ELECTRIC MACHINES - Lakehead University

ENGINEERING 2258

ELECTRIC MACHINES Laboratory Manual

Jason Servais El. Eng. Technologist

Manfred Klein El. Eng. Technologist (2008)

Department of Electrical Engineering Lakehead University Thunder Bay, ON

Revised Fall 2008

3

SAFETY 1. Some of the experiments involve voltages that could conceivably lead to serious injury or death. Therefore strict adherence to the following rules will greatly decrease the probability that accidents will occur. However, no set of rules can replace basic common sense, and all persons using the laboratory are encouraged to constantly THINK SAFETY ! 2. Always assume all circuits are energized unless you know with certainty that they are not. 3. Use one hand to make connections. 4. Never work on electrical circuits with wet or moist hands. 5. Do not play with equipment not directly involved in your experiment. 6. When in the lab do not wear clothing or jewelry which could constitute a health hazard. Shoes, preferably rubber soled ones, must be worn in the lab. Long hair presents a hazard near moving parts of machinery. 7. It is important for safety reasons for anyone to easily trace out your test circuit and, therefore do not work on a cluttered bench. 8. Never touch moving parts of machinery. 9. Think out ahead of time the consequences of closing or opening a switch. 10. Never alter an energized circuit unless you are certain of the outcome. 11. If you know or suspect that an accident is about to occur, take immediate steps tp prevent it but do not jeopardize your own safety in so doing.

THINK SAFETY

ELECTRICAL MACHINES

4

EXPERIMENTS

Policy and Rules for Laboratory Exercises.......................................................................4 1.

DC Generator........................................................................................................6

2.

DC Motor .............................................................................................................14

3.

Synchronous Generator......................................................................................20

4.

Synchronous Motor .............................................................................................28

5.

3-Phase Induction Machine.................................................................................34 Appendix A...........................................................................................................42 Appendix B ..........................................................................................................43 Appendix C ..........................................................................................................44

REFERENCES 1.

“Electric Machinery Fundamentals” Stephen J. Chapman McGraw Hill, 3rd. Ed., 1999

(class text)

5 Lakehead University

Department of Electrical Engineering

POLICY AND RULES FOR LABORATORY EXERCISES • • • •

No Food, No Beverages allowed in the laboratory room!! Keep clothes, bags, etc. OFF the benches with equipment on them. Be On Time ! Being late is annoying to your lab partners and if the experiment has progressed too far you may not be credited with doing the experiment! Safety precautions must be observed at all times to prevent electric shock, damage to instruments, etc.

COME PREPARED! BOTH THE WRITTEN LAB REP ORTS A ND LAB PERFORMANCE (INCL . A TTITUDE , PUNCTUALITY, PREPAREDNESS) WILL BE CONSIDERED FOR THE FINAL LAB MARK!

Lab Exercises General The maximum number of students in a lab work group is indicated on the sign-up sheet. Should students leave a work group for whatever reason such that only one student remains in a group, this student may join another team provided there is still room in that team without exceeding the above maximum number. Missed Lab Exercises It is mandatory to perform all lab exercises according to course requirements. Failure to perform one or more lab exercises results in a grade of "F" for the course. When a student misses a lab exercise for whatever reason he/she must notify the instructor as soon as possible. If the reasons given for the absence are satisfactory to the instructor, a make-up opportunity may be arranged. There may be a chance to let the student join another team to perform the missed lab provided this does not then exceed the max number of students in that group. If it is not possible to accommodate this then a final make-up date will be arranged to take place within one week after the end of classes. Should the student fail to attend this appointment he/she will be required to provide sufficient proof of inability to attend (medical certificate, air ticket, etc.) to avoid the "F" grade. The onus of proof lies entirely with the student! The student then must immediately make another appointment with the lab instructor! The lab report in such a case is due within one week after performance, else the "F' stands.

