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A Fair, Flexible, Zero-Waste Digital Electricity Market: A First-Principles Approach Combining Automatic Market Making, Holarchic Architectures and Shapley Theory

Shaun Sweeney, Robert Shorten, Mark O'Malley

TL;DR

This work reframes electricity markets as cyber-physical control systems that operate continuously and state-dependently on grid physics. It identifies fundamental fragilities in legacy energy-only, energy-plus-capacity, and zonal designs, proposing a holarchic Automatic Market Maker (AMM) powered by a formal fairness framework (F1–F4) and a Fair Play scarcity-allocation mechanism. The three-dimensional energy contract (magnitude, timing, reliability) enables real-time, contract-based provisioning of energy, flexibility, and reliability, while Nested Shapley remuneration ensures scalable, value-aligned generator payments. Simulation across household data and two-region networks demonstrates bounded stability, reduced waste, and fairness improvements, arguing for a digitally regulated, fairness-aware transition that preserves participation and aligns market incentives with grid physics. The architecture promises zero-waste operation, enhanced bankability, and robust equilibria under uncertainty, offering a path toward a climate-aligned, electrified economy that respects social legitimacy and democratic governance.

Abstract

This thesis presents a fundamental rethink of electricity market design at the wholesale and balancing layers. Rather than treating markets as static spot clearing mechanisms, it reframes them as a continuously online, event driven dynamical control system: a two sided marketplace operating directly on grid physics. Existing energy only, capacity augmented, and zonal market designs are shown to admit no shock robust Nash equilibrium under realistic uncertainty, instead relying on price caps, uplift, and regulatory intervention to preserve solvency and security. In response, the thesis develops a holarchic Automatic Market Maker (AMM) in which prices are bounded, exogenous control signals derived from physical tightness rather than emergent equilibrium outcomes. The AMM generalises nodal and zonal pricing through nested scarcity layers, from node to cluster to zone to region to system, such that participant facing prices inherit from the tightest binding constraint. Nodal and zonal pricing therefore emerge as special cases of a unified scarcity propagation rule. Beyond pricing, the AMM functions as a scarcity aware control system and a digitally enforceable rulebook for fair access and proportional allocation under shortage. Fuel costs are recovered through pay as bid energy dispatch consistent with merit order, while non fuel operating and capital costs are allocated according to adequacy, flexibility, and locational contribution. Large scale simulations demonstrate bounded input bounded output stability, controllable procurement costs, zero structural waste, and improved distributional outcomes. The architecture is climate aligned and policy configurable, but requires a managed transition and new operational tools for system operators and market participants.

A Fair, Flexible, Zero-Waste Digital Electricity Market: A First-Principles Approach Combining Automatic Market Making, Holarchic Architectures and Shapley Theory

TL;DR

This work reframes electricity markets as cyber-physical control systems that operate continuously and state-dependently on grid physics. It identifies fundamental fragilities in legacy energy-only, energy-plus-capacity, and zonal designs, proposing a holarchic Automatic Market Maker (AMM) powered by a formal fairness framework (F1–F4) and a Fair Play scarcity-allocation mechanism. The three-dimensional energy contract (magnitude, timing, reliability) enables real-time, contract-based provisioning of energy, flexibility, and reliability, while Nested Shapley remuneration ensures scalable, value-aligned generator payments. Simulation across household data and two-region networks demonstrates bounded stability, reduced waste, and fairness improvements, arguing for a digitally regulated, fairness-aware transition that preserves participation and aligns market incentives with grid physics. The architecture promises zero-waste operation, enhanced bankability, and robust equilibria under uncertainty, offering a path toward a climate-aligned, electrified economy that respects social legitimacy and democratic governance.

