Nested Shapley Settlement
The Shapley Value provides an attractive method for fairly allocating system value.
Unfortunately, it is also computationally expensive.
For a system containing (n) participants, every possible coalition must be considered.
The number of coalitions is
[ 2^n ]
For only twenty generators this is already more than one million possible coalitions.
National electricity systems contain thousands of generators and millions of distributed energy resources.
Direct calculation quickly becomes computationally intractable.
Exploiting Electrical Structure
Fortunately, electricity networks are not random collections of assets.
They possess a strong hierarchical structure.
Assets interact most strongly with electrically nearby assets.
For example
- households connect to feeders,
- feeders connect to substations,
- substations connect to transmission networks,
- transmission networks connect regions.
Electrical interactions become progressively weaker as distance increases.
This observation provides an opportunity for approximation.
Hierarchical Settlement
Instead of evaluating every participant simultaneously, FP-AMM performs settlement hierarchically.
Participants are first grouped according to electrical proximity.
For example
- local feeders,
- primary substations,
- grid supply points,
- transmission regions.
A Shapley settlement is first calculated within each local cluster.
Each cluster is then represented as a higher-level participant.
The process repeats recursively until the entire network has been settled.
This creates a Nested Shapley Settlement.
Advantages
The hierarchical approach provides several practical benefits.
Scalability
Large national systems become computationally tractable.
Physical Interpretation
Clusters naturally correspond to the physical structure of electricity networks.
Parallel Computation
Independent clusters can be settled simultaneously.
Local Accuracy
Interactions that matter most are captured at the local level, where electrical coupling is strongest.
Settlement Based on System Value
The purpose of the Nested Shapley approach is not to produce an exact mathematical Shapley Value for every asset in the network.
Rather, it provides a computationally practical approximation that preserves the central principle:
Participants should be compensated according to the value they contribute to the electricity system.
By combining cooperative game theory with the hierarchical structure of real electricity networks, FP-AMM creates a settlement mechanism that remains fair, interpretable and computationally scalable for national-scale power systems.