Lab Reports General It is mandatory that all lab reports must be submitted on time as specified by the lab instructor! Plagiarism Plagiarism will not be tolerated and may result in a grade of "F" for the course. Any material taken from sources like books, manuals, web sites, magazines, etc. must be clearly referenced as a footnote or under a bibliography! A re-write of a report will be granted only under exceptional circumstances! Missed Lab exercises In some courses group lab reports may be allowed by the lab instructor. The group's composition is also determined by the lab instructor. If a student fails to perform a lab exercise with his group he/she will have to write his/her own individual lab report! Late Submission The submission schedule (due date) will be made known by the attending lab instructor. Late submission results in a deduction of 0.5 marks per day out of 10 full marks. No or Partial Submission

6 A final date for submission will be clearly indicated on the sign-up sheet and/or announced by the lab instructor. If after that date not all lab reports have been submitted, the student will receive a grade of "F" for the course! The deduction of marks for late submission still applies. Format • The report must be typed. Graphs may be produced by computer, provided the software is suited for that use, i.e. grid, proper scaling and correct labelling can be achieved and the plot is smooth. If a graph is used to extract data or to provide some precise information, show precisely how the information is obtained (here it may be better to draw it on graph paper by hand - usually is faster, too). • For your report use YOUR OWN words to present your report concise, clear and clean. As pointed out above, copying etc. will be considered as plagiarism and will be severely punished by reducing marks or, in severe cases, served with an "F" as mentioned above (the provider/lender of the original work included)! • The notes/sheets containing the raw data taken by each student during the experiment are to be initialized by the attending technologist before leaving the lab and attached to the written report. Reports with the raw data missing are subject to a deduction of one full mark (= 10%)! The student is encouraged to develop and use his/her own personal style for writing and presenting his/her report. However, standard procedures in industry and research laboratories require certain information to be documented. Therefore, adhere fairly loosely to a general format like the following: - Title page (Please make an exception here: Pages stapled - no folders, plastic covers, etc): Course number, Experiment number, Experiment Title, Name, Lab partners, Date of performance - Abstract Statement of objective of the experiment (one or two sentences) Concise and pertinent outline of the theory underlying the experiment (max one page) - Experiment and Analysis If the experiment consists of two or more parts, keep the experimental and analysis sections together – the reader of your report does not want to continuously flip pages back and forth to look for data etc.! Brief outline of the method of investigation (whatever is applicable): Procedure Measurement techniques Schematic diagrams Equipment identification Data (tables) Observations relevant to the experiment and the results Arrange experimental data, and do the necessary calculations (if applicable, at least a sample calculation), to prepare for analysis Theoretical calculations (at least sample calculation) Comparison of experimental results with theory (preferably in form of tables/graphs) Probable causes and magnitude of errors - Conclusion (Summary) - Review questions - Raw data notes, attached to report, and initialized by the attending lab technologist. GOOD PRESENTATION IS OF THE UTMOST IMPORT ANCE , AS IS CORRECT ENGLISH AND GRAMMAR. EXPECT 20% OF YOUR LAB MARK ASSIGNED TO THIS AREA!! GENERAL INFORMATION EQUIPMENT If equipment needs to be signed out, contact one of the technologists. The person signing it out is responsible for it! Your marks will be held back until all equipment, books, data manuals, tools etc. are returned (i.e. your graduation might depend upon it!). Signed-out equipment has to be returned to the same technologist from whom you signed it out! Assure your name is then removed from his sign-out list! No equipment may be removed from any of the laboratories without explicit permission!

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As you see, this is very important! TAKE LABS VERY SERIOUSLY! Lakehead University, Electrical Engineering Department

July 2007

ELECTRICAL MACHINES Experiment No. 1 - 2258

8

DC Generator

DC GENERATOR Objective To study the characteristics and the performance of a Shunt DC Generator

Background Electrical generators transform mechanical energy into electrical energy. The electric motor converts electrical energy to mechanical energy. DC machines convert the internal ac currents and voltages into dc by means of a mechanism called commutation. The armature conductors are wound around the rotating part, the field coils are placed around the stator (or frame) poles. In general, the various types of DC machines (generator or motor) can be classified by the way their field is excited: Separately excited (the field is excited by a separate, external power source) Shunt (the field cct is connected parallel to the armature cct) Series (the field cct is connected in series with the armature cct) Compound (both shunt and series field circuits are connected) In a dc generator, the rotor is turned by a driving unit called a ‘prime mover’ whose speed is kept constant (diesel engine, turbine, etc.). Separate excitation requires a separate field supply and is therefore used only for applications where a wide range of controlled voltage is desired. Shunt generators excite themselves and maintain an approximately constant output voltage.

