# Enhanced Contingency Analysis—A Power System Operator Tool

^{1}

^{2}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Traditional Power System N-1 Contingency Analysis

- I
_{i−j}is the branch current (line or transformer) and - U
_{i}is the i-th node voltage.

## 3. Voltage Stability Analysis

- ΔP—bus incremental active power change,
- ΔQ—bus incremental reactive power change,
- ΔV—bus incremental voltage magnitude change,
- Δθ—bus incremental voltage phase change.

_{P}

_{θ}, J

_{PV}, J

_{Q}

_{θ}and J

_{QV}are the active power sensitivity to bus voltage phase change, active power sensitivity to bus voltage magnitude change, reactive power sensitivity to bus voltage phase change, and reactive power sensitivity to bus voltage magnitude change, respectively.

_{R}is called the reduced Jacobian matrix of the system and directly relates bus voltage magnitude with reactive power injection.

_{R}, eigenvalues ${\lambda}_{i}$ and the corresponding right and left eigenvectors are obtained. In fact, the eigenvalues and the right and left eigenvectors, similar to the concepts used in dynamic system analysis, define the modes of voltage instability. However, contrary to the concepts common in angle stability analysis, the smaller the size of an eigenvalue, the weaker the corresponding modal voltage. If a voltage mode eigenvalue equals zero it is a clear indication of imminent voltage collapse because any variation in modal reactive power will cause infinite modal voltage variation. If, however, an eigenvalue has a negative value it indicates that the system has passed the critical point of voltage stability. Therefore, the values of the eigenvalues indicate the modes (areas) that are most prone to voltage instability (modes with the smallest eigenvalues). However, the value of an eigenvalue itself is not a quantitative indicator, it is only a “warning signal” that has to be further “investigated” by proper analysis, as per the proposed methodology given in Section 5.

_{l_max_i}is the maximum incremental change of reactive loading on line l-k for all the modes, and ΔQ

_{g_max_i}is the maximum incremental change of reactive power variation on generator g for all the modes, ΔQ

_{l−k_i}is the incremental change of reactive power loss on line l-k for mode i, and ΔQ

_{g_i}is the incremental change of reactive power variation on generator g for mode i.

## 4. Reactive Power Resources and the Effect of Load Modeling on Voltage Stability

#### 4.1. Synchronous Generators

#### 4.2. Distributed Energy Resources (DERs)

#### 4.3. Battery Energy Storage Systems

#### 4.4. Regulation Transformers (Under Load Tap Changers—ULTCs)

#### 4.5. Electric Load Composition

- P
_{L}is the actual active load power, - Q
_{L}is the actual reactive load power, - P
_{0}is the base value of active load power at nominal voltage, - Q
_{0}is the base value of reactive load power at nominal voltage, - V
_{0}is the nominal voltage, - V
_{L}is the actual voltage, - α
_{Z}, α_{I}, α_{P}are the proportion of constant impedance load, constant current load and constant power load for real power, respectively. β_{Z}, β_{I}and β_{P}are similar quantities for reactive power.

## 5. Extended Contingency Analysis

_{V}[24]:

- $\left|{V}_{i}\right|$—voltage magnitude at bus i,
- $\left|{V}_{i}^{r}\right|$—rated voltage magnitude at bus i,
- $\u2206{V}_{i}^{lim}$—voltage deviation limit, above which voltage deviations are unacceptable,
- n—number of buses in the system,
- w
_{i}—real non-negative weighting factor to give higher weights to critical buses, - α—exponent of penalty function (α = 1 preferred).

- reactive power capability of distributed generation,
- energy storage reactive capability,
- synchronous generators reactive capability, and
- regulation transformer action.

