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

Babak Abdolmaleki, Gilbert Bergna-Diaz

TL;DR

The paper addresses real-time, constraint-aware steady-state optimization for MT-HVdc grids with multiple dc-GFM and ac-GFM interfaces. It derives a quasi-static input-output model $y = G_{ m red}u + w$ via Kron reduction and formulates a convex optimization with KKT conditions, then implements an online primal-dual controller to drive the system to an optimal steady state while respecting voltage and current limits. A key contribution is the online feedback optimization framework, including an event-triggered communication scheme that reduces data traffic without compromising performance, validated on an offshore MMC-based MT-HVdc grid for loss reduction and proportional current minimization. The results demonstrate robust convergence, constraint satisfaction, and significant reduction in communication load, offering a practical pathway to real-time, centralized secondary control in heterogeneous HVdc networks.

Abstract

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.

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

TL;DR

The paper addresses real-time, constraint-aware steady-state optimization for MT-HVdc grids with multiple dc-GFM and ac-GFM interfaces. It derives a quasi-static input-output model via Kron reduction and formulates a convex optimization with KKT conditions, then implements an online primal-dual controller to drive the system to an optimal steady state while respecting voltage and current limits. A key contribution is the online feedback optimization framework, including an event-triggered communication scheme that reduces data traffic without compromising performance, validated on an offshore MMC-based MT-HVdc grid for loss reduction and proportional current minimization. The results demonstrate robust convergence, constraint satisfaction, and significant reduction in communication load, offering a practical pathway to real-time, centralized secondary control in heterogeneous HVdc networks.

Abstract

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.

Paper Structure

This paper contains 20 sections, 1 theorem, 8 equations, 14 figures, 2 tables, 3 algorithms.

Table of Contents

  1. Introduction
  2. Background and Motivation
  3. Literature Review and Research Gaps
  4. Contributions
  5. Dynamic and Quasi-Static System Modelling
  6. System Dynamic Model
  7. Transmission Line Dynamics
  8. MMC Dynamics
  9. MMC Control System
  10. Quasi-Static Input-Output Model of MT-HVdc Grid
  11. Problem Statement and Optimality Conditions
  12. Proposed Central Secondary Control
  13. Optimal Steady-State Control with Primal-Dual Dynamics
  14. Convergence and Stability Analysis
  15. Reduction of Communication Traffic
  16. ...and 5 more sections

Key Result

Theorem 1

If the problem eq:Model-based_Program is convex, then under the primal-dual dynamics eq:PDD-eq:AlgebraicConstruction, the system eq:Input-OutputMap asymptotically converges to a steady state that is the optimal solution of eq:Model-based_Program.

Figures (14)

  • Figure 1: The test MT-HVdc grid based on MMC.
  • Figure 2: Cable model for dc transmission lines.
  • Figure 3: System-level dynamic model of an MMC Gilbert2018 and its control system.
  • Figure 4: The inner ac and zero-sequence circulating current control loops.
  • Figure 5: The ac grid-forming/dc grid-following (ac-GFM) outer control loops. This controller is applied to the offshore-connected MMC stations in Fig. \ref{['Fig:HVdcGrid']}
  • ...and 9 more figures

Theorems & Definitions (3)

  • Remark 1
  • Theorem 1
  • proof