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Name: __________________________

DC Drive Operating Envelopes and Induction Machines

Solve using data from the DC machine data sheet, using the "hot" resistance value for all calculations. Notethat the value ofKon the sheet is for rated (100%) field flux. Assume that the machine can safely handle asmuch current as the power converter can deliver to it. In addition, assume that all powersemiconductors are ideal with zero voltage drop when they are on.

1. Consider a 2 hp, 850 rpm dc machine connected to a single-phase, fully-controlled thyristor bridge asshown in Fig. 2.9-4 (pg. 53), assuming that the series inductance is large enough to justify theassumption of infinite output inductance. The amplitude of the ac voltage source is 210 Vrms, themaximum thyristor current is 10 A and the phase control angle can be varied over the full rangefrom 0 to rad. Assume that the maximum machine speed is 2000 rpm in either direction (i.e., 209.4 rad/s).

a) Plot the complete boundary envelope (i.e., capability curve) of the drive systems torque-speedoperating capabilities on a set ofT- axes, with torque Ton they-axis [in N-m] and speed on thex-axis [in rad/s]. Assume that the field flux is constant at its rated (100%) value. In addition,assume that the maximum armature current is determined by the maximum thyristor current ratherthan the rated machine current based on its rated power. Similarly, assume that the maximumapplied armature voltage amplitude is determined by the maximum positive and negative rectifieroutput voltage (@ = 0and = ) rather than the rated machine voltage. What are the torque,speed, machine shaft power, and phase control angle at the four corners of the operating envelope?(Hint: Do not be surprised ifPdoes not equal the rated machine power (2 hp = 1492 W))

Upper left T= ________ Nm

= ________ rad/s P = ________ W

= _______ rad

Upper right T= ________ Nm = ________ rad/s P = ________ W = _______ radLower left T= ________ Nm = ________ rad/s P = ________ W = _______ radLower right T= ________ Nm = ________ rad/s P = ________ W = _______ rad

b) Assume that a second identical single-phase thyristor bridge is added in anti-parallel as shown inFig. 2.11-1 on p. 74. Plot the complete operating envelope (i.e., capability curve) of the drivesystems torque-speed operating capabilities on a set of T- axes, assuming that the field flux is stillconstant at its rated value. What are the torque, speed, machine shaft power, and phase control angle at

the four corners of the operating envelope?

Upper left T= ________ Nm = ________ rad/s P = ________ W = _______ radUpper right T= ________ Nm = ________ rad/s P = ________ W = _______ radLower left T= ________ Nm = ________ rad/s P = ________ W = _______ radLower right T= ________ Nm = ________ rad/s P = ________ W = _______ rad

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ECE 411 - Introduction to Electric Drives - Fall 2011

c) Replot the complete operating envelope in part b) with a dual anti-parallel thyristor bridge converterassuming that the field can be weakened. What is the maximum value of torque that can be achievedat the speed extremes of -2000 rpm (=-209.4 rad/s) and +2000 rpm (=+209.4 rad/s), and what are thecorresponding values of machine output powerP, machine torque-per-Amp constantKand controlphase angle ?

= +2000 rpm

Positive torque: T= _______ Nm K= ________ Nm/A P = _________ W = _______ radNegative torque: T= _______ Nm K= ________ Nm/A P = _________ W = _______ rad

= - 2000 rpm

Positive torque: T= _______ Nm K= ________ Nm/A P = _________ W = _______ radNegative torque: T= _______ Nm K= ________ Nm/A P = _________ W = _______ rad

d) Consider the same 2 hp machine as in part a), replacing the single-phase bridge with a three-phase

version as shown in Fig. 2.9-8. Again assume infinite output inductance and constant field flux at its

rated value. If the amplitude of the input ac voltage is 210 Vrms line-to-line and the maximum

thyristor current is still 10 A, determine the new outer boundary of the drives torque-speed

operating capabilities, assuming that the phase control angle can vary from 0 to radians. What

are the torque, speed, and phase control angle at the four corners of the capability curve?

Upper left = _____________ Nm

= _____________ rad/s = ____________ rad

Upper right = _____________ Nm

= _____________ rad/s = ____________ rad

Lower left = _____________ Nm

= _____________ rad/s = ____________ rad

Lower right = _____________ Nm

= _____________ rad/s = ____________ rad

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ECE 411 - Introduction to Electric Drives - Fall 2011

2. Induction Machine Steady-State Operating Characteristics

A 3-phase 10 hp, 220 V rms (l-l), 60 Hz, 4-pole induction machine has the following equivalent circuit

parameters (see Fig. 3.5-1 on pg. 88):

r1 = 1.9 r2 = 0.93 X1= 3.24 X

2 = 1.36 Xm= 39.6 r

m=

For operation at rated voltage and frequency with 3% slip (S=0.03), calculate the steady-state values for themachine output torque

T, rotor speed rmin [mech. rad/s], mechanical output powerPo, stator currentI1,

input power factorcos , total stator copper losses 3I12r1, total rotor resistive losses 3I22r2, and efficiency.

Ignore iron losses (rm = ) and friction and windage losses so that: Effic. = Po 100%

Po+3I

12R1+3I

22R2

Plot the torque-speed curve for values of slip S between 1.0 and -1.0 on a set ofT-rm axes, with torque Ton the

y-axis [in N-m] and speed rm on thex-axis [in mech rad/s].

T = ___________ N-m

rm= _________ mech rad/s

Po = ___________ kW

I1 = ___________ A rms

cos = _________

3I12r1 = ___________ kW

3I22r2 = ___________ kW

Effic. = ___________ %

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