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Data-driven model predictive control of battery storage units

Johannes B. Lipka, Christian A. Hans

Abstract

In many state-of-the-art control approaches for power systems with storage units, an explicit model of the storage dynamics is required. With growing numbers of storage units, identifying these dynamics can be cumbersome. This paper employs recent data-driven control approaches that do not require an explicit identification step. Instead, they use measured input/output data in control formulations. In detail, we propose an economic data-driven model predictive control (MPC) scheme to operate a small power system with input-nonlinear battery dynamics. First, a linear data-driven MPC approach that uses a slack variable to account for plant-model-mismatch is proposed. In a second step, an input-nonlinear data-driven MPC scheme is deduced. Comparisons with a reference indicate that the linear data-driven MPC approximates the nonlinear plant in an acceptable manner. Even better results, however, can be obtained with the input-nonlinear data-driven MPC scheme which provides increased prediction accuracy.

Data-driven model predictive control of battery storage units

Abstract

In many state-of-the-art control approaches for power systems with storage units, an explicit model of the storage dynamics is required. With growing numbers of storage units, identifying these dynamics can be cumbersome. This paper employs recent data-driven control approaches that do not require an explicit identification step. Instead, they use measured input/output data in control formulations. In detail, we propose an economic data-driven model predictive control (MPC) scheme to operate a small power system with input-nonlinear battery dynamics. First, a linear data-driven MPC approach that uses a slack variable to account for plant-model-mismatch is proposed. In a second step, an input-nonlinear data-driven MPC scheme is deduced. Comparisons with a reference indicate that the linear data-driven MPC approximates the nonlinear plant in an acceptable manner. Even better results, however, can be obtained with the input-nonlinear data-driven MPC scheme which provides increased prediction accuracy.
Paper Structure (22 sections, 2 theorems, 36 equations, 4 figures, 1 table)

This paper contains 22 sections, 2 theorems, 36 equations, 4 figures, 1 table.

Table of Contents

  1. Introduction
  2. Mathematical Preliminaries
  3. Notation
  4. Hankel Matrix
  5. Data-Driven Representation of lti Systems
  6. Data-Driven Representation of Hammerstein Systems
  7. Model of an islanded grid
  8. Renewable Generator
  9. Conventional Unit
  10. Energy Storage Unit
  11. Power Equilibrium
  12. Reference MPC
  13. Cost Function
  14. Problem Statement
  15. Case Study
  16. ...and 7 more sections

Key Result

Theorem 1

An input sequence$\{u(k)\}^{L-1}_{k=0}$and its corresponding output sequence$\{y(k)\}^{L-1}_{k=0}$represent a trajectory of $G$ if and only if there exists a vector$\alpha\in \mathbb{R}^{N-L+1}$such thatwith$\mathbf{U}=[u(k)]^{L-1}_{k=0}$and$\mathbf{Y}=[y(k)]^{L-1}_{k=0}$it holds that

Figures (4)

  • Figure 1: Islanded grid composed of storage unit, conventional generator, renewable generator and a load. Layout from christian_hans.
  • Figure 2: System trajectory with reference mpc. (pu: per unit, d: days)
  • Figure 3: Box plots of prediction error for reference mpc (Problem \ref{['prob:reference']}) and linear data-driven mpc (Problem \ref{['prob:linear']}).
  • Figure 4: Box plots of prediction error for reference mpc and Hammerstein-type data-driven mpc.

Theorems & Definitions (5)

  • Definition 1: Persistence of Excitation
  • Remark 1
  • Theorem 1
  • Theorem 2
  • Remark 2