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Stability analysis of single-machine infinite bus system with renewable energy sources using sine cosine chimp optimization

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Abstract

The process of incorporating renewable energy sources, such photovoltaics and wind power, into the current power system has a significant effect on the power grid's stability properties. As these variable energy sources fluctuate with changes in weather conditions, ensuring the stability and reliability of the grid becomes a complex challenge. Consequently, there is a growing need for the development and application of appropriate analytical methods to address these evolving dynamics. This research work explores this issue by focusing on the investigation of a grid-connected microgrid. This microgrid incorporates solar photovoltaic and wind energy sources in addition to a synchronous generator. To improve the stability and performance of the system, a governor and power system stabilizer are used. The study applies a novel control system known as µ1-µ2/tilted integral fractional derivative with filter (µ1-µ2/TIFDN) for low-frequency oscillations within the single-machine infinite bus system. To optimize controller parameters necessary for effective operation, the research employs the sine cosine adapted chimp optimization algorithm. The resilience and robustness of the power system are evaluated and compared with conventional controllers, such as proportional integral, lead-lag, and fractional lead-lag power system stabilizer approaches, through thorough simulation and evaluation using MATLAB. Furthermore, the proposed controller approach exhibits superior performance characteristics, specifically with a reduced settling time of 12 s.

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Data sharing not applicable to this article as no datasets were generated or analyzed during the current study.

Abbreviations

MG:

Microgrid

PSS:

Power System Stabilizer

LFO:

Low-Frequency Oscillation

SCaChOA:

Sine Cosine adapted Chimp Optimization Algorithm

SG:

Synchronous Generators

PI:

Proportional Integral

FLL-PSS:

Fractional Lead-Lag PSS

JGC:

Jacobian Gain Control

MPC:

Model-Predictive Control

ESO:

Extended State Observer

M-DTA:

Mode-Based Damping Torque Analysis

STATCOM:

Static Compensator

TDFC:

Time Delayed Feedback Control

PSO:

Particle Swarm Optimization

GA:

Genetic Algorithm

EMF:

Electromotive Force

TID:

Tilt Integral Derivative

FO:

Fractional Order

ChoA:

Chimp Optimization Algorithm

LL-PSS:

Lead Lag PSS

SCA:

Sine Cosine Algorithm

RDO-SMC:

Robust disturbance observer based sliding mode controller

ANFIS:

Adaptive Neuro-Fuzzy Inference System

MFO:

Moth Flame Optimization

U:

Unoptimized case

\(Z_{{\text{T}}} ,Z_{{{\text{Tb}}}}\) :

Impedances at the terminal and infinite bus system

\(jX_{e}\) :

Reactance

\(I_{{\text{d}}}\) :

Diode current

\(I_{{{\text{sc}}}}\) :

Short-circuit current

\(q\) :

Charge

\(k\) :

Boltzmann constant

\(A\) :

Ideality factor

\(\omega_{{\text{t}}}\) :

Turbine mechanical speed

\(H_{{\text{g}}}\) :

Inertia of generator

\(\theta_{{{\text{tw}}}}\) :

Torsional angle of the shaft

\(k_{{{\text{sh}}}}\) :

Shaft coefficient

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

Electrical torque

\(\omega_{{{\text{base}}}}\) :

Base angular velocity

\(i_{fd}\) :

Changes in the direct current

\(i_{dg}\) :

D-axis current

\(i_{kd}\) :

Subtransient current in d-axis

\(r_{fd}\) :

Resistance associated with the d-axis of the generator

\(X_{d}\) :

SG d-axis synchronous reactance

\(X_{akd}\) :

SG d-axis subtransient reactance

\(\delta_{{{\text{inj}}}}\) :

Injected phase angle

\(r_{{\text{a}}}\) :

Armature resistance

\(X_{{\text{q}}}\) :

Quadrature(q)-axis reactance

\(X_{akq}\) :

Generator subtransient reactance in q-axis

\(X_{fkd}\) :

Subtransient reactance in d-axis

\(r_{kd}\) :

Rotor resistance of d-axis

\(i_{qg}\) :

q-Axis current

\(r_{kq}\) :

Resistance associated with the q-axis subtransient

\(M\) :

