Impact of Transformer Topology on Short-Circuit Analysis in Distribution Systems with Inverter-Based Distributed Generations
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
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
4.2. Short-Circuit Analysis of the IBDG-Based System
4.2.1. Decomposition and Short-Circuit Analysis: Voltage Source
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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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 |
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) | |||||||
Negative (symbol) | |||||||
Zero (symbol) |
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) | |||||||
Negative (symbol) | |||||||
Zero (symbol) |
Bus No. | Va | Vb | Vc | 3V0 | V0 | V1 | V2 | |||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
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 | Ia | Ib | Ic | 3I0 | I0 | I1 | I2 | |||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
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 |
MATLAB Code (Frequency Domain) | PSCAD/EMTDC (Time Domain) | ||||||||||||
V0 | V1 | V2 | V0 | V1 | V2 | ||||||||
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) | ||||||||||||
I0 | I1 | I2 | I0 | I1 | I2 | ||||||||
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. | Va | Vb | Vc | 3V0 | V0 | V1 | V2 | |||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
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 | Ia | Ib | Ic | 3I0 | I0 | I1 | I2 | |||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
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. | Va | Vb | Vc | 3V0 | V0 | V1 | V2 | |||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
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 | Ia | Ib | Ic | 3I0 | I0 | I1 | I2 | |||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
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. | Va | Vb | Vc | 3V0 | V0 | V1 | V2 | |||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
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 | Ia | Ib | Ic | 3I0 | I0 | I1 | I2 | |||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
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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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
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 StyleCho, 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