⚡ electrical engineering

Stateful Pricing and Allocation for Repeated Constrained DER Coordination in Distribution Networks

This paper proposes an Automatic Market Maker (AMM), a stateful cyber-physical coordination mechanism that combines dual fairness states and voltage-aware pricing to significantly reduce unserved flexible demand and export curtailment while ensuring thermal feasibility in distribution networks with high distributed energy resource penetration.

Original authors: Shaun Sweeney, Peter Kilby, Blake Penney, Komeil Moghaddasi, Sunera Mudiyanselage

Published 2026-06-23

📖 5 min read🧠 Deep dive

CC BY 4.0

Original authors: Shaun Sweeney, Peter Kilby, Blake Penney, Komeil Moghaddasi, Sunera Mudiyanselage

Original paper licensed under CC BY 4.0 (http://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

Imagine a busy neighborhood power grid as a large, shared water system. In this neighborhood, everyone has their own little water tank (batteries), some have solar panels that pump water into the system (export), and everyone needs to draw water out to run their appliances (import).

The problem is that the pipes connecting this neighborhood to the main city supply are narrow. Sometimes, everyone wants to draw water at once (import scarcity), and the pipes can't handle it. Other times, everyone is pumping water in from their solar panels at once (export congestion), and the pipes get clogged.

Traditionally, the system manager (the utility company) has two ways to handle this:

The "Hard Limit" Sign (DOE): They put up a sign saying, "You can only take X gallons today." This is safe (no pipes burst), but it's a blunt instrument. If you're a heavy user, you get cut off just as much as a light user, even if you've been cut off every day for a month. It doesn't remember who got the short end of the stick yesterday.
The "Price Tag" (DNP): They raise the price of water when it's scarce. This encourages people to use less, but it doesn't guarantee the pipes won't burst. Also, if the price is too high, it might punish the people who need the water most, while the rich neighbors just pay up and keep using it.

The Paper's Solution: The "Automatic Market Maker" (AMM)

The authors propose a new, smarter system called the Automatic Market Maker (AMM). Think of this as a smart, fair referee that sits between the water pipes and the neighbors. It doesn't just look at the pipes; it keeps a memory book for every single house.

Here is how it works, using simple analogies:

1. The "Memory Book" (Stateful Fairness)

Imagine a referee who keeps a tally for every player.

The Import Book: If your house needs to draw water but the pipes are full, the referee notes, "Sorry, you got 0% of what you asked for today." If this happens again tomorrow, the referee remembers: "This house has been unlucky for three days in a row."
The Export Book: If your solar panels are pumping water in but the pipes are clogged, the referee notes, "You were forced to stop pumping."
The Fix: When the pipes open up again, the referee looks at the book. The house that has been waiting the longest gets priority. It's like a "first-come, first-served" line, but the line resets every day to make sure no one is stuck at the back forever.

2. The "Smart Price Tags" (Bilateral Pricing)

The AMM doesn't just set a price; it sets two prices (one for buying, one for selling) based on how "stressed" the pipes are.

If the pipes are tight, the price to buy water goes up (encouraging you to save), and the price to sell water goes up (encouraging you to pump in).
Crucially, these prices are calculated by the system's physical state (like voltage), not by people trying to game the system. It's like a thermostat that automatically adjusts the temperature based on the room's actual heat, not on what the people in the room say they want.

3. The "Two-Layer" System (MV/LV Architecture)

The neighborhood has a main pipe (Medium Voltage) and 33 smaller side pipes (Low Voltage). The AMM acts like a layered management team.

The Local Team manages the small side pipes.
The Main Team manages the big main pipe.
The system constantly checks which layer is the "bottleneck" (the tightest pipe) and focuses its fairness rules there. It ensures that a problem in one small side street doesn't get ignored just because the main pipe looks fine.

What Did They Find? (The Results)

The researchers tested this "Smart Referee" against the old methods using a realistic computer simulation of an Australian neighborhood.