Mechanical torque

\(V_{{\text{t}}}\) :

Generator terminal voltage

\(T_{A}\) :

Time constant of the system

\(K_{A}\) :

Proportional constant for the AVR

\(r(t)\) :

Reference signal

\(e(t)\) :

Error signal

\(G\) :

Controller transfer function

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

Tilt controller parameter

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

Derivative controller parameter

\(s^{1/n}\) :

Transfer function component with an exponent ‘n’

\(\mu 1\) :

First exponent in the controller transfer function

\(N\) :

Population of chimp

\(m,c,f\) :

Group strategy parameters

\(X\) :

Vector

\(\min\) :

Minimize

\(\Delta P_{e}\) :

Deviations in real power

\(P_{\max }\) :

Peak power

\(V_{\max }\) :

Voltage at peak power

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

Generator torque

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

Exciter torque

\(P_{{{\text{WG}}}} ,P_{{\text{G}}} ,P_{{\text{V}}}\) :

Wind, generator, solar generated power

\(X_{{\text{b}}}\) :

Rated (Base) operating frequency

\(H\) :

Moment of inertia

\(KA\) :

Constant in Exciter

\(R\,,\,X\) :

Line resistance and reactance

\(i_{{\text{L}}} ,i_{{{\text{Line}}}}\) :

Current in the transmission line

\(f_{{\text{b}}}^{t} \left( {g_{s} } \right)\) :

Beta PDFs

\(\alpha \,{\text{and}}\,\beta\) :

Beta parameters for every segment

\(\sigma\) :

Standard deviation

\(P_{{{\text{PV}},s}}^{t}\) :

Output power of PV at time instant \(t\) for state \(s\)

\(V_{{{\text{mpp}}}} \,\,{\text{and}}\,\,I_{{{\text{mpp}}}}\) :

Voltage and current at maximum power point

\(I_{{{\text{sc}}}}\) :

Short-circuit current

\(T_{{{\text{cell}},s}}^{t}\) :

Temperature of the cell

\(N_{{{\text{OT}}}}\) :

Nominal operating cell temperature

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

Voltage temperature

\(c\) :

Rayleigh scale parameter

\({\text{prob}}_{\upsilon ,i}^{t}\) :

Probability occurrence state \(i\) for time instant \(t\)

\(s_{{{\text{co}}}}\) :

Cut-out wind speed

\(s_{{{\text{av}},w,t}}\) :

Average wind speed

\(E_{fd0}\) :

Generator field voltage

\(V_{{\text{t}}}\) :

Terminal voltage

SPV:

Solar Photovoltaic

µ1-µ2/TIFDN:

µ1-µ2/Tilted Integral Fractional Derivative with Filter

SMIB:

Single-Machine Infinite Bus

RES:

Renewable Energy Sources

FOC:

Fractional Order Controllers

LL:

Lead-Lag

SVC:

Static Var Compensator

JF:

Jacobian Functions

DMDC:

Dynamic Mode Decomposition with Control

aDPR:

Adaptive Dynamic Power Reduction

QAGTO:

Quantum Artificial Gorilla Troops Optimizer

POD-P:

Power Oscillation Damping Power

WADC:

Wide-Area Damping Controller

FFA:

Farmland Fertility Algorithm

PCC:

Point of Common Coupling

AVR:

Automatic Voltage Regulator

FOPID:

Fractional Order Proportional Integral Derivative

PID:

Proportional Integral Derivative

PI-PSS:

Proportional Integral PSS

DE:

Differential Evolution

PDF:

Probability Density Function

AGC:

Automatic Generation Control

FOBELBIC:

FO Brain Emotional Learning Based Intelligent Controller

EP:

Evolutionary Programming

\(V_{{{\text{ref}}}}\) :

Reference voltage

\(R_{e}\) :

Resistance at the terminal side

\(X_{{\text{t}}}\) :

Transformer with its own reactance

\(n_{p}\) :

Ideality factor

\(I_{{\text{r}}}\) :

Diode saturation current in reverse direction

\(V_{{\text{d}}}\) :

Voltage across diode

\(\theta\) :

Temperature

\(n_{{\text{s}}}\) :

Number of series connected solar cells

\(\omega_{{\text{r}}}\) :

