Model Order Reductions for Stability Analysis of Islanded Microgrids With Droop Control

Abstract

Abstract-Three-phase inverters subject to droop control are widely used in islanded microgrids to interface distributed energy resources to the network and to properly share the loads among different units. In this paper, a mathematical model for islanded microgrids with linear loads and inverters under frequency and voltage droop control is proposed. The model is constructed by introducing a suitable state space transformation which allows to write the closed loop model in an explicit state space form. Then, the singular perturbations technique is used to obtain reduced order models which reproduce the stability properties of the original closed loop model. The analysis shows that the currents dynamics influence the stability of the microgrid particularly for high values of the frequency droop control parameters. It is also shown that a further reduction of the model order leads to the typical oscillator model which is not able to predict the possible instability of the droop controlled system. Numerical and experimental results demonstrate the validity of the proposed models.

The Effect of Transmission-Line Dynamics on Grid-Forming Dispatchable Virtual Oscillator Control

“…As power inverters can be controlled at much faster time-scales (milliseconds), when more and more synchronous machines are replaced by inverter-based generation, the transmission line dynamics, which are typically not accounted for in the theoretical analysis, can compromise the stability of the powernetwork. For droop controlled microgrids this phenomenon has been noted in [2], [16] and it can be verified experimentally for all control methods listed above. Moreover, in [16], [17] explicit and insightful bounds on the control gains are obtained via small signal stability analysis for a steady state with zero relative angle.…”

High-Fidelity Model Order Reduction for Microgrids Stability Assessment

“…The importance of network dynamics despite its very fast nature was pointed out in [12] where a similar perturbation approach was used. In [13], the inadequacy of oversimplified models was further emphasized where it was explicitly shown that in certain situations, the full-order model predicts instability while the reduced-order (Kuramoto's) model predicts stability for a wide range of parameters. A model reduction technique based on singular perturbation theory was introduced in [14] allowing for proper exclusion of fast degrees of freedom, which is based on the formal summation of multiple orders of expansion in powers of small parameters (time scales ratio).…”

Global Phase and Magnitude Synchronization of Coupled Oscillators With Application to the Control of Grid-Forming Power Inverters

“…Remark 1 While the quasi-steady-state approximation (20) (also known as phasor approximation) of the transmission network is typically justified for conventional power systems, the electromagnetic transients of the transmission lines can compromise the stability of an inverter-based power system [41], [42]. Using results from singular perturbation analysis [43] our analysis can be extended to obtain stability guarantees that explicitly include the dynamics of transmission lines.…”