In the context of the smart grid, we propose in this paper an algorithm that forms coalitions of agents, called prosumers, that both produce and consume. It is designed to be used by aggregators that aim at selling aggregated surplus of production of the prosumers they control. We rely on real weather data sampled across stations of a given territory in order to simulate realistic production and consumption patterns for each prosumer. This enables us to capture geographical correlations among the agents while preserving the diversity due to different behaviors. As aggregators are bound to the market operator by a contract, they seek to maximize their offer while minimizing their risk. The proposed graph-based algorithm takes the underlying correlation structure of the agents into account and outputs coalitions with both high productivity and low variability. We show that the resulting diversified coalitions are able to generate higher benefits on a constrained energy market, and are more resilient to random failures of the agents.
Nevertheless, one of the key point in the Markowitz theory is to consider explicitly the correlation between the assets since they impact directly the variances of the portfolios. Since the work of @cite_5 , an interesting approach consists in computing a distance metric based on the correlation coefficients in order to organize the series in a correlation graph. Nodes represent the series considered while the edges are weighted by the metric. Because the metric can be computed for all pairs, these graphs are complete and of little use as is. Historically, the approach used by @cite_5 was to compute a minimum spanning tree as to obtain a hierarchical clustering of the series. Later on, it was pointed out that, by definition, a spanning tree could not capture the underlying clustering structure hidden in the correlation graph. In this paper, we use another classical filtering technique called @math -graph @cite_1 . It consists in selecting a threshold @math , and filtering out edges with smaller weights. As we will see further in this paper, this approach has the advantage of preserving clusters of correlated series.
@cite_5 @cite_1
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I find a hierarchical arrangement of stocks traded in a financial market by investigating the daily time series of the logarithm of stock price. The topological space is a subdominant ultrametric space associated with a graph connecting the stocks of the portfolio analyzed. The graph is obtained starting from the matrix of correlation coefficient computed between all pairs of stocks of the portfolio by considering the synchronous time evolution of the difference of the logarithm of daily stock price. The hierarchical tree of the subdominant ultrametric space associated with the graph provides a meaningful economic taxonomy. We investigate the properties of correlation based networks originating from economic complex systems, such as the network of stocks traded at the New York Stock Exchange (NYSE). The weaker links (low correlation) of the system are found to contribute to the overall connectivity of the network significantly more than the strong links (high correlation). We find that nodes connected through strong links form well defined communities. These communities are clustered together in more complex ways compared to the widely used classification according to the economic activity. We find that some companies, such as General Electric (GE), Coca Cola (KO), and others, can be involved in different communities. The communities are found to be quite stable over time. Similar results were obtained by investigating markets completely different in size and properties, such as the Athens Stock Exchange (ASE). The present method may be also useful for other networks generated through correlations.