DspEdu 2.1

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List of Articles
 

1.  Introduction

2.  The Principle of PWM

2.1 Bipolar PWM Vs Unipolar PWM

3.  Synchronous Link Based PWM Rectifier with Unity Power Factor

3.1 The Control Loops

4. Current Regulated Bilateral Converter Based PFC
 
 

[ This article was prepared for a 3-day short-term course I offered to working professionals from UPS Industry in 1998-2001 period.]
1.  Introduction

Active power factor correction using a single switch and boost topology was dealt with in another article.A bilateral AC-DC converter functioning as a switched mode rectifier is examined in this article. Control of the converter from synchronous link principle and current regulated PWM inverter principle will be covered. The operation of unipolar PWM in a single phase DC-AC converter will be examined in some detail for the sake of completeness. Single phase topology will be used throughout with brief references to three phase topologies wherever applicable.
The Single Phase DC-AC Inverter

Fig.1 shows a single phase DC-AC inverter circuit. Inverter circuit solves the low efficiency problem of linear power amplifiers in DC-AC conversion by operating the active devices in switch mode-i.e. either device has current through it with voltage at zero or it has voltage across it with zero current. But then , with a DC supply and 'Switch' mode of operation of devices , only three values of voltage can be delivered to the output namely +V,-V and 0.But what is desired at the output is a continuous wave-commonly a sinusoid. Pulse Width Modulation (PWM) solves the problem of generating a real value range of (+V,-V) for the output from three discrete values of +V,-V and 0.

2.  The Principle of PWM

Divide the period of the desired sine wave output into a large number of evenly spaced small intervals. A carrier frequency is employed for this.
In each such interval apply +V for some time and –V for the remaining time such that the average applied value over that interval is equal to the value of desired output in that interval.This scheme where +V and –V are used to synthesise the output is called Bipolar PWM.Another scheme where +V,0 are applied to synthesise the output during positive half cycle and –V,0 are applied to synthesise negative half cycle of output is called Unipolar PWM
The output will now be a pulse waveform which contains the desired output waveform in its Fourier series along with frequency components at or around harmonics of switching frequency ,i.e. the carrier frequency(or related to it)
The desired output can be extracted by a simple LC low pass filter since the frequency of desired output and the switching frequency will be widely separated.

2.1 Bipolar PWM Vs Unipolar PWM

Bipolar PWM output contains either +V or –V always. Hence, each state change involves a transition by 2V.Hence switching harmonic content in this scheme is more. In addition, the switching harmonic content is the highest when the PWM is trying to generate zero volt output after the averaging filter. Hence, it is difficult to synthesise good 'zero crossings' in a bipolar scheme unless heavy filtering(with consequent degradation in response time) is used.

Unipolar PWM uses +V and zero to make positive outputs and –V and 0 to make negative outputs. Switching Harmonic Content in this case will be small and will be zero at zero crossings. Filtering will be easy in this case. Unipolar PWM is assumed in this lecture.Fig.2 shows an implementation of Unipolar PWM and Fig.3 shows the carrier wave,sine reference and its inverted version and gate signals for the two top switches.

The carrier frequency was set at around 1.2kHz during Pspice simulation to render clarity to the above waveforms. In practice, carrier frequency in the range of 10-20kHz will be used. The Modulation Voltage was taken as a 50 Hz sine wave and the simulated waveforms at the output of the bridge and output of the LC filter are shown Fig.4.The spectral content of the inverter output (running from a 400V D.C Source) is shown in Fig.5.The 50Hz content is not shown. Notice that the lowest switching frequency content is at around twice the carrier frequency and not at the carrier frequency as it would have been in the case of Bipolar PWM.This is another attractive feature of Unipolar PWM.The LC filter used in the Pspice simulation had L=40mH,C=4.7uF &Load=100ohms.

The triangle wave sets the interval for pulse width coding and the comparison of triangle wave with modulation voltage and its inverted version results in coding of instantaneous value of modulating signal into pulse width. It is possible to see that Vo= (Vmod/Vt)xV where Vmod is the modulating signal (usually sine wave),Vt is the triangle amplitude ,V is the D.C voltage and Vo is the filtered output of the inverter. Thus the switches, filter and the circuitry needed to implement Unipolar PWM together can be treated as a single block called 'PWM Modulator' which implements a multiplication (modulation) of D.C side voltage by the modulating signal to provide the product as the filtered output.

This PWM Modulator is bi-directional. The diodes connected across the switches will prevent a reversal of polarity in the D.C side. However, current can flow into or out of the D.C source. In fact , if the load on the A.C side of the inverter is reactive ,power will flow from the A.C side to D.C side for part of the a.c cycle. Thus, the converter has four quadrant capability in the A.C side and two quadrant capability in the D.C side. Thus, it is bi-directional in power flow.

