Inequality Constraints Based Method for Fast Estimation of Droop Slope Stability Regions for MMC-Based MTDC Systems

Yuntao Zou, Jiangchao Qin, Lei Zhang, Jicheng Yu

Research output: Contribution to journalArticlepeer-review

8 Scopus citations


This paper proposes an inequality constraints based method to efficiently and quickly estimate stability regions of droop control slopes for modular multilevel converter (MMC)-based multi-terminal dc (MTDC) systems. At first, a general small-signal model of the MMC-MTDC system is developed, which consists of the dc network and the MMCs with dq controllers and multiple droop controllers. When deriving corresponding nonlinear state-space models, the edge-node matrix is introduced for the dc network modeling with arbitrary grid topology and transmission line model. Then, based on the eigenvalues sensitivity and the Taylor Series of eigenvalues, a set of inequality constraints are proposed to expeditiously estimate the suprema of the droop slopes and identify the droop slope stability regions for the MMC-MTDC system. To verify the state-space model, a comparison of dynamic responses between the math model calculation in MATLAB and the EMT simulation in PSCAD/EMTDC is conducted, which demonstrates the accuracy and the correctness of the developed small-signal model. The effectiveness of the proposed parameter stability region estimation method is demonstrated by several examinations including the supremum tests of droop slopes, the stability region sketches on accuracy, and the predicted unstable operations in PSCAD/EMTDC.

Original languageEnglish (US)
Pages (from-to)3689-3700
Number of pages12
JournalIEEE Transactions on Power Delivery
Issue number6
StatePublished - Dec 1 2021
Externally publishedYes


  • Droop control
  • eigenvalue sensitivity
  • modular multilevel converter (MMC)
  • multi-terminal dc system (MTDC)
  • stability analysis
  • stability region

ASJC Scopus subject areas

  • Energy Engineering and Power Technology
  • Electrical and Electronic Engineering


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