Noise-Scaled Euclidean Distance: A Metric for Maximum Likelihood Estimation of the PV Model Parameters

This article revisits the objective function (or metric) used in the extraction of photovoltaic (PV) model parameters. A theoretical investigation shows that the widely used current distance (CD) metric does not yield the maximum likelihood estimates (MLE) of the model parameters when there is noise in both voltage and current samples. It demonstrates that the Euclidean distance (ED) should be used instead, when the voltage and current noise powers are equal. For the general case, a new noise-scaled Euclidean distance (NSED) metric is proposed as a weighted variation of ED, which is shown to fetch the MLE of the parameters at any noise conditions. This metric requires the noise ratio (i.e., ratio of the two noise variances) as an additional input, which can be estimated by a new noise estimation (NE) method introduced in this study. One application of the new metric is to employ NSED regression as a follow-up step to existing parameter extraction methods toward fine-tuning of their outputs. Results on synthetic and experimental data show that the so-called NSED regression "add-on" improves the accuracy of five such methods and validate the merits of the NSED metric.