In this article we will discuss about:- 1. Introduction to Chopper Control of DC Motors 2. Principle of Operation of Chopper 3. Step-Up Choppers 4. Step-Up/Down Chopper 5. Chopper Control of Separately Excited DC Motor Drive 6. Step-Down Chopper with R-L-Eb Load.
Introduction to Chopper Control of DC Motors:
In many cases, conversion of dc supply source voltage to different levels is required. For example, subway cars, trolley buses, or battery operated vehicles are fed from a fixed voltage dc supply source. But for their speed control we need conversion of fixed voltage dc source to a variable voltage dc source.
Conventional methods for obtaining the variable dc voltage from a fixed dc voltage source are given below:
1. Resistance Control:
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In this method, a variable resistance is introduced between the load and the source. The drawbacks of this method are wastage of lot of energy and for a given output voltage, requirement of resistances of different values for different values of load current. This method is still employed for older traction installations.
2. Motor-Generator Set (M-G Set):
Separately excited dc generator provides a voltage which can be varied from zero to rated value with either polarity. It has disadvantages of higher cost, large bulk, low efficiency and sluggish response because of the generator field time constant.
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3. AC Link Chopper (Inverter-Rectifier):
In this method, the dc supply is first converted to ac supply by an inverter (dc to ac converter). The obtained ac supply is then stepped up or down by a transformer and then rectified back to dc by a rectifier. Because of two stages of conversion, the set-up is costly, bulky and less efficient.
4. DC Chopper (DC to DC Power Converter):
A dc chopper is a static switch to provide variable dc voltage from a source of constant dc voltage. Choppers are now being used all over the world for rapid transit systems. These are also employed in trolley cars, marine hoists, forklift trucks and mine haulers. The future electric automobiles are likely to use choppers for their speed control and braking. Chopper systems offer smooth control, high efficiency, fast response and regeneration.
Principle of Operation of Chopper:
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A dc chopper is a high speed on/off semiconductor switch that connects the load to and disconnects it from the supply and produces a chopped load voltage from a constant input supply voltage. As it is an on/off switch between source and load, it can be symbolically represented by a switch S inside a dotted rectangle, as shown in Fig. 3.16. Actually, a chopper consists of main power semiconductor device together with their turn-on and turn-off mechanisms. In low-power chopper circuits, power transistors, GTOs etc. are used widely. In high-power chopper circuits, however, thyristors are in common use.
Figure 3.17 illustrates the principle of operation of a chopper. The switch may be closed or opened by supplying on/off pulses to it. Here the mechanism of sending pulses to a switch has not been shown. A shunting diode DFW is provided across the load for freewheeling the load current when the switch S is off. When the switch S is closed, the source voltage V, assuming that voltage drop across switch S in on-state is negligible, appears across the load for the duration the switch is closed.
This duration is designated Ton. After the pulse to switch is removed the load is disconnected from the source. The energy stored in the inductor circulates a current through the freewheeling diode DFW. As a result the load is short circuited and voltage across it falls to zero but the current through the load falls exponentially, as illustrated in Fig. 3.18. The duration for which switch is off is called off time Toff. The total time of a pulse is, therefore, given by T = Ton + Toff.
Thus, a dc chopped voltage is produced at the load terminals [Fig. 3.18 (a)] and the load current is continuous as shown in Figs. 3.18 (b) and (c).
From Fig. 3.18 (a), the average load voltage Va is given by-
where α = Ton/T is called duty cycle of the circuit. It is analogous to transformation ratio of ac transformer. The value α of ranges from 0 to 1. Hence the output voltage varies between zero and supply voltage V. In the present case the output voltage is less than the supply voltage. It is, therefore, called step-down chopper. In choppers, called step-up choppers, the output voltage is more than supply voltage.
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The load current and voltage waveforms, as shown in Figs. 3.18 (b) and (a) are for R-L load. However, in case, resistive load is used in the output, the current and voltage waveforms have similar variations as illustrated in Fig. 3.18 (c) and (a).
In case of R-L load, the inductor absorbs energy from the source during on-period while same is released by it during off- period. We can write, by using conservation of energy principle;
Energy absorbed = Energy released
Above relation is similar to that for an ac transformer. Here a, the duty cycle, corresponds to transformation ratio of transformer. The output of a chopper, as can be observed from Eqs. (3.25) and (3.26), can be controlled by a variation in a, the duty cycle.
Control Strategies:
It is seen from Eq. (3.25), that, average value of output voltage, V can be controlled by periodic opening and closing of the semiconductor switch. There are two types of control strategies for operating the switches that can be used in dc choppers. These control strategies are time-ratio control (TRC) and current limit control.
