ECE4902 - Senior Design II
Variable Induction Motor Simulator
Spring 2015
Spring 2015 Final Paper
Team 1506 Members:
Geoffrey Roy (EE)
Amber Reinwald (EE)
Matthew Geary (EE)
Advisor:
Ali Bazzi
Lenze Contact:
Chris Johnson
Summary
The goal of this project is to design and develop a variable three-phase induction motor
simulator to facilitate industrial testing of variable frequency drives. With this variable induction
motor simulator a user can adjust the motor simulator’s equivalent circuit parameters to emulate
various induction motors. To add to the versatility of the motor simulator, the user can also
change the motor simulator’s load using a graphical user interface (GUI) to output loads of 0.5,
1.0, and 2.0 HP allowing for a flexible test environment.
Currently Lenze utilizes many induction motors and dynamometers to test their variable
frequency drives. This method of testing consequently takes up a large area of space and gives
off a significant amount of heat. To facilitate Lenze’s testing the use of a variable induction
motor simulator can reduce space, eliminate moving mechanical parts, and allow for a variety of
test scenarios for variable frequency drive testing, with the same accuracy and reliability as an
induction motor and dynamometer pair.
By sponsoring this project, Lenze can more efficiently test and improve their variable
frequency drive products with our variable motor simulator. This will allow Lenze to stay
competitive while providing a properly tested and safe product to their costumers.
Background
Motion control devices are a critical piece in an electro-mechanical system. To control an
AC motor’s speed and torque a motion control device adjusts the input voltage and frequency of
the motor; one such motion control device is a variable frequency drive. Some common
applications that use variable frequency drives to adjust the rotational speeds of electrical motors
are: product transportation, pump control, automotive construction, among others. Since variable
frequency drives are commonly used, the production of a well tested and well performing
product is what can set apart one company’s product from another. Due to this fact, our sponsor,
Lenze, finds it critical that all of their device lines be properly tested to ensure the performance
and reliability of their products.
Statement of Need
Currently Lenze’s test configuration consists of multiple induction motor and
dynamometer pairs which, is an accurate testing method to test variable frequency drives as the
drives are directly controlling the intended plant it was designed for. Unfortunately, depending
on how many motors are used to accomplish testing the motors can take up a large amount of
space and give off heat. The induction motors, when operational, also rotate at a driven
frequency while outputting a load that depends on the motor being driven; because the motors
are frequently rotated the use of moving mechanical parts eventually leads to replacement when
the equipment is damaged or worn out. To eliminate this problem Lenze desires a variable
induction motor simulator that can function under normal motor conditions and output loads of
0.5, 1.0, and 2.0 HP without the consequences of taking up space and moving parts.
In response to Lenze’s request our goal is to design and create a motor simulator that can
accurately simulate the multiple loads of an actual motor and by doing so we hope to reduce or
eliminate the need to use many induction motors. The motor simulator should be able to run and
be controlled by a user interface so that no outside devices other than the variable frequency
drive and motor simulator are required to operate the system. We plan to maintain a sensible cost
for parts during the design and testing phases so we are able to produce a final product at a
reasonable price. To gain an understanding and create a motor simulator, Lenze has directly
provided us with a motor and variable frequency drive, although more motor models may
become available for testing.
Theory
As previously mentioned our goal is to create an induction motor simulator that can
emulate a motor under normal motor conditions and output user specified loads of 0.5, 1.0, or 2.0
HP, which will be defined using a GUI. Before any design choice is possible an understanding of
induction motors must be obtained.
Induction motors operate by inducing time varying current in their stators. One
commonly used motor is a three-phase induction motor. With a three-phase induction motor each
stator is physically oriented 120 degrees from each other, which results in each time varying
current to also be 120 degrees out of phase. This time current results in a rotating magnetic field
that induces a rotating magnetic field in the rotor that constantly tries to catch the stator’s
rotating field. Since the magnetic field of the rotor will never catch that of the stator the motor
rotates; this is how an induction motor gets its name [1].
Figure 1: A single-phase equivalent circuit for an induction motor [1]
When an induction motor is in use the amount of power it outputs is dependent on the
slip. The slip of an induction motor is the difference between the synchronous speed of the
stators magnetic field and the spinning speed of the motors shaft. The percentage value of slip
ranges from 0% to 100% where at 0% the rotor and stator synchronous speeds are equal and at
100% the rotor is not moving. This dependency on slip is important in induction motors, as
shown in figure 1 an induction motor’s rotor resistance is directly dependent on slip. With this in
mind our variable induction motor simulator also has to have a slip dependency.
To narrow down a design choice for the motor simulator the technologies researched had
to accurately emulate an induction motor and be able to include a slip dependent load. Some
options that were researched were per-phase equivalent motor circuits, single-phase
transformers, three-phase transformers, power hardware in the loop, and field-programmable
gate arrays. The first design options of per-phase equivalent circuits and single-phase
transformers were theoretically the same options. The circuit shown in figure 1 is a single-phase
circuit for an induction motor but fundamentally induction motors and transformers are the same;
the difference being a transformer does not depend on slip and has no moving parts.
Consequently these options would involve three units to create a full motor simulator as each
single circuit or transformer represents a phase of the motor. To accurately design a motor
simulator the induced magnetic fields must be coupled. Since three single-phase equivalent
circuits or transformers cannot have their magnetic fields coupled the option to use equivalent
circuits or three single-phase transformers was ignored.
A slightly more expensive option is a single three-phase transformer. Like the first option
the equivalent circuit is the same as an induction motor’s except for the slip dependency; but
since the magnetic fields of a three-phase transformer are coupled this option is a much better
choice for a motor simulator. One downside to using a three-phase transformer is its size; a
three-phase transformer is much larger than that of any circuit or a single-phase transformer.
The last two options are also fundamentally similar. Power hardware in the loop (PHIL)
and field programmable gate arrays (FPGA) are two devices that a user can program. PHIL is a
technique that many manufacturers use to test and develop embedded systems using real time;
PHIL simulation can provide an accurate way to test and emulate a plant. For this project we
would use PHIL to simulate the induction motor. Consequently this method of simulation is very
expensive and does not provide as much of a challenge as most PHIL models can be developed
and simulated using Matlab or Simulink. The other option, FPGA, is also a method that can be
programmed to simulate a motor; the difference being that FPGAs are programmed using gate
logic and digital computation rather than Matlab or Simulink blocks. The benefit of using FPGA
is that it is much cheaper than PHIL but the downside is that it usually involves other peripheral
equipment to use and program.
To account for slip in the motor simulator we considered two choices to implement into
the simulator. The first choice was a programmable AC electronic load. With this AC load the
user can set the desired slip dependent load using a GUI; this load would represent the rotor
resistance shown in figure 1. Unfortunately this option is very expensive and outside of our
desired price range. The second more affordable option was to use a high power rheostat that
could be adjusted using a small DC motor that would be interfaced with a GUI. This option is
much cheaper and satisfies the desired output. However after reconsideration the option to use a
high-power rheostat was adjusted to using relays and high-power resistors. This final option will
give an accurate steady-state output as well as a semi transient response of a motor.
Since we want to simulate a motor, we were given motor and variable frequency drive
data to use for project. The data for the equipment is shown in Table 1 and Table 2. After all
research was conducted it was concluded that the most accurate and cheapest option for an
induction motor simulator would be to use a three-phase transformer.
Figure 2: Lenze variable frequency drive and induction motor [2-3]
Table 1: Motor data for model – MDERAXX-056-12J [2]
Voltage
(V)
Frequency
(Hz)
Power
(kW)
Rated Speed
(r/min)
Rated
Current (A)
Power
Factor
230/400
50
0.06
1325
0.38/0.22
0.58
230/460
60
0.75
1725
3.8/1.9
0.64
230/460
60
1.1
1730
4.1/2.0
0.72
230/460
60
1.5
1745
5.8/2.9
0.76
Table 2: Variable frequency drive data [3]
Power
Input Current
Model
Output
Current
Output
Frequency
Output
Voltage
A
(240V)
8.3
A
Hz
V
0.75
A
(120V)
16.6
4.2
0-500
0-230
2
1.5
13.3
8.1
7
0-500
0-230
3
2.2
17.1
10.8
9.6
0-500
0-230
HP
kW
ESV751N01SXB
1
ESV152N02YXB
ESV222N02YXB
Existing Motor Emulation Research
We thoroughly looked into work and research papers on already implemented methods of
motor emulation. We found quite a few documenting work using Power Hardware In the Loop
emulation systems, though no papers mentioned work with three-phase transformers emulating
the steady-state characteristics of an induction machine.
Power Hardware In the Loop:
There has been a decent amount of focus on general Power-Hardware-In-the-Loop
(PHIL) systems as a method to produce an accurate induction motor emulator. Hardware-In-theLoop (HIL) is a well-recognized method in which to design and assess control systems. Its
primary use is to offer more accurate simulation models than a purely mathematical model by
replacing some sections of the would-be simulation with the equivalent physical parts. A PHIL
system is designed to allow interaction between the mathematical simulation and physical
hardware, in this case the VFD.