In this experiment, we use the separate excitation configuration to find the magnetization curve, and then use the parallel connection to investigate the performance of a DC Shunt Generator. Theory See reference text, chapters 8 and 9.11 - 9.14. The dc generator investigated in this lab is of the type shown in Fig. 1.1. This generator is also called ‘self-excited’, since the generator supplies its own excitation of the field windings by having the field connected across the terminals of the machine, in parallel to the armature.


9

DC Generator

Voltage Generation To supply its own field current, the machine needs to generate some voltage EA, which in turn depends on the existence of some residual flux in the poles. However, initially there may not be enough residual flux and hence no voltage is generated. In this case a small dc voltage can be applied to create some flux in the poles. The induced voltage EA is given by:

E A = K Φ res ω

(1.1)

where, EA K

=

internally generated voltage (steady state generated emf) machine constant

=

angular velocity

=

Φ res = residual flux in the poles of the generator ω

Fig. 1.1

Equivalent circuit − d.c. shunt-generator

If there is no residual flux, then EA= 0 and IF = 0 , and the process can’t get started. This can be corrected by reversing the rotational direction of the machine, reversing the field connections, or “flashing” the field. The internally generated voltage EA is related to the terminal voltage VT by:

VT = E A − I A R A

(1.2)

I A = IF + I L

(1.3)

and,


10

DC Generator

where, IA RA VT IL RL IF RF RRh VNL VFL

= = = = = = = = = =

armature current (in Amp) armature resistance (in Ohm) terminal voltage (in Volts) load current (in Amps) load resistance (in Ohm) field current (in Amps) field resistance (in Ohm) rheostat resistance (in Ohm) generated output terminal voltage at No Load (in Volts) generated output terminal voltage at Full Load (in Volts)

The generator performance can be evaluated from the voltage regulation:

VR =

VNL − VFL × 100 % VFL

(1.4)

Power and Losses A power-flow diagram shows the relationship of input power, losses, and output power:

PIN

Armature Terminal EM = PCONV Power  POUT    PROT PCO, A PCO,F PSTRAY PBRUSHES PIN PROT PSTRAY EM PCO,A PCO,F PBRUSHES PATP POUT

= = = = = = = = =

Prime Mover Rotational Losses Stray Losses (very small, ignored) PCONVERTED = EA IA Armature copper losses IA2 RA Field copper losses IF2 RF Brush losses IA 2 Volts [W] Armature Terminal Power VT IA Output Power at shaft VT IL

In this experiment we do not measure the input power provided by the prime mover. Then POUT = PCONV − PCO − PBRUSH − PFIELD


11

DC Generator

Experiment Note the set number of the machine set you are using (on the right side of the acrylic cover) Nameplate Data Record the nameplate data of both the dc and the ac machine. Of interest are: rated power, voltage, current, and speed for the AC machine also record Design class letter and starting code (KVA-) letter Keep the notes at hand since you will need the nameplate date for the DC Motor and the Induction Motor experiments, too. Equipment Variac (Variable Transformer) Bridge Rectifier V-meter (15VDC)

Tachometer (installed on back frame) Rheostats 180Ω, 44Ω, 22Ω A-Meter (5ADC), for IL

Armature and Field Resistance Measure RA and RF using the V/A- meter method. The measurement procedure is described in Appendix B of this manual. - For the measurement of RA the switch at the instrument panel needs to be in the "Mot" position. Start with zero Volts (!!), use the supplied V-meter (set to range to cover 15V) meter to read the voltage and increase until the current IA reaches 4 A. Then compute RA. - For the measurement of RF set the switch at the panel to "Gen". Apply 100V to the field terminals and measure the current. Compute RF. Magnetization Curve and Open Circuit Characteristic Eq. 1.1 shows that the generated voltage EA is proportional to the flux and the rotational speed. Since the speed is kept constant, the emf EA is directly proportional to the flux. The flux is produced by the magnetomotive force which in turn is proportional to the field current. Thus, EA is proportional to IF and the magnetization curve is usually plotted as EA vs. IF (see Fig. 1.2). Since in the open circuit configuration EA ≅ VT , this is also frequently referred to as the ‘open circuit characteristic’ (OCC).

