# Calculation of Main Circuit Steady-State Parameters for Capacitor Commutated Converter System
## 4 Calculation Procedure of Main Circuit Parameters
### Detailed Calculation Procedure  
Under the specific control modes of the converters and the transformers, the design of the main circuit parameters is to determine all steady-state operating parameter values from the minimum DC power (0.1 pu) to the maximum DC power (1.2 pu) with a certain step (0.05 pu). For an LCC-CCC HVDC transmission system with the LCC at the rectifier side and the CCC at the inverter side, the detailed calculation procedure of the main circuit parameters is as follows:  
Step 1: According to Section 3.1, the steady-state mathematical model of the six-pulse CCC at the inverter side is firstly calculated. The capacitance value and the inductance value are determined. The effective value of the line voltage is considered as the rated line voltage at the valve side \(U_{\text{acNI}}\). The result of the apparent extinction angle is considered as the rated apparent extinction angle \(\gamma_{\text{appN}}\). Step 2: Calculate the rated ideal no-load DC voltage \(U_{\text{dioNR}}\) at the rectifier side and \(U_{\text{dioNI}}\) at the inverter side:  
\[U_{\text{dioNR}}=\frac{(\frac{U_{\text{dNR}}}{p}+U_{\text{T}})}{\cos\alpha_{ \text{N}}-(d_{\text{xR}}+d_{\text{rR}})} \tag{48}\]  
\[U_{\text{dioNI}}=\frac{3\sqrt{2}}{\pi}U_{\text{acNI}} \tag{49}\]  
where \(U_{\text{acNI}}\) is the rated line voltage at the valve side of the inverter. \(p\) is the number of six-pulse valve groups per pole. \(U_{\text{T}}\) is the forward voltage drop of a six-pulse valve group. \(U_{\text{dNR}}\) and \(U_{\text{dNI}}\) represent the rated DC voltage at the rectifier side and the inverter side, respectively, and the relationship satisfies:  
\[U_{\text{dNI}}=U_{\text{dNR}}-I_{\text{dN}}R_{\text{d}} \tag{50}\]  
Step 3: Design the tap range of the converter transformer and determine the maximum and minimum on-load tap changers of the converter transformer at both sides. The DC power ranges from the minimum value (0.1 pu) to the maximum value (1.2 pu) with a certain step (0.05 pu). For each step of the DC power, Step 4-Step 13 are executed. Step 4: Calculate the DC current \(I_{\text{d}}\) from the DC voltage \(U_{\text{dR}}\) and the DC power \(P_{\text{dR}}\) at the rectifier side:  
\[I_{\text{d}}=P_{\text{dR}}/U_{\text{dR}} \tag{51}\] \begin{table}
\begin{tabular}{c c} \hline \hline
**Factors for Operating Condition** & **Classification of the Factor** \\ \hline \multirow{4}{*}{Operating configuration} & Bipolar mode (B) \\  & Monopolar ground return mode (G) \\  & Monopolar metallic return mode (M) \\ \hline \multirow{2}{*}{Power transmission direction} & Forward direction (F) \\  & Reverse direction (R) \\ \hline \multirow{2}{*}{DC voltage level} & Full voltage operation (F) \\  & 80\% reduced voltage operation (R) \\  & 70\% reduced voltage operation (S) \\ \hline \multirow{2}{*}{DC circuit resistance} & High resistance (H) \\  & Low resistance (L) \\ \hline \multirow{4}{*}{AC system voltage level at the rectifier and the inverter side} & Maximum rated voltage \\  & Nominal voltage \\ \cline{1-1}  & Minimum rated voltage \\ \cline{1-1}  & Maximum extreme voltage \\ \cline{1-1}  & Minimum extreme voltage \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Summary of technical characteristics of various schemes. Step 5: For the rectifier, the default tap position of the converter transformer is set at the highest position. At the highest position, the corresponding firing angle and the reactive power consumption are smaller. Thus, the valve stress is reduced and the harmonic currents are diminished, which is beneficial for security and stability. For the certain tap position, \(U_{\text{dioR}}\) is calculated as follows:  
\[U_{\text{dioR}}=\frac{U_{\text{dioNR}}}{1+n_{\text{TR}}\cdot\Delta\eta}\frac{U_ {\text{acR}}}{U_{\text{acNR}}} \tag{52}\]  
where \(n_{\text{TR}}\) is the tap position of the converter transformer at the rectifier side. \(U_{\text{acR}}\) is the AC voltage at the rectifier side and \(U_{\text{acNR}}\) is the rated AC voltage at the rectifier side.