# Generation of Data-Driven Expected Energy Models for Photovoltaic Systems
## 1 Introduction  
The increasing penetration of photovoltaic (PV) systems within the energy markets has established the need for evaluating and ensuring high system reliability. In particular, a large emphasis has been placed on monitoring algorithms that can contextualize observed energy generation at a site with information about how the system would have performed in a nominal state [1]. The latter are commonly estimated through expected energy models. Expected energy models are incorporated into many PV performance monitoring tasks, including anomaly detection [2, 3, 4, 5], financial planning [6], fleet-level (site vs. site) comparisons [7], degradation analysis [7], and the evaluation of extreme weather effects [8]. The comparison of observed energy values to those derived from expected energy models serves as the basis for informing both tactical (i.e., short-term tasks such as field repair) and strategic (i.e., long-term activities such as site planning) operations and maintenance (O&M) activities.  
Expected energy models can vary from asset-level to site-level estimates [9]. Asset-level models typically focus on using parameters provided by the manufacturer (e.g., maximum power) [9, 10]. However, such approaches do not always work well for in-field performance since the parameters were developed in standardized test conditions and thus do not reflect operational conditions [11]. In response to these limitations, empirical methods that use field observations and regression methods have emerged to derive parameters across non-standardized test conditions (e.g., [12, 13]). At the site-level, most expectedenergy models leverage the correlation between power production and meteorological covariates [14; 15]. For example, the standard expected energy model from the International Electrotechnical Commission (IEC) uses irradiance and site capacity information to develop an expected energy estimate [15]. Similarly, the PVUSA model trains a regression model for a given site by estimating power production using local irradiance, temperature, and wind speed conditions [16]. Industry research shows that most expected energy estimates tend to be overestimate production by a median of 3% but could be up to 20% [17]. Although the mismatch between observed and expected generation are well-recognized [18], limited attention has been given to date for improving the accuracy of expected energy models at the site-level, especially suited for fleet-level (i.e., site vs. site) comparisons.  
This work aims to address this knowledge gap by generating a standardized, interpretable data-driven expected energy model that can be used for fleet-level comparisons. Although gradient-boosted and neural network-based methods have demonstrated significant successes for output performance [19; 20; 21], they often lack in model interpretability. In particular, models with high complexity can hide prediction biases or other vulnerabilities [22]. Thus for this work, we opted for more interpretable, regression-based models to increase the transparency of the implemented methods. In addition to identifying a more robust alternate for expected energy modeling, the associated publication of code used for training models (in the open source software pv0 ps) enables the extension of these methods to develop site-specific expected energy models for PV systems anywhere in the world or to other renewable energy systems. Such advancements in expected energy model estimates are needed to continue supporting better planning and field O&M activities, both of which ultimately influence the sustainability of PV sites. The following sections describes the data processing and model construction activities (Section 2), the performance of trained models (Section 3), and summarize primary findings (Section 4).