Towards Energysheds: A Technical Definition and Cooperative Framework for Future Power System Operations

TL;DR

This work defines energysheds as spatiotemporal energy communities using a local-generation-to-local-load ratio constraint $\mathcal{X}_k \le \frac{\sum_{i\in\mathcal{N}_k}\sum_{t\in\mathcal{T}} P^G_{i,t}}{\sum_{i\in\mathcal{N}_k}\sum_{t\in\mathcal{T}} P^L_{i,t}}$ and develops an optimization framework for operating and designing energyshed policies in a connected power system. It analyzes how resource budgets $P_S^{+}, P_S^{-}$ shape the maximum achievable ratio $\overline{\mathcal{X}}_k$ under unconstrained or constrained exports, establishing linear growth in the unconstrained case and distinct expressions under export limits. It then introduces convex (P1) and quasi-convex (P3, P6) formulations for meeting energyshed requirements and designing cooperative policies (P2, P4), enabling global-optimal solutions via epigraph transformations and bisection sweeps. A numerical case study on the IEEE 39-bus network with distributed solar demonstrates tradeoffs between energyshed boundaries, policy weights, and system costs, highlighting the equity implications and the benefits of cooperation. The results offer a tractable pathway to value and implement locally-resilient energy objectives within a larger grid, with potential extensions to AC networks and multi-energy systems.

Abstract

There is growing interest in understanding how interactions between system-wide objectives and local community decision-making will impact the clean energy transition. The concept of energysheds has gained traction in the areas of public policy and social science as a way to study these relationships. However, development of technical definitions of energysheds that permit system analysis are still largely missing. In this work, we propose a mathematical definition for energysheds, and introduce an analytical framework for studying energyshed concepts within the context of future electric power system operations. This framework is used to develop insights into the factors that impact a community's ability to achieve energyshed policy incentives within a larger connected power grid, as well as the tradeoffs associated with different spatial policy requirements. We also propose an optimization-based energyshed policy design problem, and show that it can be solved to global optimality within arbitrary precision by employing concepts from quasi-convex optimization. Finally, we investigate how interconnected energysheds can cooperatively achieve their objectives in bulk power system operations.

Figures (8)

• Figure 1: Relationship between maximum achievable local generation ratio and total energy capacity budget under different power export constraints for two energysheds $k$. The total energy capacity budget is given in per unit using the total energy demand, $\sum_{t\in\mathcal{T}} P^{\text{L}}_{k,t}$ , as a base.
• Figure 2: IEEE 39-bus New England power system matpower. Different colors represent the three control areas, and shaded regions show energyshed boundaries for the medium aggregation case in Sec. \ref{['sec:case_setup']}.
• Figure 3: Hourly load and solar PV profiles at each load bus.
• Figure 4: Capacity cost weights, $\alpha_i$ and $\beta_i$, for each load bus.
• Figure 5: Distribution of local generation ratio (a) and additional flexibility capacity (b) across load buses under different energyshed policy constraints. Buses are arranged from left to right in order of increasing generation capacity costs ($\alpha_i$). Note that $\mathcal{X}^*_k$ is larger than $2.0$ for some buses, but we truncate the plot at this value for improved legibility.

Theorems & Definitions (10)

• Proposition 1: Maximum ratio with unconstrained export
• proof
• Proposition 2: Maximum ratio with constrained export
• proof
• Proposition 3
• proof
• Proposition 4
• proof
• Proposition 5
• proof