# Impact of Flexible AC Transmission System Devices on Automatic Generation Control with a Metaheuristic Based Fuzzy PID Controller

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## Abstract

**:**

## 1. Introduction

- To recommend a teaching–learning-based optimization (TLBO)-based fuzzy PID controller for the AGC problem;
- To illustrate the superiority of the fuzzy PID controller with non-linearities such as the transport delay (TD), generation rate constraint (GRC), and governor dead band (GDB) for the AGC problem;
- To demonstrate the performance of various FACTS devices incorporated in the system;
- To observe the effectiveness of the fuzzy PID plus unified power flow controller (UPFC) device for various disturbances such as step and random step load disturbances.

## 2. Materials and Methods

#### Control Structure

_{1}and K

_{2}were the input scaling factors of the FLC. The FLC output was multiplied with K

_{P}, K

_{I}, and K

_{D}and then summed to give the total controller output. The outputs of the fuzzy controllers ${U}_{THi}$ and ${U}_{HYi}$ were the control inputs of the power system.

## 3. Teaching–Learning-Based Optimization (TLBO) Algorithm

#### 3.1. Intilization

#### 3.2. Teacher Phase

#### 3.3. Learner Phase

## 4. Results and Discussion

^{−5}; ITSE = 1.0963 × 10

^{−4}; IAE = 0.0377; ITAE = 0.5600) when compared to the SSSC (ISE = 0.0011; ITSE = 0.0025; IAE = 0.1297; ITAE = 0.7814), TCPS (ISE = 0.0018; ITSE = 0.0037; IAE = 0.1500; ITAE = 0.7040), and TCSC (ISE = 0.0018; ITSE = 0.0024; IAE = 0.1266; ITAE = 0.6194). Table 3 also reveals that the values of settling time and under shoots were lower for the UPFC-incorporated system when compared to others.

#### Robustness Analysis

## 5. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

## Appendix A

Nomenclature | Value | |

i | Subscript referred to area i (1, 2) | |

F | Nominal system frequency (Hz) | 60Hz |

${P}_{Ri}$ | Rated power of area i (MW) | 2000 MW |

$\Delta {F}_{i}$ | Incremental change in frequency of area i (Hz) | |

$\Delta {P}_{D}{}_{i}$ | Incremental step load change of area i | |

$\Delta {P}_{Tie}$ | Incremental change in tie-line power between areas 1 and 2 (p.u.) | |

$AC{E}_{i}$ | Area control error of area i | |

${B}_{i}$ | Frequency bias parameter of area i (p.u. MW/Hz) | 0.425 |

${T}_{Gi}$ | Speed governor time constant for thermal unit of area i (s) | 0.08 |

${T}_{Ti}$ | Steam turbine time constant of area i (s) | 0.3 |

${T}_{PSi}$ | Power system time constant of area i (s) | 20 |

${K}_{PSi}$ | Power system gain of area i (Hz/p.u. MW) | 120 |

${T}_{12}$ | Synchronizing coefficient between areas 1 and 2 (p.u.) | 0.0113 |

${K}_{ri}$ | Steam turbine reheat constant of area i | 0.5 |

R | Regulation parameter | 2.4 |

${T}_{ri}$ | Steam turbine reheat time constant of area i (s) | 10 |

${T}_{Wi}$ | Nominal starting time of water in penstock of area i (s) | 1 |

${T}_{RSi}$ | Hydro turbine speed governor reset time of area i (s) | 5 |

${T}_{RHi}$ | Hydro turbine speed governor transient droop time constant of area i (s) | 0.513 |

${T}_{GHi}$ | Hydro turbine speed governor main servo time constant of area i (s) | 48.7 |

${T}_{F}$ | Teaching feature | |

${t}_{sim}$ | Simulation time (s) | 50 |

${a}_{12}$ | $-{P}_{R1}/{P}_{R2}$ | −1 |

$ap{f}_{}$ | Area participation factor | 0.5 |

#### Appendix A.1. Transfer Function Model and Data for SSSC

#### Appendix A.2. Transfer Function Model and Data for TCSC

#### Appendix A.3. Transfer Function Model and Data for TCPS

#### Appendix A.4. Transfer Function Model and Data for UPFC

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**Table 1.**Parameters of Fuzzy PID controller. SSSC—static synchronous series compensator; TCSC—thyristor-controlled series capacitor; TCPS—thyristor-controlled phase shifter (TCPS); UPFC—unified power flow controller.

Controller/Parameters | Fuzzy PID | Fuzzy PID-SSSC | Fuzzy PID-TCPS | Fuzzy PID-TCSC | Fuzzy PID-UPFC |
---|---|---|---|---|---|

K_{1} | 0.3069 | 0.3346 | 1.3115 | 1.3514 | 0.4029 |

K_{2} | 0.7468 | 0.0995 | 0.8310 | 1.1099 | 0.1349 |

K_{P}_{1} | 1.2990 | 1.9143 | 0.4037 | 0.8476 | 1.4560 |

K_{I}_{1} | 0.8412 | 0.2396 | 0.2330 | 0.1426 | 1.2428 |

K_{D}_{1} | 1.1929 | 1.5844 | 0.4103 | 0.2324 | 0.2516 |

K_{3} | 1.7536 | 0.5365 | 1.2096 | 0.7176 | 0.0003 |

K_{4} | 0.8823 | 0.1064 | 0.2825 | 0.0254 | 1.2729 |

K_{P}_{2} | 0.6942 | 0.0756 | 1.8789 | 0.8073 | 0.4309 |

K_{I}_{2} | 0.4353 | 1.9600 | 0.5387 | 0.0420 | 0.6168 |

K_{D}_{2} | 0.0757 | 1.0155 | 0.3075 | 0.5739 | 0.0619 |

Type of Controller | T_{s} (Sec) | U_{s} (−ve) (Hz) | U_{s} (−ve) (puMW) | |||
---|---|---|---|---|---|---|

