DC Uncontrolled Rectifier by Using Phase- Shifting Transformer

University of Halabja (UoH)

College of Science

Physics Department

Undergraduate’s Last year Project

2020-2021

‘’Harmonics Cancellation from AC- DC

Uncontrolled Rectifier by using Phase- Shifting Transformer.’’

Prepared by: Supervised by:

Shilan Ali Faraj Mr .Farhad Muhsin Mahmood

Bushra Ahmad Abdulla

Nada Jaba Hassan

[‘’Harmonics Cancellation from AC- DC Uncontrolled Rectifier by using Phase-Shifting Transformer.’’]

Shilan Ali Faraj

Bushra Ahmad Abdulla

Nada Jaba Hassan

A thesis submitted to the

College of Science, University of Halabja

In partial fulfillment of the requirements

For the degree of Bachelor of Physics

Graduate Program in Physics

Written under the direction of

[Mr. Farhad M. Mahmood]

[May, 2021]

Contents Abstract ...... 4 Chapter one (History and background) ...... 5 Background and history of Rectifier...... 5 1.1 Rectifier : ...... 5 1.2. Inverter :...... 7 Chapter two (introduction) ...... 10 2.1 INTRODUCTION ...... 10 2.2 Single Phase Rectification...... 11 2.2.1 AC Sinusoidal Waveform ...... 12 2.3 Single Phase Rectifier ...... 13 2.3.1 Half-wave Rectification ...... 14 2.3.2 Sinusoids Average Value ...... 15 2.4 Full-wave Rectification ...... 17 2.4.1 Single Phase Full-wave Bridge Rectifier ...... 18 2.4.2 Full-wave Rectifier Output Waveform ...... 19 Three Phase Rectification ...... 25 Three-phase Waveform ...... 26 Three-phase Rectification ...... 27 2. The rectifiers load current...... 35 Chapter three (Literature Review)...... 38 3.1 Harmonics ...... 38 3.2 Fundamental Frequency ...... 39 3.3 Complex Waveforms Due To Harmonics ...... 41 3.4 Harmonics Summary ...... 45 Chapter Four (Results and Discussion)...... 46 4.1 Single phase rectifier ...... 46 4.2 Three-phase bridge diode rectifier ...... 47 4.3 12-pulse diode bridge harmonic cancellation...... 50 4.4 Harmonic Cancellation of 24-pulse Rectifier Using Phase-Shifting Transformers...... 53 CONCLUSIONS ...... 56 List of references ...... 57

Abstract Harmonic distortion is a huge problem for the power systems. But harmonic distortion can be controlled using some unique methods with the utility systems. This paper discusses the impact of using 12- pulse and 24-pulse rectifier circuit. The 24-pulse topology is generally more expensive, but produces the least Input current harmonics. In this paper pulse multiplication technique is used to mitigate the harmonic distortion from the input line current. Phase-shifting transformers are used to produce 24-pulse from 12- pulse. A comparison between 12-pulse and 24- pulse rectifier also shown in this paper. Operation of the circuits is verified through computer simulations.

Chapter one (History and background) Background and history of Rectifier. 1.1 Rectifier : The term rectifier was in common use for more than two decades prior to 1925. It was understood to mean any stationary apparatus or rotating commutator for transforming alternating into direct current.(Rotary converters, later known as synchronous converters, were in use by 1892 to convert AC power into DC power [1]. Rotary converters were manufactured until the 1950s, when germanium diodes became available. When operated to convert DC power to AC power, rotaries were dubbed “inverted rotaries.” The distinction between rectifier and converter was sometimes vague, perhaps even arbitrary, but often based on use of static or non- rotating versus rotating parts). The term rectifier is often confused with similar or related terms and phrases It is sometimes used to denote rectifier element (device) or rectifier circuit when rectifier equipment is intended. Rectifier elements can be physical devices or circuit entities In either case, rectifier elements allow current to flow in only one direction, blocking its flow in the reverse direction (I e., diodes, thyristors ) The property of rectifier elements that permits only unidirectional current flow causes some persons to call them electric “valves,” being analogous to check valves in hydraulic circuits (In some places, they are still called valves ) Rectifier circuits are electrical circuits containing rectifier and other circuit elements (resistors, capacitors, etc.) interconnected into prescribed paths or current conduction, the whole assembly (or network) providing the function of rectification. Prince reviews prior art by first examining operation of a single-phase full-wave center-tap rectifier circuit. The DC output of the rectifier circuit includes both passive resistance and reactance. His figures provide ideal waveforms of most circuit variables, including potential and current at AC and DC terminals. Fig. 1 is depicted here, on the left side of the figure, and is identified as “rectifier circuit.” This figure

