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Determining Motor Characteristics of a Doubly-fed Induction Generator
6.UAP
Matt Angle
5/16/07
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In recent years, a doubly fed induction generator has been designed and built in
the Lab for Electromagnetic and Electronic Systems at MIT. Balance problems plagued
the machine until January, when it was disassembled and the rotors were sent off to be
balanced. The beginning of my UAP was helping to disassemble and reassemble the
machine.
For the moment, we are curious as to how the machine will perform as a motor. It
appears attractive for large low-speed applications such as propulsion. The stator can be
fed with line voltage, and the power rotors can be driven with a variable frequency
waveform to produce a variable speed motor. This configuration is more efficient than
rectifying line voltage and then inverting back to AC at the required frequency for the
desired speed. The power handling requirements of the power electronics are vastly
reduced in this configuration as well.
The point of the this exercise is to acquire a v-curve for the motor. This is a plot
showing the current going in to the terminals of the machine as a function of internal
voltage when the machine is run unloaded. This gives us insight to parameters such as
the armature impedance. Normally, the internal voltage of the machine is adjusted by
varying field current. In this case, we have permanent magnets inside the machine, so
there is no field current to adjust. Our v-curve must be determined by varying the voltage
on the terminals.
To run the machine as a motor, we decided to feed power in to the stator and short
the windings of the power rotors. In steady state, the stator acts upon the permanent
magnet rotors as a synchronous permanent magnet machine, which in turn acts on the
shorted windings of the power rotor inductively. The power rotor is rigidly affixed to
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the output shaft.
Reaching this steady state proves to be a bit of a debacle. Theoretically, the
aluminum material of the permanent magnet rotor could have a current induced by the
rotating magnetic flux of the stator and thus start as an induction motor. The presence of
the permanent magnets in the rotor, however, has the potential to create harmonics in the
voltage supply as the rotor spins up, possibly leading to a situation where it will not spin
up to synchronous speed. This has not been evaluated (but could be if you want me to...).
Instead, we decided to simply spin up the shorted power rotors with an external motor.
The stationary permanent magnet rotor induces currents in the power rotor, which
interact with the magnets in the pm rotor, causing it to spin up to near the speed of the
input shaft. From here, power can be connected to the stator and the machine will
continue running as a motor for further testing
Since the machine is as large as it is, connecting power incorrectly could prove
disastrous. It is important for the phase sequence of power to match the phase sequence
corresponding to the direction of rotation of the machine. To ensure the sequences
match, my first task was to build a device called a synchronizer. It consists simply of a
lightbulb across a switch on each phase between wall power and each phase of the
machine. The theory of operation here is that the lights will light when there is a voltage
difference between that particular phase of the machine and the wall power.
The device consists of a standard three phase breaker box and six 25 watt
lightbulbs, two in series across each phase of the breaker box. A 25 watt lighbulb is
effectively a 576 Ohm resistor. Two in series is 1152 Ohm resistor.
In Figure 1, the three wall power phases are on the very left, the lightbulbs are
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shown simply as resistors, the three phases of the machine are shown as inductors on the
right side, and the three transformers across the middle compose the variable
autotransformer.
Figure 1: Three Phase Connection Diagram for the Machine
When the phase sequence is correct, the lights will flash in unison as the speed of
the machine approaches the frequency of the power. Figure 2 is an illustration of the
voltage across the lights. Intensity or light would be proportional the square of this
graph. As the speed of the machine is brought closer to synchronous speed, the flashing
slows down. When all the lights are out at the same time (meaning there is no voltage
difference across the switch on any phase), the power can be connected without
damaging anything.
When the phase sequence is off, the lights will flash sequentially at the frequency
difference between the line voltage and the machine as shown in Figure 3.
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Figure 2: Voltage across lights when phase sequences are
correct
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Figure 3: Voltage across lights when phase sequence is backwards
A third piece of the synchronizer is a three phase adjustable autotransformer.
This allows us to vary the wall voltage to the desired terminal voltage for the machine,
which allows us to determine our v-curve.
During testing of the machine, it was determined that there was a short in one of
the phases inside the machine. Luckily, the short was traced to a location accessible from
outside the machine.
Before the experiment could be run, however, there was another problem. The
motor and its mounting scheme had a critical frequency just above synchronous speed,
meaning that the machine vibrated violently at operating speed. This placed a limit on
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how long the machine could be operated.
The machine is mounted to the test bed as shown in the following picture. It is
mounted to two pieces of unistrut which are bolted to a steel base weighing many times
what the machine does. There is a pivot attached to the machine and the middle of the
unistrut, with turnbuckles at each end to pre-load the unistrut and adjust tension on the
drive belt. In this configuration, the unistrut acts as a leaf spring, allowing the apparatus
to vibrate at a natural frequencies and its harmonics.
Figure 5: Machine on testbed in old case.
