Modelling and distributed control of the power grid
The power grid is a very complex system constituted of many interacting components. Various models have been proposed in the literature with different level of complexity and accuracy. The power flow model is widely used for control and monitoring purposes. It is a static nonlinear equilibrium model which describes the balancing of active and reactive power flows in the grid. In the first part of the course we describe this model and we provide a method that allows to determine when there exists a solution of such a model and we provide a linear approximation of this solution.
In the second part of the course we use this approximation for the synthesis of a control strategy able to control the voltages in the grid by acting on the reactive power flows. This is done by applying the gradient method to an optimization problem. We show that the gradient needs not to be computed, but instead it comes for free as an output of the power grid that can be read with a suitable choice of sensors. Moreover, the algorithm that comes out is suitable for a distributed leaderless implementation.