# Calculation of Main Circuit Steady-State Parameters for Capacitor Commutated Converter System
## 1 Introduction  
The high voltage direct current system (HVDC) is currently the main means for long-distance bulk power transmission [1]. In the situation of the bulk power transmission, the line commutated converter (LCC) technology has been widely utilized. When connected to a weak AC grid, the LCC is prone to commutation failures. Moreover, the reactive power consumption of the LCC is 50-60% of the rated DC power. Although the voltage source converter (VSC) can solve most of the above issues, the power rating of this technology still cannot match the LCC. The concept of using a capacitor commutated converter (CCC) was first proposed in 1954 [2]. It was an alternative technology to the LCC and has the potential to mitigate the above drawbacks of the LCC. The series capacitors are inserted between the valve side of converter transformers and the thyristor valves to generate an additional commutation voltage. The world's first commercial CCC-HVDC project was the Garabi Project in 2000, which allowed power transmission from an Argentina network (50 Hz) to a Brazilian network (60 Hz) with a very low short circuit ratio (SCR) at the Brazilian side [3]. In 2003, the CCC technology was also chosen for Rapid City DC Tie to realize the seventh asynchronous interconnection between the eastern and western networks in North America [4]. As one of the longest transmission links in the world, the Rio Madeira Project was commissioned in 2013-2014. A part of the project was the 800 MW back-to-back CCC-HVDC that provided power in the weaker power networks of northwest Brazil [5; 6]. The CCC technology was selected for these three projects due to its suitability for application in relatively weak systems. Compared to the conventional LCC, the application of the CCC can reduce theprobability of commutation failures and is suitable for the weak AC systems. Moreover, it can reduce the shunt capacitor reactive compensation from AC filters [7]. The calculation of the main circuit parameters is essential to the design of the HVDC transmission system, which provides the steady-state operation parameters for the filter design and the calculation of harmonics. The main circuit parameter calculation aims to determine the steady-state operation characteristics (e.g., firing angle, extinction angle and ideal no-load DC voltage), steady-state parameters of the converter transformers and reactive power compensation [1]. Before further investigating the features of the CCC, it is necessary to propose a design method to calculate the main circuit parameters of the CCC-HVDC transmission system. The design methods of the main circuit parameters for the LCC, modular multilevel converter (MMC), multiterminal LCC-HVDC, multiterminal MMC-HVDC and M3C are already demonstrated in [8; 9; 10; 11; 12; 13]. With the fixed series capacitor insertions, the CCC not only increases the AC harmonics but also represents additional valve voltage stress. Moreover, the unbalanced commutation voltages of the capacitors under fault conditions may lead to the transient performance deterioration [14]. To improve the controllability of the inserted capacitors, Reference [15] introduces an approach to the CCC using an active capacitor. A three-phase voltage sourced converter (VSC) is connected to resemble the effect of the capacitor. In [16], a small-rated three-phase VSC is added between the series commutation capacitor and the thyristor-based converter in CCC. The series VSC acts as an auxiliary commutation capacitor to actively change the series capacitance and mitigate the continuous commutation failure (CF) issue of the CCC. The evolved capacitor commutated converter (ECCC), embedded with anti-parallel thyristor-based dual-directional full-bridge modules is proposed in [17], which can effectively reduce CF risks. An improved coordinated control strategy for ECCC was proposed in [18] to accelerate the commutation process under normal operation state and further reduce the CF probability under AC fault conditions.