5 is identical in topology to Prince’s, except that modern symbols for rectifier circuit elements replace his archaic vacuum tube (diode) symbols. With this small change, his figure is identical to any modern single-phase full wave center-tap rectifier circuit. Rectifier devices available to Prince in1925 were of three basic types: mechanical rectifier, electrolytic “cells,” and high vacuum [2]. or gas-discharge “tubes.” Mechanical rectifiers consist of rotating commutators driven by synchronous motors and were in use prior to 1893. Electrolytic cells also originated prior to the turn of the century and were the second rectifier devices available. They evolved experimentally from electrochemical research before existence of the electron was discovered by J.J. Thomson in 1899. Similarly, the Edison effect (1883) was discovered before knowledge of the electron, but no immediate application was made of his discovery. It was the Cooper Hewitt patents on mercury-arc rectifiers (1901) and DeForest’s three-element valve (audion, 1907) that opened the way for gas-discharge tubes.

Fig.1. Prince’s rectifier circuit.

1.2. Inverter : By 1936, Prince’s inverter appearedn in literature from all corners of the world, Europe and Japan among them. It was in common use in English technical publications or its equivalent word was used in other languages. In 1925, Prince defined inverter as the inverse of rectifier. In so doing, he depended upon his audience having a clear mental abstraction of rectifier and built upon their pre- existing concepts. Prince explained that an inverter is used to convert direct current into single or polyphase alternating current. The article explains how “the author [1] the rectifier circuit and inverted it, turning in direct current at one end and drawing out alternating current at the other.” Use of the word inverted conveys the idea of turning something upside down. What was turned upside down? Clearly, he did not mean to invert the rectlfier device(s) or rectifier circuit their orientation remains the same. Rather, he meant to invert the function or operation of the rectifier. That is why he said to draw in direct current and push out alternating current, to emphasize a new mode of operation. The inverse of

7 rectification was not an obvious extension of prior art. It required several imaginative steps by Prince to bring his readers to comprehend conversion of electric current of one form (direct) to another form (alternating) Among those innovations was grid control of current conduction Prince was not the originator of that idea, but built upon it. Although the inverter was developed and demonstrated during the 1930s, its full potential was not realized due limitations in avadable rectifier devices Both the Thyratron and the Ignitron were subject to prolonged recovery tmes, necessary to regain dielectric capability in the region of the arc As a result, they were subject to electrical faults, described as “arc- back” and “shoot-through ” They were also sensitive to ambient temperature,

Orientation, and mechanical vibration. Most largescale invetters produced in the 1930s and 1940s used natural commutation to avoid problems with dielectric recovery time [2].

Fig .2.Prince’s inverter circuit.

Chapter two (introduction) 2.1 INTRODUCTION Development of our technology in recent years, the direction of research has shifted to power electronics from power systems to produce the most efficient energy conversion. The power electronics is giving us the opportunity to shape and control large amounts of power with better efficiency. Low cost, smaller size and high energy efficiency are possible because of power electronics. Within the next 30 years, power electronics will shape and condition the electricity somewhere in the transmission network between its generation and all its users.[3] Diode is called the first solid state electronic device. Now-a-days it becomes a weighty part of power electronic era. Diode rectrifiers are used in several power systems. Diode bridge is specially used in high-power applications. Only diode contain some magnificent characteristics such as availabile, light weight, compact, high efficiency, robust for fault high current, less emission noises and etc. Three phase diode bridge constructed with six diodes. It can operate with or without transformer. Like other non-linear devices diode also affected by harmonics. Harmonics are multiples of the by harmonics. Harmonics are multiples of thefundamental frequency. The deviation from perfect sine wave isknown as harmonic distortion. Harmonic is acceptablewithin limit. Increase in core losses due to increased iron losses in transformers occured by harmonic currents at harmonic frequencies. It also increased copper losses and stray flux losses result in additional heating, and winding insulation stresses, especially if high levels of dv/dt (i.e., rate of rise of voltage) are present. Temperature cycling and possible resonance between transformer winding inductance and supply capacitance, line notching problems are produced by harmonics. [4] Several harmonic mitigation procedure are available using diode rectifiers. Some of them provide fine uncontrolled dc voltage without harmonic pollution . Every configurations cannot fullfill the demand like auto-

10 transformer based schemes fails due to higher rating magnetic, higher number of bridges, resulting in enhancement of capital cost. [5] This paper work with the three- phase multi- pulse AC to DC conversion system employing a phase- shifting transformer and a three-phase uncontrolled bridge rectifier between the supply and load side of the system. Every such converter provides 6-pulse ripple components on the output voltage, so in order to produce more sets of 6-pulse systems, a uniforphase-shift is required and hence with proper phase- shifting angle, 12, 18, 24, 30, and higher pulse systems can be produced.[6] Phase shifting transformer based configurations are really cost effective and reliable than others. In this paper we design a ac-dc converter with limited harmonic distortion with the help of phase shifting transformer. This paper represent an unique 24- pulse converter with bridge rectifier which is able to control harmonic distortion and provide best ripple factor in the output. This can be achieved by applying pulse-multiplication technique.

