Spring EE321 2010
Homework 11
Problem 1 Brushless DC Operation from a Voltage Source
The flux linkage equations for a certain PMSM may be expressed
abcs
L ss
= 0
0
0
L ss
0
0
cos r
cos(3 r )
i
cos( 2 / 3) cos(3 )
0 abcs + m
r
m3
r
cos( r + 2 / 3)
cos(3 r )
L ss
where L ss , m , and m3 are constants. The machine is wye-connected. Express the q- and daxis flux linkage equations for the machine. Your answer should involve the q- and d-axis flux
linkages, the q- and d-axis currents, and the parameters L ss , m , and m3 .
Recall
cos( r ) cos( r 2 / 3) cos( r + 2 / 3)
2
K r = sin( r ) sin( r 2 / 3) sin( r + 2 / 3)
s
3 1
1
1
2
2
2
Problem 2 Machine Connections
Why are brushless dc machines only rarely delta connected?
Problem 3 Brushless DC Operation from a Voltage Source
A three phase brushless DC machine has the following parameters: rs = 3 , Lss = 10 mH,
m = 0.17 Vs, P = 4 . It is from operating an inverter and the control is such that vs = 100 V (rms) and
v = 0.0 . The load torque is given by Tl = 2( rm / 200) 2.3 . Find the steady-state rotor speed in RPM, and
the magnitude of the stator current. What is the efficiency?
Problem 4 Brushless DC Operation from a Current Source
Consider the machine in Problem 3, with the same load torque. Instead of being supplied from a
voltage source, consider the situation if the machine is supplied from a current source (with all the current
in the q-axis). Plot the rms current, rms voltage, and efficiency of the machine as the speed is varied from
0 to 4000 RPM.
Problem 5 Brushless DC Parameter Identification
A three-phase brushless dc machine is open circuited, and is spun using a dynamometer. The a- to
b- phase voltage measured from an oscilloscope if found to be sinusoidal. The waveform has a peak-topeak voltage of 200 V, and a frequency of 82 Hz. What is m ?