Innovative Optimal Nonstandard Tripping Protection Scheme for Radial and Meshed Microgrid Systems
Abstract
:1. Introduction
1.1. Background
1.2. Literature Review
1.3. Contribution of The Paper
- For improving the performance of the protection system by integrating the DG units and during the occurrence of different fault currents in the MGs, the novel NSTCC is created with consideration to the constraints of the existing model.
- In the OCR scheme, an optimum coordination approach is utilizing NSTCC to reduce the total OT compared to traditional SCs and other NSCs presented in the literature. This paper achieves a significant reduction in total OT without a miscoordination record.
- The proposed new optimal scheme based on NSTCC is developed with a lower number of constraints compared to the optimal coordination in the literature because it uses just one flexible coordination scheme. Therefore, the new proposed approach in this work achieves the optimal solution with minimum computational costs.
- There is no communication required between the OCRs in the proposed optimal coordination strategy in this work, where the measurement of the current is acquired locally. Therefore, the proposed approach provides adequate robustness to the OCR coordination approach, decreasing the demand for communication infrastructure. Moreover, it reduces the computational cost as well as the requirement to gain way in large quantities of the MGs and grid data.
- The sensitivity improvement for the proposed optimal scheme is shown by comparing the results of the NSTCC and the standard curves under different testing and MG operation modes.
- Finally, a comparison analysis has been provided for the proposed optimum coordination approach under various faulty conditions for two DNs types: radial networks (IEEE 9-bus test system and IEC MG benchmark) as well as meshed networks (IEEE 9- and 30-bus test system). This comparison proves the proposed approach’s superiority over others, especially for minimum fault in islanding mode.
1.4. Outline of Paper
2. Problem Statement: OCR Coordination
2.1. Problem Description: Illustration-Based Analysis
2.2. The Coordination of Overcurrent Relay
3. The Proposed Methodology: Nonstandard Time Current Characteristics
3.1. Formulating the OCR Coordination Problem
Objective Function
- Coordination Criteria and Selectivity
- Relay Setting, Operating Time Bounds:
- Proposed Setting of Coefficient Bounds:
3.2. Optimization Methods for Solving the OCR Coordination Problem
3.2.1. Genetic Algorithm Optimization (GA)
3.2.2. A Hybrid Algorithm Gravitational Search Algorithm–Sequential Quadratic Programming (GSA–SQP)
4. Simulation Results and Discussion
- Radial Networks: IEEE 9-bus test system and IEC MG benchmark.
- Meshed Networks: IEEE 9-bus and IEEE 30-bus meshed networks.
4.1. Radial Networks
4.1.1. The Radial 9-Bus Test Systems
- Radial IEEE 9-Bus System without DGs: Mode 1 test results
- Radial IEEE 9-Bus System with DGs: Mode 2 test results
- Radial IEEE 9-Bus System under the islanding condition: Mode 3 test results
- Discussion of the Radial IEEE 9-Bus System results
4.1.2. The Radial IEC MG Test System
- The radial IEC MG Simulation Results in Mode 1
- The radial IEC MG Simulation Results in Mode 2
- The radial IEC MG Simulation Results in Mode 3
- Discussion of the radial IEC MG results
4.2. Meshed Networks
- The objective function for the IEEE 9-bus system is run on the MATLAB software; it includes the short-circuit calculation values for all points that have been illustrated in Figure 13 from point A to L.
- For example, when the fault occurs at the point A: for primary R1, backup R15, and R17, the fault current was 24779 A, 9150 A, and 15632 A, respectively. The OT of primary and backup relays for faults in A have been calculated based on Equation (4). The best value of the A parameter in Equation (4) will be determined by solving the cost function in Equation (6) by using GSA–SQP in the MATLAB platform.