## 6. Simulations

## 7. Results and Discussion

_{min}), indicating a possible voltage instability area. Although the second column of Table 2 indicates the mode with the smallest eigenvalue (λ

_{min}), this value alone does not tell the system operator how close the system is to voltage instability. The most valuable information is given to the system operator in columns three and four, resulting from inspection of calculated P-V and Q-V curves for buses belonging to the weakest mode. Actually, the third and fourth column explicitly give the absolute distance of a specific node (bus) from the point of voltage instability in terms of possible active and reactive loading increase, respectively. The last column confirms qualitatively what columns three and four express quantitatively, i.e., column five gives the voltage sensitivity factor of bus nodes to bus reactive power injection and thus indicates the “weakest” nodes in terms of voltage stability but gives no information on how close the system to voltage instability is.

#### 7.1. Distributed Energy Resources/Battery Energy Storage (DER/BES)

_{Qmax}, 8

_{Pmax}, 11

_{Pmax}means the operating point of the DER/BES connected at node 5 was changed from maximum active production to maximum reactive production, while the DER/BES connected at nodes 8 and 11 remains in maximum active power production regime). The third column demonstrates the increase of the corresponding eigenvalue, indicating the moving of the system away from voltage instability. Columns four and five give the allowable increase in active and reactive loading before reaching the critical point on the bus most prone to voltage instability (column four gives the percentage value of the overall active power increase from the base scenario, while column five presents the maximum possible reactive power increase for the selected node). Finally, column six gives the PIV index calculated by (7), which is used for ranking of the considered remedial actions. Of course, the ranking of remedial actions can consider other indices based on, e.g., ΔP or ΔQ, or some other combination as in [24].

#### 7.2. Synchronous Generators (SGs)

_{new}/λ

_{new}) and the possibility to increase reactive loading at the critical bus No. 6. The voltage-based performance index decreased as the voltage deviations in the analyzed subsystem also decreased with higher injection of reactive power in node 1. The overall active power loading of the analyzed subsystem remained unchanged. In the remaining two cases the reactive power output at node 1 was further increased by 10 and 20 Mvar, respectively. The results were similar to the ones in the first case, thus suggesting the inappropriateness of the considered countermeasure against voltage instability, compared to the previously considered remedial actions.

#### 7.3. Regulation Transformers

#### 7.4. Load Modeling Effects on Voltage Stability Analysis

## 8. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

## Appendix A

Line | R_{1}[Ω/km] | X_{1}[Ω/km] | B_{1}[µS/km] | l [km] | Imax [A] |
---|---|---|---|---|---|

