# Optimal Placement, Sizing and Coordination of FACTS Devices in Transmission Network Using Whale Optimization Algorithm

^{1}

^{2}

^{*}

## Abstract

**:**

## 1. Introduction

#### 1.1. Stability Issues of Power Transmission

_{1}and V

_{2}and having respective angles is given by Equation (1) [1].

_{1}= V

_{2}= V, the total power that can be transmitted on a lossless transmission line is determined by the reactance of the line. Hence, line reactance often sets the theoretical steady-state limit on power transmission. The thermal limit for practical transmission lines with resistance R may be set by I

^{2}R losses, which cause heating in a conductor. Thus, it changes the physical characteristics of the transmission line, and at a certain temperature, it may cause permanent sag. Usually, for large transmission lines reactance (X), and for small transmission line resistance (R), sets the thermal limits. However, transmission line reactance cannot be decreased significantly because of thermal limitations [2,3]. In addition, there are limitations imposed on transmission lines due to its insulation capabilities, which are referred to as dielectric limits. Total power transfer capability of transmission lines can also be restricted by stability limitations, which is because of voltage or frequency collapse, steady-state stability, sub-synchronous resonance, and transient stability. From the above discussion, it can be concluded that the loading capability of the transmission line has mainly three restrictions: stability limits, thermal limits, and dielectric limits.

#### 1.2. Controlled Parameters of Different FACTS

## 2. Modeling of FACTS

#### 2.1. Modeling of TCSC

#### 2.2. Modeling of SVC

#### 2.3. Modeling of UPFC

^{o}. The static-model of UPFC is presented in Figure 4.

## 3. Optimal Placement of FACTS

#### 3.1. Optimal Placement of TCSC

_{r}is the VAr demand at receiving bus, V

_{s}is the magnitude of the bus voltage of sending end, $\theta $ is the difference of bus angles, and $\delta $ is the impedance angle. More details about the Lmn index can be found in [38].

#### 3.2. Optimal Placement of SVC

#### 3.3. Optimal Placement of UPFC

## 4. Problem Formulation

- Bus voltages should be in their appropriate limits as$$0.95\le {V}_{j}\le 1.05$$
- Thermal limits of transmission lines$${S}_{min}\le {S}_{L}\le {S}_{max}$$
- Generator’s reactive power supply limits$${Q}_{g,\text{}min}\le {Q}_{g\text{}}\le {Q}_{g,max}$$
- Limit on the arrangements of the transformer tap setting$${T}_{i,\text{}min}\le {T}_{i}\le {T}_{i,\text{}max}$$
- SVC size constraints$$-0.9\le {Z}_{SVC}\le 0.9\text{}\left(pu\right)$$
_{SVC}is the size of the SVC in pu. - TCSC size constraints$$-0.8{X}_{L}\le \text{}{X}_{TCSC}\le 0.2{X}_{L}\text{}pu$$
_{TCSC}is the size of the TCSC in pu

## 5. Whale Optimization Algorithm

- Encircling prey
- Exploitation phase
- Exploration phase

#### 5.1. Encircling Prey

#### 5.2. Exploitation Phase

#### 5.2.1. Shrinking-Encircling Technique

#### 5.2.2. Spirals-Updating Position Technique

#### 5.3. Searching for Prey (Exploration-Phase)

_{1}A

_{2}A

_{3}… A

_{18}]. For 14 bus systems, A

_{1–4}decision variables are TCSC sizes, A

_{5–8}are SVC sizes, A

_{9–11}are UPFC sizes, A

_{12–14}are tap setting values of the transformers, and A

_{15–18}are the reactive power values of generators. Similarly, each search agent/whale is composed and initialized for the 30 bus system. The initial population matrix of 100 search-agents/whales is stored in a column matrix of 100 × 18 variables. As WOA proceeds, exploration and exploitation phases of WOA optimize values of the decision variables.

#### 5.4. Flowchart

## 6. Results and Discussions

#### 6.1. Test Case IEEE-14 Bus System

^{7}($) as compared to PSO and GA, which converged at 1.0714 × 10

^{7}($) and 1.012 × 10

^{7}($), respectively. Hence WOA saved 719 × 10

^{3}($) more as compared to PSO and 125 × 10

^{3}($) more as compared to GA. Similarly, for all other loading scenarios. Hence WOA has better convergence characteristics and provided more savings in operating cost as compared to PSO and GA.

