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Performance and Stability Analysis of Enhanced Lyapunov Function and Predictive Voltage Control with Active Damping for Single-Phase PV/Grid Electric Power System

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Abstract

As the world increasingly turns to renewable energy sources, the integration of solar photovoltaic (PV) systems into the grid has emerged as a pivotal solution. Effective control methods are paramount to harnessing the full potential of these grid-connected PV systems. While existing control methods have laid a foundation, there persists a compelling need for innovative approaches capable of surpassing the limitations of conventional methods. This paper introduces a novel nonlinear control approach utilizing an enhanced Lyapunov function for a single-phase PV/grid electric power system. High-performance operation of the solar PV system, interfacing with a grid-connected single-stage inverter, is achieved through the control of maximum PV voltage using predictive voltage control for MPPT. The enhanced Lyapunov function maintains PV voltage stability at the dc-bus by treating the difference between PV voltage and its reference as a controlled state error. Notably, this approach ensures the stability of the closed-loop PV system even under varying solar irradiances. To achieve full active power injection into the grid with high quality, the proposed enhanced Lyapunov function is augmented by integrating an LCL filter with virtual resistance as an active damping circuit for grid current feedback control. This integration introduces an opposing current to the grid-side inductance current. This compensation mechanism corrects the q-axis grid current using the dq-SRF mathematical model of the global PV/grid system. The LCL parameters and virtual resistance design methods are provided. The effectiveness of the enhanced Lyapunov function is demonstrated through simulations using MATLAB/Simulink software. The results showcase outstanding performance when compared to conventional Lyapunov function and sliding mode control strategies in achieving key objectives, including zero state errors, global stability, and the generation of a sinusoidal grid current signal with low total harmonic distortion and the unit power factor at the point of common coupling.

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Abbreviations

PVC:

Predictive voltage control

PV:

Photovoltaic

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

Output PV power

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

Output PV voltage

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

Output PV current

\(I_{ph}\) :

Light-generated current

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

Diode saturation current

\(N_{{\text{p}}} ,\;N_{{\text{S}}}\) :

Parallel and series PV cells number

\(R_{{\text{S}}} ,\;R_{sh}\) :

Equivalent series and parallel resistances of the PV array

\(A,\;K,\;T\) :

Ideal factor, Boltzmann’s constant and PV cell temperature

q :

Electron’s charge

MPPT:

Maximum power point tracking

\(V_{mpp}\) :

Maximum output PV voltage under each applied irradiance

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

Cost function

\(T_{S}\) :

Time of prediction

1,2 :

Two possible predictions index

i :

Prediction step

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

Capacitor at the dc-bus

\(L_{{{\text{inv}}}} ,\;C_{{\text{f}}} ,\;L_{{\text{g}}}\) :

Inverter-side inductance, filter capacitor, and grid-side inductance

\(R_{{{\text{AD}}}}\) :

Virtual resistance

\(R_{{{\text{inv}}}} ,\;R_{g}\) :

Internal resistance of both inductances filter

\(I_{{{\text{inv}}}} ,\;V_{{{\text{inv}}}}\) :

Output ac—single-phase inverter current and voltage

\(I_{L}\) :

Grid-side inductance current

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

Active damping current through the virtual resistance

\(I_{{{\text{grid}}}} ,\;V_{{{\text{grid}}}}\) :

Output ac—single-phase grid current and voltage

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

Output voltage across the filter capacitor

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

Nonlinear loads current

\(\omega_{{\text{g}}} ,\;\omega_{{{\text{res}}}} ,\;\omega_{{{\text{sw}}}}\) :

Grid, resonance, and switching frequencies respectively

SPLL:

Single-phase looked loop

SRF:

Synchronous reference frame

\(\alpha_{d} ,\alpha_{q}\) :

Control laws of single-phase single-stage inverter in dq-SRF

\(T_{1} ,T_{2} ,T_{3} ,T_{4}\) :

Switching states of the singe-phase inverter

\(P_{{{\text{grid}}}} ,\;Q_{{{\text{grid}}}} ,\;S_{{{\text{grid}}}}\) :

Active, reactive and apparent powers of the grid

PCC:

Point of common coupling

THD:

Total harmonic distortion

rms:

Root mean square

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Authors and Affiliations

  1. DRIVE Lab, University of Burgandy, Nevers, France

    Halima Ikaouassen

  2. High National School of Chemistry, IbnTofail University, ENSC, B.P. 242, Kenitra, Morocco

    Abderraouf Raddaoui

  3. Center for Research and Innovation in Energy Intelligence, CR2Ie, Sept-Iles, QC, Canada

    Miloud Rezkallah

Authors
  1. Halima Ikaouassen
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  2. Abderraouf Raddaoui
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  3. Miloud Rezkallah
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Corresponding author

Correspondence to Halima Ikaouassen.

Appendix

Appendix

See Table 4.

Table 4 Electric Power System parameters
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Ikaouassen, H., Raddaoui, A. & Rezkallah, M. Performance and Stability Analysis of Enhanced Lyapunov Function and Predictive Voltage Control with Active Damping for Single-Phase PV/Grid Electric Power System. Iran J Sci Technol Trans Electr Eng (2024). https://doi.org/10.1007/s40998-023-00686-7

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