Fig. 1.2

Magnetization Curve


12

DC Generator

The magnetization curve can be measured with either the shunt circuit configuration as well as with the separately exited circuit configuration. Since we want to investigate the shunt type generator it may appear to be logical to use this circuit for the measurement. However, since the machine needs to provide its own field current, and the field current is limited by the internal field resistance, the generated open circuit voltage will reach its maximum before reaching or even coming close to the saturation area. Conversely, when the field current is supplied externally it can be adjusted to an amount sufficiently large so that the voltage EA can reach the saturation area. Therefore, for the procurement of the magnetization curve we use the external or separate excitation. Later on, for the measurement of the output characteristics under load we then use the shunt circuit as outlined earlier. Connect the circuit shown in Fig. 1.3. All meters are already wired in and located at the back panel.

How to use the AC Drive: Switch power ‘ON ’. Push ‘START’ to start the prime mover. Adjust the potentiometer on the AC drive unit until the desired speed is reached. Then, for the remainder of the experiment, the pot can stay in that position and the AC drive is simply switched on and off by pressing START/STOP. After a Stop and Re-Start the drive accelerates the ac machine until it reaches the previously set speed.

On the back panel, confirm that the mode switch is set to ‘Gen’ ! Adjust the prime mover speed until rated speed of the generator is reached and keep it constant. Using the variac to increase IF from 0 in increments of approx. 50mA to 500mA (IFmax ~ 10% of rated current, i.e ~ 0.5A). Try to do this slowly and in one smooth sweep to avoid hysteresis effects. Do NOT try to set a precise value for VT by varying the voltage up and down! Carefully record IF, VF and VT .

Fig. 1.3

Connection diagram − no load (OCC) characteristic


13

DC Generator

Start-Up As mentioned earlier, in a shunt-connected generator configuration, the initial generation of an emf in the generator depends on a residual flux remaining in the poles. Also, if the field resistance is larger than a certain critical resistance, the terminal voltage VT remains at the residual level and will not build up. This problem will be investigated here. With the circuit shown in Fig. 1.4., set the field rheostat RRh to a value of approx. 180 Ω.

Figure 1.4

Connection diagram − Start up test

Start the prime mover and bring it to the rated generator speed. Observe the terminal voltage VT . There will be no output voltage, i.e. no voltage generated. Now decrease the field resistance slowly. When the voltage does begin to build up, stop the machine and measure the resistance of the rheostat. This is the ‘critical resistance’ RC which, when exceeded, prevents the voltage build-up as shown in Fig. 1.5. Since RRh is in series with RF, RC = field resistance RF + external RRh

Fig. 1.5

OCC characteristics


14

DC Generator

Terminal Characteristics This part of the experiment investigates the machine under load Usually the machine is run at a constant speed set by the prime mover. The generator provides its own field current which, however, depends on its terminal voltage. Connect the circuit as shown in Fig.1.6. Use the supplied A-meter (5ADC) for IL. The field is shunted directly to the armature, with no external resistance added.

Fig. 1.6

Connection diagram − generator under load

Bring the prime mover up to rated speed. Starting with the 180Ω-rheostat fully inserted, connect the load resistances as required (observe the current rating limits!) to obtain several load currents in 0.5A-increments from near zero (180Ω-rheostat set to full resistance) to full load (see nameplate) or as high a load current the generator can sustain, by decreasing the rheostat resistance. Keep n = constant, adjust AC drive unit if necessary! •

To avoid damage to the rheostats or the motor, select the proper rheostat for the particular current range by observing the current ratings (shown on the glider) and by calculating the approx. resistance value for the desired current.

