## 2 A Voltage Ride-Through (VRT) Control Model for Energy Storage Systems
\begin{cases}\begin{array}{l}u_{rd}^{*}=u_{1d}+u_{cd}-\Big{(}\frac{K_{ll}}{s} +K_{iP}\Big{)}(i_{rq}^{*}-i_{d})\\ u_{rq}^{*}=u_{1q}-u_{cd}-\Big{(}\frac{K_{ll}}{s}+K_{iP}\Big{)}(i_{rq}^{*}-i_{q} \Big{)}\end{array}\end{cases}  \tag{4}\]  
In the above equations: \(K_{iI},K_{iP}\): integral and proportional coefficients of the dq-axis current inner-loop control. Under steady-state operation, the active power outer-loop control and reactive power outer-loop control can be expressed as follows:  
\[ \begin{cases}\begin{array}{l}i_{rd}^{*}=\Big{(}\frac{K_{i,JP}}{s}+K_{p,lp} \Big{)}(P_{r}^{*}-P_{e})\\ i_{rq}^{*}=\Big{(}\frac{K_{i,JR}}{s}+\frac{K_{p,lq}}{s}\Big{)}(Q_{r}^{*}-Q_{e}) \end{array}\end{cases}  \tag{5}\]  
Figure 2: Mathematical model of grid–connected converter control for energy storage systems. In the above equations: \(K_{p,Jp},K_{i,Jp}\): proportional and integral coefficients of the active power outer-loop control; \(K_{p\_{Jq}},K_{i,Jq}\): proportional and integral coefficients of the reactive power outer-loop control; \(P_{r}^{*},Q_{r}^{*}\): active power reference and reactive power reference; and \(P_{e},Q_{e}\): actual active power and actual reactive power. When grid voltage dip faults occur, the grid-connected converter of the ESS must comply with the HVRT/LVRT requirements specified in the Chinese Standard Technical Requirements for Power Conversion System of Electrochemical Energy Storage System [23]. Under normal grid conditions, the energy storage system typically adopts a dual-loop control framework. The outer-loop control operates in active/reactive power (PQ) mode, adjusting the active power reference (\(P_{r}^{*}\)) and reactive power reference (\(Q_{r}^{*}\)); the inner-loop control employs dq-axis decoupled current control via a voltage source converter (VSC) to track the outer-loop references, thereby outputting the desired currents. This architecture prioritizes meeting power dispatch requirements while dynamically responding to fluctuations in grid frequency and voltage. When grid voltage faults, such as dips or swells, are detected, the outer-loop control switches from PQ mode to a voltage/current-coordinated control mode, prioritizing grid voltage support. A fault-specific current control strategy dynamically generates reactive current references based on voltage deviations, effectively mitigating voltage collapse. Concurrently, the inner-loop current control imposes saturation limits to restrict output currents within the converter's rated capacity, preventing hardware damage. The fault-period current reference equations are defined as follows:  
\[\left\{ \begin{array}{l}i_{\text{dLVRT}}^{*}=K_{1}(0.85-U_{t})I_{N}\\ i_{\text{dLVRT}}^{*}=\min(i_{rd}^{*}\sqrt{I_{\text{max}}^{2}-i_{q\text{LVRT}}^ {*2}})\\ i_{\text{dHVRT}}^{*}=K_{2}(U_{t}-1.15)I_{N}\\ i_{\text{dHVRT}}^{*}=\min(i_{rd}^{*}\sqrt{I_{\text{max}}^{2}-i_{q\text{HVRT}}^ {*2}})\end{array} \right. \tag{6}\]  
In the equations \(i_{\text{dHVRT}}^{*},i_{\text{dHVRT}}^{*},i_{\text{dLVRT}}^{*},i_{\text{dLVRT}}^ {*},\) d-axis and q-axis refer to currents under HVRT conditions and d-axis and q-axis refer to currents under LVRT conditions; \(K_{1}\), \(K_{2}\): reactive power support coefficient; \(I_{N}\): rated output current value of the AC terminal; and \(U_{t}\): ratio of the actual AC terminal voltage to its rated voltage. \[\left\{ \begin{array}{l}u_{1q}=\left(\frac{k_{il}}{s}+K_{ip}\right)\left(i_{rd }^{*}-i_{d}\right)+u_{rd}^{*}-u_{cd}\\ u_{1q}=\left(\frac{k_{il}}{s}+K_{ip}\right)\left(i_{mq}^{*}-i_{q}\right)+u_{ qq}^{*}+u_{cq}\end{array} \right. \tag{7}\]  
Parameter Identification Method Based on Dynamic Trajectory Feature Extraction and Hybrid Optimization  
The parameter identification method, based on dynamic trajectory feature extraction and hybrid optimization, leverages critical trajectory features extracted from system dynamic response data to construct a parameter sensitivity model, effectively mitigating interference from redundant information.