# Fault ride-Through Control Strategy for Variable Speed Pumped Storage Unit with Full-Size Converter
## 3 Analysis of Fault Ride-Through Characteristics  
### LVRT Characteristics  
As shown in Figure 1, \(P_{\rm m}\), \(P_{\rm s}\), and \(P_{\rm g}\) represent the turbine mechanical power, the active power delivered to the RSC, and the active power delivered by the GSC to the grid, respectively. When the FSC-VSPSU operates under the power generation condition normally, the power on both sides of the converter is balanced, i.e., \(P_{\rm m}=P_{\rm s}=P_{\rm g}\). Therefore, the DC bus voltage value \(U_{\rm dc}\) satisfies Equation (3). \[CU_{dc}\frac{dU_{dc}}{dt}=P_{s}-P_{g}=\Delta P=0 \tag{3}\]  
The unbalanced power \(\Delta P\) is approximately zero under normal operating conditions, and the DC bus voltage \(U_{\rm dc}\) remains constant. Once the system voltage drops, it is considered that the converter has a certain current limit value, and the current will not suddenly change. When the current reaches the current limit value, the voltage at the grid connection point decreases. Consequently, the active power \(P_{\rm g}\) on the grid side decreases, while the active power \(P_{\rm s}\) of the power transmitted by the generator changes less. Therefore, the unbalanced power \(\Delta P\) will be greater than zero, and the DC bus voltage will increase. Assuming that the FSC-VSPSU operates at rated power, at this time the grid voltage and the active current are \(e_{\rm gd}\) and \(i_{\rm gd}\), respectively. The grid voltage drops to \(e_{\rm gd1}\), and the active current drops to \(i_{\rm gd1}\). Without considering the current limiting of the inverter, the GSC is controlled by zero reactive power. According to the principle of power balance, the grid-side power \(P_{\rm g1}\) during the fault period satisfies Equation (4). \[P_{g1}=e_{gd1}i_{gd1} \tag{4}\]  
Assuming that the minimum voltage during the fault period and the maximum overcurrent capacity of the converter are \(k_{\rm u}\) times the rated voltage and \(k_{\rm i}\) times the rated  
Figure 5: Governor system diagram in the pumping conditions. (**a**) Governor model in the pumping condition. (**b**) Pump simulation model. current, respectively, and it is also assumed that the DC voltage does not suddenly change at the moment of the fault. After the converter current limitation is activated, the DC power satisfies Equation (5). \[CU_{dc}\frac{dU_{dc}}{dt}=e_{gd}i_{gd}-k_{u}e_{gd}k_{i}i_{gd} \tag{5}\]  
Consequently, during the low voltage period, the DC voltage satisfies Equation (6):  
\[U_{dc}=\int_{t_{0}}^{t_{1}}\frac{(1-k_{u}k_{i})P_{g}}{CU_{dc0}}+U_{dc0} \tag{6}\]  
where \(U_{dc0}\) represents the rated DC voltage during normal operation. Therefore, the deeper the system voltage drop, the smaller the overcurrent capacity of GSC and the higher the DC overvoltage. By neglecting the power loss of the water pump turbine unit, the generator rotor speed \(\omega\) satisfies Equation (7):  
\[J_{T}\omega_{g}\frac{d\omega_{g}}{dt}=P_{m}-P_{s} \tag{7}\]  
where \(J_{T}\) is the rotational inertia of the rotor. Due to the regulation time scale of the governor system being in the second level and the hysteresis effect of water, the mechanical power \(P_{m}\) remains basically unchanged for a short period after a disturbance occurs. However, the electromagnetic power output \(P_{s}\) is blocked. Therefore, during the low-voltage period of the system, the unit speed will fluctuate. When the FSC-VSPSU operates under pumping conditions, referring to the analysis of power generation conditions, the DC voltage under pumping conditions satisfies Equation (8). \[U_{dc}=\int_{t_{0}}^{t_{1}}\frac{(k_{u}k_{i}-1)P_{g}}{CU_{dc0}}+U_{dc0} \tag{8}\]  
Therefore, the deeper the system voltage drop, the smaller the overcurrent capacity of GSC, and the lower the DC voltage. According to this, it can be inferred that the voltage on the DC capacitor will significantly decrease. Although there is no risk of overvoltage, if the DC voltage is too low, the converter will deviate from the stable operating point, potentially leading to unstable operation.