# Steam Turbine and Governor

Model the dynamics of speed governing system, steam turbine, and multimass shaft

Libraries:
Simscape / Electrical / Specialized Power Systems / Electrical Machines / Synchronous Machine Control

## Description

The Steam Turbine and Governor block implements a complete tandem-compound steam prime mover, including a speed governing system, a four-stage steam turbine, and a shaft with up to four masses.

The speed governing system consists of a proportional regulator, a speed relay, and a servomotor controlling the gate opening. It is similar to one of the models proposed in [1].

The steam turbine has four stages, each modeled by a first-order transfer function. The first stage represents the steam chest while the three other stages represent either reheaters or crossover piping. The boiler is not modeled and boiler pressure is constant at 1.0 pu. Fractions F2 to F5 are used to distribute the turbine power to the various shaft stages:

The shaft models a four-mass system, which is coupled to the mass in the Synchronous Machine model for a total of five masses. The machine's mass is labeled mass #1. The mass in the Steam Turbine and Governor block, which is closest to the machine's mass, is mass #2, while the mass farthest from the machine is mass #5. The shaft is characterized by mass inertias H, damping factors D, and rigidity coefficients K. If you choose to simulate a single-mass shaft, the entire four-mass shaft subsystem in the Steam Turbine and Governor block is disabled and all the torque from the turbine is added together and applied to the machine's mass.

### Examples

The `power_thermal` example illustrates the use of the Steam Turbine and Governor block.

## Ports

### Input

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Reference speed, in pu. It is normally connected to a Constant block with the value set to 1.0 pu.

Reference electrical power in pu. It is set to a constant value corresponding to the initial active power drawn from the Synchronous Machine block connected to the Steam Turbine and Governor block.

Generator speed, in pu. This is one of the signals in the last output of the Synchronous Machine model (internal variables).

Generator power angle deviation. It is also one of the signals in the last output of the Synchronous Machine model (internal variables).

### Output

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Speed deviations, in pu, of masses 5, 4, 3, and 2.

Torques, in pu, transmitted by masses 5, 4, 3, and 2.

Gate opening, in pu.

Mechanical power Pm for the Synchronous Machine block, in pu.

## Parameters

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To edit block parameters interactively, use the Property Inspector. From the Simulink® Toolstrip, on the Simulation tab, in the Prepare gallery, select .

Rotor type: single mass or multimass tandem-compound. If you choose a single-mass system, the multimass shaft subsystem in the Steam Turbine and Governor block is disabled and the turbine's output torques are summed together and applied to the single mass in the Synchronous Machine block.

Gain Kp, permanent droop Rp (pu), and dead-zone width Dz (pu). Set gain to 3 if you want to use the steam flow feedback loop. Otherwise, set gain to 1.

Speed relay and gate servomotor time constants Tsr (s) and Tsm (s).

Minimum and maximum gate opening speed vgmin and vgmax (both in pu/s), and minimum and maximum gate opening gmin and gmax (both in pu).

Synchronous speed of the generator driven by the steam turbine (rpm).

Turbine time constants T2 to T5 (s). Numbered consistently with turbine torque fractions and mass numbers; i.e., T5 is the time constant of the first turbine stage, which models the steam chest.

Turbine torque fractions F2 to F5. Must total 1, otherwise an error message appears. Fraction numbers correspond to mass numbers; i.e., F2 is the fraction of torque to be applied to mass #2 of the multimass shaft.

Coefficients of inertia H2 to H5 (s) are associated with the masses of the multimass shaft.

#### Dependencies

To enable this parameter, set Generator type to `Tandem-compound (multi-mass)`.

Stiffness coefficients K12 to K45 (pu/rad), associated with the masses of the multimass shaft. K12 corresponds to the rigidity coefficient between masses #1 and #2, and so on.

#### Dependencies

To enable this parameter, set Generator type to `Tandem-compound (multi-mass)`.

Damping factors D2 to D5 (pu torque / puspeed deviation) associated with the masses of the multimass shaft.

#### Dependencies

To enable this parameter, set Generator type to `Tandem-compound (multi-mass)`.

Initial mechanical power Pm0 (pu) and initial generator angle Θe0 (degrees).

Initial mechanical power is automatically updated by the load flow utility of the Powergui block. Initial angle is also computed by the load flow utility and is written in the associated Synchronous Machine block dialog box.

#### Dependencies

To enable this parameter, set Generator type to `Tandem-compound (multi-mass)`.

Initial mechanical power.

Initial mechanical power is automatically updated by the load flow utility of the Powergui block. Initial angle is also computed by the load flow utility and is written in the associated Synchronous Machine block dialog box.

#### Dependencies

To enable this parameter, set Generator type to `Tandem-compound (single mass)`.

## References

[1] IEEE committee report, “Dynamic models for steam and hydro turbines in power system studies,” IEEE Transactions on Power Apparatus and Systems, Vol. PAS-92, No. 6, 1973, pp. 1904-1915.

[2] IEEE Subsynchronous resonance working group, “Second benchmark model for computer simulation of subsynchronous resonance,” IEEE Transactions on Power Apparatus and Systems, Vol. PAS-104, No. 5, 1985, pp. 1057-1066.

## Version History

Introduced before R2006a