This paper deals with energy management in smart districts using distributed model predictive control (DMPC). We investigate two decomposition methods, primal and dual decomposition, for problems where a shared resource has to be distributed optimally amongst sub systems. The objective is to compare these two decomposition methods with a focus on how well they are suited in the context of smart district energy management. In primal decomposition a coordinator layer is directly affecting resource limits to the sub problems whereas in dual decomposition virtual prices are used to stimulate the sub areas to change their resource consumption behavior in a desired way. Both methods are demonstrated to be able to converge to the globally optimal energy distribution in simulations, provided that the limit on the shared resource is chosen in a reasonable range. This result is particularly interesting regarding the fact that in the dual decomposition case, the number of degrees of freedom of the coordinator problem is only a fraction of the number of degrees of freedom in primal decomposition.Index Terms-Distributed Model Predictive Control, smart grid, primal and dual decomposition.
International audienceThe increasing amount of PV (photovoltaic) power plants comes along with an increased instability in the power grid due to the high uncertainty of the PV power production. As a stabilizing measure, grid operators introduce regulations on the injected power profiles comprising the obligation to declare in advance the predicted power production as well as penal- ties which apply in case these previously declared production profiles were not respected. In order to meet these regulations power plant owners are forced to invest into expensive storage capacities. In this work an algorithm is proposed which allows to determine the optimal battery size that maximizes the to-be- expected revenue of such an installation for a given regulative framework. Moreover the scheme explicitly takes into account the uncertainty in the PV power production and it provides guaranteed lower bounds on the to-be-expected revenue at a configurable probability. The underlying method allowing to achieve these objectives are randomized algorithm
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