# Optimal Congestion Management with FACTS Devices for Optimal Power Dispatch in the Deregulated Electricity Market

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## Abstract

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## 1. Introduction

#### Paper Contribution

- This paper implements the MMFO technique for reducing the curtailment in power transactions to provide contract power dispatch requested by market participants.
- Congestion management is performed by employing three different curtailment strategies: group curtailment, separate curtailment, and point-to-point curtailment.
- Effectively reduces the overload in the transmission line by employing UPFC.
- The use of FACTS devices reduces the total cost of rescheduling by 27.14% and 29.4% in 14-bus and 30-bus systems, respectively.

## 2. Problem Formulation

#### 2.1. Mathematical Modeling of Optimal Power Dispatch

#### 2.2. Power Transactions in a Deregulated Environment

#### 2.3. Congestion Management by Using Curtailment Strategies

**point-to-point curtailment strategy**, the curtailment of requested power injected at a GENCO must be the same as the curtailment of requested power extracted at a DISCO. In this case, the objective function becomes

**group curtailment strategy**, the main aim is to provide the requested power without any curtailment, although individual generators inside that group have to be rescheduled, and when curtailment is needed, it must spread among the participants of that group. So the objective function for the optimal dispatch problem becomes

**separate curtailment strategy**, the concern is to minimize the change at every GENCO and DISCO of the concerned group based upon the willingness-to-pay factor, considering the group power balance constraint. For this objective function becomes

## 3. Facts Devices for Modeling of Optimal Power Dispatch

#### Modeling of UPFC

## 4. MFO Algorithm

#### Mathematical Formulation for Updating Moths’ Spiral Path and Distance

## 5. Modified MFO (MMFO) Technique

#### 5.1. Mathematical Formulation for Updating Moths’ Spiral Path and Distance

#### 5.2. Optimal Power Dispatch Using MMFO

## 6. Case Studies and Discussions

#### 6.1. Case Studies

#### 6.1.1. Case 1: IEEE 14-Bus System

- A.
**The group curtailment strategy**is applied to both groups, and the curtailment follows a linear relationship among the loads of each group. The willingness to pay price factor is chosen as 1 $/MWh ($ signifies an arbitrary unit of currency) for all the participants in the groups.- B.
- The curtailment strategy is the same as in A, but the willingness to pay price factor for group-1 is chosen three times as often as in group-2.
- C.
- Here, the GENCOs of group-1 follow a
**separate curtailment strategy**, and the willingness to pay price factor for bus-4 is three times that of bus-2. Others follow the same strategy as A. - D.
- Here, group-2 follows a
**point-to-point curtailment strategy**for dispatching bilateral contracts between buses 3–6, 3–10, and 3–13. Others follow the same strategy as A.

Gr. No. | Bus No. | Desired Generation and Load (MW) | Case 2A | Case 2B | Case 2C | Case 2D | |
---|---|---|---|---|---|---|---|

1 | Gene. | 2 | 157.7 | 157.7 | 157.7 | 150.9 | 157.7 |

4 | 98.0 | 77.8 | 78.04 | 81.26 | 79.709 | ||

Load | 7 | 102.9 | 94.771 | 94.87 | 93.43 | 95.53 | |

9 | 57.8 | 53.234 | 53.289 | 52.482 | 53.66 | ||

11 | 53.5 | 49.274 | 49.325 | 48.57 | 49.67 | ||

12 | 16.1 | 14.274 | 14.844 | 14.61 | 14.94 | ||

14 | 25.4 | 23.394 | 23.118 | 23.06 | 23.58 | ||

2 | Gene. | 3 | 214.1 | 209.96 | 201.83 | 203.81 | 202.85 |

Load | 6 | 167.8 | 164.55 | 158.18 | 159.71 | 164.05 | |

10 | 19.0 | 18.633 | 17.912 | 18.082 | 15.25 | ||

13 | 27.3 | 26.772 | 26.772 | 25.98 | 23.551 | ||

Loss | 1 | 29.78 | 27.896 | 26.73 | 26.24 | 26.77 | |

Total Transaction byGene. (2 + 3 + 4) | 469.8 | 445.46 | 437.58 | 435.98 | 440.25 | ||

