# Automatic Generation Control of Multi-Source Interconnected Power System Using FOI-TD Controller

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## Abstract

**:**

## 1. Introduction

## 2. Power System Model

## 3. Controller Structure

## 4. Optimization Techniques

#### 4.1. Fitness Dependent Optimization (FDO)

- Initialization: A population of scout bees are randomly initialized ${X}_{k}(1,2n)$. The number of scout bees is equal to the size of the population, and each scout has six terms known as ${K}_{d}$, ${K}_{i}$, ($\lambda $), ($\mu $), ${K}_{p}$, and n denotes the FOTID/FOI-TD controller gains. Where each scout indicates the solution potential and attempts to look for an optimal hive (solution) by randomly examining more positions.
- Moment process: In this step, the scout bees updated the current position (${X}_{k,t,f}$ ), by including pace (P) to the next location (${X}_{k,t+1,f}$) for searching an optimal position and is given by below expression.$${X}_{k,t+1}={X}_{k,t}+p.$$
- Fitness weight (Fw): The pace is typically depend on Fitness weight (Fw) which can be expressed as$$Fw=|\frac{{X}_{k,t,f}^{*}}{{X}_{k,t,f}}|-\alpha $$$$\begin{array}{ccc}\hfill p& =& R{X}_{k,t,f};\mathrm{if}\phantom{\rule{4.pt}{0ex}}\alpha =0\phantom{\rule{3.33333pt}{0ex}}or\phantom{\rule{3.33333pt}{0ex}}\alpha =1\phantom{\rule{3.33333pt}{0ex}}\phantom{\rule{3.33333pt}{0ex}}or\phantom{\rule{3.33333pt}{0ex}}{X}_{k,t,f}=0\hfill \end{array}$$$$\begin{array}{ccc}\hfill p& =& \left(\right)open="\{"\; close>\begin{array}{c}-\alpha ({X}_{k,t,f}-{X}_{k,t,f}^{*})-1\phantom{\rule{4.pt}{0ex}}\mathrm{if}\phantom{\rule{4.pt}{0ex}}0\alpha 1\phantom{\rule{4.pt}{0ex}}\mathrm{and}\phantom{\rule{4.pt}{0ex}}R0\hfill \\ -\alpha ({X}_{k,t,f}-{X}_{k,t,f}^{*})\phantom{\rule{4.pt}{0ex}}\mathrm{if}\phantom{\rule{4.pt}{0ex}}0\alpha 1\phantom{\rule{4.pt}{0ex}}\mathrm{and}\phantom{\rule{4.pt}{0ex}}R\ge 0\hfill \end{array}\hfill \end{array}$$
- Stopping criteria: The stopping criteria determine the fitness value of each scout bee at termination condition.

#### 4.2. I-FDO Algorithm

- Updating the position of scout bees:The location of the scout bee is modified in the I-FDO algorithm by including two parametric terms, Cohesion (C) and Alignment (A), to the FDO algorithm. Both terms are important indicators of group motion: Cohesion (C) refers to tendency of scouts to the neighborhood’s center of mass, while alignment (A) is the pace pairing of individuals in the neighborhood or class with that of other individuals. The new position of scout bee is expressed as$${X}_{K,t+1}={X}_{K,t}+A*\frac{1}{C}.$$$${A}_{j}=\sum _{j=1}^{N}\frac{{Q}_{j}}{N}.$$$${C}_{j}=\sum _{j=1}^{N}\frac{{X}_{j}}{N}-X.$$
- Weight factor Randomization: In lieu of the primary FDO, the weight factor ($\alpha $) is assumed to be 1 or 0, while in the I-FDO method, it is produced within the range of 0 and 1 with the help of a random fitness weight control phenomenon. Normally, a weight factor in FDO is set to 0. The improvement of fitness weight in the I-FDO algorithm can be written as$$Fw=|\frac{{X}_{K,t,f}^{*}}{{X}_{K,t,f}}|$$