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Figure 6: Closeup of Machine Mounting
In order to move the critical frequency away from the operating point, we needed
to push up the fundamental frequency of oscillation. Given that this is a spring-mass
system, the obvious thing to do was increase the spring constant of the unistrut. This was
accomplished by bolting shorter pieces of unistrut to the bottom of the long pieces
supporting the machine.
Now that the vibration issues were solved and the synchronizer was built, the
experiment could be run. The machine was slowly spun up so the permanent magnet
rotors would closely follow the speed of the power rotors. The machine was then
synchronized and the voltage was swept such that we reached the current limits of the
supply circuit. At each voltage point, current on each phase was measured.
The results are shown in the following plot. Needless to say, this form of curve is
not what we were looking for. Something was clearly wrong. For one, the phases are
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supposed to be symmetric, so they should all reach a current minimum at the same
terminal voltage. This minimum should actually be zero. The plot does show us,
however, that the impedance of the machine is low. This impedance determines the slope
of the line on either side of the minimum point. The lines should be straight, but are
obviously not.
Figure 7: Experimental V-Curve Red = Phase A, Green = Phase B, Blue = Phase C
The experiment was run again, this time with more variables recorded, namely,
the voltage at each phase. It was determined that the calibration of the variable
autotransformer is slightly off, as the rms value of voltage of phases A and C were the
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same, but B was about 2% lower. The curve ended up looking similar to the first one.
A model was developed to see if these results could be matched. It assumed that
the internal voltage magnitude matched the external voltage magnitude and that the
phases of the machine were balanced and symmetric. It took in to account the low
voltage on phase B as well. The phase angles of the power line were then varied until the
graph looked like the data. The result of tweaking the model can be seen in Figure 8.
The solid lines are the experimental data as shown in Figure 7, while the dotted lines are
simulation results.
Figure 8: Experimental vs. Simulation V-Curve
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To obtain the match between model and data above, Phase A of the wall is -.21°,
Phase B is -122.1°, and Phase C is 122.5°, s shown in Table 1. The internal voltage of
the machine is 105V RMS. The impedance of Phase A is .283 Ohms and the impedance
of Phase B and C is .339 Ohms. The Matlab script used to create these graphs is included
at the end.
Internal Voltage RMS
Reactance
Supply Phase Angle
Phase A
Phase B Phase C
105
105
105
0.283
0.339
0.339
-0.21
-122.1
122.5
Table 1: Parameters required to fit data
While the model accounts for only first order effects, it is convincing enough for
us to say that there is something slightly unbalanced in the system. The stator of the
machine may be constructed such that it has these offsets. More likely, however, is the
proposition that one phase is heavily loaded in the lab somewhere.
The V-curve is well explained by the hypothesis above, but there is still another
curiosity of the system. On the second experiment, waveforms of the current and voltage
going in to each phase were recorded at that phase’s minimum current voltage. The
results can be seen in Figures 9-11.
Clearly, these waveforms are messy. Figure 12 shows the power spectral
densities of each of the phase currents. In each, we see significant amounts of 3rd, 5th,
and 7th harmonic content, implying saturation somewhere in the system. The likely
culprit is the variable autotransformer.
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Figure 9: Phase A
Figure 10: Phase B
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Figure 11: Phase C
Figure 12: Power Spectral Density of Phase Currents
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Appendix A:
function[] = phaseoffset()
load vcurvedata.mat
we = 60*2*pi;
t = [0:.01/60:2*pi/60];
ve = [100:.5:109];
offset = 2.5*pi/180;
d_a = -.21*pi/180;
d_b = (-2.1)*pi/180;
d_c = (2.5)*pi/180;
vea = ve.*exp(i*d_a);
veb = ve*.98.*exp(i*(-2*pi/3 + d_b));
vec = ve.*exp(i*(2*pi/3 + d_c));
% machine
xa = .20; % actual value is sqrt(2) times this number... working in RMS
xb = .24;
xc = .24;
wm = 60*2*pi;
vm = 105;
vma = vm;
vmb = vm*exp(-i*2*pi/3);
vmc = vm*exp(i*2*pi/3);
% currents in the machine...
vmid = 1/(1/xa + 1/xb + 1/xc) * ((vea-vma)/xa + (veb-vmb)/xb + (vec-vmc)/xc);
ia = (vea - vma - vmid)/xa;
ib = (veb - vmb - vmid)/xb;
ic = (vec - vmc - vmid)/xc;
figure(1)
plot(ve,abs(ia),'r',ve,abs(ib),'g',ve,abs(ic),'b')
title('Simulated Motor V-Curve')
xlabel('Phase Voltage')
ylabel('Phase Current')
figure(2)
plot(vA,iA,'r',vA,iB,'g',vA,iC,'b')
title('Acutal Motor V-Curve')
xlabel('Phase Voltage')
ylabel('Phase Current')
figure(3)
plot(ve,abs(ia),'r:',ve,abs(ib),'g:',ve,abs(ic),'b:',vA,iA,'r',vA,iB,'g',vA,iC,'b')
title('Acutal vs Simulated Motor V-Curve')
xlabel('Phase Voltage RMS')
ylabel('Phase Current RMS')
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Appendix B:
function[] = synchronizer()
% show what happens when phases reversed...
