**NSF CMMI-1933243: **Optimizing Risk in a Gauss-Markov Process - Energy Storage Strategies for Renewable Integration

**Project Description:**

All power derived from renewable energy resources such as wind and solar depends on the weather. Changes in power from renewables can be predictable, e.g. due to the rising and setting of the sun - or can be hard to predict, e.g. due to clouds blocking out the sun. Consumer demand for power, likewise, has always been partly predictable and partly random. The amount of power a utility must generate is the consumer demand minus the renewable power generated. As power from renewables increases, the unpredictable part of this required generation also increases. Utilities have begun to respond to this increased risk by investing in battery storage and quick-start generators. However, there is currently no way to quantify the risk caused by renewable energy resources – meaning utilities don’t know how many batteries to buy or how to use them efficiently. For example, a utility might buy 1 GWh of battery storage. However, the 1 GWh is useless if it is discharged too early in the day and is unavailable when a storm blows in and reduces solar production unexpectedly. The goal of this project, then, is to develop accurate weather-based models to forecast the probability that renewable generators will experience large drops in production. The project then proposes algorithms to use these risk models to determine optimal battery charge-discharge programs for both consumers and utilities. In addition, the project uses these models to determine optimal electricity pricing structures - including demand charges – for a regulated utility.

This project has three areas of focus. The first focus is to develop useful Gauss-Markov (G-M) models of solar generation. These models are based on datasets provided by Wunderground and Arizona utility SRP and condition on pressure changes, humidity and temperature. Machine Learning is then used to map daily forecast data to the model which is most effective at reducing cost. The second focus is to solve stochastic Dynamic Programming (DP) problems with non-separable objective functions. Specifically, minimizing the expected maximum of a G-M process and computing the probability distribution of the maximum of a G-M process over a finite time-interval. Such stochastic DPs are reformulated using the recently proposed Naturally Forward Separable (NFS) framework which allows them to be solved recursively using the Bellman equation with minimal computation time. The third focus is to apply the NFS DP framework to newly developed models of solar generation and produce algorithms for optimal battery programming and associated spinning reserve. These algorithms are then used to propose a model for optimal utility pricing of consumption and demand charges based on principles of feedback and not based on marginal pricing. The algorithms are also used to evaluate the impact on risk and cost of utility-owned solar vs rooftop solar.

**Project Duration:**

09/01/2019-08/31/2022

**Project Personnel:**

Matthew M. Peet (PI), Arizona State University

Morgan Jones (PhD), Arizona State University

**Industry Collaborators:**

Robert Hess, SRP

**Associated Publications at ASU:**

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