Abstract

This thesis presents a fundamental rethink of electricity market design at the wholesale and balancing layers. Rather than treating markets as static spot clearing mechanisms, it reframes them as a continuously online, event driven dynamical control system: a two sided marketplace operating directly on grid physics. Existing energy only, capacity augmented, and zonal market designs are shown to admit no shock robust Nash equilibrium under realistic uncertainty, instead relying on price caps, uplift, and regulatory intervention to preserve solvency and security. In response, the thesis develops a holarchic Automatic Market Maker (AMM) in which prices are bounded, exogenous control signals derived from physical tightness rather than emergent equilibrium outcomes. The AMM generalises nodal and zonal pricing through nested scarcity layers, from node to cluster to zone to region to system, such that participant facing prices inherit from the tightest binding constraint. Nodal and zonal pricing therefore emerge as special cases of a unified scarcity propagation rule. Beyond pricing, the AMM functions as a scarcity aware control system and a digitally enforceable rulebook for fair access and proportional allocation under shortage. Fuel costs are recovered through pay as bid energy dispatch consistent with merit order, while non fuel operating and capital costs are allocated according to adequacy, flexibility, and locational contribution. Large scale simulations demonstrate bounded input bounded output stability, controllable procurement costs, zero structural waste, and improved distributional outcomes. The architecture is climate aligned and policy configurable, but requires a managed transition and new operational tools for system operators and market participants.

Paper Structure

This paper contains 634 sections, 14 theorems, 338 equations, 67 figures, 26 tables, 1 algorithm.

Key Result

Lemma 4.1

Consider a retail electricity supplier operating over a horizon $[0,T]$ with: Assume that there exists a shock interval $I = [t_s, t_s + \Delta] \subset [0,T]$ such that and that demand is strictly positive on $I$, i.e. $Q(t) \ge \underline{Q} > 0$ for all $t \in I$. Then, irrespective of the supplier's operational efficiency or tariff design (as long as it respects the price cap), there exists

Figures (67)

  • Figure 1: Conceptual flow from problem to implemented solution
  • Figure 2: Conceptual holarchy of the electricity system. The UK-wide system (Layer 1) contains electrically defined clusters capturing dominant congestion patterns (Layer 2), which in turn contain regions or network areas (Layer 3), within which individual households and businesses reside (Layer 4). A further layer of individual devices and controllable assets (Layer 5) operates within households and sites but is not shown for clarity. Each layer is simultaneously a whole (with respect to the layers below) and a part (of the layer above), and may serve as the natural unit of analysis, allocation, or regulation for different stakeholders.
  • Figure 3: Architecture of the proposed digital market platform, showing the interaction between edge participants, the continuous online market instance, the Automatic Market Maker (AMM), data stores, and governance/control interfaces.
  • Figure 4: Software architecture of the continuous online market instance and Automatic Market Maker (AMM). Governance and external systems (top) interact with the digital market platform (middle), which hosts the API gateway, AMM and Fair Play control engine, data stores, analytics, and settlement services. Edge participants (bottom) connect via APIs and telemetry, forming the cyber--physical control architecture described in this chapter.
  • Figure 5: Illustration of the retail product space in the magnitude--impact plane. Each point represents an underlying usage profile (household or SME), classified by (i) the quantity of energy it seeks to consume from non-zero-marginal-cost supply and (ii) its contribution to system tightness during scarce periods. Reliability / Quality-of-Service (QoS) is an additional, independent contract dimension and is not shown here.
  • ...and 62 more figures

Theorems & Definitions (29)

  • Lemma 4.1: Structural Insolvency under Price Caps
  • proof
  • Lemma 4.2: Risk--Volume Separation Instability
  • proof
  • Lemma 4.3: Affordability Failure without Retail Price Caps
  • proof
  • Proposition 4.1: Layered Markets Converge to the Energy--Only Limit in Stress Events
  • Corollary 4.1: No Simultaneous Solvency and Affordability under Separated Retail Risk
  • Proposition 4.2: Non-Existence of a Shock-Robust Nash Equilibrium in the Legacy Retail Game
  • Lemma 4.4: Arbitrariness and Sensitivity of VoLL in LMP-Based Scarcity Pricing
  • ...and 19 more