An internal model approach to (optimal) frequency regulation in power grids with time-varying voltages

Abstract

This paper studies the problem of frequency regulation in power grids under unknown and possible time-varying load changes, while minimizing the generation costs. We formulate this problem as an output agreement problem for distribution networks and address it using incremental passivity and distributed internal-model-based controllers. Incremental passivity enables a systematic approach to study convergence to the steady state with zero frequency deviation and to design the controller in the presence of time-varying voltages, whereas the internal-model principle is applied to tackle the uncertain nature of the loads.

A modular design of incremental Lyapunov functions for microgrid control with power sharing

“…Similar to [38,Remark 5] it can be shown that if the assumption above is satisfied then necessarily V ∈ R N >0 . Furthermore, in case the network is a tree, it is easy to observe that (52) is satisfied if and only if there exists V ∈ R N >0 such that…”

“…Another way, is to express the dynamics of the system using directly (η, ω, V ) variables, similarly as in [38]. However, we do not adopt this approach here in order to better contrast our results with others in the literature on oscillator synchronization that are mostly working with (θ, ω, V ) coordinates [14], [32], [27], [20].…”

“…Observe that, by setting u Q = u Q and bearing in mind (38), the equalities (31), (33), (35) and (34) can be written in a unified manner as…”

A relaxed characterization of ISS for periodic systems with multiple invariant sets

“…evolve on the circle), the corresponding Lyapunov function of [3], [4] has also to be periodic, which is a severe requirement. Paramount examples of such systems are the forced nonlinear pendulum [17], [19], power systems [32], [35], [43], [44], microgrids [36], [42], phase-locked loops [25], [26], and complex networks of oscillators [40], [12], [41].…”

Optimal power dispatch in networks of high-dimensional models of synchronous machines

“…in [14]. However, the swing equations are inaccurate and only valid on a specific time scale up to the order of a few seconds so that asymptotic stability results are often invalid for the actual system [2], [6], [8].…”