The "No Memory" Problem: They found that simply adding a price tag to the old "Hard Limit" system actually made things worse. It hurt the people who needed water most because they couldn't afford the high price, while the wealthy neighbors just paid up.
The "Greedy" Problem: They tried a system that just served the biggest requests first (Greedy). This didn't help much either; it was almost as unfair as the old system.
The AMM Success:
- Less Thirst: The AMM reduced the amount of water people couldn't get by 76%.
- No Burst Pipes: It kept the system safe with zero "thermal violations" (no pipes burst).
- Fairness: It made the system much fairer. The "worst-off" neighborhood got 91.4% of what they asked for, compared to only 86% with the old system.
- The Trade-off: There is another method (called FET/FOT/FUH) that is even more fair (99% for everyone), but it requires a super-computer to plan the whole year in advance. The AMM is slightly less fair than that super-planner, but it works in real-time, second-by-second, without needing to predict the future.

The Bottom Line

The paper argues that for a power grid full of solar panels and batteries, you need a memory. You can't just look at the problem right now; you have to remember who has been treated unfairly in the past.

The AMM is a system that combines real-time safety checks (making sure pipes don't burst) with fairness memory (making sure the same people aren't always cut off) and smart price signals (telling people when to use power). It's not a perfect solution that beats every other method in every category, but it is the first to combine all these features into a single, real-time system that works for machines talking to machines.

The authors suggest that the best future solution might be to combine the AMM's real-time fairness with the super-planner's long-term fairness, getting the best of both worlds.

Technical Summary: Stateful Pricing and Allocation for Repeated Constrained DER Coordination

1. Problem Statement

Distribution networks with high penetrations of Distributed Energy Resources (DERs) face a recurring allocation problem: limited network capability must be distributed repeatedly over time under two distinct conditions:

Import Scarcity: When available import capacity is insufficient to satisfy all flexible demand requests.
Export Congestion: When local export capacity is limited, requiring generation curtailment.

Existing mechanisms address these issues only partially. Dynamic Operating Envelopes (DOEs) enforce hard feasibility bounds but typically operate interval-by-interval without maintaining participant-level state to correct repeated disadvantage over time. Dynamic Network Prices (DNPs) provide allocative signals but cannot guarantee aggregate feasibility and lack intertemporal tracking. Furthermore, recent "fair-over-time" DOE formulations (e.g., FET, FOT, FUH) improve export-side equity through offline optimization but lack bilateral scarcity signals, real-time operation, and import-side participant-level correction.

The paper identifies a gap in mechanisms that simultaneously satisfy five requirements: (1) strict feasibility, (2) scarcity signaling, (3) transparent allocation rules, (4) intertemporal correction for repeated disadvantage, and (5) strategic robustness against machine-to-machine (M2M) exploitation.

2. Methodology: The Automatic Market Maker (AMM)

The authors propose the Automatic Market Maker (AMM), a stateful cyber-physical coordination layer designed for M2M DER access. The AMM operates as an additive layer on top of physical feasibility bounds, combining four functional components:

Bidirectional Fairness States: The protocol maintains dual delivery-state variables for each participant $n$ $n$ :
- $f^{srv}_n$ : Tracks the cumulative service delivery ratio under import scarcity (delivered vs. requested).
- $f^{exp}_n$ : Tracks the cumulative curtailment delivery ratio under export congestion (realized vs. available).
  These states feed back into future allocation weights, providing intertemporal correction.
Bounded Bilateral Deficit-Driven Pricing: Buy and sell prices are determined by system state rather than bid values. A composite scarcity signal $\tilde{\alpha}_{t,n}$ , derived from physical quantities (including voltage deviation), drives prices. A bounded implementation uses a Logarithmic Market Scoring Rule (LMSR) tightness signal $\lambda_e(t)$ to ensure prices remain within bounds while reflecting network stress.
Feasibility-Constrained Matching: The AMM solves a Linear Programming (LP) problem to match buyers and sellers. This matching is subject to hard constraints (energy/power limits, time windows, and holonic network capacity) before fairness weighting is applied. This ensures no thermal violations occur.
Two-Tier MV/LV Architecture: The system operates on a hierarchical structure (one Medium Voltage feeder and 33 Low Voltage feeders). An active coordination layer is selected per interval based on which layer is currently tighter (dominant), ensuring constraints are respected at the most critical level.

