# Investigating Various Severity Factor Behaviors for Operational Risk Assessment

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## 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, ${P}_{c}$.
- The quantification of severity factor, ${F}_{s}\left(c\right)$.

#### 2.2. Probability of Contingency ${P}_{c}$

- Component Unavailability Model $Q\left(t\right)$

- 2.
- Contingency Definition

#### 2.3. Severity Factors ${F}_{s}\left(c\right)$

- 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 ${F}_{UV}\left(c\right)$

#### 3.4. Mathematical Formulation of Overvoltage Severity Factor ${F}_{OV}\left(c\right)$

#### 3.5. Mathematical Formulation of Extreme-Loading Severity Factor ${F}_{EL}\left(c\right)$

#### 3.6. Mathematical Formulation of System Collapse Severity Factor ${F}_{SC}\left(c\right)$

## 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 ${F}_{EL}$ Behavior

#### 5.2. Operational Risk of Undervoltage ${F}_{UV}\left(c\right)$ Severity Factor Behavior

#### 5.3. Operational Risk of Overvoltage ${F}_{OV}\left(c\right)$ Severity Factor Behavior

#### 5.4. Operational Risk of System Collapse Severity Factor ${F}_{SC}\left(c\right)$ 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

- Billinton, R.; Bollinger, K.E. Transmission System Reliability Evaluation Using Markov Processes. IEEE Trans. Power Appar. Syst.
**1968**, PAS-87, 538–547. [Google Scholar] [CrossRef] - Mallard, S.A.; Thomas, V.C. A Method for Calculating Transmission System Reliability. IEEE Trans. Power Appar. Syst.
**1968**, PAS-87, 824–834. [Google Scholar] [CrossRef] - Billinton, R.; Allan, R.N. Reliability Assessment of Large Electric Power Systems; Springer Science & Business Media: Berlin/Heidelberg, Germany, 1988. [Google Scholar]
- Billinton, R.; Allan, R. Reliability Evaluation of Power Systems; Springer Science & Business Media: Berlin/Heidelberg, Germany, 1996. [Google Scholar]
- Endrenyi, J. Reliability Modelling in Electric Power Systems; Wiley: New York, NY, USA, 1978. [Google Scholar]
- Choi, J.; Tran, T.T.; El-Keib, A.A.; Thomas, R.J.; Oh, H.; Billinton, R. A method for transmission system expansion planning considering probabilistic reliability criteria. IEEE Trans. Power Syst.
**2005**, 20, 1606–1615. [Google Scholar] [CrossRef] - Rei, A.M.; da Silva, A.M.L.; Jardim, J.; Mello, J.C.O. Static and dynamic aspects in bulk power system reliability evaluations. IEEE Trans. Power Syst.
**2000**, 15, 189–195. [Google Scholar] [CrossRef] - Billinton, R. Composite System Reliability Evaluation. IEEE Trans. Power Appar. Syst.
**1969**, PAS-88, 276–281. [Google Scholar] [CrossRef] - Singh, C.; Mitra, J. Composite system reliability evaluation using state space pruning. IEEE Trans. Power Syst.
**1997**, 12, 471–479. [Google Scholar] [CrossRef] - Urgun, D.; Chanan, S. A Hybrid Monte Carlo Simulation and Multi Label Classification Method for Composite System Reliability Evaluation. IEEE Trans. Power Syst.
**2019**, 34, 908–917. [Google Scholar] [CrossRef] - Peng, L.; Hu, B.; Xie, K.; Tai, H.M.; Ashenayi, K. Analytical model for fast reliability evaluation of composite generation and transmission system based on sequential Monte Carlo simulation. Int. J. Electr. Power Energy Syst.
**2019**, 109, 548–557. [Google Scholar] [CrossRef] - Ramezanzadeh, S.P.; Mirzaie, M.; Shahabi, M. Reliability assessment of different HVDC transmission system configurations considering transmission lines capacity restrictions and the effect of load level. Int. J. Electr. Power Energy Syst.
**2021**, 128, 106754. [Google Scholar] [CrossRef] - Kamruzzaman, M.; Bhusal, N.; Benidris, M. A convolutional neural network-based approach to composite power system reliability evaluation. Int. J. Electr. Power Energy Syst.
**2021**, 135, 107468. [Google Scholar] [CrossRef] - Jun, Q.; Girgis, A. Optimization of power system reliability level by stochastic programming. Electr. Power Syst. Res.
**1993**, 26, 87–95. [Google Scholar] - Edimu, M.; Alvehag, K.; Gaunt, C.T.; Ronald, H. Analyzing the perfromance of a time-dependent probabilistic approaches for bulk network reliability assessment. Electr. Power Syst. Res.
