## 3 Control Mechanism for LCC-HVDC with a Synchronous Condenser
### Control Mechanism for the Synchronous Condenser  
The basic control mechanism for the SC is shown in Figure 3. The measured AC voltage and excitation current, shown as \(U_{\mathrm{t}}\) and \(I_{\mathrm{\!f}}\), respectively, are the input variables, and the excitation voltage \(E_{\mathrm{\!f}}\) is generated via proportional-integral (PI) function and then delivered to the exciter system. The SC adopts the constant voltage control mode to adjust the AC bus voltage during both steady-state and transient situations. When an AC fault is applied at the AC busbar, the increase in the excitation current causes the excitation voltage of the SC to increase in order to provide a certain amount of reactive power needed for AC voltage regulation. If the fault is serious or lasts for a longer time, the excitation current could reach the maximum over-excitation current value. This will activate the maximum excitation current limitation function by the control-signal of the \(I_{\mathrm{\!f}}\)-mark to limit the excitation current around the referenced value of \(I_{\mathrm{\!f}}\)-mark. However, it is not allowed to keep the maximum over-excitation current as \(I_{\mathrm{\!f}}\)-mark for a long time. When the operating time of SC with \(I_{\mathrm{\!f}}\)-mark exceeds the allowable time, the anti-time over-excitation limiter will activate the over-excitation current limitation function by the control-signal of OEL_mark, so as to limit the over-excitation current to a level of \(I_{\mathrm{\!f}}\)-ref under which the SC can keep operating for a longer time, finally to avoid the internal overheating of the SC. Using the Area Ratio of Commutation Failure Probability to Evaluate the Effect of SCs on the Commutation Failure Immunity of LCC-HVDC  
In order to further study the suppression effect of SCs on the commutation failure of the LCC-HVDC system, firstly, the simulation from PSCAD/EMTDC with different numbers of SCs was compared to verify the effectiveness of the SCs on suppressing the commutation failure. Then, a new index called area ratio of commutation failure probability was proposed. Finally, the area ratio of commutation failure probability index was used to evaluate the suppression effect of the SCs on  
Figure 3: Control mechanism for the synchronous condenser. Figure 2: Control mechanism for the LCC-HVDC system. the commutation failure of the LCC-HVDC system under different short circuit ratios (SCRs) at the inverter side. The following three cases were considered:  
_Case 1_: No synchronous condenser is connected at the AC bus of the inverter side;  
_Case 2_: One synchronous condenser with rated capacity of 100 Mvar is connected at the AC bus of the inverter side;  
_Case 3_: Two synchronous condensers each with rated capacity of 100 Mvar are connected at the AC bus of the inverter side;  
Validation of the Effectiveness of the SCs in Suppressing the Commutation Failure of the LCC-HVDC System  
Three-phase fault is the most serious fault among all types of AC faults. Therefore, the same three-phase fault was applied at the inverter bus of three cases to verify the effectiveness of the SC on suppressing commutation failure. The fault inductance value was set to 1.28H (the smallest inductance value that does not result in commutation failure in case 1), the fault time was 5.1s, and the fault duration was 0.05s. The comparison of dynamic responses under the three-phase fault is shown in Figure 4.  
The comparison of the dynamic responses of different cases in Figure 4, showed that the DC voltage, DC current, DC power, AC bus voltage, \(\gamma\) and the reactive power of SCs all dropped or rose in varying degrees when the fault occured. Among them, the change range of Case 1 was the largest, on the contrary, it was the smallest in Case 3.