## 2 Mechanism of Using the ESS to Suppress Electromechanical Oscillation
### Mechanism Analysis of ESS-Based Oscillation Suppression
\(K_{\mathrm{q}}\) is the control coefficient of the ESS, which characterizes the ability of the ESS to control the dynamic characteristics of the power system, and the expressions of \(K_{\mathrm{g}}\) and \(K_{\mathrm{q}}\) are respectively (the subscript \"0\" denotes the steady-state point value)  
\[K_{\mathrm{g}}=X\bigg{(}\frac{P_{\mathrm{e0}}}{V_{0}}\bigg{)}^{2}\bigg{(} \frac{kX^{2}I_{\mathrm{q0}}}{E^{2}V_{0}\sin\delta_{0}}\cdot\frac{-k}{1+k} \bigg{)}+\frac{\cos\delta_{0}}{\sin\delta_{0}}P_{\mathrm{e0}}, \tag{5}\]  
\[K_{\mathrm{q}}=\frac{X}{E^{2}}\bigg{(}\frac{P_{\mathrm{e0}}}{V_{0}}\bigg{)}^{ 2}\frac{kX}{\sin\delta_{0}}\bigg{(}V_{0}-\frac{k}{1+k}\bigg{)}, \tag{6}\]  
When the ESS utilizes the feedback signal of the rotor speed of the SG and adopts the PID controller, its output current \(I_{\mathrm{q}}\) is:  
\[I_{\mathrm{q}}=\bigg{(}K_{\mathrm{p}}+\frac{K_{\mathrm{i}}}{s}+sK_{\mathrm{d} }\bigg{)}\Delta\omega, \tag{7}\]  
where, \(K_{\mathrm{p}}\), \(K_{\mathrm{i}}\), and \(K_{\mathrm{d}}\) are the corresponding parameters of the PID controller of the ESS. Linearizing (7) and taking (2) into account, we will have:  
\[\Delta I_{\mathrm{q}}=-K_{\mathrm{p}}\Delta\omega-K_{\mathrm{i}}\Delta\delta -sK_{\mathrm{d}}\Delta\omega, \tag{8}\]  
Substituting (8) into (4), the output electromagnetic power of the equivalent SG that is affected by the ESS can be obtained:  
\[\Delta P_{\mathrm{e}}=\big{(}K_{\mathrm{g}}+K_{\mathrm{i}}K_{\mathrm{q}} \big{)}\Delta\delta+\big{(}K_{\mathrm{p}}+sK_{\mathrm{d}}\big{)}K_{\mathrm{ q}}\Delta\omega, \tag{9}\]  
Substituting (9) into (1) and considering \(\Delta P_{\mathrm{m}}=0\), the swing equation of the equivalent SG that is affected by the ESS can be converted into:\[\left(2H+K_{\rm q}K_{\rm d}\right)\frac{{\rm d}\Delta\omega}{{\rm d}t}=-\left(K_{ \rm g}+K_{\rm q}K_{\rm i}\right)\Delta\delta-\left(D+K_{\rm q}K_{\rm P}\right) \Delta\omega, \tag{10}\]  
By comparing (10) with (2), it can be seen that when the rotor speed of the SG is fed back and the PID controller is adopted, the controller parameters will simultaneously and equivalently change the inertia coefficient, the synchronization coefficient, and the damping coefficient of the SG-based power system at the same time, where the P controller mainly affects the damping ability of the system; the I controller mainly affects the synchronization ability of the system; the \(D\) controller mainly affects the system inertia, and:  
\[\left\{ \begin{array}{l}T_{\rm D}=D+K_{\rm q}K_{\rm P}\\ T_{\rm S}=K_{\rm g}+K_{\rm q}K_{\rm i}\\ T_{\rm I}=2H+K_{\rm q}K_{\rm d}\end{array} \right., \tag{11}\]  
Equation (11) shows that the ESS in the oscillation suppression mode can equivalently change the inertia effect, damping capacity and synchronization ability of the power system, thereby affecting the oscillation amplitude, the oscillation period, and the oscillation time. However, if the ESS adopts a control scheme with fixed parameters, it cannot automatically adjust the system inertia and damping ability according to the operating state of the SG-dominated power system, and thus better oscillation suppression performance cannot be achieved.