2.2 Single Phase Rectification. Rectification is the process of linking an AC power supply to a connected DC load by means of solid-state semiconductor devices.

Figure (3) Single-phase diode rectifier.

Rectification converts an oscillating sinusoidal AC voltage source into a constant current DC voltage supply by means of diodes, thyristors, transistors, or converters. This rectifying process can take on many forms with half-wave, full-wave, uncontrolled and fully-controlled rectifiers transforming a single- phase or three- phase supply into a constant DC level. In this tutorial we will look at single-phase rectification and all its forms. Rectifiers are one of the basic building blocks of AC power conversion with half-wave or full-wave rectification generally performed by semiconductor diodes. Diodes allow alternating currents to flow through them in the forward direction while blocking current flow in the reverse direction creating a fixed DC voltage level making them ideal for rectification. However, direct current which has been rectified by diodes is not as pure as that obtained from say, a battery source, but has voltage changes in the form of ripples superimposed on it as a result of the alternating supply. But for single phase rectification to take place, we need an AC sinusoidal waveform of a fixed voltage and frequency as shown [7].

2.2.1 AC Sinusoidal Waveform

Fig(4) AC Sinusoidal Waveform

AC waveforms generally have two numbers associated with them. The first number expresses the degree of rotation of the waveform along the x-axis by which the alternator has rotated from 0-to-360o. This value is known as the period (T) which is defined as the interval taken to complete one full cycle of the waveform. Periods are measured in units of degrees, time, or radians. The relationship between a sine waves periods and frequency is defined as: T = 1/ƒ. The second number indicates the amplitude of the value, either current or voltage, along the y-axis. This number gives the instantaneous value from zero to some peak or maximum value ( AMAX, VMAX or IMAX ) indicating the sine waves greatest amplitude before returning back to zero again. For a sinusoidal waveform there are two maximum or peak values, one for the positive and one for the negative half-cycles. But as well as these two values, there are two more which are of interest to us for rectification purposes. One is the sinusoidal waveforms Average Value and the other is its RMS Value. The average value of a waveform is obtained by adding the instantaneous values of voltage (or current) over one half-cycle and is found as: 0.6365*VP. Note that the average value over one complete cycle of a symmetrical sine wave will be zero as the average positive half-wave is cancelled by the opposite average negative half- wave. That is +1 + (-1) = 0. The RMS, root mean squared or effective value of a sinusoid (a sinusoid is another name for a sine wave) delivers the same amount of energy to a resistance as does a DC supply of the same value. The root mean square (rms) value of a sinusoidal voltage (or current) is defined as: 0.7071*VP.

2.3 Single Phase Rectifier All single phase rectifiers use solid state devices as their primary AC-to-DC converting device. Single phase uncontrolled half-wave rectifiers are the simplest and possibly the most widely used rectification circuit for small power levels as their output is heavily affected by the reactance of the connected load. For uncontrolled rectifier circuits, semiconductor diodes are the most commonly used device and are

13 so arranged to create either a half-wave or a full-wave rectifier circuit. The advantage of using diodes as the rectification device is that by design they are unidirectional devices having an inbuilt one-way pn-junction. This pn-junction converts the bi- directional alternating supply into a one-way unidirectional current by eliminating one-half of the supply. Depending upon the connection of the diode, it could for example pass the positive half of the AC waveform when forward-biased, while eliminating the negative half-cycle when the diode becomes reverse-biased. The reverse is also true by eliminate the positive half or the waveform and passing the negative half. Either way, the output from a single diode rectifier consists of only one half of the 360o waveform as shown.

2.3.1 Half-wave Rectification

Fig. (5) Half-wave Rectification

The single-phase half-wave rectifier configuration above passes the positive half of the AC supply waveform with the negative half being eliminated. By reversing the direction of the diode we can pass negative halves and eliminate the positive halves of the AC waveform. Therefore the output will be a series of positive or negative pulses. Thus there is no voltage or current applied to the connected load, RL for half

14 of each cycle. In other words, the voltage across the load resistance, RL consists of only half waveforms, either positive or negative, as it operates during only one-half of the input cycle, hence the name of half-wave rectifier. Hopefully we can see that the diode allows current to flow in one direction only producing an output which consists of half-cycles. This pulsating output waveform not only varies ON and OFF every cycle, but is only present 50% of the time and with a purely resistive load, this high voltage and current ripple content is at its maximum. This pulsating DC means that the equivalent DC value dropped across the load resistor, RL is therefore only one half of the sinusoidal waveforms value. Since the maximum value of the waveforms sine function is 1 ( sin(90o) ), the Average or Mean DC value taken over one-half of a sinusoid is defined as: 0.637 x maximum amplitude value. So during the positive half-cycle, AAVE equals 0.637*AMAX. However as the negative half- cycles are removed due to rectification by the reverse biased diode, the average value of the waveform during this negative half-cycle will be zero as shown.