% electricity from the wall...
figure(1)
we = 60*2*pi;
t = [0:.01/60:2*pi/60];
vea = 120*exp(i*we*t);
veb = 120*exp(i*(we*t - 2*pi/3));
vec = 120*exp(i*(we*t + 2*pi/3));
plot(t,vea,'r',t,veb,'g',t,vec,'b')
title('Phases A, B, and C vs time')
% when phases match
figure(2)
wm = 30*2*pi;
vmia = 120*exp(i*wm*t);
vmib = 120*exp(i*(wm*t - 2*pi/3));
vmic = 120*exp(i*(wm*t + 2*pi/3));
via = abs(vea-vmia);
vib = abs(veb-vmib);
vic = abs(vec-vmic);
plot(t,via,'r',t,vib,'g',t,vic,'b')
title('Voltage Across Lamp When Frequency is slightly off')
% when phases are off
figure(3)
wm = 30*2*pi;
vmoa = 120*exp(i*wm*t);
vmob = 120*exp(i*(wm*t + 2*pi/3));
vmoc = 120*exp(i*(wm*t - 2*pi/3));
voa = abs(vea-vmoa);
vob = abs(veb-vmob);
voc = abs(vec-vmoc);
plot(t,voa,'r',t,vob,'g',t,voc,'b')
title('Voltage Across Lamp When Frequency is slightly off and two phases are reversed')
% when amplitude is off
figure(4)
wm = 30*2*pi;
vmva = 50*exp(i*wm*t);
vmvb = 50*exp(i*(wm*t - 2*pi/3));
vmvc = 50*exp(i*(wm*t + 2*pi/3));
vva = abs(vea-vmva);
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vvb = abs(veb-vmvb);
vvc = abs(vec-vmvc);
plot(t,vva,'r',t,vvb,'g',t,vvc,'b')
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Appendix C:
function[] = uap()
load uapworkplace.mat
tA = tek00001(:,1);
tB = tek00002(:,1);
tC = tek00005(:,1);
iA = tek00001(:,2);
iB = tek00002(:,2);
iC = tek00005(:,2);
figure(1)
subplot(2,1,1),plot(tek00000(:,1),tek00000(:,2))
xlabel('Time(sec)')
title('Phase A Voltage RMS')
subplot(2,1,2),plot(tA,iA)
xlabel('Time(sec)')
figure(2)
subplot(2,1,1),plot(tek00003(:,1),tek00003(:,2))
xlabel('Time(sec)')
title('Phase B Voltage RMS')
subplot(2,1,2),plot(tB,iB)
xlabel('Time(sec)')
figure(3)
subplot(2,1,1),plot(tek00004(:,1),tek00004(:,2))
xlabel('Time(sec)')
title('Phase C Voltage RMS')
subplot(2,1,2),plot(tC,iC)
xlabel('Time(sec)')
%hold on
%fit curves....
%sinfit = fittype('A*sin(60*x+a) + B*sin(180*x+b) + C*sin(300*x+c) + D*sin(420*x+d)');
%sinopts = fitoptions('Method','NonlinearLeastSquares');
%[phAfit phAgood] = fit(tA,iA,sinfit,sinopts)
%subplot(6,1,2),plot(tA,phAfit(tA),'r')
sample_rate = 10000/.2;
f = sample_rate*(0:.5e4-1)/1e4;
figure(4)
ffta = fft(tek00001(:,2)-mean(tek00001(:,2)),1e4);
Paa = ffta.*conj(ffta)/1e4;
subplot(3,1,1),plot(f(1:1e2),Paa(1:1e2))
xlabel('Frequency in Hz')
axis([0,500,0,2e5])
fftb = fft(tek00002(:,2)-mean(tek00002(:,2)),1e4);
Pbb = fftb.*conj(fftb)/1e4;
subplot(3,1,2),plot(f(1:1e2),Pbb(1:1e2))
xlabel('Frequency in Hz')
axis([0,500,0,2e5])
fftc = fft(tek00005(:,2)-mean(tek00005(:,2)),1e4);
Pcc = fftc.*conj(fftc)/1e4;
subplot(3,1,3),plot(f(1:1e2),Pcc(1:1e2))
xlabel('Frequency in Hz')
axis([0,500,0,2e5])
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figure(5)
plot(f(1:1e2),Paa(1:1e2),'r',f(1:1e2),Pbb(1:1e2),'g',f(1:1e2),Pcc(1:1e2),'b')
h = legend('Frequency Content Phase A','Frequency Content Phase B','Frequency Content
Phase C',3);
set(h,'Interpreter','none')
axis([0,500,0,6e4])
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Appendix D:
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