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Chaotic multi verse optimizer based fuzzy logic controller for frequency control of microgrids

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Abstract

This paper represents an arrangement of fuzzy PD and derivative filter based PID controller (FPIDF) with its optimally designed membership functions and is employed for the load frequency control (LFC) of isolated multi- microgrids. The performance of a recently developed multi verse optimizer (MVO) algorithm is improved by introducing chaotic map appropriately in the algorithm. The improved algorithm, named as CMVO algorithm is applied to tune the proportional integral derivative (PID) controller gains for the LFC of microgrid. The superiority of the proposed CMVO algorithm is examined by its superior performance compared to MVO PID, recently published IAYA PID, JAYA PID and GA PID in the microgrid system. Further, CMVO based FPIDF with its optimized membership position (FPIDF-OM) outperforms compared to CMVO based FPIDF, IJAYA tuned FPID and FPD/PI-PD controller in microgrid system. Better dynamic performances are found with the proposed technique for stochastic type wind power, solar irradiance and load variations in the microgrid compared with FPIDF and PID. The robustness of the proposed technique is established by the sensitivity analysis. The proposed design approach has been extended to a microgrid model including biogas turbine generator, biodiesel engine generator and aqua electrolyser along with fuel cell unit. Finally, OPAL-RT based hardware-in-the-loop simulation of proposed techniques has been done.

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Abbreviations

i:

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

Ri :

Speed regulation constant (p.u.)

Bi :

Frequency bias constant (p.u.)

KTi, TTi :

Gain(p.u.) and time(s) constants of turbine, respectively

KGi, TGi :

Gain(p.u.) and time(s) constants of speed governor, respectively

KWTi, TWTi :

Gain(p.u.) and time(s) constants of wind turbine (WT) unit, respectively

KPVi, TPVi :

Gain(p.u.) and time(s) constants of photovoltaic(PV) unit, respectively

KBESSi, TBESSi :

Gain(p.u.) and time(s) constants of battery energy storage system(BESS) unit, respectively

KFESSi, TFESSi :

Gain(p.u.) and time(s) constants of flywheel energy storage system(FESS) unit, respectively

Mi :

Inertia constant (p.u.)

Di :

Damping constant (p.u.)

T12 :

Synchronizing coefficient

T CR, T BG, Xc, Yc, b B,TBT :

Biogas turbine generator (BGTG) unit’s combustion reaction delay, biogas delay, lead time, lag time, valve actuator and discharge time constants respectively

K VA, T VA, K BE, T BE :

Biodiesel engine generator (BDEG) unit’s valve gain, valve actuator delay, engine gain and time constants respectively

K AEi, T AEi :

Gain(p.u.) and time (s) constants of Aqua electrolyser (AE) unit, respectively

K FCi, T FCi :

Gain(p.u.) and time (s) constants of Fuel cell (FC) unit, respectively

P n :

Fraction of WT and PV power

Pf1, Pf2 :

Participation factors of BGTG and BDEG respectively.

∆PLi :

Incremental change in load power demand in area-i

∆Fi, ∆PTie :

System frequency and tie line power deviation (p.u.), respectively

PPVi, PWTi :

Power generated from PV and WT (p.u.) respectively

m :

Number of objects(variables to be optimized) in Multi Verse Optimizer (MVO)/Chaotic MVO (CMVO) algorithm

n :

Number of universes (solutions) in MVO/CMVO algorithm

U:

Matrix of size (n × m) for random populations

\({{u}_{i}}^{j}\) :

Element of U representing jth parameter of ith universe,(i = 1 to n, j = 1 to m)

\(NI(Ui): \mathrm{n}\mathrm{o}\mathrm{r}\mathrm{m}\mathrm{a}\mathrm{l}\mathrm{i}\mathrm{z}\mathrm{e}\mathrm{d} \mathrm{i}\mathrm{n}\mathrm{f}\mathrm{l}\mathrm{a}\mathrm{t}\mathrm{i}\mathrm{o}\mathrm{n} \mathrm{r}\mathrm{a}\mathrm{t}\mathrm{e}\) :

ith universe

\({{u}_{k}}^{j}\) :

jth Parameter of kth universe (chosen by roulette wheel selection method)

T:

Maximum time(maximum number of iterations)

t :

Current time (Current iteration)

\({u}_{j}^{*}\) :

jth Parameter of the fittest solution u*obtained so far

\({\mathrm{l}\mathrm{l}}_{\mathrm{j} },{\mathrm{u}\mathrm{l}}_{\mathrm{j}}\) :

Lower and upper limit of jth variable

\({\mathrm{W}\mathrm{E}\mathrm{P}}_{\mathrm{m}\mathrm{i}\mathrm{n}} ,{ \mathrm{W}\mathrm{E}\mathrm{P}}_{\mathrm{m}\mathrm{a}\mathrm{x}}\) :

Minimum and maximum value of wormhole existence probability (WEP), respectively

sp :

Parameter signifies the speedy and precision of local search over the cycles

\({c}_{t}\) :

Random number generated by Chebyshev map in CMVO algorithm

c0 :

Initial value in Chebyshev map

\({TDR}_{C}\) :

Travelling distance rate (TDR) value modified by Chebyshev map

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Acknowledgements

The authors would like to thank Electrical Engineering department, Veer Surendra Sai University of Technology, Burla, Odisha, India for facilitating their Computational Laboratory for conducting OPAL-RT based HIL real time simulation.

Author information

Authors and Affiliations

  1. Electrical Engineering Department, VSSUT, Burla, Odisha, 768018, India

    Bibhuti Prasad Sahoo & Sidhartha Panda

Authors
  1. Bibhuti Prasad Sahoo
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  2. Sidhartha Panda
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Correspondence to Bibhuti Prasad Sahoo.

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Appendices

Appendix 1: Nominal values of the system investigated [22, 37, 38]

System parameter

Value

System parameter

Value

R1

0.05

Di

1

R2

0.04

T12

1.4

B1

10

T BG

0.23 s

B1

12.5

T CR

0.01 s

TTi

0.4

Xc

0.6

TGi

0.1

Yc

1 s

TWTi

0.5

b B

0.05

TPVi

1.5

TBT

0.2 s

TBESSi

0.1

K VA

1

TFESSi

0.1

T VA

0.05 s

KTi

1

K BE

1

KGi

1

T BE

0.5 s

KBESS1

 − 3

K AEi

0.002

KBESS2

 − 4

K FCi

1/50

KFESS1

 − 1.5

T AEi

0.5 s

KFESS1

 − 2

T FCi

4 s

KWTi

1

P n

0.6

KPVi

1

Pf1

0.75

Mi

8

Pf2

0.25

Appendix 2

Pseudo code of CMVO algorithm

figure a

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Sahoo, B.P., Panda, S. Chaotic multi verse optimizer based fuzzy logic controller for frequency control of microgrids. Evol. Intel. 14, 1597–1618 (2021). https://doi.org/10.1007/s12065-020-00405-9

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  • DOI: https://doi.org/10.1007/s12065-020-00405-9

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