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predefined value N , which corresponds to the safety limit imposed by technological
constraints (
φ 1 ). We also want that each coalition is able to supply electricity to all
the loads, so as the energetic balance between generation and consumption must
be positive (
φ 2 ). Finally, each coalition must realise a desired generation profile of
electricity that would qualify them as VPP (
φ 3 ). Formally:
φ 1 : |S j |≤N ∀j ∈{ 1 , ..., m}
φ 2 :
β i > 0
a i ∈S j
φ 3 :
β i = ψ
a i ∈P j
where
P j = P∩S j ,and
ψ
represents the desired energetic profile that each coali-
tion wants to achieve.
v
: S→ [ 1 , 1]
is a function that for every coalition of the set
S
returns its util-
ity value. Each provider agent
a i
is characterized by an association coefficient
γ i,j
that represents the percentage contribution of
a i to coalition
S j 's desired energetic
profile
, accounting as well for the encountered power loss in the course of trans-
mission. Thus, the utility function of the coalition, v , is defined as the sum of the
association coefficients of the
ψ
PA
members:
v
( S j )=
γ i,j
a i ∈P j
A resulting value of 1 signifies the ideal situation of an energetically equlibrated coali-
tion able of supplying demand.
The goal of the coordination problem is obtaining a partitioning of
A
into a coalition
structure
and at the same time maximises
the social welfare 2 of the system, without jeopardizing the functionality of any of the
coalitions. We leave aside for now what this trade-off implies and further develop on
this issue in Sections 4 and 5.
S
that complies with the set of constraints
Φ
4
Coalition Self-adaptation Mechanism
The mechanism presented hereafter proposes an organizational design for managing
the smart grid actors, that operates at the level of the electricity distribution network.
Namely, the foremost issue we address in this paper regards the notion of stability that a
system of a given random coalition structure is capable to achieve, given the dynamism
of the environment. This represents an adaptive process, providing much needed flexi-
bility and functional scalability.
The mechanism proceeds as follows. Each coalition designates a coordinator agent
( CA ) which shall be performing the inter-coalition negotiations. There are numerous
2
For computing the social welfare of the system we mean the typical interpretation of averaging
over the utilities of all coalitions.
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