# A Resilient Integrated Resource Planning Framework for Transmission Systems: Analysis and Optimization

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## Abstract

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## 1. Introduction

- Introduction of a resilient IRP framework for the transmission system, incorporating analysis, evaluation, and optimization considering HILP events.
- Proposal of the proximity index, a metric based on the closeness of outage lines to generators, facilitating the selection of HILP events from a broad array of randomly generated multiple-line outage scenarios.
- Development of a methodology for conducting power flows on islands formed due to multiple-line outages and calculating the total load curtailment in the outage scenario.
- Introduction of the resilience metric ELC to quantify the anticipated load curtailment in all HILP scenarios, serving as a measure for resilience planning.
- Proposal of the strategic placement of DER investments to achieve a desired level of resilience.

## 2. Proposed Framework

#### 2.1. Outage Data Generation, Selection of HILP Events, and Scenario Reduction

Algorithm 1: Load Curtailment (LC)-based Scenario Reduction |

#### 2.2. Evaluation of the Base Case Resilience of the System

#### 2.3. Re-Evaluation of System Resilience with Additional Resources

## 3. Case Studies and Discussion

#### 3.1. Simulation Setup

#### 3.2. Analysis of the Outage Scenarios

#### 3.3. Scenario Reduction and Evaluation of the Base Case Resilience

#### 3.4. Resilience Enhancement through Optimal Placement of DERs

#### 3.5. Comparison of HILP-Based Planning with Traditional Reliability-Based Planning

#### 3.6. Scalability Challenges

## 4. Conclusions and Future Work

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## Abbreviations

CC | Connected Component |

DER | Distributed Energy Resource |

ELC | Expected Load Curtailment |

GA | Genetic Algorithm |

HILP | High-Impact Low-Probability |

IEEE | Institute of Electrical and Electronics Engineers |

IRP | Integrated Resource Planning |

LC | Load Curtailment |

PI | Proximity Index |

## Appendix A

Bus | Rated Voltage (kV) | Max Voltage Limit (pu) | Min Voltage Limit (pu) |
---|---|---|---|

1 | 138 | 1.05 | 0.95 |

2 | 138 | 1.05 | 0.95 |

3 | 138 | 1.05 | 0.95 |

4 | 138 | 1.05 | 0.95 |

5 | 138 | 1.05 | 0.95 |

6 | 138 | 1.05 | 0.95 |

7 | 138 | 1.05 | 0.95 |

8 | 138 | 1.05 | 0.95 |

9 | 138 | 1.05 | 0.95 |

10 | 138 | 1.05 | 0.95 |

11 | 230 | 1.05 | 0.95 |

12 | 230 | 1.05 | 0.95 |

13 | 230 | 1.05 | 0.95 |

14 | 230 | 1.05 | 0.95 |

15 | 230 | 1.05 | 0.95 |

16 | 230 | 1.05 | 0.95 |

17 | 230 | 1.05 | 0.95 |

18 | 230 | 1.05 | 0.95 |

19 | 230 | 1.05 | 0.95 |

20 | 230 | 1.05 | 0.95 |

21 | 230 | 1.05 | 0.95 |

22 | 230 | 1.05 | 0.95 |

23 | 230 | 1.05 | 0.95 |

24 | 230 | 1.05 | 0.95 |

Bus | Active Power (MW) | Reactive Power (MVAr) |
---|---|---|

1 | 108 | 22 |

2 | 97 | 20 |

3 | 180 | 37 |

4 | 74 | 15 |

5 | 71 | 14 |

6 | 136 | 28 |

7 | 125 | 25 |

8 | 171 | 35 |

9 | 175 | 36 |

10 | 195 | 40 |

13 | 265 | 54 |

14 | 194 | 39 |

15 | 317 | 64 |

16 | 100 | 20 |

18 | 333 | 68 |

19 | 181 | 37 |

20 | 128 | 26 |

Bus | Active Power (MW) | Rated Voltage (pu) | Min Reactive Power Limit (MVAr) | Max Reactive Power Limit (MVAr) | Max Active Power Limit (MW) | Min Active Power Limit (MW) |
---|---|---|---|---|---|---|

1 | 172 | 1.035 | −50 | 80 | 192 | 62.4 |

2 | 172 | 1.035 | −50 | 80 | 192 | 62.4 |

7 | 240 | 1.025 | 0 | 180 | 300 | 75 |

14 | 0 | 0.98 | −50 | 200 | 0 | 0 |

15 | 215 | 1.014 | −50 | 110 | 215 | 66.3 |

16 | 155 | 1.017 | −50 | 80 | 155 | 54.3 |

18 | 400 | 1.05 | −50 | 200 | 400 | 100 |

21 | 400 | 1.05 | −50 | 200 | 400 | 100 |

22 | 300 | 1.05 | −60 | 96 | 300 | 60 |

23 | 660 | 1.05 | −125 | 310 | 660 | 248.6 |

From Bus | To Bus | Line Resistance ($\mathbf{\Omega}$) | Line Reactance ($\mathbf{\Omega}$) | Line Capacitance (nF) |
---|---|---|---|---|