4.2.1. Description of the Meshed 9-Bus Test Systems under Study
4.2.2. Description of the Meshed 30-Bus Test Systems under Study
4.2.3. Discussion of the Meshed Network Results
5. Conclusions
Author Contributions
Funding
Data Availability Statement
Conflicts of Interest
References
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Ref. | Year | Coefficient Types of Coordination Protection Scheme | Number of Variables | Modes of the Operation | DNs Types | Curve Used | |||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|
Constants | Variables | One Variable | Two Variables | Three Variables | Without DGs | Grid- Connecting | Islanding | Radial | Meshed | IEC NI Standard | Logarithmic Function | ||
[15] | 1993 | ✓ | ✗ | ✗ | ✗ | ✗ | ✓ | ✗ | ✗ | ✗ | ✓ | ✓ | ✗ |
[16] | 2014 | ✓ | ✗ | ✗ | ✗ | ✗ | ✓ | ✓ | ✗ | ✗ | ✓ | ✓ | ✗ |
[17] | 2017 | ✓ | ✗ | ✗ | ✗ | ✗ | ✓ | ✓ | ✗ | ✓ | ✗ | ✓ | ✗ |
[18] | 2018 | ✗ | ✓ | ✗ | ✗ | ✓ | ✗ | ✓ | ✗ | ✓ | ✗ | ✓ | ✗ |
[19] | 2007 | ✓ | ✗ | ✗ | ✓ | ✗ | ✓ | ✗ | ✗ | ✓ | ✗ | ✗ | ✓ |
[20] | 2017 | ✗ | ✓ | ✗ | ✗ | ✗ | ✗ | ✓ | ✗ | ✓ | ✓ | ✓ | ✗ |
[21] | 2017 | ✓ | ✗ | ✗ | ✗ | ✗ | - | - | - | ✓ | ✓ | ✓ | ✗ |
[22] | 2022 | ✗ | ✓ | ✗ | ✓ | ✗ | ✓ | ✗ | ✗ | ✗ | ✓ | ✓ | ✗ |
[23] | 2015 | ✗ | ✓ | ✗ | ✓ | ✗ | ✓ | ✓ | ✗ | ✗ | ✓ | ✓ | ✗ |
[24] | 2017 | ✓ | ✗ | ✗ | ✗ | ✗ | ✗ | ✓ | ✓ | ✓ | ✓ | ✓ | ✗ |
[25] | 2021 | ✓ | ✗ | ✗ | ✗ | ✗ | ✓ | ✓ | ✓ | ✓ | ✗ | ✗ | ✓ |
[26] | 2022 | ✓ | ✗ | ✗ | ✗ | ✗ | ✓ | ✓ | ✗ | ✓ | ✗ | ✗ | ✓ |
Proposed approach | ✗ | ✓ | ✓ | ✗ | ✗ | ✓ | ✓ | ✓ | ✓ | ✓ | ✗ | ✓ |
Stages | Explanation |
---|---|
Stage 1: Initiate the inhabitants | Applying IEEE9 and IEC MG models and calculating the short circuits. Early possible profiles of the OCR operation time (1000 profiles). |
Stage 2: Population assessment | For each solution, the prime assessment can be obtained via solving the optimum OF, Equation (5) under bounds from Equations (6) to (9). |
Stage 3: Selecting | The two most excellent OCR OT profiles will be selected as a parent. |
Stage 4: Crossing | For the following generation, a child profile will be launched, which will keep the popular genes while the rest of them will be chosen from the parent’s profile at random. The child profile must be a solution within the bounds of possibility. |
