Stability Analysis of a Nonlinear Distributed Control Framework for Current Sharing and Voltage Containment in DC Microgrids: The Fast Communication Scenario

TL;DR

The paper tackles stability in nonlinear distributed control for DC microgrids that must simultaneously share current proportionally and contain voltages within safe bounds. It develops a global exponential stability proof using singular perturbation theory with explicit time-scale separation between fast communication-based inner loops and slower electrical dynamics, supported by a composite Lyapunov analysis. The authors introduce a nonlinear leakage term and provide tuning guidelines, validating the approach through time-domain simulations and small-signal analysis under network reconfiguration and communication delays. The work demonstrates near-optimal steady-state operation under practical conditions, while highlighting trade-offs between stability guarantees and current-sharing accuracy, and outlines directions to relax time-scale requirements in future work.

Abstract

As renewable energy generation becomes increasingly integrated into electrical grids, there is a critical need for a paradigm shift toward control schemes that ensure safe, stable, and scalable operations. Hence, in this study, we explore the stability guarantees of a promising control proposal for cyber-physical DC microgrids (MGs), specifically designed to simultaneously achieve proportional current sharing and voltage containment within pre-specified limits. Our scalable stability result relies on singular perturbation theory to prove global exponential stability by imposing a sufficient time-scale separation at the border between the inner(decentralized) and outer(distributed) nested loops, and thus, ensuring that the system reaches the desired (optimal) steady state under appropriate tuning verifying some stability conditions. To prove the effectiveness of our method, our findings are supported by testing the control method in a time-domain simulation case study involving a low-voltage DC microgrid, as well as a small-signal stability analysis

Figures (7)

• Figure 1: DC microgrid
• Figure 2: Hyperbolic tangent functions
• Figure 3: Practical tuning guidelines
• Figure 4: Case-specific microgrid
• Figure 5: Simulation results for Case Study 1 (a)-(c) (first row), Case Study 2 (d)-(f) (second row), Case Study 3 (g)-(i) (third row); (a), (d), and (g) generators voltages; (b), (e), and (h) leakage function; (c), (f), and(i) integrations errors; Imposed load changes in Case Study 1 & 2: t=5: activation of distributed controller, $t=10: \mathrm{Inc.} G_1^\mathrm{cte} 45\%$, $t=17: \mathrm{Inc.} I_1^\mathrm{cte} 75\%$, $t=22: \mathrm{Inc.} G_2^\mathrm{cte} 500\%$ and $\mathrm{Inc.} I_1^\mathrm{cte} 800\%$, $t=24: \mathrm{Red.} I_4^\mathrm{cte} 35\%$, $t=28: \mathrm{Inc.} G_3^\mathrm{cte} 900\%$, $t=35: \mathrm{Red.} G_3^\mathrm{cte} 80\%$, $t=38: \mathrm{Red.} I_3^\mathrm{cte} 90\%$; Imposed disconnections in Case Study 1&2: $t\in[45,52]$ Disc. DG1, $t\in[60, 68]$ Disc. load 2,$t\in[75,83]$ Disc. TL between load 3 and 4; Imposed load changes in Case Study 3: $t=5:$ activation of distributed controller, $t=10: \mathrm{Inc.} I_1^\mathrm{cte} 50\%$, $t=17: \mathrm{Red.} I_4^\mathrm{cte} 13\%$, $t=20: \mathrm{Red.} G_1^\mathrm{cte} 40\%$, $t=24: \mathrm{Inc.} G_2^\mathrm{cte} 5\%$, $t=31: \mathrm{Inc.} G_3^\mathrm{cte} 17\%$, $t=37: \mathrm{Red.} I_3^\mathrm{cte} 45\%$, $t=38: \mathrm{Red.} G_3^\mathrm{cte} 7\%$; Imposed disconnections in Case Study 3: $t\in[45,52]$ Disc. DG1, $t\in[60, 68]$ Disc. TL between load 3 and 4

Theorems & Definitions (5)

• Lemma 1
• Remark 1
• Theorem 1
• proof
• Remark 2