Synchronization and Power Sharing for Droop-Controlled Inverters in Islanded Microgrids (1206.5033v3)

Abstract: Motivated by the recent and growing interest in smart grid technology, we study the operation of DC/AC inverters in an inductive microgrid. We show that a network of loads and DC/AC inverters equipped with power-frequency droop controllers can be cast as a Kuramoto model of phase-coupled oscillators. This novel description, together with results from the theory of coupled oscillators, allows us to characterize the behavior of the network of inverters and loads. Specifically, we provide a necessary and sufficient condition for the existence of a synchronized solution that is unique and locally exponentially stable. We present a selection of controller gains leading to a desirable sharing of power among the inverters, and specify the set of loads which can be serviced without violating given actuation constraints. Moreover, we propose a distributed integral controller based on averaging algorithms which dynamically regulates the system frequency in the presence of a time-varying load. Remarkably, this distributed-averaging integral controller has the additional property that it maintains the power sharing properties of the primary droop controller. Our results hold without assumptions on identical line characteristics or voltage magnitudes.

• The paper derives necessary and sufficient synchronization conditions for droop-controlled inverters using the Kuramoto model.
• It establishes proportional power sharing by selecting droop coefficients relative to inverter ratings and provides bounds to prevent overload.
• The study introduces a robust distributed integral controller to restore nominal frequency and enhance system resilience under dynamic conditions.

Synchronization and Power Sharing for Droop-Controlled Inverters in Islanded Microgrids

The paper "Synchronization and Power Sharing for Droop-Controlled Inverters in Islanded Microgrids" by John W. Simpson-Porco, Florian Dörfler, and Francesco Bullo addresses the challenges and dynamics associated with the operation of DC/AC inverters in an isolated microgrid environment. The authors leverage insights from the theory of coupled oscillators to characterize the network behavior of such inverters and propose novel control strategies that ensure desired performance in power sharing and synchronization.

Key Contributions

Kuramoto Model and Synchronization Criteria

A significant theoretical contribution of the paper is the modeling of a network of droop-controlled inverters as a Kuramoto model of phase-coupled oscillators. This mathematical representation enables the application of established results from oscillator synchronization theory to the microgrid context. The authors derive necessary and sufficient conditions for the existence and local exponential stability of a synchronized state. The core synchronization criterion, derived from this model, states that synchronization is achieved if the normalized load power is feasible, characterized by the relationship $\|\mathrm{diag}(\{a_{ij}\}_{\{i,j\}\in\mathcal{E})^{-1}\xi\|_{\infty} < 1$. This criterion is both intuitive and practically significant, offering a clear physical interpretation related to the maximum allowable active power flow through each line.

Power Sharing and Actuation Constraints

The paper explores the parameters necessary to share power proportionally among inverters, asserting that if droop coefficients are selected proportionally to the power ratings of the inverters, then proportional power sharing is naturally achieved. This is formalized as the condition $P_i^*/D_i = P_j^*/D_j$ and $P_i^*/\overline{P}_i = P_j^*/\overline{P}_j$ for all inverters $i,j$. Additionally, the authors provide explicit bounds on loads that ensure that no inverter exceeds its rated power capacity, thus maintaining the safe and stable operation of the network.

Distributed Integral Control

To dynamically manage the system frequency in response to fluctuating loads, they introduce a distributed integral controller based on averaging algorithms. Specifically, the proposed distributed-averaging proportional-integral (DAPI) control has the dual advantage of restoring the network to the nominal frequency while preserving the foundational power sharing properties enabled by primary droop control. The controller does not rely on a time-scale separation between primary droop control and secondary integral correction, enabling a more robust and responsive control strategy under dynamic conditions.

Practical and Theoretical Implications

The theoretical advancements presented in this paper have substantial practical implications. By facilitating synchronization and efficient power sharing without the need for centralized control, the proposed droop and DAPI controls bolster the robustness and resilience of microgrids. This enhanced stability is crucial in islanded operation scenarios where microgrids must operate autonomously and resiliently without relying on external grids.

Moreover, the robustified stability condition underscores the applicability of the presented approach even in the face of parameter uncertainties, such as variations in line susceptances or voltage magnitudes. This robustness makes the control strategies particularly suitable for real-world applications where precise parameter knowledge may not always be feasible.

Future Directions

The results presented in this paper pave the way for several future research directions. Notably, the authors highlight the need for further exploration into reactive power sharing, particularly under non-ideal conditions where inductive approximations of lines may not hold. Extending the nonlinear analysis to include general interconnections and mixed line conditions would significantly broaden the applicability of the proposed methods. Additionally, investigating control strategies that can seamlessly integrate both active and reactive power management in a unified framework is a fertile ground for future work.

The integration of stronger synchronization and power sharing principles into the evolving landscape of smart grid technology will likely catalyze the development of even more advanced and reliable microgrid systems, contributing to the overall stability and efficiency of modern power networks.