1. Time-Ratio Control:
In this control strategy, the value Ton/T of is varied. This is affected in two ways namely variable frequency control and constant frequency control.
(a) Variable Frequency Control (FM):
Under such scheme the chopping frequency f is kept variable and for this purpose either (a) on time, Ton or (b) off time, Toff is kept constant. This scheme is, therefore, called frequency modulation scheme and is illustrated in Fig. 3.19.
In Fig. 3.19 (a) and (b) on time Ton is kept constant while off time Toff of the switch is variable. The duty cycles in two figures are α1 = Ton/Ton + Toff = ¾ and α2 = 1/2 respectively.
Figure 3.19 (c) and (d) are for variable on time Ton and constant off time Toff. The duty cycle in the two cases are respectively 1/4 and 2/5. This technique is suitable for switches which require forced commutation to turn off.
(b) Constant Frequency Control:
Under this control scheme the chopping period T remains constant but the pulse width T is varied to control the output. This is, therefore, called pulse width modulation (PWM) control. The scheme is illustrated in Fig. 3.20. In the figure, time T = Ton + Toff is constant but Ton and Toff both are variable. The duty cycles of α = 0.75 and 0.50 are shown, respectively, in Figs. 3.20 (a) and (b).
Variable frequency control has some disadvantage as compared to constant frequency control method which are:
(i) Chopping frequency is required to be varied over a large range to control the output. Thus the output has wide range of harmonics. The design of a filter to remove such a wide range of harmonics is quite difficult.
(ii) For the control of duty cycle the off period may be so large that load current falls to zero between two consecutive pulses. This leads to discontinuity in the load current which is not desirable.
(iii) For the control of duty cycle a, frequency variations would be wide. As such, there is a possibility of interference with signaling and telephone lines in frequency modulation control.
For above reasons PWM control is preferred over FM control in chopper circuits.
2. Current Limit Control:
Under this scheme the chopper is switched on and off between upper and lower limits of load current. As the load current exceeds upper limit the chopper is turned off. The load current now freewheels until it reaches the lower value prescribed. As the load current attains lower limit, the chopper is switched on. As the freewheeling operation is involved in this scheme, a storage element is a necessity in the load. As the load current varies between two prescribed limits, this scheme is applicable only either at constant frequency or at constant turn on time Ton.
The waveforms for current limit control are shown in Fig. 3.21. In this case the load current is continuous and difference between upper and lower values of current decides the switching frequency. At smaller values of difference in current, the switching frequency is higher. As a result the ripples in the output are reduced. As an example the switching frequencies of the chopper for Ia max and Ia max as upper limits of the current are, respectively 1/T’ and 1/T where I’a max < Ia max and T’ < T. By further reducing the difference between upper and lower limits of the current the switching frequency can be increased correspondingly which leads to reduction in the ripple content in the output.
Example 1:
For a dc to dc converter shown in Fig. 3.17, the source voltage is 200 volts, load resistance 10 and duty cycle a = 0.4. If load is resistive, calculate the following (a) Average load voltage (b) Thyristor average current (c) Average and rms freewheeling diode currents (d) Effective input resistance of chopper.
Solution:
For resistive load, the load voltage and load current are in phase:
Step-Up Choppers:
In a step-down chopper the output voltage lies between zero and supply voltage. However, there are techniques by which the output of a chopper obtained is higher than the supply voltage. Such types of choppers are called step-up choppers. The circuit diagram of a step-up chopper is shown in Fig. 3.22 (a). In figure, the chopper is represented by a switch S.
In this chopper, a large inductor in series with the supply voltage source is essential, as shown in Fig. 3.22 (a). When the chopper is on, the current flows through inductance L, chopper S and power supply source, as shown in Fig. 3.22 (b). During this on-period Ton, the inductor L stores energy.
When the chopper is off, the inductor current is forced to flow through the diode and load for a period Toff because the inductor current cannot die instantaneously. As the current tends
to decrease, polarity of the emf induced in the inductor is reversed, as illustrated in Fig. 3.22 (c).
Assuming negligible voltage drop across diode D, the voltage equation for outer loop may be written as-
-Va + eL + V = 0
or Va =V + eL …(3.27)
If the rate of fall of current through inductor is di/dt, Eq. (3.27) may be written as-
Va = V + L di/dt …(3.28)
It means that the inductor voltage adds to the source voltage to force the inductor current into the load. In this manner, the energy stored in inductor is released to load. Here, higher value of inductance L is preferred for getting lesser ripple in the output.