1–2 | 0.12 | 0.4 | 2.89 | 14.0 | 645 |

1–3 | 0.12 | 0.4 | 2.89 | 29.9 | 645 |

1–12 | 0.12 | 0.41 | 2.80 | 43.0 | 645 |

1–15 | 0.19 | 0.43 | 2.68 | 13.8 | 470 |

1–16 | 0.19 | 0.43 | 2.68 | 6.8 | 470 |

1–12 | 0.06 | 0.41 | 2.68 | 32.8 | 1280 |

11–12 | 0.12 | 0.41 | 2.80 | 23.4 | 645 |

12–13 | 0.12 | 0.41 | 2.80 | 10.2 | 645 |

2–3 | 0.12 | 0.4 | 2.89 | 18.8 | 645 |

3–4 | 0.12 | 0.41 | 2.81 | 12.1 | 645 |

3–8 | 0.12 | 0.4 | 2.89 | 20.7 | 645 |

4–5 | 0.12 | 0.4 | 2.80 | 9.0 | 645 |

5–6 | 0.12 | 0.4 | 2.80 | 26.7 | 645 |

6–7 | 0.12 | 0.41 | 2.80 | 12.5 | 645 |

7–8 | 0.12 | 0.4 | 2.80 | 29.9 | 645 |

8–9 | 0.12 | 0.41 | 2.78 | 10.0 | 645 |

9–10 | 0.12 | 0.41 | 2.78 | 20.0 | 645 |

10–11 | 0.12 | 0.42 | 2.80 | 19.3 | 645 |

12–13 | 0.12 | 0.41 | 2.80 | 10.1 | 645 |

13–14 | 0.12 | 0.41 | 2.80 | 6.7 | 645 |

14–15 | 0.24 | 0.35 | 2.68 | 35.3 | 470 |

15–16 | 0.12 | 0.41 | 2.78 | 6.7 | 645 |

15–17 | 0.12 | 0.40 | 2.89 | 13.2 | 645 |

Bus | P [MW] | Q [Mvar] |
---|---|---|

2 | 2.2 | 0 |

3 | 7.8 | −8.8 |

4 | 2.1 | 0.4 |

5 | 5.7 | −0.9 |

6 | 19.1 | 4.5 |

7 | 9.0 | 2.2 |

8 | 50.0 | 8.8 |

9 | 22.0 | 4.6 |

10 | 27.1 | 4.8 |

11 | 7.8 | −1.6 |

13 | 43.4 | 3.3 |

14 | 37.5 | 3.7 |

15 | 17.9 | 0.6 |

17 | 4.5 | −0.5 |

## References

- Doraiswami, R.; Carvalho, M.F.H. Reliability Indices for a Power Network Considering Static, Transient, and Dynamic Performance. IEEE Trans. Reliab.
**1979**, R-28, 120–123. [Google Scholar] [CrossRef] - Guler, T.; Gross, G. Detection of Island Formation and Identification of Causal Factors Under Multiple Line Outages. IEEE Trans. Power Syst.
**2007**, 22, 505–513. [Google Scholar] [CrossRef] - Dong, H.; Cui, L. System Reliability Under Cascading Failure Models. IEEE Trans. Reliab.
**2016**, 65, 929–940. [Google Scholar] [CrossRef] - Zio, E.; Sansavini, G. Modeling Interdependent Network Systems for Identifying Cascade-Safe Operating Margins. IEEE Trans. Reliab.
**2011**, 60, 94–101. [Google Scholar] [CrossRef][Green Version] - El-Kady, M.A.; El-Sobki, M.S.; Sinha, N.K. Reliability Evaluation for Optimally Operated, Large, Electric Power Systems. IEEE Trans. Reliab.
**1986**, 35, 41–47. [Google Scholar] [CrossRef] - Shuai, Z.; Hu, Y.; Peng, Y.; Tu, C.; Shen, Z.J. Dynamic Stability Analysis of Synchronverter-Dominated Microgrid Based on Bifurcation Theory. IEEE Trans. Ind. Electron.
**2017**, 64, 7467–7477. [Google Scholar] [CrossRef] - Rocco, C.M.; Ramirez-Marquez, J.E.; Salazar, D.E.; Yajure, C. Assessing the Vulnerability of a Power System Through a Multiple Objective Contingency Screening Approach. IEEE Trans. Reliab.
**2011**, 60, 394–403. [Google Scholar] [CrossRef] - Ding, T.; Li, C.; Yan, C.; Li, F.; Bie, Z. A Bilevel Optimization Model for Risk Assessment and Contingency Ranking in Transmission System Reliability Evaluation. IEEE Trans. Power Syst.
**2017**, 32, 3803–3813. [Google Scholar] [CrossRef] - Street, A.; Oliveira, F.; Arroyo, J.M. Contingency-Constrained Unit Commitment with n–K Security Criterion: A Robust Optimization Approach. IEEE Trans. Power Syst.
**2011**, 26, 1581–1590. [Google Scholar] [CrossRef] - Wang, Q.; Watson, J.; Guan, Y. Two-stage robust optimization for N-k contingency-constrained unit commitment. IEEE Trans. Power Syst.
**2013**, 28, 2366–2375. [Google Scholar] [CrossRef] - Levitin, G. Optimal Defense Strategy Against Intentional Attacks. IEEE Trans. Reliab.