If the D.C side is a source (battery, rectified D.C or even a charged capacitor) and the A.C side terminated in passive load ,average power flow is from the D.C source to A.C side load. If the A.C side is terminated in a source and D.C side is loaded by resistor ,power flow is from A.C side to D.C side(provided suitable control strategy is implemented).If both sides are terminated in sources power can flow in either direction depending on the command from the control system. Thus, whether this PWM Modulator is an Inverter or Rectifier or AC-DC Link or for that matter a Static Condenser or an Active Power Filter depends on the Control Strategy involved.

3.  Synchronous Link Based PWM Rectifier with Unity Power Factor

A Synchronous Link is a pair of A.C sources with same frequency connected together through an inductive reactance. It is well known that (i) in a Synchronous Link, active power flows from the leading source to lagging source and is = (V1V2/X) Sin d where d is the angle of lead , V1,V2 are magnitudes of source voltages and X is the link reactance (ii) the reactive power flows from the higher voltage magnitude source to the lower voltage magnitude source and is = (V1/X)(V1-V2) Cos d .A Synchronous Link is shown in Fig.6.

Usually the angle d is small and Cosd is unity. Hence in a practical Synchronous Link,the active power flow is proportional to phase angle and reactive power is more or less decided by difference in voltage magnitudes. Hence the source V2 can absorb active power from V1 and maintain the power factor at source V1 at unity if it can (i) control its own phase shift with respect to V1 and (ii) control its own magnitude to be equal to the magnitude of V1.This is what is done in a Synchronous Link based PWM Rectifier.The source V2 is synthesised using a PWM Modulator described in the last section. This PWM Modulator runs from a charged Capacitor at its D.C side. The voltage across the D.C side capacitor is the output of PWM Rectifier.The control system prepares the required modulation voltage in such a way that the phase angle and magnitude of voltage synthesised by the Inverter have the right values.Fig.7 shows the power circuit diagram for this rectifier.

3.1 The Control Loops

The control objectives are (i) maintain the D.C voltage across Co at a set constant level against variations in the DC side load and A.C side voltage and (ii) maintain the a.c source current pure sinusoid at unity power factor. The control strategy will be to (i) sense D.C side voltage,compare it with reference and form the error signal, process the error signal (ii) use this processed error signal to decide the phase shift of the modulating signal which is a phase locked sine wave and (iii) sense the a.c source voltage and decide the amplitude of the modulating signal to produce an inverter output voltage which is equal to the sensed a.c source voltage. A block diagram representation of the strategy is given in Fig. 8.

The PLL based SineWave generator generates a fixed amplitude sine wave that has same frequency as that of the a.c source and is in phase with it. This wave is given a phase lag which is proportional to the control voltage coming from the error amplifier. The phase shifted sine wave amplitude is adjusted in the variable gain amplifier .The gain of the amplifier is decided by the magnitude of the a.c source as calculated by the rectifier and averaging filter block. The final phase shifted ,amplitude adjusted sine wave becomes the modulating signal for the PWM Modulator.

The PLL Sine Wave generation is usually done digitally .High frequency clock, which is frequency locked with a.c source, is produced by frequency multiplication using PLL.This clock is used to run a binary UP/DOWN counter. The counter output is used as the address bytes for an EPROM which has the sine table written in it. The read out value is converted into analog value by DACs.Phase shifting is achieved by manipulating the counter reset signal. In this scheme ,the phase angle can be adjusted only once in a cycle. 

The D.C side capacitor will have a second harmonic content due to the same reason as explained in the case of Single switch boost PFC in the first part. This second harmonic has to be filtered out in the error amplifier if third harmonic distortion is to be avoided in the a.c side current. This filtering contributes to reduction of open loop bandwidth. In addition, the rectification and averaging filter on the a.c voltage also reduces open loop bandwidth. And,in any case ,phase angle between the inverter output and a.c source can be adjusted only once in a cycle. To conclude ,the system response will be slow. If this slow response goes along with an inductor which is too small in value,the closed loop system will be slow and under damped resulting in severe power flow oscillations in the link. The inductor has to be large enough to limit the amplitude of power flow oscillations under transient conditions. But , with a large inductance,the drop across it due to the active current flow may not be negligible and hence power factor will only be close to unity and will not be unity.

The compensator design for this control system can be tricky due to factors mentioned above. Also the link containing the capacitor,PWM Modulator,link inductor and a.c source has a second order dynamics due to L and Co and this dynamics will be usually very much under damped. In addition,the open loop gain is heavily dependent on the d.c side load and a.c side voltage magnitude.