During the time Ton, when the chopper is on, the energy stored in the inductor is given by-
W1 = Voltage x average current through L x Ton
= V x Ia x Ton …(3.29)
Above Eq. (3.29) is based on the assumption that the variation of output current is linear.
During the period Ton, the current through the inductor rises to peak value I2 while during off period Toff it falls to value I1 and rises again to I2 in the next on state of the chopper. It is shown in Fig. 3.22 (d). Thus, in a cycle the average value of current is given by Ia = I1 + I2/2 inductor L is given by-
W1 = V x I1 + I2/2 x Ton …(3.30)
and this energy is released by the inductor to the load during the off-period, Toff Thus energy released by inductor L during off period is given by-
W0 = Voltage across inductor x average current through inductor x Toff
Assuming the system to be lossless, in the steady-state the two energies will be equal i.e.,
The value of α, the duty cycle lies between zero and unity. Corresponding average values of load voltage Va lies between V and infinity. Thus the output voltage of step-up chopper is never less than the supply voltage V i.e., for 0 ≤ α ≤ 1 the output voltage of step-up chopper lies in the range V ≤ Va ≤ α.
The step-up chopper can be employed for regenerative braking of dc motors even at low operating speeds. Let V represent the motor armature voltage and Va the dc source voltage in Fig. 3.22 (a). Regenerative braking takes place when (V + L di/dt) exceeds Va. Even at decreasing motor speeds, duty cycle α can be so adjusted that (V + L di/dt) voltage Va.
Example 2:
A step-up chopper shown in Fig. 3.22 (a) is fed by a dc source of 220 volts. The inductance has value of 30 mH. If load voltage is 250 volts across a resistance of 10 ohms, calculate average current and duty cycle.
Solution:
Average value of load voltage is-
Va = V/1- α = 250 volts
Or 250 = 220/1- α
Or α = 1-220/250 = 0.12 (ans)
Average load current = Va/R = 250/10 = 25 A (ans)
Step-Up/Down Chopper:
A chopper can also be used for stepping up or down the supply voltage by varying its duty cycle. The principle of operation is illustrated in Fig. 3.23. As shown, the output voltage polarity is opposite to that of input voltage V.
When the chopper is on, the supply current flows through the path V+ – chopper – inductor L – V_. As a result energy is stored in the inductor. When the chopper is made off, the current through the inductor L decreases. As a result an emf is induced in the inductor with lower end positive and the energy stored in the inductor is released through the load and diode and the voltage across the load is negative as illustrated. It is thus used to reverse the polarity of load voltage w.r.t. source voltage.
The energy stored in inductor L during on-period Ton is given by-
W1 = V x average current x Ton
But the average current through the inductor, as in case of step-up chopper is-
During off period the energy released by inductor to the load is-
Under steady-state condition, assuming no loss of power.
Energy stored in inductor = Energy released to load
Substituting Ton/T = α in above equation, we have-
Equation (3.35) can be used for step-up and step-down operation of chopper. In the range 0 < α < 0.5 the circuit operates in step-down mode while for duty cycle in the range 0.5 < α < 1 it acts as a step-up chopper.
Example 3:
A step-up/step-down chopper has an input voltage of 125 V and output voltage of 200 V. If the period of conduction is 1 ms, determine the frequency of switching pulse.
Solution:
Average output voltage, Va = 200 V
Supply voltage, V = 125 V
Period of conduction, Ton = 1 ms = 0.001 s
Since output voltage of step-up/step-down chopper is given by-
Chopper Control of Separately Excited DC Motor Drive:
Chopper drives can be operated in the following modes:
1. Motoring mode.
2. Regenerative braking mode.
3. Rheostatic braking mode.
1. Motoring Mode:
Figure 3.24 (a) illustrates this mode of operation with a one quadrant chopper feeding the motor from dc supply of voltage V, the field being excited from a separate source. Figure 3.24 (b) shows the quadrant of operation. When the chopper conducts, voltage across the motor armature is supply voltage V, and when it blocks, voltage across the motor armature is zero. Therefore, both average voltage and current are positive and power can flow from supply source to the load, and thus, represents motoring operation. The voltage across the motor armature is given as-
Va = αV …(3.36)
where α is the duty cycle of the chopper.
Freewheeling diode DFW is necessary so that the armature current may flow when the chopper is off. The power supplied to the motor is given as-
P=VaIa = αVIa …(3.37)
The current drawn from the supply is-
I = αla …(3.38)
By varying the duty cycle α, the speed of the motor can be controlled.
