arXiv subjects

Gilbert Bergna-Diaz

Publications and source records attributed to Gilbert Bergna-Diaz.

8 recordsLinked to original sources

arXiv2026

Large-Signal Stability Guarantees for a DC Microgrid with Nested Nonlinear Distributed Control: The Slow Communication Scenario

The increasing integration of renewable energy sources into electrical grids necessitates a paradigm shift toward advanced control schemes that guarantee safe and stable operations with scalable properties. Accordingly, this paper investigates large-signal stability guarantees for cyber-physical DC microgrids employing a nonlinear distributed consensus-based control scheme to enable coordinated integration and management of distributed generation units within an expandable framework. The proposed control framework adopts nested control loops; inner (decentralized) and outer (distributed), specifically designed to simultaneously achieve uniform voltage containment within pre-specified limits, and proportional current sharing in steady state. Our scalable stability result relies on singular perturbation theory and Lyapunov arguments to prove global exponential stability when imposing a sufficient time-scale separation at the border between the nested control loops, while relying on some practical parameter-setting schemes. The effectiveness and versatility of the proposed control strategy are then validated through time-domain simulations performed on a case-specific low-voltage DC microgrid and the modified IEEE 33-bus radial distribution system. Moreover, a small-signal stability analysis is conducted to derive practical guidelines that enhance the applicability of the method.

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arXiv2026

Stability of a DC Microgrid with a Nonlinear Nested Control Framework: The Fast Communication Scenario

As modern power systems continue to evolve into multi-agent, converter-dominated systems that demand reliable, stable, and optimal control architectures within an expandable framework, this paper investigates scalable stability guarantees of a promising nonlinear communication-reliant control framework for DC microgrids. Particularly, relying on nested control loops; inner decentralized(primary) and outer distributed(secondary), the control configurations are designed to simultaneously achieve proportional current sharing and voltage containment within pre-specified limits, at the converged steady state. By enforcing sufficient time-scale separation at the boarder between the control loops, the system admits a singular perturbation formulation, allowing global exponential stability (G.E.S.) to be established via Lyapunov arguments. Although the theoretical G.E.S. certificate is structurally scalable, the stability guarantees depends on a sufficiently large permanent leakage, introduced in the primary controller. Thus, the results of this paper emphasize the importance of appropriate practical tuning guidelines and electrical parameter selection. The effectiveness of the proposed method is validated through case studies on a low-voltage DC microgrid under load variations and topological changes (and communication time-delays), followed by a small-signal stability analysis.

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arXiv2026

DC Microgrids with Nested Nonlinear Distributed Control: Scalable Large-Signal Stability and Voltage Containment

This paper investigates a cyber-physical DC microgrid employing a nonlinear distributed consensus-based control scheme for coordinated integration and management of distributed generating units within an expandable framework. Relying on nested primary andsecondary control loops; a (distributed) outer-loop and a (decentralized) inner-loop, the controller achieves proportional current sharing among all distributed generation units, while dynamically operating within predefined voltage limits. A rigorous Lyapunov-based stability analysis establishes a scalable global exponential stability certificate under some tuning conditions and sufficient time-scale separation between the control loops, based on singular perturbation theory. An optimization-based tuning strategy is then formulated to identify and subsequently diminish unstable operating conditions. In turn, various practical tuning strategies are introduced to provide stable operations while facilitating near-optimal proportional current sharing. The effectiveness of the proposed control framework and tuning approaches are finally supported through time-domain simulations of a case-specific low-voltage DC microgrid.

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arXiv2025

Optimal Steady-State Secondary Control of MT-HVdc Grids with Reduced Communications

In this paper, we propose a centralized secondary control for the real-time steady-state optimization of multi-terminal HVdc grids under voltage and current limits. First, we present the dynamic models of the grid components, including the modular multilevel converter (MMC) stations and their different control layers. We also derive the quasi-static input-output model of the system, which is suitable for the steady-state control design. Second, we formulate a general optimization problem using this quasi-static model and find the Karush-Kuhn-Tucker optimality conditions of its solutions. Third, we propose a secondary control based on primal-dual dynamics to adjust the voltage setpoints of the dispatchable MMCs, with which the system asymptotically converges to a steady state that satisfies these optimality conditions. Fourth, we provide a communication triggering mechanism to reduce the communication traffic between the secondary control unit and the MMC stations. Finally, we verify our proposal for different case studies by adapting it to an offshore multi-terminal HVdc grid composed of heterogeneous MMC stations simulated in the MATLAB/Simulink environment. The problems of proportional current minimization and loss reduction are two special case studies.

