# PV Fleet Modeling via Smooth Periodic Gaussian Copula

arXiv: https://arxiv.org/abs/2307.00004 · HTML: https://mlsanity.com/paper/2307.00004/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 10 of its 51 references that are in the map.
- First posted on arXiv 5 Jun 2023.

## Builds on (most cited first, 10 of 10)

- [Convex optimization](https://mlsanity.com/paper/2106.01946/) (2021)
- [CVXPY: A Python-Embedded Modeling Language for Convex Optimization](https://mlsanity.com/paper/1603.00943/) (2016)
- [A Rewriting System for Convex Optimization Problems](https://mlsanity.com/paper/1709.04494/) (2017)
- [Convex Potential Flows: Universal Probability Distributions with Optimal Transport and Convex Optimization](https://mlsanity.com/paper/2012.05942/) (2020)
- [Matrix Completion with Quantified Uncertainty through Low Rank Gaussian Copula](https://mlsanity.com/paper/2006.10829/) (2020)
- [Jacobian Determinant of Normalizing Flows](https://mlsanity.com/paper/2102.06539/) (2021)
- [A Distributed Method for Fitting Laplacian Regularized Stratified Models](https://mlsanity.com/paper/1904.12017/) (2019)
- [Gaussian Process Regression for Probabilistic Short-term Solar Output Forecast](https://mlsanity.com/paper/2002.10878/) (2020)
- [Fitting Laplacian Regularized Stratified Gaussian Models](https://mlsanity.com/paper/2005.01752/) (2020)
- [Signal Decomposition Using Masked Proximal Operators](https://mlsanity.com/paper/2202.09338/) (2022)

## Abstract (arXiv)

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.