A stability analysis for a maximum power point tracking (MPPT) scheme based on extremum-seeking control is developed for a photovoltaic (PV) array supplying a dc-to-dc switching converter. The global stability of the extremum-seeking algorithm is demonstrated by means of Lyapunov's approach. Subsequently, the algorithm is applied to an MPPT system based on the "perturb and observe" method. The steady-state behavior of the PV system with MPPT control is characterized by a stable oscillation around the maximum power point. The tracking algorithm leads the array coordinates to the maximum power point by increasing or decreasing linearly with time the array voltage. Off-line measurements are not required by the control law, which is implemented by means of an analog multiplier, standard operational amplifiers, a flip-flop circuit and a pulsewidth modulator. The effectiveness of the proposed MPPT scheme is demonstrated experimentally under different operating conditions.
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Leyva et al. (2006) studied this question.
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