A method to evaluate the performance of said HIL simulation is to observe the
“transparency” of the system, as presented by M. Bacic, by which the ideally seamless
integration between the simulation and the real components is measured. PHIL is an increasingly
relevant method to experiment with variable drives and test their performance. Some form of
power hardware is simulated and interfaced with the variable drive to be tested and the feedback
is looped back to the interfaced device so that there is full communication between the device
and the simulator. This loop ideally emulates the full performance of the variable drive and the
electronic device that is commonly used to test said device. O. Vodyakho et al. presents a new
approach in emulating an induction machine with a transformer-based coupling network between
the interface and the variable drive. The end result of this method contains no rotating
components. While the use of PHIL simulation has begun to surface as an effective method for
testing it is important to note that there is a need for focus on the interfacing section of the
simulation system. It is not as simple as plugging the hardware into a port on the computer and
communicating simulation data; natural coupling comes from this additional piece. X. Wu et al.
proposes using a time-variant first-order system to approximate the behavior of the hardware.
Also discussed are the problems that arise in development of the interface due to sampling rate,
delay, quantization, and saturation, among other things. R. Wei et al. details methods of which to
mathematically evaluate a PHIL simulation’s accuracy, while testing a variable drive. It is
important to have as much accuracy as possible so that irregularities are not wrongly attributed to
the variable drive. This particular method of analysis addresses the evaluation of systems for
which there is no available reference for the simulation aspect.
The general consensus on PHIL systems is that the option for real components to be
connected to the simulation is a great way to create a design meant to eventually connect to the
real components. This allows for extensive analysis and reworking before building the final
design. However, while it is an excellent method for motor emulation, the cost of the interfacing
equipment for the PHIL system is high and may cause this option to be ruled out for projects
with smaller budgets.
Field Programmable Gate Arrays:
Within the study and research of induction motor simulation, one of the more popular
forms of simulation is using a field programmable gate array (FPGA) in a PHIL system. There
are many IEEE research papers on the subject and many of them have the same motivations
behind the use of FPGAs.
A group of researchers from Shahid Chamran University performed experiments on the
effect of a three-phase induction motor drive driven by FPGA. They focused on an FPGA based
speed control IC for three-phase induction motor drives. The speed control was controlled by
adjusting modulation index and frequency from the FPGA side. Their conclusion was that
because of the programmable system on chip design (PsoC) allowing the programming of logic
devices, and the architecture of gate arrays through digital logic gates and configurable blocks,
the FPGA-based induction drive is a low cost and high performance solution for induction motor
emulation.
Another group of researchers from the Bengal Engineering and Science University
focused on building an FPGA-based real-time emulator of an induction motor. Due to the highspeed characteristics and parallelism of and induction motor the group choose to emulate using a
FPGA. While the emulator was tested under start-up and variable load torque conditions the
researchers were attempting to form a base method for a speed and flux estimator, and several
control schemes, such as direct torque control and field-oriented control for induction motors.
The researches preferred the FPGA-based model due to the reduced cost and physical space, and
the use of hardware binary arithmetic (adders and multipliers) to enable the use of low sampling
periods while complex models are processed.
The last team from the University of San Luis Potosi focused on an FPGA platform to
run a WRIM (wound rotor induction motor) in different reference frames in real-time simulation.
With a focus on real-time simulation (running a model that can execute at the same rate as the
actual physical system) the researches felt that FPGA had a clear advantage due to its high-speed
and its ability to implement any system module by its equivalent circuit model. This in
combination with its parallel execution capacity helps provide a very short execution time. The
researchers concluded that this method was a very accurate and proficient way to emulate an
induction motor.
Across the multiple research documents, the main reasons researchers used FPGAs in
their induction motor experiments is for its reprogrammable and configurable logic blocks and
its parallelism, along with its high-speed characteristics. This allows very short execution times
at a relatively inexpensive rate, providing stable and accurate induction motor simulation models
in the form of its equivalent circuit model. All of these traits are useful for our emulation, so we
did consider the use of an FPGA PHIL system.
So, to conclude on our research there are extensive materials available on the subject of
emulating an induction machine using variations of a power hardware in the loop system.
However, there were no available materials on a simplified motor emulator that emulates steady
state behavior with discrete slip values. This is likely due to the value of accuracy of the
emulation over efficient cost that we value.
Solution
As mentioned before through our extensive research we narrowed our research down to
three possible routes for our induction motor simulator design. The first option was an equivalent
transformer configuration. Since transformers ideally behave like induction motors without any
moving parts this was an ideal solution at first glance. Also, coupling of the magnetic fields was
not possible with three separate single-phase transformers, so we determined a three-phase
transformer would be a more accurate option. The other options evaluated were a PHIL or a
FPGA system. For these options there would be much more room to customize our design to
match our motor’s characteristics. However, these options proved far too expensive and as we
needed a relatively cheap motor simulator these options were out of the question. As a result,
weighing the pros and cons of these options we decided to use a three-phase transformer as our
induction motor simulator solution. This option in conjunction with a slip dependent load can
emulate transient and steady state conditions. The benefits of accurate simulation and relatively
low cost outweighs the other more expensive, but just as accurate, options.
By choosing to use a three-phase transformer for this project we need to emulate the
motor’s slip. Initially in our first design, the most desirable option for slip accuracy was an
electronic AC electronic load as it can be programmed directly from computer software to do
simulate any sweeps or settings needed with minimal user input. However, this possibility was
far too expensive. In its place, we chose to use a smaller DC motor, of which the smaller moving
parts were acceptable in comparison to the main motor we aim to emulate. We would use the DC
motor to control and rotate a high power rheostat to emulate the slip dependent load.
After considering other potentially cheaper options we redesigned the way to emulate slip
with a cheaper and more reliable option than a DC motor and rheostat. By using a resistor bank
and relay board we can properly emulate slip by selecting single resistors or a resistor parallel
combination to get a steady state or transient load. In order to accomplish this method we have to
calculate the correct resistors for the resistor bank. To get the appropriate resistor values the
torque-speed plot of our motor had to be obtained. With the torque-speed plot we can obtain
motor slip values at a particular torque load in the motors linear region and calculate the needed
load resistance at that point. To control our relay we need to design a circuit board that will
communicate relay signals to select our load and interface with a GUI so a user can command
the system. This alternative design solution will be a much cheaper and just as accurate solution
for our induction motor simulator.
Prototype Iterations
The first simulator prototype we considered is shown in figure 3. A Lenze VFD drove
this initial prototype design and a GUI and DC motor combination controlled the simulators
output. The output of this prototype would have emulated slip by having the user set either a
specific slip value or send a command for the DC motor to sweep across a wide resistance range
very quickly; by doing this the simulator would have a transient output like a real motor. Figure
4 shows a flow chart of the prototype.
Figure 3: Initial Simulator Prototype
VFD
Drives
transformer
with varying
voltage and
frequency
Transformer
Outputs a
voltage and
current
waveform like
a motor
DC Motor
Rotates high
power
rheostats based
on user input
Delta-Rheostat
Outputs either
steady-state or
transient power
based on the
user input
GUI
Command for a
single or
transient slip
resistance
Figure 4: Initial Simulator Prototype Flow Chart
Our second, and current, prototype that we are developing uses a resistor bank and a relay
system instead of a DC motor to emulate slip; this prototype is shown in figure 5. Like the initial
prototype a Lenze VFD will drive the motor simulator; the main difference with this prototype is
the use of a resistor bank and relay system. For this prototype a set of four power resistors will be
placed in parallel and the relay system will select either a single value/combination or sweep
through many combinations of resistors for a transient response. This essentially will give us the
same output as our initial prototype design. Overall this option will be cheaper and more reliable
than our previous design.
Figure 5: Current Simulator Prototype Design
VFD
Drives
transformer
with varying
voltage and
frequency
Transformer
Outputs a
voltage and
current
waveform like
a motor
GUI
Commands for
a single or
transient slip
resistance, and
output power
NI Card
Commands for
which relays
will be turned
on in the delta
connected load
Relay Board
Circuit board
with relays on
it; this will
control the
resistors used
for the load
Δ-Connected
Resistor Bank
Selected
Resistor values
emulate steady
state or
transient slip
Figure 6: Current Simulator Prototype
Flow Chart
Current Project State
Currently, this semester, we have successfully completed our variable induction motor
simulator. After conducting motor characterization tests to obtain equivalent motor parameters
for our simulations we were able to create a simulation for an induction motor and a three-phase
transformer as a motor emulator as our proof of concept. With this proof of concept we were able
to come up with a relationship between our motors and transformer to calculate the needed
resistors in our resistor bank. Following the receiving of all our parts we put together our relay
board, resistor bank, and finally the complete induction motor simulator.
Motor and Transformer Parameter Extracting
After completing the DC, no load, and locked rotor tests on our motors and the DC, short
circuit, and open circuit tests on our transformer we were able to calculate our equivalent
parameters; our calculated motor values are shown in table 3 and transformer values in table 4.
The notation used for the motor parameters are based off of the motor equivalent circuit from
figure 1.
