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In the DEZENT project we had established a distributed base model for negotiating electric power from widely distributed (renewable) power sources on multiple levels in succession. Negotiation strategies would be intelligently adjusted by the agents, through (distributed) reinforcement learning procedures. The distribution of the negotiated power quantities (under distributed control as well) occurs such that the grid stability is guaranteed, under 0.5 sec. The major objective in this paper was to deal, on the same level of granularity, with short-term power balance fluctuation, in terms of a peak demand and supply management exhibiting highly dynamic, self-organizing, autonomous yet coordinated algorithms under fine-grained distributed control. Our extensive experiments show very clearly that these short-term fluctuations could be leveled down by 70 - 75 %. In this way we have tackled, for the quickly increasing renewable power systems, a crucial problem of its stability, in a novel way that scales very easily due to the completely decentralized control.