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Network-Aware and Welfare-Maximizing Dynamic Pricing for Energy Sharing

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

Abstract

The proliferation of behind-the-meter (BTM) distributed energy resources (DER) within the electrical distribution network presents significant supply and demand flexibilities, but also introduces operational challenges such as voltage spikes and reverse power flows. In response, this paper proposes a network-aware dynamic pricing framework tailored for energy-sharing coalitions that aggregate small, but ubiquitous, BTM DER downstream of a distribution system operator's (DSO) revenue meter that adopts a generic net energy metering (NEM) tariff. By formulating a Stackelberg game between the energy-sharing market leader and its prosumers, we show that the dynamic pricing policy induces the prosumers toward a network-safe operation and decentrally maximizes the energy-sharing social welfare. The dynamic pricing mechanism involves a combination of a locational ex-ante dynamic price and an ex-post allocation, both of which are functions of the energy sharing's BTM DER. The ex-post allocation is proportionate to the price differential between the DSO NEM price and the energy-sharing locational price. Simulation results using real DER data and the IEEE 13-bus test systems illustrate the dynamic nature of network-aware pricing at each bus, and its impact on voltage.

Network-Aware and Welfare-Maximizing Dynamic Pricing for Energy Sharing

Abstract

The proliferation of behind-the-meter (BTM) distributed energy resources (DER) within the electrical distribution network presents significant supply and demand flexibilities, but also introduces operational challenges such as voltage spikes and reverse power flows. In response, this paper proposes a network-aware dynamic pricing framework tailored for energy-sharing coalitions that aggregate small, but ubiquitous, BTM DER downstream of a distribution system operator's (DSO) revenue meter that adopts a generic net energy metering (NEM) tariff. By formulating a Stackelberg game between the energy-sharing market leader and its prosumers, we show that the dynamic pricing policy induces the prosumers toward a network-safe operation and decentrally maximizes the energy-sharing social welfare. The dynamic pricing mechanism involves a combination of a locational ex-ante dynamic price and an ex-post allocation, both of which are functions of the energy sharing's BTM DER. The ex-post allocation is proportionate to the price differential between the DSO NEM price and the energy-sharing locational price. Simulation results using real DER data and the IEEE 13-bus test systems illustrate the dynamic nature of network-aware pricing at each bus, and its impact on voltage.
Paper Structure (18 sections, 3 theorems, 53 equations, 3 figures)

This paper contains 18 sections, 3 theorems, 53 equations, 3 figures.

Table of Contents

  1. Introduction
  2. Proposed Framework and Network Model
  3. Energy Sharing Mathematical Model
  4. DER Modeling
  5. Payment, Surplus, and Profit Neutrality
  6. Energy Sharing Payment
  7. Energy Sharing Stackelberg Game
  8. Network-Aware Pricing and Equilibrium
  9. Network-Aware Dynamic Pricing
  10. Optimal Prosumer Decisions
  11. Ex-Post Allocation
  12. Stackelberg Equilibrium
  13. Energy Sharing Payment Uniformity
  14. Numerical Study
  15. Conclusion
  16. ...and 3 more sections

Key Result

Lemma 1

Under every bus $i\in {\cal B}$, given the pricing policy $\chi^\ast$, the prosumer's optimal consumption is By definition, the aggregate net consumption is where $\bm{\pi}^\ast:=(\pi^\ast_1,\ldots,\pi^\ast_B)$, and $Z_0^{\psi^\ast}(\bm{\pi}^\ast(\bm{g})) > 0$ if $G_0 < \sigma_1(\bm{g})$, $Z_0^{\psi^\ast}(\bm{\pi}^\ast(\bm{g})) = 0$ if $G_0 \in [\sigma_1(\bm{g}),\sigma_2(\bm{g})]$, and $Z_0^{\ps

Figures (3)

  • Figure 1: A 4-bus energy-sharing platform. $Z_0,Z_i, z_{n} \in \mathbb{R}$ are the net consumption of the whole energy sharing platform, net consumption of bus $i$, and net consumption of prosumer $n$, respectively. $\overline{z}_n\geq 0$ and $\underline{z}_n \leq0$ are the prosumer's import and export OEs, respectively.
  • Figure 2: The IEEE 13-bus test feeder.
  • Figure 3: Summary of the numerical tests on the four considered scenarios. The lower panel reports the ex-ante energy prices obtained after solving the energy sharing platform optimization problem \ref{['eq:community_optimization']}. The upper panel shows the cumulative power demand at each bus obtained after the energy sharing operator dispatched the energy prices. The middle panel reports the resulting bus voltage magnitudes.

Theorems & Definitions (6)

  • Definition 1: Profit neutrality
  • Lemma 1: Prosumer optimal consumption
  • proof
  • Theorem 1
  • proof
  • Lemma 2: Maximum welfare under centralized operation