Power System Stabilizers (PSS)
PSS are used to add an additional signal $v_s$ to the input signal of the AVR: $v_\text{ref} = v_\text{ref}^{\text{avr}} + v_s$.
Fixed PSS [PSSFixed]
This is a simple model that set the stabilization signal to be equal to a desired constant value $v_s = v_{s}^{\text{fix}}$. The absence of PSS can be modelled using this component with $v_s^{\text{fix}} = 0$.
Simple PSS [PSSSimple]
This is the most basic PSS that can be implemented, on which the stabilization signal is a proportional controller over the frequency and electrical power:
\[\begin{align} v_s = K_{\omega}(\omega - \omega_s) + K_p(\omega \tau_e - P_{\text{ref}}) \tag{1a} \end{align}\]
IEEE Stabilizer [IEEEST]
The 7th-order PSS model is:
\[\begin{align} A_4 \dot{x}_1 &= u - A_3 x_1 - x_2 \tag{2a} \\ \dot{x}_2 &= x_1 \tag{2b} \\ A_2\dot{x}_3 &= x_2 - A_1 x_3 - x_4 \tag{2c}\\ \dot{x}_4 &= x_3 \tag{2d}\\ T_2\dot{x}_5 &= \left(1 - \frac{T_1}{T_2}\right) y_f - x_5 \tag{2e}\\ T_4\dot{x}_6 &= \left(1 - \frac{T_3}{T_4}\right) y_{LL1} - x_6 \tag{2f}\\ T_6\dot{x}_7 &= -\left(\frac{K_s T_5}{T_6} y_{LL2} + x_7 \right) \tag{2g} \end{align}\]
with
\[\begin{align*} y_f &= \frac{T_4}{T_2} x_2 + \left(T_3 - T_1 \frac{T_4}{T_2}\right) x_3 + \left(1 - \frac{T_4}{T_2}\right)x_4 \\ y_{LL1} &= x_5 + \frac{T_1}{T_2} y_f \\ y_{LL2} &= x_6 + \frac{T_3}{T_4} y_{LL1} \\ y_{out} &= x_7 + \frac{K_s T_5}{T_6} y_{LL2} \\ V_s &= \text{clamp}(y_{out}, \text{Ls}_\text{min}, \text{Ls}_\text{max}) \end{align*}\]
on which $u$ is the input signal to the PSS, that depends on the flag. Currently, rotor speed, electric torque, mechanical torque and voltage magnitude are supported inputs.
STAB1 PSS [STAB1]
The 3rd-order PSS model is:
\[\begin{align} T \dot{x}_1 &= K \omega - x_1 \tag{3a} \\ T_3\dot{x}_2 &= \left(1 - \frac{T_1}{T_3}\right) x_1 - x_2 \tag{3b} \\ T_4\dot{x}_3 &= \left(1 - \frac{T_2}{T_4}\right) y_{LL} - x_2 \tag{3c} \\ \end{align}\]
with
\[\begin{align*} y_{LL} = x_2 + \frac{T_1}{T_3} x_1 \\ y_{out} = x_3 + \frac{T_2}{T_4} y_{LL} \\ V_s = \text{clamp}(y_{out}, -H_{lim}, H_{lim}) \end{align*}\]