4. Current Regulated Bilateral Converter Based PFC

In the Synchronous Link scheme ,the D.C output was controlled by controlling the lag angle of the inverter generated voltage and power factor was controlled by maintaining equality between the inverter output voltage and a.c source voltage. Both are indirect ways to achieve the control objectives. In Current Regulated scheme , the Converter is first converted into a regulated current source under feed back action i.e. the inverter is gated in such a way that the current flowing through the filter inductance at the output follows a reference current wave form on an instant to instant basis. This current reference wave form is then constrained to have sinusoidal shape and to be in phase with the a.c line voltage. Its amplitude is left as free variable ,to be decided by the d.c output voltage control loop. Thus, there are two control loops-the inner current control loop which ensures that the switches are gated in such a way that the inverter output current tracks the reference current rapidly and without error and an outer voltage control loop which maintains the d.c output voltage constant by driving the current control loop suitably. The link inductance L is unnecessary. It is not that this is not a synchronous link. It is. The phase angle and magnitude of inverter output will be according to the principles brought out earlier with the filter inductance taking on the role of link reactance. It is that we do not try to control phase and magnitude of inverter output ,rather we catch the quantity we want control and control it directly-that quantity is the a.c side current.

As in the case of boost type PFC, there are many current control schemes for Bilateral Converter also. Prominent among them are hysterisis current control and feed forward current control. Hysterisis current control is covered in this lecture. Feed forward current control will be covered in another lecture in another context.
Hysterisis Current Control

In hysterisis current control,the filter inductance current is sensed by means of a CT and is compared with the reference current waveform received from the voltage control loop. The current error is amplified and presented to a hysterisis comparator. The comparator changes state when the error exceeds a preset value in positive and negative directions. The comparator state change is used to decide which of the switches should be on and which should be off. For e.g. say the actual current drawn by the inverter from a.c line is less than what it should be, then the inverter should present a lower voltage against the line so as to increase the current drawn and hence the gate logic switches off A+ and B- and switches on A- and B+. A block diagram of this control strategy is shown in Fig.9. 

The disadvantages of this control scheme are variable switching frequency,bipolar PWM and the related high level of switching harmonics,bad wave shape in the line side when d.c side is not loaded etc. These are the usual disadvantages associated with hysterisis schemes.

The current control virtually eliminates one order (that of inductance) from the dynamics since it effectively converts the inductor line into a current source line. This results in ease of design of the voltage control loop and faster response against variations in the D.C output voltage. The open loop dynamics is of first order –contributed by the output capacitor and D.C. load .The voltage control loop dynamics and loop design is similar to the design in the case of single switch boost type PFC covered in the first part of this lecture and is not repeated here.

The disadvantages associated with fixed error band hysterisis current control can be alleviated largely by employing either variable band scheme or by using error triangularisation. However, both strategies will add to control hardware complexity. Many fixed frequency current control strategies exist for the control of this PWM rectifier. The are not covered here due to paucity of space.
Comparison with Single Switch Boost type PFC
If rectification is the aim, it looks as if one does not need bilateral power flow capability in the PFC conveter. However, there are definite advantages in choosing the bilateral structure as the underlying converter.

The Single Switch PFC can not bring down the output capacitor voltage quickly down to set point if it overshoots during load throw or start up. The error amplifier saturates and the circuit reduces the current into capacitor to zero. However, the circuit is incapable of discharging the capacitor into the a.c supply. The Bilateral Converter based PFC has this capability and results in a tighter control of output voltage.

The above point may not be of much significance in a conventional on-line UPS context since the battery across the d.c bus makes a d.c bus voltage control almost superfluous. However an on-line UPS with battery directly across the d.c bus suffers from the well known a.c ripple current problem in the battery. This a.c ripple current in the battery reaches a maximum at full load. Large and continuous ripple current in battery affects the battery life adversely and affects the charging efficacy too. One method to avoid a.c ripple (when a.c line is present and healthy) is to prevent current delivery into battery and supply the UPS inverter from a d.c capacitor whose charge is maintained by a PFC circuit i.e when line is present the d.c side capacitor delivers power to Inverter and when the line is absent the Battery comes in either directly through a diode (in that case the PFC control will maintain the d.c capacitor voltage at few volt above the battery voltage when line is present) or through a dc-dc step up converter. A separate charging circuit for the battery will be needed in this scheme. This scheme is used typical in large rating UPS with small backup times and internal SMF batteries. And the Bilateral Converter based PFC is ideal for this topology.

Also, a bilateral converter based front-end can be easily programmed to take or deliver reactive power to the a.c line by suitable modification in the current reference. This makes it possible to combine a UPS with static reactive power compensator in the same equipment. The reactive power compensation capability can be used to compensate the lagging reactive power taken by some other plant load.

Boost type PFC line current waveform will show distortion at zero crossings due to cut-in behavior of diodes. In addition, it can enter discontinuous mode of operation with current distortion and increased ripple level at low loads. Both these effects are eliminated in Bilateral Converter based PFC.

Bilateral Converter based PFC can be controlled in such a manner that it can deliver lagging reactive power into the a.c source. It can, thereby, work as a rectifier and static capacitor simultaneously if necessary.