**2013**, 104, 156–163. [Google Scholar] [CrossRef] - Heylen, E.; Ovaere, M.; Proost, S.; Deconink, G.; Hertem, D.V. A multi-dimensional analysis of reliability criteria: From deterministic N − 1 to a probabilistic approach. Electr. Power Syst. Res.
**2018**, 167, 290–300. [Google Scholar] [CrossRef] - Anstine, L.T.; Burke, R.E.; Casey, J.E.; Holgate, R.; John, R.S.; Stewart, H.G. Application of Probability Methods to the Determination of Spinning Reserve Requirements for the Pennsylvania-New Jersey-Maryland Interconnection. IEEE Trans. Power Appar. Syst.
**1963**, 82, 726–735. [Google Scholar] [CrossRef] - Wang, P.; Gao, Z.; Bertling, L. Operational Adequacy Studies of Power Systems With Wind Farms and Energy Storages. IEEE Trans. Power Syst.
**2012**, 27, 2377–2384. [Google Scholar] [CrossRef] - Janssen, A. Operating Considerations in Reliability of Modelling of Wind-Assisted Utility Systems. Wind Eng.
**1982**, 6, 193–205. [Google Scholar] - Vazquez, M.A.; Kirschen, D.S. Estimating the Spinning Reserve Requirements in Systems with Significant Wind Power Generation Penetration. IEEE Trans. Power Syst.
**2009**, 24, 114–124. [Google Scholar] [CrossRef] - Da Silva, A.M.L.L.; Sales, W.S.; Manso, L.A.D.F.; Billinton, R. Long-Term Probabilistic Evaluation of Operating Reserve Requirements With Renewable Sources. IEEE Trans. Power Syst.
**2010**, 25, 106–116. [Google Scholar] [CrossRef] - Billinton, R.; Karki, B.; Karki, R.; Ramakrishna, G. Unit Commitment Risk Analysis of Wind Integrated Power Systems. IEEE Trans. Power Syst.
**2009**, 24, 930–939. [Google Scholar] [CrossRef] - Bouffard, F.; Galiana, F.D. An electricity market with a probabilistic spinning reserve criterion. IEEE Trans. Power Syst.
**2004**, 19, 300–307. [Google Scholar] [CrossRef] - Zhou, Z.; Botterud, A. Dynamic Scheduling of Operating Reserves in Co-Optimized Electricity Markets with Wind Power. IEEE Trans. Power Syst.
**2013**, 29, 160–171. [Google Scholar] [CrossRef] - Patton, A. A probability method for bulk power system security assessment: I–basic concepts. IEEE Trans. Power Appar. Syst.
**1972**, PAS-91, 54–61. [Google Scholar] [CrossRef] - Patton, A. A probability method for bulk power system security assessment: II–development of probability methods for normally operating components. IEEE Trans. Power Appar. Syst.
**1972**, PAS-91, 2480–2485. [Google Scholar] [CrossRef] - Patton, A. A probability method for bulk power system security assessment: III–models for standby generators and field data collection and analysis. IEEE Trans. Power Appar. Syst.
**1972**, PAS-91, 2486–2493. [Google Scholar] [CrossRef] - Patton, A. Assessment of the security of operating electric power systems using probability methods. Proc. IEEE
**1974**, 62, 892–901. [Google Scholar] [CrossRef] - Singh, C.; Patton, A.; Lago-Gonzalez, A.; Vojdani, A.; Gross, G.; Wu, F.; Balu, N. Operating considerations in reliability modeling of interconnected systems-an analytical approach. IEEE Trans. Power Syst.
**1988**, 3, 1119–1126. [Google Scholar] [CrossRef] - Da Silva, A.M.L.; Endrenyi, J.; Wang, L. Integrated treatment of adequacy and security in bulk power system reliability evaluations. IEEE Trans. Power Syst.
**1993**, 8, 275–285. [Google Scholar] [CrossRef] - Loparo, K.A.; Malek, F.A. A probabilistic approach to dynamic power system security. IEEE Trans. Circuits Syst.
**1990**, 37, 787–798. [Google Scholar] [CrossRef] - Khan, M.; Roy, B. Composite system spinning reserve assessment in interconnected systems. IEEE Proc. Gener. Transm. Distrib.
**1995**, 142, 305–309. [Google Scholar] [CrossRef] - Gooi, H.B.; Mendes, D.; Bell, K.; Kirschen, D.S.; Kirschen, D.S. Optimal scheduling of spinning reserve. IEEE Trans. Power Syst.
**1999**, 14, 1485–1492. [Google Scholar] [CrossRef] - Da Silva, A.L.; Alvarez, G. Operating reserve capacity requirements and pricing in deregulated markets using probabilistic techniques. IET Gener. Transm. Distrib.
**2007**, 1, 439–446. [Google Scholar] [CrossRef] - Zio, E. The future of risk assessment. Reliab. Eng. Syst. Saf.
**2018**, 177, 176–190. [Google Scholar] [CrossRef] - Li, W. Risk Assessment of Power Systems Models, Methods and Applications; John Wiley & Sons: New York, NY, USA, 2014. [Google Scholar]
- Ciapessoni, E.; Cirio, D.; Kjølle, G.; Massucco, S.; Pitto, A.; Sforna, M. Probabilistic Risk-Based Security Assessment of Power Systems Considering Incumbent Threats and Uncertainties. IEEE Trans. Smart Grid