Stage 5: Mutating | In each iteration, a single gene is mutated to update the child profile randomly. In this study, the setting of mutation is 0.1 |
Step 6: The model output and optimal solution | Reaching the maximum number of iterations (200 iterations) by repeating the stages that have been mentioned above, starting with stage 2. |
Relays | STCC [25] TMS | NSS [25] TMS | NSTCC | |
---|---|---|---|---|
TMS | A | |||
R1 | 0.010 | 0.010 | 0.010 | 5.003 |
R2 | 0.139 | 0.171 | 0.300 | 5.000 |
R3 | 0.239 | 0.264 | 0.395 | 5.002 |
R4 | 0.322 | 0.345 | 0.486 | 5.000 |
R5 | 0.010 | 0.010 | 0.010 | 5.001 |
R6 | 0.139 | 0.171 | 0.300 | 5.000 |
R7 | 0.235 | 0.264 | 0.396 | 5.000 |
R8 | 0.319 | 0.345 | 0.479 | 5.017 |
R9 | 0.367 | 0.384 | 0.501 | 5.000 |
R10, R11, R12 | ||||
Overall OT(s) | 9.352 | 8.848 | 8.224 |
Relays | STCC [25] TMS | NSS [25] TMS | NSTCC | |
---|---|---|---|---|
TMS | A | |||
R1 | 0.010 | 0.010 | 0.010 | 5.001 |
R2 | 0.139 | 0.171 | 0.276 | 5.084 |
R3 | 0.237 | 0.264 | 0.397 | 5.001 |
R4 | 0.321 | 0.345 | 0.437 | 5.001 |
R5 | 0.010 | 0.0100 | 0.010 | 5.001 |
R6 | 0.139 | 0.166 | 0.277 | 5.022 |
R7 | 0.062 | 0.161 | 0.177 | 5.004 |
R8 | 0.237 | 0.258 | 0.373 | 5.017 |
R9 | 0.010 | 0.010 | 0.010 | 5.003 |
R10 | 0.010 | 0.010 | 0.010 | 5.002 |
R11 | 0.118 | 0.132 | 0.191 | 5.001 |
R12 | 0.367 | 0.384 | 0.466 | 5.001 |
Overall OT(s) | 11.282 | 10.353 | 9.327 |
Relays | STCC [25] TMS | NSS [25] TMS | NSTCC | |
---|---|---|---|---|
TMS | A | |||
R1 | ||||
R2 | ||||
R3 | ||||
R4 | ||||
R5 | 0.010 | 0.010 | 0.010 | 2.000 |
R6 | 0.039 | 0.077 | 0.291 | 2.050 |
R7 | 0.137 | 0.129 | 0.438 | 2.049 |
R8 | ||||
R9 | ||||
R10 | ||||
R11 | ||||
R12 | ||||
Overall, OT(s) | 1.373 | 1.34 | 1.187 |
[36] | [29] | [51] | [52] | NSTCC | ||
---|---|---|---|---|---|---|
Relay | TMS | TMS | TMS | TMS | Coefficient A | TMS Proposed |
R1 | ||||||
R2 | 0.128 | 0.0500 | 0.05 | 0.0500 | 4.800 | 0.0501 |
R3 | ||||||
R4 | 0.259 | 0.1787 | 4.58 | 0.2306 | 4.800 | 0.3977 |
R5 | ||||||
R6 | 0.402 | 0.3223 | 2.16 | 0.7715 | 4.886 | 0.9223 |
R7 | 0.290 | 0.2060 | 0.05 | 0.055 | 4.826 | 0.1117 |
