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Fig. 1.
Social welfare of the system in number of steps. a) normal behavior ; b)induced variations
occur otherwise at the coalition level and which would severely affect the VPP in our
scenario. Such a situation would have corresponded to the undesired case of a VPP
unable to assure an acceptable match of supply with demand. In by doing so, the mech-
anism proposed herein is able of improving on the quality of the local optima reached,
while still employing a straightforward self-organizing scheme that avoids an other-
wise exponential lookahead. The negotiation is based on the actor's local perspective,
not assuming the configuration of the other coalitions to be known. The experiments
performed reveal that the procedure leads to a local optimum rapidly, to a higher av-
erage social welfare and even more importantly, decreases the occurrence of coalitions
far from equilibrium.
Figure 1 points out the average percent increase in social welfare, that the system
manages to attain from an initial state to a stable one, achieved during the course of the
adaptation phase. The system proves to reach a stable organization in approximately 50
steps by agreeing on reassigning DERs between coalitions according to the argumenta-
tion scheme proposed. The optimal allocation of DERs, given the sufficient availability
of energy in the grid would yield a social welfare of 1. However, achieving this is not
always necessarily the case, as the coalitions are highly dependent on the actual dis-
tribution of DERs in the network, while being ought to obey as well the constraints
referring to their energetic potential.
As the graph in Figure 1(a) illustrates, a stable configuration of the system is abruptly
reached, meaning that the agreements realized earlier improve the social welfare more
than the ones performed later. Furthermore, the solution applied is an anytime algorithm
that achieves a monotonic improvement of the global (social) welfare of the system,
which can thus only improve at each time step. This is obviously an important aspect
when the best solution needs to be reached in a bounded amount of time. Hence we
comply with our objective of converging abruptly to an efficient and stable configuration
of the system.
Transferring actors individually between coalitions as opposed to bundles of actors,
although more time consuming, avoids a known outcome, that of concentrating the
