# Strategic Placement of Solar Power Plant and Interline Power Flow Controllers for Prevention of Blackouts

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## Abstract

**:**

## 1. Introduction

## 2. Mathematical Modelling

#### 2.1. Mathematical Modelling of IPFC

_{1}= V

_{l}∟θ

_{l}(l = i, j, k) and V

_{l}, θ

_{l}are the magnitude and angle of V

_{l}.

_{in}is the complex controllable series injected voltage source which represents the series compensation of the series converter.

_{in}is defined as Vse

_{in}= Vse

_{in}∟θse

_{in}(n = j, k).

_{in}and θse

_{in}are the magnitude and angle of Vse

_{in}.

_{in}is the series transformer impedance.

#### 2.2. Inequality Constraints

## 3. Problem Formulation

#### 3.1. Placement of Solar Power Plant and IPFC

#### Proposed Line Severity Index

_{ij}is the Line Severity Index (LSI) of the line connected to bus i and bus j.

_{ij}

_{(max)}is Maximum MVA rating of the line between bus i and bus j.

_{ij}is the actual MVA rating of the line between bus i and bus j.

#### 3.2. Tuning of IPFC

#### 3.2.1. Minimization of Voltage Deviation

_{k}is the voltage magnitude at bus k.

#### 3.2.2. Improvement of Security Margin

_{L}= No. of load buses.

## 4. Methodology

## 5. Results

#### IEEE 57 Bus System

## 6. Conclusions

- Solar power systems can effectively reduce the stress on the existing system.
- The IPFC along with the solar power unit has reduced the active and reactive losses in the power system.
- The voltage deviation, security margin and line severity can be controlled within acceptable limits by the proposed method even in the situation of n-1 contingencies. This helps in avoiding any further disruptions in the power system. Thus, the proposed method is an effective means of avoiding blackouts in the country.

## 7. Future Prospects

- More Solar and wind units may be installed to study its effect.
- The more effective indices may be developed for the effective placement of solar and wind units.
- Other methods of placements may be incorporated into the system.
- The proposed method may be implemented on larger transmission systems to study its effectiveness.

## 8. Limitations

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## Nomenclature

P_{i}, Q_{i} | Inverter active and reactive power. |

V_{l—}V_{l}∟θ_{l} (l = i, j, k) and V_{l}, θ_{l} | Magnitude and angle of V_{l}. |

Vse_{in,} ∟θse_{in} | Magnitude and angle of Vse_{in} |

Vse_{in} | Complex controllable series injected voltage source, series compensation of the series converter |

n | bus j, k - common bus connected to IPFC. |

Zse_{in} | Series transformer impedance |

Pni and Qni | Active and reactive power flows leaving bus n connected to IPFC |

gin, bin | Conductance and susceptance of a transmission line respectively |

S | Solar irradiance |

L(S) | Lognormal function |

P(s) | Solar electric power generated |

Pmin | Minimum output power of the PV unit |

Sst, Sc | Standard and critical point solar irradiance respectively |

Sij | Apparent power flow in line ij |

MVA_{ij(max)} | Maximum MVA rating of the line between bus i and bus j |

MVA_{ij} | Actual MVA rating of the line between bus i and bus j |

a | Multiplying factor. |

V_{k} | Voltage magnitude at bus k |

J_{L} | No. of load buses |

µ, σ | Mean and standard deviation of the log-normal probability function respectively |

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**Figure 2.**Methodology followed for Solar Power and IPFC placement and tuning [14].

S. No. | Contingency Condition | Active Power Loss (MW) | Reactive Power Loss (MVAR) | SM (p.u.) | VD (p.u.) |
---|---|---|---|---|---|

