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Co-optimizing Consumption and EV Charging under Net Energy Metering

Minjae Jeon, Lang Tong, Qing Zhao

TL;DR

This work tackles co-optimization of deferrable EV charging and flexible household demand in a household with behind-the-meter DER under a net energy metering tariff, formulating a stochastic dynamic program over a finite horizon. It uncovers a procrastination threshold policy: in each interval, optimal charging is delayed as long as possible and only the minimum necessary is charged, with offline thresholds that decouple the continuous-action problem into closed-form decisions. The net consumption is shown to be a monotone, three-zone function of available DER, featuring a net-zero region to reduce grid exports; thresholds can be computed offline given the DER distribution. Empirical studies on real renewable, consumption, and EV data demonstrate substantial surplus gains (e.g., up to about 30–65% for 8–12 hour horizons) compared with renewable-independent baselines, highlighting the practical impact of structured co-optimization under NEM tariffs.

Abstract

We consider the co-optimization of flexible household consumption, electric vehicle charging, and behind-the-meter distributed energy resources under the net energy metering tariff. Using a stochastic dynamic programming formulation, we show that the solution to the dynamic programming co-optimization is a procrastination threshold policy that delays and minimizes electricity purchasing for EV charging in each time interval. The policy thresholds can be computed off-line, simplifying the continuous action space dynamic optimization to decoupled closed-form charging and consumption decisions. Empirical studies using renewable, consumption, and EV data demonstrate the benefits of co-optimization.

Co-optimizing Consumption and EV Charging under Net Energy Metering

TL;DR

This work tackles co-optimization of deferrable EV charging and flexible household demand in a household with behind-the-meter DER under a net energy metering tariff, formulating a stochastic dynamic program over a finite horizon. It uncovers a procrastination threshold policy: in each interval, optimal charging is delayed as long as possible and only the minimum necessary is charged, with offline thresholds that decouple the continuous-action problem into closed-form decisions. The net consumption is shown to be a monotone, three-zone function of available DER, featuring a net-zero region to reduce grid exports; thresholds can be computed offline given the DER distribution. Empirical studies on real renewable, consumption, and EV data demonstrate substantial surplus gains (e.g., up to about 30–65% for 8–12 hour horizons) compared with renewable-independent baselines, highlighting the practical impact of structured co-optimization under NEM tariffs.

Abstract

We consider the co-optimization of flexible household consumption, electric vehicle charging, and behind-the-meter distributed energy resources under the net energy metering tariff. Using a stochastic dynamic programming formulation, we show that the solution to the dynamic programming co-optimization is a procrastination threshold policy that delays and minimizes electricity purchasing for EV charging in each time interval. The policy thresholds can be computed off-line, simplifying the continuous action space dynamic optimization to decoupled closed-form charging and consumption decisions. Empirical studies using renewable, consumption, and EV data demonstrate the benefits of co-optimization.
Paper Structure (27 sections, 7 theorems, 34 equations, 5 figures)

This paper contains 27 sections, 7 theorems, 34 equations, 5 figures.

Table of Contents

  1. Introduction
  2. Related works
  3. Summary of results and contributions
  4. Problem Formulation
  5. EV charging and consumption model
  6. BTM DER $(r_t)$
  7. Remaining charging demand $(y_t)$ and constraints
  8. Household Consumption $(\mathbf d_t)$
  9. Net consumption ($z_t$)
  10. NEM TOU tariff model
  11. NEM payment $(P^{\pi_t}(z_t))$
  12. NEM TOU tariff model
  13. EV charging consumption co-optimization
  14. Model Assumption
  15. Optimal EV owner decision
  16. ...and 12 more sections

Key Result

Theorem 1

NEM TOU tariff parameters satisfying A1, and $r_t$ is a sequence of independent random variables, optimal net consumption $z_t^*$ is a piecewise linear function of $r_t$ and partitioned into 3 zones, for $t\in \mathcal{T}$ EV charging and consumption decisions are : If $r_t \in [0,\Delta_t^+(y_t))\,$ for all $i = 1, \ldots, K$ If $r_t \in (\Delta_t^-(y_t), R]\,$ for all $i = 1, \ldots, K$ If $r_t

Figures (5)

  • Figure 1: NEM scheme for the household with EV. Direction of arrow indicates positive direction of energy flow.
  • Figure 2: TOU scheme and decision horizon
  • Figure 3: Net consumption regions in the state space
  • Figure 4: Impact of $T$ on the performance
  • Figure 5: Impact of $\pi_t^+ - \pi_t^-$ on the performance of the optimal policy

Theorems & Definitions (13)

  • Theorem 1: Optimal net consumption
  • Proposition 1: Recursive relation of procrastination threshold
  • Theorem 2: Optimal procrastination threshold
  • Theorem 3: Prosumer consumption decision under NEM X
  • Proposition 2
  • proof
  • Proposition 3
  • proof
  • proof
  • Lemma 1
  • ...and 3 more