## 5. Performance Validation

**Scenario-1:**

**Scenario-2:**

#### Sensitivity Analysis

## 6. Conclusions and Future Directions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Conflicts of Interest

## Appendix A

**Table A1.**Parameter and value of two-area IPS [7].

Parameters | Values | Parameters | Values |
---|---|---|---|

${\beta}_{1}$,${\beta}_{2}$ | 0.431 MW/Hz | ${T}_{gh}$ | 0.080 s |

${R}_{th1},{R}_{th2},{R}_{hy1}$ | 2.40 Hz/p.u | ${T}_{gh}$ | 0.080 s |

${R}_{hy2},{R}_{g1},{R}_{g2}$ | 2.40 Hz/p.u | ${T}_{t}$ | 0.30 s |

${K}_{1}$ | 0.30 | ${T}_{r}$ | 10 s |

${K}_{P}$ | 68.95 | ${T}_{p}$ | 11.490 s |

${T}_{12}$ | 0.0430 | ${T}_{rh}$ | 28.70 s |

${a}_{12}$ | −1 | ${T}_{w}$ | 1 s |

${T}_{rs}$ | 5 s | ${y}_{c}$ | 1 s |

${T}_{gh}$ | 0.60 s | ${x}_{c}$ | 0.60 s |

${K}_{g}$ | 0.1304 | ${K}_{DC}$ | 1 |

${x}_{g}$ | 1 | ${b}_{g}$ | 0.050 s |

${K}_{t}$ | 0.5434 | ${T}_{F}$ | 0.230 s |

${K}_{h}$ | 0.3268 | ${T}_{cr}$ | 0.010 s |

Parameters | Values | Parameters | Values |
---|---|---|---|

Population No ${N}_{P}$ | 30 | Generation No ${N}_{g}$ | 60 |

Lower bound ${L}_{b}$ | −2 | Upper bound ${U}_{b}$ | 2 |

No of Dimensions ${N}_{d}$ | 15 | Weight Factor $\gamma $ | 0.0 |

random number $\alpha $ | [−1, 1] |

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**Figure 6.**Multi-source interconnected PS with FOTID and FOI-TD controllers. (

**a**) FOTID Controller with $\Delta {F}_{1}$; (

**b**) FOTID Controller with $\Delta {F}_{2}$; (

**c**) FOTID Controller with $\Delta {P}_{tie}$; (

**d**) FOI-TD Controller with $\Delta {F}_{1}$; (

**e**) FOI-TD Controller with $\Delta {F}_{2}$; (

**f**) FOI-TD Controller with $\Delta {P}_{tie}$

**Figure 7.**Multisource interconnected PS with I-FDO algorithm. (

**a**) FOTID Controller with $\Delta {F}_{1}$; (

**b**) FOTID Controller with $\Delta {F}_{2}$; (

**c**) FOTID Controller with $\Delta {P}_{tie}$.

**Figure 8.**Sensitivity analysis of different parameters. (

**a**) FOTID Controller with $\Delta {F}_{1}$; (

**b**) FOTID Controller with $\Delta {F}_{2}$; (

**c**) FOTID Controller with $\Delta {P}_{tie}$.

Acronym | Definition | Acronym | Definition |
---|---|---|---|

PSO | Particle Swarm Optimization | $\lambda $ | Fractional integrator order |

FOPID | Fractional Order Proportional Integral Derivative | n | Tilt non zero real number |

TID | Tilted Integral Derivative | $\mu $ | Fractional derivative order |

I-TD | Integral-Tilt Derivative | TD | Time Delay |

IPS | Interconnected Power System | BD | Boiler Dynamics |

GRC | Generation Rate Constraint | GDB | Governor Dead Band |

FLC | Fuzzy Logic Controller | FOC | Fractional Order Controller |

I-FDO | Improved- Fitness Dependent Optimizer | TLBO | Teaching Learning based Optimizer Algorithm |

ITSE | Integral Time Square Error | GDZ | Governor Dead Zone |

SLP | Step Load Perturbation | $\Delta F$ | System frequency deviation |

$\Delta {P}_{tie}$ | Tie-line Power deviation | ITAE | Integral Time Absolute Error |

