Investigating Various Severity Factor Behaviors for Operational Risk Assessment
Abstract
:1. Introduction
- Four different severity factor definitions are proposed, quantifying four different impacts of a contingency on the transmission system: extreme loading; overvoltage; undervoltage; and voltage instability. A general formulation is given, and for three of the four definitions, a numerical threshold is proposed.
- The operational risk is calculated and analyzed for these four definitions, using a commonly used test system, the IEEE 39-Bus New England system, under varying operating conditions.
- The behavior of the severity factor for individual contingencies is compared with the behavior of the operational risk index for the system as a whole, for increasing system loading. It is shown that multiple definitions of severity factor, and thus of operational risk indices, are needed to obtain a complete picture of the operational security of a transmission system.
2. Operational Risk Calculation
2.1. Operational Risk Procedural Flow
- The computation of probability of contingency, .
- The quantification of severity factor, .
2.2. Probability of Contingency
- Component Unavailability Model
- 2.
- Contingency Definition
2.3. Severity Factors
- Severity factor for overvoltage.
- Severity factor for undervoltage.
- Severity factor for extreme loading.
- Severity factor for system collapse.
2.4. Reliability and Operational Risk Indices
2.5. Case Study
3. Designing of Technical Severity Factors and Their Thresholds
3.1. Alternative Severity Factors
- Technical severity factors, quantifying the impact of a contingency in terms of voltage, current, power, etc., in the transmission grid.
- Economic severity factors, quantifying the contingency impact in terms of financial consequences for the grid owner and/or the customers.
- Customer severity factors, quantifying the contingency impact on the customers, e.g., to quantify the number of customers affected by the contingency.
3.2. Attributes of Severity Factor
- The SF should represent the consequences of a certain contingency.
- The SF should be understandable physically in the grid.
- The SF should be deterministic, and it should show the degree of violation.
- The voltage should be within a certain band.
- The current or loading of the equipment should be below a certain maximum permissible value.
- The system should be voltage-stable. The severity factor is calculated for steady-state analysis.
3.3. Mathematical Formulation of Undervoltage Severity Factor
3.4. Mathematical Formulation of Overvoltage Severity Factor
3.5. Mathematical Formulation of Extreme-Loading Severity Factor
3.6. Mathematical Formulation of System Collapse Severity Factor
4. System-Level Operational Risk Behavior under Varying Operating Conditions
4.1. Operational Risk of Extreme Loading (OREL) Behavior under Varying Operating Conditions
4.2. Operational Risk of Overvoltage (OROV) Behavior under Varying Operating Conditions
4.3. Operational Risk of Undervoltage (ORUV) Behavior under Varying Operating Conditions