R8 | ||||||
R9 | ||||||
R10 | 0.128 | 0.0500 | 0.05 | 0.0500 | 4.801 | 0.0500 |
R11 | ||||||
R12 | 0.010 | 0.0500 | 0.05 | 0.0500 | 4.800 | 0.0504 |
R13, R14, R15 | ||||||
OT(s) | 6.64 | 4.99 | 4.4 | 4.19 | - | 2.42 |
[36] | [29] | [51] | [52] | NSTCC | ||
---|---|---|---|---|---|---|
Relay | TMS | TMS | TMS | TMS | Coefficient A | TMS |
R1 | 0.174 | 0.137 | 0.217 | 0.3893 | 4.801 | 0.188 |
R2 | 0.139 | 0.050 | 0.050 | 0.050 | 4.800 | 0.251 |
R3 | 0.087 | 0.050 | 0.050 | 0.050 | 4.801 | 0.050 |
R4 | 0.278 | 0.189 | 0.235 | 0.421 | 4.801 | 0.066 |
R5 | 0.172 | 0.115 | 0.197 | 0.394 | 4.801 | 0.050 |
R6 | 0.401 | 0.320 | 1.550 | 0.819 | 4.853 | 3.000 |
R7 | 0.284 | 0.244 | 0.050 | 0.273 | 4.820 | 0.103 |
R8 | 0.223 | 0.191 | 0.567 | 0.606 | 4.801 | 0.050 |
R9 | 0.069 | 0.050 | 0.050 | 0.050 | 4.808 | 0.050 |
R10 | 0.141 | 0.050 | 0.050 | 0.050 | 4.801 | 0.050 |
R11 | 0.244 | 0.218 | 0.470 | 0.452 | 4.802 | 0.144 |
R12 | 0.150 | 0.050 | 0.050 | 0.050 | 4.840 | 0.050 |
R13 | 0.194 | 0.167 | 0.325 | 0.746 | 4.800 | 0.245 |
R14 | 0.116 | 0.100 | 0.104 | 0.172 | 4.801 | 0.145 |
R15 | 0.170 | 0.136 | 0.280 | 0.297 | 4.801 | 0.115 |
OT(s) | 17.48 | 13.66 | 11.6 | 12.48 | - | 4.69 |
[36] | [29] | [51] | [52] | NSTCC | ||
---|---|---|---|---|---|---|
Relay | TMS | TMS | TMS | TMS | Coefficient A | TMS |
R1 | 0.173 | 0.137 | 0.548 | 0.389 | 6.000 | 0.154 |
R2 | 0.105 | 0.050 | 0.050 | 0.050 | 6.000 | 0.050 |
R3 | 0.086 | 0.050 | 0.050 | 0.050 | 6.000 | 0.050 |
R4 | 0.211 | 0.157 | 0.938 | 0.529 | 6.000 | 0.365 |
R5 | 0.209 | 0.155 | 0.862 | 0.862 | 6.000 | 3.000 |
R6 | 0.181 | 0.151 | 0.685 | 0.243 | 6.000 | 3.000 |
R7 | ||||||
R8 | 0.248 | 0.218 | 0.519 | 0.499 | 6.000 | 0.376 |
R9 | 0.069 | 0.050 | 0.050 | 0.050 | 6.000 | 0.050 |
R10 | 0.112 | 0.050 | 0.050 | 0.050 | 6.000 | 0.050 |
R11 | 0.265 | 0.240 | 0.490 | 0.431 | 6.000 | 0.415 |
R12 | 0.105 | 0.050 | 0.050 | 0.050 | 6.000 | 0.050 |
R13 | 0.193 | 0.167 | 0.778 | 0.100 | 6.000 | 0.200 |
R14 | 0.116 | 0.099 | 0.372 | 0.104 | 6.000 | 0.117 |
R15 | 0.177 | 0.148 | 0.670 | 0.630 | 6.000 | 1.827 |
OT(s) | 15.56 | 12.63 | 9.99 | 8.96 | - | 4.055 |
Backup Relay | Primary Relay | CTI (s) | Backup Relay | Primary Relay | CTI (s) |