Deviation in Power Transaction (MW) | 24.34 | 32.22 | 33.82 | 29.55 | |||

Rescheduling Cost of generation ($/h) | 913 | 1229.08 | 1309.78 | 1126.76 |

Tr. Line No. | Line Designation | Line Rating (p.u.) | Line Loading (p.u.) | ||
---|---|---|---|---|---|

without FACTS | with TCSC [10] | with UPFC | |||

8 | 4–11 | 0.2500 | 0.3222 | 0.2933 | 0.2580 |

#### 6.1.2. Case 2: IEEE 30-Bus System

- A.
**The group curtailment strategy**is applied to all the groups, and the curtailment follows a linear relationship among the loads of each group. The willingness to pay price factor is chosen as 1$/MWh ($ signifies an arbitrary unit of currency) for all the participants in the groups.- B.
- Here, groups 1 and 2 follow a
**point-to-point curtailment strategy**for dispatching bilateral contracts. Others follow the same strategy as A.

Gr. No. | Bus No. | Desired Gene. and Load (MW) | Case 2A | Case 2B | |
---|---|---|---|---|---|

1 | Gene. | 2 | 67.65 | 63.84 | 58.24 |

Load | 8 | 11.4 | 10.94 | 9.25 | |

10 | 34.2 | 33.26 | 31.14 | ||

13 | 16.8 | 15.35 | 13.64 | ||

16 | 5.25 | 4.29 | 4.21 | ||

2 | Gene. | 4 | 40.6 | 36.84 | 31.33 |

Load | 7 | 3.6 | 3.14 | 2.51 | |

18 | 3.8 | 3.28 | 2.68 | ||

19 | 13.25 | 12.74 | 11.23 | ||

20 | 3.3 | 2.7 | 1.85 | ||

24 | 13.05 | 12.17 | 11.21 | ||

29 | 3.6 | 2.81 | 1.85 | ||

3 | Gene. | 3 | 44.41 | 40.23 | 40.54 |

5 | 24.15 | 20.27 | 20.71 | ||

6 | 28.03 | 23.96 | 23.98 | ||

Load | 12 | 8.7 | 7.1 | 7.3 | |

14 | 9.4 | 8.12 | 8.31 | ||

15 | 12.5 | 11.24 | 11.32 | ||

17 | 13.6 | 11.68 | 11.7 | ||

21 | 26.28 | 23.14 | 23.45 | ||

23 | 4.83 | 3.92 | 3.95 | ||

26 | 5.38 | 4.74 | 4.75 | ||

30 | 15.9 | 14.42 | 14.45 | ||

Loss | 1 | 15.27 | 14.34 | 13.69 | |

Total Transaction by Gene. (2 + 3 + 4 + 5 + 6) | 204.84 | 185.14 | 174.8 | ||

Deviation in Power transaction (MW) | 19.7 | 30.04 | |||

Rescheduling Cost of generation ($/h) | 664.88 | 947.19 |

Line Designation | Line Rating (p.u.) | Line Loading (p.u.) | |
---|---|---|---|

without FACTS | with UPFC | ||

1–2 | 1.3 | 2.327 | 1.317 |

2–4 | 0.65 | 0.856 | 0.648 |

2–6 | 0.65 | 0.945 | 0.65 |

#### 6.2. Discussions: 14-Bus System and 30-Bus System

## 7. Conclusions

## Author Contributions

## Funding

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## Nomenclature

OPD | optimal power dispatch |

MFO | moth flame optimization |

MMFO | modified moth flame optimization |

GENCOs | generating companies |

DISCOs | distribution companies |

LMPD | locational marginal-price dispatch |

UPFC | unified power flow controller |

A | a constant matrix that shows curtailment strategies follows by market utilities |

w | diagonal matrix having elements of willingness-to-pay price factor |

${P}_{i}\text{}\mathrm{and}\text{}{P}_{i0}$ | actual and desired control variables respectively i.e., active power injection or extraction. |

u | number of market participants |

${P}_{Gi}\text{}\mathrm{and}\text{}{Q}_{Gi}$ | active and reactive power generation of GENCO-i |