**2007**, 56, 148–157. [Google Scholar] [CrossRef] - Levitin, G.; Hausken, K. Redundancy vs. Protection vs. False Targets for Systems Under Attack. IEEE Trans. Reliab.
**2009**, 58, 58–68. [Google Scholar] [CrossRef] - Ejebe, G.C.; Wollenberg, B.F. Automatic Contingency Selection. IEEE Trans. Power Appar. Syst.
**1979**, PAS-98, 97–109. [Google Scholar] [CrossRef] - Mikolinnas, T.A.; Wollenberg, B.F. An Advanced Contingency Selection Algorithm. IEEE Trans. Power Appar. Syst.
**1981**, PAS-100, 608–617. [Google Scholar] [CrossRef] - Irisarri, G.D.; Sasson, A.M. An Automatic Contingency Selection Method for On-Line Security Analysis. IEEE Trans. Power Appar. Syst.
**1981**, PAS-100, 1838–1844. [Google Scholar] [CrossRef] - Peterson, N.M.; Tinney, W.F.; Bree, D.W. Iterative Linear AC Power Flow Solution for Fast Approximate Outage Studies. IEEE Trans. Power Appar. Syst.
**1972**, PAS-91, 2048–2056. [Google Scholar] [CrossRef] - Zaborszky, J.; Whang, K.; Prasad, K. Fast Contingency Evaluation Using Concentric Relaxation. IEEE Trans. Power Appar. Syst.
**1980**, PAS-99, 28–36. [Google Scholar] [CrossRef] - Brandwajn, V.; Lauby, M.G. Complete bounding method for AC contingency screening. IEEE Trans. Power Syst.
**1989**, 4, 724–729. [Google Scholar] [CrossRef] - Irisarri, G.; Levner, D.; Sasson, A.M. Automatic Contingency Selection for On-Line Security Analysis-Real-Time Tests. IEEE Trans. Power Appar. Syst.
**1979**, PAS-98, 1552–1559. [Google Scholar] [CrossRef] - Che, L.; Liu, X.; Li, Z. Preventive Mitigation Strategy for the Hidden N-k Line Contingencies in Power Systems. IEEE Trans. Reliab.
**2018**, 67, 1060–1070. [Google Scholar] [CrossRef] - Babalola, A.; Belkacemi, R.; Zarrabian, S. Real-time cascading failures prevention for multiple contingencies in smart grids through a multi-agent system. IEEE Trans. Smart Grid
**2018**, 9, 373–385. [Google Scholar] [CrossRef] - Chatterjee, D.; Webb, J.; Gao, Q.; Vaiman, M.Y.; Vaiman, M.M.; Povolotskiy, M. N-1-1 AC Contingency Analysis as a Part of NERC Compliance Studies at Midwest ISO. In Proceedings of the Transmission and Distribution Conference and Exposition, 2010 IEEE PES, New Orleans, LA, USA, 19–22 April 2010; pp. 1–7. [Google Scholar] [CrossRef]
- Mitra, P.; Vittal, V.; Keel, B.; Mistry, J. A Systematic Approach to N-1-1 Analysis for Power System Security Assessment. IEEE Power Energy Technol. Syst. J.
**2016**, 3, 71–80. [Google Scholar] [CrossRef] - Omran, S.; Broadwater, R.; Hambrick, J.; Dilek, M.; Thomas, C.; Kreikebaum, F. Power flow control and N-1 contingency analysis with DSRs in unbalanced transmission networks. Electr. Power Syst. Res.
**2016**, 136, 223–231. [Google Scholar] [CrossRef] - Abe, S.; Fukunaga, Y.; Isono, A.; Kondo, B. Power System Voltage Stability. IEEE Trans. Power Appar. Syst.
**1982**, PAS-101, 3830–3840. [Google Scholar] [CrossRef] - Kundur, P. Power System Stability and Control; McGraw-Hill: New York, NY, USA, 1994. [Google Scholar]
- Yang, J.; Li, G.; Wu, D.; Suo, Z. The impact of distributed wind power generation on voltage stability in distribution systems. In Proceedings of the 2013 IEEE PES Asia-Pacific Power and Energy Engineering Conference (APPEEC), Kowloon, China, 8–11 December 2013; pp. 1–5. [Google Scholar] [CrossRef]
- Song, Y.; Hill, D.J.; Liu, T. Static Voltage Stability Analysis of Distribution Systems Based on Network-Load Admittance Ratio. IEEE Trans. Power Syst.