3. Key Contributions

The paper makes six specific contributions:

Bidirectional Fairness Formalization: Introduction of dual delivery-state variables ( $f^{srv}_n, f^{exp}_n$ ) that track participant-level history for both import and export directions, a feature unique among the compared mechanisms.
Bounded Bilateral Pricing: A pricing mechanism driven by a common deficit signal and voltage-aware scarcity, utilizing LMSR-derived tightness to prevent unbounded price spikes.
Feasibility-Constrained Matching: An explicit LP formulation that enforces hard feasibility before applying fairness weights, with computational complexity $O(\max_\ell N_\ell^2)$ per interval.
Voltage-Aware Scarcity Interpretation: The use of voltage deviation as a directly measurable network stress indicator to drive the scarcity signal, validated under passive inverter assumptions.
Strategic Robustness Analysis: An architectural analysis showing that the protocol limits gains from timing exploitation and forecast inflation through deadline-constrained matching and consistency monitoring, without claiming full incentive compatibility.
Empirical Evaluation: A comprehensive benchmark on the CSIRO MV+33LV feeder dataset comparing eight mechanisms, including the novel finding that adding a stateless price signal to a stateless DOE worsens outcomes.

4. Experimental Results

Experiments were conducted on a 12-month horizon using the CSIRO MV+33LV dataset, comparing the AMM against:

Baseline DOE (equal allocation).
DOE-GREEDY (greedy allocation within DOE).
DOE+DNP (DOE augmented with price signals).
DNP (price-only).
Fair-over-time DOE variants (FET, FOT, FUH).

Key Findings:

Import Scarcity: Relative to equal-allocation DOE, the AMM reduced unserved flexible demand by 76% (from 96.0 MWh to 23.2 MWh) with zero thermal violations.
Export Congestion: Export curtailment was reduced from 85.4 MWh to 64.5 MWh.
The "H1b" Counterintuitive Finding: Augmenting a stateless DOE with a DNP price signal (Scenario 1b) worsened outcomes, increasing unserved energy to 109.4 MWh and lowering the worst-feeder delivery fraction. This suggests that without intertemporal memory, price signals can concentrate remaining capacity on already-advantaged nodes, exacerbating inequity.
Heuristic vs. State: The DOE-GREEDY variant performed marginally worse than standard DOE, confirming that changing the allocation heuristic alone does not improve outcomes in the absence of statefulness.
Fairness Metrics: The AMM achieved an annual inter-feeder Jain index of 0.9998, outperforming all stateless DOE variants from month 6 onwards. The worst-feeder delivery fraction improved from 0.860 (DOE) to 0.914 (AMM).
Comparison with FET/FOT/FUH: The fair-over-time DOE mechanisms achieved higher worst-feeder equity (0.989–0.990) via explicit max-min optimization. However, they operate offline over predetermined horizons and lack bilateral scarcity signals and import-side correction.

5. Significance and Claims

The paper claims that statefulness is a fundamental design dimension for repeated constrained DER coordination. The primary contribution is architectural: a coordination protocol that combines bounded bilateral pricing, hard feasibility, and participant-level intertemporal fairness states in a single real-time layer.

The authors explicitly state that the AMM does not claim to dominate existing fair-over-time optimization methods (FET/FOT/FUH) on max-min fairness metrics. Instead, the AMM addresses different operational objectives:

AMM: Real-time operation, bilateral scarcity signaling, and import-side correction without look-ahead requirements.
FET/FOT/FUH: Offline optimization of fairness over predetermined horizons.

The paper concludes that these approaches are potentially composable. The identified direction for future work is combining the AMM's stateful pricing and real-time coordination with the FET/FOT/FUH approach to MV envelope computation. The results suggest that scarcity pricing without memory may be insufficient—and potentially counterproductive—for achieving equitable long-run outcomes in active distribution networks.