2. Regenerative Braking Mode:
When the motor is to be stopped, brakes are to be applied. In regenerative braking the motor is made to operate as a generator and the kinetic energy of the motor is converted into electrical energy and returned to the supply. Fig. 3.25 (a) shows the circuit diagram for this mode of operation. During regenerative braking mode, the chopper is gated so that the motor armature is short circuited through the chopper. Kinetic energy of the motor is partly dissipated in armature resistance Ra and partly stored in inductance La. When chopper is turned off, freewheeling diode DFW, is turned on and the energy stored in inductance La is returned to the supply source (provided the source is receptive).
The operation is in second quadrant, as illustrated in Fig. 3.25 (b).
The average voltage Vch is given as-
Vch = (1 – α) V …(3.39)
Regenerated power Pg is given as-
Pg =Vch x Ia = (1 – α) V Ia …(3.40)
where Ia is the armature current
Generated voltage Es is given as-
Eg =Vch + IaRa = (l – α) V + IaRa …(3.41)
3. Rheostatic Braking Mode:
Figure 3.26 (a) illustrates the circuit for this mode of operation. In this mode also the motor is made to operate as a generator and the kinetic energy of the motor is converted into electrical energy. This electrical energy is dissipated in braking resistance Rb connected to the terminals, as illustrated in the figure. When this mode is to be used, chopper is turned on by a gate pulse.
The kinetic energy is partly dissipated in armature resistance Ra and partly stored in armature inductance La. When chopper is turned off, the energy stored in inductance La is transferred to braking resistance Rb and dissipated as heat.
The average current in braking resistance Rb is given as lb = (1 – α) Ia …(3.42)
where Ia is the armature current. Voltage across braking resistance Rb,
Vb = IbRb = RbIa (1 – α) …(3.43)
Power dissipated in braking resistance Rb,
Pb = Ia2Rb (1 – α)2…(3.44)
In this mode also the operation is in second quadrant, as illustrated in Fig. 3.26 (b).
It is also possible to combine the regenerative and rheostatic braking modes. Regenerative braking is used when the supply system is receptive. During remaining period the rheostatic braking is used.
Step-Down Chopper with R-L-Eb Load:
The choppers are widely employed for speed control of dc motors in industrial and traction drives. Figure 3.27 (a) shows the basic chopper circuit for the control of a dc series motor. The chopper is shown to consist of a force-commutated thyristor, it could well be a transistor switch. It offers one-quadrant drive [Fig. 3.27 (b)].
Armature current is assumed continuous and ripple free. The waveforms for the source voltage V, armature terminal voltage va, armature current ia, supply current i and freewheeling-diode current iDFW are shown in Fig. 3.27 (c). From these waveforms we have-
Average value of voltage across motor,
Va = Ton/T V = α V = f Ton V …Refer to Eq. (3.25)
where α = Duty cycle = Ton/T and f = Chopping frequency = 1/T
Power delivered to load (motor)
= Average value of voltage across motor × average motor current
= VaIa = αVIa
Average supply current
= Ton/T Ia = α Ia
Input power to chopper
= Average supply voltage x average source current = VαIa For the motor armature circuit,
Va = αV = Eb + Ia (Ra + Rse) = ke ωm + la (Ra + Rse) or Motor speed,
ωm = αV-Ia(Ra + Rse) /ke …(3.45)
From above Eq. (3.45) it is obvious that the armature terminal voltage and therefore, speed of the dc motor can be controlled by varying the duty cycle α of the chopper.
So far, armature current ia has been assumed ripple free and accordingly waveforms in Fig. 3.27 (c) are drawn. But in practice, the motor armature current increases during chopper on period and decreases during chopper off period, as illustrated in Fig. 3.28.
For R-L-Eb type of load, Eb is load voltage (back emf of motor). When the chopper is switched on for a period Ton and power is supplied to R-L-Eb load. By using Kirchhoff’s voltage law (KVL) in the loop consisting of V, chopper and R-L-Eb load, we have-
When chopper is off, the load current continues flowing through the freewheeling diode due to energy stored in the inductor. The KVL for the loop containing R-L-Eb and DFW yields
The above Eqs. (3.46) and (3.47) can be solved by using Laplace transform. It is seen from Fig. 3.28 that initial value of load current is Imin for Eq. (3.46) and Imax for Eq. (3.47).
So Laplace transform of Eqs. (3.46) and (3.47) we have-
From Eq. (3.48), we have-
Laplace inverse of above equation is-
Similarly the time domain expression for current from Eq. (3.49) is-
Here R = Armature resistance Ra + series field resistance Rse
and L = Armature inductance + series field inductance Lse.
The values of maximum current Imax and minimum current Imin can be determined by using the fact that i (t) = Imin when t = 0 and i (t’) = Imax when t’ = 0. The values are found to be-
