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We present a method for jointly modeling power generation from a fleet of photovoltaic (PV) systems. We propose a white-box method that finds a function that invertibly maps vector time-series data to independent and identically distributed standard normal variables. The proposed method, based on a novel approach for fitting a smooth, periodic copula transform to data, captures many aspects of the data such as diurnal variation in the distribution of power output, dependencies among different PV systems, and dependencies across time. It consists of interpretable steps and is scalable to many systems. The resulting joint probability model of PV fleet output across systems and time can be used to generate synthetic data, impute missing data, perform anomaly detection, and make forecasts. In this paper, we explain the method and demonstrate these applications.

We provide a methodology for estimating the losses due to soiling for photovoltaic (PV) systems. We focus this work on estimating the losses from historical power production data that are unlabeled, i.e. power measurements with time stamps, but no other information such as site configuration or meteorological data. We present a validation of this approach on a small fleet of typical rooftop PV systems. The proposed method differs from prior work in that the construction of a performance index is not required to analyze soiling loss. This approach is appropriate for analyzing the soiling losses in field production data from fleets of distributed rooftop systems and is highly automatic, allowing for scaling to large fleets of heterogeneous PV systems., Comment: 7 pages, 10 figures, 3 tables

We consider the well-studied problem of decomposing a vector time series signal into components with different characteristics, such as smooth, periodic, nonnegative, or sparse. We describe a simple and general framework in which the components are defined by loss functions (which include constraints), and the signal decomposition is carried out by minimizing the sum of losses of the components (subject to the constraints). When each loss function is the negative log-likelihood of a density for the signal component, this framework coincides with maximum a posteriori probability (MAP) estimation; but it also includes many other interesting cases. Summarizing and clarifying prior results, we give two distributed optimization methods for computing the decomposition, which find the optimal decomposition when the component class loss functions are convex, and are good heuristics when they are not. Both methods require only the masked proximal operator of each of the component loss functions, a generalization of the well-known proximal operator that handles missing entries in its argument. Both methods are distributed, i.e., handle each component separately. We derive tractable methods for evaluating the masked proximal operators of some loss functions that, to our knowledge, have not appeared in the literature., Comment: The manuscript has 61 pages, 22 figures and 2 tables. Also hosted at https://web.stanford.edu/~boyd/papers/sig_decomp_mprox.html. For code, see https://github.com/cvxgrp/signal-decomposition

A novel unsupervised machine learning approach for analyzing time-series data is applied to the topic of photovoltaic (PV) system degradation rate estimation, sometimes referred to as energy-yield degradation analysis. This approach only requires a measured power signal as an input--no irradiance data, temperature data, or system configuration information. We present results on a data set that was previously analyzed and presented by NREL using RdTools, validating the accuracy of the new approach and showing increased robustness to data anomalies while reducing the data requirements to carry out the analysis., Comment: Presented at 46th IEEE Photovoltaic Specialists Conference (2019), accepted with revisions to IEEE Journal of Photovoltaics, final proof submitted November 2019

We present an algorithm that estimates a clear sky performance signal from the measured power of a PV system. The algorithm uses only observed power output, and assumes no knowledge of weather, irradiance data, or system configuration metadata. This is a novel approach to understanding the clear sky behavior of an installed PV system, that does not rely on traditional atmospheric and geometric modeling techniques., Comment: Presented at 45th IEEE Photovoltaic Specialists Conference