Smart Grids, Solar Power and Renewable Energies

Kuramoto Oscillators

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Kuramoto model is the behavior of a large set of coupled oscillators. It is mainly designed with the systems of chemical and biological oscillators. It also has its global applications in neuroscience.  In smart grid architectures there arises a synchronization problem for the network-reduced model of a power system with nontrivial transfer of conductances. Our goal is to exploit the relationship between the power network model and a first-order model of coupled oscillators. Nonuniform Kuramoto oscillators are characterized by multiple time constants, nonhomogeneous coupling, and nonuniform phase shifts. In kuramoto model, each of the oscillators is considered to have its own intrinsic natural frequency and each is coupled equally to all other oscillators. The original analysis of synchronization is accomplished by Kuramoto in the case of mean-field coupling. Analysis of the mean-field KM is made with white noise forcing terms. In power grids if the network is lossless and the voltage levels |Vi| at all nodes i ∈ V1 ∪ V2 are constant, then the maximum real power transfer between any two nodes   i, j ∈ V1 ∪ V2 is aij = |Vi| · |Vj | · =(Yij ), where =(Yij ) denotes the susceptance of the transmission line.

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