# Power Stability Analysis and Evaluation Criteria of Dual-Infeed HVDC with LCC-HVDC and VSC-HVDC
## 4 Evaluation Criteria for the Power Stability of Hybrid Dual-Infeed HVDC Systems
### Effective Short Circuit Ratio (ESCR)
#### 4.2.1 Case 1: VSC-HVDC Constant Reactive Power Control Mode  
According to the analysis in Section 3.4, when the VSC-HVDC is in constant reactive power control mode, the power stability of the system is different under different rated transmission power of VSC-HVDC. From Equations (5) and (6), it can be seen that the connection of VSC-HVDC is equivalent to that of a constant power load at the converter bus. In the following, the relationship between PSI and ESCR is investigated under different system parameters.  
1. The influence of parameter \(P_{\text{dN2}}\)Change the rated transmission power of VSC-HVDC, and investigate the relationship between PSI and ESCR under different \(P_{\text{dN2}}\). Figure 6 shows the curves of PSI versus ESCR when \(P_{\text{dN2}}\) is 0 p.u., 0.5 p.u., 1.0 p.u. and 1.5 p.u., respectively. It can be seen that: under the same \(P_{\text{dN2}}\), the greater the ESCR is, the greater the PSI is, and the better the power stability of the system is. The obtained ESCR when PSI = 0 is defined as the critical effective short circuit ratio (CESCR) of the system, which is the minimum requirement for the normal and stable operation of the HVDC system. Taking \(P_{\text{dN2}}\) = 0.5 p.u. as an example, the CESCR of the system is 1.64. It means that only when ESCR > 1.64 can the HVDC system operate normally and stably. Comparing the four curves in Figure 6, we can conclude that the value of CESCR increases with the increase of \(P_{\text{dN2}}\). When \(P_{\text{dN2}}\) increases from 0 p.u. to 1.5 p.u., the variable range of CESCR is 1.52-2.0.  
Figure 5: Calculation process of power stability index curve PSI–ESCR.  
The influence of parameter \(Z_{2}\)  
Change the equivalent impedance of the AC system corresponding to VSC-HVDC, and investigate the relationship between PSI and ESCR under different \(Z_{2}\). Figure 7 shows the curves of PSI versus ESCR when \(P_{\text{dN2}}\) = 0.5 p.u., \(Z_{2}\) is 0.2 p.u., 0.35 p.u., 0.55 p.u. and 0.75 p.u., respectively. It can be seen that under the same \(Z_{2}\), PSI increases with the increase of ESCR. The smaller \(Z_{2}\) is, the smaller the CESCR of the system is. The variable range of CESCR is 1.59\(\sim\)1.75.  
According to Figures 6-8, when the VSC-HVDC is in constant reactive power control mode, the relationship between PSI and ESCR is summarized as follows:  
1. ESCR has a clear indicative function on the power stability of the hybrid dual-infeed HVDC system. The greater the ESCR is, the better the power stability of the system is.
2. The value of CESCR is affected by system parameters. The greater \(P_{\text{AN2}}\) is, the greater the CESCR is; the greater \(Z_{2}\) is, the greater the CESCR is; the greater \(Z_{12}\) is, the smaller the CESCR is.
3. The greater the ESCR is, the smaller the influence of system parameters on the indicative function of ESCR is. Among the above three system parameters, \(P_{\text{AN2}}\) has the greatest influence on the quantitative relationship between PSI and ESCR, and the variable range of CESCR is 1.52-2.0.