FP-AMM Operational Coordination

What O1 demonstrates

Request R1 initially sees 21:00 as one of the cheapest available periods and books capacity there. That commitment changes the booked state immediately, raising the operational price at 21:00 before R2 is evaluated.

R2 therefore sees a different price curve from R1 and first selects an alternative interval. This is the central sequential-clearing property: participants do not all observe the same static low-price interval and respond simultaneously.

Each accepted request changes the state against which the next request is evaluated.

What O2 demonstrates

Both requests require the same 14 kWh of energy and have the same 7 kW maximum power, but they expose very different temporal flexibility to the mechanism.

The inflexible request can only be served between 18:00 and 21:00. It therefore schedules four half-hour periods between 19:00 and 20:30, at operational prices ranging from approximately £91/MWh to £118/MWh.

The flexible request has until 07:00 to receive exactly the same amount of energy. FP-AMM evaluates that larger feasible window against the rolling future state and instead schedules the request between 01:00 and 02:30, where operational prices are approximately £16–£18/MWh.

The result demonstrates that forward coordination does not require a separate forward market or a centrally issued charging schedule. The request simply declares when it can consume, and the continuously clearing mechanism uses that flexibility to place consumption into more favourable future periods.

In FP-AMM, real-time and forward coordination are therefore part of the same mechanism: flexibility changes the feasible set, and the rolling operational state determines where within that set the request is scheduled.

What O3 demonstrates

O3 demonstrates that an operational electricity price is determined by the marginal energy physically available to a location, rather than by adding network scarcity charges to a single system-wide energy price.

In the first case, NODE-A has sufficient local energy available. The request is therefore supplied locally and faces a local operational price of approximately £10.05/MWh.

In the second case, local energy is insufficient but the connection to the wider system is unconstrained. The marginal energy can therefore be imported, and the request faces the supplying SYSTEM price of approximately £20.08/MWh.

In the third case, local energy is again insufficient, but the import interface is now the limiting physical resource. Although cheaper energy exists elsewhere in the system, the request cannot freely access it. The binding interface therefore governs the downstream operational price at approximately £61.44/MWh.

O3 therefore shows that locational prices can be either above or below wider-system prices. The relevant price emerges from where the marginal unit of energy can physically be supplied and whether the network permits that energy to reach the requesting location.

What O4 demonstrates

O4 demonstrates how FP-AMM resolves operational price through a nested electricity-system hierarchy without adding together prices from every network level.

Each level calculates its own operational price independently from its local physical state. The mechanism then moves outward through the hierarchy only as far as necessary to find the level capable of supplying the marginal unit of energy.

In the first case, LV1 has sufficient local energy available, so the request is supplied locally at approximately £8.21/MWh.

In the second case, LV1 cannot supply the marginal unit, but FEEDER-1 can. The feeder therefore governs the request price at approximately £20.50/MWh.

In the third case, neither LV1 nor FEEDER-1 can supply the required marginal energy, so the mechanism resolves upward again to REGION-A, which becomes the governing level at approximately £24.38/MWh.

The fourth case demonstrates the complementary constraint rule. LV4 requires upstream energy, but its import interface is binding. Although cheaper energy exists at FEEDER-2, REGION-A and SYSTEM level, that energy cannot freely reach the device. The binding F2-LV4 interface therefore governs the operational price at approximately £78.12/MWh.

O4 therefore shows that the end-device price is neither inherited mechanically from the system nor formed by summing network charges. It emerges from the level or interface that physically governs the marginal supply available to that device.

Order-sensitivity results

Total served energy was identical under all four orderings: 1,024.5 kWh, equivalent to 20.893% of the 4,903.5 kWh requested. No ordering produced a physical constraint violation.

Differences are measured against the original arrival ordering. A changed schedule does not necessarily imply a change in the total energy served to that request.

What O5 demonstrates

O5 demonstrates that the sequential holarchical mechanism remains physically feasible and computationally lightweight when processing 1,000 requests. Every ordering respected all network constraints, and average clearing time remained approximately 0.05 milliseconds per request.

Aggregate served energy was invariant across arrival, random, priority and fairness-weighted orderings. Each ordering scheduled the same 1,024.5 kWh, showing that the physical capacity available to the mechanism was used consistently.

Individual outcomes were not invariant. Depending on the ordering, between 342 and 371 requests received a different quantity of energy, while between 370 and 400 requests received a different schedule relative to arrival order.

O5 therefore confirms both the scalability of continuously sequential clearing and the importance of explicitly governing request order. Order dependence is not hidden: it becomes a measurable allocation-design question that can be addressed through priority, fairness and other transparent sequencing rules.

The interactive replay presents a deterministic 40-request sample from the full experiment. The aggregate benchmark covers all 1,000 requests under each of the four orderings.