Mechanical speed of rotor

\(H_{{\text{t}}}\) :

Inertia of turbine

\(C_{{{\text{sh}}}}\) :

Damping coefficient

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

Mechanical torque

\({\text{d}}/{\text{d}}t\) :

Rate of change in time (t)

\(X_{ffd}\) :

SG direct(d)-axis transient reactance

\(X_{afd}\) :

Synchronous reactance in d-axis

\(X_{fkd}\) :

Subtransient reactance in q-axis

\(\omega \,_{0}\) :

Synchronous angular velocity

\(E\) :

Generated EMF

\(X_{1}\) :

Transient reactance associated with the SG

\(V_{{{\text{inj}}}}\) :

Injected voltage

\(R_{1}\) :

Sum of rotor resistance

\(\omega_{g}\) :

Synchronous angular velocity

\(i_{qg}\) :

Generator q-axis current

\(i_{kq}\) :

q-Axis subtransient current

\(X_{kkd}\) :

SG d-axis subtransient short-circuit reactance

\(X_{{\text{t}}}\) :

Transient reactance associated with the SG

\(X_{kkq}\) :

SG q-axis subtransient short-circuit reactance

\(\delta_{g}\) :

Rotor angle

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

Mechanical torque generated by the generator

\(V_{{{\text{ref}}}}\) :

Predetermined reference value

\(E\) :

Voltage error

\(V_{{{\text{ref}}}}\) :

Reference set value

\(u(t)\) :

Controlled input

\(y(t)\) :

System output

\(N\) :

Constant used in the transfer function

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

Integral controller parameter

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

Second derivative controller parameter

\(s\) :

Laplace variable

\(\mu 2\) :

Second exponent in the controller transfer function

\(t\) :

Predefined number of iterations

\(a,d\) :

Chimp acceleration and direction

ITSE:

Integral of time multiplied by the squared error

\(\Delta \omega_{e}\) :

Deviations in angular frequency

\(V_{{{\text{oc}}}}\) :

Open circuit voltage

\(I_{\max }\) :

Current at maximum range

\(I_{{{\text{sc}}}}\) :

Short-circuit current

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

Turbine torque

\(V_{{\text{b}}}\) :

Base voltage

\(G,B\) :

Load conductance and susceptance in the system

\(T_{d0}{\prime}\) :

Field open circuit time constant

\(D\) :

Damping factor

\(TA\) :

Voltage regulator time constant

\(j\) :

Imaginary part

\(V_{{{\text{pcc}}}}\) :

Voltage in the PCC

\(g_{s}\) :

PV irradiation

\(\mu\) :

Mean

\(g_{s1} \;{\text{and}}\;g_{s2}\) :

PV irradiation limits

\(N\) :

PV modules count

\(V_{{{\text{cell}},s}}^{t} \,\,{\text{and}}\,\,I_{{{\text{cell}},s}}^{t}\) :

Cell voltage and current

\(K_{i}\) :

Current temperature

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

Ambient temperature

\(V_{{{\text{OC}}}}\) :

Open circuit voltage

\(\upsilon\) :

Wind speed

\(\upsilon_{w1} \;{\text{and}}\;\upsilon_{w2}\) :

Wind speed limit

\(s_{{{\text{ci}}}}\) :

Cut-in wind speed

\(s_{{\text{r}}}\) :

Rated wind speed

\(P_{{\text{r}}}\) :

WT rated power

\(X_{d}^{\prime }\) :

Transient reactance

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Authors and Affiliations

  1. Department of Electrical and Electronics Engineering, Kumaraguru College of Technology, Coimbatore, Tamil Nadu, 641049, India

    N. Mohana Sundaram

  2. Department of Electronics and Communication Engineering, Kumaraguru College of Technology, Coimbatore, Tamil Nadu, 641049, India

    Rani Thottungal

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Appendix

Appendix

Parameter specifications are shown in Table

Table 8 Parameter specifications
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8.

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Mohana Sundaram, N., Thottungal, R. Stability analysis of single-machine infinite bus system with renewable energy sources using sine cosine chimp optimization. Electr Eng (2024). https://doi.org/10.1007/s00202-024-02450-4

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