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Uncertainty and Autarky: Cooperative Game Theory for Stable Local Energy Market Partitioning

Saurabh Vaishampayan, Maryam Kamgarpour

Abstract

Local energy markets empower prosumers to form coalitions for energy trading. However, the optimal partitioning of the distribution grid into such coalitions remains unclear, especially in constrained grids with stochastic production and consumption. This analysis must take into account the interests of both the grid operator and the constituent prosumers. In this work, we present a cooperative game theoretic framework to study distribution grid partitioning into local energy market coalitions under uncertain prosumption and grid constraints. We formulate the optimal stable partitioning problem to balance the interests of the grid operator with that of prosumers. Under deterministic load and generation, we show that the largest market coalition is the optimal stable partition. For the case of stochastic loads and generation, we provide an algorithm to evaluate the optimal stable partition. Numerical experiments are performed on benchmark and real world distribution grids. Our results help in understanding how uncertainty affects local energy market partitioning decisions in constrained distribution grids.

Uncertainty and Autarky: Cooperative Game Theory for Stable Local Energy Market Partitioning

Abstract

Local energy markets empower prosumers to form coalitions for energy trading. However, the optimal partitioning of the distribution grid into such coalitions remains unclear, especially in constrained grids with stochastic production and consumption. This analysis must take into account the interests of both the grid operator and the constituent prosumers. In this work, we present a cooperative game theoretic framework to study distribution grid partitioning into local energy market coalitions under uncertain prosumption and grid constraints. We formulate the optimal stable partitioning problem to balance the interests of the grid operator with that of prosumers. Under deterministic load and generation, we show that the largest market coalition is the optimal stable partition. For the case of stochastic loads and generation, we provide an algorithm to evaluate the optimal stable partition. Numerical experiments are performed on benchmark and real world distribution grids. Our results help in understanding how uncertainty affects local energy market partitioning decisions in constrained distribution grids.
Paper Structure (23 sections, 3 theorems, 19 equations, 13 figures, 4 tables, 1 algorithm)

This paper contains 23 sections, 3 theorems, 19 equations, 13 figures, 4 tables, 1 algorithm.

Table of Contents

  1. Introduction
  2. Preliminaries
  3. Distribution grid partitions
  4. Power flow model
  5. Partition costs under two-stage energy dispatch
  6. Ex-ante stage
  7. Ex-post stage
  8. Total costs for a grid partition
  9. Coalition cost model
  10. Coalition cost under coupled power flow constraints
  11. Coalition cost under decoupled power flow
  12. Partitioning objectives
  13. DSO's perspective: optimal partitioning
  14. Prosumers' perspective: stable partitioning
  15. Optimal stable partitioning
  16. ...and 8 more sections

Key Result

Proposition 4.1

(Coalition costs for strict self-consumption and single boundary node) For any $P=\{F_i\}_{i=1}^L$ under Assumptions assm:boundarynode-assm:strictselfconsume, the coalition costs eq:coalitioncostsexternalities are given as Here $\mathcal{B}_{F_i}(\boldsymbol{\hat{U}})$, eq:boundaryzeroexchangecoalitionproposition are power flow constraints for radial graph for coalition $F_i$, and $\boldsymbol{S}

Figures (13)

  • Figure 1: An example of a partition of a radial distribution grid
  • Figure 2: Two-stage costs under imperfect forecasts
  • Figure 3: Cost recovery via tariffs to LEMs in a partition
  • Figure 4: An example of externalities. The voltage at the PCC for the blue LEM coalition depends on upstream LEM configuration. If upstream prosumers self-consume in separate coalitions (left), there is reduced flow and voltage drop across their connecting edge compared to forming single LEM (right).
  • Figure 5: Optimal stable partition under forecasts and realizations
  • ...and 8 more figures

Theorems & Definitions (8)

  • Definition 2.1
  • Proposition 4.1
  • Proposition 5.1
  • Example 1
  • Example 2
  • Definition 5.1
  • Definition 5.2
  • Theorem 6.1