Identification of photovoltaic arrays' maximum power extraction point via dynamic regressor extension and mixing

Abstract

This paper deals with the problem of identification of photovoltaic arrays' maximum power extraction point-information that is encrypted in the current-voltage characteristic equation. We propose a new parameterisation of the classical five parameter model of this function that, combined with the recently introduced identification technique of dynamic regressor extension and mixing, ensures a fast and accurate estimation of all unknown parameters. A concavity property of the current-voltage characteristic equation is then exploited to directly identify the desired voltage operating point. Realistic numerical examples via computer simulations are presented to assess the performance of the proposed approach.

Parameter identification of linear time‐invariant systems using dynamic regressor extension and mixing

“…which is strictly stronger than the monotonicity property (6). The relationship between the condition Δ(t) ∉  2 and (t) ∈ PE is far from obvious for arbitrary regressor vectors (t) (see the work of Aranovskiy et al 1 for examples, which show that neither one of the conditions is stronger than the other).…”

“…Remark 3. [1][2][3][4][5][6]11 Remark 4. Besides the important element-by-element monotonicity property of the parameter errors captured by (12), this feature is instrumental to eliminate the need to overparameterize nonlinear regressions to obtain a linear one, a practice that, as is well known, 7,8,13 entails a serious performance degradation.…”

“…This and other advantages of DREM have been discussed in a series of publications. [1][2][3][4][5][6]11 Remark 4. It is well known that nonsquare integrability and PE of a signal are not equivalent properties, even in the scalar case.…”

“…A new procedure to design parameter estimators for linear and nonlinear regressions, called dynamic regressor extension and mixing (DREM), was recently proposed in the work of Aranovskiy et al 1 The technique has been successfully applied in a variety of identification and adaptive control problems. [2][3][4][5][6] For linear regressions, DREM estimators outperform classical gradient or least-squares estimators in the following precise aspect: independent of the excitation conditions, DREM guarantees monotonicity of each element of the parameter error vector that is much stronger than monotonicity of the vector norm, which is ensured with classical estimators. Another interesting property of DREM is that its convergence is established without the usual restrictive requirement of regressor persistence of excitation (PE).…”

A state observer for sensorless control of magnetic levitation systems

“…The first step in our design is the reconstruction of the flux, which is done by combining the parameter estimation-based observers (PEBO) recently reported in [22] with the dynamic regressor extension and mixing (DREM) parameter estimation technique of [1]. The combination of these two new techniques has been proven highly successful in the solution of several complex practical problems [2,3,24]-see also [23] for the reformulation of DREM as a functional Luenberger observer. With the knowledge of the flux we propose suitably tailored nonlinear observers for the mechanical coordinates, obtaining in this way a globally convergent solution to the posed observation problem.…”