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AGC of restructured multi-area multi-source hydrothermal power systems incorporating energy storage units via optimal fractional-order fuzzy PID controller

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Abstract

Owing to nonlinear structure and uncertain load demand characteristics, expert and intelligent automatic generation control (AGC) is inevitable for coherent operation and control of electric power system. Hence, in this paper, to mitigate the frequency and power deviations efficiently under sudden load demand conditions, a novel fractional-order fuzzy PID (FOFPID) controller is suggested in AGC of restructured multi-area multi-source hydrothermal power systems. The parameters of FOFPID controller are optimized by utilizing bacterial foraging optimization algorithm. The controller is implemented on restructured two- and three-area systems. It is observed that the advocated method shows superiority over fuzzy PID, fractional-order PID and conventional PID control schemes. Energy storage units such as redox flow batteries (RFB) which show extremely long charge–discharge life cycle and outstanding quick response to alleviate the system oscillations under disturbances have further been incorporated into the studied systems to analyze their efficacy in boosting AGC performance. Analysis of results reveals that with RFB, system transient performance improves significantly. It is also observed that the obtained results satiate the AGC requirement under different power transactions taking place in a deregulated market in the presence/absence of appropriate generation rate constraint treated for thermal and hydro plants. Finally, the robustness of the presented approach is demonstrated against the wide variations in the system parameters and initial loading condition.

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Author information

Authors and Affiliations

  1. Department of Electrical and Electronics Engineering, Maharaja Surajmal Institute of Technology, C4, Janakpuri, New Delhi, 110058, India

    Yogendra Arya

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  1. Yogendra Arya
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Corresponding author

Correspondence to Yogendra Arya.

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Human participants and/or animals

This research is not related to the involvement of human and/or animals.

Appendices

Appendix 1: Nomenclature and system data [4, 9, 11]

F 0

60 Hz; nominal system frequency

K RFB

1.8; gain of RFB

R

R1 = 2 Hz/puMW, R2 = 2.4 Hz/puMW; speed governor regulation parameter

T d

0 s; time delay constant of RFB

B

0.425 (= β); frequency bias constant

∆Pg

Incremental change in area power generation

K PS

100; power system gain

∆PG

Incremental change in GENCO output

T PS

20 s; power system time constant

p

Number of parameters to be optimized

T G

0.08 s; speed governor time constant

S

Number of bacteria

T T

0.3 s; thermal turbine time constant

N S

Swimming length after which tumbling of bacteria will be carry out in a chemotactic loop

T RH

48.7 s; hydro turbine speed governor transient droop time constant

N C

Number of iterations to be undertaken in a chemotactic loop (NC > NS)

T R

5 s; hydro turbine speed governor reset time

N re

Maximum number of reproduction to be carry out

T GH

0.513 s; hydro turbine speed governor main servo time constant

N ed

Maximum number of elimination–dispersal events

T W

1 s; water starting time constant

P ed

Probability with which elimination–dispersal will go on

T12, T13

0.0707 puMW/rad; synchronizing coefficient

K 1

Proportional input scaling factor gain of fuzzy controller

cpfij

Contract participation factor of jth DISCO with ith GENCO

K 2

Derivative input scaling factor gain of fuzzy controller

∆PD

Incremental change in load power demand in an area

γ

Order of input derivative of fuzzy controller

∆PUC

Incremental change in uncontracted load power demanded by DISCO

K P

Proportional gain of controller

∆F

Incremental change in the area frequency

K I

Integral gain of controller

∆PC

Incremental change in the speed changer position

K D

Derivative gain of controller

K r

0; reset gain of RFB

λ

Order of output integrator of fuzzy controller

Tr

0 s; reset time constant of RFB

μ

Order of output derivative of fuzzy controller

Appendix 2

2.1 Justification for the choice of number and types of membership functions

Firstly, for the justification of employing 5 membership functions (mfs), a comparative study is carried out using 3, 5 and 7 mfs in FOFPID controller for AGC of two-area restructured power system with RFB considering poolco-based transactions. Identical mfs are used for inputs and output and in both areas of the system having nominal horizontal range of mfs [−1, 1]. The parameters of FOFPID are optimized via BFOA for 3 and 7 mfs. Figure 12a incorporates ∆F1 response with 3, 5 and 7 mfs. From the analysis of Fig. 12a, it is evident that ∆F1 response indicates better dynamic performance in terms of lesser undershoot and settling time with 5 mfs compared to 3 and 7 mfs. The undershoot with 3 mfs is more than that of 5 mfs and worst with 7 mfs. However, settling time is better with 7 mfs in comparison with 3 mfs. The findings are analogous to the findings of [47]. Hence, the overall performance of 5 mfs is superior to 3 or 7 mfs, which makes 5 mfs a very effective choice in AGC study of restructured multi-source hydrothermal power systems.

Fig. 12
figure 12

System dynamic responses with FOFPID controller for poolco-based transactions a ∆F1 of two-area hydrothermal system with varied number of mfs and b ∆F1 of three-area hydrothermal system with different types of mfs

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To justify the choice of selecting triangular mfs in the current study, the simulations are also carried out with trapezoidal and Gaussian mfs. Three-area restructured multi-source hydrothermal power system without RFB is simulated for poolco-based transactions with FOFPID controller using trapezoidal and Gaussian mfs. FOFPID controller is again optimized with trapezoidal and Gaussian mfs by means of BFOA. It should be noted that identical trapezoidal and Gaussian mfs are used for both inputs and one output for all areas of the system under study with nominal horizontal range of mfs [−1, 1]. Figure 12b includes ∆F1 response with triangular, trapezoidal and Gaussian mfs. From the scrutiny of Fig. 12b, it is apparent that ∆F1 response is the best with triangular mfs [28]. With triangular mfs, result shows lesser undershoot, overshoot and settling time as well as faster response. The response with trapezoidal mfs shows larger overshoot and undershoot, but settling time is very much competitive with triangular mfs. The result with Gaussian mfs demonstrates higher undershoot, lower overshoot and larger settling time compared to trapezoidal mfs. Hence, it can be concluded that the best choice of mfs is triangular for AGC studies of multi-area restructured power systems.

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Arya, Y. AGC of restructured multi-area multi-source hydrothermal power systems incorporating energy storage units via optimal fractional-order fuzzy PID controller. Neural Comput & Applic 31, 851–872 (2019). https://doi.org/10.1007/s00521-017-3114-5

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