---|---|---|---|---|---|
15 | 1 | 0.200 | 11 | 13 | 0.200 |
17 | 1 | 0.218 | 21 | 13 | 0.200 |
4 | 2 | 0.200 | 16 | 14 | 0.200 |
1 | 3 | 0.200 | 19 | 14 | 0.200 |
6 | 4 | 0.200 | 13 | 15 | 0.200 |
3 | 5 | 0.200 | 19 | 15 | 0.201 |
8 | 6 | 0.200 | 2 | 16 | 0.200 |
23 | 6 | 0.203 | 17 | 16 | 0.200 |
5 | 7 | 0.200 | 2 | 18 | 0.309 |
23 | 7 | 0.200 | 15 | 18 | 0.317 |
10 | 8 | 0.200 | 13 | 20 | 0.322 |
7 | 9 | 0.200 | 16 | 20 | 0.322 |
12 | 10 | 0.200 | 11 | 22 | 0.309 |
9 | 11 | 0.200 | 14 | 22 | 0.320 |
14 | 12 | 0.203 | 5 | 24 | 0.318 |
21 | 12 | 0.235 | 8 | 24 | 0.315 |
Relay | STCC [8] | NSTCC with Constant Coefficient A | NSTCC | ||||||||
---|---|---|---|---|---|---|---|---|---|---|---|
TMS | Ip | TMS | A | Ip | TMS | A | Ip | ||||
R1 | 0.276 | 2.500 | 0.629 | 0.680 | 5.800 | 0.500 | 0.201 | 0.645 | 6.250 | 0.500 | 0.029 |
R2 | 0.091 | 2.500 | 0.332 | 0.107 | 5.800 | 0.500 | 0.157 | 0.102 | 6.250 | 0.500 | 0.155 |
R3 | 0.197 | 2.500 | 0.524 | 0.264 | 5.800 | 0.500 | 0.146 | 0.267 | 6.250 | 0.500 | 0.161 |
R4 | 0147 | 2.500 | 0.408 | 0.243 | 5.800 | 0.500 | 0.171 | 0.234 | 6.250 | 0.500 | 0.176 |
R5 | 0.139 | 2.500 | 0.470 | 0.110 | 5.800 | 0.500 | 0.143 | 0.118 | 6.250 | 0.500 | 0.159 |
R6 | 0.219 | 2.500 | 0.509 | 0.528 | 5.800 | 0.500 | 0.042 | 0.500 | 6.250 | 0.050 | 0.646 |
R7 | 0.221 | 2.500 | 0.515 | 0.553 | 5.800 | 0.500 | 0.044 | 0.521 | 6.250 | 0.050 | 0.674 |
R8 | 0.138 | 2.500 | 0.467 | 0.109 | 5.800 | 0.500 | 0.141 | 0.117 | 6.250 | 0.050 | 0.157 |
R9 | 0.148 | 2.500 | 0.402 | 0.244 | 5.800 | 0.500 | 0.157 | 0.234 | 6.250 | 0.500 | 0.163 |
R10 | 0.312 | 3.525 | 0.912 | 0.263 | 5.800 | 0.500 | 0.143 | 0.265 | 6.250 | 0.500 | 0.158 |
R11 | 0.148 | 2.500 | 0.402 | 0.107 | 5.800 | 0.500 | 0.157 | 0.102 | 6.250 | 0.500 | 0.155 |
R12 | 0.197 | 2.500 | 0.766 | 0.630 | 5.800 | 0.500 | 0.186 | 0.602 | 6.250 | 0.500 | 0.027 |
R13 | 0.092 | 2.500 | 0.334 | 0.175 | 5.800 | 0.500 | 0.101 | 0.145 | 6.250 | 0.500 | 0.091 |
R14 | 0.272 | 2.500 | 0.619 | 0.288 | 5.800 | 0.500 | 0.118 | 0.166 | 6.250 | 0.500 | 0.076 |
R15 | 0.190 | 2.500 | 0.508 | 0.299 | 5.800 | 0.500 | 0.123 | 0.165 | 6.250 | 0.500 | 0.075 |
