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Optimal Solar Investment and Operation under Asymmetric Net Metering

Nathan Engelman Lado, Ahmed Alahmed, Audun Botterud, Saurabh Amin

TL;DR

The paper studies the joint investment and operation of a behind-the-meter prosumer under asymmetric and time-varying NEM tariffs. By endogenizing PV capacity, it derives that the optimal solar size $g^*$ satisfies $g^*=\max\{0,\min\{\bar{g},g^\dagger\}\}$ with $c^g=F(g^\dagger)$, where $F(\cdot)$ is a $\psi$-weighted sum of import/export prices and marginal utilities across regimes. It identifies a PV effect: tariff changes in one period induce cross-period shifts in net demand and consumption via adjustments in $g^*$, with the effect attenuated when a net-zero self-consumption regime dominates. Net-zero periods damp investment sensitivity, and compared to fixed-PV benchmarks, endogenous PV yields smaller payment changes in response to import-price increases and larger changes for export-price reductions. A Massachusetts case study illustrates how tariff design, peak timing, and PV endogeneity jointly shape PV sizing, net demand, and payments, providing regulators and utilities with a framework to evaluate NEM reforms.

Abstract

We examine the joint investment and operational decisions of a prosumer, a customer who both consumes and generates electricity, under net energy metering (NEM) tariffs. Traditional NEM schemes provide temporally flat compensation at the retail price for net energy exports over a billing period. However, ongoing reforms in several U.S. states are introducing time-varying prices and asymmetric import/export compensation to better align incentives with grid costs. While prior studies treat PV capacity as exogenous and focus primarily on consumption behavior, this work endogenizes PV investment and derives the marginal value of solar capacity for a flexible prosumer under asymmetric NEM tariffs. We characterize optimal investment and show how optimal investment changes with prices and PV costs. Through this analysis, we identify a PV effect: changes in NEM pricing in one period can influence net demand and consumption in generating periods with unchanged prices through adjustments in optimal PV investment. The PV effect weakens the ability of higher import prices to increase prosumer payments, with direct implications for NEM reform. We validate our theoretical results in a case study using simulated household and tariff data derived from historical conditions in Massachusetts.

Optimal Solar Investment and Operation under Asymmetric Net Metering

TL;DR

The paper studies the joint investment and operation of a behind-the-meter prosumer under asymmetric and time-varying NEM tariffs. By endogenizing PV capacity, it derives that the optimal solar size satisfies with , where is a -weighted sum of import/export prices and marginal utilities across regimes. It identifies a PV effect: tariff changes in one period induce cross-period shifts in net demand and consumption via adjustments in , with the effect attenuated when a net-zero self-consumption regime dominates. Net-zero periods damp investment sensitivity, and compared to fixed-PV benchmarks, endogenous PV yields smaller payment changes in response to import-price increases and larger changes for export-price reductions. A Massachusetts case study illustrates how tariff design, peak timing, and PV endogeneity jointly shape PV sizing, net demand, and payments, providing regulators and utilities with a framework to evaluate NEM reforms.

Abstract

We examine the joint investment and operational decisions of a prosumer, a customer who both consumes and generates electricity, under net energy metering (NEM) tariffs. Traditional NEM schemes provide temporally flat compensation at the retail price for net energy exports over a billing period. However, ongoing reforms in several U.S. states are introducing time-varying prices and asymmetric import/export compensation to better align incentives with grid costs. While prior studies treat PV capacity as exogenous and focus primarily on consumption behavior, this work endogenizes PV investment and derives the marginal value of solar capacity for a flexible prosumer under asymmetric NEM tariffs. We characterize optimal investment and show how optimal investment changes with prices and PV costs. Through this analysis, we identify a PV effect: changes in NEM pricing in one period can influence net demand and consumption in generating periods with unchanged prices through adjustments in optimal PV investment. The PV effect weakens the ability of higher import prices to increase prosumer payments, with direct implications for NEM reform. We validate our theoretical results in a case study using simulated household and tariff data derived from historical conditions in Massachusetts.
Paper Structure (18 sections, 6 theorems, 33 equations, 5 figures, 3 tables)

This paper contains 18 sections, 6 theorems, 33 equations, 5 figures, 3 tables.

Table of Contents

  1. Introduction
  2. Prosumer Decisions Model and Payment
  3. Optimal Sizing and Operational Decisions
  4. Case Study - A Household in Massachusetts
  5. Conclusion
  6. AI Usage Disclosure
  7. Statement and Proof of Lemma \ref{['lem:bireform']}
  8. Proof of Lemma \ref{['lem:opt_decision']}:
  9. Proof of Theorem \ref{['thm:optimality_cond']}:
  10. Proof of Corollary \ref{['corr:optdaggernvert']}
  11. Proof of Proposition \ref{['prop:monotonicity']}
  12. Proposition \ref{['prop:payment']} and its Proof
  13. Justification of Table \ref{['tab:comparative-statics']}.
  14. Own-period quantities (first row)
  15. Other period quantities ($t\neq\tau$)
  16. ...and 3 more sections

Key Result

Lemma 1

Figures (5)

  • Figure 1: Optimal consumption (blue) and optimal net demand (green) under NEM..
  • Figure 2: The marginal value of an additional unit of solar for a prosumer.
  • Figure 3: Left: Optimal solar as a function of the import price $\pi^+$. Right: Distribution of net demand for a single period as a function of the import price.
  • Figure 4: Marginal value of an additional unit of solar capacity.
  • Figure 5: Contour plots comparing the impact of price changes on the prosumer's optimal solar capacity, total net demand with optimal PV capacity, total net demand with fixed PV capacity, total payment with optimal PV capacity, and total payment with fixed PV capacity.

Theorems & Definitions (6)

  • Lemma 1: Optimal Operational Decisions
  • Theorem 1: Optimality Condition for Solar Investment
  • Corollary 1
  • Proposition 1
  • Lemma 2
  • Proposition 2