Synchronous machine with simplified transformation, simplified representation, and fundamental or standard parameterization
Simscape / Electrical / Electromechanical / Synchronous
The Synchronous Machine Model 2.1 block models a synchronous machine with one field winding and one damper on the d-axis and one damper on the q-axis. You use fundamental or standard parameters to define the characteristics of the machine. This block contains a dq Park transformation, so use it only for balanced operation.
If the block is in a network that is compatible with the frequency-time simulation mode, you can perform a load-flow analysis on the network. A load-flow analysis provides steady-state values that you can use to initialize the machine.
For more information, see Perform a Load-Flow Analysis Using Simscape Electrical and Frequency and Time Simulation Mode. For an example that shows how initialize an synchronous machine using data from a load flow analysis, see Synchronous Machine Initialization with Loadflow.
The synchronous machine equations are expressed with respect to a rotating reference frame, defined by
where:
θe is the electrical angle.
N is the number of pole pairs.
θr is the rotor angle.
The Park transformation maps the synchronous machine equations to the rotating reference frame with respect to the electrical angle. The Park transformation is defined by
The Park transformation is used to define the per-unit synchronous machine equations. The stator voltage equations are defined by
and
where:
e”d and e”q are the d-axis and q-axis voltages behind subtransient reactances.
Ra is the stator resistance.
id and iq are the d-axis and q-axis stator currents, defined by
ia, ib, and ic are the stator currents flowing from port ~ to port n.
x”d and x”q are the d-axis and q-axis subtransient reactances.
ed and eq are the d-axis and q-axis stator voltages, defined by
va, vb, and vc are the stator voltages measured from port ~ to neutral port n.
The rotor voltage equation is defined by
where:
Rfd is the resistance of rotor field circuit.
ifd is the per-unit field current using the synchronous machine model reciprocal per-unit system.
efd is the per-unit field voltage using the synchronous machine model reciprocal per-unit system.
The voltage-behind-transient-reactance equations are defined by
and
where:
xd and xq are the d-axis and q-axis synchronous reactances.
T”d0 and T”q0 are the d-axis and q-axis subtransient open-circuit time constants.
Efd is the per-unit field voltage using the exciter model nonreciprocal per-unit system.
x’d is the d-axis transient reactance.
e’q is the q-axis voltage behind transient reactance.
T’d0 is the d-axis transient open-circuit time constant.
The rotor torque is defined by
These defining equations do not describe the parameters you can set in the dialog box. To see their relationship with the equation coefficients, see the book of P. Kundur about understanding, modeling, analyzing, and mitigating power system stability and control problems [1].
You can perform display actions using the Electrical menu on the block context menu.
Right-click the block and, from the Electrical menu, select an option:
Display Base Values displays the machine per-unit base values in the MATLAB® Command Window.
Display Associated Base Values displays associated per-unit base values in the MATLAB Command Window.
Display Associated Initial Conditions displays associated initial conditions in the MATLAB Command Window.
The Variables settings allow you to specify the priority and initial target values for block variables before simulation. For more information, see Set Priority and Initial Target for Block Variables.
For this block, the Variables settings are visible only if, in the
Initial Conditions settings, the Initialization
option parameter is set to Set targets for rotor angle and
Park's transform variables
.
[1] Kundur, P. Power System Stability and Control. New York: McGraw Hill, 1993.
[2] Lyshevski, S. E. Electromechanical Systems, Electric Machines and Applied Mechatronics. Boca Raton, FL: CRC Press, 1999.
[3] Pal, M. K. Lecture Notes on Power System Stability. June, 2007.
Synchronous Machine Field Circuit | Synchronous Machine Measurement | Synchronous Machine Model 1.0 | Synchronous Machine Round Rotor | Synchronous Machine Salient Pole