This paper introduces a control induced time-scale separation scheme for a multiterminal high-voltage direct current system used for large scale integration of renewable energy sources. The main idea is to provide a detailed theoretical analysis to the long stand practice that consists of the empirical design of two control loops for the terminals. Experience has shown that such loops, i.e., current and voltage control loops, when heuristically tuned, often display very different dynamics. In this paper, singular perturbation theory is applied to give explanation and fundamental analysis on why and how the two control loops work and how to achieve the timescale separation between various state variables. Mathematical analysis is also carried out to illustrate a clear tradeoff between system performance (actuator constraint) and the size of the region of attraction of the controller. Numerical simulations for a system with four terminals are presented to evaluate the system performance and illustrate the theoretical analysis.

中文翻译：

---

使用下垂控制的多端子高压直流系统的控制引起的时标分离

本文介绍了一种用于大规模集成可再生能源的多端子高压直流系统的控制感应时标分离方案。主要思想是为长期使用的实践提供详细的理论分析，其中包括端子的两个控制回路的经验设计。经验表明，这种回路（即电流和电压控制回路）在进行启发式调整时通常会显示出截然不同的动态特性。本文采用奇异摄动理论对两个控制回路的工作原理和原因以及如何实现各个状态变量之间的时标分离进行解释和基础分析。还进行了数学分析，以说明系统性能（执行器约束）与控制器吸引区域大小之间的明显权衡。提出了具有四个端子的系统的数值仿真，以评估系统性能并说明理论分析。