Transcript תפקיד המורה-טכנולוג כמתווך ידע בעבודת צוות מורים מפתחי קורסים מתוקשבים

The mathematical model of the induction
machine:
Voltages:
Vs g  Rs * is g 
Vrg  Rr * irg 
Inductances:
Ls  Lm  Lsl
Lr  Lm  Lrl
Torque:
Currents:
d Fs g
dt
d Frg
dt
is  Ks * Fs  Km * Fr
 G * wk * Fs g
ir  Kr * Fr  Km * Fs
 G * ( wk  wm ) * Frg
Ls
Lrl * Lm  Lsl * Lm  Lrl * lsl
Ls
Kr 
Lm * Lsl  Lm * Lrl  Lsl * Lrl
Lm
Km 
Lrl * Lm  Lsl * Lm  Lrl * lsl
Ks 
3
3
Te  * p * ( Fs  is )  * p * (G * Fs  is )  Fds * iqs  Fqs * ids
4
4
dwm
Te  J
 Bm * wm  Tl
dt
The steady state analysis of the induction
machine:
The synchronous speed is defined by:
60 * F
nsync 
[rpm]
p
2 *  * F nsync * 2 * 
 sync 

[rad/sec]
p
60
The difference between the synchronous speed and the rotor
speed is defined as slip:
nsync  nm
s
nsync
If the machine rotates at a smaller speed than the synchronous
speed, the machine behaves as a motor (the slip is positive).
If the speed is higher than the synchronous speed, the machine
behaves as a generator (the slip is negative).
The steady state analysis of the induction
machine:
The equivalent circuit of one phase of the induction machine:
The impedance of the machine would be:
Zeq  Rs  jX s 
1
1
 jBm 
R
( r )  jX r
s
V ph
The phase current would be: I ph 
Z
eq
The thermal model of the induction machine:
The heating of the machine occurs as a result of power
losses inside the machine.
Plosses=Pcu+Pfer=Pin-Pout
The temperature of the machine can be calculated by the
following differential equation:
C
dT
 Plosses  Pradiation
dt
Pradiation
- the heat radiation of the machine.
C- thermal capacitance of the machine.
These two parameters must be provided by the manufacturer.
The simulation circuit:
Performance of the voltage controller:
In order to understand the performance of the voltage controller
the following circuit is presented:
The output of the voltage controller for different
firing angles:
a. 
b.
 100
60
Definitions:
1.   phase angle
Phase angle is the angle between phase voltage and phase
current. When the machine operates as motor, this angle
would be: 0    90. 
When the machine operates as generator, this angle would be:
90    180
2.   firing angle
The firing angle is the angle between point at which the phase
voltage is zero to point of conduction of the appropriate
thyristor.
Definitions:
3.   delay angle
The delay from the point at which the phase current reaches
zero to the point when next thyristor is fired, called the
delay angle.     
The firing angle must be greater than the phase angle. If the
firing angle is smaller than phase angle, the delay angle will be
negative. In this case, in the steady state, the machine would
operate as usual, as if there were no SCRs, and it would not be
influenced by the changes in firing angle. However, the
transient behavior will be influenced.
Examples:
Example 1.
2. Motor:
Motor:
Example
  80
  100
40
In this case, the currents and the voltages in the steady state
will not be influenced by the thyristors.
Matlab simulation
In order to perform the simulation in Matlab, two files must be
built:
1. The fire.m file. This file is used for definition of parameters
for the firing control of thyristors. These parameters are
used in the pulse generators in the Simulink file.
2. The Simulink machine.mdl file. In this file the circuit itself
is built.
The fire.m file:
a=input('enter a:')
With the help of this file, the only
T=0.02;
parameter that the user must insert
d=ax*(T/2)/180;
to the program is the firing angle.
pw=(((T/2)-d)/T)*100;
Other parameters for pulse
when:
generators are calculated
a- firing angle.
automatically by the fire.m file.
T- period (sec).
d- phase delay for the pulse generator (sec).
Pw- pulse width (% of the period).
The machine.mdl file:
Parameters of the simulated circuit:
Three phase voltage source:
Induction machine:
Va  3000, v
Vb  300  120, v
Rotor type: squirrel cage.
Vc  300120, v
Rs=1.435 ohm
Rr=1 ohm
Ls=2 mHy
Lr=2 mHy
Lm=49.31 mHy
Inertia=0.009 kg*m*m
Number of poles=2
The measurements:
The measurement of
harmonics
The measurement of
RMS and THD
The measurement of
Pin
The measurement of
fluxes
The measurement of
Pout
The results of the measurements:
1. Firing angle=80 degrees, machine operates as motor.
It ismachine
clear thatisinunloaded,
this case therefore
the firingitangle
is smaller
than the
The
operates
as a motor.
phase
angle, state,
therefore
the delaywould
angle operate
is negative:
degrees.
In
the steady
the machine
as an-5inductive
The stator currents in the steady state will be continuous.
load.
The phase angle in the steady state can be calculated by
calculation of the machine's impedance.
Z eq  R1  jX 1 
1
1

