Download ES205 Lab 4 - Modeling of a Motor-Generator Set - Rose

ES205 Lab 4 - Modeling of a Motor-Generator Set (Prelab)
Objective
The objective of this pre-lab exercise is to construct a Simulink model for a motor-generator set,
where both machines are armature-controlled. Nominal system parameters are given . You will
use this model for the lab.
Introduction:
Electric motors and generators are both machines which are used to convert one type of energy
into another usable form. In most commercial electric motors and generators, a magnetic field
acts as a coupler between a stationary member, called the stator, and a moving member called
the rotor. The stator may be made from permanent magnets, which is usually used in smaller
machines, or made from coils of wire, which is common in larger machines. The purpose of the
stator in an armature controlled motor is to set up a constant magnetic flux through the machine.
The rotor contains a number of wire coils, each identical and distributed around the periphery of
the rotor. These wire coils on the rotor are called the armature windings. The armature
windings are connected to a segmented disk called the commutator. The segmented nature of the
commutator acts as a switching mechanism as the rotor turns. At different positions of the rotor,
different windings of the armature are connected to the external leads. If electricity is supplied
to the leads, then the two magnetic fields which are set up by the stator and the armature will
effectively push off of one another. When the armature coils are powered in just the correct
sequence, forces are produced which cause the rotor to continually rotate. This is what we call
an electric motor.
If the leads are connected to a closed circuit when the
rotor is manually driven, a current is induced in the
wire leads as the armature coils cut through the
magnetic flux field supplied by the stator. In this
mode of operation the device is called a generator and
provides a way to convert rotational mechanical
energy back into electrical energy. Simply put, an
electric motor and electric generator are essentially the
same device. The difference is that the motor converts
electrical energy into rotation mechanical energy
while a generator converts rotational mechanical
energy into electrical energy. A schematic of a
coupled motor-generator system is shown in Figure 1.
Tg
Generator
k
Motor
Bm.
Jg
+θg, ωg
Bg
Jm
Tm
+θm, ωm
Figure 1: Schematic of a motor generator
system
Development of Equations
The diagram shown in Figure 2 is a schematic representation for the motor-generator set that will
be demonstrated in the lab. The subscripts “M” and “G” refer to motor and generator
respectively. The compliance of the shaft is also accounted for on the model with the spring
constant, K, in Figure 2.
Figure 2: Model of motor generator system
The output variables we will consider in this lab will be the armature current, iam, the generator
current, iag, the angular velocity of the motor, ωm, the angular velocity of the generator, ωg, and
the voltage across the load, vg. Since the machines are armature-controlled, both field currents
are assumed to be held constant at their rated values of 0.5 A.
The EOM for the motor armature circuit can be obtained using KVL and applying the definition
of the back emf to result in
− v m + i am R am + L am
di am
+ K e ωm = 0
dt
(1)
A FBD for the motor rotor is shown in Figure 3. Applying conservation of angular momentum
the EOM for the rotor of the motor is given by
Jm
d 2θm
dθ
= K t i am − B m − k (θ m − θ g )
2
dt
dt
k(θm- θg)
B ωm
(2)
αm
Tm=Kt iam
Jm
+θm, ωm
Figure 3: FBD of the motor rotor
A FBD for the generator rotor is shown in Figure 4. Applying conservation of angular
momentum the EOM for the rotor of the generator is given by
Jg
d 2θg
dt 2
= −K t i ag − B
dθ g
dt
− k (θ g − θ m )
Tg=Kt iag
B ωg
(3)
αg
Jg
+θg, ωg
k(θm- θg)
Figure 4: FBD of the generator rotor
Applying KVL the EOM for the armature circuit of the generator is given by
di ag
− K e ω g + i ag R ag + L ag
+ i ag R L = 0
dt
(4)
Procedure for drawing a block diagram
Take the above numbered equations and develop a simulation diagram for both machines coupled
together. Each summing block corresponds to one of the numbered equations, that is (1)-(4). The
output of each summing junction is labeled for your convenience. You will need to put the
equations in the Laplace domain before you make your diagram.
(L am s + R am )i am
Σ
(Js + B)ω m
Σ
(Js + B)ω G
Σ
(R ag + R L + L ag s)i ag
Σ
Since it is not possible for all the ES205 section to meet in the Power Lab, data was taken by a
professor and will be provided for you. The equipment used is shown in Figure 5.
Measurement devices
Control panel
Motor-generator
Figure 5: Equipment in the Power Lab.
A close-up of the motor-generator is shown in Figure 6.
Motor
Generator
Flexible coupling
Figure 6: Close up of the equipment in the Power Lab
Nominal values for the system parameters for the motor and generator are shown below:
Armature Resistance = 3.33 Ω
Armature Inductance = 81.7 mH,
Motor Voltage = 120 V,
Load Resistance = 85.7 Ω
Torque Constant = Voltage Constant = 0.9234 V/(rad/s) when both field currents are at 0.5A
Shaft Stiffness = 0.5 N-m/rad,
Rotor Inertia = 2.33 x 10-3 kg-m2,
Viscous Damping = 6 x 10-4 N-m-sec.
Task 1 – Develop a Simulink model
Using the nominal values for the system parameters set up a Simulink model which implements
your simulation diagram. The input is vm which is applied as a 120 V step at t=0. The output
variables are: iam, iag, vg, ωm, and ωg. Be sure not to use any differentiators.
Create an m-file to run your Simulink model using the nominal values given and create plots of
the five output variables.
What you will need to show your professor:
• Your hand drawn Simulink Model
• You do not need to print out the plots of the output variables, but your instructor will
check to see if you have a program that runs at the beginning of the lab period.