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A Decentralized Market Mechanism for Energy Communities under Operating Envelopes

Ahmed S. Alahmed, Guido Cavraro, Andrey Bernstein, Lang Tong

Abstract

We propose an operating envelopes (OEs) aware energy community market mechanism that dynamically charges/rewards its members based on two-part pricing. The OEs are imposed exogenously by a regulated distribution system operator (DSO) on the energy community's revenue meter and is subject to a generalized net energy metering (NEM) tariff design. By formulating the interaction of the community operator and its members as a Stackelberg game, we show that the proposed two-part pricing achieves a Nash equilibrium and maximizes the community's social welfare in a decentralized fashion while ensuring that the community's operation abides by the OEs. The market mechanism conforms with the cost-causation principle and guarantees community members a surplus level no less than their maximum surplus when they autonomously face the DSO. The dynamic and uniform community price is a monotonically decreasing function of the community's aggregate renewable generation. We also analyze the impact of exogenous parameters such as NEM rates and OEs on the value of joining the community. Lastly, through numerical studies, we showcase the community's welfare, and pricing, and compare its members' surplus to customers under the DSO's regime.

A Decentralized Market Mechanism for Energy Communities under Operating Envelopes

Abstract

We propose an operating envelopes (OEs) aware energy community market mechanism that dynamically charges/rewards its members based on two-part pricing. The OEs are imposed exogenously by a regulated distribution system operator (DSO) on the energy community's revenue meter and is subject to a generalized net energy metering (NEM) tariff design. By formulating the interaction of the community operator and its members as a Stackelberg game, we show that the proposed two-part pricing achieves a Nash equilibrium and maximizes the community's social welfare in a decentralized fashion while ensuring that the community's operation abides by the OEs. The market mechanism conforms with the cost-causation principle and guarantees community members a surplus level no less than their maximum surplus when they autonomously face the DSO. The dynamic and uniform community price is a monotonically decreasing function of the community's aggregate renewable generation. We also analyze the impact of exogenous parameters such as NEM rates and OEs on the value of joining the community. Lastly, through numerical studies, we showcase the community's welfare, and pricing, and compare its members' surplus to customers under the DSO's regime.
Paper Structure (33 sections, 9 theorems, 81 equations, 7 figures, 3 tables)

This paper contains 33 sections, 9 theorems, 81 equations, 7 figures, 3 tables.

Table of Contents

  1. Introduction and Background
  2. OEs-aware Energy Sharing: Models, Pricing Axioms, and Stackelberg Game
  3. Energy Community Structure
  4. Community Member DER, Payment, and Surplus
  5. Community DER
  6. Community Members Surplus
  7. Benchmark Prosumer: DER, Payment, and Surplus
  8. Axiomatic Community Pricing
  9. Bi-level Optimization
  10. Lower Level -- Members’ Optimal Consumption Policy
  11. Upper Level -- Operator's Optimal Pricing Policy
  12. Stackelberg Equilibrium
  13. Two-Part Pricing and Stackelberg Equilibrium
  14. OEs-Aware Pricing Policy
  15. OE-Aware Pricing Policy: Structure and Intuitions
  16. ...and 18 more sections

Key Result

Proposition 1

The OEs-aware prices are ordered as and the prices $\chi^+(r_{\cal N}), \chi^z(r_{\cal N})$ and $\chi^-(r_{\cal N})$ are monotonically decreasing with $r_{\cal N}$.

Figures (7)

  • Figure 1: $N$-members energy community with aggregate-level OEs (top), and member-level OEs (bottom). Member consumption, renewables, and net consumption are denoted by $d_i \in \mathbb{R}_+, r_i\in \mathbb{R}_+, z_i \in \mathbb{R}$, respectively, whereas $z_{{\cal N}}\in \mathbb{R}$ denotes the aggregate net consumption. $\overline{z}_i\in \mathbb{R}_+, \underline{z}_i\in \mathbb{R}_-$ ($\overline{z}_{{\cal N}}\in \mathbb{R}_+, \underline{z}_{{\cal N}}\in \mathbb{R}_-$) are the member- (aggregate-) level import and export envelopes, respectively. The arrow direction indicates positive quantities.
  • Figure 2: Community pricing policy with OEs (blue) and without OEs AlahmedTong:24TEMPR (yellow), compared to the DSO NEM X (red) under optimal community members' response shown in Lemma \ref{['lem:OptSchedule']}, all with respect to aggregate renewables $r_{{\cal N}}$.
  • Figure 3: Optimal aggregate consumption (brown), net consumption (red), and the OEs-aware pricing policy (blue) with respect to aggregate renewables $r_{{\cal N}}$.
  • Figure 4: VoC of every member (Corollary \ref{['corol:PositiveVoC']}). $\Delta_1^i-\Delta_4^i$ are the thresholds of prosumer's $i$ benchmark optimal consumption policy.
  • Figure 5: Percentage surplus difference and payment for the $N=20$ members. Members with black asterisks are those with no BTM generation.
  • ...and 2 more figures

Theorems & Definitions (10)

  • Definition 1: Cost-causation principle
  • Proposition 1
  • Lemma 1: Member optimal consumption
  • Lemma 2: Cost-causation conformity
  • Theorem 1: Equilibrium and welfare optimality
  • Corollary 1: Member and community net-consumption complementarity
  • Proposition 2: VoC comparative statics analysis
  • Theorem 2: Surplus optimality
  • Lemma 3: Benchmark prosumer optimal response and maximum surplus
  • Lemma 4: Community maximum welfare