 jBm 
R
( 2 )  jX 2
s
1
 1.435  j 0.628 
 16.1885, 
1
1
j

1
15.49
1
( )  j 0.628
0
The stator currents, rotor currents, mechanical
speed and torque:
At t=0 sec, when the source voltages are applied to the
I_stator
machine, the machine's speed is zero and the slip is 1.The
steady state begins at t=0.5 sec, when the machine has
reached the synchronous I_rotor
speed. The synchronous speed of
the motor is 314.2 rad/sec.
When
The machine's
the machine
torque
hasisreached
maximal
thewhen
synchronous
the speedspeed,
is lowthe
and
wm
slip
the becomes
torque becomes
zero and
zero
thewhen
resistance
the machine
Rr/s becomes
rotatesinfinite
at the
and
synchronous
the rotor currents
speed. become zero.
Torque
The harmonics of stator current of phase ‘a’ :
First harmonic
Second harmonic
Third harmonic
Fifth harmonic
The RMS, THD of the stator current in phase 'a':
i_a rms
i_a THD
Stator and rotor fluxes:
The fluxes are obtained from the measurement demux block,
are in the d-q frame and they must be converted to the regular
abc frame.
The following block was built in order to perform the conversion:


1 0 
 Fa  
 F
1
3
 F   - * q 
 
 b  2
2   Fd 
 Fc  

1
3

 2
2 
Converted stator and rotor fluxes:
Rotor fluxes
Stator fluxes
The results of the measurements:
2. Firing angle=100 degrees, machine operates as motor.
Now the machine is loaded by the external load of 6 N*m at the
time of t=1.5 sec, when the machine has reached the steady state.
At t=1.5 sec, the phase angle is changed from 85 degrees to 72
degrees. The delay angle is now 28 degrees. As it was mentioned
before, if the delay angle is higher, the THD will be also higher.
The stator currents, rotor currents, mechanical
speed and torque:
When the machine is loaded,
the induced torque of the
I_stator
machine rises from average zero to average 6 N*m.
I_rotor
When the machine is loaded at t=1.5 sec, the amplitude of the
currents in the steady state jumps from 16.5A to 21.5A
From the comparison of statorwm
currents, it is clear that when
the delay angle increased, the distortion of the currents also
increases.
Torque
When the machine is loaded, the mechanical speed falls from
314 rad/sec to 265.5 rad/sec.
The harmonics of stator current of phase ‘a’ :
First harmonic
Second harmonic
The fifth harmonic becomes much more dominative after the
machine is loaded. This is the reason that the currents become
more distorted after the machine
is loaded.
Third harmonic
Fifth harmonic
The RMS, THD of the stator current in phase 'a':
i_a rms
i_a THD
54%
14%
Converted stator and rotor fluxes:
Rotor fluxes
Stator fluxes
The results of the measurements:
3. Firing angle=100 degrees, machine operates as generator.
Now the machine is loaded by the negative external load of -6
N*m at the time of t=1.5 sec, when the machine has reached the
steady state. In this case the machine is driven at higher speed
than the synchronous speed. The machine will deliver the power
to the grid.
At t=1.5 sec, the phase angle is changed from 85 degrees to 97
degrees. The delay angle is now smaller than in the previous
cases: 3 degrees. The distortion of currents must be very low.
The stator currents, rotor currents, mechanical
speed and torque:
I_stator
The induced torque of generator in the steady state is –6 N*m.
I_rotor
After the machine is loaded with negative torque, the stator
currents amplitude rises to 20A.
wm
Torque
When the negative torque is applied, the speed rises from 314
rad/sec (synchronous speed) to 318.6 rad/sec.
The harmonics of stator current of phase ‘a’ :
First harmonic
Second harmonic
The amplitude of fifth harmonic in the generator’s steady state
is 0.3A and it almost doesn't influence the sine form of the
Third harmonic
currents.
Fifth harmonic
The RMS, THD of the stator current in phase 'a':
i_a rms
i_a THD
14%
2%
Converted stator and rotor fluxes:
Rotor fluxes
Stator fluxes
The input active power Pin:
When the machine starts to operate as generator, the input active
power becomes negative because now the power is supplied from
the machine to the grid.
The output active power Pout and the mean Pout:
Pout
Mean Pout
The difference between the original thesis
simulations to the presented simulations:
The original Simulink simulation circuit for my thesis was
different from the simulation circuit that was presented.
The difference is that in the original simulation was not used the
fire.m file. The firing angle control of the thyristors was done by
the synchronized 6-pulse generator.
The differences between the simulations:
The difference of stator currents in the second case (unloaded
machine and firing angle of 100 degrees):
The stator current in the original thesis simulation circuit:
