# Calculation of Main Circuit Steady-State Parameters for Capacitor Commutated Converter System
## 1 Introduction
In [2], the fully controlled insulated gate bipolar transistor (IGBT) submodules (SMs) are used to form the full-bridge capacitor module. This novel hybrid converter configuration aims to eliminate commutation failures under serious faults. To effectively alleviate the limitation of IGBTs for ultra HVDC systems, Reference [19] proposes an approach using a thyristor based controllable capacitor (TBCC) to eliminate CF and reduce the loss from the power devices. Reference [20] proposes a control strategy for a hybrid HVDC system comprising a CCC connected in series with a two-stage VSC. Reference [21] gives a literature review about the mitigation of the commutation failure. The CCC technology is one of the improvements to converters, which focus on the topological structure of the entire converter. The series capacitor is considered in [22] with the capacitance selection factors. However, the detailed CCC system model is not derived. For a CCC, the series capacitors are inserted between the valve side of converter transformers and the thyristor valves to realize the elimination of the commutation failure when connected to the weak AC system. This CCC technology is economical and easy to realize, which has potential in the future engineering application. However, the above researches mainly focus on the topology improvement for the CCC to further enhance the transient characteristics during the commutation failure. The main circuit parameters of the CCC are directly given and the design method is not even mentioned in these studies. Thus, this paper systematically provides a design method of the main circuit parameters, which is beneficial for the further research of the CCC. The contribution of this paper is as follows:  
(1) The calculation method of the commutation capacitor in a six-pulse CCC is proposed in this paper. Firstly, the waveform of the commutation capacitors is depicted in detail. Then the commutation process is derived to obtain a steady-state mathematical model of the CCC. After applying the proposed selection principles (the limitations of the valve stress and the reactive power consumption), the value of the commutation capacitor is determined. (2) The design method and the detailed calculation procedure of the main circuit parameters for a two-terminal LCC-CCC HVDC transmission system are proposed in this paper. The calculation formulas of the operation parameters at both converter sides are presented. The paper also gives a modified Guizhou-Guangdong II \(\pm\)500 kV/3000 MW LCC-CCC HVDC transmission system to verify the validity of the proposed calculation method. The simulation and calculation results are compared to further illustrate the features of the CCC. The organization of this paper is as follows. In Section 2, the topology of a \(\pm\)500 kV/3000 MW LCC-CCC HVDC transmission system is proposed. In Section 3, the steady-state mathematical model of the CCC is presented and the calculation formulas of the main circuit parameters are given. In Section 4, the basic factors required for the main circuit parameter calculation are explained and a detailed calculation procedure is given. In Section 5, a case study under a certain operating condition is presented to verify the validity of the proposed calculation method. A simulation in PSCAD/EMTDC is carried out to reflect the characteristics of the CCC and give a comparison between the experimental and calculation results. Finally, conclusions are drawn in Section 6.