Learning and Optimization for Price-based Demand Response of Electric Vehicle Charging

TL;DR

This paper addresses modeling price-based demand response (PBDR) in EV charging and optimizing station operation under price-driven uncertainty. It introduces a decision-focused end-to-end framework that learns a demand predictor $\hat{e}=f(c;\theta)$ and a differentiable QP optimizer that minimizes the downstream cost $\mathcal{L}(\theta)$ by backpropagating through the optimal solution $x^{*}(\theta)$. The gradient is computed via KKT differentiation, using a differentiable programming approach inspired by OptNet to obtain $\partial x^{*}/\partial \theta$. Experiments on synthetic PBDR patterns and real price data show that the end-to-end method reduces the actual operation cost by more than $20\%$ compared to a predict-then-optimize baseline, with larger gains when training data are limited.

Abstract

In the context of charging electric vehicles (EVs), the price-based demand response (PBDR) is becoming increasingly significant for charging load management. Such response usually encourages cost-sensitive customers to adjust their energy demand in response to changes in price for financial incentives. Thus, to model and optimize EV charging, it is important for charging station operator to model the PBDR patterns of EV customers by precisely predicting charging demands given price signals. Then the operator refers to these demands to optimize charging station power allocation policy. The standard pipeline involves offline fitting of a PBDR function based on historical EV charging records, followed by applying estimated EV demands in downstream charging station operation optimization. In this work, we propose a new decision-focused end-to-end framework for PBDR modeling that combines prediction errors and downstream optimization cost errors in the model learning stage. We evaluate the effectiveness of our method on a simulation of charging station operation with synthetic PBDR patterns of EV customers, and experimental results demonstrate that this framework can provide a more reliable prediction model for the ultimate optimization process, leading to more effective optimization solutions in terms of cost savings and charging station operation objectives with only a few training samples.

Figures (5)

• Figure 1: (1a). Proposed EV demand estimation and charging station operation model. EV customers have various patterns of demand response to price. (1b). Proposed end-to-end charging demand forecasts and charging scheduling framework. With optimization task-based loss $\mathcal{L}$, our model propagates loss derivative with respect to neural network model's parameter $\theta$ to help train the prediction model $f(\cdot)$.
• Figure 2: Examples of EV PBDR patterns. Individual EV's charging demand is a function of charging price.
• Figure 3: (\ref{['fig:subfig1']}) shows the synthetic price-based demand response (PBDR) patterns used in the simulation; (\ref{['fig:subfig2']}) shows the real-world hourly commercial electricity purchase price Purchase with colors indicating different price-time ranges. We set this peak-valley purchase price as $\bm{p}$ in our simulation.
• Figure 4: (a) operation costs during training, results averaged over 5 runs; (b) comparisons of sub-evaluation metrics.
• Figure 5: Comparison of two-step approach and our decision-focused end-to-end framework on station-level charging power (one example from test dataset).