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arXiv2023

Distributed Optimization for Reactive Power Sharing and Stability of Inverter-Based Resources Under Voltage Limits

Reactive power sharing and containment of voltages within limits for inverter-based resources (IBRs) are two important, yet coupled objectives in ac networks. In this article, we propose a distributed control technique to simultaneously achieve these objectives. Our controller consists of two components: a purely local nonlinear integral controller which adjusts the IBR voltage setpoint, and a distributed primal-dual optimizer that coordinates reactive power sharing between the IBRs. The controller prioritizes the voltage containment objective over reactive power sharing at all points in time; excluding the IBRs with saturated voltages, it provides reactive power sharing among all the IBRs. Considering the voltage saturation and the coupling between voltage and angle dynamics, a formal closed-loop stability analysis based on singular perturbation theory is provided, yielding practical tuning guidance for the overall control system. To validate the effectiveness of the proposed controller for different case studies, we apply it to a low-voltage microgrid and a microgrid adapted from the CIGRE medium-voltage network benchmark, both simulated in the MATLAB/Simulink environment.

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arXiv2021

PID passivity-based droop control of power converters: Large-signal stability, robustness and performance

We present a full review of PID passivity-based controllers (PBC) applied to power electronic converters, discussing limitations, unprecedented merits and potential improvements in terms of large-signal stability, robustness and performance. We provide four main contributions. The nominal case is first considered and it is shown, under the assumption of perfect knowledge of the system parameters, that the PID-PBC is able to guarantee global exponential stability of a desired operating point for any positive gains. Second, we analyze robustness of the controller to parameters uncertainty for a specific class of power converters, by establishing precise stability margins. Third, we propose a modification of the controller by introducing a leakage, in order to overcome some of the intrinsic performance and robustness limitations. Interestingly, such controller can be interpreted at steady-state as a droop between the input and the passive output, similar to traditional primary controllers. Fourth, we robustify the design against saturation of the control input via an appropriate monotone transformation of the controller. The obtained results are thoroughly discussed and validated by simulations on two relevant power applications: a dc/dc boost converter and an HVDC grid-connected voltage source converter.

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arXiv2021

Distributed Control and Optimization of DC Microgrids: A Port-Hamiltonian Approach

This article proposes a distributed secondary control scheme that drives a dc microgrid to an equilibrium point where the generators share optimal currents, and their voltages have a weighted average of nominal value. The scheme does not rely on the electric system topology nor its specifications; it guarantees plug-and-play design and functionality of the generators. First, the incremental model of the microgrid system with constant impedance, current, and power devices is shown to admit a port-Hamiltonian (pH) representation, and its passive output is determined. The economic dispatch problem is then solved by the Lagrange multipliers method; the Karush-Kuhn-Tucker conditions and weighted average formation of voltages are then formulated as the control objectives. We propose a control scheme that is based on the Control by Interconnection design philosophy, where the consensus-based controller is viewed as a virtual pH system to be interconnected with the physical one. We prove the regional asymptotic stability of the closed-loop system using Lyapunov and LaSalle theorems. Equilibrium analysis is also conducted based on the concepts of graph theory and economic dispatch. Finally, the effectiveness of the presented scheme for different case studies is validated with a test microgrid system, simulated in both MATLAB/Simulink and OPAL-RT environments.

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arXiv2017

Generalized Voltage-based State-Space Modelling of Modular Multilevel Converters with Constant Equilibrium in Steady-State

This paper demonstrates that the sum and difference of the upper and lower arm voltages are suitable variables for deriving a generalized state-space model of an MMC which settles at a constant equilibrium in steady-state operation, while including the internal voltage and current dynamics. The presented modelling approach allows for separating the multiple frequency components appearing within the MMC as a first step of the model derivation, to avoid variables containing multiple frequency components in steady-state. On this basis, it is shown that Park transformations at three different frequencies ($+ω$, $-2ω$ and $+3ω$) can be applied for deriving a model formulation where all state-variables will settle at constant values in steady-state, corresponding to an equilibrium point of the model. The resulting model is accurately capturing the internal current and voltage dynamics of a three-phase MMC, independently from how the control system is implemented. The main advantage of this model formulation is that it can be linearised, allowing for eigenvalue-based analysis of the MMC dynamics. Furthermore, the model can be utilized for control system design by multi-variable methods requiring any stable equilibrium to be defined by a fixed operating point. Time-domain simulations in comparison to an established average model of the MMC, as well as results from a detailed simulation model of an MMC with 400 sub-modules per arm, are presented as verification of the validity and accuracy of the developed model.

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