Table 3: Calculated equivalent motor parameters
Induction Motor
Parameter
R1 – Stator Resistance
R2 – Rotor Resistance
RC – Core Resistance
X1 – Stator Reactance
X2 – Rotor Reactance
XM – Mutual Reactance
Lenze
Motor
138.808 
137.256 
2.606 k
93.241 
139.862 
1.683 k
1 HP
Motor
6.25 
4.03 
624.4 
3.14 
7.71 
57.75 
1.5 HP
Motor
1.4481 
0.8536 
624.49 
1.556 
2.336 
45.11 
2 HP
Motor
4.6 
4.35 
780 
5.43 
5.43 
100.845 
Table 4: Calculated equivalent transformer parameters
Transformer Parameter
RP – Primary Resistance
RS – Secondary Resistance
RC – Core Resistance
XP – Primary Reactance
XS – Secondary Reactance
XM – Mutual Reactance
ACME
Transformer
138.808 
137.256 
2.606 k
93.241 
139.862 
1.683 k
With these calculated equivalent circuit parameters we are able to create a more realistic
three-phase transformer motor simulator model to simulate as a proof of concept for our design.
Induction Motor Model Simulation and Results
As a proof of concept for our design we needed to simulate a realistic motor model to
compare to our three-phase transformer motor simulator model. Ideally the two models would
have very similar steady-state responses and power outputs.
Using the values from table 3 and table 5 the results from our induction motor simulation
are shown below.
Table 5: Induction motor simulation parameters
Induction Motor
Simulation Parameters
L1 – Stator Inductance
L2 – Rotor Inductance
LM – Mutual Inductance
TFL – Full Torque Load
J – Inertial Constant
P – Number of Poles
Lenze
Motor
0.2968 H
0.4452 H
5.355 H
0.38 Nm
0.003 kg𝑚2
4 Poles
1 HP
Motor
0.0083 H
0.0205 H
0.1532 H
4.048 Nm
0.032 kg𝑚2
4 Poles
1.5 HP
Motor
0.0041 H
0.0062 H
0.1197 H
5.89 Nm
0.045 kg𝑚2
4 Poles
Figure 7: Induction motor Simulink model
2 HP
Motor
0.0173 H
0.0173 H
0.3210 H
10.5 Nm
0.004 kg𝑚2
4 Poles
Figure 8: Induction Motor Rotor and Stator Current Waveforms (Left) and Induction Motor RPMs (Right)
Figure 9: Induction Motor Torque (Left) and Induction Motor Output Power (Right)
From our induction motor simulation we have a model to compare our three-phase
transformer model to. The results show that the motor is running at full torque and full rotations
per minute, which results in the correct output power of 1.5 HP. We desire our transformer motor
simulator model to have the same steady state power as our induction motor.
Three-Phase Transformer Model Simulation and Results
To complete the proof of concept for our design we needed to also simulate a realistic
transformer model to compare to our induction motor model. We accomplished this by using the
values in table 4 and 6 in conjunction with the two-wattmeter method. In order to emulate an
induction motor with a three-phase transformer our first step was to design our transformer
system model. To do this, we set up the input to the three-phase transformer identically as the
induction motor. To get the correct output of the transformer the model was connected to three
delta-connected resistors that would represent our slip dependent load.
Table 6: Transformer simulation parameters
Transformer Parameter
LP – Primary Inductance
LS – Secondary Inductance
LM – Mutual Inductance
ACME
Transformer
0.0441 H
0.0110 H
12.7624 H
Figure 10: Three-Phase Transformer as a Motor Simulator Model
Figure 11: Output Power for Three-Phase Transformer Simulator Model
The power output, in figure 11, is equivalent to that of the induction motor’s power
output. With these results our proof of concept was complete; based off the multiple motor
simulations we ran we were able to get the necessary resistor values needed to build our
prototype.
Experimental Results and Transformer Relationship
After receiving our transformer we were able to complete a steady-state comparison to
our simulation using single delta-connected resistors. Our transformer was driven with a Lenze
VFD and the input and output powers were measured using the two-wattmeter method. The
resulting data is shown in table 7 and 8.
Table 7: Loaded transformer input power
Input Power (VFD)
Resistance (Ω)
Power (w)
Volts (V)
Current (A)
100
326.5
220.7
0.91
80
397.8
220.4
1.12
75
422.4
221.6
1.19
50
593.9
220
1.71
35
815.7
220.2
2.38
25
1077.5
218.8
3.2
20
1304.2
218.1
3.89
15
1671.9
217.8
5.05
Table 8: Loaded transformer output power
Output Power (VFD)
Resistance (Ω)
Power (w)
Volts (V)
Current (A)
100
307
100.9
1.75
80
376.1
100.2
2.11
75
395.8
99.3
2.3
50
562.8
96.7
3.35
35
756.6
93.5
4.66
25
1000.3
91.3
6.31
20
1186.9
88.6
7.4
15
1484.4
86.5
9.96
This data confirmed the steady-state resistances needed to get the correct output power
for motor simulation (values bolded in tables 7 and 8). With this data and our simulations we
were able to create a relationship for the steady-state resistances of the transformer; the
relationship is as follows:
𝑅𝐿𝑜𝑎𝑑
𝑅𝑟′ 𝑅𝑟′
= 2− 3+𝐶
𝑎
𝑎
Where:
𝑅𝑟′ = Slip dependent rotor resistance of a motor
𝑎 = Turns ratio of the transformer
𝐶 = Motor constant (changes with each motor)
This relationship proved accurate to find the steady-state resistances needed for our
transformer. To obtain 𝑅𝑟′ at full torque from a motor the torque vs. speed plot of the
characterized motor had to be obtained (Shown in figures 13,15 and 17). Using the torque vs.
speed plots, one can get the slip value, at the full rated torque, from the plot and using the
𝑅 (1−𝑠)
equation 𝑅𝑟′ = 𝑟 𝑠 the desired 𝑅𝑟′ value can be calculated. This is the method we used to
calculate the needed steady-state resistance values for our prototype.
Hardware
The transformer we will be using is a 3kVA, three-phase, 60 Hz general-purpose
transformer within an outdoor rated enclosure. The enclosed transformer stands at 12.37” wide,
10.38” tall, and 7.47” in depth and will cost ~$500. We decided 3kVA is a sufficient power
rating, and that it would be better to purchase one three-phase transformer, rather than three
single-phase transformers. This is due to the three-phase transformer being a coupled system,
theoretically providing more accurate results than three decoupled single-phase transformers.
We were originally going to purchase three high-powered rheostats in order to control the
slip for our system. However, this had a chance of being too costly, and our project risked being
scaled back from a maximum output of two-horsepower to one-horsepower in order to save
money. The three rheostats would be connected in a delta formation and all controlled by one
single step motor. The step motor, controlled by a GUI, would change the resistance of the
rheostats depending in the desired slip for the system.
To control the rheostats in our original design, a step motor along with an Arduino board
were going to be used. A GUI would be implemented using the Arduino board to control the slip
value and the output power of the system. The desired slip would be entered into the GUI, and
the step motor would then read the message from the GUI and turn the three rheostats in order to
reach the desired resistance.
A step motor was chosen over a DC motor for accuracy purposes. A DC motor, when
turned off, may still turn a little after due to its inertia. A step motor is specifically designed to
avoid this problem, and is more useful as a position controller.
Before we purchased these parts, however, our group and our sponsor mutually decided
to approach our problem from a different angle. Our new approach to our design is to use a series
of relays connected to resistors in order to provide different resistances, and thus different slip
values. We will have three separate resistor banks, one for each phase of the transformer, all
connected in a delta formation. Inside each of these three banks will be four resistors in parallel
all attached to their own relay. Depending on the slip desired, different combinations of relays
can be turned on or off, providing a total of sixteen different resistance values (Table 5).
Table 9: Relay Look up Table
Relay 1
50Ω/15Ω
0
0
0
0
0
0
0
0
1
1
1
1
1
1
1
1
Relay 2
Relay 3
Relay 4
0.5 HP Resistor
94Ω/25Ω 50Ω/140Ω 188Ω/175Ω
Bank
0
0
0
0.00 Ω
0
0
1
188.00 Ω
0
1
0
140.00 Ω
0
1
1
80.24 Ω
1
0
0
94.00 Ω
1
0
1
62.67 Ω
1
1
0
56.24 Ω
1
1
1
43.29 Ω
0
0
0
50.00 Ω
0
0
1
39.49 Ω
0
1
0
36.84 Ω
0
1
1
30.80 Ω
1
0
0
32.64 Ω
1
0
1
27.81 Ω
1
1
0
26.46 Ω
1
1
1
23.20 Ω
1, 1.5 & 2 HP
Resistor Bank
0.00 Ω
117.00 Ω
50.00 Ω
35.03 Ω
25.00 Ω
20.59 Ω
16.67 Ω
14.59 Ω
15.00 Ω
13.29 Ω
11.54 Ω
10.50 Ω
9.38 Ω
8.68 Ω
7.89 Ω
7.39 Ω
*NOTE: Notation for relay resistances (0.5 HP Resistor Bank resistors / 1, 1.5 & 2 HP Resistor Bank resistors)
A single National Instruments (NI) relay card will control the relays in the system; this
card will select single or multiple relays in each phase; allowing current to go through certain
single or parallel resistors in each phase of the resistor bank. While this design provides fewer
options for testing a certain slip value, it provides a much cheaper alternative to our previous
rheostat design. Lenze has also emphasized that a transient output is not critical, as they will use
this prototype for end-of-the-line testing and only really require accurate steady-state power.
Graphical User Interface
The graphical user interface to be paired with the hardware of our project has been built
in LabVIEW. Its purpose is to control the load resistances on the transformer.