R16 | 0.189 | 2.500 | 0.508 | 0.172 | 5.800 | 0.500 | 0.100 | 0.146 | 6.301 | 0.500 | 0.092 |
R17 | 0.500 | 0.542 | 0.287 | 5.800 | 0.890 | 0.000 | 0.179 | 6.250 | 0.813 | 0 | |
R18 | 0.072 | 1.979 | 0.232 | 0.034 | 5.800 | 1.553 | 0.103 | 0.010 | 6.364 | 0.500 | 0.015 |
R19 | 0.315 | 1.693 | 0.302 | 5.800 | 0.537 | 0.000 | 0.130 | 6.250 | 1.035 | 0 | |
R20 | 0.064 | 2.201 | 0.205 | 0.017 | 5.800 | 0.785 | 0.033 | 0.010 | 6.250 | 0.500 | 0.014 |
R21 | 0.482 | 0.597 | 0.188 | 5.800 | 1.445 | 0.000 | 0.116 | 6.250 | 1.632 | 0 | |
R22 | 0.092 | 1.902 | 0.229 | 0.049 | 5.800 | 0.668 | 0.093 | 0.010 | 6.250 | 0.500 | 0.015 |
R23 | 0.424 | 0.682 | 0.214 | 5.800 | 0.871 | 0.000 | 0.222 | 6.354 | 0.817 | 0 | |
R24 | 0.101 | 0.964 | 0.271 | 0.010 | 5.800 | 0.500 | 0.019 | 0.010 | 6.250 | 0.500 | 0.019 |
OT(s) | 8.892 | 2.377 | 1.870 |
Backup Relay | Primary Relay | CTI (s) | Backup Relay | Primary Relay | CTI (s) | Backup Relay | Primary Relay | CTI (s) |
---|---|---|---|---|---|---|---|---|
1 | 3 | 0.300 | 15 | 19 | 0.300 | 25 | 24 | 0.300 |
2 | 4 | 0.514 | 15 | 36 | 0.463 | 28 | 1 | 0.301 |
2 | 22 | 0.300 | 16 | 19 | 0.310 | 28 | 2 | 0.413 |
3 | 4 | 0.300 | 16 | 34 | 0.301 | 28 | 10 | 0.300 |
3 | 21 | 0.436 | 16 | 36 | 0.488 | 29 | 1 | 0.319 |
4 | 5 | 0.300 | 17 | 19 | 0.301 | 29 | 2 | 0.431 |
4 | 18 | 0.305 | 17 | 34 | 0.305 | 29 | 9 | 0.301 |
5 | 6 | 0.300 | 17 | 35 | 0.349 | 30 | 29 | 0.300 |
6 | 7 | 0.331 | 18 | 38 | 0.300 | 31 | 28 | 0.300 |
6 | 8 | 0.300 | 19 | 37 | 0.301 | 32 | 30 | 0.300 |
7 | 27 | 0.302 | 20 | 2 | 0.443 | 33 | 31 | 0.300 |
8 | 26 | 0.300 | 20 | 9 | 0.300 | 34 | 32 | 0.300 |
9 | 12 | 0.300 | 20 | 10 | 0.317 | 35 | 17 | 0.606 |
10 | 11 | 0.300 | 21 | 1 | 0.327 | 35 | 33 | 0.317 |
11 | 13 | 0.300 | 21 | 9 | 0.301 | 36 | 16 | 0.507 |
12 | 14 | 0.300 | 21 | 10 | 0.317 | 36 | 33 | 0.302 |
13 | 15 | 0.300 | 22 | 20 | 0.300 | 37 | 5 | 0.453 |
14 | 16 | 0.301 | 23 | 21 | 0.647 | 37 | 23 | 0.300 |
14 | 17 | 0.378 | 23 | 22 | 0.300 | 38 | 34 | 0.302 |
15 | 19 | 0.300 | 24 | 18 | 0.458 | 38 | 35 | 0.342 |
15 | 35 | 0.332 | 24 | 23 | 0.300 | 38 | 36 | 0.474 |
Relay | STCC [8] | NSTCC with Constant Coefficient A | NSTCC | ||||||||
---|---|---|---|---|---|---|---|---|---|---|---|