**2019**, 34, 2270–2280. [Google Scholar] [CrossRef] - Fatehi, F.; Rashidinejad, M.; Gharaveisi, A.A. Contingency Ranking Based on a Voltage Stability Criteria Index. In Proceedings of the 2007 Large Engineering Systems Conference on Power Engineering, Montreal, QC, Canada, 10–12 October 2007; pp. 142–147. [Google Scholar] [CrossRef]
- Abed, A.M. WSCC voltage stability criteria, undervoltage load shedding strategy, and reactive power reserve monitoring methodology. In Proceedings of the 1999 IEEE Power Engineering Society Summer Meeting. Conference Proceedings (Cat. No.99CH36364), Edmonton, AB, Canada, 18–22 July 1999; Volume 1, pp. 191–197. [Google Scholar] [CrossRef]
- Chen, M. Dynamic contingency re-definition in power system security analysis. In Proceedings of the 2011 4th International Conference on Electric Utility Deregulation and Restructuring and Power Technologies (DRPT), Weihai, China, 6–9 July 2011; pp. 63–66. [Google Scholar] [CrossRef]
- Jirjees, M.A.; Al-Nimma, D.A.; Al-Hafidh, M.S.M. Voltage stability enhancement based on voltage stability indices using FACTS controllers. In Proceedings of the 2018 International Conference on Engineering Technology and their Applications (IICETA), Al-Najaf, Iraq, 8–9 May 2018; pp. 141–145. [Google Scholar] [CrossRef]
- Hu, Z. The influence of STATCOM operation on voltage stability of power grid. In Proceedings of the 2019 4th International Conference on Intelligent Green Building and Smart Grid (IGBSG), Yi-chang, China, 6–9 September 2019; pp. 354–357. [Google Scholar] [CrossRef]
- Chakravorty, M.; Patra, S. Voltage stability analysis using conventional methods. In Proceedings of the 2016 International Conference on Signal Processing, Communication, Power and Embedded System (SCOPES), Paralakhemundi, India, 3–5 October 2016; pp. 496–501. [Google Scholar] [CrossRef]
- Lian, S.; Minami, S.; Morii, S.; Kawamoto, S. Analysis method of voltage stability for bulk power system by P-V and Q-V curves considering dynamic load. In Proceedings of the 2009 IEEE/PES Power Systems Conference and Exposition, Seattle, WA, USA, 15–18 March 2009; pp. 1–6. [Google Scholar] [CrossRef]
- CIGRE Report No. 325, Review of On-Line Dynamic Security Assessment Tools and Techniques. WG C4.601. 2007. Available online: https://e-cigre.org/publication/325-review-of-on-line-dynamic-security-assessment-tools-and-techniques (accessed on 15 December 2020).
- Gao, B.; Morrison, G.K.; Kundur, P. Voltage stability evaluation using modal analysis. IEEE Power Eng. Rev.
**1992**, 7, 1529–1542. [Google Scholar] [CrossRef] - Esmaeil Moghadam, D.; Shiri, A.; Sadr, S.; Khaburi, D.A. A practical method for calculation of over-excited region in the synchronous generator capability curves. In Proceedings of the 2014 IEEE 23rd International Symposium on Industrial Electronics (ISIE), Istanbul, Turkey, 1–4 June 2014; pp. 727–732. [Google Scholar] [CrossRef]
- Kueck, J.; Kirby, B.; Rizy, T.; Li, F.; Fall, N. Reactive Power from Distributed Energy. Electr. J.
**2006**, 19, 27–38. [Google Scholar] [CrossRef] - Kawabe, K.; Yokoyama, A. Study on short-term voltage stability improvement using batteries on extra-high voltage network. In Proceedings of the 2013 IEEE Grenoble Conference, Grenoble, France, 16–20 June 2013; pp. 1–3. [Google Scholar] [CrossRef]
- Cabrera-Tobar, A.; Bullich-Massaguew, E.; Aragues-Penalba, M. Active and Reactive Power Control of a PV Generator for Grid Code Compliance. Energies