•

If this current rating is exceeded switch the prime mover off. Exchange the rheostat with one of lower resistance but higher current rating. When connecting the new rheostat make sure it is initially set to the maximum resistance to avoid damage due to high currents. Then re-start the prime mover and continue with the experiment.

For each value of IL, measure VT , IA, n and IF. Most likely VT will break down before the rated current can be achieved. Stop the experiment when IL and VT begin to decrease, and note IMAX and VT.


15

DC Generator

Analysis 1. Plot the OCC (EA vs. IF) on graph paper (EA = VT, NO LOAD). 2. Obtain a reasonable value for the critical resistance RC from the graph and compare with the (approximate) value found from measurement. Show how you did this. 3. Using the data from your load measurement, plot the RF-line onto the magnetization curve (VT [LOAD] vs IF). Determine RF and compare with the value found earlier. 4. Plot VT vs IL (on graph paper) using the measured results of loading the generator. 5. Making use of the same graph, calculate the voltage regulation (VNL is at IL = 0). 6. For IL = 2A and the corresponding IF find EA from the OCC-curve. Using the measured values for RA and RF, calculate POUT by finding the internally generated power PCONV and subtracting the losses as shown in the theory section. Compare the result with the measured POUT = VT IL. 7. If the rotational losses PROT are assumed to be ~ 24.6 W, what would be the efficiency η = POUT / PIN be? (The value for the rotational losses comes from a separate experiment, but can be used here) 8. Comment on the overall performance of the dc generator. Keep notes for RA, RF for the following labs

Conclusion Comment on your results and the performance of the generator.


16

DC Motor

DC MOTOR Objective To study the characteristics and the performance of both a separately excited and a shunt connected D.C. Motor

Background There is no physical difference between the d.c. generator and the d.c. motor. The only difference between the two is the direction of power flow. Separately excited and shunt dc motors exhibit a linear relationship between speed and torque. This allows for excellent speed control and, despite the fact that they are more expensive than induction motors, these motors still find a wide range of applications.

Theory See reference text, chapters 8 and 9.1-9.10. The equivalent circuits of the separately excited and shunt dc motors are the same as for the generator, but with the direction of currents reversed (see Figs. 2.1 and 2.2):

Fig. 2.1

Fig. 2.2

Equivalent circuit

Equivalent Circuit

Separately excited

Shunt Excitation


17

DC Motor

While dc generators are compared by their voltage regulation, dc motors are compared by their speed regulation. Speed regulation is defined by

SR =

ω NL − ω FL × 100 [%] ω FL

(Eq. 2.1)

If it is assumed that the voltage applied to the motor, VT , is kept constant, then the relevant equations are:

E A = K Φω

(Eq. 2.2)

E A = VT − I A R A

(Eq. 2.3)

T = K ΦI A

(Eq. 2.4)

IL = IA

(Eq. 2.5)

VF RF

(Eq. 2.6)

Internally generated voltage and Developed torque For the separately excited motor

IF =

I L = IA + I F

For the shunt motor

VT RF

(Eq. 2.8)

2π n 60

(Eq. 2.9)

IF = Angular velocity in rad/sec

ω =

(Eq. 2.7)

where n is in rev/min [rpm] Input Power (power applied to exterior terminals) Efficiency

Copper losses, sep.excited Copper losses, shunt Rotational losses

η=

PIN = VT I L

(Eq. 2.10)

POUT × 100 [%] PIN

(Eq. 2.11)

PCo = I A 2 RA

(Eq. 2.12a)

PCo = I 2A R A + I F2 RF

(Eq. 2.12b)

PROT = PIN ( NL ) − PCo ( NL )

(Eq. 2.13)

Core losses and stray losses are usually small and will be ignored.