TMS | Ip | TMS | A | Ip | TMS | A | Ip | ||||
R1 | 0.304 | 3.816 | 0.901 | 0.647 | 5.800 | 1.595 | 0.458 | 0.550 | 4.301 | 2.294 | 0.274 |
R2 | 0.346 | 1.500 | 0.713 | 0.3223 | 5.800 | 2.207 | 0.352 | 0.331 | 4.185 | 2.594 | 0.164 |
R3 | 0.276 | 2.756 | 0.946 | 0.395 | 5.800 | 1.895 | 0.707 | 0.323 | 4.199 | 2.501 | 0.441 |
R4 | 0.258 | 2.693 | 0.766 | 0.424 | 5.800 | 1.669 | 0.525 | 0.477 | 4.089 | 1.892 | 0.237 |
R5 | 0.263 | 1.659 | 0.661 | 0.317 | 5.800 | 1.690 | 0.436 | 0.2932 | 4.212 | 2.438 | 0.317 |
R6 | 0.160 | 1.981 | 0.607 | 0.1801 | 5.800 | 1.831 | 0.443 | 0.1756 | 4.123 | 2.028 | 0.301 |
R7 | 0.173 | 1.824 | 0.430 | 0.203 | 5.800 | 1.529 | 0.215 | 0.2582 | 4.024 | 1.620 | 0.041 |
R8 | 0.157 | 1.587 | 0.372 | 0.190 | 5.800 | 1.500 | 0.199 | 0.227 | 4.121 | 1.689 | 0.074 |
R9 | 0.313 | 3.353 | 0.901 | 0.622 | 5.800 | 1.656 | 0.523 | 0.535 | 4.131 | 2.537 | 0.293 |
R10 | 0.312 | 3.525 | 0.912 | 0.713 | 5.800 | 1.500 | 0.487 | 0.746 | 4.188 | 2.174 | 0.278 |
R11 | 0.280 | 2.784 | 1.053 | 0.910 | 5.800 | 2.214 | 0.910 | 0.410 | 4.388 | 2.538 | 0.736 |
R12 | 0.217 | 3.594 | 0.765 | 0.440 | 5.800 | 1.500 | 0.525 | 0.392 | 4.099 | 1.946 | 0.252 |
R13 | 0.249 | 2.618 | 0.872 | 0.431 | 5.800 | 1.525 | 0.712 | 0.3734 | 4.141 | 2.523 | 0.538 |
R14 | 0.216 | 2.140 | 0.772 | 0.285 | 5.800 | 1.500 | 0.550 | 0.188 | 4.181 | 1.706 | 0.243 |
R15 | 0.233 | 1.606 | 0.757 | 0.298 | 5.800 | 1.500 | 0.612 | 0.283 | 4.116 | 1.836 | 0.408 |
R16 | 0.268 | 3.071 | 0.793 | 0.507 | 5.800 | 1.500 | 0.463 | 0.5937 | 4.089 | 1.660 | 0.083 |
R17 | 0.147 | 1.629 | 0.318 | 0.246 | 5.800 | 1.620 | 0.187 | 0.207 | 4.058 | 1.924 | 0.010 |
R18 | 0.241 | 2.493 | 0.735 | 0.439 | 5.800 | 1.500 | 0.562 | 0.416 | 4.119 | 1.946 | 0.312 |
R19 | 0.241 | 2.839 | 0.728 | 0.447 | 5.800 | 1.627 | 0.535 | 0.468 | 4.116 | 2.142 | 0.320 |
R20 | 0.144 | 2.398 | 0.499 | 0.254 | 5.800 | 1.500 | 0.430 | 0.217 | 4.143 | 1.943 | 0.256 |
R21 | 0.1604 | 1.500 | 0.377 | 0.201 | 5.800 | 1.855 | 0.277 | 0.179 | 4.194 | 1.874 | 0.106 |
R22 | 0.1702 | 4.008 | 0.694 | 0.358 | 5.800 | 1.945 | 0.624 | 0.363 | 4.144 | 2.518 | 0.449 |
R23 | 0.210 | 2.568 | 0.731 | 0.401 | 5.800 | 1.500 | 0.646 | 0.405 | 4.092 | 2.096 | 0.468 |