1 | 2 | 0.495144 | 2.647116 | 6422.525403 |

1 | 3 | 10.398024 | 40.220928 | 796.7218673 |

1 | 5 | 4.151592 | 16.09218 | 318.967321 |

2 | 4 | 6.246432 | 24.128748 | 477.7545463 |

2 | 6 | 9.464868 | 36.56448 | 724.2926067 |

3 | 9 | 5.865552 | 22.66236 | 448.504268 |

4 | 9 | 5.103792 | 19.748628 | 391.3965817 |

5 | 10 | 4.342032 | 16.815852 | 332.896025 |

6 | 10 | 2.647116 | 11.52162 | 34,250.68307 |

7 | 8 | 3.027996 | 11.693016 | 231.216486 |

8 | 9 | 8.131788 | 31.441644 | 622.6130677 |

8 | 10 | 8.131788 | 31.441644 | 622.6130677 |

11 | 13 | 3.2269 | 25.1804 | 500.9319097 |

11 | 14 | 2.8566 | 22.1122 | 440.7599086 |

12 | 13 | 3.2269 | 25.1804 | 500.9319097 |

12 | 23 | 6.5596 | 51.1014 | 1017.909686 |

13 | 23 | 5.8719 | 45.7585 | 911.6058177 |

14 | 16 | 2.645 | 20.5781 | 410.1724746 |

15 | 16 | 1.1638 | 9.1517 | 182.5217369 |

15 | 21 | 3.3327 | 25.921 | 516.4763434 |

15 | 24 | 3.5443 | 27.4551 | 547.0637773 |

16 | 17 | 1.7457 | 13.7011 | 273.281172 |

16 | 19 | 1.587 | 12.2199 | 243.1951714 |

17 | 18 | 0.9522 | 7.6176 | 151.934303 |

17 | 22 | 7.1415 | 55.7037 | 1109.170555 |

18 | 21 | 1.7457 | 13.7011 | 273.281172 |

19 | 20 | 2.6979 | 20.9484 | 417.6939748 |

20 | 23 | 1.4812 | 11.4264 | 228.1521711 |

21 | 22 | 4.6023 | 35.8662 | 714.0410805 |

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**Figure 1.**(

**a**) Hypothetical transmission network with six buses, (

**b**) graph theory representation of the network, (

**c**) outage of lines 4–5 and 4–6 in the network, and (

**d**) creation of two connected components (or islands) due to the outage.

**Table 1.**Optimization results in the case of the IEEE 24-bus system with different values of target ELC.

ELC Reduction (MW) | Target ELC (MW) | Optimal DER Locations (Buses) | Optimal DER Capacities (MW) | Total DER Capacity (MW) |
---|---|---|---|---|

10 | 246.125 | 6 | 20 | 20 |

20 | 236.125 | 3, 8, 13, 14, 15 | 20, 10, 40, 30, 10 | 110 |

30 | 226.125 | 1, 3, 13, 14 | 40, 60, 30, 40 | 170 |

40 | 216.125 | 4, 5, 15, 16, 19 | 30, 10, 60, 120, 20 | 240 |

50 | 206.125 | 1, 2, 6, 10, 14, 16 | 30, 50, 100, 30, 10, 50 | 270 |

60 | 196.125 | 2, 3, 6, 9, 13 | 120, 80, 10, 70, 50 | 330 |

70 | 186.125 | 1, 4, 6, 8, 10, 14, 19 | 30, 20, 110, 10, 20, 140, 140 | 470 |

80 | 176.125 | 1, 3, 6, 10, 16, 20 | 80, 110, 90, 30, 100, 110 | 520 |

90 | 166.125 | 2, 3, 7, 10, 13, 14, 16, 19 | 150, 80, 50, 10, 50, 100, 90, 100 | 630 |

100 | 156.125 | 1, 2, 3, 5, 7, 15, 16, 19 | 90, 50, 120, 90, 30, 140, 120, 60 | 700 |

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**MDPI and ACS Style**

Gautam, M.; McJunkin, T.; Hruska, R.
A Resilient Integrated Resource Planning Framework for Transmission Systems: Analysis and Optimization. *Sustainability* **2024**, *16*, 2449.
https://doi.org/10.3390/su16062449

**AMA Style**

Gautam M, McJunkin T, Hruska R.
A Resilient Integrated Resource Planning Framework for Transmission Systems: Analysis and Optimization. *Sustainability*. 2024; 16(6):2449.
https://doi.org/10.3390/su16062449

**Chicago/Turabian Style**

Gautam, Mukesh, Timothy McJunkin, and Ryan Hruska.
2024. "A Resilient Integrated Resource Planning Framework for Transmission Systems: Analysis and Optimization" *Sustainability* 16, no. 6: 2449.
https://doi.org/10.3390/su16062449