More specifically, the GUI communicates a series of bits to an NI DAQ card that has
been installed into the computer. The card controls where to pass a supply voltage within a
connector block in the pattern of the communicated bits. The outputs of the connector block are
connected to a bank of relays that are in turn connected to the load resistors in order to vary the
load resistance per delta branch.
The user has the ability to select the intended horsepower to emulate between 0.5, 1.0,
1.5, and 2.0 horsepower. This selection affects the ordering of the resistor configurations for the
transient run and their locations along the single slip slider. The 0.5 horsepower setting also
requires a different resistor bank as a whole and the GUI differentiates between the two resistor
banks by referencing this selection. There is also a toggle switch to select to either run a full
transient of all slip values or run a single slip value setting. From here the GUI reads the inputs in
the corresponding pane. The single slip slider allows the user to select an individual level to
activate and hold until further user input is supplied or the system is powered down. The
transient slip options are a series of hold times, measured in seconds, the GUI cycles once
through all slip levels in sequence while holding each for the user supplied hold times. If the user
sets a hold time of 0, the GUI skips over that slip level. Once the transient is finished and the
final hold time has passed, the GUI deactivates all relays to avoid overheating the resistors.
The block diagram of the GUI primarily sifts through the user inputs with a series of case
structures in order to arrive at the specific DAQ command that carries out the intended setting.
The only other command that is used is to carry out the hold times of the transient slip. The block
diagram is labeled within every case structure such that a future user can understand and amend
the code easily.
Overall, the intent of the transient slip setting is to allow observation of the entire torque
curve with an emphasis on the rising torque behavior. The single slip setting is intended for use
more with observing the linear region of the torque curve or for getting particular discrete levels
along the curve, it can also be considered a snapshot of these parts of the curve.
Figure 12: Graphical User Interface of the system. This provides the user with the ability to run the
system at single slip values or run a transient response.
Prototype Results
Once our prototype was completed we conducted extensive testing to ensure the accuracy
of our project. Similarly to our preliminary testing we drove our transformer with a Lenze VFD
and measured the input and output powers, for every resistor combination, using the twowattmeter method. For comparison we used a Lenze VFD to drive a 1.5 HP motor in parallel to
compare its input and output power with our results; these values are shown below. The data
confirmed the accuracy of prototype and proved that a transformer can be used as a means to
emulate an induction motor.
Table 10: Loaded transformer input and output powers for 0.5 HP Resistor bank
Resistance (Ω)
Input Power (VFD)
Output Power
(Transformer)
Power
(w)
Volts
(V)
Current
(A)
Power
(w)
Volts
(V)
Current
(A)
0.00
0.00
0.00
0.00
0.00
0.00
0.00
188.00
187.20
222.00
0.50
173.00
105.10
0.95
140.00
248.50
220.10
0.69
231.60
103.00
1.30
80.24
395.00
220.70
1.10
374.90
99.60
2.15
94.00
344.00
221.10
0.97
324.90
100.80
1.87
62.67
488.70
220.00
1.40
459.00
97.80
2.70
56.24
537.70
220.00
1.50
507.00
97.10
3.00
43.29
674.00
219.80
1.96
628.00
95.10
3.80
50.00
583.00
220.00
1.70
551.70
95.70
3.29
39.49
715.00
220.00
2.10
674.60
94.50
4.10
36.84
765.00
219.70
2.20
709.00
93.70
4.40
30.80
887.00
220.00
2.60
830.00
92.60
5.10
32.64
850.00
219.60
2.50
788.00
93.00
4.89
27.81
974.00
219.50
2.87
903.00
91.80
5.60
26.46
1017.00
219.10
3.00
939.00
91.10
5.90
23.20
1038.00
219.70
3.40
1038.00
90.10
6.60
*Note: space below is intentionally left blank
Table 11: Loaded transformer input and output powers for 1, 1.5 & 2 HP Resistor bank
Input Power (VFD)
Resistance (Ω)
Output Power
(Transformer)
Power
(w)
Volts
(V)
Current
(A)
Power
(w)
Volts
(V)
Current
(A)
0.00
0.00
0.00
0.00
0.00
0.00
0.00
117.00
288.00
221.20
0.80
270.85
102.10
1.53
50.00
590.00
220.10
1.70
554.40
96.51
3.33
35.03
808.00
220.00
2.40
749.00
93.70
4.64
25.00
1063.00
219.10
3.15
982.90
91.10
6.20
20.59
1259.00
218.20
3.70
1143.00
88.50
7.40
16.67
1505.00
218.00
4.50
1354.00
87.50
8.90
14.59
1699.00
218.60
5.10
1481.00
85.70
10.00
15.00
1611.00
217.10
4.80
1441.70
86.10
9.56
13.29
1809.00
218.40
5.40
1589.00
85.30
10.78
11.54
2014.00
217.10
6.10
1740.00
83.10
12.10
10.50
2190.00
217.30
6.60
1857.80
82.50
13.10
9.38
2398.00
216.10
7.30
2028.00
81.00
14.50
8.68
2525.00
217.30
7.70
2121.00
79.50
15.20
7.89
2950.00
216.00
8.40
2265.00
78.50
16.50
7.39
2852.00
216.30
8.80
2324.00
76.89
17.30
Table 12: Loaded motor input and output power
Load
(%)
100
Torque
(Nm)
5.80
Input Power
(VFD)
Output Power
(Motor)
1456.23
1036.07
90
5.30
1326.21
952.12
80
4.80
1199.82
867.02
70
4.30
1076.72
780.64
60
3.80
958.88
693.03
50
3.30
843.59
604.70
40
2.80
731.38
515.09
30
2.30
620.44
425.25
20
1.80
511.98
333.66
10
1.30
402.92
241.77
Table 13: Resistor combinations per motor power for transient response
Order
#
0.5 HP
1 HP
1.5 HP
2 HP
0
0.00
0.00
0.00
0.00
1
188.00
117.00
117.00
117.00
2
140.00
50.00
50.00
50.00
3
94.00
25.00
35.02
35.02
4
62.67
20.59
25.00
25.00
5
50.00
16.67
16.67
20.59
6
36.84
15.00
15.00
16.67
7
30.80
14.59
14.59
14.59
8
23.20
10.50
11.53
13.29
9
26.47
9.38
10.50
11.53
10
27.81
8.68
9.38
10.50
11
32.63
7.89
8.67
9.38
12
39.49
7.39
7.89
8.67
13
43.29
11.53
7.39
7.89
14
56.24
13.29
13.29
7.39
15
80.24
35.02
20.59
15.00
The prototype testing proved many uses for this project. From the data shown in Tables
10-12 it can be shown that the induction motor simulator can be used to emulate steady state and
transient values. The simulator can also be used to emulate motors at varying percentages of its
full load (shown in table 14). Since our project only has a possible 16 points of a motors torque
vs. speed and power curves a user can decide to either focus on the rising torque side of the
curves or the linear region (figures 13-18) since all the powers occur at those points of the curve;
this adds to the versatility of our project.
Table 14: Loaded motor data compared to loaded transformer data (1, 1.5 and 2 HP Resistor Bank)
Load
(%)
Resistance
(Ω)
Input Power
(VFD)
Output Power
(Motor)
Input Power
(VFD)
Output Power
(Transformer)
100
20.59
1456.23
1036.07
1259.00
1143.00
90
25.00
1326.21
952.12
1063.00
982.90
70
35.03
1076.72
780.64
808.00
749.00
10
117.00
402.92
241.77
288.00
270.85
As shown in the data our induction motor simulator perfectly corresponds to the torque
vs. speed and power plots of induction motors, however since there are only 16 points due to our
resistor bank we can not have a perfectly continuous plot. If we could incorporate more
resistances we would be able to obtain a more continuous plot and incorporate nearly the full
transient of a motor, but consequently having more resistances would result in a much larger
resistor bank. Since the resistor banks are modular it is easy to switch our resistors if different
points in a motors transient is desired. As it stands the data points obtained are shown below.
Figure 13: 1 HP torque vs. speed plot. Theoretical data is a solid
line and experimental data are circles
Figure 14: 1 HP output power plot. Theoretical data is a solid line
and experimental data are circles
Figure 15: 1.5 HP torque vs. speed plot. Theoretical data is a
solid line and experimental data are circles
Figure 16: 1.5 HP output power plot. Theoretical data is a solid
line and experimental data are circles
Figure 17: 2 HP torque vs. speed plot. Theoretical data is a solid
line and experimental data are circles
Figure 18: 2 HP output power plot. Theoretical data is a solid line
and experimental data are circles
The plots above describe how we have been able to directly emulate 16 points of a
motors torque vs. speed and power curves. The circles on the plots are our prototype data, which
accurately portrays the motor data, however since we wanted to have a semi transient response of
a motor we arranged the order of the resistors to give us the rising side of the curves rather than
the linear region. However with our GUI the single slip option can be used to focus on the linear
region as the data we collected correspond to that region as well; but due to our limited 16
different options the whole spectrum of the motors curves cannot be achieved.
Overall our induction motor simulator, using a transformer and resistor bank as a means
of simulation, has accurately emulated a motor. Since we didn’t have access to other motor
powers we were only able to emulate and compare our data to a 1.5 HP motor; this data,
however, proves that we can accurately emulate 16 points of a motors transient and linear region.
