Johannes Schiffer

Conditions for stability of droop-controlled inverter-based microgrids

We consider the problem of stability analysis for droop-controlled inverter-based microgrids with meshed topologies. The inverter models include variable frequencies as well as voltage amplitudes. Conditions on the tuning gains and setpoints for frequency and voltage stability, together with desired active power sharing, are derived in the paper. First, we prove that for all practical choices of these parameters global boundedness of trajectories is ensured. Subsequently, assuming the microgrid is lossless, a port-Hamiltonian description is derived, from which sufficient conditions for stability are given. Finally, we propose for generic lossy microgrids a design criterion for the controller gains and setpoints such that a desired steady-state active power distribution is achieved. The analysis is validated via simulation on a microgrid based on the CIGRE (Conseil International des Grands Reseaux Electriques) benchmark medium voltage distribution network.

Voltage Stability and Reactive Power Sharing in Inverter-Based Microgrids With Consensus-Based Distributed Voltage Control

We propose a consensus-based distributed voltage control (DVC) that solves the problem of reactive power sharing in autonomous inverter-based microgrids with dominantly inductive power lines and arbitrary electrical topology. Opposed to other control strategies available thus far, the control presented here does guarantee a desired reactive power distribution in steady state while only requiring distributed communication among inverters, i.e., no central computing nor communication unit is needed. For inductive impedance loads and under the assumption of small phase angle differences between the output voltages of the inverters, we prove that the choice of the control parameters uniquely determines the corresponding equilibrium point of the closed-loop voltage and reactive power dynamics. In addition, for the case of uniform time constants of the power measurement filters, a necessary and sufficient condition for local exponential stability of that equilibrium point is given. The compatibility of the DVC with the usual frequency droop control for inverters is shown and the performance of the proposed DVC is compared with the usual voltage droop control via simulation of a microgrid based on the Conseil International des Grands Réseaux Electriques (CIGRE) benchmark medium voltage distribution network.

Synchronization of droop-controlled microgrids with distributed rotational and electronic generation

We consider the problem of frequency synchronization and power sharing in a lossy droop-controlled autonomous microgrid with distributed rotational and electronic generation (MDREG). At first, we establish equivalence of the dynamics of a regulated synchronous generator and a droop-controlled inverter with low pass filter. We then give a necessary and sufficient condition for local synchronization of the microgrid by using ideas from graph theory and second order consensus algorithms. In addition, we show that sources in an MDREG can achieve a desired active power distribution via frequency droop control and provide synchronization conditions for a lossless microgrid as a special case. Our analysis is further validated via a simulation example of a lossy microgrid based on the CIGRE benchmark medium voltage distribution network.

A survey on modeling of microgrids-From fundamental physics to phasors and voltage sources

Microgrids are an increasingly popular class of electrical systems that facilitate the integration of renewable distributed generation units. Their analysis and controller design requires the development of advanced (typically model-based) techniques naturally posing an interesting challenge to the control community. Although there are widely accepted reduced order models to describe the dynamic behavior of microgrids, they are typically presented without details about the reduction procedure|hampering the understanding of the physical phenomena behind them. The present paper aims to provide a complete modular model derivation of a three-phase inverter-based microgrid. Starting from fundamental physics, we present detailed dynamical models of the main microgrid components and clearly state the underlying assumptions which lead to the standard reduced model representation with inverters represented as controllable voltage sources, as well as static network interconnections and loads.

On power sharing and stability in autonomous inverter-based microgrids

We consider the problem of voltage and frequency stability for an autonomous inverter-based microgrid. An LMI-based decentralized feedback control design is derived that stabilizes the system under the consideration of droop-like controllers aiming to achieve power sharing among the different generation units. We provide a design procedure that accounts for uncertainties in line impedances and loads while guaranteeing zero steady-state frequency deviation.

A consensus-based distributed voltage control for reactive power sharing in microgrids

We propose a consensus-based distributed voltage control (DVC), which solves the problem of reactive power sharing in autonomous meshed inverter-based microgrids with inductive power lines. Opposed to other control strategies available thus far, the DVC does guarantee reactive power sharing in steady-state while only requiring distributed communication among inverters, i.e. no central computing nor communication unit is needed. Moreover, we provide a necessary and sufficient condition for local exponential stability. In addition, the performance of the proposed control is compared to the usual voltage droop control [1] in a simulation example based on the CIGRE benchmark medium voltage distribution network.

Precise robot motions using dual motor control

High motion performance, stiffness, and accuracy are crucial for industrial robot applications, but these requirements are in practice contradictory. Using a novel type of robot, the so called Gantry Tau, new combinations of stiffness and accuracy are in principle possible, except for the backlash in the drive-trains of each joint.

Droop-controlled inverter-based microgrids are robust to clock drifts

Clock drift in digital controllers is of great relevance in many applications. Since almost all real clocks exhibit drifts, this applies in particular to networks composed of several individual units, each of which being operated with its individual clock. In the present work, we investigate the effect of clock drifts in inverter-based microgrids. Via a suitable model that incorporates this phenomenon, we prove that clock inaccuracies hamper synchronization in microgrids, in which the individual inverters are operated with a fixed uniform constant electrical frequency. In addition, we show that the well-known frequency droop control renders stability of a lossless microgrid robust with respect to clock inaccuracies. This claim is established by using stability results reported previously by the authors for lossless inverter-based microgrids with ideal clocks. We also discuss the effect of clock drifts on active power sharing. The analysis is illustrated via a simulation example.

On stability of a distributed averaging PI frequency and active power controlled differential-algebraic power system model

We consider the problems of stability, frequency restoration and optimal steady-state resource allocation in a heterogeneous and structure-preserving differential-algebraic equation (DAE) power system model. Thereby, we include constant-power-controlled loads (CPCLs) and constant-power-controlled sources (CPCSs) explicitly in the analysis and network control design. This results in a power system model with mixed algebraic as well as first- and second-order differential dynamics. We show that the abovementioned control objectives can be achieved via a distributed averaging proportional integral (DAPI) control and, in particular, extend the stability proof in [1] to the resulting closed-loop DAE system.

A Lyapunov approach to control of microgrids with a network-preserved differential-algebraic model

We provide sufficient conditions for asymptotic stability and optimal resource allocation for a network-preserved microgrid model with active and reactive power loads. The model considers explicitly the presence of constant-power loads as well as the coupling between the phase angle and voltage dynamics. The analysis of the resulting nonlinear differential algebraic equation (DAE) system is conducted by leveraging incremental Lyapunov functions, definiteness of the load flow Jacobian and the implicit function theorem.