SimPowerSystems |

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

**Library**

**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 p.u. 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.

**Dialog Box and Parameters**

**Generator type**- Specifies 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.
**Regulator**- The gain Kp, permanent droop Rp (p.u.), and dead-zone width Dz (p.u.). Set gain to 3 if you want to use the steam flow feedback loop. Otherwise, set gain to 1.
**Time constants**- The speed relay and gate servomotor time constants Tsr (s) and Tsm (s).
**Gate Limits**- The minimum and maximum gate opening speed vgmin and vgmax (both in p.u./s), and minimum and maximum gate opening gmin and gmax (both in p.u.).
**Turbine time constants**- The 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**- The 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.
**Multi-mass shaft**- Only visible if generator type is multimass. Coefficients of inertia H2 to H5 (s), stiffness coefficients K12 to K45 (p.u./rad), and damping factors D2 to D5 (p.u. torque / p.u. speed deviation) associated with the masses of the multimass shaft. K12 corresponds to the rigidity coefficient between masses #1 and #2, and so on.

**Initial conditions**- If the shaft is multimass, enter the initial mechanical power Pm0 (p.u.) and initial generator angle e0 (deg). If the shaft is single mass, enter only initial mechanical power.
- Initial mechanical power can be computed 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.

**Inputs and Outputs**

The first input is the speed reference, in p.u. It is normally connected to a Constant block with the value set to 1.0 p.u.

The second input is the electrical power reference, in p.u. 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.

The third input is the generator's speed, in p.u. This is one of the signals in the last output of the Synchronous Machine model (internal variables).

The fourth input is the generator's power angle deviation. It is also one of the signals in the last output of the Synchronous Machine model (internal variables).

The first output is a vector containing the speed deviations, in p.u., of masses #5 to #2, in that order.

The second output is also a vector containing the torques, in p.u., transmitted by masses #5 to #2.

The third output is the mechanical power, in p.u., that you must connect to the first input of a Synchronous Machine block.

**Example**

The `psbthermal.mdl`

demo illustrates the use of the Steam Turbine and Governor block. This system is an IEEE benchmark used to study subsynchronous resonance and particularly torque amplification after a fault on a series-compensated power system [2]. It consists in a single generator connected to an infinite bus via two transmission lines, one of which is series compensated. The subsynchronous mode introduced by the compensation capacitor after a fault has been applied and cleared excites the oscillatory torsional modes of the multimass shaft and the torque amplification phenomenon can be observed. Open the Simulink diagram by typing `psbthermal`

.

This system is slightly different from the one presented in [2]. Since we are using the Synchronous Machine mass as the first mass, we cannot model the exciter's mass as is done in [2]. Therefore, our system has only three masses, representing the generator's rotor (mass #1), and the turbine's low and high pressure stages (masses #2 and #3, respectively).

In order to start the simulation in steady state, a load flow was performed on the system, setting the generator as a **PV generator** with initial power of 100 kW (1e5 W). This is done to simulate an initially unloaded generator. The load flow returns initial mechanical power of 100 010 W. This value was converted into p.u. by dividing it by the generator's nominal VA rating (600e6 VA) and the result was entered as the first initial condition in the Steam Turbine and Governor block. The second initial condition is the generator's initial angle. This value is computed by the load flow and is written in the initial conditions vector of the generator. After the load flow is finished, you can open the Synchronous Machine block dialog box and copy the initial angle in the Steam Turbine and Governor block dialog box. The Steam Turbine and Governor block is now correctly initialized. The electrical power (load) reference, the second input of the Steam Turbine and Governor block, is set to the desired electrical power supplied by the generator, in p.u. (1e5/600e6, or 0.1/600).

This test is performed without regulators. The speed governing system is forced to output a constant value by setting the gate opening limits very close to each other, around the initial gate opening, which is also the initial mechanical power in p.u. (100 010/600e6, or 0.00016668 p.u.). The machine's excitation voltage is also set to a constant value (1.00358 p.u.), which is computed by the load flow.

Set the simulation parameters as follows:

- Integrator type:
`Variable-step`

,`ode23tb`

- Stop time:
`0.5 s`

- Integration options: Use default options, except for Max step size, which you set to
`50e-6.`

This is not absolutely required, but the simulation runs faster if this value is set as prescribed.

Run the simulation by choosing **Start** from the **Simulation** menu. Once the simulation is completed, observe the mass speed deviations and torques and the fault current.

The peak values of all these signals correspond within 3% to those given in Table 5, case 1A, of [2]. The torque amplification is clearly observed on all masses of the shaft system. The high-pressure mass (#3) transmits a peak torque of 1.91 p.u. to the low-pressure mass (#2), while the low-pressure mass transmits a peak torque of 4.05 p.u. to the generator's rotor (mass #1).

**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.

**See Also**

Excitation System, Hydraulic Turbine and Governor, Powergui, Synchronous Machine

Simplified Synchronous Machine | Surge Arrester |