Steady-State Optimal Frequency Control for Lossy Power Grids with Distributed Communication

Abstract

We present a distributed and price-based control approach for frequency regulation in power grids with nonzero line conductances. Both grid and controller are modeled as a port-Hamiltonian system, where the grid model consists of differential as well as algebraic equations. Simulations show that the resulting controller asymptotically stabilizes the frequency while maintaining minimum overall generation costs in steady state and being robust in terms of clock drifts and uncontrollable loads. Moreover, it is shown that active power sharing can be achieved by an appropriate choice of the cost function.

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

“…The parameter values for all nodes, listed in Tables 2-4, are based on Trip et al (2016) and Kölsch et al (2019a), whereby the "virtual" moments of inertia of inverter nodes were selected to be considerably smaller than the corresponding moments of inertia of generator nodes. All values are given in p.u.…”

“…The voltage limits are set to [0.98 1.02] and the upper bound for active power generation is set to 0.6. We choose D c to be identical to the plant incidence matrix D p after it has been pointed out in Kölsch et al (2019a) that the specific choice of D c has little influence on the convergence speed to the desired equilibrium. The initial values of disturbance input vector d = col{p , q } and state vector x = col{x p , ξ 1 , ξ 2 } are chosen such that the closed-loop system starts in synchronous mode with ω(t = 0) = 0 and such that a number of voltage magnitudes are already close to or at their limits of 0. state, regardless of the total generation, thus active power sharing is given.…”

Distributed Frequency Regulation for Heterogeneous Microgrids via Steady State Optimal Control

“…For this reason, steady state optimal control by real-time dynamic pricing poses an advantageous control concept especially for large scale networks, since it enables communication of network imbalances via a price signal, see [5] for a survey on current research directions regarding frequency regulation. This kind of controller features a distributed architecture for frequency restoration based on neighbor-to-neighbor communication and local measurements which is able to reach a desired economic optimum at steady state and thus provides a unifying approach incorporating all three control layers [6]. A common assumption made in previous publications on dynamic pricing methods for frequency regulation, e.g.…”

“…[7], is that all power lines are lossless, which is in fact an incorrect assumption especially for medium and low voltage grids. Practically, if controllers like the one proposed in [7] are used, a synchronous frequency ω is achieved which deviates from the nominal frequency ω n [6].…”

“…synchronous generators for conventional power plants as well as inverters for renewable sources. The controller design is based on [7], [8] and our previous work [6] by integrating an inverter model based on [9] in the underlying microgrid model. Both system and controller are represented as a port-Hamiltonian system, which results in a closed-loop system that is again port-Hamiltonian.…”