A distributed scheme for secondary frequency control with stability guarantees and optimal power allocation

We consider the problem of distributed secondary frequency regulation in power networks such that stability and an optimal power allocation are guaranteed. This is a problem that has been widely studied in the literature, where two main control schemes have been proposed, usually referred to as ’Primal-Dual’ and ’distributed averaging proportional–integral (DAPI)’ respectively. However, each has its limitations, with the former incorporating additional information flow requirements which may limit its applicability, and with the existing literature on the latter relying on static models for generation and demand, which is restrictive. We propose a novel control scheme that aims to overcome these issues by making use of generation measurements in the control policy. In particular, our controller relies on practical measurements and allows distributed stability and optimality guarantees to be deduced for a broad range of linear generation dynamics, that can be of higher order. We show how the controller parameters can be selected in a computationally efficient way by solving appropriate linear matrix inequalities (LMIs). Furthermore, we demonstrate how the proposed analysis applies to various examples of turbine governor dynamics by using realistic numerical data. The practicality of our analysis is demonstrated with numerical simulations on the Northeast Power Coordinating Council (NPCC) 140-bus system that verify that our proposed controller achieves convergence to the nominal frequency, an economically optimal power allocation, and improved performance compared to existing schemes used in the literature.