.4384 | −131.35 |

3 | 0.0907 | 120.00 | 1.0039 | −53.31 | 0.9646 | 160.36 | 0.5358 | −131.35 | 0.1786 | −131.35 | 0.6517 | 56.23 | 0.4384 | −131.35 |

4 | 0.1815 | 120.00 | 1.0607 | −49.37 | 0.9850 | 165.56 | 0.5358 | −131.35 | 0.1786 | −131.35 | 0.6966 | 62.94 | 0.4384 | −131.35 |

5 | 0.3231 | 88.42 | 1.0792 | −38.44 | 0.9224 | 157.84 | 0.0000 | 0.00 | 0.0000 | 0.00 | 0.7172 | 65.40 | 0.4384 | −131.35 |

From | To | I_{a} | I_{b} | I_{c} | 3I_{0} | I_{0} | I_{1} | I_{2} | |||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|

Bus No. | Bus No. | Mag (pu) | Phase Angle (°) | Mag (pu) | Phase Angle (°) | Mag (pu) | Phase Angle (°) | Mag (pu) | Phase Angle (°) | Mag (pu) | Phase Angle (°) | Mag (pu) | Phase Angle (°) | Mag (pu) | Phase Angle (°) |

1 | 2 | 1.6383 | −65.13 | 2.6358 | 116.81 | 1.0000 | −60.00 | 0.0000 | 0.00 | 0.0000 | 0.00 | 1.3625 | −115.41 | 1.2990 | −11.35 |

2 | F | 3.8970 | −41.35 | 0.0000 | 0.00 | 0.0000 | 0.00 | 3.8970 | −41.35 | 1.2990 | −41.35 | 1.2990 | −41.35 | 1.2990 | −41.35 |

3 | 2 | 1.0001 | −150.00 | 1.0000 | 90.00 | 1.0000 | −30.00 | 0.0000 | 0.00 | 0.0000 | 0.00 | 1.0000 | −150.00 | 0.0000 | −131.35 |

4 | 3 | 1.0001 | −150.00 | 1.0000 | 90.00 | 1.0000 | −30.00 | 0.0000 | 0.00 | 0.0000 | 0.00 | 1.0000 | −150.00 | 0.0000 | −131.35 |

5 | 4 | 1.0001 | −150.00 | 1.0000 | 90.00 | 1.0000 | −30.00 | 0.0000 | 0.00 | 0.0000 | 0.00 | 1.0000 | −150.00 | 0.0000 | −131.35 |

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## Share and Cite

**MDPI and ACS Style**

Cho, N.; Yoon, M.; Choi, S.
Impact of Transformer Topology on Short-Circuit Analysis in Distribution Systems with Inverter-Based Distributed Generations. *Sustainability* **2022**, *14*, 9781.
https://doi.org/10.3390/su14159781

**AMA Style**

Cho N, Yoon M, Choi S.
Impact of Transformer Topology on Short-Circuit Analysis in Distribution Systems with Inverter-Based Distributed Generations. *Sustainability*. 2022; 14(15):9781.
https://doi.org/10.3390/su14159781

**Chicago/Turabian Style**

Cho, Namhun, Myungseok Yoon, and Sungyun Choi.
2022. "Impact of Transformer Topology on Short-Circuit Analysis in Distribution Systems with Inverter-Based Distributed Generations" *Sustainability* 14, no. 15: 9781.
https://doi.org/10.3390/su14159781