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Model Predictive Controller-Based Voltage and Frequency Regulation in Renewable Energy Integrated Power System Coordinated with Virtual Inertia and Redox Flow Battery

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Abstract

This manuscript discusses the concurrent voltage and frequency control problem for an interconnected system having three areas, each containing thermal and diesel units in conjunction with renewable integration from a separate source. In the first case study, renewable sources like wind, solar, and geothermal have been incorporated using a static transfer function-based model without considering variability in wind and solar. In the second case study, the dynamic model of wind and solar has been considered after incorporating the deterministic drifts and stochastic fluctuations. The paper presents Harris hawks optimized model predictive controller (MPC-HHO) to curtail the frequency and voltage fluctuations caused due to the sudden change in loading pattern. Additionally, the authors have incorporated various dynamic energy storage devices like virtual inertia and redox flow battery (VI-RFB) in coordination with the MPC-HHO controller. From the obtained results, it has been validated that the transient response from the proposed MPC-HHO controller coordinated with VI-RFB has superior characteristics when compared with state-of-the-art methodologies available in the existing literature. Further, the most prevalent nonlinearities present in the realistic power system have been considered and their effects on the controller’s performance have been investigated and the robustness of the proposed MPC-HHO controller coordinated with VI-RFB has been successfully validated.

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Abbreviations

LFC:

Load frequency control

AVR:

Automatic voltage regulator

MPC:

Model predictive controller

HHO:

Harris hawks optimization

WOA:

Whale optimization algorithm

GWO:

Grey wolf optimization

PSO:

Particle swarm optimization

AGC:

Automatic generation control

SLP:

Step load perturbation

EV:

Electric vehicle

RFB:

Redox flow battery

VI:

Virtual inertia

MO:

Measured output

MV:

Manipulated variable

PO:

Peak overshoot

PU:

Peak undershoot

ST:

Settling time

ACE:

Area control error

STPP:

Solar thermal power plant

RES:

Renewable energy sources

\(\Delta f_{i}\) :

Incremental change in frequency in area i

\(V_{i}\) :

Terminal voltage in area i

\(f\) :

Nominal frequency of the system

P(g):

Power generation output from RES

\(T_{{{\text{pi}}}}\) :

Equivalent time constant of load model

\(\eta\) :

Normalization constant 1 for RES modelling

\(\partial\) :

Normalization constant 2 for RES modelling

\(\beta\) :

Mean value of the generated power from RES

\(\Gamma\) :

Time dependent switching signal

\(B_{i}\) :

Frequency-bias coefficient of area i

\(R_{i}\) :

Governor droop characteristic of area i

G(s):

Low-pass transfer function

\(K_{{{\text{VIi}}}}\) :

Gain of virtual inertia block

\(T_{{{\text{VIi}}}}\) :

Time constant of virtual inertia block

y1:

Coefficient involved with output variation in MPC objective function

u1:

Coefficient involved with input variation in MPC objective function

du1:

Coefficient involved with rate of change of input in MPC objective function

\(K_{{{\text{RFBi}}}}\) :

Gain coefficient of RFB in area i

\(T_{{{\text{RFBi}}}}\) :

Time constant of RFB in area i

\({\text{ACE}}_{i}\) :

Area control error in area i

\(\Delta T_{{{\text{pij}}}}\) :

Tie-line power error between area i and area j

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Acknowledgements

The presented study has been supported by H. P. Council for Science, Technology & Environment (HIMCOSTE), SCST & E (R&D)/2019-20, beneath project Grant No. STC/F(8)-6/2019(R&D 2019-20)-408, H. P., India, awarded to second author.

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Authors and Affiliations

  1. Electrical Engineering Department, National Institute of Technology Hamirpur, Hamirpur, Himachal Pradesh, 177005, India

    Vineet Kumar, Veena Sharma & R. Naresh

Authors
  1. Vineet Kumar
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  2. Veena Sharma
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  3. R. Naresh
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Corresponding author

Correspondence to Vineet Kumar.

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Appendix

Appendix

i = 1, 2, and 3. T (Simulation Period) = 100 s. \(f\) = 60 Hz. SLP = 0.01 pu MW. AVR Model: \(K_{{{\text{Ai}}}}\) = 10; \(T_{{{\text{Ai}}}}\) = 0.1 s; \(K_{{{\text{Ei}}}}\) = 1; \(T_{{{\text{Ei}}}}\) = 0.4 s; \(K_{{{\text{Fi}}}}\)  = 0.8; \(T_{{{\text{Fi}}}}\) = 1.4 s; \(K_{1}\) = 1; \(K_{2}\) = − 0.1; \(K_{3}\) = 0.5; \(K_{4}\) = 1.4; \(P_{s}\) = 0.145 \(K_{{{\text{Si}}}}\) = 1; \(T_{{{\text{Si}}}}\) = 0.05 s. LFC model: Geothermal System: \(T_{{{\text{gGeo}}}}\) = 0.1 s; \(T_{{{\text{tGeo}}}}\) = 0.1 s. STPP system: \(K_{s}\) = 1.0; \(T_{s}\) = 1 s; \(K_{{{\text{gs}}}}\) = 1.0; \(T_{{{\text{ts}}}}\) = 3.0 s. Wind System: \(T_{w1}\) = 0.6 s; \(T_{w2}\) = 0.041 s; \(K_{w1}\) = 1.25; \(K_{w2}\) = 1.4; \(G_{B}\) = 1. Thermal system: \(T_{{{\text{gi}}}}\) = 0.08 s; \(T_{{{\text{ti}}}}\) = 0.3 s; \(T_{{{\text{ri}}}}\) = 10 s; \(K_{{{\text{ri}}}}\) = 0.5 s. Diesel system: \(K_{{{\text{dii}}}}\) = 16.5. \(T_{{{\text{jk}}}} =\) 0.08 pu. \(R\) = 2.4 Hz/pu MW. B = 0.425 pu MW/Hz. \(H_{i}\) = 5 s. \(K_{{{\text{pi}}}}\) = 1/\(D_{i}\) = 120 Hz/pu MW. \(T_{{{\text{pi}}}}\) = \(2H_{i} /f_{i} D_{i}\) (= 20 s). \(f\) = Nominal frequency of the system = 60 Hz. RFB Model; \(T_{{{\text{RFBi}}}}\) = 0; \(K_{{{\text{RFBi}}}}\) = 1.8. Virtual Inertia: \(K_{{{\text{VI}}}}\) = 0.08; \(T_{VI}\) = 10. Stochastic Modelling of RES: Wind Model; \(\eta\) = 0.8; \(\beta\) = 10; \(\partial\) = 1. Solar Model: \(\eta\) = 0.7; \(\beta\) = 2; \(\partial\) = 0.1.

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Kumar, V., Sharma, V. & Naresh, R. Model Predictive Controller-Based Voltage and Frequency Regulation in Renewable Energy Integrated Power System Coordinated with Virtual Inertia and Redox Flow Battery. Iran J Sci Technol Trans Electr Eng 47, 159–176 (2023). https://doi.org/10.1007/s40998-022-00561-x

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