Prototype Images and Setup
To conduct our experimenting we had to put together our resistor banks and relay board.
Our finished product was ran by driving the transformer with a Lenze VFD, which was
connected, to our delta-connected resistor bank and relay board. The completed pictures are
shown below. The pictures show every component of our induction motor simulator. In the
picture of the experimental setup our relay board is connected with a cable to our NI DAQ card
within the computer tower; the relay board is also directly connected to the transformer and
resistor banks to complete the delta connection. The computer we are using has the NI card
driver software as well as LabView, which is what our GUI is constructed from. To run the tests
on our prototype we used our GUI to test each individual value as well as the transients; we
measured the input and output powers using the two-wattmeter method.
Figure 19: Lenze 3 HP
VFD
Figure 20: ACME 3 kVA transformer in
outdoor enclosure
Figure 22: Resistor bank – 1, 1.5,
and 2 HP bank (top three layers); 0.5
HP bank (bottom three layers)
Figure 21: Relay board – Red connectors are
for 1, 1.5, and 2 HP resistor bank; Black
connectors are for 0.5 HP resistor bank
Figure 23: Experimental setup – relay board connected to NI card inside the
computer tower
Prototype Significance
Considering the original problem to be solved that Lenze proposed to us we have been
able to show that our induction motor simulator has solved many of those issues. Our motor
simulator does not need a dynamometer to obtain output power and waveforms thus this greatly
reduces space for Lenze. Further more since our simulator can accurately emulate four different
motor powers Lenze could take away these motors alleviating even more space.
Since we chose to use electromagnetic relays as a part of our load, the relays are the only
moving parts in our simulator; however compared to the degradation of a motor, due to constant
rotation, the small movement and degradation of a relay is completely negligible. Some other
advantages that our simulator has to an induction motor are its weight and lack of vibration. Our
simulator is made up of light material and doesn’t move so there is no need to account for
vibration and it is easily moveable; this is a big upgrade from a motor. The way we designed our
simulator we made it easy to change and or resize. Since the material we used is cheap the
resistor banks can be resized to incorporate more or less resistors, which can add to the
variability of the simulator.
Overall our induction motor simulator has many advantages to using an actual induction
motor; although it cannot emulate a full transient our simulator can accurate emulate a pseudotransient which will undoubtedly facilitate Lenze’s end-of-the-line testing.
Project Phases and Milestones
We have completed and optimized our induction motor simulator so there are no further
tasks required. However the tasks and milestones we conducted for this project are shown above.
Budget
While there is no concrete budget for this project, Lenze would like to remain in the
$1500-$3000 range. Based on our current projections this is well within our ability to meet. With
our budget in mind, the most cost-effective strategy would be to purchase a 3kVA, three-phase
transformer to imitate an induction motor. This is more efficient and cheaper than purchasing
three, single-phase transformers, where the magnetic fields would be decoupled and take up
more space. In addition to the three-phase transformer, initially three high-power rheostats along
with a small stepper motor to adjust the potentiometer were going to be purchased to control the
slip. While Lenze requested no moving parts, this small motor has been confirmed to not be an
issue as it is not large, dangerous, or loud.
Upon more discussion with our sponsor we have decided instead of using a stepper motor
in conjunction to high power rheostats we have opted to go with a relay board and resistor bank.
This will be a much cheaper option as Lenze has many of the required parts, which will cost
them nothing. From this idea we would only need to purchase a NI card to control the relays.
After completion the total costs required for this project were less than Lenze allotted; a
summary table of our expenses are shown below.
Table 15: Project expenses
Item
Transformer (Delta – 3kVA)
Relays (Electromagnetic)
Power Resistors
NI Card (and Accessories)
Various Tech Service Construction
Total
Unit Cost
~ $500.00
~ $2.00
~ $3.00
$443.00
~ $300.00
~ $1435.00
Lenze Cost
~ $500.00
$0.00
$0.00
$443.00
~ $300.00
~ $1243.00
Qty.
1
24
48
1
1
N/A
Conclusion
This project required us to utilize engineering skills, technical knowledge, and teamwork
to produce a working product. Prior to the project we did not learn about induction machines in
our classes so this project provided a challenge for us; but in the end we gained an understand of
induction motors and a way to properly emulate one. As a result of the knowledge we gained we
were able to create an accurate way to simulate various induction motors using a three-phase
transformer, relays, and a resistor bank and in doing so created a product that in many ways has
advantages to using an actual induction motor. We know our product will help facilitate Lenze’s
end-of-the-line VFD testing.
Acknowledgements
We are very thankful for our sponsor Lenze, Chris Johnson, Mark Collins, and Neil
Pande for helping us understand variable frequency drives and transformers more. We are also
very appreciative for Chris being able to get us all necessary parts and equipment to us when we
needed them. We would also like to thank our UConn Engineering advisor and graduate
students, Ali Bazzi, Artur Ulatowski, Yiqi Liu, and Weiqiang Chen for pointing us in the right
directions with our project, teaching us, and taking the time to help us with anything we needed;
we greatly appreciate all that you have done for us.
Personnel and Collaborators
Lenze Americas Corporation
Uxbridge, MA 01569
Program Manager
Christopher Johnson
christoper.johnson@lenze.com
University of Connecticut
Storrs, CT 06269
Faculty Advisor
Ali Bazzi
bazzi@engr.uconn.edu
Senior Engineering Student
Geoffrey Roy
geoffrey.roy@uconn.edu
Senior Engineering Student
Matthew Geary
matthew.r.geary@uconn.edu
Senior Engineering Student
Amber Reinwald
Amber.reinwald@uconn.edu
References:
[1]
[2]
[3]
[4]
Knight. “Electrical Machines”. EE 332 – Electrical Drives [Online]. Available:
http://people.ucalgary.ca/~aknigh/electrical_machines/machines_main.html. [Accessed:
October, 2014]
Lenze AC Tech Corporation. “StockMotors AC motors 90W to 315kW three phase squirrel
cage induction motors,” Catalog: MDERA0601.
Lenze AC Tech Corporation. “SMVector – Frequency Inverter Operating Instructions,”
Document: SV01N_13418587
F. Nekoei et al., "Three-phase induction motor drive by FPGA."Electrical Engineering
(ICEE), 2011 19th Iranian Conference on, pp.1, 1, 17-19 May 2011
[5]
M. Esparza et al., "Real-time emulator of an induction motor: FPGA-based
implementation," Electrical Engineering, Computing Science and Automatic Control
(CCE), 2012 9th International Conference on, pp.1, 6, 26-28 Sept. 2012
[6] S.Tola, M. Sengupta, "Real-time simulation of an induction motor in different reference
frames on a FPGA platform," Power Electronics, Drives and Energy Systems (PEDES),
2012 IEEE International Conference on, pp.1, 6, 16-19 Dec. 2012
[7] M. Bacic, "On hardware-in-the-loop simulation," Decision and Control, 2005 and 2005
European Control Conference. CDC-ECC '05. 44th IEEE Conference on, pp.3194, 3198,
12-15 Dec. 2005
[8] O. Vadyakho et al., "An Induction Machine Emulator for High-Power Applications
Utilizing Advanced Simulation Tools With Graphical User Interfaces," Energy Conversion,
IEEE Transactions on, vol.27, no.1, pp.160, 172, March 2012
[9] X. Wu et al, "A novel interface for power-hardware-in-the-loop simulation," Computers in
Power Electronics, 2004. Proceedings. 2004 IEEE Workshop on, pp.178, 182, 15-18 Aug.
