## 2 Mechanism of Using the ESS to Suppress Electromechanical Oscillation
### Mechanism Analysis of ESS-Based Oscillation Suppression  
In order to analyze the mechanism of ESS suppression of electromechanical oscillation, the system equivalent model shown in Figure 1 is firstly simplified on the electromechanical time scale, as shown in Figure 3. It should be noted that in order to fully combine the cost advantage of reactive power-based methods and the technical advantage of active power-based schemes, this paper allows the ESS to work in the reactive power-based suppression mode. Its active power is mainly used to compensate  
Figure 1: Equivalent model of synchronous generator (SG)-dominated power system with an energy storage system (ESS). the power loss of the ESS itself to ensure the DC side voltage stability. Since the active power required to maintain the DC side voltage stability is small and negligible, the control strategy shown in Figure 2 can minimize the ESS cost while achieving the desired suppression performance. Therefore, the electromechanical model of the ESS shown in Figure 3 can be viewed as a reactive current source. In addition, the voltage vector diagram of the simplified system model on the electromechanical time scale is shown in Figure 4. X and X represent the equivalent reactance, and \(I_{\text{q}}\) is the reactive current injected by the ESS to the grid. Figure 4: Voltage vector diagram of an equivalent system. Figure 3: Equivalent model on the electromechanical time scale. Figure 2: Control diagram of an ESS with the feedback signal of the rotor speed. (**a**) Conventional control with fixed controller parameters; (**b**) Proposed control with variable controller parameters. When analyzing the stability of an SG-based power system, the linearized model of the swing equation of SG is usually used, namely:  
\[\left\{ \begin{array}{l}\frac{\mathrm{d}\Delta\delta}{\mathrm{d}t}=\omega_{0} \Delta\omega\\ T_{\mathrm{J}}\frac{\mathrm{d}\Delta\omega}{\mathrm{d}t}=\Delta P_{\mathrm{m}}- \Delta P_{\mathrm{e}}\end{array} \right., \tag{1}\]  
To investigate the physical mechanism of dynamic stability of a power system, the electric torque analysis method adopts the equivalent inertia coefficient \(T_{\mathrm{J}}\), the synchronization coefficient \(T_{\mathrm{S}}\), and the damping coefficient \(T_{\mathrm{D}}\) to characterize the inertia, synchronization, and damping effects of the SG-based system, respectively [15]. Assume the input mechanical power of the equivalent SG is constant, that is \(\Delta P_{\mathrm{m}}=0\), (1) can be rewritten as the following standard equation:  
\[\left\{ \begin{array}{l}\frac{\mathrm{d}\Delta\delta}{\mathrm{d}t}=\omega_{0} \Delta\omega\\ T_{\mathrm{J}}\frac{\mathrm{d}\Delta\omega}{\mathrm{d}t}=-T_{\mathrm{S}}\Delta \delta-T_{\mathrm{D}}\Delta\omega\end{array} \right., \tag{2}\]  
According to the above models on the electromechanical time scale, the output electromagnetic power of the equivalent SG in Figure 1 can be expressed as:  
\[P_{\mathrm{e}}=\frac{EV}{X}\sin\alpha=\frac{EV}{X}\frac{E\sin\delta}{(1+k)V+ kXI_{\mathrm{q}}}, \tag{3}\]  
Simplifying (3) and linearizing it at the steady-state point of the power system, the intermediate variable \(V\) can be eliminated, and we will have:  
\[\Delta P_{\mathrm{e}}=K_{\mathrm{g}}\Delta\delta-K_{\mathrm{q}}\Delta I_{ \mathrm{q}}, \tag{4}\]  
where, \(K_{\mathrm{g}}\) is the synchronization coefficient of the power system itself, which characterizes the synchronization ability of the power system.