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of DERs that are connected through an informational infrastructure and act in a coor-
dinated way as a single entity. The challenging problem related to the implementation
of the VPP concept is the distributed control of the DERs, mainly due to the stochastic
behaviour of the system and the heterogeneity of the devices involved.
The aim of this work is modelling the coordination of virtual power plants in the
sense of coalitional games. Instead of considering centralized architectures [10], we
claim that a dynamic, bottom-up, approximation of optimal VPP configurations is more
effective to ensure flexibility and robustness to the system.
The remaining of this paper is organized as follows. We begin in Section 2 by gener-
ally discussing existing techniques for team formation in MAS. In Section 3 we discuss
the formalization of the problem. Our agent-based organizational model is introduced
in the fourth section with emphasis on the coalition self-adaptation scheme proposed. In
Section 5 we present experimental results and point towards future work, while Section
6 concludes the paper.
2
Related Work
In the following we give a brief review, addressing teamwork in agent organizations and
more precisely, the problem of structuring a set of individuals as a team of cooperative
agents that pursue an institutional goal, then asses their applicability to MAS scenarios.
Coalitional games are denoted by a set of players
that seek to
coalesce into cooperative groups, which represent in fact an agreement of the respective
players for acting within the game as a single entity. The outcome that each of these
coalitions can achieve for itself is defined in terms of a characteristic function
A = { 1 , 2 ,...n}
v
, which
weights the worth (utility) of a coalition S in a game,
v ( S )
. Thus, a coalitional game
can be uniquely defined as a pair
.
An important body of work has been devoted to the question of how to best parti-
tion a group of agents (the problem domain is non-superadditive), which is essentially
a combinatorial problem with an exponential search space [14]. The proposed solu-
tions can be analysed according to different attributes of the solution method, such as
optimality, centralisation, dynamism and stability.
A first class of algorithms are those that are run centrally by an omniscient agent that
tries to find an optimal solution, or at least a solution that is bounded from optimal. As a
subclass, a common practice is that of employing dynamic programming solutions [12].
The complexity of such algorithms, although significantly better than an exhaustive enu-
meration of all coalition structures, is prohibitive in the number of agents, being usually
suitable for situations of at most 20 agents. The second subclass of this category of algo-
rithms is built upon interpreting the problem in the sense of a coalition structure graph,
introduced by Sandholm in [13]. Extensions of this approach consider different pruning
techniques in order to establish solutions bounded from optimal, such as the one pro-
posed in [4]. For instance, using this algorithm one may compute a faster solution when
smaller bounds are desirable. Still, this type of algorithms remain severely prohibitive
in terms of scalability. Same is the case for the state-of-the-art algorithm [11], which
divides the search space into partitions based on integer partition and performs branch
and bound search.
( A,v )
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