High-Fidelity Model Order Reduction for Microgrids Stability Assessment

Abstract

Proper modeling of inverter-based microgrids is crucial for accurate assessment of stability boundaries. It has been recently realized that the stability conditions for such microgrids are significantly different from those known for largescale power systems. While detailed models are available, they are both computationally expensive and can not provide the insight into the instability mechanisms and factors. In this paper, a computationally efficient and accurate reduced-order model is proposed for modeling the inverter-based microgrids. The main factors affecting microgrid stability are analyzed using the developed reduced-order model and are shown to be unique for the microgrid-based network, which has no direct analogy to large-scale power systems. Particularly, it has been discovered that the stability limits for the conventional droop-based system (ω − P/V − Q) are determined by the ratio of inverter rating to network capacity, leading to a smaller stability region for microgrids with shorter lines. The theoretical derivation has been provided to verify the above investigation based on both the simplified and generalized network configurations. More importantly, the proposed reduced-order model not only maintains the modeling accuracy but also enhances the computation efficiency. Finally, the results are verified with the detailed model via both frequency and time domain analyses.

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.…”

Contraction and Robustness of Continuous Time Primal-Dual Dynamics

“…Furthermore, saddlenode dynamics also appear naturally in Brayton-Moser potentials [27], [28], which suggests an additional path for future research. Application-wise, we plan to explore the effect of inductive line delays [28], [29], on the performance of secondary controls [5] in microgrids.…”

“…Hence, whenever η k τ k+1 ρ k+1 < 1 we have Next, as long as the system f k is contracting, we have z k − z k ≤ ( ż k + d k ) /β k . Using (29), assuming ξ k < β k (1 − η k τ k+1 ρ k+1 ), we arrive at (28).…”

Frequency Stability of Synchronous Machines and Grid-Forming Power Converters

“…We model the lines via nominal π sections (i.e., with RLC dynamics), model the transformers via three-phase linear transformer models, and consider constant impedance loads (see Table I for the parameters). We emphasize that the line dynamics cannot be neglected in the presence of grid-forming converters due to potential adverse interactions between their fast response and the line dynamics [16], [24], [29].…”

“…While the synchronous machine perfectly meets classic power system control objectives on slower time scales, the dominant feature of GFCs is their fast response. However, the fast response of GFCs can also result in unforeseen interactions with other parts of the system such as the slow SM response (shown here), line dynamics (see [16], [29]), and line limits [43].…”