# Optimal Storage Arbitrage under Net Metering using Linear Programming

## TL;DR

This paper develops a linear programming approach for optimal energy storage arbitrage under net metering, incorporating uncertainties in load, prices, and renewable generation within a predictive control framework.

## Contribution

It introduces a novel LP formulation for energy arbitrage considering ramping, capacity, efficiency, and net metering, with uncertainty handled via ARMA and MPC.

## Key findings

- Sensitivity analysis shows impact of ramping constraints on arbitrage profitability.
- Optimal strategies depend on the ratio of selling to buying prices.
- The approach effectively manages uncertainties in load and renewable generation.

## Abstract

We formulate the optimal energy arbitrage problem for a piecewise linear cost function for energy storage devices using linear programming (LP). The LP formulation is based on the equivalent minimization of the epigraph. This formulation considers ramping and capacity constraints, charging and discharging efficiency losses of the storage, inelastic consumer load and local renewable generation in presence of net-metering which facilitates selling of energy to the grid and incentivizes consumers to install renewable generation and energy storage. We consider the case where the consumer loads, electricity prices, and renewable generations at different instances are uncertain. These uncertain quantities are predicted using an Auto-Regressive Moving Average (ARMA) model and used in a model predictive control (MPC) framework to obtain the arbitrage decision at each instance. In numerical results we present the sensitivity analysis of storage performing arbitrage with varying ramping batteries and different ratio of selling and buying price of electricity.