Some very interesting phenomena can occur when large synchronous machines interact with a power system network. The result can be a sub-synchronous resonance (SSR), which can (and has) literally torn machines shafts apart. The cause of this disaster is the interaction between the mechanical torque placed on turbines and the opposite electrical torque produced by the power system. The resulting torsional stresses on the mechanical connecting shaft, combined with the effect of many masses oscillating back and forth, can be very destructive. A very detailed model of the turbine, generator, and the mechanical shaft, which couples the mechanical and electrical systems, is required to study such phenomena.
Turbine models have been developed which can accurately represent the dynamics of many masses connected to a single rotating shaft. The models are presently dimensioned to accommodate 6 masses (ex. 5 turbines and 1 generator, or 4 turbines, 1 generator and 1 exciter), but more masses can easily be added if the program is re-dimensioned.
The shaft dynamics and the rotating masses are represented pictorially in Figure 7-7:
Figure 7-7 - Graphical Model of Multi-Mass Shaft Dynamics
Where,
|
|
Inertia constant |
|
|
Shaft spring constant |
|
|
Mechanical torque on turbines |
|
|
Electrical torque on generators |
|
|
Mass angle (reference on generator) |
Springs represent the dynamics of the shaft. The torque exerted by the spring is proportional to the relative mechanical angles between adjacent masses.
In addition, two damping coefficients are included: The self-damping coefficient creates a torque on the specified mass, which is proportional to its own speed. Thus, the self-damping feature could be used to represent friction and windage for each mass. This torque is applied in steady state as well as in transient conditions.
The mutual damping coefficient creates a torque, which is proportional to the difference in speed from one mass to the next. Thus, this coefficient will not produce torques in steady state, but will damp out oscillations between masses.
Each mass has its own associated inertia constant which reflects the actual size of the mass on the shaft.
The total mechanical torque applied to the shaft (from a governor for example) can be proportioned among each turbine mass. The electrical torque produced by the electrical power system is applied to the generator mass only and opposes the mechanical input torque. In the model a positive electrical torque corresponds to the generation of electrical power. If an exciter is to be included on the shaft, the input torque on it will be 0.0, but self and mutual damping will still be present.
The effects of multiple shaft masses are modeled separately using the Multi-mass Torsional Shaft component. This component interfaces directly with the machine models.
The multi-mass output is ignored when the machine rotor is locked, however, the multi-mass model is initialized to the machine conditions.
The multi-mass turbine model may be initialized along with the machine when it changes state freely running machine.