_{best}) and global best (G

_{best}), thus, increasing its chances of jamming at some local optima instead of the global optima [44].

#### 6.2. Test Case IEEE 30 Bus System

^{7}$. Using the Lmn sensitivity index, suitable locations for the TCSCs placement in the IEEE 30 bus system are branches 7, 15, and 20. Similarly, using the PV curves, buses with higher voltage deviations with increasing loads are 26, 29, and 30, thus, they are weak buses and the SVC’s are positioned at these buses.

## 7. Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 5.**Predictor and corrector scheme used in CPF [39].

**Figure 6.**Shrinking-encircling technique [42].

**Figure 7.**Spiral-updating position technique [42].

**Figure 13.**Change in Operating cost with the addition of FACTS at 150% reactive loading using PSO, GA, and WOA.

**Figure 14.**Change in operating cost with the addition of FACTS at 200% reactive loading using PSO, GA, and WOA.

**Figure 16.**Comparison of real losses without and with FACTS in the IEEE-30 system using different techniques.

**Figure 19.**Change in operating cost with the addition of FACTS at 150% reactive loading using PSO, GA, and WOA.

**Figure 20.**Change in the operating cost with the addition of FACTS at 200% reactive loading using PSO, GA, and WOA.

**Table 1.**Comparison of basic types of FACTS devices based on their impact on different applications.

FACTS Device | Real Power Flow | Transient Stability | Voltage Control | Dynamic Stability |
---|---|---|---|---|

Thyristor-controlled series-compensators (TSSC, TCSC) | Medium | Strong | Small | Medium |

Static synchronous compensators (STATCOM) | Small | Medium | Strong | Medium |

Static-VAR-Compensators (TCS, SVC, TRS) | Small | Small | Strong | Medium |

Unified-Power-Flow-Controllers (UPFC) | Strong | Medium | Strong | Medium |

Test-System | No. of TCSC | No. of SVCs | No. of UPFCs | No. of Tap Settings of Transformer | Var Generation Units |
---|---|---|---|---|---|

IEEE-14 bus system | 4 | 4 | 3 | 3 | 4 |

IEEE-30 bus system | 3 | 3 | 3 | 4 | 5 |

**Table 3.**Cost of power loss and operating cost of the system with FACTS in the IEEE-14 bus system using different techniques.

Percentage Reactive Loadings | Total Cost of Power Loss of System (A) $ | Algorithm Used to Minimize Objective Function | FACTS Devices Cost ($) | Operating Cost with FACTS Devices (B) $ |
---|---|---|---|---|

200 | 1.1952 × 10^{7} | PSO | 3.433 × 10^{5} | 1.172 × 10^{7} |

GA | 2.988 × 10^{5} | 1.1029 × 10^{7} | ||

WOA | 2.870 × 10^{5} | 1.0891 × 10^{7} | ||

150 | 1.1442 × 10^{7} | PSO | 3.033 × 10^{5} | 1.1199 × 10^{7} |

GA | 2.580 × 10^{5} | 1.0318 × 10^{7} | ||

WOA | 2.525 × 10^{5} | 1.021 × 10^{7} | ||

100 | 1.1226 × 10^{7} | PSO | 3.677 × 10^{5} | 1.0714 × 10^{7} |

GA | 3.202 × 10^{5} | 1.012 × 10^{7} | ||

WOA | 2.424 × 10^{5} | 0.9995 × 10^{7} |

**Table 4.**Optimal setting of variables by PSO, GA, and WOA at various loading scenarios in IEEE-14 bus system.

Fitness Function Variables | Optimal Settings at 200% Reactive Loading (p.u) | Optimal Settings at 150% Reactive Loading (p.u) | Optimal Settings at 100% Reactive Loading (p.u) | ||||||
---|---|---|---|---|---|---|---|---|---|

