Unbiased Extremum Seeking for MPPT in Photovoltaic Systems

TL;DR

The paper tackles maximum power point tracking (MPPT) in photovoltaic systems by addressing steady-state bias inherent in traditional extremum seeking (ES). It introduces two model-free algorithms: exponential unbiased ES (uES) for exponential convergence to the MPP and unbiased prescribed-time ES (uPT-ES) for convergence within a user-defined horizon, both employing time-varying perturbations and demodulation gains, with uPT-ES using chirp signals for finite-time excitation. Theoretical results establish local exponential and prescribed-time convergence guarantees under convexity and excitation conditions, while hardware-in-the-loop experiments confirm improved convergence speed and reduced dithering compared to classical ES under static and dynamic irradiance. The work offers a practical, robust MPPT approach with unbiased convergence and finite-time performance, with potential extensions to distributed PV systems.

Abstract

This paper presents novel extremum seeking (ES) strategies for maximum power point tracking (MPPT) in photovoltaic (PV) systems that ensure unbiased convergence and prescribed-time performance. Conventional ES methods suffer from steady-state bias due to persistent dither signal. We introduce two novel ES algorithms: the exponential unbiased ES (uES), which guarantees exponential convergence to the maximum power point (MPP) without steady-state oscillation bias, and the unbiased prescribed-time ES (uPT-ES), which ensures convergence within a user-defined time horizon. Both methods leverage time-varying perturbation amplitudes and demodulation gains, with uPT-ES additionally utilizing chirp signals to enhance excitation over finite-time intervals. Experimental results on a hardware-in-the-loop testbed validate the proposed algorithms, demonstrating improved convergence speed and tracking accuracy compared to classical ES, under both static and time-varying environmental conditions.

Figures (8)

• Figure 1: Block diagram of a PV system comprising a PV module, a DC/DC boost converter, and a load. The duty cycle $d$ is perturbed by an MPPT controller to maximize the output power $P = VI$, which is influenced by variations in solar irradiance and temperature.
• Figure 2: P-V curves of a PV panel under (a) varying irradiance at 25$^\circ C$ and (b) varying temperature at 1000 $W/m^2$. Increased irradiance raises both power and optimal voltage, while higher temperature lowers the maximum power and shifts the optimal voltage leftward.
• Figure 3: Exponential uES scheme. The design employs an exponentially decaying function $\alpha$ to gradually diminish the effect of the perturbation signal $a\sin(\omega t)$, while its multiplicative inverse $\frac{1}{\alpha}$ correspondingly amplifies the effect of the demodulation signal $\frac{2}{a}\sin(\omega t)$.
• Figure 4: uPT-ES scheme. This design extends the exponential uES shown in Fig. \ref{['ESBlock']} by incorporating the factor $\mu^q$, with $q \geq 1$, into all system dynamics, and by replacing the perturbation and demodulation signals with hyperbolic chirps.
• Figure 5: The experimental setup of the PV system.

Theorems & Definitions (4)

• Theorem 1
• proof
• Theorem 2
• proof