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Intraday Battery Dispatch for Hybrid Renewable Energy Assets

Thiha Aung, Mike Ludkovski

TL;DR

This work tackles intraday dispatch for hybrid wind and BESS assets by formulating a finite-horizon stochastic control problem that tracks day-ahead targets while respecting battery constraints. It develops SHADOw-GP, a regression Monte Carlo method that uses Gaussian Process surrogates to approximate continuation values and optimal controls, enabling efficient, nonparametric treatment of nonlinear dynamics. The authors derive an explicit linear-quadratic solution for benchmarking and validate the approach with a realistic Texas-7k grid, showing meaningful deviation reductions and substantial ED savings from retrofitted hybrids; they also explore alternative objectives to account for battery degradation and curtailment. The results demonstrate practical benefits of hybridization, including longer-duration batteries and nontrivial grid-wide cost improvements, and point to extensions such as price-aware firming and multi-market co-optimization.

Abstract

We develop a mathematical model for intraday dispatch of co-located wind-battery energy assets. Focusing on the primary objective of firming grid-side actual production vis-a-vis the preset day-ahead hourly generation targets, we conduct a comprehensive study of the resulting stochastic control problem across different firming formulations and wind generation dynamics. Among others, we provide a closed-form solution in the special case of a quadratic objective and linear dynamics, as well as design a novel adaptation of a Gaussian Process-based Regression Monte Carlo algorithm for our setting. Extensions studied include an asymmetric loss function for peak shaving, capturing the cost of battery cycling, and the role of battery duration. In the applied portion of our work, we calibrate our model to a collection of 140+ wind-battery assets in Texas, benchmarking the economic benefits of firming based on outputs of a realistic unit commitment and economic dispatch solver.

Intraday Battery Dispatch for Hybrid Renewable Energy Assets

TL;DR

This work tackles intraday dispatch for hybrid wind and BESS assets by formulating a finite-horizon stochastic control problem that tracks day-ahead targets while respecting battery constraints. It develops SHADOw-GP, a regression Monte Carlo method that uses Gaussian Process surrogates to approximate continuation values and optimal controls, enabling efficient, nonparametric treatment of nonlinear dynamics. The authors derive an explicit linear-quadratic solution for benchmarking and validate the approach with a realistic Texas-7k grid, showing meaningful deviation reductions and substantial ED savings from retrofitted hybrids; they also explore alternative objectives to account for battery degradation and curtailment. The results demonstrate practical benefits of hybridization, including longer-duration batteries and nontrivial grid-wide cost improvements, and point to extensions such as price-aware firming and multi-market co-optimization.

Abstract

We develop a mathematical model for intraday dispatch of co-located wind-battery energy assets. Focusing on the primary objective of firming grid-side actual production vis-a-vis the preset day-ahead hourly generation targets, we conduct a comprehensive study of the resulting stochastic control problem across different firming formulations and wind generation dynamics. Among others, we provide a closed-form solution in the special case of a quadratic objective and linear dynamics, as well as design a novel adaptation of a Gaussian Process-based Regression Monte Carlo algorithm for our setting. Extensions studied include an asymmetric loss function for peak shaving, capturing the cost of battery cycling, and the role of battery duration. In the applied portion of our work, we calibrate our model to a collection of 140+ wind-battery assets in Texas, benchmarking the economic benefits of firming based on outputs of a realistic unit commitment and economic dispatch solver.

Paper Structure

This paper contains 30 sections, 2 theorems, 75 equations, 16 figures, 1 table, 1 algorithm.

Table of Contents

  1. Introduction
  2. Problem Formulation
  3. Wind Power Generation Dynamics
  4. State-of-Charge Dynamics
  5. Stochastic Control Problem
  6. Explicit Solution via Linear-Quadratic Approximation
  7. Numerical Algorithm
  8. SHADOw-GP Algorithm
  9. Simulation Design
  10. Gaussian Process Emulator for Q
  11. Gaussian Process emulator for B
  12. Toy Linear-Quadratic (LQ) Case Study with Stationary Dynamics
  13. Experiments on Texas-7k grid
  14. Calibration of Wind Dynamics
  15. SHADOw-GP Evaluation
  16. ...and 15 more sections

Key Result

Proposition 1

Assume that the solution $\bar{V}$ of unconstrained_HJB is $\mathcal{C}^{1,2}([0,T] \times \mathcal{D})$. When the mean-reversion level is constant, $m_t = m$$\forall t\in [0,T]$, the value function is explicitly given by: where the functions $P_1, \ldots, P_6$ solve the system of backward Ricatti ordinary differential equations with $\kappa = \frac{1}{1+c_1}$. Moreover, the optimal control in u

Figures (16)

  • Figure 1: A schematic description of optimizing the output $(O_k)$ of a hybrid wind asset.
  • Figure 2: Left panel: Learned control policy $(X,I) \mapsto \widehat{B}_{GP,k}(X,I)$ for the setting of Section \ref{['ssec:4.5']} at $k=0$ as a function of SoC $I$ and wind generation $X$. The dispatch target is $M_0=5$MW. Right panel: Difference between the LQ and GP-based controls without power and capacity constraints, $\bar{B}_{LQ,0}(X,I)- \widecheck{B}_{GP,0}(X,I)$ at $k=0$.
  • Figure 3: Top panel: A trajectory of $(X_k)$ following \ref{['eq:OU']} with constant mean $\mathbb{E}[X_k]=5$ along with firmed hybrid output $(O_k)$ following LQ and SHADOw-GP controls. Bottom panel: Corresponding SoC trajectories $({I}^{LQ,*}_k)$ and $({I}^{GP,*}_k)$.
  • Figure 4: Left panel: Boxplot of the calibrated volatility $\sigma^{\ell}_{r}$ across 149 wind assets in Texas-7k, shown as a function of bin $r=1,\ldots, 10$. Right panel: Wind generation ratio scenarios generated by \ref{['eq:non-gaussian OU']} for Foard City Wind Farm on 2018-04-05. The dotted lines are 5 sample hourly trajectories; the light blue band is the 80% scenario band. We also show the day-ahead forecast (orange) and the actual generation ratio on that day (blue).
  • Figure 5: Simulation design $\bar{\mathcal{D}}^v_k$ of size $N_{loc}=600$ for the model calibrated to Foard City Wind Farm. We use LHS on the indicated time-dependent adaptive rectangular training domain; the 40 black dots represent the fencing mechanism. The colors indicate the (kernel-based) density of resulting optimized trajectories $(X_k,I^*_k)$. Left panel: $k=2$. Right panel: $k=6$.
  • ...and 11 more figures

Theorems & Definitions (7)

  • Remark 1
  • Remark 2
  • Remark 3
  • Proposition 1
  • Proposition 2
  • Remark 4
  • Remark 5