18

DC Motor

However, brush losses may be considered: assuming a voltage drop of 2V across the brushes, the loss would be

PBR = I A 2V

(Eq. 2.14)

POUT = PIN − PCo − PRot

(Eq. 2.15)

Then the power applied to the shaft is given by:

The maximum power POUT that the motor can sustain over time is the rated power stated on the nameplate. Thus the torque applied to the shaft is given by

T=

POUT ω

(Eq. 2.16)

The power-flow diagram for the DC motor is just the opposite from the DC generator: EM = PCONV = EA IA PIN =  POUT    PCO,F PCO,A PROT PBRUSHES Speed control Speed control can be achieved by varying IF or IA, or both. To vary IF, either VF or RF needs to be varied. In the case of the shunt motor, VF = VT , and since VT is usually a constant value, a change in RF is the common method. IA can also be varied either by varying EA (i.e. VT ) or using a rheostat for control of IA. Summary: • Varying IF by varying RF : This is the preferred method. It requires a rheostat for a relatively small current and works for both motor configurations. • Varying IF by varying VF : This can be done in the case of a separately excited motor, but not for a shunt motor since in this configuration VF = VT , which usually remains unchanged. • Varying IA with the help of a rheostat is seldom used since the losses in the rheostat are large and decrease the efficiency of the motor considerably. • Varying IA by varying VT is the preferred method.


19

DC Motor

Experiment 2 - variacs 2 - bridges

1 - rheostat 180 Ω 1 - A meter, 5A dc

1 - Tachometer

The experiment uses ‘Dynamic Braking’. The ac machine is used as a load to the dc motor. For that purpose, a dc current (via a rectifier bridge) is applied to two of the three phases which can be varied with the variac and produces a counter-torque on the ac machine and thus a brake action on the dc machine. Assume the induction machine Yconnected! Nameplate data Record the nameplate data of both the dc and the ac machine. Armature and field resistance Measure RA and RF using the Voltmeter/Ammeter method. The measurement is described in Appendix B of this manual. If you are using the same set of machines as in Experiment No. 1 you can use the already measured data.

Separately excited dc motor Connect the circuit shown in Fig. 2.3.

Fig. 2.3

Connection diagram − separately excited d.c. motor

Set the mode switch on the back panel to ‘Mot’ ! Set VT to 0V (variac fully counterclockwise)! Set the rheostat to minimum resistance and apply VF to the field terminals (switch dcdrive 'ON'). VF should read about 100V and IF approx. 400 mA. It is imperative that the field excitation is established before the armature voltage is applied!


20

DC Motor

It is also important to keep an eye on the field to avoid any interruption. Should that occur for whatever reason immediately interrupt the armature current IA (switch off variac or use panel switch).

Measurement of Torque Apply the terminal voltage VT . Increase it slowly until the rated speed is reached. Then keep VT constant throughout this part of the experiment. Increase the braking current IBR from approx. 0 A to 3.5A (= approx. rated current of the AC machine) in steps of 0.5A. For each step, note IA, VT and n.

Speed Control With RRh = min., bring speed to n ~ 1500 rpm and set the breaking load current IBR = 3A. Re-adjust n ~ 1500 rpm ! • With VT = constant, vary IF from ~ 400mA to ~ 250mA in steps of 50mA with the rheostat RF and note n. • With IF ~ 400mA = constant (RRh = min), vary VT from ~70 to ~40V in steps of 5V with the variac and note n.

Shunt motor Connect the circuit as shown in Figure 2.4.

Fig. 2.4

Connection diagram − shunt motor

Torque measurement Set the rheostat to minimum resistance. With a close watch for the armature current IA, start the motor carefully (high inrush current!) by applying VT slowly at first and then increasing smoothly until rated speed (n = 1750 rpm) is reached. Then keep VT constant throughout this part of the experiment. Apply the braking load current IBR and repeat the measurements as in the previous configuration. In addition, note IF.


21

DC Motor

Speed control With no load applied (IBR = 0) and the rheostat set to min (RRh ~ 0), start the motor and adjust to n ~ 1500 rpm. Then apply the load, IBR = 3A. Re-adjust VT to set speed to n ~ 1500. • Note VT and keeping it constant (adjust variac if necessary), vary IF from ≈ 240mA to ≈ 160mA in steps of 20mA. Record n. • Set VT = 60V and adjust IF = 200mA with the rheostat. Keeping IF = constant (adjust rheostat as necessary), vary VT from 60V to 50V in steps of 2V. Record n.