**2016**, 7, 2890–2903. [Google Scholar] [CrossRef] - Vefsnmo, H.; Kjølle, G.; Jakobsen, S.H.; Ciapessoni, E.; Cirio, D.; Pitto, A. Risk assessment tool for operation: From threat models to risk indicators. In Proceedings of the 2015 IEEE Eindhoven PowerTech, Eindhoven, The Netherlands, 29 June–2 July 2015. [Google Scholar]
- Li, W.; Korczynski, J. Risk evaluation of transmission system operation modes: Concept, method and application. In Proceedings of the 2002 IEEE Power Engineering Society Winter Meeting Conference Proceedings (Cat. No.02CH37309), New York, NY, USA, 27–31 January 2002. [Google Scholar]
- Perninge, M.; Söder, L. A Stochastic Control Approach to Manage Operational Risk in Power Systems. IEEE Trans. Power Syst.
**2011**, 27, 1021–1031. [Google Scholar] [CrossRef] - Jmii, H.; Meddeb, A.; Chebbi, S. Newton-Raphson Load Flow Method for Voltage Contingency Ranking. In Proceedings of the 2018 15th International Multi-Conference on Systems, Signals & Devices (SSD), Yasmine Hammamet, Tunisia, 19–22 March 2018. [Google Scholar]
- Singh, S.N.; Srivastava, L.; Sharma, J. Fast voltage contingency screening and ranking using cascade neural network. Electr. Power Syst. Res.
**2000**, 53, 197–205. [Google Scholar] [CrossRef] - Pandit, M.; Srivastava, L.; Sharma, J. Cascade fuzzy neural network based voltage contingency screening and ranking. Electr. Power Syst. Res.
**2003**, 67, 143–152. [Google Scholar] [CrossRef] - Mikolinnas, T.A.; Wollenberg, B. An Advanced Contingency Selection Algorithm. IEEE Trans. Power Appar. Syst.
**1981**, PAS-100, 608–617. [Google Scholar] [CrossRef] - Du, Y.; Li, F.; Li, J.; Zheng, T. Achieving 100x Acceleration for N-1 Contingency Screening With Uncertain Scenarios Using Deep Convolutional Neural Network. IEEE Trans. Power Syst.
**2019**, 34, 3303–3305. [Google Scholar] [CrossRef] - Kaplunovich, P.; Turitsyn, K. Fast and Reliable Screening of N-2 Contingencies. IEEE Trans. Power Syst.
**2016**, 31, 4243–4252. [Google Scholar] [CrossRef] - Almeida, S.A.B.d.; Pestana, R.; Barbosa, F.M. Integration of common cause faults in the operational probabilistic approach. In Proceedings of the 2010 IEEE 11th International Conference on Probabilistic Methods Applied to Power Systems, Singapore, 14–17 June 2010. [Google Scholar]
- Bhuiyan, M.Z.A.; Anders, G.J.; Philhower, J.; Du, S. Review of static risk-based security assessment in power system. IET Cyber-Phys. Syst. Theory Appl.
**2019**, 4, 233–239. [Google Scholar] [CrossRef] - Wan, H.; McCalley, J.D.; Vittal, V. Risk Based Voltage Security Assessment. IEEE Trans. Power Syst.
**2000**, 15, 1247–1254. [Google Scholar] [CrossRef] - Dai, Y.; McCalley, J.D.; Samra, N.A.; Vittal, V. Annual Risk Assessment for Overload Security. IEEE Trans. Power Syst.
**2001**, 16, 616–623. [Google Scholar] [CrossRef] - Feng, Y.; Wu, W.; Zhang, B.; Li, W. Power System Operation Risk Assessment Using Credibility Theory. IEEE Trans. Power Syst.
**2008**, 23, 1309–1318. [Google Scholar] [CrossRef] - Ni, M.; McCalley, J.D.; Vittal, V.; Tayyib, T. Online Risk-Based Security Assessment. IEEE Trans. Power Syst.
**2003**, 18, 258–265. [Google Scholar] [CrossRef] - Ni, M.; McCalley, J.D.; Vittal, V.; Greene, S.; Ten, C.-W.; Ganugula, V.S.; Tayyib, T. Software Implementation of Online Risk-Based Security Assessment. IEEE Trans. Power Syst.
**2003**, 18, 1165–1172. [Google Scholar] [CrossRef] - Jong, M.D.; Papaefthymiou, G.; Palensky, P. A Framework for Incorporation of Infeed Uncertainty in Power System Risk-Based Security Assessment. IEEE Trans. Power Syst.
