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8/10/2019 Module2 New PartA

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CONVERTERS IN ELECTRIC DRIVE SYSTEMS (Part A)

CONTROLLED RECTIFIER

The controlled rectifier converts AC voltage to a DC voltage in a controlled manner. In this section, we will discusson the control and modeling of a controlled rectifier applied in DC drive systems. The modeling of this converter isan important step in the designing of a controller for the closed loop control system typically found in electricaldrives. We will limit our model to a continuous current mode for a single-phase rectifier (The continuous currentmode means that the output current of the converter will always be larger than zero). The modeling and control

discussed for the single-phase rectifier can be readily applied to a three-phase controlled rectifier.

In controlled rectifier, the output DC voltage is controlled by controlling the delay angles (or firing angles) of theSCRs used in the converter. We have seen in our previous course (undergraduate course) that a relationshipbetween the average voltage V a , and the delay angle (or firing angle) of a single-phase controlled rectifier, ! , isgiven by:

(1)

where ! is the delay angle, V m is the peak input voltage and V a is the average output voltage. Note that thisequation is only valid for continuous current mode. It describes the average behavior of the rectifier over a periodof the output voltage. For a given delay angle, the instantaneous output voltage will contain ripple at the multiples ofthe input voltage frequency (100Hz and 300Hz for a single and three phase rectifier with 50Hz supply frequency). Ifthe load inductance is low, this low frequency ripple will be reflected in the output current and hence the torque ofthe DC motor. Low inductance can also results in a discontinuous armature current; hence it is customary to addexternal inductance to the armature circuit.

In the equation (1), the relation between the delay angle and V a is nonlinear as depicted in Figure 1.

Figure 1 Transfer characteristic of a single phase converter with continuous current

Control technique

As part of the feedback control system in electrical drives, it is desirable that the relationship between the control

signal and the average output voltage to be linear especially when a linear controller (such as a PI controller) isemployed. As an example, Figure 2 shows a closed loop current control system for a DC motor drive employing asingle phase controlled rectifier. In DC drives (or in other type of electrical drives), it is normally necessary to controlthe motor current since it is, in most of the cases, proportional to the developed motor torque. This is especially truefor a separately DC motor or a permanent magnet DC motor. The reference current (or reference torque) iscompared with actual current and the error is fed to the current controller (e.g. PI controller) to generate the controlsignal, v c. The firing circuit is responsible in generating the pulses used to trigger the SCRs so that the desiredaverage voltage is produced at the output of the converter. As we have seen before, the relation between ! and theaverage voltage V a is non-linear due to the cosine term present in the expression. If the relationship between v c and! is linear, obviously the relationship between v c and V a will be non-linear. While it is true that we can linearize (1)for the purpose of designing the controller, this however only valid for a small perturbation around an operating point

!

"

= cosV2

V ma

!

mV2

!"

mV2

2

!!

+vin "

+

va

"

Va

!

Ia


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of the delay angle. The controller will not be optimized at a different operating point or delay angle. On the otherhand, if we can establish an inverse cosine relation between v c and ! , then the relation between v c and V a willbecome linear.

Figure 2 Current control loop employing controlled rectifier

There are several possible techniques that can be used to construct the firing circuit. One can use analog circuits,digital circuits or microprocessors. The scheme that results in an inverse cosine relation between v c and ! is knownas the cosine-crossing scheme. An example of a firing circuit implementation that uses analog circuit is shown inFigure 3 (this is extracted from P.C. Sen, Thyristor DC Drives ). As discussed in the lecture, it can be shown that therelationship between v c and ! is given by:

!!"

#$$%

&=' (

s

c1

V

vcos (2)

where V s is the maximum value of control signal v c. If (2) is substitute into (1), the relation between v c and V a isgiven as:

s

cma

vvV2V

!

= (3)

The same scheme can be applied to generate the firing signals for a three-phase controlled rectifier.

Control Model

It should be noted that using the cosine-crossing scheme as discussed above only gives a linear relationshipbetween the average output voltage and the control signal. The average output voltage is available for everysampling interval, determined by the type of converters used. For instance, a 3phase fully controlled rectifier willhave an average output voltage that is averaged over 3.33ms ( = 10 x 10 3 6) and 10ms ( = 20 x 10 3 2) for a 1phase converter. This can be considered as a sampled data system with sampling period of 3.33ms or 10ms

respectively. At the instance the control signal changes (e.g. a step change), there may be some time elapse(delays) before the changes in output voltage takes place. This delay can have a maximum value equal to thesampling period as illustrated in Figure 4 for a single-phase converter. A normal practice is to take the averagedelay as half of the maximum delay. That is 1.67ms and 5ms for the single-phase and three-phase respectively.

firingcircuit

currentcontroller

controlledrectifier

!

+

Va

vc iref


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Figure 3 Cosine crossing scheme (a) circuit,(b) timing diagram ( extracted from Thysritor DC Drives, PC Sen )

(a)

(b)


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Figure 4 Delay in singlephase controlled rectifier

In developing the model of the converter to be used in the control system design, the sampling effect and delaycharacteristics have to be taken into considerations. With the time delay included, the converter can be modeled asshown in Figure 5 ( for singlephase controlled rectifier):

Where

Figure 5 Controlled Rectifier model

We can, however, neglect the sampling effect of the output voltage by designing the closedloop bandwidth (forexample a current loop bandwidth) much smaller than the sampling frequency, typically (1/10)th of the samplingfrequency. By doing so, we will ensure that the control signal does not change faster than the capability of theconverter to produce a change in the average output voltage. To further simplifed the design, the delay can also beremoved provided that the closed-loop bandwidth is small enough. The control system based on this simplifiedmodel however does take into account on the inter-sampling behavior, which can be critical and cause instability.

