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Firefly algorithm-based load frequency controller design of a two area system composing of PV grid and thermal generator

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Abstract

In this paper, firefly algorithm (FA) for optimal tuning of PI controllers for load frequency control of hybrid system composing of photovoltaic (PV) system and thermal generator is introduced. Also, maximum power point tracking of PV is considered in the design process. The block diagram of the hybrid system is performed. To robustly tune the parameters of controllers, a time domain-based objective function is established which is solved by the FA. Simulation results are presented to show the improved performance of the suggested FA-based controllers compared with genetic algorithm (GA). These results show that the proposed controllers present better performance over GA in terms of settling times and different indices.

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Abbreviations

f :

The system frequency in Hz

i :

Subscript referring to area (\(i = 1, 2\))

\({R}_{{i}}\) :

The regulation constant (Hz/p.u MW) for area i

\({K}_\mathrm{g}, {T}_\mathrm{g}\) :

The gain and time constant in second of governor for thermal unit

\({K}_\mathrm{t}, {T}_\mathrm{t}\) :

The gain and time constant in second of turbine

\({T}_\mathrm{r}\) :

The reheat time constant in second

\({K}_\mathrm{r}\) :

The p.u megawatt rating of high pressure stage for area i

\({T}_\mathrm{P}, {K}_\mathrm{P}\) :

The time constant and gain of power system respectively for thermal unit

\(\Delta {P_\mathrm{tie}}_{i}\) :

The difference between the actual tie-line power and scheduled one

B :

The biasing factor in p.u MW/Hz

\({K}_{\mathrm{P}_{i}}, {K}_{{\mathrm{I}_i}}\) :

The gains of PI controller of area i

\({T}_{12}\) :

Synchronizing coefficient

J :

Objective function

\({U}_{i}\) :

The control signal of area i

\({K}_{i}\) :

The controller of area i

\({K}_{{\mathrm{P}_i}}^{\min }, {K}_{{\mathrm{P}_i}}^{\max }\) :

The minimum and maximum limit of proportional gain of area i

\({K}_{{\mathrm{I}_i}}^{\min }, {K}_{{\mathrm{I}_i}}^{\max }\) :

The minimum and maximum limit of integral gain of area i

LFC:

Load frequency control

GA:

Genetic algorithm

FL:

Fuzzy logic

NN:

Neural network

PI:

Proportional plus integral

FA:

Firefly algorithm

ACE:

Area control error

PV:

Photovoltaic system

MPPT:

Maximum power point tracking

IAE:

The integral of absolute value of the error

ITAE:

The integral of the time multiplied absolute value of the error

ISE:

The integral of square error

ITSE:

The integral of time multiply square error

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Author information

Author notes

  1. E. S. Ali

    Present address: Electrical Department, Faculty of Engineering, Jazan University, Jazan, Saudi Arabia

Authors and Affiliations

  1. Electric Power and Machine Department, Faculty of Engineering, Zagazig University, Zagazig, Egypt

    S. M. Abd-Elazim & E. S. Ali

Authors
  1. S. M. Abd-Elazim
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  2. E. S. Ali
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Corresponding author

Correspondence to E. S. Ali.

Appendix

Appendix

The system data are as shown below:

  1. (a)

    The parameters of the thermal system: \(T_P=20\,\text {s}\); \({T}_\mathrm{t} =0.3\,\text {s}\); \({T}_\mathrm{r}==10\,\text {s}\); \(T_{12}=0.545\,\text {p.u}\); \({T}_\mathrm{g}=0.08\,\text {s}\); \({K}_\mathrm{P} =120\,\text {Hz/p.u MW}\); \(B=0.8\,\hbox {p.u MW/Hz}\); \({a}_{12}=-1\); \(R=0.4\) Hz/p.u MW; \({K}_{\mathrm{r1}}=0.33\,\text {p.u MW}\).

  2. (b)

    The parameters of FA: the contrast of the attractiveness \(=\) 1.0; the attractiveness \(=\) 0.1 at \({r}=0\); randomization parameter \((\alpha )=0.1\); maximum number of generations \(=\) 100; number of fireflies \(=\) 50.

  3. (c)

    The parameters of GA are as follows: max generation \(=\) 100; population size \(=\) 50; crossover probabilities \(=\) 0.75; mutation probabilities \(=\) 0.1.

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Abd-Elazim, S.M., Ali, E.S. Firefly algorithm-based load frequency controller design of a two area system composing of PV grid and thermal generator. Electr Eng 100, 1253–1262 (2018). https://doi.org/10.1007/s00202-017-0576-5

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  • DOI: https://doi.org/10.1007/s00202-017-0576-5

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