**2019**, 12, 3872. [Google Scholar] [CrossRef][Green Version] - Maknouninejad, A.; Kutkut, N.; Batarseh, I.; Qu, Z. Analysis and control of PV inverters operating in VAR mode at night. In Proceedings of the Innovative Smart Grid Technologies (ISGT), Anaheim, CA, USA, 17–19 January 2011; IEEE: New York, NY, USA, 2011. [Google Scholar] [CrossRef][Green Version]
- Williams, J.R.; Ellis, A.; Nelson, R.; Von Engeln, E.; Walling, R.; MacDowell, J.; Casey, L.; Seymour, E.; Peter, W.; Barker, C.; et al. Review of existing reactive power requirements for variable generation. In Proceedings of the 2012 IEEE Power and Energy Society General Meeting, San Diego, CA, USA, 22–26 July 2012; pp. 1–7. [Google Scholar] [CrossRef]
- Kalverkamp, F.; Schowe-von der Brelie, S.; Nguyen, T.D.; Mertens, T.; Meuser, M. Comparative analysis of European Grid Codes and compliance standards for distributed power generation plants with respect to future requirements of ENTSO-E and CENELEC. In Proceedings of the International ETG Congress, Bonn, Germany, 17–18 November 2015; VDE Verlag: Berlin, Germany, 2015; pp. 605–610, ISBN 978-3-8007-4121-2. [Google Scholar]
- Diaz-Gonzalez, F.; Sumper, A.; Gomis-Bellmunt, O. Energy Storage in Power Systems, 1st ed.; John Wiley & Sons Ltd.: Chichester, UK, 2016; pp. 97–102. [Google Scholar]
- Energy Systems Integration Group. Available online: https://www.esig.energy/wiki-main-page/pv-plant-power-flow-modeling-guide/ (accessed on 27 December 2020).
- Wang, W.; He, W.; Cheng, J.; Huang, X.; Liu, H. Active and reactive power coordinated control strategy of battery energy storage system in active distribution network. In Proceedings of the 32nd Youth Academic Annual Conference of Chinese Association of Automation (YAC), Hefei, China, 19–21 May 2017; pp. 462–465. [Google Scholar] [CrossRef]
- Liu, X.; Niu, X.; Zhu, Y.; Zhu, C. Influence of Regulation of OLTC Transformation Ratio on Voltage Stability. In Proceedings of the 2013 Fourth International Conference on Digital Manufacturing & Automation, Qingdao, China, 29–30 June 2013; pp. 696–700. [Google Scholar] [CrossRef]
- Duan, J.; Zhu, S. The effect of OLTC on static voltage stability limit. In Proceedings of the 2011 Asia-Pacific Power and Energy Engineering Conference, Wuhan, China, 25–28 March 2011; pp. 1–4. [Google Scholar] [CrossRef]
- Overbye, T.J. Effects of load modelling on analysis of power system voltage stability. Int. J. Electr. Power Energy Syst.
**1994**, 16, 329–338. [Google Scholar] [CrossRef] - Arif, A.; Wang, Z.; Wang, J.; Mather, B.; Bashualdo, H.; Zhao, D. Load Modeling—A Review. IEEE Trans. Smart Grid
**2018**, 9, 5986–5999. [Google Scholar] [CrossRef] - Guo, H.; Rudion, K.; Abildgaard, H.; Komarnicki, P.; Styczynski, Z.A. Parameter estimation of dynamic load model using field measurement data performed by OLTC operation. In Proceedings of the 2012 IEEE Power and Energy Society General Meeting, San Diego, CA, USA, 22–26 July 2012; pp. 1–7. [Google Scholar] [CrossRef]
- Vignesh, V.; Chakrabarti, S.; Srivastava, S.C. An experimental study on the load modelling using PMU measurements. In Proceedings of the IEEE PES T&D Conference and Exposition, Chicago, IL, USA, 14–17 April 2014; pp. 1–5. [Google Scholar] [CrossRef]

