Loss distribution analysis and accurate calculation method for bulk-power MMC

Song et al. Protection and Control of Modern Power Systems https://doi.org/10.1186/s41601-023-00313-x (2023) 8:56 Protection and Control of Modern Power Systems Open Access ORIGINAL RESEARCH Loss distribution analysis and accurate calculation method for bulk‑power MMC Yonghui Song1, Yongjie Luo1 and Xiaofu Xiong1* Abstract Accurate evaluation of power losses in a modular multilevel converter (MMC) is very important for circuit component selection, cooling system design, and reliability analysis of power transmission systems. However, the existing converter valve loss calculation methods using the nearest level modulation (NLM) method and the traditional sortingbased capacitor voltage balancing strategy are inaccurate since the submodule (SM) switching logics in the MMC arms are uncertain. To solve this problem, the switching principle of the SMs in the sorting-based voltage balancing strategy is analyzed. An accurate MMC power loss calculation method based on the analysis of loss distribution of various SM topologies, including half-bridge submodule (HBSM), full-bridge submodule (FBSM) and clamp double submodule (CDSM), is proposed in this paper. The method can accurately calculate the losses caused by the extra switching actions during the capacitor voltage balancing process, thus greatly increasing the calculation accuracy of switching losses compared with existing methods. Simulation results based on a practical ± 350 kV/1000 MW MMCHVDC system with variety of MMC topologies with different voltage balancing strategies demonstrate the effectiveness of the proposed method. Keywords Modular multilevel converter, Extra switching losses calculation, Nearest level modulation 1 Introduction The modular multilevel converter-based high voltage direct current (MMC-HVDC) system has advantages of modular design, independent control of active and reactive power, and low output voltage harmonics etc., and it has been widely applied in the fields of renewable energy grid connection, and DC power grids [1–3]. Accurate calculation of valve losses is a critical basis for circuit component selection, cooling system design and reliability evaluation of the system [4, 5]. However, the numbers of submodules (SMs) and semiconductor devices in high-voltage large-capacity MMC-HVDCs have also increased dramatically, especially when the *Correspondence: Xiaofu Xiong 1 State Key Laboratory of Power Transmission Equipment and System Security and New Technology, School of Electrical Engineering, Campus A, Chongqing University, Shapingba District, Chongqing 400044, China full-bridge submodule (FBSM) or clamp double submodule (CDSM) topology with DC short-circuit fault clearing capability are adopted. The very large numbers of semiconductor devices and the complicated transient characteristics of converter valves have brought challenges to the accurate calculation of MMC losses. Loss calculation of an MMC is closely related to its modulation methods and capacitor voltage balancing strategies. The loss calculation based on carrier phaseshifted pulse width modulation (CPS-PWM) method has been well studied [6]. The loss distribution characteristics and calculation of IGBTs and diodes under CPS-PWM are deduced in [7, 8]. The junction temperature fluctuation characteristics of each switching device are analyzed by deriving the average and effective values of the switching device current [9]. However, the influence of junction temperatures on the loss calculation of switching devices is not considered. Linear interpolation is adopted to iteratively calculate the junction temperatures of semiconductor devices in [10], where the conduction losses © The Author(s) 2023. Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/. Song et al. Protection and Control of Modern Power Systems (2023) 8:56 and switching losses of IGBTs and diodes are calculated though electromagnetic transient simulation based on temperature feedback. A loss calculation method of halfbridge submodule (HBSM) is proposed based on the detailed analysis of semiconductor device working principle and the converter valve thermal model. This provides data support for MMC reliability analysis and full cycle life assessment [11]. However, CPS-PWM is not suitable for high-voltage large-capacity MMC-HVDC systems. The nearest level modulation (NLM) method based on a sorting algorithm to achieve capacitor voltage balance is widely applied in real high-voltage large-capacity MMCHVDC systems, in which the switching frequency and loss characteristics are significantly different from the CPS-PWM method [12]. Although the conduction losses can be well estimated with sufficient accuracy by various methods [13, 14], research on switching losses is still limited, especially for the MMC with the NLM method. The switching actions of the SMs under the NLM method can be divided into two parts: necessary switching and extra switching. The necessary switching is the change of SM numbers caused by the AC output voltage changes of the MMC arms according to the references, while the extra switching is the alternation of SMs to achieve capacitor voltage balance. The complexity and randomness of the switching actions restrict the calculation accuracy of the extra switching losses. One of the most popular methods for calculating switching losses is through simulation [15]. However, it has disadvantages of being time-consuming and requiring a detailed model. This limits its application. The other method relies on analytical models based on specific assumptions, such as ideal sinusoidal arm current and voltage references [16, 17]. These are simple and computationally-efficient. However, considerable estimation errors exist because of the neglect of the harmonics in the current and voltage. Therefore, a linear relationship between the switching losses and the average current is applied for the essential and additional switching loss estimation [18]. A method to calculate the upper limit value of switching losses of an MMC is also proposed in [19, 20]. This multiplies the maximum switching energy by the estimated average switching frequency. However, the errors of the methods prop (...truncated)