2.3.2 Sinusoids Average Value

Fig.(6) Sinusoids Average Value

So for a half-wave rectifier, 50% of the time there is an average value of 0.637*AMAX and 50% of the time there is zero. If the maximum amplitude is 1, the average or DC value equivalent seen across the load resistance, RL will be:

Thus the corresponding expressions for the average value of voltage or current for a half-wave rectifier with pulsating DC is given as:

Note that the maximum value, AMAX is that of the input waveform, but we could also use its RMS, or “root mean squared” value to find the equivalent DC output value of a single phase half-wave rectifier. To determine the average voltage for a half-wave rectifier, we multiply the RMS value by 0.9 (form factor) and divide the product by 2, that is multiplying it by 0.45 giving:

Then we can see that a half-wave rectifier circuit converts either the positive or negative halves of an AC waveform, depending on the diodes direction, into a pulsed DC output which has an equivalent DC value of 0.318*AMAX or 0.45*ARMS as shown.

Half-wave Rectifier Average Voltage

Fig. (7) output of half wave rectifier.

In practice, VDC would be slightly less due to the forward biased 0.7 volt voltage drop across the rectifying diode. One of the main disadvantages of a single-phase half-wave rectifier is that there is no output during half of the available input sinusoidal waveform resulting in a low average value as we have seen. One way to overcome this is to use more diodes to produce a full-wave rectifier.

2.4 Full-wave Rectification Unlike the previous half-wave rectifier, the full-wave rectifier utilises both halves of the input sinusoidal waveform to provide a unidirectional output. This is because the full-wave rectifier basically consists of two half-wave rectifiers connected together to feed the load. The single phase full-wave rectifier does this by using four diodes arranged in a bridge arrangement passing the positive half of the waveform as before but inverting the negative half of the sine wave to create a pulsating DC output. Even though the the voltage and current output from the rectifier is pulsating, it does not reverse direction using the full 100% of the input waveform and thus providing full- wave rectification.

2.4.1 Single Phase Full-wave Bridge Rectifier

Fig.(8) Single Phase Full-wave Bridge Rectifier

This bridge configuration of diodes provides full-wave rectification because at any time two of the four diodes are forward biased while the other two are reverse biased. Thus there are two diodes in the conduction path instead of the single one for the half-wave rectifier. Therefore there will be a difference in voltage amplitude between VIN and VOUT due to the two forward voltage drops of the serially connected diodes. Here as before, for simplicity of the maths we will assume ideal diodes. So how does the single phase full-wave rectifier work. During the positive half cycle of VIN, diodes D1 and D4 are forward biased while diodes D2 and D3 are reverse biased. Then for the positive half cycle of the input waveform, current flows along the path of: D1 – A – RL – B – D4 and back to the supply. During the negative half cycle of VIN, diodes D3 and D2 are forward biased while diodes D4 and D1 are reverse biased. Then for the negative half cycle of the input waveform, current flows along the path of: D3 – A – RL – B – D2 and back to the supply. In both cases the positive and negative half-cycles of the input waveform produce positive output peaks regardless of polarity of input waveform and as such the load current, i always flows in the SAME direction through the load, RL between points or nodes A and B. Thus the negative half-cycle of the source becomes a positive half-cycle at load. So whichever set of diodes are conducting, node A is always more positive than node

B. Therefore the load current and voltage are unidirectional or DC giving us the following output waveform.

2.4.2 Full-wave Rectifier Output Waveform

Fig. (9) Full-wave Rectifier Output Waveform

Although this pulsating output waveform uses 100% of the input waveform, its average DC voltage (or current) is not at the same value. We remember from above that the average or mean DC value taken over one-half of a sinusoid is defined as: 0.637 x maximum amplitude value. However unlike half-wave rectification above, full-wave rectifiers have two positive half-cycles per input waveform giving us a different average value as shown.

