Shafts

The shaft component defines the rotating mass of the synchronous generator.

Rotor Mass Shaft PowerSystems.SingleMass

This is the standard model, on which one single mass (typically the rotor) is used to model the entire inertia of the synchronous generator. Each generator's rotating frame use a reference frequency $\omega_s$, that typically is the synchronous one (i.e. $\omega_s = 1.0$). The model defines two differential equations for the rotor angle $\delta$ and the rotor speed $\omega$:

\[\begin{align} \dot{\delta} &= \Omega_b(\omega - \omega_s) \tag{1a} \\ \dot{\omega} &= \frac{1}{2H}(\tau_m - \tau_e - D(\omega-\omega_s)) \tag{1b} \end{align}\]

Five-Mass Shaft PowerSystems.FiveMassShaft

This model describes model connecting a high-pressure (hp) steam turbine, intermediate-pressure (ip) steam turbine, low-pressure (lp) steam pressure, rotor and exciter (ex) connected in series (in that order) in the same shaft using a spring-mass model:

\[\begin{align} \dot{\delta} &= \Omega_b(\omega - \omega_s) \tag{2a} \\ \dot{\omega} &= \frac{1}{2H} \left[- \tau_e - D(\omega-\omega_s)) - D_{34} (\omega-\omega_{lp}) - D_{45}(\omega-\omega_{ex}) + K_{lp}(\delta_{lp-\delta}) +K_{ex}(\delta_{ex}-\delta) \right] \tag{2b} \\ \dot{\delta}_{hp} &= \Omega_b(\omega_{hp} - \omega_s) \tag{2c} \\ \dot{\omega}_{hp} &= \frac{1}{2H_{hp}} \left[ \tau_m - D_{hp}(\omega_{hp}-\omega_s) - D_{12}(\omega_{hp} - \omega_{ip}) + K_{hp}(\delta_{ip} - \delta_{hp}) \right] \tag{2d} \\ \dot{\delta}_{ip} &= \Omega_b(\omega_{ip} - \omega_s) \tag{2e} \\ \dot{\omega}_{ip} &= \frac{1}{2H_{ip}} \left[- D_{ip}(\omega_{ip}-\omega_s) - D_{12}(\omega_{ip} - \omega_{hp}) -D_{23}(\omega_{ip} - \omega_{lp} ) + K_{hp}(\delta_{hp} - \delta_{ip}) + K_{ip}(\delta_{lp}-\delta_{ip}) \right] \tag{2f} \\ \dot{\delta}_{lp} &= \Omega_b(\omega_{lp}-\omega_s) \tag{2g} \\ \dot{\omega}_{lp} &= \frac{1}{2H_{lp}} \left[ - D_{lp}(\omega_{lp}-\omega_s) - D_{23}(\omega_{lp} - \omega_{ip}) -D_{34}(\omega_{lp} - \omega ) + K_{ip}(\delta_{ip} - \delta_{lp}) + K_{lp}(\delta-\delta_{lp}) \right] \tag{2h} \\ \dot{\delta}_{ex} &= \Omega_b(\omega_{ex}-\omega_s) \tag{2i} \\ \dot{\omega}_{ex} &= \frac{1}{2H_{ex}} \left[ - D_{ex}(\omega_{ex}-\omega_s) - D_{45}(\omega_{ex} - \omega) + K_{ex}(\delta - \delta_{ex}) \right] \tag{2j} \end{align}\]