${P}_{Di}\text{}\mathrm{and}\text{}{Q}_{Di}$ | active and reactive power demand of DISCO-i |

${P}_{Gi}^{min},{P}_{Gi}^{max}$ and ${Q}_{Gi}^{min},{Q}_{Gi}^{max}$ | active and reactive power’s lower and upper limits of GENCO-i |

${V}_{i}^{min}\text{}\mathrm{and}\text{}{V}_{i}^{max}$ | voltage limit of GENCO-i |

G | number of group transfers |

${{P}_{b}}_{ij}$ | power injection at GENCO-i in pursuance of bilateral contract with aDISCO-j. |

${{L}_{b}}_{ji}$ | power extraction by DISCO-j in pursuance of bilateral contract with aGENCO-i. |

${{P}_{m}}_{ig}$ | power injection at GENCO-i under multilateral contract |

${{L}_{m}}_{jg}$ | power extraction by DISCO-j under multilateral contract |

## Appendix A

Ref. | Problem’s Objective | Methodology | Techniques Used |
---|---|---|---|

[1] (2019) | minimize congestion rent | optimal power flow and available transfer capability | Gravitational search assisted algorithm |

[2] (2015) | minimizing fuel and emission penalty cost of generators and congestion management | Optimal Location of Series FACTS Devices | Hybrid Bacterial Foraging and Nelder Mead Algorithm |

[4] (1998) | Minimize transaction deviation for congestion management | Load curtailment using curtailment strtageies | Optimal power flow |

[10] (2000) | minimize the curtailment of the contracted powers in a power market | Curtailment strategy | Optimal power flow |

[25] (2021) | Minimize congestion cost | Voltagesecurity margin (λ) and corrected transient energy margin (CTEM) | MultiObjective Dragonfly Algorithm (MODA) |

[33] (2019) | Minimization of Active Power Rescheduling Cost | By Identifying the Participating Rescheduling Generators | Twin Extremity Chaotic Map Adaptive Particle Swarm Optimization |

[43] (2017) | improving voltage profile and reducing the power loss | Optimal placement and sizing of DGs | Moth flame optimization |

[44] (2023) | minimize the cost of rescheduling and the total change in power after rescheduling. | sensitivity based rescheduling of generators | improved monarch butterfly optimization |

[45] (2022) | optimizes the generating power and manages the congestion with minimized rescheduling cost. | rescheduling of generators | Hybridizing lion and moth search models |

[46] (2022) | lower the cost of active and reactive power of the generators | reduce the deviation of rescheduled active and reactive power from scheduled values | Particle Swarm Optimization Algorithm |

[47] (2023) | reduce transmission network congestion in a pool-based energy market | active power rescheduling of generators via Optimal DG Capacity | Firefly algorithm |

[48] (2023) | minimum congestion cost | rescheduling of generators | Hybrid Deep Neural Network |

[49] (2022) | minimizes the congestion with the smallest possible rescheduling price | rescheduling of generators | Particle Swarm Optimization with Distributed Acceleration Constants |

[50] (2023) | Optimal location and sizing of DGs | optimum placement and sizing of DGs to be integrated with a transmission line system | Load Flow Based Scheme |

[51] (2022) | minimum voltage security margin (VSM) index to eliminate the congestion of electrical lines | Transmission Switching (TS) based cost-effective approach | Load Flow Based Scheme |