**Figure 1.**Classification of power system operating states (based on [36]).

**Figure 2.**Classification of power system stability (based on [36]).

**Figure 7.**Comparison of different technology effects on voltage stability indicators and remedial actions.

Contingency Number | Contingency (Line or Generator) | λ_{1}[-] | Mode 1 Area (Bus) |
---|---|---|---|

0 | Base case (N-0) | 0.416 | 6–7 |

1 | 3–4, L | 0.325 | 5 |

2 | 1–11–13, L | 0.335 | 11 |

3 | 4–5, L | 0.348 | 5 |

4 | 8–3, L | 0.353 | 8–9 |

5 | 1–3, L | 0.355 | 6–7 |

6 | 1–2, L | 0.356 | 6–7 |

7 | 2–3, L | 0.366 | 6–7 |

8 | 1, G | 0.368 | 6–7 |

9 | 10–11, L | 0.376 | 10 |

10 | 5–6, L | 0.390 | 6 |

11 | 7–8, L | 0.397 | 7 |

12 | 1–13, L | 0.403 | 6–7 |

13 | 8–9, L | 0.405 | 9 |

14 | 14–15, L | 0.405 | 6–7 |

15 | 6–7, L | 0.411 | 6–7 |

16 | 9–10, L | 0.411 | 6–7 |

17 | 1–15, L | 0.412 | 6–7 |

18 | 13–14, L | 0.415 | 6–7 |

Scenario | λ_{min}[-] | Mode Area (Bus) | Bus No./ΔP_{crit}[-]/[%] * | Bus No./ΔQ_{crit}[-]/[Mvar] | Bus No./U-Q_{max}[-]/[%/Mvar] |
---|---|---|---|---|---|

Base case | 0.416 | 6 and 7 | 6/>87 | 6/87.6 | 6/0.17 |

7/>83 | 7/85.5 | 7/0.17 | |||

No. 1 (most severe) | 0.325 | 5 | 5/>72 | 5/41.3 | 5/0.36 |

No. 18 (least severe) | 0.415 | 6 and 7 | 6/>88 | 6/87.9 | 6/0.17 |

7/>84 | 7/85.6 | 7/0.17 |

**Table 3.**Voltage stability indicators and ranking of remedial actions (distributed energy resources/battery energy storage, DER/BSS) for contingency No. 7.

Remedial Action Number | Remedial Action | λ_{new}/λ_{old}[-] | ΔP System * [%] | ΔQ at Bus 6 [Mvar] | PI_{V}[-] |
---|---|---|---|---|---|

0 | 5_{Pmax}, 8_{Pmax}, 11_{Pmax} | 1.000 | 72 | 71.4 | 0.399 |

1 | 5_{Qmax}, 8_{Pmax}, 11_{Pmax} | 1.027 | 75 | 76.6 | 0.227 |

2 | 5_{Pmax}, 8_{Qmax}, 11_{Pmax} | 1.025 | 75 | 75.2 | 0.202 |

3 | 5_{Pmax}, 8_{Pmax}, 11_{Qmax} | 1.016 | 73 | 73.7 | 0.228 |

4 | 5_{Qmax}, 8_{Qmax}, 11_{Pmax} | 1.049 | 78 | 80.5 | 0.189 |

5 | 5_{Qmax}, 8_{Pmax}, 11_{Qmax} | 1.041 | 77 | 79.2 | 0.175 |

6 | 5_{Pmax}, 8_{Qmax}, 11_{Qmax} | 1.038 | 76 | 77.7 | 0.148 |

7 | 5_{Qmax}, 8_{Qmax}, 11_{Qmax} | 1.062 | 79 | 83.1 | 0.251 |

**Table 4.**Voltage stability indicators and ranking of remedial actions (synchronous generator, SG) for contingency No. 7.

