Passivation of Clustered DC Microgrids with Non-Monotone Loads

TL;DR

This work tackles voltage stability in DC microgrids with non-monotone ZIP loads and partial steady-state power by formulating clusters containing voltage-setting and voltage-following buses. It introduces decentralized controllers that render each cluster output strictly equilibrium independent passive (OS-EIP) and provides LMIs to verify this property, with a reduced-order variant obtained through singular perturbation theory for robustness. The approach ensures asymptotic stability of interconnected clusters and the overall microgrid, even under parameter variations and topology changes, by exploiting passivity and Laplacian structure. Simulations on a 21-bus network demonstrate voltage regulation at setting buses, transient damping at following buses, and bounded energy needs, validating practical applicability and robustness of the proposed framework.

Abstract

In this paper, we consider the problem of voltage stability in DC networks containing uncertain loads with non-monotone incremental impedances and where the steady-state power availability is restricted to a subset of the buses in the network. We propose controllers for powered buses that guarantee voltage regulation and output strictly equilibrium independent passivity (OS-EIP) of the controlled buses, while buses without power are equipped with controllers that dampen their transient behaviour. The OS-EIP of a cluster containing both bus types is verified through a linear matrix inequality (LMI) condition, and the asymptotic stability of the overall microgrid with uncertain, non-monotone loads is ensured by interconnecting the OS-EIP clusters. By further employing singular perturbation theory, we show that the OS-EIP property of the clusters is robust against certain network parameter and topology changes.

Figures (9)

• Figure 1: A bus comprising a DC-DC buck converter, an LC filter and a nonlinear load, which connects to a $\pi$-model transmission line (blue). Each bus is equipped with a voltage setting controller ($j \in \mathcal{S}_{}$) or a voltage following controller ($k \in \mathcal{F}_{}$).
• Figure 2: A 21-bus DC microgrid partitioned into four clusters. Each cluster comprises buses with voltage setting controllers in $\mathcal{S}_{}$, buses with voltage following controllers in $\mathcal{F}_{}$, and lines with arbitrary directions in $\mathcal{E}_{}$. Lines in $\mathcal{T}_{}$ interconnect buses in different clusters.
• Figure 3: A nonlinear ZIP load (blue) which is separated into a linear function (purple) and a monotone increasing nonlinear function (orange).
• Figure 4: Simulated line current and bus voltage for a transmission line connecting a bus with a static P load and a voltage following controller \ref{['eq:Control:Voltage_following']} to a ideal voltage supply, (a) shows the trajectories over time and (b) plots the bus voltage vs. the line current.
• Figure 5: Interconnection of the clusters with the external lines and the monotone load functions.

Theorems & Definitions (47)

• Definition 1: Dissipative system, See vdSchaft2017Arcak2006
• Definition 2: ZSO, ZSD vdSchaft2017
• Definition 3: EIP
• Remark 1
• Remark 2
• Remark 3
• Remark 4
• Remark 5
• Proposition 4
• proof