Price Formation
The purpose of an Automatic Market Maker is to determine prices algorithmically.
The central challenge is therefore not how to clear a market, but how to design the pricing function.
Different markets require different pricing functions because they are attempting to achieve different objectives.
For example, Uniswap seeks to maximise liquidity. Prediction markets seek to aggregate information. Electricity systems have a very different objective.
The pricing function should therefore be derived from the behaviour we wish to encourage.
What Should an Electricity Market Optimise?
Unlike most markets, electricity cannot be stored economically at scale and must be transported through a physical network with finite capacity.
Consequently, not every transaction is equally desirable.
Some transactions improve the performance of the electricity system.
Others increase congestion, create voltage problems or require renewable generation to be curtailed.
The objective of the FP-AMM is therefore not to maximise trading activity.
Instead, its objective is to maximise the useful utilisation of the electricity system.
More specifically, the market seeks to:
- maximise renewable energy utilisation,
- maximise utilisation of existing network infrastructure,
- minimise renewable curtailment,
- minimise network congestion,
- encourage flexibility when and where it provides value,
- discourage behaviour that worsens scarcity.
Prices are therefore designed to encourage these outcomes.
Price as a Control Signal
Traditional electricity markets typically treat price as the outcome of market clearing.
FP-AMM instead treats price as a control signal.
The purpose of the pricing function is to influence the future behaviour of participants.
If the network is becoming congested, prices should discourage additional consumption.
If renewable generation is being curtailed, prices should encourage additional demand.
Rather than describing the current state of the system, prices become an active mechanism for steering the system towards a more desirable operating point.
Scarcity and Abundance
At any instant, every location within the electricity system exists somewhere on a spectrum between abundance and scarcity.
During periods of abundance:
- renewable generation exceeds demand,
- network capacity is available,
- additional consumption is desirable.
During periods of scarcity:
- available supply becomes limited,
- network capacity becomes constrained,
- additional consumption should be discouraged.
The pricing function therefore responds continuously to the physical state of the system.
Buy Prices
Consumers should be encouraged to consume electricity when doing so improves the operation of the electricity system.
Consequently:
- buy prices decrease when renewable generation is abundant,
- buy prices decrease when spare network capacity exists,
- buy prices increase as available supply becomes scarce,
- buy prices increase as network utilisation approaches its limits.
This encourages flexible demand to move naturally towards periods where energy is plentiful and infrastructure is underutilised.
Sell Prices
Generators should be encouraged to provide energy precisely when the electricity system requires it.
Consequently:
- sell prices increase during scarcity,
- sell prices increase when network support is valuable,
- sell prices decrease during periods of renewable abundance,
- sell prices decrease when additional generation provides little additional system benefit.
This encourages investment towards generation that contributes genuine system value rather than simply maximising annual energy production.
A Family of Pricing Curves
Unlike many Automatic Market Makers, FP-AMM does not use a single fixed pricing equation.
Instead, it defines a family of pricing curves.
The appropriate curve depends on the current operating state of the electricity system.
Conceptually, the pricing function can be written as
[ P = f(S, D, N) ]
where
- (S) represents available supply,
- (D) represents consumer demand,
- (N) represents the physical state of the electricity network.
The precise mathematical form of the pricing function is less important than the principle that prices should respond continuously to changes in physical system conditions.
Different operating conditions naturally produce different pricing behaviour.
Detecting System Conditions
An Automatic Market Maker can only produce sensible prices if it possesses an accurate estimate of the current state of the electricity system.
Fortunately, modern electricity networks generate large quantities of operational data.
Examples include:
Market Information
- submitted buy bids,
- submitted sell bids,
- accepted commitments,
- renewable forecasts,
- battery state of charge,
- expected demand.
Physical Measurements
- voltage,
- frequency,
- transformer loading,
- feeder loading,
- thermal utilisation,
- power flows.
These measurements collectively provide an estimate of network "busyness".
For example:
- persistent undervoltage often indicates excessive local demand,
- persistent overvoltage often indicates excess local generation,
- high transformer loading indicates limited remaining capacity,
- lightly loaded feeders indicate opportunities to increase utilisation.
Rather than relying solely on market information, FP-AMM combines market signals with physical measurements to estimate the current operating state of the electricity network.
Prices Should Follow Physics
The defining principle of FP-AMM is that prices should emerge from the physical state of the electricity system.
The market is not attempting to discover an abstract equilibrium price.
Instead, it continuously estimates how close the system is to scarcity, congestion or renewable surplus and adjusts prices accordingly.
When renewable energy is abundant and network capacity is available, prices naturally fall to encourage additional consumption.
When supply becomes scarce or network limits begin to bind, prices rise to discourage demand and attract additional generation.
The pricing function therefore transforms physical measurements of the electricity network into economic incentives that coordinate the behaviour of millions of independent devices.
The following sections derive the mathematical form of this pricing function and show how it can be extended to respect network constraints while continuously clearing the electricity market.