Change of rotation Set IBR to 0 (no load). - Run the machine shortly and note the direction of rotation. - Stop the machine. Switch field off! Change the polarity of the field voltage. Switch field on again. Re-start the machine again and just long enough (to avoid damage to the meters because some of which will go in the wrong direction) to note the direction of rotation. Stop, switch field off and change the polarity of the field back. Switch field on again, and start the machine shortly to verify that the direction is as it was initially. - Now change the polarity of the armature voltage and repeat the exercise above, again just long enough to note the direction of rotation.

Analysis For both the separately excited machine and the shunt machine: (for the rotational losses assume 24.6W) 1. 2. 3. 4. 5. 6. 7. 8. 9.

Table all your results Calculate and plot T vs IA Plot n vs T (Plot the results for both Calculate and plot η vs T configurations on the same Plot n vs IF (with VT = const.) graph for comparison) Plot n vs VT (with IF = const.) Find efficiency η = POUT (Shaft) / PIN Calculate speed regulation (For all plots use graph paper!) How can you change the direction of rotation?

Questions a) Why has the field always to be connected first and must not be interrupted? b) Can you design a circuit or some device to protect the motor in case the field connection accidentally opens? (Hand sketch sufficient)

Conclusion Comment on your results and the performance of the motor.


22

DC Motor


23

Synchronous Generator

SYNCHRONOUS GENERATOR Objective To measure the impedances of a Synchronous Generator. Theory See reference text, chapter 5. The synchronous generator requires a prime mover to turn the rotor of the machine. A dc current applied to the rotor winding produces a rotating magnetic field which in turn induces a three-phase voltage within the stator windings, quite similar to a transformer action. As the name implies, the frequency is given by:

f =

nm p 120

(Eq. 4.1)

where f nm p

= = =

frequency [Hz] mechanical speed [rpm] number of poles

For a 4-pole machine such as the one used in this experiment, to achieve a frequency of 60 Hz the speed needs to be exactly n = 1800 rpm, i.e. the rotor must rotate at 1800 revolutions/minute. The voltage induced in the stator is given by

E A = K Φω

(Eq. 4.2)

where K Φ ω

= = =

a machine constant depending on number of poles etc. flux angular velocity

Eq. (4.2) shows that EA is proportional to the flux Φ . The flux depends on the rotor current which is the field current IF. Similarly as in the dc generator, IF depends on the flux and since EA is directly proportional to flux, this relationship is shown in Fig. 4.1.


Fig. 4.1

24


The magnetization curve

This is known as the magnetization curve or the open circuit curve of the machine. The synchronous generator can be represented by an equivalent circuit on per phase basis (assuming the system is balanced), as shown in Fig. 4.2:

Fig. 4.2

Equivalent circuit on per phase basis

For a Y-connected stator as in our machine, we have:

VT = 3 Vϕ

(Eq. 4.3)

or

Vϕ = E A =

VT 3

(Eq. 4.4)

where Vt is the terminal voltage. To find the parameters of the equivalent circuit, three quantities must be found: 1) The relationship between field current IF and flux, i.e. between field current IF and EA 2) The synchronous reactance XS 3) The armature resistance RA Item (3) can be found by means of the V/A-meter method used in previous experiments (or see Appendix B). In a pinch, an Ω-meter will suffice.


25


Item (1) can be found by performing the open circuit test. The result is a plot EA vs IF (open circuit characteristic OCC). The linear portion is called the “air gap line” (Fig. 4.1). Item (2) is found by performing the short circuit test. The resulting plot shows the relationship IA vs IF (see Fig. 4.3), called the short circuit characteristic SCC:

Fig. 4.3 Plotting the results of both the open circuit test (OCC) and the short circuit test (SCC) onto the same graph, XS can be found by

XS ≈

Consider Fig. 4.4:

Fig. 4.4

E A Vϕ, oc ≈ IA I A,,SC

(Eq. 4.5)


26


From the plot • • • •

Choose a field current Find the internal generated voltage EA = Vϕ,OC from the OCC at that field current Find the short circuit current IA,SC at that field current Calculate XS

From Figs 4.1 and 4.4 we have:

IA =

with RA