Spatiotemporal Model Reduction of Inverter-Based Islanded Microgrids

Abstract

Computationally efficient and scalable models that describe droop-controlled inverter dynamics are key to modeling, analysis, and control in islanded microgrids. Typical models developed from first principles in this domain describe detailed dynamics of the power electronics inverters, as well as the network interactions. Consequently, these models are very involved; they offer limited analytical insights and are computationally expensive when applied to investigate the dynamics of large microgrids with many inverters. This calls for the development of reduced-order models that capture the relevant dynamics of higher order models with a lower dimensional state space while not compromising modeling fidelity. To this end, this paper proposes model-reduction methods based on singular perturbation and Kron reduction to reduce large-signal dynamic models of inverter-based islanded microgrids in temporal and spatial aspects, respectively. The reduced-order models are tested in a modified IEEE 37-bus system and verified to accurately describe the original dynamics with lower computational burden. In addition, we demonstrate that Kron reduction isolates the mutual inverter interactions and the equivalent loads that the inverters have to support in the microgrid-this aspect is leveraged in the systematic selection of droop coefficients to minimize power losses and voltage deviations.

Reduced-Order Small-Signal Model of Microgrid Systems

“…The inverter output powers and the states from the current controllers are more sensitive to perturbation than other slow states in the system. This shows that the method developed in [22] is not generic and cannot be applied to a system such as the one proposed in this paper.…”

“…The standard IEEE-37 bus is modified by adding seven inverters in seven different nodes. Details of the modified system including the load and line parameters are given in [22]. The modified system's one-line diagram is shown in Fig.…”

“…The IEEE-37 bus is modified for islanded microgrid application. The system load and line parameters are given in [22]. There are seven inverters at seven different buses as shown in Fig.…”

“…Related to this work, singular perturbation method was applied in [22]. The inverter model used in that paper excluded the filter capacitors.…”

Design of optimal coupling gains for synchronization of nonlinear oscillators

“…For the simulations that follow, we pick α = 0.90, β = 4, ω = 2π60 rad/s, ε = 0.19; conductances of the lines in the IEEE-37-bus network are sourced from [27]. Fig.…”