Tt | Turbine Time Constant | Tw | wind turbine constant |

Tg | Governor time constant | R | Droop Constant |

Techniques | Performance Indices | |||
---|---|---|---|---|

ITSE | ISE | ITAE | IAE | |

I-FDO-FOTID | 0.00004 | 0.00009 | 0.0006 | 0.0147 |

I-FDO-FOI-TD | 0.00003 | 0.00001 | 0.0005 | 0.0036 |

FDO-FOTID | 0.00004 | 0.00002 | 0.0023 | 0.0210 |

FDO-FOI-TD | 0.00012 | 0.00010 | 0.0045 | 0.0023 |

TLBO-FOTID | 0.00022 | 0.00026 | 0.0023 | 0.0096 |

TLBO-FOI-TD | 0.00029 | 0.00008 | 0.0010 | 0.0093 |

PSO-FOTID | 0.00042 | 0.00021 | 0.0024 | 0.0096 |

PSO-FOI-TD | 0.00033 | 0.00056 | 0.0098 | 0.0663 |

Controller Parameters | Scenario-1 | Scenario-2 | ||||||
---|---|---|---|---|---|---|---|---|

I-FDO | FDO | TLBO | PSO | FOI-TD | FOTID | I-TD | PID | |

${K}_{p1}$ | 1.01 | 1.90 | 1.99 | 0.08 | 1.02 | 1.09 | 0.01 | 1.05 |

${K}_{i1}$ | 1.60 | 1.06 | 2.00 | 0.86 | 1.03 | 0.02 | 0.03 | 1.50 |

${K}_{d1}$ | 1.20 | 0.61 | 1.73 | 1.17 | 0.30 | 0.40 | 0.90 | 0.04 |

$\lambda 1$ | 0.16 | 0.10 | 0.06 | 0.02 | 0.13 | 0.42 | 0.50 | 0.08 |

$\mu 1$ | 0.72 | 0.42 | 0.90 | 0.07 | 0.19 | 0.04 | 0.010 | 0.13 |

n_{1} | 0.12 | 0.92 | 0.01 | 0.52 | 0.09 | 0.30 | 0.38 | 0.60 |

${K}_{p2}$ | 1.10 | 1.90 | 1.09 | 1.08 | 1.5 | 1.04 | 1.56 | 1.82 |

${K}_{i2}$ | 0.63 | 0.06 | 1.60 | 1.86 | 1.03 | 1.02 | 0.02 | 0.03 |

${K}_{d2}$ | 1.00 | 1.60 | 0.70 | 1.17 | 0.30 | 0.23 | 1.98 | 1.06 |

$\lambda 2$ | 0.69 | 0.03 | 0.06 | 0.02 | 0.01 | 0.02 | 0.00 | 0.08 |

$\mu 2$ | 0.17 | 0.04 | 0.90 | 0.021 | 0.19 | 0.04 | 0.01 | 0.13 |

n_{2} | 0.13 | 0.91 | 0.10 | 0.02 | 0.01 | 0.30 | 0.08 | 0.60 |

${K}_{p3}$ | 1.60 | 1.06 | 2.00 | 0.86 | 1.03 | 0.02 | 0.03 | 1.50 |

${K}_{i3}$ | 1.20 | 0.61 | 1.73 | 1.17 | 0.30 | 0.40 | 0.90 | 0.04 |

${K}_{d3}$ | 1.01 | 1.90 | 1.99 | 0.08 | 1.02 | 1.09 | 0.01 | 1.05 |

$\lambda 3$ | 0.13 | 0.91 | 0.10 | 0.02 | 0.01 | 0.30 | 0.08 | 0.60 |

$\mu 3$ | 0.07 | 1.04 | 0.90 | 0.021 | 0.19 | 0.04 | 0.01 | 0.13 |

n_{3} | 0.69 | 0.03 | 0.06 | 0.02 | 0.01 | 0.02 | 0.00 | 0.08 |

Controller with Techniques | Settling Time ${\mathit{T}}_{\mathit{s}}\mathit{s}$ | Overshoot ${\mathit{O}}_{\mathbf{sh}}$ | Undershoot ${\mathit{U}}_{\mathbf{sh}}$ | ||||||
---|---|---|---|---|---|---|---|---|---|