1 | Healthy System | 191.9 | 982.5 | 1.17 | 1.7 |

2 | 1–4 | 194.3 | 995.3 | 1.16 | 1.7 |

3 | 1–14 | 216.8 | 1110.2 | 1.23 | 1.8 |

4 | 1–10 | 233.8 | 1198.0 | 1.23 | 1.96 |

5 | 2–3 | 197.6 | 1011.8 | 1.16 | 1.70 |

6 | 3–4 | 195.8 | 1002.8 | 1.15 | 1.74 |

7 | 4–15 | 198.1 | 1014.2 | 1.18 | 1.78 |

8 | 14–15 | 192.9 | 987.6 | 1.16 | 1.73 |

9 | 4–14 | 200.1 | 1024.6 | 1.17 | 1.76 |

10 | 13–14 | 227.8 | 1167.1 | 1.23 | 1.86 |

11 | 12–13 | 253.3 | 1298.3 | 1.22 | 1.96 |

12 | 12–11 | 228.6 | 1171.3 | 1.20 | 1.77 |

13 | 11–10 | 221.9 | 1136.9 | 1.22 | 1.85 |

14 | 4–5 | 196.5 | 1003.6 | 1.20 | 1.74 |

**Table 2.**Line Severity Index of transmission lines connected to load buses for line 12–13 contingency condition.

S. No. | Contingency Condition | Line Severity Index (p.u.) |
---|---|---|

1. | 3–4 | 3.49 |

2. | 4–15 | 5.12 |

3. | 12–13 | Contingency Line |

4. | 12–11 | 16.11 |

5. | 11–10 | 8.66 |

6. | 6–7 | 14 |

7. | 7–8 | 14.56 |

8. | 11–16 | 6.71 |

9. | 21–22 | 13.46 |

10. | 27–29 | 0.13 |

11. | 29–30 | 0.16 |

12. | 12–20 | 0.59 |

13. | 13–17 | 0.16 |

14. | 24–45 | 0.81 |

15. | 24–41 | 0.73 |

16. | 41–45 | 0.47 |

17. | 40–41 | 0.28 |

18. | 41–42 | 1.29 |

19. | 42–43 | 0.063 |

20. | 42–44 | 0.114 |

Parameter | Healthy System | System Contingency | With Solar Unit &IPFC | IPFC Tuning |
---|---|---|---|---|

Active Power Loss (MW) | 87.372 | 102.126 | 98.747 | 91.139 |

Reactive Power Loss (MVAR) | 445.172 | 523.159 | 500.62 | 467.78 |

Voltage Deviation (p.u.) | 1.12 | 1.1828 | 1.1318 | 1.1105 |

Security Margin (p.u.) | 0.92 | 1.79 | 1.41 | 1.35 |

S. No. | From Bus-To Bus | LSI for Line 5–6 Contingency (p.u.) | LSI with Solar Power and IPFC (p.u.) |
---|---|---|---|

1. | 4–5 | 2.695507 | 1.946862 |

2. | 13–14 | 0.138384 | 0.68796 |

3. | 13–15 | 0.279629 | 0.347864 |

4. | 4–18 | 0.152256 | 0.051076 |

5. | 4–18 | 0.152256 | 0.034708 |

6. | 11–13 | 0.037133 | 1.06193 |

7. | 14–15 | 0.32251 | 0.008668 |

8. | 28–29 | 0.120062 | 0.549526 |

9. | 7–29 | 0.67322 | 0.008354 |

10. | 11–43 | 0.113771 | 0.257759 |

11. | 44–45 | 0.325242 | 0.000361 |

12. | 38–49 | 0.031542 | 0.056644 |

13. | 32–33 | 0.01428 | 0.007762 |

14. | 34–32 | 0.029207 | 0.007569 |

15. | 38–44 | 0.194922 | 0.10614089 |

16. | 10–51 | 0.199273 | 0.11418384 |

17. | 13–49 | 0.198919 | 0.037791 |

S. No. | Parameter | Value of System Parameter for Line 5–6 Outage | Healthy System |
---|---|---|---|

1 | Active Power Loss (MW) | 81.49 | 58.604 |

2 | Reactive Power Loss (MVAR) | 280.35 | 225.717 |

3 | Voltage Deviation (p.u.) | 1.1 | 1.01 |

4 | Security Margin (p.u.) | 1.9 | 1.12 |

S. No. | Parameter | Healthy System | With Contingency | With Solar Power and IPFC | With Tuned IPFC |
---|---|---|---|---|---|

1 | Active Power Loss (MW) | 58.604 | 81.49 | 73.106 | 65.24 |

2 | Reactive Power Loss (MVAR) | 225.717 | 280.35 | 249.050 | 231.12 |

3 | Voltage Deviation (p.u.) | 1.01 | 1.1 | 1.08 | 0.988 |

4 | Security Margin (p.u.) | 1.12 | 1.9 | 1.68 | 1.3 |

S. No. | Volt without Contingency (p.u.) | Volt with Contingency at 5–6 (p.u.) | Volt with Optimal IPFC and Solar Unit (p.u.) |
---|---|---|---|

