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(5.5) (5.6) Ih - rms value of the net harmonic current.

Solution: a. For wt>a (figure 5.1) with discontinuous current:

From now on the motor current ia’ flows through the diode until it becomes zero: (5.16) with ia’(0) = ia(p) (5.17) (5.18)

5. CONTROLLED RECTIFIER D.C. BRUSH MOTOR DRIVES

Table 5.1. Phase controlled rectifier circuits

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- As the d.c. motor current, when fed from phase controlled a.c. - d.c. converters, is not constant and a.c. supply current is not sinusoidal, adequate performance indexes for the motor - converter combination should be defined.
- The main performance indexes related to the motor are:
- the torque - speed characteristic;
- nature of motor current - continuous or discontinuous;
- average motor current Ia:

If the supply voltage is a pure sinusoid only the fundamental of input current will produce the mean input power and thus:

(5.4)

where: V - rms supply phase voltage;

I - rms supply phase current;

I1 - rms fundamental component of a.c. supply current;

j1 - angle between supply voltage and current fundamentals.

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- harmonic factor HF:

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5.3. SINGLE P.E.S. CONTROLLED RECTIFIER factor:

- A d.c. brush motor with separate excitation with the data: Kelp = 2Wb, Ra = 5W, La = 0.1H is fed through a thyristor (figure 5.1) from a single phase a.c. source whose voltage is .
- The motor speed is considered constant at n = 750rpm.
- a. Calculate the motor current ia time variation for a delay angle a = +300;
- b. How the motor voltage Va varies in time?
- c. How ia varies in time in presence of a free wheeling diode in parallel with the motor armature (figure 5.1)? The thyristor and the diode are considered as ideal switches.

(5.8)

Electric Drives

Figure 5.1. A d.c. brush motor supplied through a thyristor factor:

with the initial condition ia = 0 for w1t = a = p/6.

The steady state solution is:

(5.9)

and finally:

(5.10)

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The complete solution: factor:

(5.11)

For t = t1 = a / w1 = p/(6.2p.60) = 1.3888.10-3 s ia(t) = 0

and thus:

(5.12)

and

(5.13)

(5.14)

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Finally (5.15) factor:

Equation (5.15) is valid for w1t > p/6 until the current becomes zero soon after w1t =p as shown in figure 5.1.

- b. The motor voltage is equal to the source voltage as long as the thyristor is on and becomes equal to minus the e.m.f.:
- ,when the motor current is zero
- (figure 5.1)
- c. In presence of the free wheeling diode D, the latter starts conducting when V(t) becomes negative (w1t =p).

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(5.19) factor:

A’ = 12.78319 A.

Thus (5.20)

The current ia’ = 0 for w1t’ = 7.070.

The motor voltage Va becomes zero during the time interval when the free wheeling diode is conducting (1800 to 1800+7.070).

Electric Drives

5.5. THE SINGLE PHASE FULL CONVERTER factor:

A d.c. motor of 7kW and 1200rpm rating with separate excitation is supplied through a single phase full converter as shown in figure 5.3.a. The other data are Ra = 0.2W, rated current Iar = 40A, Kelp = 10Wb, the a.c. supply voltage (rms) is 260V.

a. Draw the voltage and current waveforms for steady state and finite motor armature inductance and a = 450 and a = 1350.

b. For a firing angle of a = 300 and rated motor current (rectifier regime) calculate: motor speed, torque and supply power factor, neglecting the motor current ripple.

c. By reversing the field current the motor back e.m.f. Eg is reversed; for rated current calculate: converter firing angle a’ and the power fed back to the supply.

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a.) factor:

Figure 5.3. The d.c. brush motor fed through a single phase full converter

a.) the converter b.), c.), d.), e.) - voltage and current waveforms for motor action

(a = 450)

f.), g.), h.) - for generator action (a = 1350)

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Solution factor::

a. The waveforms of currents and voltages are shown on figure 5.3. It should be noted that because the motor inductance is not very high the armature current, and speed pulsate with time.