2004
[10] R. Wei et al., "An Effective Method for Evaluating the Accuracy of Power Hardware-inthe-Loop Simulations," Industry Applications, IEEE Transactions on, vol.45, no.4,
pp.1484, 1490, July-Aug. 2009
Appendix – Matlab Code and Circuit Diagrams
% Senior Design Team 1506 Motor Parameter Calculations
% Motor Test Values (Lenze Motor)
% DC Test - Measurements
Vabdc = 35.72;
Vbcdc = 35.69;
Vacdc = 35.75;
%Volts
%Volts
%Volts
Iabdc = 0.386;
Ibcdc = 0.386;
Iacdc = 0.386;
%Amps
%Amps
%Amps
% No Load Test - Measurements
Vacnl = 201.674;
Vbcnl = 200.160;
%Volts
%Volts
Iacnl = 252.603e-3;
Ibcnl = 239.767e-3;
%Amps
%Amps
Pacnl = 7.6862;
Pbcnl = 38.777;
%Watts
%Watts
% Locked Rotor Test - Measurements
Vaclr = 80.775;
Vbclr = 80.844;
%Volts
%Volts
Iaclr = 387.478e-3;
Ibclr = 387.281e-3;
%Amps
%Amps
Paclr = 10.648;
Pbclr = 30.779;
%Watts
%Watts
% DC Test - Calculations
Vdc = (Vabdc + Vbcdc + Vacdc)/3;
Idcavg = (Iabdc + Ibcdc + Iacdc)/3;
Idc = Idcavg;
%Volts
%Amps
%Amps
% No Load Test - Calculations
Vnl = (Vacnl + Vbcnl)/2;
Inlavg = (Iacnl + Ibcnl)/2;
Inl = Inlavg/sqrt(3);
Pnl = (Pacnl + Pbcnl)/3;
% Locked Rotor Test - Calculations
%Volts
%Amps
%Amps
%Watts
Vlr = (Vaclr + Vbclr)/2;
Ilravg = (Iaclr + Ibclr)/2;
Ilr = Ilravg/sqrt(3);
Plr = (Paclr + Pbclr)/3;
%Volts
%Amps
%Amps
%Watts
% Determine Rs
Rs = 3*Vdc/(2*Idc);
%Ohms
% Determine Rr
Zlr = Vlr/Ilr;
Rlr = Plr/(Ilr)^2;
Rr = Rlr - Rs;
%Ohms
%Ohms
%Ohms
% Determine Xs & Xr (NEMA B: Xs = .4*Xlr' and Xr = .6*Xlr')
Xlr = sqrt(Zlr^2 - Rlr^2);
Xlrprime = Xlr;
Xs = .4*Xlrprime;
Xr = .6*Xlrprime;
%Ohms
%Ohms
%Ohms
%Ohms
% Determine Xm
Snl = Vnl*Inl;
Qnl = sqrt(Snl^2 - Pnl^2);
Xm = Vnl^2/Qnl;
%VA
%VA
%Ohms
% Determine Rc
Rc = Vnl^2/Pnl;
%Ohms
% Determine Inductance Values
f = 50;
Ls = Xs/(2*pi*60);
Lr = Xr/(2*pi*60);
Lm = Xm/(2*pi*60);
%Hz
%H
%H
%H
% Senior Design Team 1506 Simulation Script
% Simulation Parameters
T_s = 20e-6;
% VFD Parameters
f = 60;
V = 230;
Vpeak = V*sqrt(2)/sqrt(3);
% Running Frequency (Hz)
% Input Voltage (V)
% Peak Input Voltage (V)
% 1 HP Motor Parameters
%
%
%
%
%
%
%
%
%
%
%
%
%
%
%
%
%
fm = 60;
Vm = 230;
P = 1*745.69;
Tau = 4.048;
Rs = 6.25;
Rr = 4.03;
Rc = 624.4;
Xs = 3.14;
Xr = 7.71;
Xm = 57.75;
Lls = Xs/(2*pi*fm);
Llr = Xr/(2*pi*fm);
Lm = Xm/(2*pi*fm);
Ls = Lls + Lm;
Lr = Llr + Lm;
Jm = 0.0323;
Bm = 0.00;
%
%
%
%
%
%
%
%
%
%
%
%
%
%
%
%
%
Frequency of motor (Hz)
Voltage of motor (V)
Power (W)
Torque Load
Stator Resistance (Ohms)
Rotor Resistance (Ohms)
Core Resistance (Ohms)
Stator Reactance (Ohms)
Rotor Reactance (Ohms)
Magnitizing Reactance (Ohms)
Stator Leakage Inductance (H)
Rotor Leakage Inductance (H)
Magnitizing Inductance (H)
Stator Inductance (H)
Rotor Inductance (H)
Inertial Constant ((kg.m^2)
Friction Constant (N.m.s)
% 1.5 HP Motor Parameters
fm = 60;
Vm = 230;
P = 1.5*745.69;
Tau = 5.89;
Rs = 1.4481;
Rr = 0.8536;
Rc = 624.49;
Xs = 1.5576;
Xr = 2.336;
Xm = 45.11;
Lls = 0.0041;
Llr = 0.0062;
Lm = 0.1197;
Ls = Lls + Lm;
Lr = Llr + Lm;
Jm = 0.0445;
Bm = 0.001;
% 2 HP Motor Parameters
%
%
%
%
%
%
%
%
%
%
%
%
%
%
%
%
%
Frequency of motor (Hz)
Voltage of motor (V)
Power (W)
Torque Load
Stator Resistance (Ohms)
Rotor Resistance (Ohms)
Core Resistance (Ohms)
Stator Reactance (Ohms)
Rotor Reactance (Ohms)
Magnitizing Reactance (Ohms)
Stator Leakage Inductance (H)
Rotor Leakage Inductance (H)
Magnitizing Inductance (H)
Stator Inductance (H)
Rotor Inductance (H)
Inertial Constant ((kg.m^2)
Friction Constant (N.m.s)
%
%
%
%
%
%
%
%
%
%
%
%
%
%
%
%
%
fm = 50;
Vm = 230;
P = 2*745.69;
Tau = 10.5;
Rs = 4.6;
Rr = 4.35;
Rc = 780;
Xs = 5.43;
Xr = 5.43;
Xm = 100.845;
Lls = Xs/(2*pi*fm);
Llr = Xr/(2*pi*fm);
Lm = Xm/(2*pi*fm);
Ls = Lls + Lm;
Lr = Llr + Lm;
Jm = 0.004;
Bm = 0.000;
%
%
%
%
%
%
%
%
%
%
%
%
%
%
%
%
%
Frequency of motor (Hz)
Voltage of motor (V)
Power (W)
Torque Load
Stator Resistance (Ohms)
Rotor Resistance (Ohms)
Core Resistance (Ohms)
Stator Reactance (Ohms)
Rotor Reactance (Ohms)
Magnitizing Reactance (Ohms)
Stator Leakage Inductance (H)
Rotor Leakage Inductance (H)
Magnitizing Inductance (H)
Stator Inductance (H)
Rotor Inductance (H)
Inertial Constant ((kg.m^2)
Friction Constant (N.m.s)
%
%
%
%
%
%
%
%
%
%
%
%
%
%
%
%
%
Frequency of motor (Hz)
Voltage of motor (V)
Power (W)
Torque Load
Stator Resistance (Ohms)
Rotor Resistance (Ohms)
Core Resistance (Ohms)
Stator Reactance (Ohms)
Rotor Reactance (Ohms)
Magnitizing Reactance (Ohms)
Stator Leakage Inductance (H)
Rotor Leakage Inductance (H)
Magnitizing Inductance (H)
Stator Inductance (H)
Rotor Inductance (H)
Inertial Constant ((kg.m^2)
Friction Constant (N.m.s)
% 3 HP Motor Parameters
%
%
%
%
%
%
%
%
%
%
%
%
%
%
%
%
%
fm = 60;
Vm = 230;
P = 3*745.69;
Tau = 11.9;
Rs = 0.435;
Rr = 0.816;
Rc = 500;
Xs = 0.754;
Xr = 0.754;
Xm = 26.13;
Lls = Xr/(2*pi*fm);
Llr = Xs/(2*pi*fm);
Lm = Xm/(2*pi*fm);
Ls = Lls + Lm;
Lr = Llr + Lm;
Jm = 0.089;
Bm = 0.001;
% Transformer Parameters (From Parameter Calculations)
Pt = 3000;
Vp = 480;
Vs = 240;
% VA
% Volts
% Volts
Rp = 3.4987;%2.4432;
Rst = 0.8747;%0.6108;
Rc = 3.85515e4;%6.2585e3;
Lp = 0.0441;%0.172;
Lst = 0.0110;%0.0043;
Lmt = 12.7624;%7.0513;
%
%
%
%
%
%
Rload = 23;
% Load Resistance (Ohms)
Primary Resistance (Ohms)
Secondary Resistance (Ohms)
Core Resistance (Ohms)
Primary Inductance (H)
Secondary Inductance (H)
Magnitization Inductance (H)
% Team 1506 Transformer Characterization Calculations
% Transformer Information
S = 3000;
Vp = 480;
Vs = 240;
a = Vp/Vs;
Zp = Vp^2/S;
Zs = Vs^2/S;
%
%
%
%
%
%
VA - Real Power of Transformer
Volts
Volts
Turns ratio
Primary Impedence (ohms)
Secondary Impedence (ohms)
%
%
%
%
Ohms
Ohms
Ohms
Ohms
% DC Test
RHeq
RH =
RXeq
RX =
= 2.3;
3/2*RHeq;
= 0.6;
3/2*RXeq;
% Tests Done on the High Voltage Side
% Open Circuit Test
PHOC1 = 36.157;
PHOC2 = -18.033;
PFHOC1 = .695;
PFHOC2 = .373;
VHOC12 = 484.671;
VHOC23 = 482.125;
VHOC13 = 480.311;
IHOC1 = .095075;
IHOC2 = .107358;
IHOC3 = .100676;
%
%
%
%
%
%
%
%
%
%
Watts
Watts
i
i
Volts
Volts
Volts
Amps
Amps
Amps
% Open Circuit Per Phase
Voc = (VHOC12 + VHOC23 + VHOC13)/3;
Ioc = (IHOC1 + IHOC2 + IHOC3)/(3*sqrt(3));
Poc = (PHOC1 + PHOC2)/3;
% Short Circuit Test
PHSC1 = 335;
PHSC2 = 485;
PFHSC1 = .668;
PFHSC2 = .978;
VHSC12 = 83.1;
VHSC23 = 81.3;
VHSC13 = 81.3;
IHSC1 = 6.25;
IHSC2 = 6.25;
IHSC3 = 6.25;
%
%
%
%
%
%
%
%
%
%
Watts
