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On Net Energy Metering X: Optimal Prosumer Decisions, Social Welfare, and Cross-Subsidies

Ahmed S. Alahmed, Lang Tong

TL;DR

It is shown that the optimal prosumer decision has three modes and a stochastic Ramsey pricing program that maximizes social welfare subject to the revenue break-even constraint for the regulated utility is formulated.

Abstract

We introduce NEM X, an inclusive retail tariff model that captures features of existing net energy metering (NEM) policies. It is shown that the optimal prosumer decision has three modes: (a) the net-consuming mode where the prosumer consumes more than its behind-the-meter distributed energy resource (DER) production when the DER production is below a predetermined lower threshold, (b) the net-producing mode where the prosumer consumes less than its DER production when the DER production is above a predetermined upper threshold, and (c) the net-zero energy mode where the prosumer's consumption matches to its DER generation when its DER production is between the lower and upper thresholds. Both thresholds are obtained in closed-form. Next, we analyze the regulator's rate-setting process that determines NEM X parameters such as retail/sell rates, fixed charges, and price differentials in time-of-use tariffs' on and off-peak periods. A stochastic Ramsey pricing program that maximizes social welfare subject to the revenue break-even constraint for the regulated utility is formulated. Performance of several NEM X policies is evaluated using real and synthetic data to illuminate impacts of NEM policy designs on social welfare, cross-subsidies of prosumers by consumers, and payback time of DER investments that affect long-run DER adoptions.

On Net Energy Metering X: Optimal Prosumer Decisions, Social Welfare, and Cross-Subsidies

TL;DR

It is shown that the optimal prosumer decision has three modes and a stochastic Ramsey pricing program that maximizes social welfare subject to the revenue break-even constraint for the regulated utility is formulated.

Abstract

We introduce NEM X, an inclusive retail tariff model that captures features of existing net energy metering (NEM) policies. It is shown that the optimal prosumer decision has three modes: (a) the net-consuming mode where the prosumer consumes more than its behind-the-meter distributed energy resource (DER) production when the DER production is below a predetermined lower threshold, (b) the net-producing mode where the prosumer consumes less than its DER production when the DER production is above a predetermined upper threshold, and (c) the net-zero energy mode where the prosumer's consumption matches to its DER generation when its DER production is between the lower and upper thresholds. Both thresholds are obtained in closed-form. Next, we analyze the regulator's rate-setting process that determines NEM X parameters such as retail/sell rates, fixed charges, and price differentials in time-of-use tariffs' on and off-peak periods. A stochastic Ramsey pricing program that maximizes social welfare subject to the revenue break-even constraint for the regulated utility is formulated. Performance of several NEM X policies is evaluated using real and synthetic data to illuminate impacts of NEM policy designs on social welfare, cross-subsidies of prosumers by consumers, and payback time of DER investments that affect long-run DER adoptions.

Paper Structure

This paper contains 33 sections, 5 theorems, 39 equations, 6 figures, 3 tables.

Table of Contents

  1. Introduction
  2. Related work
  3. Summary of results and contributions
  4. Notations and nomenclature
  5. NEM X Tariff Model
  6. A multi-timescale decision model
  7. NEM X tariff model
  8. NEM 1.0, NEM 2.0, and potential successors
  9. NEM 1.0
  10. NEM 2.0
  11. NEM 3.0 and beyond
  12. Optimal Prosumer Decision under NEM X
  13. Optimal prosumer decision
  14. Structural properties of prosumer decisions
  15. Two-threshold decision policy and piece-wise linear demand
  16. ...and 18 more sections

Key Result

Theorem 1

Given NEM parameter $\pi=(\pi^+,\pi^-,\pi^0)$ and the marginal utilities $(V_1, \cdots, V_M)$ of consumption devices, under A1-A3 and non-degeneracy condition of (eq:prosumerOPT), the optimal prosumer consumption policy is given by two thresholds that partition the range of DER production into three zones:

Figures (6)

  • Figure 1: NEM X tariff model in a billing period.
  • Figure 2: Structure of optimal prosumer schedule (Note that the figure is not sketched at scale). Top-left: the optimal consumption level for device $i$ as a function of the BTM generation $r$. Rest of the figures: The surpluses $S^+$ (red) and $S^-$ (green) of the prosumer as functions of demand $d$ under $\pi^+$ and $\pi^-$, respectively. The surplus function under NEM X is $S$ (black).
  • Figure 3: Marginal utilities of three devices.
  • Figure 4: Normalized social welfare and customers surpluses gain/loss.
  • Figure 5: Cost-shifts from prosumers.
  • ...and 1 more figures

Theorems & Definitions (5)

  • Theorem 1: Prosumer decision under NEM X
  • Proposition 1: Load priority ranking rule
  • Theorem 2: NEM X comparative static
  • Lemma 1: Schedule in the net production and consumption zones
  • Lemma 2: Schedule in the net-zero zone