$\mathbf{\Delta}{\mathit{F}}_{1}$ | $\mathbf{\Delta}{\mathit{F}}_{2}$ | $\mathbf{\Delta}{\mathit{P}}_{\mathit{tie}}$ | $\mathbf{\Delta}{\mathit{F}}_{1}$ | $\mathbf{\Delta}{\mathit{F}}_{2}$ | $\mathbf{\Delta}{\mathit{P}}_{\mathit{tie}}$ | $\mathbf{\Delta}{\mathit{F}}_{1}$ | $\mathbf{\Delta}{\mathit{F}}_{2}$ | $\mathbf{\Delta}{\mathit{P}}_{\mathit{t}\mathit{i}\mathit{e}}$ | |

I-FDO-FOI-TD | 10.13 | 11.4 | 11.2 | 0.00014 | 0.00024 | 0.0000 | −0.0088 | −0.0059 | −0.0009 |

FDO-FOI-TD | 13.15 | 11.6 | 11.9 | 0.00022 | 0.00029 | 0.00000 | −0.0066 | −0.0095 | −0.0008 |

TLBO-FOI-TD | 11.60 | 13.4 | 16.4 | 0.00090 | 0.00094 | 0.00063 | −0.0089 | −0.0093 | −0.0046 |

PSO-FOI-TD | 13.30 | 12.8 | 16.9 | 0.00049 | 0.00055 | 0.00024 | −0.0068 | −0.0066 | −0.0044 |

I-FDO-FOTID | 10.70 | 11.9 | 8.6 | 0.00037 | 0.00040 | 0.00610 | −0.0199 | −0.0097 | −0.0049 |

FDO-FOTID | 10.86 | 12.2 | 8.72 | 0.00065 | 0.00050 | 0.00043 | −0.0050 | −0.0067 | −0.0053 |

TLBO-FOTID | 12.70 | 11.4 | 9.10 | 0.00054 | 0.00080 | 0.00017 | −0.0016 | −0.0097 | −0.0049 |

PSO-FOTID | 10.90 | 12.9 | 12.2 | 0.00120 | 0.00107 | 0.00110 | −0.0100 | −0.0097 | −0.0073 |

WCA-I-TD [30] | 12.29 | 29.45 | 30.50 | 0.00280 | 0.0011 | 0.0070 | −0.0109 | −0.0035 | −0.0022 |

FPA-FOTID [31] | 25.59 | 23.25 | 18.77 | 0.00680 | 0.01170 | 0.00260 | −0.0245 | −0.0228 | −0.0044 |

Controller with Techniques | Settling Time ${\mathit{T}}_{\mathit{s}}\mathit{s}$ | Overshoot ${\mathit{O}}_{\mathbf{sh}}$ | Undershoot ${\mathit{U}}_{\mathbf{sh}}$ | ||||||
---|---|---|---|---|---|---|---|---|---|

$\Delta {\mathit{F}}_{\mathbf{1}}$ | $\Delta {\mathit{F}}_{\mathbf{2}}$ | $\Delta {\mathit{P}}_{\mathit{tie}}$ | $\Delta {\mathit{F}}_{\mathbf{1}}$ | $\Delta {\mathit{F}}_{\mathbf{2}}$ | $\Delta {\mathit{P}}_{\mathit{tie}}$ | $\Delta {\mathbf{F}}_{\mathbf{1}}$ | $\Delta {\mathbf{F}}_{\mathbf{2}}$ | $\Delta {\mathbf{P}}_{\mathit{tie}}$ | |