Full-wave Rectifier Average Value

Fig. (10) Full-wave Rectifier Average Value

Here we can see that for a full-wave rectifier, for each positive peak there is an average value of 0.637*AMAX and as there are two peaks per input waveform, this means there are two lots of average value summed together. Thus the DC output voltage of a full-wave rectifier is twice that of the previous half-wave rectifier. If the maximum amplitude is 1, the average or DC value equivalent seen across the load resistance, RL will be:

Thus the corresponding expressions for the average value of voltage or current for a full-wave rectifier is given as:

As before, the maximum value, AMAX is that of the input waveform, but we could also use its RMS, or root mean squared value to find the

20 equivalent DC output value of a single phase full-wave rectifier. To determine the average voltage for a full-wave rectifier, we multiply the RMS value by 0.9 giving:

Then we can see that a full-wave rectifier circuit converts BOTH the positive or negative halves of an AC waveform into a pulsed DC output that has a value of 0.637*AMAX or 0.9*ARMS as shown.

Full-wave Rectifier Average Voltage

Fig. (11) Full-wave Rectifier Average Voltage

Full-wave Half-controlled Bridge Rectifier

Full-wave rectification has many advantages over the simpler half-wave rectifier, such as the output voltage is more consistent, has a higher average output voltage, the input frequency is doubled by the process of rectification, and requires a smaller capacitance value smoothing capacitor if one is required. But we can improve on the design of the bridge rectifier by using thyristors instead of diodes in its design. By

21 replacing the diodes within a single phase bridge rectifier with thyristors, we can create a phase-controlled AC-to-DC rectifier for converting the constant AC supply voltage into a controlled DC output voltage. Phase controlled rectifiers either half- controlled or fully controlled, have many applications in variable voltage power supplies and motor control.The single phase bridge rectifier is what is termed an “uncontrolled rectifier” in that the applied input voltage is passed directly to the output terminals providing a fixed average DC equivalent value. To convert an uncontrolled bridge rectifier into a single phase half-controlled rectifier circuit we just need to replace two of the diodes with thyristors (SCR’s) as shown.

Half-controlled Bridge Rectifier

Fig.(12) Half-controlled Bridge Rectifier

In the half-controlled rectifier configuration, the average DC load voltage is controlled using two thyristors and two diodes. As we learnt in our tutorial about Thyristors, a thyristor will only conduct (“ON” state) when its Anode, (A) is more positive than its Cathode, (K) and a firing pulse is applied to its Gate, (G) terminal. Otherwise it remains inactive.We also learnt that once “ON”, a thyristor is only

22 turned “OFF” again when its gate signal is removed and the anode current has fallen below the thyristors holding current, IH as the AC supply voltage reverse biases it. So by delaying the firing pulse applied to the thyristors gate terminal for a controlled period of time, or angle (α), after the AC supply voltage has passed the zero-voltage crossing of the anode-to-cathode voltage, we can control when the thyristor starts to conduct current and hence control the average output voltage.

Half-controlled Bridge Rectifier

Fig.(13) Half-controlled Bridge Rectifier

During the positive half cycle of the input waveform, current flows along the path of: SCR1 and D2, and back to the supply. During the negative half cycle of VIN, conduction is through SCR2 and D1 and back to the supply. It is clear then that one thyristor from the top group (SCR1 or SCR2) and its corresponding diode from the bottom group (D2 or D1) must conduct together for any load current to flow. Thus the average output voltage, wave is dependent on the firing angle α for the two thyristors included in the half-controlled rectifier as the two diodes are uncontrolled and pass current whenever forward biased. So for any gate firing angle, α, the average output voltage is given by:

Half-controlled Rectifier Average Output Voltage

Note that the maximum average output voltage occurs when α = 1 but is still only 0.637*VMAX the same as for the single phase uncontrolled bridge rectifier. We can take this idea of controlling the average output voltage of the bridge one step further by replacing all four diodes with thyristors giving us a Fully-controlled Bridge Rectifier circuit.

Fully-controlled Bridge Rectifier

Single phase fully-controlled bridge rectifiers are known more commonly as AC- to-DC converters. Fully-controlled bridge converters are widely used in the speed control of DC machines and is easily obtained by replacing all four diodes of a bridge rectifier with thyristors as shown.

Fully-controlled Bridge Rectifier

Fig. (14) Fully-controlled Bridge Rectifier

Three Phase Rectification 3-phase rectification is the process of converting a balanced 3-phase power supply into a fixed DC supply using solid state diodes or thyristors [8]

Fig(15). Three Phase Rectification

We saw in the previous tutorial that the process of converting an AC input supply into a fixed DC supply is called Rectification with the most popular circuits used to perform this rectification process is one that is based on solid-state semiconductor diodes. In fact, rectification of alternating voltages is one of the most popular applications of diodes, as diodes are inexpensive, small and robust allowing us to create numerous types of rectifier circuits using either individually connected diodes or with just a single integrated bridge rectifier module. Single phase supplies such as those in houses and offices are generally 120 Vrms or 240 Vrms phase-to-neutral, also called line-to-neutral (L-N), and nominally of a fixed voltage and frequency producing an alternating voltage or current in the form of a sinusoidal waveform being given the abbreviation of “AC”. Three-phase rectification, also known as polyphase rectification circuits are similar to the previous single-phase rectifiers, the difference this time is that we are using three, single-phase supplies connected together that have been produced by one single three-phase generator. The advantage here is that 3-phase rectification circuits can be used to power many industrial applications such as motor control or battery charging which require higher power

25 requirements than a single-phase rectifier circuit is able to supply. 3-phase supplies take this idea one step further by combining together three AC voltages of identical frequency and amplitude with each AC voltage being called a “phase”. These three phases are 120 electrical degrees out-of-phase from each other producing a phase sequence, or phase rotation of: 360o ÷ 3 = 120o as shown.