Simulation example Closed loop current control system A closed loop current control system (Figure 2) was developed using Matlab/SIMULINK blocks and is shown inFigure 6(a). The model is constructed using the blocks from the SimPowerSystem toolbox. The simulation uses thesingle phase bridge configuration and the firing pulses are obtained from the 6 pulse generator (since no 4-pulsegenerator is available). The PI controller is designed using the small signal model as discussed above, however the

closed loop bandwidth is selected to be a decade lower than the sampling frequency (i.e. 1/10 of 628.3 rad/s = 62.8rad/s). The load is selected such that the current is continuous: R = 10 # , L = 300mH. The reference current isalways positive since the converter can operate in the first and fourth quadrants. Simulation results in Figure 6(b)shows that the output current is able to follow the reference although with a high low frequency ripple and poordynamics.

s2T

Ke)s(G!

=

vc(s) Va (s) G(s)

s

m

V

V2K

!

= , T = 5 ms


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5

(a)

(b)

Figure 6 Simulation of controlled rectifier (a) SIMULINK blocks, (b) Reference and output currents, output voltage

Quadrant of Operation

A controlled rectifier can only be operated in 2 quadrants. The output current I a (see Figure 1) can only flow in onedirection due to the unidirectional current property of the SCRs, however, based on equation (1), for ! > 90, theaverage output voltage V a of a controlled rectifier can be reversed. Thus the two quadrants that the controlledrectifier operates are (1) when the voltage and current are positive (V a > 0 and I a > 0), and (2) when the current ispositive but the voltage reversed, i.e. when ! > 90 o (Va < 0, I a >0). When used in a separately excited DC motordrive, the converter can only provide operations in forward motoring and reverse braking quadrants, thus is notsuitable for applications requiring forward braking mode. Modifications to the circuit and control have to beintroduced so that the controlled rectifier can be used for 4-quadrant operations:

Continuous

powergui

v+-

Voltage Measurement4

v+-

Voltage Measurement3

v+-

Voltage Measurement2 g

A

B

+

-

Universal Bridge

Step

SignalGenerator1

Series RLC Branch

Scope2

Scope

Saturation

PID

PID Controller1

u

In2

In5

Out1

Firing circuitcosine

i+ -

Current Measurement1

i +-

Current Measurement

s

-+

Controlled Voltage Source

10

Constant

AC Voltage Source

1 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 2 0

5

10

15

1 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 2 -400

-200

0

200

400

iref

iout


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(a) Dual converters

Two controlled rectifiers connected back- to back is used as shown in Figure 7. Converter 1 provides operations inQ1 and Q4, whereas converter 2 operates in Q2 and Q3. There are two control schemes that can be used for thisconfiguration:

(i) Operating each converter one at a time (non-simultaneous operation).When operation from Q1 to Q2 is required (i.e. from forward motoring to forward braking), theoperation of the converter has to be switched from converter 1 to converter 2. Before the switching canbe made, the armature current has to be forced to zero by increasing the delay angle of converter 1 tothe highest possible value. When the current goes to zero, a certain deadtime is needed beforeconverter 2 is operated to ensure that the SCRs for converter 1 recover the reverse blocking capability.

After this deadtime, rectifier 2 is activated. The initial delay angle of converter 2 is set to the highestvalue and gradually reduced ( advance firing scheme ) so that armature current builds up. The currentis regulated to the allowable maximum value through current control loop. The motor decelerates andaccelerates in reverse direction with converter 2 in operation.

(ii) Operating both converters simultaneously (simulataneous operation).Both converters are operated simultaneously such as they produced the same average voltage. Forinstance, if converter 1 operates with ! 1, then the delay angle of converter 2 should be (180 o- ! 1).This control scheme produces circulating current since the instantaneous voltages of the twoconverters are not the same. To reduce the circulating current an interphase reactor is needed which

will inevitably introduce losses, cost and weight. As both converters are always in operation, there isno deadtime delay (as discussed in (i)) involved.

Figure 7 Four-quadrant operation with dual converter

(b) Single converter with reversing switch

Using this technique, only one fully controlled rectifier is needed, however reversing switches (contactors) areneeded in order to provide the reverse current flow (see Figure 8). When F1 and F2 are closed (R1 and R2 opened),the converter operates in Q1 and Q4, and when R1 and R2 close, the converter operates in Q2 and Q3. Similar tonon-simultaneous operation of dual converter, before the contactors can be opened (and closed), the current has tobe forced to zero by advancing the delay angle. The delay angle is then gradually reduced and controlled such thatthe safe limit is not exceeded using current control loop.

Figure 8 Four-quadrant operation with single converter

Converter1 (Q1)

$

T

Converter1 Q4

Converter2 (Q2)

Converter2 Q3

F1

F2

R1

R2 + Va -

3phasesupply

3-phasesupply

3-phasesupply

Converter 1 Converter 2

+Va "

$

T

F1 and F2 areclosed (Q1)

R1 and R2 areclosed Q3

R1 and R2 areclosed Q2

F1 and F2 areclosed Q4

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