Motor action is obtained for a = 450 when both the motor and converter average input powers are positive. For generator action (a = 1350) the motor current remains positive but the motor average voltage Va is negative. Thus both the motor and converter input average powers are negative for generating.

b. As the motor current is considered ripple - free we use only the average values of voltage and current while the speed is also constant.

The average motor voltage Vav is:

(5.31)

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The motor torque T factor:e is:

(5.32)

The motor speed n is:

(5.33)

As the primary current is now rectangular (40A) the rms current I1 = 40A. The power from the supply, neglecting the losses,

.

Thus the supply power factor:

(5.34)

c. For generator action the polarity of induced voltage should be reversed:

(5.35)

Thus the motor voltage Va becomes:

(5.36)

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Finally: (5.37) factor:

The regenerated power:

(5.38)

As for this regime, either the flux lp or the speed n changes sign the motor torque opposes the motion providing generator braking.

In the process the motor speed and e.m.f. decrease and in order to keep the current constant the firing angle a>900 in the converter should be modified accordingly.

For the motor as above, having La = 2mH, calculate the following:

d. For a = 600 and constant speed n = 1200 rpm draw the voltage and current waveforms knowing that the motor current is discontinuous.

e. Calculate the motor current waveform for n = 600 rpm.

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Solution factor::

As the motor electrical time constant te = La / Ra = 2.10-3 / 0.2 = 10ms is small, when the voltage becomes zero (for w1t = p), the motor current decays quickly to zero along the angle b (from p to p+b) with b<a and thus the current is discontinuous. As a increases, for a given speed n (and e.m.f. eg), the average voltage Vav decreases with respect to the case of continuous current.

The discontinuity of current contributes to a sluggish dynamic response as during zero current motor internal torque control is lost. The situation occurs especially at low torques (and currents). Special measures such as flux weakening (reducing lp) for low torques leads to reduced a at high speeds avoiding the discontinuity in current.

Figure 5.4. D.c brush motor supplied from a full converter - discontinuous current mode

Electric Drives

With the speed considered constant the voltage equation is: factor:

(5.39)

with ia = 0 for w1t1 = a, the solution of above equation is:

(5.40)

for and thus:

(5.41)

(5.42)

The current becomes again zero for w1t2 = p+b:

(5.43)

The solution for b is .

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5.7. THE THREE PHASE FULL CONVERTER - MOTOR SIDE factor:

A three phase full converter (figure 5.6) supplying a d.c. motor has the data: line voltage VL = 220V (rms), Kelp = 10Wb, Ra = 0.2W and neglect the ripples in the motor current.

a. For Ls equal to zero calculate the output average voltage as a function of the delay angle a and; for a = 300 determine the motor speed for Ia = 50A.

b. Considering the a.c. source inductance Ls0 determine the expression of the output voltage as a function of a and Ia and calculate the motor speed for Ia = 50A, a = 300 and Ls = 11mH.

c. Calculate the overlapping angle at commutation for case b.).

Solution:

The principle of operation is quite similar to that of the previous case. However only a 600 conduction of each pair of thyristors occurs as shown in figure 5.6.

In the absence of a.c. source inductances Ls (Ls = 0) the commutation is instantaneous. The average output voltage Vav is:

(5.48)

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Figure 5.6. D.c. brush motor fed from a three phase full converter

Consequently Vav<0 (Vav>0) depending on a. For a<90 the average output voltage Vav is positive, that is rectifier mode; for a>90 Vav<0 and thus the inverter mode is obtained. The motor current remains positive irrespective of a. Two quadrant operation is obtained.

Electric Drives

The motor voltage equation is: converter

(5.49)

(5.50)

b. The effect of a.c. source inductances Ls on current commutation is shown in figure 5.7 for the case of constant motor current (similar to the diode full converter (chapter 3)). The commutation between T1 and T5 is not anymore instantaneous; an overlapping angle u occurs. The effect of actual commutation is in fact a reduction of output voltage Vd determined by the area Au when a kind of shortcircuit occurs between phases a and c.