Three-phase Waveform

Fig (16). Three-phase Waveform

The advantage here is that a three-phase alternating current (AC) supply can be used to provide electrical power directly to balanced loads and rectifiers. Since a 3-phase supply has a fixed voltage and frequency it can be used by a rectification circuit to produce a fixed voltage DC power which can then be filtered resulting in an output DC voltage with less ripple compared to a single-phase rectifying circuit.

Three-phase Rectification Having seen that a 3-phase supply is just simply three single-phases combined together, we can use this multi-phase property to create 3-phase rectifier circuits.As with single-phase rectification, three-phase rectification uses diodes, thyristors, transistors, or converters to create half-wave, full-wave, uncontrolled and fully- controlled rectifier circuits transforming a given three-phase supply into a constant DC output level. In most applications a three-phase rectifier is supplied directly from the mains utility power grid or from a three-phase transformer if different DC output level is required by the connected load. As with the previous single-phase rectifier, the most basic three-phase rectifier circuit is that of an uncontrolled half-wave rectifier circuit which uses three semiconductor diodes, one diode per phase as shown.

Half-wave Three-phase Rectification

Fig.(17) Half-wave Three-phase Rectification

So how does this three-phase half-wave rectifier circuit work. The anode of each diode is connected to one phase of the voltage supply with the cathodes of all three diodes connected together to the same positive point, effectively creating a diode-

“OR” type arrangement. This common point becomes the positive (+) terminal for the load while the negative (-) terminal of the load is connected to the neutral (N) of the supply. Assuming a phase rotation of Red-Yellow-Blue (VA – VB – VC) and the red phase (VA) starts at 0o. The first diode to conduct will be diode 1 (D1) as it will have a more positive voltage at its anode than diodes D2 or D3. Thus diode D1 conducts for the positive half-cycle of VA while D2 and D3 are in their reverse- biased state. The neutral wire provides a return path for the load current back to the supply.120 electrical degrees later, diode 2 (D2) starts to conduct for the positive half-cycle of VB (yellow phase). Now its anode becomes more positive than diodes D1 and D3 which are both “OFF” because they are reversed-biased. Similarly, 120o later VC (blue phase) starts to increase turning “ON” diode 3 (D3) as its anode becomes more positive, thus turning “OFF” diodes D1 and D2. Then we can see that for three-phase rectification, whichever diode has a more positive voltage at its anode compared to the other two diodes it will automatically start to conduct, thereby giving a conduction pattern of: D1 D2 D3 as shown.

Half-wave Three-phase Rectifier Conduction Waveform

Fig.(18) Half-wave Three-phase Rectifier Conduction Waveform

From the above waveforms for a resistive load, we can see that for a half-wave rectifier each diode passes current for one third of each cycle, with the output waveform being three times the input frequency of the AC supply. Therefore there are three voltage peaks in a given cycle, so by increasing the number of phases from a single-phase to a three-phase supply, the rectification of the supply is improved, that is the output DC voltage is smoother. For a three-phase half-wave rectifier, the supply voltages VA VB and VC are balanced but with a phase difference of 120o giving:

VA = VP*sin(ωt – 0o)

VB = VP*sin(ωt – 120o)

VC = VP*sin(ωt – 240o)

Thus the average DC value of the output voltage waveform from a 3-phase half- wave rectifier is given as:

As the voltage supplies peak voltage, VP is equal to VRMS*1.414, it follows that VP is equal to VP/1.414 giving 0.707*VP, so the average DC output voltage of the rectifier can be expressed in terms of the rms (root-mean-squared) phase voltage giving:

3-phase Rectification Example No1

A half-wave 3-phase rectifier is constructed using three individual diodes and a 120VAC 3-phase star connected transformer. If it is required to power a connected load with an impedance of 50Ω, Calculate, a) the average DC voltage output to the load. b) the load current, c) the average current per diode. Assume ideal diodes. a). The average DC load voltage:

VDC = 1.17*Vrms = 1.17*120 = 140.4 volts

Note that if we were given the peak voltage (Vp) value, then:

VDC would equal 0.827*Vp or 0.827*169.68 = 140.4V. b). The DC load current:

IL = VDC/RL = 140.4/50 = 2.81 amperes c). The average current per diode:

ID = IL/3 = 2.81/3 = 0.94 amperes

One of the disadvantages of half-wave 3-phase rectification is that it requires a 4- wire supply, that is three phases plus a neutral (N) connection. Also the average DC output voltage is low at a value represented by 0.827*VP as we have seen. This is because the output ripple content is three times the input frequency. But we can improve on these disadvantages by adding three more diodes to the basic rectifier circuit creating a three-phase full-wave uncontrolled bridge rectifier.