R24 | 0.202 | 2.236 | 0.772 | 0.302 | 5.800 | 2.158 | 0.764 | 0.346 | 4.084 | 2.168 | 0.596 |
R25 | 0.252 | 2.663 | 0.365 | 5.800 | 2.885 | 0.000 | 0.329 | 4.599 | 3.105 | 0.000 | |
R26 | 0.111 | 1.510 | 0.625 | 0.100 | 5.800 | 1.500 | 0.334 | 0.116 | 4.089 | 1.623 | 0.293 |
R27 | 0.122 | 1.636 | 0.557 | 0.100 | 5.800 | 1.500 | 0.285 | 0.107 | 4.021 | 1.597 | 0.210 |
R28 | 0.193 | 2.549 | 0.963 | 0.259 | 5.800 | 1.808 | 0.690 | 0.235 | 4.174 | 2.157 | 0.572 |
R29 | 0.164 | 2.673 | 0.731 | 0.2801 | 5.800 | 1.500 | 0.597 | 0.269 | 4.064 | 1.742 | 0.375 |
R30 | 0.184 | 3.672 | 0.901 | 0.378 | 5.800 | 1.797 | 0.808 | 0.366 | 4.101 | 2.371 | 0.589 |
R31 | 0.219 | 3.069 | 0.903 | 0.401 | 5.800 | 1.559 | 0.734 | 0.390 | 4.119 | 2.159 | 0.541 |
R32 | 0.209 | 3.217 | 0.953 | 0.473 | 5.800 | 1.500 | 0.910 | 0.487 | 4.159 | 1.906 | 0.685 |
R33 | 0.286 | 3.177 | 0.843 | 0.582 | 5.800 | 1.500 | 0.582 | 0.604 | 4.092 | 2.209 | 0.285 |
R34 | 0.252 | 3.661 | 0.834 | 0.629 | 5.800 | 1.500 | 0.631 | 0.712 | 4.098 | 1.962 | 0.329 |
R35 | 0.229 | 2.453 | 0.729 | 0.301 | 5.800 | 1.718 | 0.301 | 0.312 | 4.072 | 2.089 | 0.302 |
R36 | 0.100 | 1.500 | 0.222 | 0.140 | 5.800 | 4.168 | 0.315 | 0.123 | 4.636 | 2.725 | 0.161 |
R37 | 0.214 | 2.355 | 0.703 | 0.385 | 5.800 | 1.500 | 0.606 | 0.408 | 4.084 | 1.930 | 0.408 |
R38 | 0.194 | 2.888 | 0.790 | 0.352 | 5.800 | 1.644 | 0.690 | 0.217 | 4.108 | 2.046 | 0.418 |
OT(s) | 26.826 | 19.727 | 12.231 |
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Abeid, S.; Hu, Y.; Alasali, F.; El-Naily, N. Innovative Optimal Nonstandard Tripping Protection Scheme for Radial and Meshed Microgrid Systems. Energies 2022, 15, 4980. https://doi.org/10.3390/en15144980
Abeid S, Hu Y, Alasali F, El-Naily N. Innovative Optimal Nonstandard Tripping Protection Scheme for Radial and Meshed Microgrid Systems. Energies. 2022; 15(14):4980. https://doi.org/10.3390/en15144980
Chicago/Turabian StyleAbeid, Salima, Yanting Hu, Feras Alasali, and Naser El-Naily. 2022. "Innovative Optimal Nonstandard Tripping Protection Scheme for Radial and Meshed Microgrid Systems" Energies 15, no. 14: 4980. https://doi.org/10.3390/en15144980