Remedial Action Number | Remedial Action | λ_{new}/λ_{old}[-] | ΔP System * [%] | ΔQ at Bus 6 [Mvar] | PI_{V}[-] |
---|---|---|---|---|---|

0 | Q_{SG} = 41 Mvar | 1.000 | 72 | 71.4 | 0.399 |

1 | Q_{SG} = 51 Mvar | 1.005 | 72 | 72.3 | 0.327 |

2 | Q_{SG} = 61 Mvar | 1.008 | 72 | 72.7 | 0.283 |

3 | Q_{SG} = 71 Mvar | 1.011 | 72 | 72.7 | 0.242 |

**Table 5.**Voltage stability indicators and ranking of remedial actions (under load tap changer, ULTC) for contingency No. 7.

Remedial Action Number | Remedial Action | λ_{new}/λ_{old}[-] | ΔP System * [%] | ΔQ at Bus 6 [Mvar] | PI_{V}[-] |
---|---|---|---|---|---|

0 | AVR in normal operation | 1.000 | 72 | 71.4 | 0.399 |

1 | AVR blocked in neutral position | 1.003 | 86 | 77.0 | 0.302 |

2 | AVR blocked in optimum position before contingency | 1.003 | 81 | 75.5 | 0.378 |

BASE CASE ZIP Model Parameters | λ_{min}[-] | ΔP_{crit}[%] | ΔQ_{crit}[Mvar] | U-Q_{max}[%/Mvar] |
---|---|---|---|---|

P_{ZIP}: 33%/33%/33% | 0.414 | >87 | >87.5 | 0.17 |

Q_{ZIP}: 33%/33%/33% | ||||

P_{ZIP}: 50%/0%/50% | 0.414 | >87 | >87.5 | 0.17 |

Q_{ZIP}: 50%/0%/50% | ||||

P_{ZIP}: 0%/0%/100% | 0.407 | >85 | >86.9 | 0.17 |

Q_{ZIP}: 0%/0%/100% | ||||

P_{ZIP}: 100%/0%/0% | 0.421 | >88 | >88.0 | 0.16 |

Q_{ZIP}: 100%/0%/0% | ||||

N-1 CASE No. 7ZIP Model Parameters | ||||

P_{ZIP}: 33%/33%/33% | 0.365 | >72 | >71.3 | 0.20 |

Q_{ZIP}: 33%/33%/33% | ||||

P_{ZIP}: 50%/0%/50% | 0.364 | >72 | >71.3 | 0.19 |

Q_{ZIP}: 50%/0%/50% | ||||

P_{ZIP}: 0%/0%/100% | 0.357 | >71 | >70.6 | 0.20 |

Q_{ZIP}: 0%/0%/100% | ||||

P_{ZIP}: 100%/0%/0% | 0.372 | >74 | >71.8 | 0.19 |

Q_{ZIP}: 100%/0%/0% |

Publisher’s Note: MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations. |

© 2021 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Bulat, H.; Franković, D.; Vlahinić, S. Enhanced Contingency Analysis—A Power System Operator Tool. *Energies* **2021**, *14*, 923.
https://doi.org/10.3390/en14040923

**AMA Style**

Bulat H, Franković D, Vlahinić S. Enhanced Contingency Analysis—A Power System Operator Tool. *Energies*. 2021; 14(4):923.
https://doi.org/10.3390/en14040923

**Chicago/Turabian Style**

Bulat, Hrvoje, Dubravko Franković, and Saša Vlahinić. 2021. "Enhanced Contingency Analysis—A Power System Operator Tool" *Energies* 14, no. 4: 923.
https://doi.org/10.3390/en14040923