1. | 1.04 | 1.04 | 1.04 |

2. | 0.98 | 0.98 | 1.01 |

3. | 0.935 | 0.935 | 0.985 |

4. | 0.9159 | 0.873 | 0.9841 |

5. | 0.8666 | 0.6111 | 0.8403 |

6. | 0.93 | 0.95 | 0.98 |

7. | 0.9501 | 0.9577 | 0.9789 |

8. | 1.005 | 1.005 | 1.005 |

9. | 0.97 | 0.97 | 0.98 |

10. | 0.9325 | 0.9324 | 0.9487 |

11. | 0.9326 | 0.9324 | 0.9291 |

12. | 0.965 | 0.965 | 0.965 |

13. | 0.9391 | 0.9388 | 0.9027 |

14. | 0.9361 | 0.9358 | 0.8249 |

15. | 0.9482 | 0.948 | 0.9255 |

16. | 0.9789 | 0.9786 | 0.9782 |

17. | 1.012 | 1.0122 | 1.0123 |

18. | 0.8649 | 0.8236 | 0.9346 |

19. | 0.7755 | 0.7475 | 0.8674 |

20. | 0.7352 | 0.7161 | 0.8404 |

21. | 0.7888 | 0.7842 | 0.8297 |

22. | 0.7963 | 0.7945 | 0.8261 |

23. | 0.7935 | 0.7919 | 0.8249 |

24. | 0.7646 | 0.7661 | 0.8221 |

25. | 0.6345 | 0.6355 | 0.7543 |

26. | 0.7711 | 0.7731 | 0.8269 |

27. | 0.837 | 0.8421 | 0.8835 |

28. | 0.8694 | 0.8756 | 0.9122 |

29. | 0.8944 | 0.9013 | 0.9348 |

30. | 0.5853 | 0.5861 | 0.7287 |

31. | 0.5011 | 0.5013 | 0.6952 |

32. | 0.476 | 0.4753 | 0.7181 |

33. | 0.4643 | 0.4636 | 0.715 |

34. | 0.6859 | 0.6846 | 0.7729 |

35. | 0.7085 | 0.7072 | 0.7825 |

36. | 0.7305 | 0.7292 | 0.7949 |

37. | 0.7478 | 0.7465 | 0.8036 |

38. | 0.8037 | 0.8023 | 0.8275 |

39. | 0.7436 | 0.7423 | 0.8025 |

40. | 0.7277 | 0.7263 | 0.7948 |

41. | 0.8142 | 0.8137 | 0.8761 |

42. | 0.7277 | 0.7269 | 0.8241 |

43. | 0.8867 | 0.8864 | 0.9127 |

44. | 0.8336 | 0.8325 | 0.8476 |

45. | 0.9109 | 0.9103 | 0.9043 |

46. | 0.8214 | 0.8203 | 0.8199 |

47. | 0.8078 | 0.8066 | 0.8168 |

48. | 0.8115 | 0.8103 | 0.8241 |

49. | 0.8492 | 0.8483 | 0.8519 |

50. | 0.8513 | 0.8506 | 0.8583 |

51. | 0.9167 | 0.9165 | 0.9305 |

52. | 0.8269 | 0.8328 | 0.8958 |

53. | 0.82 | 0.8253 | 0.8821 |

54. | 0.8772 | 0.8803 | 0.9177 |

55. | 0.9438 | 0.9447 | 0.9629 |

56. | 0.6805 | 0.6795 | 0.8073 |

57. | 0.605 | 0.6037 | 0.7929 |

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## Share and Cite

**MDPI and ACS Style**

Mishra, A.; Venkata, N.K.G.; Bali, S.K.; Bathina, V.R.; Ramisetty, U.M.; Gollapudi, S.; Habib Fayek, H.; Rusu, E.
Strategic Placement of Solar Power Plant and Interline Power Flow Controllers for Prevention of Blackouts. *Inventions* **2022**, *7*, 30.
https://doi.org/10.3390/inventions7010030

**AMA Style**

Mishra A, Venkata NKG, Bali SK, Bathina VR, Ramisetty UM, Gollapudi S, Habib Fayek H, Rusu E.
Strategic Placement of Solar Power Plant and Interline Power Flow Controllers for Prevention of Blackouts. *Inventions*. 2022; 7(1):30.
https://doi.org/10.3390/inventions7010030

**Chicago/Turabian Style**

Mishra, Akanksha, Nagesh Kumar Gundavarapu Venkata, Sravana Kumar Bali, Venkateswara Rao Bathina, Uma Maheswari Ramisetty, Srikanth Gollapudi, Hady Habib Fayek, and Eugen Rusu.
2022. "Strategic Placement of Solar Power Plant and Interline Power Flow Controllers for Prevention of Blackouts" *Inventions* 7, no. 1: 30.
https://doi.org/10.3390/inventions7010030