[52] (2021) | To Minimize Real Power Losses, Generation Cost and Voltage Deviations | Optimal Location of TCSC | Improved Grey Wolf Optimization (IGWO) |

Generator Number | Voltage Limits | Reactive Power Limits | ||
---|---|---|---|---|

${\mathit{V}}_{\mathit{i}}^{\mathit{m}\mathit{i}\mathit{n}}$ | ${\mathit{V}}_{\mathit{i}}^{\mathit{m}\mathit{a}\mathit{x}}$ | ${\mathit{Q}}_{\mathit{i}}^{\mathit{m}\mathit{i}\mathit{n}}$ | ${\mathit{Q}}_{\mathit{i}}^{\mathit{m}\mathit{a}\mathit{x}}$ | |

1 | 0.95 | 1.08 | 0 | 40 |

2 | 0.95 | 1.08 | 0 | 60 |

3 | 0.95 | 1.08 | −20 | 100 |

4 | 0.95 | 1.08 | 0 | 87 |

5 | 0.95 | 1.09 | 0 | 35 |

Generator Number | Voltage Limits | Reactive Power Limits | ||
---|---|---|---|---|

${\mathit{V}}_{\mathit{i}}^{\mathit{m}\mathit{i}\mathit{n}}$ | ${\mathit{V}}_{\mathit{i}}^{\mathit{m}\mathit{a}\mathit{x}}$ | ${\mathit{Q}}_{\mathit{i}}^{\mathit{m}\mathit{i}\mathit{n}}$ | ${\mathit{Q}}_{\mathit{i}}^{\mathit{m}\mathit{a}\mathit{x}}$ | |

1 | 0.96 | 1.06 | −30 | 100 |

2 | 0.96 | 1.043 | −30 | 100 |

3 | 0.96 | 1.01 | −30 | 100 |

4 | 0.96 | 1.01 | −30 | 100 |

5 | 0.96 | 1.082 | −30 | 100 |

6 | 0.96 | 1.071 | −30 | 100 |

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**Table 1.**Average and standard deviation values of MMFO in comparison with other techniques for unimodal benchmark functions.

F | MMFO | MFO | PSO | GSA | GA | |||||
---|---|---|---|---|---|---|---|---|---|---|

Average | Std. dev. | Average | Std. dev. | Average | Std. dev. | Average | Std. dev. | Average | Std. dev. | |

F1 | 5.1296 × 10^{−28} | 9.581 × 10^{−28} | 0.000117 | 0.00015 | 1.321152 | 1.153887 | 608.2328 | 464.6545 | 21886.03 | 2879.58 |

F2 | 1.9844 × 10^{−17} | 3.017 × 10^{−17} | 0.000639 | 0.000877 | 7.715564 | 4.132128 | 22.75268 | 3.365135 | 56.51757 | 5.660857 |

F3 | 333.333 | 1268.5 | 696.7309 | 188.5279 | 736.3931 | 361.7818 | 135760.8 | 48652.63 | 37010.29 | 5572.212 |

F4 | 0.0056 | 0.0140 | 70.68646 | 5.275051 | 12.97281 | 2.634432 | 78.78198 | 2.814108 | 59.14331 | 4.648526 |

F5 | 3066 | 16421 | 139.1487 | 120.2607 | 77360.83 | 51156.15 | 741.003 | 781.2393 | 31321418 | 5264496 |

F6 | 1.6528 × 10^{−27} | 4.777 × 10^{−27} | 0.000113 | 9.87 × 10^{−5} | 286.6518 | 107.0796 | 3080.964 | 898.6345 | 20964.83 | 3868.109 |

F7 | 0.0056 | 0.0048 | 0.091155 | 0.04642 | 1.037316 | 0.310315 | 0.112975 | 0.037607 | 13.37504 | 3.08149 |

**Table 2.**Average and standard deviation values of MMFO in comparison with other techniques for multimodal benchmark functions.

