Distributed Frequency Regulation for Heterogeneous Microgrids via Steady State Optimal Control

Distributed Frequency and Voltage Control for AC Microgrids based on Primal-Dual Gradient Dynamics

“…To prove that x p fulfills (30a), we first recall that for each equilibrium of ( 14) it holds that ω = 0 (cf. Proposition 1 in Kölsch et al (2019b)). Accordingly, ( 5) and ( 7) can be written as 33) is equivalent to (30a) if and only if there exists a ν ∈ R mc with D c ν = φ.…”

“…The dynamics of the individual generator, inverter and load nodes are modeled by the following descriptor system, cf. Kölsch et al (2019b):…”

“…The positive definiteness condition is satisfied locally due to Assumption 2. To investigate (53), with the same reasoning as in Kölsch et al (2019b), for constant disturbance input d , ( 14) can be expressed in the form…”

“…In particular, no communication of superordinate set points by a higher-level authority is necessary. The controller design is based on a nonlinear port-Hamiltonian model for AC microgrids (Kölsch et al (2019b)) and allows for a distributed implementation. The remainder of the paper is structured as follows.…”

“…The remainder of the paper is structured as follows. After some notational preliminaries, in section 2, we briefly recall the underlying microgrid model from Kölsch et al (2019b) and then formalize the requirements for the desired closedloop equilibrium. In section 3, we derive a price-based controller for frequency and voltage regulation that meets the previously formulated requirements.…”