Model the dynamics of a speed governing system, steam turbine, and multimass shaft
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 .
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
|Note If you do not want to simulate all four masses in the multimass shaft, simply set the inertia of unwanted masses to 0. The rigidity coefficient and damping factor corresponding to omitted masses are not considered. When masses are not simulated, the remaining system is "compressed" toward the generator, i.e., if only two masses are used (excluding the generator), they are masses #2 and #3. The input data for the masses considered are shifted accordingly. In any case, inertias must be consistent with torque fractions. You cannot set an inertia to 0 and set the corresponding torque fraction to a nonzero value. However, you can set a torque fraction to 0 and set the corresponding mass inertia to a nonzero value.|
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.
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 . 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
This system is slightly different from the one presented in . Since we are using the Synchronous Machine mass as the first mass, we cannot model the exciter's mass as is done in . 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:
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 . 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).
 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.
 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.
Excitation System, Hydraulic Turbine and Governor, Powergui, Synchronous Machine
|Simplified Synchronous Machine||Surge Arrester|