**2017**, 33, 613–621. [Google Scholar] [CrossRef] - Bollen, M.; Nazir, Z. Operational Risk Assessment–Time for a Smarter Look at Reliability for Power Transmission Systems. 2022. Available online: https://smartgrid.ieee.org/bulletins/june-2022/operational-risk-assessment-time-for-a-smarter-look-at-reliability-for-power-transmission-systems (accessed on 20 July 2022).
- Liu, P.Q.; Li, H.-Q.; Du, Y.; Zeng, K. Risk assessment of power system security based on component importance and operation state. In Proceedings of the 2014 International Conference on Power System Technology, Chengdu, China, 20–22 October 2014. [Google Scholar]
- Ciapessoni, E.; Cirio, D.; Grillo, S.; Massucco, S.; Pitto, A.; Silvestro, F. Operational Risk Assessment and control: A probabilistic approach. In Proceedings of the 2010 IEEE PES Innovative Smart Grid Technologies Conference Europe (ISGT Europe), Gothenburg, Sweden, 11–13 October 2010. [Google Scholar]
- Winter, W.H. Measuring and reporting overall reliability of bulk electricity systems. In Proceedings of the 1980CIGRE Session, Paris, France, 27 August–4 September 1980. Paper No. 32-15. [Google Scholar]
- Winter, W.H. Disturbance performance of bulk electricity systems. In Proceedings of the 1986 C1GRE Session, Paris, France, 27 August–4 September 1986. Paper No. 37/38/39-02. [Google Scholar]
- Schneider, A.; Raksany, J.; Gunderson, R.; Fong, C.; Roy, B.; Neill, P.M.O.; Silverstein, B. Bulk system reliability-measurement and indices. IEEE Trans. Power Syst.
**1989**, 4, 829–835. [Google Scholar] [CrossRef] - 5th CEER Benchmarking Report on the Quality of Electricity Supply. 2005. Available online: https://www.ceer.eu/documents/104400/-/-/0f8a1aca-9139-9bd4-e1f5-cdbdf10c4609 (accessed on 20 July 2022).
- Allan, R. Power system reliability assessment—A conceptual and historical review. Reliab. Eng. Syst. Saf.
**1994**, 46, 3–13. [Google Scholar] [CrossRef] - Nazir, Z.; Bollen, M.H. Operational Risk Assessment of Transmission Systems: A review. Int. J. Electr. Power Energy Syst.
**2022**. submitted. [Google Scholar] - Cupelli, M.; Cardet, C.D.; Monti, A. Voltage stability indices comparison on the IEEE-39 bus system using RTDS. In Proceedings of the 2012 IEEE International Conference on Power System Technology (POWERCON), Auckland, New Zealand, 30 October–2 November 2012. [Google Scholar]
- Rahmouni, W.; Benasla, L. Transient stability analysis of the IEEE 39-bus power system using gear and block methods. In Proceedings of the 2017 5th International Conference on Electrical Engineering-Boumerdes (ICEE-B), Boumerdes, Algeria, 29–31 October 2017. [Google Scholar]
- Kundur, P. Power System Stability and Control, Toronto; McGraw-Hill: New York, NY, USA, 2022. [Google Scholar]
- IEEE. 1366-2012 IEEE Guide for Electric Power Distribution Reliability Indices; IEEE Standard Association: Piscataway, NJ, USA, 2012. [Google Scholar]
- Song, X.; Wang, Z.; Xin, H.; Gan, D. Risk-based dynamic security assessment under typhoon weather for power transmission system. In Proceedings of the 2013 IEEE PES Asia-Pacific Power and Energy Engineering Conference (APPEEC), Hong Kong, China, 8–11 December 2013. [Google Scholar]
- Pour, M.M.; Taheri, I.; Marzooni, M.H. Assessment of transmission outage Contingencies’ effects on bidding strategies of electricity suppliers. Int. J. Electr. Power Energy Syst.
**2020**, 120, 106053. [Google Scholar] - Valle, L.D.; Fantazzini, D.; Giudici, P. Copulae and Operational Risks. Int. J. Risk Assess. Manag. Forthcom.
**2006**, 9, 238–257. [Google Scholar] - Giudici, P.; Bilotta, A. Modelling Operational Losses: A Bayesian Approach. Qual. Reliab. Eng. Int.
**2004**, 20, 407–417. [Google Scholar] [CrossRef] - Jorion, P. Value at Risk-The New Benchmark for Managing Financial Risk, 3rd ed.; McGraw-Hill Professional: New York, NY, USA, 2007. [Google Scholar]
- IEEE. P1366/D5-IEEE Draft Guide for Electric Power Distribution Reliability Indices; IEEE: Piscataway, NJ, USA, 2022; pp. 1–40. [Google Scholar]

