Probabilistic Day-Ahead Battery Scheduling based on Mixed Random Variables for Enhanced Grid Operation

TL;DR

This work tackles grid uncertainty arising from renewable variability by enabling residential BESS to share deviations between the home and the grid. It introduces an analytical approach that uses mixed random variables to asymmetrically allocate prosumption uncertainty and embeds this in an expectation-based nonlinear stochastic optimization to compute probabilistic schedules and grid exchanges. The authors validate the method on real-world data across three scenarios, showing that grid uncertainties can be reduced without increasing homeowner costs and that BESS can provide targeted flexibility during critical periods. This framework offers a practical path for prosumers to actively enhance grid stability and resilience through probabilistic day-ahead scheduling.

Abstract

The increasing penetration of renewable energy sources introduces significant challenges to power grid stability, primarily due to their inherent variability. A new opportunity for grid operation is the smart integration of electricity production combined with battery storages in residential buildings. This study explores how residential battery systems can aid in stabilizing the power grid by flexibly managing deviations from forecasted residential power consumption and PV generation. The key contribution of this work is the development of an analytical approach that enables the asymmetric allocation of quantified power uncertainties between a residential battery system and the power grid, introducing a new degree of freedom into the scheduling problem. This is accomplished by employing mixed random variables - characterized by both continuous and discrete events - to model battery and grid power uncertainties. These variables are embedded into a continuous stochastic optimization framework, which computes probabilistic schedules for battery operation and power exchange with the grid. Test cases demonstrate that the proposed framework can be used effectively to reduce and quantify grid uncertainties while minimizing electricity costs. It is also shown that residential battery systems can be actively used to provide flexibility during critical periods of grid operation. Overall, this framework empowers prosumers to take an active role in grid stabilization, contributing to a more resilient and adaptive energy system.

Figures (5)

• Figure 1: General setting. Residential prosumption, power, and grid power are in balance: $P_L=P_B+P_G.$
• Figure 2: The continuous prosumption (a) can be represented by the two dependent distributions (b) and (c), containing continuous and discrete parts. The power uncertainty (b) is defined over a closed interval. The grid power uncertainty (c) contains a discrete event at zero.
• Figure 3: Forecasted residential prosumption $P_L$ for a typical day. The production is expected to dominate the consumption most of the time.
• Figure 4: The overall shape, variance, and level of asymmetry of the forecasted prosumption $f_{\Delta P_L}$ vary highly throughout the day. All have an expected value of zero.
• Figure 5: Case 1 - Minimizing residential electricity costs by enhancing self-sufficiency. All states coincide, making the schedule deterministic. All uncertainties are shifted toward the grid.