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A Compensation Mechanism for EV Flexibility Services using Discrete Utility Functions

Juan S. Giraldo, Nataly Banol Arias, Edgar Mauricio Salazar Duque, Gerwin Hoogsteen, Johann L. Hurink

Abstract

Compensation mechanisms are used to counterbalance the discomfort suffered by users due to quality service issues. Such mechanisms are currently used for different purposes in the electrical power and energy sector, e.g., power quality and reliability. This paper proposes a compensation mechanism using EV flexibility management of a set of charging sessions managed by a charging point operator (CPO). Users' preferences and bilateral agreements with the CPO are modelled via discrete utility functions for the energy not served. A mathematical proof of the proposed compensation mechanism is given and applied to a test scenario using historical data from an office building with a parking lot in the Netherlands. Synthetic data for 400 charging sessions was generated using multivariate elliptical copulas to capture the complex dependency structures in EV charging data. Numerical results validate the usefulness of the proposed compensation mechanism as an attractive measure both for the CPO and the users in case of energy not served.

A Compensation Mechanism for EV Flexibility Services using Discrete Utility Functions

Abstract

Compensation mechanisms are used to counterbalance the discomfort suffered by users due to quality service issues. Such mechanisms are currently used for different purposes in the electrical power and energy sector, e.g., power quality and reliability. This paper proposes a compensation mechanism using EV flexibility management of a set of charging sessions managed by a charging point operator (CPO). Users' preferences and bilateral agreements with the CPO are modelled via discrete utility functions for the energy not served. A mathematical proof of the proposed compensation mechanism is given and applied to a test scenario using historical data from an office building with a parking lot in the Netherlands. Synthetic data for 400 charging sessions was generated using multivariate elliptical copulas to capture the complex dependency structures in EV charging data. Numerical results validate the usefulness of the proposed compensation mechanism as an attractive measure both for the CPO and the users in case of energy not served.
Paper Structure (12 sections, 1 theorem, 15 equations, 7 figures, 1 table)

This paper contains 12 sections, 1 theorem, 15 equations, 7 figures, 1 table.

Table of Contents

  1. Introduction
  2. Problem Definition and Proposed Compensation Mechanism
  3. Problem definition
  4. Proposed compensation mechanism
  5. Mathematical Model for EV Flexibility Management and Discrete Utility Functions
  6. Charging Sessions
  7. Users' Utility Functions
  8. Charging Point Operator (CPO)
  9. Study Case, Tests, and Results
  10. T1 - The CPO is able to serve at least the acceptable energy to all sessions
  11. T2 - The CPO is unable to serve at least the acceptable energy to all sessions
  12. Conclusions

Key Result

Proposition 1

If $\boldsymbol{u}_{n}$ is capped such that $u\left(\phi_{n}\right)\leq\mathrm{C}_{n}\mathrm{e}_{n}$ for each charging session $n\in\Omega_{N}$, the energy cost in energy_cost_user is revenue adequate for the CPO if at least the acceptable energy is served to all sessions.

Figures (7)

  • Figure 1: Representation of an arbitrary discrete utility function at a charging session $n$ with $\kappa=3$.
  • Figure 2: Distribution of charging session profiles: (a) and (b) measured historical data. (c) and (d) synthetically generated data.
  • Figure 3: CPO's power consumption and cumulative energy. (a) Energy limit $\overline{\mathcal{E}}=8.2\,$MWh. (b)~Energy limit~$\overline{\mathcal{E}}=6.2\,$MWh.
  • Figure 4: T1 - PDF and CDF for the charging sessions. (a) Energy served. (b) Energy not served. (c) User compensation. (d) Final energy cost.
  • Figure 5: T1 - Selected charging sessions. (a) Energy served, required, and acceptable. (b) Users' charging cost, compensation, and total.
  • ...and 2 more figures

Theorems & Definitions (2)

  • Proposition 1
  • proof