Watts
i
i
Volts
Volts
Volts
Amps
Amps
Amps
% Short Circuit Per Phase
% Volts
% Amps
% Watts
Vsc = (VHSC12 + VHSC23 + VHSC13)/3;
Isc = (IHSC1 + IHSC2 + IHSC3)/(3*sqrt(3));
Psc = (PHSC1 + PHSC2)/3;
% Volts
% Amps
% Watts
% From Open Circuit Test
Iphaseoc = (IHOC1 + IHOC2 + IHOC3)/3;
Soc = Voc*Iphaseoc;
Qoc = sqrt(Soc^2 - Poc^2);
Rc = Voc^2/Poc;
Xm = Voc^2/Qoc;
% Amps
% Watts
% Watts
% Ohms
% Ohms
% From Short Circuit Test
Iphasesc = (IHSC1 + IHSC2 + IHSC3)/3;
Ssc = Vsc*Iphasesc;
Qsc = sqrt(Ssc^2 - Psc^2);
Req = Psc/(3*Isc^2);
Xeq = Qsc/Isc^2;
% Amps
% Watts
% Watts
% Ohms (Rp + Rs')
% Ohms (Xp + Xs')
% Determining Parameters
Xp = Xeq/2;
Xsprime = Xp;
Xs = Xsprime/a^2;
% Ohms
% Ohms
% Ohms
Rp = Req/2;
Rsprime = Rp;
Rs = Rsprime/a^2;
% Ohms
% Ohms
% Ohms
% Results
f = 60;
% Hertz
Rp = Rp
% Primary Resistance (Ohms)
Rs = Rs
% Secondary Resistance (Ohms)
Rct = Rc
% Core Resistance (Ohms)
Xp = Xp
% Primary Reactance (Ohms)
Xs = Xs
% Secondary Reactance (Ohms)
Xm = Xm
% Mutual Reactance (Ohms)
Lp = Xp/(2*pi*f)
% Primary Inductance (H)
Ls = Xs/(2*pi*f)
% Secondary Inductance (H)
Lmt = Xm/(2*pi*f)
% Mutual Inductance (H)
% Torque Vs Speed Curve for Resistance Calculation of Transformer
% Matlab script to calulcate an induction motor torque vs speed curve
% using the Thevenin equivalent circuit
% 1 HP Motor Equivalent circuit parameters
Rs
Rr
Rc
Xs
Xr
Xm
=
=
=
=
=
=
6.25;
4.03;
624.4;
3.14;
7.71;
57.75;
Vline = 230;
p = 4;
f = 60;
R1 = Rs;
R2 = Rr;
X1 = Xs;
X2 = Xr;
Xm = Xm;
%
%
%
%
%
%
Stator Resistance (Ohms)
Rotor Resistance (Ohms)
Core Resistance (Ohms)
Stator Reactance (Ohms)
Rotor Reactance (Ohms)
Magnitizing Reactance (Ohms)
%
%
%
%
%
%
%
%
Line Voltage (V)
Number of Motor Poles
Driving Frequency
Stator Resistance
Rotor Resistance
Stator Reactance
Rotor Reactance
Magnetization Branch Reactance
% Supply connection
Delta = true;
if (Delta)
V1 = Vline;
% Volts
else % Y-connection
V1 = Vline/sqrt(3); % Volts
end
% Synchronous speed
ns = 120*f/p;
ws = 4*pi*f/p;
% Synchronous Speed
% Synchronous Speed
% Slip range
s = 1:-0.001:0;
% slip from 1 to 0.01 in 0.01 increments
% Machine Speed at each slip
nm = (1-s)*ns;
% Thevenin circuit parameters:
Zth
Rth
Xth
Vth
=
=
=
=
(R1+j*X1)*j*Xm/(R1+j*(X1+Xm));
% Complex Impedance
real(Zth);
imag(Zth);
Vline*(Xm/sqrt(R1^2+(X1+Xm)^2)); % Complex Voltage
% Torque for each slip
% *** Note: Torque for slip = 0 isn't calculated, this would cause a
%
division by zero. Torque = 0 at s = 0
for i = 1:length(s)-1;
Torque(i) = 3*Vth^2*(R2/s(i))*(1/ws)/((Rth+R2/s(i))^2+(Xth+X2)^2);
end
Torque(length(s)) = 0;
% Torque and Speed Plot
RPMO = [0 174.6 340.2 552.6 624.6 714.6 750.6 765 912.6 977.4 1012 ...
1067 1091 1683 1699 1757];
TO = [13.8 14.72 15.67 17.01 17.49 18.1 18.34 18.44 19.42 19.81 20 ...
20.28 20.38 9.904 8.917 4.048];
figure(1)
%Plot for Torque Vs. RPM
scatter(RPMO,TO);
hold on;
plot(nm,Torque);
title(' 1 HP Torque Vs. Speed');
xlabel('Mechanical Speed (rpm)');
ylabel('Torque (Nm)');
hold off;
% Power Plot
PO = [0 270.85 554.4 982.9 1143 1354 1441.7 1481 1857.8 2028 2121 ...
2265 2324 1740 1589 749];
t = [0 0.039 0.075 0.123 0.1387 0.1588 0.1668 0.17 0.2 0.217 0.225 ...
0.237 0.242 0.375 0.377 0.389];
Power = nm.*Torque.*pi/30;
tp = linspace(0,0.4,1001);
figure(2)
scatter(t,PO);
hold on;
plot(tp,Power)
title('1 HP Output Power')
xlabel('Time (s)')
ylabel('Power (W)')
hold off;
%
%
%
%
%
%
figure(2)
%Plot for Torque Vs. Slip
plot(s,Torque);
set(gca,'XDir','reverse')
title('Torque Vs. Slip');
xlabel('Slip');
ylabel('Torque (Nm)');
% % For a Full look at all Torque Vs Speed Regions of the induction Motor
%
%
%
%
%
%
%
%
%
%
%
%
%
%
%
%
%
%
%
%
%
%
%
%
%
%
%
%
sfull = 2:-0.01:-1;
% Full slip to see full T vs. S
nmfull = (1-sfull)*ns;
Zth
Rth
Xth
Vth
=
=
=
=
(R1+j*X1)*j*Xm/(R1+j*(X1+Xm));
real(Zth);
imag(Zth);
Vline*(Xm/sqrt(R1^2+(X1+Xm)^2));
% Complex Impedance
% Complex Voltage
for i = 1:length(sfull);
Torque2(i) = 3*Vth^2*(R2/sfull(i))*(1/ws)/((Rth+R2/sfull(i))^2+...
(Xth+X2)^2);
end
Torque2(:,201) = 0;
figure(3)
%Full Plot for Torque Vs. RPM
plot(nmfull,Torque2);
title('Torque Vs. Speed');
xlabel('Mechanical Speed (rpm)');
ylabel('Torque (Nm)');
figure(4)
%Full Plot for Torque Vs. Slip
plot(sfull,Torque2);
set(gca,'XDir','reverse')
title('Torque Vs. Slip');
xlabel('Slip');
ylabel('Torque (Nm)');
%%%%%%%%%%%%%%%%%%%%%%%%% Resistance Calculation %%%%%%%%%%%%%%%%%%%%%%%%%%
% Calculated Resistor Values for Motor Emulator
% Full Torque = 4.048
% Torqe Values from the Plot
T0 = Torque(:,978);
% Slip Values Based off Torque Plots
s0 = s(:,978);
% Rr' Values Calculated from the slip values to use in motor emulator
Rr0 = Rs*(1-s0)/s0;
% Resistance Values Needed for Transformer
a = 2;
% Turn Ratio
Rload = Rr0/a^2-Rr0/a^3+2
% Torque Vs Speed Curve for Resistance Calculation of Transformer
% Matlab script to calulcate an induction motor torque vs speed curve
% using the Thevenin equivalent circuit
% 1.5 HP Motor Equivalent circuit parameters
Rs
Rr
Rc
Xs
Xr
Xm
=
=
=
=
=
=
1.4481;
0.8536;
624.49;
1.5576;
2.336;
45.11;
%
%
%
%
%
%
Stator Resistance (Ohms)
Rotor Resistance (Ohms)
Core Resistance (Ohms)
Stator Reactance (Ohms)
Rotor Reactance (Ohms)
Magnitizing Reactance (Ohms)
Vline = 230;
p = 4;
f = 60;
R1 = Rs;
R2 = Rr;
X1 = Xs;
X2 = Xr;
Xm = Xm;
%
%
%
%
%
%
%
%
Line Voltage (V)
Number of Motor Poles
Driving Frequency
Stator Resistance
Rotor Resistance
Stator Reactance
Rotor Reactance
Magnetization Branch Reactance
% Supply connection
Delta = true;
if (Delta)
V1 = Vline;
% Volts
else % Y-connection
V1 = Vline/sqrt(3); % Volts
end
% Synchronous speed
ns = 120*f/p;
ws = 4*pi*f/p;
% Synchronous Speed
% Synchronous Speed
% Slip range
s = 1:-0.001:0;
% slip from 1 to 0.01 in 0.01 increments
% Machine Speed at each slip
nm = (1-s)*ns;
% Thevenin circuit parameters:
Zth
Rth
Xth
Vth
=
=
=
=
(R1+j*X1)*j*Xm/(R1+j*(X1+Xm));
% Complex Impedance
real(Zth);
imag(Zth);
Vline*(Xm/sqrt(R1^2+(X1+Xm)^2)); % Complex Voltage
% Torque for each slip
% *** Note: Torque for slip = 0 isn't calculated, this would cause a
%
division by zero. Torque = 0 at s = 0
for i = 1:length(s)-1;
Torque(i) = 3*Vth^2*(R2/s(i))*(1/ws)/((Rth+R2/s(i))^2+(Xth+X2)^2);
end
Torque(length(s)) = 0;
%Torque and Speed Plot
RPMOH = [0 73.8 145.8 196.2 248.4 329.4 347.4 354.6 406.8 426.6 459 ...
