Simplified Synchronous Machine (SimPowerSystems)

Model the dynamics of a simplified three-phase synchronous machine

Library

Machines

Description

The Simplified Synchronous Machine block models both the electrical and mechanical characteristics of a simple synchronous machine.

The electrical system for each phase consists of a voltage source in series with an RL impedance, which implements the internal impedance of the machine. The value of R can be 0 but the value of L must be positive.

The Simplified Synchronous Machine block implements the mechanical system described by

where

Although the parameters can be entered in either SI units or per unit in the dialog box, the internal calculations are done in per unit. The following block diagram illustrates how the mechanical part of the model is implemented. Notice that the model computes a deviation with respect to the speed of operation, and not the absolute speed itself.

Dialog Box and Parameters

In the powerlib library you can choose between two Simplified Synchronous Machine blocks to specify the electrical and mechanical parameters of the model.

Connection type: Specifies number of wires used in three-phase Y connection: either three-wire (neutral not accessible) or four-wire (neutral is accessible).
Nominal: The nominal apparent power Pn (VA), frequency fn (Hz), and rms line-to-line voltage Vn (V). Used to compute nominal torque and convert SI units to p.u.
Mechanical: The moment of inertia (N.m or p.u.) and damping factor. The damping factor has been scaled to act like the damping factor of a second-order system. This means, for example, that for no overshoot and minimum settling time, a damping factor of 0.9 is used.
Internal impedance: The resistance R ( or p.u.) and reactance L (H or p.u.) for each phase.
Initial conditions: The initial speed deviation (% of nominal), rotor angle (deg), line current magnitudes (A or p.u.), and phase angles (deg). These values can be computed by the load flow utility of the Powergui block.

Note These two blocks simulate exactly the same simplified synchronous machine model; the only difference is the way of entering the parameter units.

Inputs and Outputs

The first input of the Simplified Synchronous Machine block is the mechanical power supplied to the machine. This input can be a constant or the output of the Hydraulic Turbine and Governor block. The frequency of the voltage sources depends on the mechanical speed of the machine. The amplitude of these voltages is given by the second input of the block, which can be a constant or the output of a voltage regulator. If you use SI units these two inputs should be in watts and volts phase-to-phase rms. If you use p.u. both inputs should be in p.u.

The first three outputs are the electrical terminals of the stator. The last output of the block is a vector containing the following 12 variables:

1-3: Line currents (flowing out of the machine) ia, ib, ic
4-6: Terminal voltages va, vb, vc
7-9: Internal voltages ea, eb, ec
10: Mechanical angle
11: Rotor speed
12: Electrical power Pe

These variables can be demultiplexed by using the special Machines Measurement Demux block provided in the Machines library.

Assumptions

The electrical system of the Simplified Synchronous Machine block consists solely of a voltage source behind a synchronous reactance and resistance. All the other self and magnetizing inductances of the armature, field, and damping windings are neglected. The three voltage sources and RL impedance branches are Y-connected (three wires). The load might or might not be balanced.

Example

The psbsimplealt.mdl demo uses the Simplified Synchronous Machine block to represent a 1000 MVA 315 kV equivalent source connected to an infinite bus (three AC Voltage Source blocks). The Synchronous Machine block is used as a synchronous generator. The internal resistance of the machine is set to 0.02 p.u., or 1.9845 ohms. Its inductance is set in such a way that the total impedance is 1 p.u. (L = 263.15 mH). The inertia of the machine is 56290 kg.m².

In this example, the machine has an initial speed deviation of 0.5%. The initial mechanical angle and phase currents i_a, i_b, and i_c are set to 0. The power transfer between the machine and the bus is given by the following relation:

With the preceding parameters, the steady state internal voltage is 30° ahead of the terminal voltage ( = +30°). The machine is supplied with 505 MW of mechanical power in order to compensate for its resistive losses. The electrical angle is displayed as the phase difference between the internal and terminal voltages of phase A. With simulation parameters set as follows, the results shown below are obtained:

Integrator type: Stiff, ode15s
Stop time: 2.0
Integration options: Use default settings

The speed vs. time graph clearly shows that the machine is initially running at a speed of 1.005 p.u. (1809 rpm) and that speed stabilizes itself at its nominal value of 1800 rpm. As expected, the electrical power supplied by the machine stabilizes at 500 MW. The power angle also settles at its expected value of 30°. The mechanical system is clearly underdamped, the damping factor being set to 0.3.

Series RLC Load Steam Turbine and Governor