Optimal Linear Controller for Minimizing DC Voltage Oscillations in MMC-Based Offshore Multiterminal HVDC Grids

Abstract

The paper aims at minimizing DC voltage oscillations in offshore multiterminal highvoltage direct current (HVDC) grids based on modular multilevel converters (MMCs). The DC voltage stability is a crucial factor in multiterminal HVDC networks since it is associated with the grid power balance. Furthermore, DC voltage oscillations can cause the propagation of significant disturbances to the interconnected AC grids. This paper proposes an optimal control technique based on semidefinite programming to improve the DC voltage stability margins under the worst-case perturbation scenario. A centralized optimal linear feedback controller is introduced to achieve this goal while ensuring compliance with the control inputs' and state variables' constraints. Furthermore, the methodology is adapted to develop a decentralized optimal linear feedback controller with naturally decoupled constraints on the control inputs and state variables. It is shown that the proposed centralized and decentralized optimal linear controllers can minimize the DC voltage oscillations under the worst-case perturbation scenario in the presence or absence of the droop control gain. The performance of these controllers is verified via eigenvalue stability analysis and time-domain simulations of the MMC-based four-terminal HVDC test grid. Finally, a DC voltage oscillation index is introduced as a potential decision-support criterion. Its applicability is exemplified by identifying, among several options, the HVDC link that gives minimum DC voltage oscillations between independent point-to-point networks while considering the wind intermittency effect.INDEX TERMS DC voltage oscillations, modular multilevel converter, offshore multiterminal HVDC grid, centralized and decentralized optimal linear feedback controller

Stability improvement of MMC‐based hybrid AC/DC grids through the application of a decentralized optimal controller

“…Since the above optimization problem (15)–(20) is non‐convex in its objective and constraints, it is not straightforward to obtain its optimal solution. However, as shown in [23], it is possible to approximate it as a convex SDP problem using the Lyapunov stability and LMI theories such that $$ J_{osci}\le \tilde{J}_{osci}$$: $$\begin{eqnarray} \frac{1}{\tilde{J}_{osci}}=\max _{s_{i}>0,\,Q_{i}>0,\,\bm {Y},\,w,\,y_{i}} w \end{eqnarray}$$ $$\begin{eqnarray} {\rm s.t.} \def\eqcellsep{&}\begin{bmatrix} (\bm {AQ}+\bm {BY})+(\bm {AQ}+\bm {BY})^T & \bm {QC^T}\\[6pt] \bm {CQ} & -I \end{bmatrix}\le 0,\end{eqnarray}$$ $$\begin{eqnarray} \def\eqcellsep{&}\begin{b...$$…”

“…x corresponding to its largest eigenvalue. The interested reader is referred to [23] for more details on definitions and derivations of ( 31)-(37) since they are not the main focus of the paper.…”

“…We adapted the methodology to our objective to minimize the DC voltage oscillations in MMC-based multiterminal HVDC grids [23,31]. Furthermore, the centralized optimal controller was developed to be decentralized or block-diagonal to match the grid sparsity pattern and eliminate the communication over long distances between converter stations.…”

“…Since the above optimization problem ( 15)-( 20) is nonconvex in its objective and constraints, it is not straightforward to obtain its optimal solution. However, as shown in [23], it is possible to approximate it as a convex SDP problem using the Lyapunov stability and LMI theories such that J osci ≤ Josci :…”

“…We have initially proposed an analytical methodology to derive a decentralized optimal controller with constraints on the grid control inputs and state variables, under the worst‐case perturbation scenario, to minimize the DC voltage oscillations in MMC‐based offshore multiterminal HVDC grids [23]. The optimization problem formulation is inspired by [24], in which the goal was to minimize the generator frequency deviations in AC grids using a centralized optimal controller.…”