F | MMFO | MFO | PSO | GSA | GA | |||||
---|---|---|---|---|---|---|---|---|---|---|

Average | Std. dev. | Average | Std. dev. | Average | Std. dev. | Average | Std. dev. | Average | Std. dev. | |

F8 | −8775.10 | 795.4405 | −8496.78 | 725.8737 | −3571 | 430.7989 | −2352.32 | 382.167 | −6331.19 | 332.5668 |

F9 | 20.2687 | 11.1062 | 84.60009 | 16.16658 | 124.2973 | 14.25096 | 31.00014 | 13.66054 | 236.8264 | 19.03359 |

F10 | 1.0125 × 10^{−14} | 1.435 × 10^{−14} | 1.260383 | 0.72956 | 9.167938 | 1.568982 | 3.740988 | 0.171265 | 17.84619 | 0.531147 |

F11 | 0.00284 | 0.00258 | 0.01908 | 0.021732 | 12.41865 | 4.165835 | 0.486826 | 0.049785 | 179.9046 | 32.43956 |

F12 | 0.0622 | 0.1506 | 0.894006 | 0.88127 | 13.87378 | 5.85373 | 0.46344 | 0.137598 | 34131682 | 1893429 |

F13 | 0.0029 | 0.0049 | 0.115824 | 0.193042 | 11813.5 | 30701.9 | 7.617114 | 1.22532 | 1.08 × 10^{8} | 3849748 |

Congested Line | Line Rating (p.u.) | Congestion Situation | with UPFC |
---|---|---|---|

4–11 | 0.2500 | Before | 0.2580 |

After | 0.2460 |

Gr. No. | Bus No. | Desired Generation and Load (MW) | GA [29] | PSO [35] | MFO | MMFO | |
---|---|---|---|---|---|---|---|

1 | Gene. | 2 | 157.7 | 157.7 | 157.7 | 157.7 | 157.7 |

4 | 98.0 | 83.92 | 84.67 | 85.94 | 88.52 | ||

Load | 7 | 102.9 | 96.48 | 96.75 | 97.29 | 97.85 | |

9 | 57.8 | 54.9 | 55.06 | 55.98 | 56.17 | ||

11 | 53.5 | 50.43 | 50.81 | 51.34 | 51.45 | ||

12 | 16.1 | 15.41 | 15.48 | 15.64 | 15.81 | ||

14 | 25.4 | 23.94 | 24.27 | 24.39 | 24.94 | ||

2 | Gene. | 3 | 214.1 | 210.9 | 211.53 | 212.52 | 213.34 |

Load | 6 | 167.8 | 165.81 | 165.9 | 167.7 | 167.85 | |

10 | 19.0 | 18.62 | 18.74 | 17.87 | 18.54 | ||

13 | 27.3 | 26.5 | 26.8 | 26.95 | 26.95 | ||

Loss | 1 | 30.349 | 28.834 | 28.834 | 25.346 | 24.226 | |

Total Transaction by Gene. | 469.8 | 452.52 | 453.9 | 456.16 | 459.56 | ||

Deviation in Power Transaction (MW) | 17.28 | 15.9 | 13.64 | 10.24 | |||

Rescheduling Cost of gene. ($/h) | 798.96 | 749.01 | 699.42 | 665.16 |

Techniques | without FACTS | GA | PSO | MFO | MMFO |
---|---|---|---|---|---|

Time (S) | 19.055 | 18.847 | 17.855 | 17.107 | 16.910 |

Congested Line | Line Rating (p.u.) | Congestion Situation | with UPFC |
---|---|---|---|

1–2 | 1.30 | Before | 1.317 |

After | 1.294 |

Gr. No. | Bus No. | Desired Gene. and Load (MW) | GA [29] | PSO [35] | MFO | MMFO | |
---|---|---|---|---|---|---|---|