475.2 500.4 511.2 1784 1789];
TOH = [33.63 34.79 35.99 36.88 37.84 39.43 39.8 39.95 41.06 41.5 42.24 ...
42.61 43.21 43.47 8.542 5.89];
figure(1)
%Plot for Torque Vs. RPM
scatter(RPMOH,TOH);
hold on;
plot(nm,Torque);
title(' 1.5 HP Torque Vs. Speed');
xlabel('Mechanical Speed (rpm)');
ylabel('Torque (Nm)');
hold off;
% Power Plot
POH = [0 270.85 554.4 749 982.9 1354 1441.7 1481 1740 1857.8 2028 ...
2121 2265 2324 1589 1143];
t = [0 0.0165 0.0327 0.0431 0.055 0.073 0.077 0.078 0.09 0.095 0.1 ...
0.106 0.111 0.1134 0.396 0.398];
Power = nm.*Torque.*pi/30;
tp = linspace(0,0.4,1001);
figure(2)
scatter(t,POH);
hold on;
plot(tp,Power)
title('1.5 HP Output Power')
xlabel('Time (s)')
ylabel('Power (W)')
hold off;
%
%
%
%
%
%
figure(2)
%Plot for Torque Vs. Slip
plot(s,Torque);
set(gca,'XDir','reverse')
title('Torque Vs. Slip');
xlabel('Slip');
ylabel('Torque (Nm)');
% % For a Full look at all Torque Vs Speed Regions of the induction Motor
%
%
%
%
%
%
%
%
%
%
%
%
%
%
sfull = 2:-0.01:-1;
% Full slip to see full T vs. S
nmfull = (1-sfull)*ns;
Zth
Rth
Xth
Vth
=
=
=
=
(R1+j*X1)*j*Xm/(R1+j*(X1+Xm));
real(Zth);
imag(Zth);
Vline*(Xm/sqrt(R1^2+(X1+Xm)^2));
% Complex Impedance
% Complex Voltage
for i = 1:length(sfull);
Torque2(i) = 3*Vth^2*(R2/sfull(i))*(1/ws)/((Rth+R2/sfull(i))^2+...
(Xth+X2)^2);
end
Torque2(:,201) = 0;
%
%
%
%
%
%
%
%
%
%
%
%
figure(3)
%Full Plot for Torque Vs. RPM
plot(nmfull,Torque2);
title('Torque Vs. Speed');
xlabel('Mechanical Speed (rpm)');
ylabel('Torque (Nm)');
figure(4)
%Full Plot for Torque Vs. Slip
plot(sfull,Torque2);
set(gca,'XDir','reverse')
title('Torque Vs. Slip');
xlabel('Slip');
ylabel('Torque (Nm)');
%%%%%%%%%%%%%%%%%%%%%%%%% Resistance Calculation %%%%%%%%%%%%%%%%%%%%%%%%%%
% Calculated Resistor Values for Motor Emulator
% Full Torque = 5.89
% Torqe Values from the Plot
T0 = Torque(:,995);
% Slip Values Based off Torque Plots
s0 = s(:,995);
% Rr' Values Calculated from the slip values to use in motor emulator
Rr0 = Rs*(1-s0)/s0
% Resistance Values Needed for Transformer
a = 2;
% Turn Ratio
Rload = Rr0/a^2-Rr0/a^3-10
% Torque Vs Speed Curve for Resistance Calculation of Transformer
% Matlab script to calulcate an induction motor torque vs speed curve
% using the Thevenin equivalent circuit
% 2 HP Motor Equivalent circuit parameters
Rs
Rr
Rc
Xs
Xr
Xm
=
=
=
=
=
=
4.6;
4.35;
780;
5.43;
5.43;
100.845;
Vline = 230;
p = 4;
f = 50;
R1 = Rs;
R2 = Rr;
X1 = Xs;
X2 = Xr;
Xm = Xm;
%
%
%
%
%
%
Stator Resistance (Ohms)
Rotor Resistance (Ohms)
Core Resistance (Ohms)
Stator Reactance (Ohms)
Rotor Reactance (Ohms)
Magnitizing Reactance (Ohms)
%
%
%
%
%
%
%
%
Line Voltage (V)
Number of Motor Poles
Driving Frequency
Stator Resistance
Rotor Resistance
Stator Reactance
Rotor Reactance
Magnetization Branch Reactance
% Supply connection
Delta = true;
if (Delta)
V1 = Vline;
% Volts
else % Y-connection
V1 = Vline/sqrt(3); % Volts
end
% Synchronous speed
ns = 120*f/p;
ws = 4*pi*f/p;
% Synchronous Speed
% Synchronous Speed
% Slip range
s = 1:-0.001:0;
% slip from 1 to 0.01 in 0.01 increments
% Machine Speed at each slip
nm = (1-s)*ns;
% Thevenin circuit parameters:
Zth
Rth
Xth
Vth
=
=
=
=
(R1+j*X1)*j*Xm/(R1+j*(X1+Xm));
% Complex Impedance
real(Zth);
imag(Zth);
Vline*(Xm/sqrt(R1^2+(X1+Xm)^2)); % Complex Voltage
% Torque for each slip
% *** Note: Torque for slip = 0 isn't calculated, this would cause a
%
division by zero. Torque = 0 at s = 0
for i = 1:length(s)-1;
Torque(i) = 3*Vth^2*(R2/s(i))*(1/ws)/((Rth+R2/s(i))^2+(Xth+X2)^2);
end
Torque(length(s)) = 0;
% Torque and Speed Plots
RPMT = [0 118.5 231 300 379.5 433.5 502.5 538.5 570 615 651 699 724.5 ...
763.5 781.5 1422];
TT = [21.03 22.08 23.14 23.8 24.6 25.15 25.85 26.21 26.53 26.97 27.31 ...
27.74 27.96 28.26 28.39 10.5];
figure(1)
%Plot for Torque Vs. RPM
scatter(RPMT,TT);
hold on;
plot(nm,Torque);
title(' 2 HP Torque Vs. Speed');
xlabel('Mechanical Speed (rpm)');
ylabel('Torque (Nm)');
hold off;
% Power Plot
PT = [0 270.85 554.4 749 982.9 1143 1354 1481 1589 1740 1857.8 2028 ...
2121 2265 2324 1441.7];
t = [0 0.0312 0.061 0.08 0.1016 0.1157 0.1335 0.142 0.1524 0.1632 ...
0.1732 0.187 0.1932 0.204 0.2084 0.38];
Power = nm.*Torque.*pi/30;
tp = linspace(0,0.4,1001);
figure(2)
scatter(t,PT);
hold on;
plot(tp,Power)
title('2 HP Output Power')
xlabel('Time (s)')
ylabel('Power (W)')
hold off;
%
%
%
%
%
%
%
%
figure(2)
%Plot for Torque Vs. Slip
plot(s,Torque);
set(gca,'XDir','reverse')
title('Torque Vs. Slip');
xlabel('Slip');
ylabel('Torque (Nm)');
% For a Full look at all Torque Vs Speed Regions of the induction Motor
%
%
%
%
%
%
%
%
%
%
%
%
%
%
sfull = 2:-0.01:-1;
% Full slip to see full T vs. S
nmfull = (1-sfull)*ns;
Zth
Rth
Xth
Vth
=
=
=
=
(R1+j*X1)*j*Xm/(R1+j*(X1+Xm));
real(Zth);
imag(Zth);
Vline*(Xm/sqrt(R1^2+(X1+Xm)^2));
% Complex Impedance
% Complex Voltage
for i = 1:length(sfull);
Torque2(i) = 3*Vth^2*(R2/sfull(i))*(1/ws)/((Rth+R2/sfull(i))^2+...
(Xth+X2)^2);
end
Torque2(:,201) = 0;
%
%
%
%
%
%
%
%
%
%
%
%
figure(3)
%Full Plot for Torque Vs. RPM
plot(nmfull,Torque2);
title('Torque Vs. Speed');
xlabel('Mechanical Speed (rpm)');
ylabel('Torque (Nm)');
figure(4)
%Full Plot for Torque Vs. Slip
plot(sfull,Torque2);
set(gca,'XDir','reverse')
title('Torque Vs. Slip');
xlabel('Slip');
ylabel('Torque (Nm)');
%%%%%%%%%%%%%%%%%%%%%%%%% Resistance Calculation %%%%%%%%%%%%%%%%%%%%%%%%%%
% Calculated Resistor Values for Motor Emulator
% Full Torque = 10.5
% Torqe Values from the Plot
T0 = Torque(:,944);
% Slip Values Based off Torque Plots
s0 = s(:,944);
% Rr' Values Calculated from the slip values to use in motor emulator
Rr0 = Rs*(1-s0)/s0;
% Resistance Values Needed for Transformer
a = 2;
% Turn Ratio
Rload = Rr0/a^2-Rr0/a^3+5