ES205 Analysis & Design of Engineering Systems

ES205 Analysis & Design of Engineering Systems

Lab 4 - Modeling of a Motor-Generator Set

Objective

The objective of this part of the lab exercise is to construct a Simulink model for a motor-generator set, where both machines are armature-controlled; and to use this model to predict the behavior of a matched set in the lab, given the attached machine parameter data.

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 usually used in smaller machines or made from coils of wire common in larger machines. The purpose of the stator 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 segmental 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 instead 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 cuts through the field of magnetic flux supplied by the stator. This 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.

A generator converts rotational mechanical

energy into electrical energy.

Development Of Equations

The diagram shown below 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.

Since the machines are armature-controlled, both field currents are held constant at their rated values of 0.5 A.

Applying KVL, the armature circuit of the motor is modeled as:

or converting this to the Lapace equation form

(Eq 1)

Applying the FBD, the rotor of the

motor is modeled by:

Representing this in the Laplace equation form gives

(Eq 2)

Likewise, the rotor of the generator

is modeled by

with the Laplace equation given by

(Eq. 3)

Applying KVL, the armature circuit of the generator is modeled by:

or in Laplace equation form

(Eq. 4)

Throughout these equation, the following definitions apply

and (Eq. 5 & 6)

Procedure

Take the above equations numbered above and develop a simulation diagram for both machines coupled together. Each summing block corresponds to one of the boxed equations, that is Eq. 1 – 4. The output of each summing junction is labeled for your convenience.

Next, using the parameters given in the next section setup a Simulink program which implements your simulation diagram. The input is vM which is applied as a step at t=0. The output variables are: iaM, iaG, vG, wM, and wG. Be sure to use integrators instead of differentiators.

Simulate the condition of the motor starting with the generator loaded and plot the output variables. Simulate the system for 2 seconds. From the plots determine the following for each output variable: Peak Time

Percent Overshoot

and Steady-state Value.

Compare these with the results taken in the lab demo. After using the initial values adjust the parameters that you think have the most uncertainty to better match the recorded plots. For example, do you steady state values match? Does the frequency match?

Parameter Values (Identical machines)

Armature Resistance = 3.33 W,

Armature Inductance = 81.7 mH,

Motor Voltage = 120 V,

Load Resistance = 85.7 W,

Torque Constant = Voltage Constant = 0.9234 V/rad/s,

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.

Reporting of Results for Part 2

First, your team will write a memo-style progress report which will be due one week following completion of the lab. It will:

-- report on the characteristics found as described in the procedure above

-- discuss what parameters were adjusted and why

-- state comparisons made between the simulation and the recorded plots

-- attach the Simulink diagram constructed and the plots that were made.

Secondly, a formal report will also be due for this lab. It will be a formal report due during the 6th week. It will have a format as discussed in the “Guidelines & Standards for Writing Assignments” handout. Its primary goal will be to describe the simulation and present the results. It is to include all plots correctly and properly labeled and titled.. It should also explain in detail the comparison between the simulated results and the actual oscilloscope output traces.