1 | Gene. | 2 | 67.65 | 64.28 | 64.98 | 66.54 | 66.63 |

Load | 8 | 11.4 | 11.12 | 11.21 | 11.36 | 11.38 | |

10 | 34.2 | 33.46 | 33.57 | 33.98 | 34 | ||

13 | 16.8 | 15.38 | 15.64 | 15.98 | 16.1 | ||

16 | 5.25 | 4.32 | 4.38 | 5.14 | 5.15 | ||

2 | Gene. | 4 | 40.6 | 37.26 | 38.24 | 39.58 | 39.86 |

Load | 7 | 3.6 | 3.23 | 3.345 | 3.36 | 3.45 | |

18 | 3.8 | 3.31 | 3.375 | 3.45 | 3.69 | ||

19 | 13.25 | 12.84 | 12.935 | 13.18 | 13.2 | ||

20 | 3.3 | 2.72 | 2.875 | 3.12 | 3.2 | ||

24 | 13.05 | 12.24 | 12.485 | 12.96 | 12.98 | ||

29 | 3.6 | 2.92 | 2.985 | 3.21 | 3.34 | ||

3 | Gene. | 3 | 44.41 | 40.42 | 40.67 | 42.24 | 44.12 |

5 | 24.15 | 20.89 | 21.054 | 22.27 | 23.28 | ||

6 | 28.03 | 24.24 | 24.98 | 26.94 | 26.52 | ||

Load | 12 | 8.7 | 7.38 | 7.51 | 8.12 | 8.56 | |

14 | 9.4 | 8.22 | 8.28 | 8.94 | 9.24 | ||

15 | 12.5 | 11.286 | 11.52 | 12.1 | 12.25 | ||

17 | 13.6 | 11.69 | 11.89 | 12.59 | 12.94 | ||

21 | 26.28 | 23.744 | 23.92 | 25.04 | 25.78 | ||

23 | 4.83 | 3.98 | 4.19 | 4.68 | 4.67 | ||

26 | 5.38 | 4.78 | 4.83 | 5.02 | 5.24 | ||

30 | 15.9 | 14.47 | 14.56 | 14.96 | 15.24 | ||

Loss | 1 | 15.27 | 14.17 | 13.65 | 11.31 | 10.94 | |

Total Transaction by Gene. (2 + 3 + 4 + 5 + 6) | 204.84 | 187.09 | 189.924 | 195.57 | 200.41 | ||

Deviation in Power Transaction (MW) | 17.75 | 14.916 | 9.27 | 4.43 | |||

Rescheduling Cost of generation ($/h) | 601.14 | 546.48 | 493.6 | 469.12 |

Techniques | without FACTS | GA | PSO | MFO | MMFO |
---|---|---|---|---|---|

Time (S) | 25.72 | 24.84 | 24.32 | 23.625 | 23.10 |

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© 2023 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 (https://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Sahoo, A.; Hota, P.K.; Sahu, P.R.; Alsaif, F.; Alsulamy, S.; Ustun, T.S.
Optimal Congestion Management with FACTS Devices for Optimal Power Dispatch in the Deregulated Electricity Market. *Axioms* **2023**, *12*, 614.
https://doi.org/10.3390/axioms12070614

**AMA Style**

Sahoo A, Hota PK, Sahu PR, Alsaif F, Alsulamy S, Ustun TS.
Optimal Congestion Management with FACTS Devices for Optimal Power Dispatch in the Deregulated Electricity Market. *Axioms*. 2023; 12(7):614.
https://doi.org/10.3390/axioms12070614

**Chicago/Turabian Style**

Sahoo, Abhilipsa, Prakash Kumar Hota, Preeti Ranjan Sahu, Faisal Alsaif, Sager Alsulamy, and Taha Selim Ustun.
2023. "Optimal Congestion Management with FACTS Devices for Optimal Power Dispatch in the Deregulated Electricity Market" *Axioms* 12, no. 7: 614.
https://doi.org/10.3390/axioms12070614