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Towards Input-Convex Neural Network Modeling for Battery Optimization in Power Systems

Arash Omidi, Tanmay Mishra, Mads R. Almassalkhi

TL;DR

The work tackles non-convexities in battery energy storage optimization caused by nonlinear, part-load inverter efficiencies within energy reservoir models. It proposes input-convex neural networks (ICNNs) to obtain convex surrogates, offering relaxed ICNN and Big-M ICNN formulations evaluated on PV smoothing and revenue-maximization tasks. Results show Relaxed ICNN often delivers the best practical balance between feasibility and accuracy, while Big-M ICNN provides higher revenue at the cost of computation; the full NLP remains suboptimal due to non-convexity. The findings point to ICNN-based convexification as a promising approach for real-time grid optimization and motivate further theoretical analysis and richer battery models.

Abstract

Battery energy storage systems (BESS) play an increasingly vital role in integrating renewable generation into power grids due to their ability to dynamically balance supply. Grid-tied batteries typically employ power converters, where part-load efficiencies vary non-linearly. While this non-linearity can be modeled with high accuracy, it poses challenges for optimization, particularly in ensuring computational tractability. In this paper, we consider a non-linear BESS formulation based on the Energy Reservoir Model (ERM). A data-driven approach is introduced with the input-convex neural network (ICNN) to approximate the nonlinear efficiency with a convex function. The epigraph of the convex function is used to engender a convex program for battery ERM optimization. This relaxed ICNN method is applied to two battery optimization use-cases: PV smoothing and revenue maximization, and it is compared with three other ERM formulations (nonlinear, linear, and mixed-integer). Specifically, ICNN-based methods appear to be promising for future battery optimization with desirable feasibility and optimality outcomes across both use-cases.

Towards Input-Convex Neural Network Modeling for Battery Optimization in Power Systems

TL;DR

The work tackles non-convexities in battery energy storage optimization caused by nonlinear, part-load inverter efficiencies within energy reservoir models. It proposes input-convex neural networks (ICNNs) to obtain convex surrogates, offering relaxed ICNN and Big-M ICNN formulations evaluated on PV smoothing and revenue-maximization tasks. Results show Relaxed ICNN often delivers the best practical balance between feasibility and accuracy, while Big-M ICNN provides higher revenue at the cost of computation; the full NLP remains suboptimal due to non-convexity. The findings point to ICNN-based convexification as a promising approach for real-time grid optimization and motivate further theoretical analysis and richer battery models.

Abstract

Battery energy storage systems (BESS) play an increasingly vital role in integrating renewable generation into power grids due to their ability to dynamically balance supply. Grid-tied batteries typically employ power converters, where part-load efficiencies vary non-linearly. While this non-linearity can be modeled with high accuracy, it poses challenges for optimization, particularly in ensuring computational tractability. In this paper, we consider a non-linear BESS formulation based on the Energy Reservoir Model (ERM). A data-driven approach is introduced with the input-convex neural network (ICNN) to approximate the nonlinear efficiency with a convex function. The epigraph of the convex function is used to engender a convex program for battery ERM optimization. This relaxed ICNN method is applied to two battery optimization use-cases: PV smoothing and revenue maximization, and it is compared with three other ERM formulations (nonlinear, linear, and mixed-integer). Specifically, ICNN-based methods appear to be promising for future battery optimization with desirable feasibility and optimality outcomes across both use-cases.

Paper Structure

This paper contains 17 sections, 16 equations, 8 figures, 3 tables.

Table of Contents

  1. INTRODUCTION
  2. Battery Energy Storage Modeling
  3. Energy Reservoir Model (ERM)
  4. Input Convex Neural Network
  5. Methodology
  6. Full Nonlinear Formulation
  7. Constant Efficiency Linear Formulation
  8. Relaxed ICNN formulation
  9. Big-M ICNN formulation
  10. Power Systems Battery Use-Cases
  11. PV Smoothing
  12. Revenue Maximization
  13. Simulation and Results
  14. PV Smoothing
  15. Revenue Maximization
  16. ...and 2 more sections

Figures (8)

  • Figure 1: The block diagram of BESS
  • Figure 2: Part-load efficiency curve for commercial inverters Faranda
  • Figure 3: Block diagram of ICNN architecture for $f_\text{ICNN}$
  • Figure 4: ICNN-based approximation of charging $f_{\text{ICNN}}(.)$
  • Figure 5: Comparison of the simulation results for the PV smoothing problem using nonlinear, linear, and Relaxed ICNN models (with $\lambda = 1.6\times10^{-3}$) (a) Output power (Smoothed PV power: Battery+PV) (b) Optimal battery dispatch (c) Battery SoC
  • ...and 3 more figures