∆F_{1} | ∆F_{2} | ∆P_{Tie} | ∆F_{1} | ∆F_{2} | ∆P_{Tie} | |

Fuzzy PID | 19.71 | 18.36 | 16.88 | 0.0408 | 0.014 | 0.0036 |

Fuzzy PID-SSSC | 17.87 | 18.10 | 16.88 | 0.0271 | 0.006 | 0.0002 |

Fuzzy PID-TCPS | 17.07 | 22.35 | 4.76 | 0.0222 | 0.015 | 0.0035 |

Fuzzy PID-TCSC | 15.69 | 21.65 | 4.52 | 0.0077 | 0.037 | 0.0765 |

Fuzzy PID-UPFC | 8.84 | 17.35 | 4.28 | 0.0053 | 0.007 | 0.0052 |

**Table 3.**Function values. ITAE—integral of time-weighted absolute error (ITAE); ISE—integral of squared error; ITSE—integral of time-weighted squared error; IAE—integral of absolute error.

Type of Controllers | Objective Functions (J_{S}) | |||
---|---|---|---|---|

J_{1} = ISE | J_{2} = IAE | J_{3} = ITSE | J_{4} = ITAE | |

Fuzzy PID | 0.0030 | 0.1901 | 0.0060 | 0.8506 |

Fuzzy PID-SSSC | 0.0011 | 0.1297 | 0.0025 | 0.7814 |

Fuzzy PID-TCPS | 0.0018 | 0.1500 | 0.0037 | 0.7040 |

Fuzzy PID-TCSC | 0.0018 | 0.1266 | 0.0024 | 0.6194 |

Fuzzy PID-UPFC | 9.0459 × 10^{−5} | 0.0377 | 1.0963 × 10^{−4} | 0.5600 |

Fuzzy PID | Fuzzy PID- | Fuzzy PID- | Fuzzy PID- | Fuzzy PID- |
---|---|---|---|---|

SSSC | TCPS | TCSC | UPFC | |

−0.0250 + 0.9207i | −33.3056 | −9.1524 | −47.4704 | −93.2746 |

−0.0250 − 0.9207i | −5.015 | −0.4488 + 0.8518i | −2.1673 | −10.7105 |

−0.0500 + 0.0000i | −4.408 | −0.4488 − 0.8518i | −0.4123 | −4.07 |

−2 | −0.0280 + 0.9190i | −0.0500 | −0.05 | −0.0849 |

−1.9493 | −0.0280 − 0.9190i | −2 | −2 | −2 |

−0.0205 | −0.1001 | −1.9493 | −1.9493 | −1.9493 |

−2 | −0.05 | −0.0205 | −0.0205 | −0.0205 |

−1.9493 | −2 | −2 | −2 | −2 |

−0.0205 | −1.9493 | −1.9493 | −1.9493 | −1.9493 |

−0.1 | −0.0205 | −0.0205 | −0.0205 | −0.0205 |

−3.3333 | −2 | −0.1 | −0.1 | −0.1 |

−12.5 | −1.9493 | −3.3333 | −3.3333 | −3.3333 |

−0.1 | −0.0205 | −12.5 | −12.5 | −12.5 |

−3.3333 | −0.1 | −0.1 | −0.1 | −0.1 |

−12.5 | −3.3333 | −3.3333 | −3.3333 | −3.3333 |

−12.5 | −12.5 | −12.5 | −12.5 | |

−0.1 | ||||

−3.3333 | ||||

−12.5 |

Variation of Parameter | % Change | Settling Time Ts (s) | Obj | ||
---|---|---|---|---|---|

∆F_{1} | ∆F_{2} | ∆P_{Tie} | ITAE | ||

Nominal | 0 | 8.84 | 17.35 | 4.28 | 0.2433 |

Loading condition | +25 | 8.84 | 17.34 | 4.28 | 0.2433 |

−25 | 8.83 | 17.34 | 4.28 | 0.2434 | |

T_{g} | +25 | 9.05 | 17.50 | 4.25 | 0.2465 |

−25 | 8.47 | 17.50 | 4.25 | 0.2391 | |

T_{t} | +25 | 8.23 | 16.24 | 4.11 | 0.2327 |

−25 | 9.52 | 18.94 | 8.01 | 0.3089 | |

T_{12} | +25 | 9.31 | 16.90 | 4.03 | 0.2394 |

−25 | 7.90 | 17.96 | 4.34 | 0.2445 |

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**MDPI and ACS Style**

Pilla, R.; Azar, A.T.; Gorripotu, T.S.
Impact of Flexible AC Transmission System Devices on Automatic Generation Control with a Metaheuristic Based Fuzzy PID Controller. *Energies* **2019**, *12*, 4193.
https://doi.org/10.3390/en12214193

**AMA Style**

Pilla R, Azar AT, Gorripotu TS.
Impact of Flexible AC Transmission System Devices on Automatic Generation Control with a Metaheuristic Based Fuzzy PID Controller. *Energies*. 2019; 12(21):4193.
https://doi.org/10.3390/en12214193

**Chicago/Turabian Style**

Pilla, Ramana, Ahmad Taher Azar, and Tulasichandra Sekhar Gorripotu.
2019. "Impact of Flexible AC Transmission System Devices on Automatic Generation Control with a Metaheuristic Based Fuzzy PID Controller" *Energies* 12, no. 21: 4193.
https://doi.org/10.3390/en12214193