Comparison of Statistical and Deterministic Smoothing Methods to Reduce the Uncertainty of Performance Loss Rate Estimates

Abstract

With the large increase of installed photovoltaic (PV) capacity introduced in the energy system, one aspect that becomes increasingly important is the long-term reliability of the energy output and, thus, the estimation of the performance loss rate (PLR) for the different technologies on the market. Reliable performance metrics and statistical methods are needed to exploit continuous outdoor measurements, in order to assess the long-term performance and, thus, the financial viability of solar PV systems, as well as their long-term stability as an important part of the energy mix. This paper presents and compares seven different methodologies to extract reliable long-term performance indicators from monitored field data. The methods can be grouped into four different approaches. First, a simple computation of the performance ratio (PR) is used as a benchmark for the other methods. Second, these PR values are fitted to two sinusoidal functions that emulate the climatic influence and a decaying trend that represents the degradation of the PV array. Third, two kinds of time-series decomposition [namely classical series decomposition and seasonal-trend decomposition based on local regression (STL)] are applied, and the trend is linearized to find the PLR. Finally, two methods are presented that aim to utilize the physical properties of the material to correct for seasonal fluctuations, namely the correction to standard test conditions of the PR via normal operating conditions ( $\text{PR}_{\text{NOCT}}$ ) and a performance metric called array photovoltaic for utility system applications (PVUSA). In this work, the degradation rates from the different computational methods are presented. The main focus is on the understanding of the uncertainty associated with each of the methods. All the methods yield comparable results; however, the statistical time-series methods deliver the highest accuracy in almost all the investigated cases, especially for technologies affected by metastable effects. On average, the two periodic methods halve the uncertainty and the time-series methods reduce the uncertainty, on average, to 45%, whereas the methods $\text{PR}_{\text{NOCT}}$ and $\text{PVUSA}$ reduce to only 75% of the benchmark method. Methods that are trying to incorporate the module physics ( $\text{PR}_{\text{NOCT}}$ and $\text{PVUSA}$ ) work best to reduce the uncertainty only for technologies, in which the temperature behavior is well known, i.e., crystalline-silicon-based modules. For this reason, the usage of the STL method for the computation of the PLR is proposed.