Optimal Energy Arbitrage using Linear Programming

Code repo for our 2019 paper: Optimal Storage Arbitrage under Net Metering using Linear Programming

Authors: Md Umar Hashmi, Arpan Mukhopadhyay, Ana Bu\v{s}i'c, and Jocelyne Elias

INRIA, DI ENS, Ecole Normale Sup'erieure, CNRS, PSL Research University, Paris, France

Contact: umar.hashmi123@gmail.com

Introduction

We formulate energy storage arbitrage problem using linear programming. The LP formulation is possible due to piecewise linear convex cost functions. In this formulation we consider: (a) net-metering compensation (with selling price at best equal to buying price) i.e. $\kappa_i \in [0,1]$, (b) inelastic load, (c) consumer renewable generation, (d) storage charging and discharging losses, (e) storage ramping constraint and (f) storage capacity constraint. Using numerical results we perform sensitivity analysis of energy storage batteries for varying ramp rates and varying ratio of selling and buying price of electricity.

Variables: (i) p_b(i) Buying price at time instant i (ii) p_s(i) Selling price at time instant i (iii) z_i denotes net-load without storage output; it includes inelastic consumer load and consumer renewable generation (iv) \kappa_i is the ratio of selling price and buying price at time i (v) \eta_{dis}, \eta_{ch} charging and discharging efficiency of the battery (vi) \kappa_i is the ratio of selling price and buying price at time i (vii) x_i denotes change in battery charge level at time instant i

Code Dependencies

All code are implemented in MATLAB.