4.4. Operational Risk of System Collapse (ORSC) Behavior
4.5. Interrelation between Various System-Level Operational Risks
5. Further Analysis of Severity Factor Behavior under Varying Operating Conditions
5.1. Operational Risk of Extreme Loading Severity Factor Behavior
5.2. Operational Risk of Undervoltage Severity Factor Behavior
5.3. Operational Risk of Overvoltage Severity Factor Behavior
5.4. Operational Risk of System Collapse Severity Factor Behavior
6. Discussion
6.1. Technical Severity Factor
6.2. Customer Severity Factor
6.3. Economic Severity Factor
6.4. Standardization of Severity Factors
6.5. Additional Further Work
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Conflicts of Interest
References
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40% GLL (5th OC) | 50% GLL (6th OC) | ||||
---|---|---|---|---|---|
OREL | ORSC | OREL | ORSC | ||
1389 | ✓ | ✖ | 1389 | ✖ | ✓ |
537 | ✓ | ✖ | 537 | ✖ | ✓ |
414 | ✓ | ✖ | 414 | ✖ | ✓ |
1121 | ✓ | ✖ | 1121 | ✖ | ✓ |
786 | ✓ | ✖ | 786 | ✖ | ✓ |
536 | ✓ | ✖ | 536 | ✖ | ✓ |
1331 | ✓ | ✖ | 1331 | ✖ | ✓ |
861 | ✓ | ✖ | 861 | ✖ | ✓ |
70% GLL | 80% GLL | ||||
---|---|---|---|---|---|
ORUV | ORSC | ORUV | ORSC | ||
801 | ✓ | ✖ | 801 | ✖ | ✓ |
892 | ✓ | ✖ | 892 | ✖ | ✓ |
659 | ✓ | ✖ | 659 | ✖ | ✓ |
993 | ✓ | ✖ | 993 | ✖ | ✓ |
142 | ✓ | ✖ | 142 | ✖ | ✓ |
700 | ✓ | ✖ | 700 | ✖ | ✓ |
1170 | ✓ | ✖ | 1170 | ✖ | ✓ |
Contingency Probability | 0.008 | 0.0631 | 0.0378 | 0.0841 | 0.042 | 0.0796 | 0.1055 | 0.0573 | 0.0615 | 0.1849 | 0.114 |
Contingency Number | 2 | 137 | 377 | 414 | 446 | 537 | 555 | 950 | 952 | 1331 | 1356 |
Std OC | 123% | 238.90% | 282.00% | 576.10% | 361.10% | 244% | 499% | 383.10% | 273.10% | 254.90% | 358.80% |
10% (2nd OC) | 136.40% | 263.90% | 159.50% | 650.50% | 407.70% | 166% | 773.90% | 428.30% | 302.80% | 440.10% | N.C |
20% (3rd OC) | 150.10% | 289.50% | 341.40% | 734.20% | 460.80% | 185% | N.C | 477.50% | OV | 494.30% | N.C |
30% (4th OC) | 164.40% | 315.90% | 372.20% | 834.50% | 526.60% | 208.20% | N.C | 533.50% | OV, UV | 558.40% | N.C |
40% (5th OC) | 179.40% | 343.20% | 403.90% | 987.80% | N.C | 632.50% | N.C | OV, UV | OV, UV | 650.20% | N.C |
50% (6th OC) | 204.80% | 1661% | 435.80% | N.C | N.C | N.C | N.C | 870.10% | OV, UV | N.C | N.C |
60% (7th OC) | 369.50% | 401.90% | 471.10% | N.C | N.C | N.C | N.C | N.C | 473.60% | N.C | N.C |
70% (8th OC) | 403.20% | 434.30% | 508.40% | N.C | N.C | N.C | N.C | N.C | 517% | N.C | N.C |
80% (9th OC) | 443.10% | 470.10% | 548.50% | N.C | N.C | N.C | N.C | N.C | 571.40% | N.C | N.C |
90% (10th OC) | 403.20% | 434% | 508.40% | N.C | N.C | N.C | N.C | N.C | 517% | N.C | N.C |
Contingency Probability | 0.0567 | 0.1849 | 0.1002 | 0.103 | 0.1057 | 0.114 | 0.1223 | 0.1528 | 0.1094 | 0.1151 |
Contingency Number | 891 | 1331 | 1351 | 1352 | 1353 | 1356 | 1359 | 1370 | 1405 | 1407 |
STD: OC | 1.1642 | 1.3305 | 1.0372 | 0.9891 | 1.1097 | 1.6016 | 1.159 | 1.3767 | 1.1555 | 1.017 |
10%GLL (2nd OC) | 1.3363 | 1.6962 | 1.5358 | 1.2538 | 1.6033 | N.C | 1.4345 | 2.3204 | 1.8285 | 2.7823 |
20%GLL (3rdOC) | 1.557 | 2.0903 | N.C | 1.7328 | N.C | N.C | 1.848 | 3.7776 | 2.8812 | N.C |