The peak of stator currents in the first cycle of simulation.
The stator current in the original thesis simulation circuit:
The Psim simulations:
Unlike
Simulink, in Psim
there
is no option
Torque
measurement-he
internal
mechanical
The simulation circuit: systemforofmeasurement
of rotor
currents. by the
the machine can
be described
The stator current in phase ‘a’ is measured by the
following equation:
current sensor and from the current sensor is
dwm
passed to the control part of( JPsim.
J
)*
T T
machine
There are two ways to measure the speed
of the machine:
The signal
is transmitted
to the Simulink
1. Mechanical
speed
can be measured
by for
RMS, THD
and harmonics calculations.
speed sensor
(in rpm)
2. Mechanical speed can be measured by
accessing the internal equivalent circuit of
the machine’s mechanical system. This is
done
byphase
the mechanical-electrical
Three
wttmeter
interface block. The output of this block is
the mechanical speed of the machine (in
rad/sec).
Firing control
load
dt
em
load
Co-simulation between Psim and Simulink:
The Psim file:
The purpose of this circuit is to simulate resistor of 1 ohm
connected through the thyristors to the sine voltage source of 10 v.
The firing angle of the thyristors is 100 degrees. The voltage
control is performed in Psim. The output voltage of the thyristors
is sent to Simulink file, which represents the behavior of the
resistor of 1 ohm.
The tested circuit:
The Simulink file file:
The influence of Rm resistance:
In order to measure the output voltage of the thyristors, the
resistor Rm must be inserted in parallel to the voltage sensor.
The resistance Rm must be set to very high value in order to
diminish it’s influence on the circuit’s current.
When the resistor is set to 1 Mohm, the following current
results are obtained:
The influence of Rm resistance:
When Rm is set to 1 ohm, the following results are
obtained:
Now the results are logical but Rm has changed the true value
of the current, which is supposed to flow for resistor of 1ohm.
The influence of Rm resistance:
If the simulation for Rm=1 Mohm is done only in Psim, without
the co-simulation with Simulink, the results are correct.
The Psim simulation circuit:
The conclusion is that there must be a problem with cosimulation of programs for higher values of Rm.
The use in Simcoupler for simulation of case 3:
The following parameters will be measured in Psim:
1. RMS, THD and harmonics of the phase ‘a’ stator current.
2. The average of the output active power.
In order to perform these measurements, the I_a and Pout signals
are sent to the Simulink by Simcoupler.
The measurements results for case 3:
Stator currents
wm
Torque
The harmonics of stator current of phase ‘a’ :
First harmonic
Second harmonic
Third harmonic
Fifth harmonic
The RMS, THD of the stator current in phase 'a':
i_a rms
i_a THD
14%
2%
The input active power and output active power:
Pin
Mean Pout
Pout
Pout
The Plecs&Matlab co-simulation:
The contents of Plecs block:
The complete simulation circuit, including
measurements:
The measurements results for case 4:
Stator currents
Rotor currents
wm
Induced torque
The harmonics of stator current of phase ‘a’ :
First harmonic
Second harmonic
Third harmonic
Fifth harmonic
The RMS, THD of the stator current in phase 'a':
i_a rms
i_a THD
14%
2%
The rotor and stator fluxes:
Rotor fluxes
Stator fluxes
Powers:
Pin
Pout
Mean Pout
Summary:
User interface of the programs:
The Psim program has most simple user interface.
1. The control of switches is simpler than in Simulik and Plecs.
2. The elements can be chosen very quickly and easily from the
elements library.
The Psim program is much more simple in use than Matlab and
Plecs.
The signals processing and measurement options:
Simulink has more options for signal processing and measurements
than Psim or Plecs. Therefore, Simulink is often used in cosimulation with other programs.
Summary:
Run time of the simulation:
Psim has the fastest run time. It took about 10 seconds to simulate
the circuit of case 3. Simulink is slower than Psim. It took about 1
minute to simulate the circuit of case 3.
In Plecs and Simulink co-simulation, it took 1 hour to simulate the
circuit of case 3.
Co-simulation with Simulink:
Plecs was designed especially for co-simulation with Simulink.
ny Plecs circuit can be co-simulated with Simulink, includinig the
option of “breaking” the power circuit by controlled current and
voltage sources.
Summary:
Psim should be co-simulated with Simulink only in the case of
signal processing. It is not reccomended to “break” the Psim’s
power circuit by controlled current and voltage sources, because
there are cases when it won’t work.