PSO | GA | WOA | PSO | GA | WOA | PSO | GA | WOA | |

SVC (7) | 0.003 | 0.201 | 0.041 | 0.051 | 0.160 | 0.029 | 0.011 | 0.090 | 0.001 |

SVC (9) | 0.022 | 0.170 | 0.034 | 0.012 | 0.120 | 0.290 | 0.061 | 0.052 | 0.001 |

SVC (11) | 0.194 | 0.112 | 0.005 | 0.125 | 0.070 | 0.094 | 0.002 | 0.040 | 0.061 |

SVC (14) | 0.127 | 0.061 | 0.002 | 0.102 | 0.102 | 0.081 | 0.194 | 0.150 | 0.001 |

TCSC (8) | 0.001 | 0.014 | 0.050 | 0.086 | 0.124 | 0.005 | 0.034 | 0.102 | 0.060 |

TCSC (9) | 0.002 | 0.008 | 0.050 | 0.018 | 0.001 | 0.059 | 0.011 | 0.016 | −0.040 |

TCSC (15) | 0.014 | 0.024 | 0.061 | 0.000 | 0.067 | 0.073 | 0.040 | 0.043 | 0.051 |

TCSC (18) | 0.001 | 0.000 | 0.019 | 0.001 | 0.017 | 0.000 | 0.001 | 0.011 | 0.091 |

UPFC (3) | 0.006 | 0.019 | 0.004 | 0.000 | 0.008 | 0.031 | 0.170 | 0.001 | 0.001 |

UPFC (2) | 0.280 | 0.000 | 0.001 | 0.002 | 0.009 | 0.001 | 0.003 | 0.039 | 0.100 |

UPFC (5) | 0.001 | 0.001 | 0.009 | 0.070 | 0.001 | 0.311 | 0.000 | 0.002 | 0.000 |

QG (2) | 0.122 | 0.154 | 0.601 | 0.015 | 0.681 | 0.600 | 0.312 | 0.613 | 0.551 |

QG (3) | 0.321 | 0.277 | 0.581 | 0.419 | 0.083 | 0.369 | 0.389 | 0.667 | 0.481 |

QG (6) | 0.415 | 0.091 | 0.182 | 0.225 | 0.184 | 0.487 | 0.413 | 0.519 | 0.101 |

QG (8) | 0.087 | 0.623 | 0.163 | 0.451 | 0.212 | 0.098 | 0.513 | 0.082 | 0.682 |

TAP (8) | 0.982 | 1.018 | 0.900 | 0.913 | 0.976 | 1.0300 | 0.905 | 1.054 | 0.901 |

TAP (9) | 0.995 | 0.919 | 0.991 | 0.985 | 0.992 | 0.902 | 0.991 | 0.981 | 0.978 |

TAP (10) | 0.957 | 0.996 | 0.985 | 0.996 | 1.000 | 1.013 | 0.916 | 0.985 | 0.901 |

**Table 5.**Cost of power loss and operating cost of the system with the FACTS in the IEEE-30 bus system using different techniques.

Percentage Reactive Loading | Total Cost of Power Loss of System (A) ($) | Algorithm Used to Minimize Objective Function | FACTS Devices Cost ($) | Operating Cost with FACTS (B) ($) |
---|---|---|---|---|

200 | 1.4902 × 10^{7} | PSO | 3.774 × 10^{5} | 1.393 × 10^{7} |

GA | 3.517 × 10^{5} | 1.325 × 10^{7} | ||

WOA | 3.527 × 10^{5} | 1.318 × 10^{7} | ||

150 | 1.443 × 10^{7} | PSO | 3.479 × 10^{5} | 1.3601 × 10^{7} |

GA | 3.082 × 10^{5} | 1.215 × 10^{7} | ||

WOA | 3.028 × 10^{5} | 1.205 × 10^{7} | ||

100 | 1.4152 × 10^{7} | PSO | 3.136 × 10^{5} | 1.266 × 10^{7} |

GA | 2.908 × 10^{5} | 1.177 × 10^{7} | ||

WOA | 2.791 × 10^{5} | 1.1703 × 10^{7} |

**Table 6.**Optimal settings of variables by PSO, GA, and WOA at various loading scenarios in IEEE-30 bus system.

Fitness Function Variables | Optimal Setting at 200% Reactive Loading | Optimal Setting at 150% Reactive Loading | Optimal Setting at 100% Reactive Loading | ||||||
---|---|---|---|---|---|---|---|---|---|