I-FDO-FOTID | 12.6 | 7.6 | 12.6 | 0.000086 | 0.000003 | 0.00172 | −0.00142 | −0.00213 | −0.01520 |

I-FDO-PID | 17.6 | 13.0 | 17.6 | 0.00022 | 0.000136 | 0.00742 | −0.00150 | −0.00428 | −0.01960 |

I-FDO-I-TD | 15.2 | 17.6 | 17.7 | 0.00117 | 0.004030 | 0.004740 | −0.01056 | −0.00824 | −0.00707 |

I-FDO-FOI-TD | 15.1 | 12.9 | 13.9 | 0.000588 | 0.000554 | 0.00274 | −0.01056 | −0.00682 | −0.00916 |

Parameters Variation | Settling Time ${\mathit{T}}_{\mathit{s}}\mathit{s}$ | Overshoot ${\mathit{O}}_{\mathbf{sh}}$ | Undershoot ${\mathit{U}}_{\mathbf{sh}}$ | |||||||
---|---|---|---|---|---|---|---|---|---|---|

Parameter | % change | $\Delta {\mathit{F}}_{\mathbf{1}}$ | $\Delta {\mathit{F}}_{\mathbf{2}}$ | $\Delta {\mathit{P}}_{\mathit{tie}}$ | $\Delta {\mathit{F}}_{\mathbf{1}}$ | $\Delta {\mathit{F}}_{\mathbf{2}}$ | $\Delta {\mathit{P}}_{\mathit{tie}}$ | $\Delta {\mathit{F}}_{\mathbf{1}}$ | $\Delta {\mathit{F}}_{\mathbf{2}}$ | $\Delta {\mathit{P}}_{\mathit{tie}}$ |

R | +50% | 15.1 | 12.9 | 13.9 | 0.000588 | 0.000554 | 0.00274 | −0.01056 | −0.00682 | −0.00916 |

−50% | 12.6 | 7.6 | 12.6 | 0.000086 | 0.000003 | 0.00172 | −0.00142 | −0.00213 | −0.01520 | |

${T}_{g}$ | +50% | 15.2 | 17.6 | 17.7 | 0.00117 | 0.004030 | 0.004740 | −0.01056 | −0.00824 | −0.00707 |

−50% | 17.6 | 13.0 | 17.6 | 0.00022 | 0.000136 | 0.00742 | −0.00150 | −0.00428 | −0.01960 | |

${T}_{t}$ | +50% | 14.7 | 17.4 | 16.9 | 0.000721 | 0.00319 | 0.00444 | −0.01085 | −0.00813 | −0.01190 |

−50% | 15.1 | 12.9 | 15.1 | 0.000152 | 0.000000 | 0.00430 | −0.00138 | −0.00360 | −0.01810 | |

${T}_{w}$ | +50% | 14.8 | 12.7 | 15.4 | 0.000873 | 0.000660 | 0.00336 | −0.01056 | −0.00686 | −0.01190 |

−50% | 13.9 | 8.2 | 13.9 | 0.000169 | 0.000022 | 0.00263 | −0.00118 | −0.00258 | −0.01520 |

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## Share and Cite

**MDPI and ACS Style**

Daraz, A.; Malik, S.A.; Waseem, A.; Azar, A.T.; Haq, I.U.; Ullah, Z.; Aslam, S.
Automatic Generation Control of Multi-Source Interconnected Power System Using FOI-TD Controller. *Energies* **2021**, *14*, 5867.
https://doi.org/10.3390/en14185867

**AMA Style**

Daraz A, Malik SA, Waseem A, Azar AT, Haq IU, Ullah Z, Aslam S.
Automatic Generation Control of Multi-Source Interconnected Power System Using FOI-TD Controller. *Energies*. 2021; 14(18):5867.
https://doi.org/10.3390/en14185867

**Chicago/Turabian Style**

Daraz, Amil, Suheel Abdullah Malik, Athar Waseem, Ahmad Taher Azar, Ihsan Ul Haq, Zahid Ullah, and Sheraz Aslam.
2021. "Automatic Generation Control of Multi-Source Interconnected Power System Using FOI-TD Controller" *Energies* 14, no. 18: 5867.
https://doi.org/10.3390/en14185867