Full-wave Three-phase Rectification

The full-wave three-phase uncontrolled bridge rectifier circuit uses six diodes, two per phase in a similar fashion to the single-phase bridge rectifier. A 3-phase full- wave rectifier is obtained using two half-wave rectifier circuits. The advantage here is that the circuit produces a lower ripple output than the previous half-wave 3-phase rectifier as it has a frequency of six times the input AC waveform. Also, the full- wave rectifier can be fed from a balanced 3–phase 3-wire delta connected supply as no fourth neutral (N) wire is required. Consider the full-wave 3-phase rectifier circuit below.

Full-wave Three-phase Rectification

Fig. (19) Full-wave Three-phase Rectification

As before, assuming a phase rotation of Red-Yellow-Blue (VA – VB – VC) and the red phase (VA) starts at 0o. Each phase connects between a pair of diodes as shown. One diode of the conducting pair powers the positive (+) side of load, while the other diode powers the negative (-) side of load. Diodes D1 D3 D2 and D4 form a bridge rectifier network between phases A and B, similarly diodes D3 D5 D4 and D6 between phases B and C and D5 D1 D6 and D2 between phases C and A. Thus diodes D1 D3 and D5 feed the positive rail and depending on which one has a more positive voltage at its anode terminal conducts. Likewise, diodes D2 D4 and D6 feed the negative rail and whichever diode has a more negative voltage at its cathode terminal conducts. Then we can see that for three-phase rectification, the diodes conduct in matching pairs giving a conduction pattern for the load current of: D1-2 D1-6 D3-6 D3-6 D3-4 D5-4 D5-2 and D1-2 as shown.

Full-wave Three-phase Rectifier Conduction Waveform

Fig(20) Full-wave Three-phase Rectifier Conduction Waveform

In 3-phase power rectifiers, conduction always occurs in the most positive diode and the corresponding most negative diode. Thus as the three phases rotate across the rectifier terminals, conduction is passed from diode to diode. Then each diode conducts for 120o (one-third) in each supply cycle but as it takes two diodes to conduct in pairs, each pair of diodes will conduct for only 60o (one-sixth) of a cycle at any one time as shown above. Therefore we can correctly say that for a 3-phase rectifier being fed by “3” transformer secondaries, each phase will be separated by 360o/3 thus requiring 2*3 diodes. Note also that unlike the previous half-wave rectifier, there is no common connection between the rectifiers input and output terminals. Therefore it can be fed by a star connected or a delta connected

33 transformer supply. So the average DC value of the output voltage waveform from a 3-phase full-wave rectifier is given as:

Where: VS is equal to (VL(PEAK) ÷ √3) and where VL(PEAK) is the maximum line-to-line voltage (VL*1.414).

3-phase Rectification Example No2

A 3-phase full-wave bridge rectifier is required to fed a 150Ω resistive load from a 3-phase 127 volt, 60Hz delta connected supply. Ignoring the voltage drops across the diodes, calculate: 1. the DC output voltage of the rectifier and 2. the load current.

1. the DC output voltage:

The RMS (Root Mean Squared) line voltage is 127 volts. Therefore the line-to-line peak voltage (VL-L(PEAK)) will be:

As the supply is 3-phase, the phase to neutral voltage (VP-N) of any phase will be:

Note that this is basically the same as saying:

Thus the average DC output voltage from the 3-phase full-wave rectifier is given as:

Again, we can reduce the maths a bit by correctly saying that for a given line-to-line RMS voltage value, in our example 127 volts, the average DC output voltage is:

2. The rectifiers load current. The output from the rectifier is feeding a 150Ω resistive load. Then using Ohms law the load current will be:

Uncontrolled 3-phase rectification uses diodes to provide an average output voltage of a fixed value relative to the value of the input AC voltages. But to vary the output voltage of the rectifier we need to replace the uncontrolled diodes, either some or all of them, with thyristors to create what are called half-controlled or fully-controlled bridge rectifiers. Thyristors are three terminal semiconductor devices and when a suitable trigger pulse is applied to the the thyristors gate terminal when its Anode– to-Cathode terminal voltage is positive, the device will conduct and pass a load current. So by delaying the timing of the trigger pulse, (firing angle) we can delay

35 the instant in time at which the thyristor would naturally switch “ON” if it were a normal diode and the moment it starts to conduct when the trigger pulse is applied.

