Project
AA4-9
Volatile Electricity Markets and Battery Storage: A Model-Based Approach for Optimal Control
Project Heads
Christian Bayer, Dörte Kreher, Manuel Landstorfer
Project Members
Wilfried Kenmoe Nzali
Project Duration
01.04.2022 − 31.03.2025
Located at
WIAS
Description
We model together a volatile electricity market with a stationary battery storage device to reduce an electricity consumer’s overall cost. This is achieved by a stochastic optimal control problem with a virtual battery as constraint to determine charging and discharging. Our goal is to develop a mathematical tool that empowers electrical energy consumers to reduce their energy expenses through the integration of a Stationary Battery Storage Devices (SBSD) within their local electricity supply system (refer to the Figure). We assume that operating the SBSD does not affect the electricity market as a whole. Initially, our focus is on formulating a stochastic optimal control problem that accounts for the continuous time-dependent charging and discharging of the virtual battery. The charging and discharging strategies are influenced by various factors, including (i) the electricity price market, (ii) forecast indicators such as wind conditions and forward prices, and (iii) specific conditions for the battery, such as degradation effects. This is achieved by a combination of stochastic and PDE based modeling, numerical simulations and data processing.
External Website
Ongoing work
In the first stage, we construct and solve the optimal control problem using three main modules: the battery module, the price module, the Optimizer module.
a) Battery Module: Constant Voltage Model: This model is defined in terms of the state of charge (SOC) with a constant voltage. Here, the control variable is the SOC.
Variable Voltage Model: This model features a non-constant voltage, where the control is applied directly to the voltage.
b)Price Module: We begin with an Ornstein-Uhlenbeck (OU) model that incorporates jumps and also seasonality that effectively captures the behavior of price trajectories over days, weeks, and years.
c) Optimizer module.This Module solve the Optimal control problem using Least Square Monte Carlo and return the value function and the optimal strategy. One can see the recap on the figure section.
Related Publications
Related Pictures
The left branch sketches a typical consumer buying electricity for fixed annual market prices. The right branch sketches our project, combining electricity spot markets with SBSDs to reduce the overall cost for a consumer.
A schematic representation illustrating the process for solving the optimal control problem.
We observe that the value function exhibits smooth behaviour, as demonstrated in the analytical section. Additionally, it is evident that the value function decreases with respect to the electricity spot price and does not increase with respect to the state of charge. This indicates that the minimum consumption cost occurs when there is available energy in the battery and when the electricity price is lower.
Optimal strategy for one sample path for a time horizon of T=72 hours and
initial control y_0 = 0, considering a battery that can satisfy the power demand for 24 hours.
Total consumption cost vs Battery duration over the period of one week. We see how the battery can help us or not to minimize the consumption cost. More precisely, we see that having a battery with a Battery duration of $\mathcal{T}=12$ can help to minimize the most our cost such that we can save up to . This saving percentage will obviously increase with time, for example if we are looking for a strategy over $T=2$ years.