Analytical monodromy matrix method for small-signal stability analysis of grid-connected modular multilevel converter systems
The modular multilevel converter (MMC) has been widely used in high-voltage/high-power applications, e.g., high-voltage direct current transmission. However, its nonlinear time-periodic nature leads to complex harmonic interactions and then complicates the small-signal stability modeling and analysi...
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Elsevier
2025-03-01
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| Series: | International Journal of Electrical Power & Energy Systems |
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| Online Access: | http://www.sciencedirect.com/science/article/pii/S0142061524006422 |
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| author | Xiaofan Jia Hua Ye |
| author_facet | Xiaofan Jia Hua Ye |
| author_sort | Xiaofan Jia |
| collection | DOAJ |
| description | The modular multilevel converter (MMC) has been widely used in high-voltage/high-power applications, e.g., high-voltage direct current transmission. However, its nonlinear time-periodic nature leads to complex harmonic interactions and then complicates the small-signal stability modeling and analysis of grid-connected MMC systems. To address this, the linear time-periodic (LTP) theory and the Floquet theory-based monodromy matrix method are applied in this paper. First, an analytical expression of the monodromy matrix (i.e., the state transition matrix over a period) for the LTP model of grid-connected MMC systems is constructed by applying the Chebyshev collocation method. In addition to avoiding time-consuming numerical integration, the analytical matrix facilitates to perform the derivative-based eigenvalue sensitivity analysis. Then, the system free-response solution is efficiently computed by means of a set of analytical state transition matrices. The effective oscillation components in critical LTP modes and relative contributions thus can be identified. On this basis, the participation factor analysis and damping ratio analysis can be performed to gain insightful characterization of system dynamics. The correctness and effectiveness of the proposed method are verified on an exemplary grid-connected MMC system by both numerical and experimental results. |
| format | Article |
| id | doaj-art-bb2435a0631441518dc43894367e4487 |
| institution | Kabale University |
| issn | 0142-0615 |
| language | English |
| publishDate | 2025-03-01 |
| publisher | Elsevier |
| record_format | Article |
| series | International Journal of Electrical Power & Energy Systems |
| spelling | doaj-art-bb2435a0631441518dc43894367e44872025-01-19T06:23:59ZengElsevierInternational Journal of Electrical Power & Energy Systems0142-06152025-03-01164110419Analytical monodromy matrix method for small-signal stability analysis of grid-connected modular multilevel converter systemsXiaofan Jia0Hua Ye1Key Laboratory of Power System Intelligent Dispatch and Control of Ministry of Education (Shandong University), Jinan, 250061, ChinaShandong Research Institute of Industrial Technology, Jinan, 250101, China; Key Laboratory of Power System Intelligent Dispatch and Control of Ministry of Education (Shandong University), Jinan, 250061, China; Corresponding author at: Shandong Research Institute of Industrial Technology, Jinan, 250101, and Key Laboratory of Power System Intelligent Dispatch and Control of Ministry of Education (Shandong University), Jinan, 250061, China, .The modular multilevel converter (MMC) has been widely used in high-voltage/high-power applications, e.g., high-voltage direct current transmission. However, its nonlinear time-periodic nature leads to complex harmonic interactions and then complicates the small-signal stability modeling and analysis of grid-connected MMC systems. To address this, the linear time-periodic (LTP) theory and the Floquet theory-based monodromy matrix method are applied in this paper. First, an analytical expression of the monodromy matrix (i.e., the state transition matrix over a period) for the LTP model of grid-connected MMC systems is constructed by applying the Chebyshev collocation method. In addition to avoiding time-consuming numerical integration, the analytical matrix facilitates to perform the derivative-based eigenvalue sensitivity analysis. Then, the system free-response solution is efficiently computed by means of a set of analytical state transition matrices. The effective oscillation components in critical LTP modes and relative contributions thus can be identified. On this basis, the participation factor analysis and damping ratio analysis can be performed to gain insightful characterization of system dynamics. The correctness and effectiveness of the proposed method are verified on an exemplary grid-connected MMC system by both numerical and experimental results.http://www.sciencedirect.com/science/article/pii/S0142061524006422Floquet characteristic multiplier (FCM)Linear time-periodic (LTP) systemModular multilevel converter (MMC)Monodromy matrix methodSmall-signal stability |
| spellingShingle | Xiaofan Jia Hua Ye Analytical monodromy matrix method for small-signal stability analysis of grid-connected modular multilevel converter systems International Journal of Electrical Power & Energy Systems Floquet characteristic multiplier (FCM) Linear time-periodic (LTP) system Modular multilevel converter (MMC) Monodromy matrix method Small-signal stability |
| title | Analytical monodromy matrix method for small-signal stability analysis of grid-connected modular multilevel converter systems |
| title_full | Analytical monodromy matrix method for small-signal stability analysis of grid-connected modular multilevel converter systems |
| title_fullStr | Analytical monodromy matrix method for small-signal stability analysis of grid-connected modular multilevel converter systems |
| title_full_unstemmed | Analytical monodromy matrix method for small-signal stability analysis of grid-connected modular multilevel converter systems |
| title_short | Analytical monodromy matrix method for small-signal stability analysis of grid-connected modular multilevel converter systems |
| title_sort | analytical monodromy matrix method for small signal stability analysis of grid connected modular multilevel converter systems |
| topic | Floquet characteristic multiplier (FCM) Linear time-periodic (LTP) system Modular multilevel converter (MMC) Monodromy matrix method Small-signal stability |
| url | http://www.sciencedirect.com/science/article/pii/S0142061524006422 |
| work_keys_str_mv | AT xiaofanjia analyticalmonodromymatrixmethodforsmallsignalstabilityanalysisofgridconnectedmodularmultilevelconvertersystems AT huaye analyticalmonodromymatrixmethodforsmallsignalstabilityanalysisofgridconnectedmodularmultilevelconvertersystems |