Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

Reliable Frequency Regulation through Vehicle-to-Grid: Encoding Legislation with Robust Constraints

Dirk Lauinger, François Vuille, Daniel Kuhn

Abstract

Problem definition: Vehicle-to-grid increases the low utilization rate of privately owned electric vehicles by making their batteries available to electricity grids. We formulate a robust optimization problem that maximizes a vehicle owner's expected profit from selling primary frequency regulation to the grid and guarantees that market commitments are met at all times for all frequency deviation trajectories in a functional uncertainty set that encodes applicable legislation. Faithfully modeling the energy conversion losses during battery charging and discharging renders this optimization problem non-convex. Methodology/results: By exploiting a total unimodularity property of the uncertainty set and an exact linear decision rule reformulation, we prove that this non-convex robust optimization problem with functional uncertainties is equivalent to a tractable linear program. Through extensive numerical experiments using real-world data, we quantify the economic value of vehicle-to-grid and elucidate the financial incentives of vehicle owners, aggregators, equipment manufacturers, and regulators. Managerial implications: We find that the prevailing penalties for non-delivery of promised regulation power are too low to incentivize vehicle owners to honor the delivery guarantees given to grid operators.

Reliable Frequency Regulation through Vehicle-to-Grid: Encoding Legislation with Robust Constraints

Abstract

Problem definition: Vehicle-to-grid increases the low utilization rate of privately owned electric vehicles by making their batteries available to electricity grids. We formulate a robust optimization problem that maximizes a vehicle owner's expected profit from selling primary frequency regulation to the grid and guarantees that market commitments are met at all times for all frequency deviation trajectories in a functional uncertainty set that encodes applicable legislation. Faithfully modeling the energy conversion losses during battery charging and discharging renders this optimization problem non-convex. Methodology/results: By exploiting a total unimodularity property of the uncertainty set and an exact linear decision rule reformulation, we prove that this non-convex robust optimization problem with functional uncertainties is equivalent to a tractable linear program. Through extensive numerical experiments using real-world data, we quantify the economic value of vehicle-to-grid and elucidate the financial incentives of vehicle owners, aggregators, equipment manufacturers, and regulators. Managerial implications: We find that the prevailing penalties for non-delivery of promised regulation power are too low to incentivize vehicle owners to honor the delivery guarantees given to grid operators.

Paper Structure

This paper contains 13 sections, 14 theorems, 84 equations, 7 figures, 1 table.

Table of Contents

  1. Introduction
  2. Problem Description
  3. Time Discretization
  4. Linear Programming Reformulation
  5. Numerical Experiments
  6. Model Parametrization
  7. Backtesting Procedure and Baseline Strategy
  8. Experiments: Set-up, Results and Discussion
  9. Conclusions
  10. Acknowledgments
  11. Problem Data and Model Parameters
  12. Vehicle Aggregator
  13. Proofs

Key Result

Theorem 1

The problems pb:Rc and pb:R are equivalent.

Figures (7)

  • Figure 1: Empirical cumulative distribution function (cdf) of the daily standard deviation of $\delta$ and the maximum standard deviation of any scenario in $\hat{\mathcal{D}}$ or in $\mathcal{D}$.
  • Figure 2: Frequency deviation signals (left) and their state-of-charge trajectories (right).
  • Figure 3: Value of vehicle-to-grid in 2019 under different simulation scenarios.
  • Figure 4: Value of vehicle-to-grid in 2019 versus penalties for non-delivery.
  • Figure 5: Value of vehicle-to-grid in 2019 as a function of C-rate and activation ratio.
  • ...and 2 more figures

Theorems & Definitions (35)

  • Remark 1
  • Remark 2
  • Remark 3: Uncertain driving patterns
  • Remark 4: Traditional charging stations
  • Example 1: Risks of ignoring intra-period fluctuations
  • Theorem 1: Lossless time discretization
  • Theorem 2: Lossless linearization
  • Theorem 3: Linear programming reformulation
  • Remark 5: Robustification reduces complexity
  • Remark 6: Futility of solving a multistage model
  • ...and 25 more