**Figure 8.**Severity factor in terms of number of non-convergence contingencies under different operating conditions.

**Table 1.**OREL: Contingencies comparison under two operating conditions, where the yellow color indicates that these contingencies are contributing to the operational risk and the red color that they are not contributing.

40% GLL (5th OC) | 50% GLL (6th OC) | ||||
---|---|---|---|---|---|

${C}_{n}$ | OREL | ORSC | ${C}_{n}$ | OREL | ORSC |

1389 | ✓ | ✖ | 1389 | ✖ | ✓ |

537 | ✓ | ✖ | 537 | ✖ | ✓ |

414 | ✓ | ✖ | 414 | ✖ | ✓ |

1121 | ✓ | ✖ | 1121 | ✖ | ✓ |

786 | ✓ | ✖ | 786 | ✖ | ✓ |

536 | ✓ | ✖ | 536 | ✖ | ✓ |

1331 | ✓ | ✖ | 1331 | ✖ | ✓ |

861 | ✓ | ✖ | 861 | ✖ | ✓ |

**Table 2.**ORUV: Contingency comparison under two operating conditions, where the yellow color indicates that these contingencies are contributing to the operational risk and the red color that they are not contributing.

70% GLL | 80% GLL | ||||
---|---|---|---|---|---|

${C}_{n}$ | ORUV | ORSC | ${C}_{n}$ | 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 |

**Table 4.**Severity factor behavior of operational risk of undervoltage for varying operating conditions.

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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**MDPI and ACS Style**

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

**AMA Style**

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 Style**

Nazir, 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