PSO | GA | WOA | PSO | GA | WOA | PSO | GA | WOA | |

SVC (26) | 0.041 | 0.045 | 0.057 | 0.051 | 0.031 | 0.049 | 0.021 | 0.032 | 0.000 |

SVC (29) | 0.194 | 0.211 | 0.049 | 0.143 | 0.117 | 0.240 | 0.078 | 0.046 | 0.010 |

SVC (30) | 0.142 | 0.108 | 0.0418 | 0.072 | 0.093 | 0.140 | 0.055 | 0.048 | 0.018 |

TCSC (15) | 0.026 | 0.014 | 0.050 | 0.086 | 0.124 | 0.005 | 0.034 | 0.102 | 0.060 |

TCSC (7) | 0.015 | 0.024 | 0.061 | 0.000 | 0.067 | 0.073 | 0.040 | 0.043 | 0.051 |

TCSC (20) | 0.048 | 0.008 | 0.050 | 0.018 | 0.001 | 0.059 | 0.011 | 0.016 | −0.040 |

UPFC (3) | 0.018 | 0.011 | 0.241 | 0.011 | 0.028 | 0.051 | 0.017 | 0.011 | 0.041 |

UPFC (6) | 0.003 | 0.034 | 0.004 | 0.037 | 0.005 | 0.031 | 0.023 | 0.013 | 0.041 |

UPFC (4) | 0.025 | 0.028 | 0.031 | 0.024 | 0.009 | 0.051 | 0.016 | 0.037 | 0.001 |

QG (2) | 0.318 | 0.158 | 0.590 | 0.267 | 0.042 | 0.131 | 0.198 | 0.267 | 0.610 |

QG (5) | 0.248 | 0.103 | 0.290 | 0.364 | 0.698 | 0.591 | 0.014 | 0.388 | 0.509 |

QG (8) | 0.023 | 0.191 | 0.501 | 0.611 | 0.045 | 0.610 | 0.581 | 0.314 | 0.098 |

QG (11) | 0.518 | 0.208 | 0.191 | 0.317 | 0.142 | 0.519 | 0.318 | 0.301 | 0.611 |

QG (13) | 0.032 | 0.605 | 0.189 | 0.345 | 0.298 | 0.181 | 0.676 | 0.097 | 0.184 |

TAP (11) | 0.914 | 0.904 | 1.034 | 0.982 | 0.914 | 0.991 | 0.948 | 0.903 | 1.032 |

TAP (12) | 1.038 | 0.981 | 1.050 | 0.938 | 0.901 | 0.990 | 0.934 | 1.012 | 0.920 |

TAP (15) | 0.902 | 0.958 | 1.043 | 0.984 | 0.918 | 1.020 | 0.931 | 0.907 | 1.018 |

TAP (36) | 0.918 | 0.905 | 0.988 | 0.901 | 0.926 | 1.038 | 0.938 | 0.994 | 0.991 |

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**MDPI and ACS Style**

Nadeem, M.; Imran, K.; Khattak, A.; Ulasyar, A.; Pal, A.; Zeb, M.Z.; Khan, A.N.; Padhee, M.
Optimal Placement, Sizing and Coordination of FACTS Devices in Transmission Network Using Whale Optimization Algorithm. *Energies* **2020**, *13*, 753.
https://doi.org/10.3390/en13030753

**AMA Style**

Nadeem M, Imran K, Khattak A, Ulasyar A, Pal A, Zeb MZ, Khan AN, Padhee M.
Optimal Placement, Sizing and Coordination of FACTS Devices in Transmission Network Using Whale Optimization Algorithm. *Energies*. 2020; 13(3):753.
https://doi.org/10.3390/en13030753

**Chicago/Turabian Style**

Nadeem, Muhammad, Kashif Imran, Abraiz Khattak, Abasin Ulasyar, Anamitra Pal, Muhammad Zulqarnain Zeb, Atif Naveed Khan, and Malhar Padhee.
2020. "Optimal Placement, Sizing and Coordination of FACTS Devices in Transmission Network Using Whale Optimization Algorithm" *Energies* 13, no. 3: 753.
https://doi.org/10.3390/en13030753