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Operating-Envelopes-Aware Decentralized Welfare Maximization for Energy Communities

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

Abstract

We propose an operating-envelope-aware, prosumer-centric, and efficient energy community that aggregates individual and shared community distributed energy resources and transacts with a regulated distribution system operator (DSO) under a generalized net energy metering tariff design. To ensure safe network operation, the DSO imposes dynamic export and import limits, known as dynamic operating envelopes, on end-users' revenue meters. Given the operating envelopes, we propose an incentive-aligned community pricing mechanism under which the decentralized optimization of community members' benefit implies the optimization of overall community welfare. The proposed pricing mechanism satisfies the cost-causation principle and ensures the stability of the energy community in a coalition game setting. Numerical examples provide insights into the characteristics of the proposed pricing mechanism and quantitative measures of its performance.

Operating-Envelopes-Aware Decentralized Welfare Maximization for Energy Communities

Abstract

We propose an operating-envelope-aware, prosumer-centric, and efficient energy community that aggregates individual and shared community distributed energy resources and transacts with a regulated distribution system operator (DSO) under a generalized net energy metering tariff design. To ensure safe network operation, the DSO imposes dynamic export and import limits, known as dynamic operating envelopes, on end-users' revenue meters. Given the operating envelopes, we propose an incentive-aligned community pricing mechanism under which the decentralized optimization of community members' benefit implies the optimization of overall community welfare. The proposed pricing mechanism satisfies the cost-causation principle and ensures the stability of the energy community in a coalition game setting. Numerical examples provide insights into the characteristics of the proposed pricing mechanism and quantitative measures of its performance.
Paper Structure (24 sections, 6 theorems, 66 equations, 5 figures, 1 table)

This paper contains 24 sections, 6 theorems, 66 equations, 5 figures, 1 table.

Table of Contents

  1. Introduction
  2. Energy Sharing Model and Benchmark
  3. Energy Community Structure
  4. Energy Community DER
  5. BTM and community shared DER
  6. Net consumption
  7. Energy Community Payments and Surpluses
  8. Community Payments and Profit
  9. Community Members Surplus and Decision Problem
  10. Benchmark Model, Surplus and Decision Problem
  11. Generalized Cost-Causation Principle
  12. Operating-Envelopes-Aware Dynamic NEM
  13. Operating-Envelopes-Aware Dynamic NEM
  14. Operating-Envelopes-Aware Dynamic NEM Properties and Structure
  15. Community Member Problem and Optimal Decisions
  16. ...and 9 more sections

Key Result

Lemma 1

Given the announced market mechanism, every member $i \in \mathcal{N}$'s optimal decisions obey a two-threshold policy with thresholds that schedule the consumption as where $\bm{d}^\Omega_{i} = \max\{\underline{\bm{d}}_i,\min\{\bm{f}_i(\bm{1} \Omega),\overline{\bm{d}}_i\} \}$ with $\Omega=\{\mu_1^\ast,\Gamma^{\hbox{\tiny DNEM}}, \mu_2^\ast\}$ and $\mu_1^\ast\geq \Gamma^{\hbox{\tiny DNEM}} \geq

Figures (5)

  • Figure 1: Energy community framework. Member consumption and renewables are $d_i \in \mathbb{R}_+, r_i \in \mathbb{R}_+$, respectively, and member and aggregate net consumption, and community (central) DER are $z_i\in \mathbb{R},z_\mathcal{N} \in \mathbb{R}, g_\mathcal{N}\in \mathbb{R}_+$, respectively. The direction of the arrows indicates positive quantities.
  • Figure 2: OEs-aware D-NEM and NEM prices under optimal community member response.
  • Figure 3: Community members optimal consumption and net consumption under the OEs-aware D-NEM.
  • Figure 4: Monthly welfare gain (%) over NEM - Passive Benchmark under $-\underline{z}_i= \overline{z}_i=3$kW (left) and $-\underline{z}_i= \overline{z}_i=\infty$ (right). The bar chart shows the aggregate community generation $b_\mathcal{N}$.
  • Figure 5: Normalized average monthly welfare (%) under varying OEs.

Theorems & Definitions (8)

  • Definition 1: Generalized cost-causation principle
  • Definition 2: Decentralized welfare optimality
  • Lemma 1: Optimal member decisions
  • Theorem 1: Individual rationality
  • Theorem 2: Decentralized welfare optimality
  • Theorem 3: Conformity with the generalized cost-causation principle
  • Lemma 2: Benchmark prosumer optimal response and maximum surplus
  • Lemma 3: Community maximum welfare