30%GLL (4th OC) | 1.8683 | 2.6369 | N.C | N.C | N.C | N.C | 2.3334 | N.C | N.C | N.C |
40%GLL (5th OC) | 2.47 | 3.8621 | N.C | N.C | N.C | N.C | 3.387 | N.C | N.C | N.C |
50%GLL (6th OC) | N.C | N.C | N.C | N.C | N.C | N.C | N.C | N.C | N.C | N.C |
60%GLL (7th OC) | N.C | N.C | N.C | N.C | N.C | N.C | N.C | N.C | N.C | N.C |
70%GLL (8th OC) | N.C | N.C | N.C | N.C | N.C | N.C | N.C | N.C | N.C | N.C |
80%GLL (9th OC) | N.C | N.C | N.C | N.C | N.C | N.C | N.C | N.C | N.C | N.C |
90%GLL (10th OC) | N.C | N.C | N.C | N.C | N.C | N.C | N.C | N.C | N.C | N.C |
Contingency Probability | 0.05 | 0.0107 | 0.0569 | 0.0225 | 0.0236 | 0.0268 | 0.1402 | 0.1459 | 0.1204 | 0.073 | 0.0818 | 0.0924 |
Contingency Number | 56 | 77 | 130 | 229 | 230 | 233 | 875 | 878 | 980 | 1015 | 1019 | 1190 |
STD (OC) | 0.0605 | 0.0729 | 0.0617 | 0.0958 | 0.133 | 0.0631 | 0.0863 | 0.0658 | 0.0801 | 0.1017 | 0.0912 | 0.0752 |
10%GLL (2nd OC) | 0.0597 | 0.0682 | 0.0567 | 0.0337 | 0.1196 | 0.0595 | 0.0859 | 0.0636 | 0.0849 | 0.1071 | 0.0867 | 0.079 |
20%GLL (3rd OC) | 0.0583 | 0.0571 | 0.0518 | 0.0209 | 0.0374 | 0.0451 | 0.0813 | 0.0466 | 0.0852 | 0.1132 | 0.0884 | 0.0835 |
30%GLL (4th OC) | 0.0563 | 0.0528 | 0.0522 | 0.0046 | 0.0276 | 0.0452 | 0.0279 | 0.044 | 0.0908 | 0.1201 | 0.0689 | 0.0893 |
40% GLL (5th OC) | 0.0535 | 0.0417 | 0.0525 | 0.0039 | 0.0069 | 0.0453 | 0.0177 | 0.0438 | 0.0972 | 0.1278 | 0.0696 | 0.0957 |
50%GLL (6th OC) | 4.80 × 10−2 | 3.98 × 10−9 | 8.02 × 10−10 | 3.44 × 10−9 | 0.0073 | 1.22 × 10−9 | 0.0198 | 3.44 × 10−10 | 0.0803 | 0.1371 | 0.0057 | 0.1124 |
60% GLL (7th OC) | 2.47 × 10−2 | 4.73 × 10−9 | 2.14 × 10−9 | 2.14 × 10−9 | 2.14 × 10−9 | 1.67 × 10−9 | 2.14 × 10−9 | 2.14 × 10−9 | 5.99 × 10−2 | 0.1462 | 1.49 × 10−8 | 1.12 × 10−1 |
70% GLL(8th OC) | 1.96 × 10−2 | 6.61 × 10−9 | 6.78 × 10−9 | 6.77 × 10−9 | 6.79 × 10−9 | 6.06 × 10−9 | 6.79 × 10−9 | 6.76 × 10−9 | 6.27 × 10−2 | 0.1571 | 2.58 × 10−8 | 5.26 × 10−2 |
80% GLL (9th OC) | 1.43 × 10−8 | 5.30 × 10−8 | 2.13 × 10−8 | 2.14 × 10−8 | 2.13 × 10−8 | 2.03 × 10−9 | N.C | 2.13 × 10−8 | 2.14 × 10−8 | N.C | 4.12 × 10−8 | 5.66 × 10−2 |
90%GLL (10th OC) | 6.57 × 10−8 | 6.61 × 10−8 | 6.60 × 10−8 | N.C | 6.40 × 10−8 | 6.44 × 10−9 | N.C | 6.58 × 10−8 | 6.61 × 10−8 | N.C | 5.57 × 10−8 | 6.13 × 10−2 |
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Nazir, Z.; Bollen, M.H.J. Investigating Various Severity Factor Behaviors for Operational Risk Assessment. Electricity 2022, 3, 325-345. https://doi.org/10.3390/electricity3030018
Nazir Z, Bollen MHJ. Investigating Various Severity Factor Behaviors for Operational Risk Assessment. Electricity. 2022; 3(3):325-345. https://doi.org/10.3390/electricity3030018
Chicago/Turabian StyleNazir, Zunaira, and Math H. J. Bollen. 2022. "Investigating Various Severity Factor Behaviors for Operational Risk Assessment" Electricity 3, no. 3: 325-345. https://doi.org/10.3390/electricity3030018
APA StyleNazir, Z., & Bollen, M. H. J. (2022). Investigating Various Severity Factor Behaviors for Operational Risk Assessment. Electricity, 3(3), 325-345. https://doi.org/10.3390/electricity3030018