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On the Optimality of Procrastination Policy for EV charging under Net Energy Metering

Minjae Jeon, Lang Tong, Qing Zhao

TL;DR

The paper addresses co-optimizing EV charging, flexible loads, behind-the-meter solar, and storage under time-of-use net energy metering tariffs. It shows that a procrastination threshold policy—charging EVs at the last possible intervals—is optimal without storage, and that with storage the net consumption becomes a two-threshold, piecewise-linear function of renewable generation, while thresholds remain computable offline. A myopic storage policy is proposed and shown to be optimal when storage SoC constraints are non-binding, with numerical results indicating a small gap (about 0.5%–7.5%) to an oracle and superior performance to MPC and non-co-optimized policies. The work demonstrates significant potential for online, threshold-based strategies to efficiently coordinate EV charging, flexible loads, and DERs under NEM tariffs, with implications for grid-supportive residential energy management.

Abstract

We consider the problem of behind-the-meter EV charging by a prosumer, co-optimized with rooftop solar, electric battery, and flexible consumptions such as water heaters and HVAC. Under the time-of-use net energy metering tariff with the stochastic solar production and random EV charging demand, a finite-horizon surplus-maximization problem is formulated. We show that a procrastination threshold policy that delays EV charging to the last possible moment is optimal when EV charging is co-optimized with flexible demand, and the policy thresholds can be computed easily offline. When battery storage is part of the co-optimization, it is shown that the net consumption of the prosumer is a two-threshold piecewise linear function of the behind-the-meter renewable generation under the optimal policy, and the procrastination threshold policy remains optimal, although the thresholds cannot be computed easily. We propose a simple myopic solution and demonstrate in simulations that the performance gap between the myopic policy and an oracle upper bound appears to be 0.5-7.5%.

On the Optimality of Procrastination Policy for EV charging under Net Energy Metering

TL;DR

The paper addresses co-optimizing EV charging, flexible loads, behind-the-meter solar, and storage under time-of-use net energy metering tariffs. It shows that a procrastination threshold policy—charging EVs at the last possible intervals—is optimal without storage, and that with storage the net consumption becomes a two-threshold, piecewise-linear function of renewable generation, while thresholds remain computable offline. A myopic storage policy is proposed and shown to be optimal when storage SoC constraints are non-binding, with numerical results indicating a small gap (about 0.5%–7.5%) to an oracle and superior performance to MPC and non-co-optimized policies. The work demonstrates significant potential for online, threshold-based strategies to efficiently coordinate EV charging, flexible loads, and DERs under NEM tariffs, with implications for grid-supportive residential energy management.

Abstract

We consider the problem of behind-the-meter EV charging by a prosumer, co-optimized with rooftop solar, electric battery, and flexible consumptions such as water heaters and HVAC. Under the time-of-use net energy metering tariff with the stochastic solar production and random EV charging demand, a finite-horizon surplus-maximization problem is formulated. We show that a procrastination threshold policy that delays EV charging to the last possible moment is optimal when EV charging is co-optimized with flexible demand, and the policy thresholds can be computed easily offline. When battery storage is part of the co-optimization, it is shown that the net consumption of the prosumer is a two-threshold piecewise linear function of the behind-the-meter renewable generation under the optimal policy, and the procrastination threshold policy remains optimal, although the thresholds cannot be computed easily. We propose a simple myopic solution and demonstrate in simulations that the performance gap between the myopic policy and an oracle upper bound appears to be 0.5-7.5%.
Paper Structure (28 sections, 8 theorems, 33 equations, 5 figures, 1 algorithm)

This paper contains 28 sections, 8 theorems, 33 equations, 5 figures, 1 algorithm.

Table of Contents

  1. Introduction
  2. Related works
  3. Summary of results and contributions
  4. Problem Formulation
  5. EV charging, consumption, and storage model
  6. BTM DER $(r_t)$
  7. Remaining charging demand $(y_t)$
  8. Household consumption $(\mathbf d_t)$
  9. Battery storage operation $(e_t)$
  10. Net consumption ($z_t$)
  11. NEM ToU tariff model
  12. NEM payment $(P^{\pi_t}(\cdot))$
  13. NEM ToU tariff model
  14. Co-optimization of EV charging, consumption, and storage
  15. Procrastination threshold policy (co-optimization without battery)
  16. ...and 13 more sections

Key Result

Theorem 1

The optimal EV charging $v_t^*$ and consumption $d_{ti}^*$ decisions are monotone increasing function of $r_t$, and for all $i$ and $t$ where $\nu \in [\pi_t^-, \pi_t^+]$ satisfies, $r_t = v_t^* + \sum_{i=1}^I d_{ti}^*$. $\tau_t$ and $\delta_t$ are characterized by :

Figures (5)

  • Figure 1: NEM scheme of the household with the BTM storage and EV. The direction of arrow indicates the direction of the power flow.
  • Figure 2: ToU scheme and decision horizon
  • Figure 3: Procrastination threshold policy for $\delta_t < y_t < \tau_t$.
  • Figure 4: Myopic optimal policy for $\delta_t = 0 < y_t < \sigma_t^- < \sigma_t^+$.
  • Figure 5: Relative performance gap of the MO(blue), CCO(red), NCO(yellow), MPC(purple), PR(green) to the oracle policy for different $\pi_t^+ - \pi_t^-$ is plotted. The estimated mean of renewable is scaled by 0.5, 1, 1.5 for the figures from left to right.

Theorems & Definitions (13)

  • Theorem 1: Procrastination threshold policy
  • Proposition 1: Procrastination charging behavior
  • Theorem 2: Myopic policy
  • Theorem 3: Optimality of myopic policy
  • proof
  • Lemma 1
  • proof
  • Proposition 2: Storage salvage value under non-binding SoC assumption
  • Proposition 3: Storage-total load complementarity condition
  • Proposition 4: Optimal storage operation
  • ...and 3 more