(5.51)

This is so since the current in phase a is zero for w1t = a and equal to Id for w1t = a +u. The average voltage is reduced by 3 / p Au.

Electric Drives

Finally the average voltage is equal to that already found for Ls = 0 minus

3 / p Au:

(5.52)

Figure 5.7. The current commutation in presence of a.c. source side inductances Ls

Electric Drives

As we can see the angle u is not required to calculate the output voltage Vd. However it is needed to ensure reliable operation in the inverter mode (a>900). The second Kirchoff law for phase a and c during commutation provides the equation:

(5.53)

with , that is (5.54)

Thus:

(5.55)

with (5.56)

(5.57)

and finally (5.58)

Electric Drives

Thus knowing output voltage Va and Id we may calculate the overlapping angle u.

In the inverter mode (a>900) the commutation should be finished before a + u = p in order to allow the turn off time toff required for the recombination of

charged particles in the thyristors ( ) for negative voltage along the turning off thyristors.

The rectifier voltage Vd for a=p / 6 and Id = 50 is:

(5.59)

(5.60)

The reduction of output voltage for the same a due to commutation with 18V has contributed to a notable reduction in speed, for 50A, from 1484.58 rpm to 1376.58 rpm.

c. To calculate the overlapping angle u we use the expression derived above:

(5.61)

A considerable value for u has been obtained.

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5.8. THE THREE PHASE FULL CONVERTER - SOURCE SIDE ASPECTS output voltage V

For the three phase full converter and d.c. motor in the previous example with Ls = 0 for a = 00, a = 450 with Id = 50A determine:

a. The waveforms of a.c. source current and its harmonics factor.

b. The rms of source current fundamental and of the total source current.

c. The displacement power factor for Ls = 0 and Ls = 1mH for a = 450.

d. Calculate the line voltage and voltage distorsion due to Ls = 1mH

and a = 450.

Solution:

a. As the motor armature current is considered constant the a.c. source current is rectangular as shown in figure 5.8.a and b.

The presence of a.c. source inductances Ls0 leads to the overlapping

angle u0.

b. The rms value of the current fundamental, Ia1, is:

(5.62)

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Figure 5.8. A.c. source currents in a three phase full converter and constant motor current

a.) for a = 0, Ls = 0; b.) for a = 450, Ls = 0; c.) for a = 450, Ls = 1mH

Electric Drives

For the total a.c. source current which is made of rectangular 1200 wide “blocks”:

(5.63)

In the absence of Ls the displacement power factor (DPF) angle is equal to a and thus the DPF is:

(5.64)

In the presence of Ls the displacement power factor is approximately:

(5.65)

To calculate u for a = 450 we use equation (5.58):

(5.66)

Finally:

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The current commutation in the presence of L rectangular 120s produces a further reduction of displacement power factor.

In general the DPF decreases with a increasing which constitutes a notable disadvantage of phase delay a.c. - d.c. converters. Special measures are required to improve DPF with a increasing.

d. The a.c. source current overlapping during commutation produces notches in the line voltage. From figure 5.9. we may obtain Vab = Van - Vbn of the waveform shown in figure 5.9.

Figure 5.9. A.c source line voltage notches due to Ls (commutation)

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Considering u as small, the deep notch depth is considered equal to

and thus the notch width u is approximately:

(5.67)

The depth of shallow notches is considered half of that of deep notches. IEEEE standard 519 - 1981 suggests the limitation of line notches to 250ms (5.4. electrical degrees) and the deep notch depth to 70% of rated peak line voltage in order to perform satisfactorily.

Special filtering is required to cope with more recent standards. The voltage distorsion due to notches depends on the harmonics currents In and the a.c. source inductance Ls:

(5.68)

with due to the almost rectangular form of a.c. source

current.

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5.9. THE DUAL CONVERTER - FOUR QUADRANT OPERATION equal to

Figure 5.10. Dual converter with circulating current supplying a d.c. brush motor

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