Thus with a controlled 3-phase rectification which uses thyristors instead of diodes, we can control the value of the average DC output voltage by controlling the firing angle of the thyristor pairs and so the rectified output voltage becomes a function of the firing angle, α. Therefore the only difference to the formula used above for the average output voltage of a 3-phase bridge rectifier is in the cosine angle, cos(α) of the firing or triggering pulse. So if the firing angle is zero, (cos(0) = 1), the controlled rectifier performs similar to the previous 3-phase uncontrolled diode rectifier with the average output voltages being the same.

Three-phase Rectification Summary

We have seen in this tutorial that three-phase rectification is the process of converting a 3-phase AC supply into a pulsating DC voltage as rectification converts the input power supply of a sinusoidal voltage and frequency into a fixed voltage DC power. Thus power rectification changes an alternating supply into a unidirectional supply. But we have also seen that 3-phase half-wave uncontrolled rectifiers, which use one diode per phase, require a star connected supply as a fourth neutral (N) wire to close the circuit from load to source. The 3-phase full-wave bridge rectifier which use two diodes per phase requires just three mains lines, without neutral, such as that provided by a delta connected supply. Another advantage of a full-wave bridge rectifier is that the load current is well balanced across the bridge improving efficiency (the ratio of output DC power to input power supplied) and reducing the ripple content, both in amplitude and frequency, as compared to the half-wave configuration. By increasing the number of phases and diodes within the bridge configuration it is possible to obtain a higher average DC

36 output voltage with less ripple amplitude as for example, in 6-phase rectification each diode would conduct for only one-sixth of a cycle. Also, multi-phase rectifiers produce a higher ripple frequency means less capacitive filtering and a much smoother output voltage. Thus 6, 12, 15 and even 24-phase uncontrolled rectifiers can be designed to improve the ripple factor for various applications

Chapter three (Literature Review). 3.1 Harmonics Harmonics are unwanted higher frequencies which superimposed on the fundamental waveform creating a distorted wave pattern [9].

Fig. (21) sinusoidal wave

In an AC circuit, a resistance behaves in exactly the same way as it does in a DC circuit. That is, the current flowing through the resistance is proportional to the voltage across it. This is because a resistor is a linear device and if the voltage applied to it is a sine wave, the current flowing through it is also a sine wave so the phase difference between the two sinusoids is zero. Generally when dealing with alternating voltages and currents in electrical circuits it is assumed that they are pure and sinusoidal in shape with only one frequency value, called the “fundamental frequency” being present, but this is not always the case. In an electrical or electronic device or circuit that has a voltage-current characteristic which is not linear, that is, the current flowing through it is not proportional to the applied voltage. The alternating waveforms associated with the device will be different to a greater or

38 lesser extent to those of an ideal sinusoidal waveform. These types of waveforms are commonly referred to as non-sinusoidal or complex waveforms. Complex waveforms are generated by common electrical devices such as iron-cored inductors, switching transformers, electronic ballasts in fluorescent lights and other such heavily inductive loads as well as the output voltage and current waveforms of AC alternators, generators and other such electrical machines. The result is that the current waveform may not be sinusoidal even though the voltage waveform is. Also most electronic power supply switching circuits such as rectifiers, silicon controlled rectifier (SCR’s), power transistors, power converters and other such solid state switches which cut and chop the power supplies sinusoidal waveform to control motor power, or to convert the sinusoidal AC supply to DC. Theses switching circuits tend to draw current only at the peak values of the AC supply and since the switching current waveform is non-sinusoidal the resulting load current is said to contain Harmonics.Non-sinusoidal complex waveforms are constructed by “adding” together a series of sine wave frequencies known as “Harmonics”. Harmonics is the generalised term used to describe the distortion of a sinusoidal waveform by waveforms of different frequencies. Then whatever its shape, a complex waveform can be split up mathematically into its individual components called the fundamental frequency and a number of “harmonic frequencies”. But what do we mean by a “fundamental frequency”.

3.2 Fundamental Frequency A Fundamental Waveform (or first harmonic) is the sinusoidal waveform that has the supply frequency. The fundamental is the lowest or base frequency, ƒ on which the complex waveform is built and as such the periodic time, Τ of the resulting complex waveform will be equal to the periodic time of the fundamental frequency.

Let’s consider the basic fundamental or 1st harmonic AC waveform as shown.

Fig.(22) Fundamental Frequency

Where: Vmax is the peak value in volts and ƒ is the waveforms frequency in Hertz (Hz).We can see that a sinusoidal waveform is an alternating voltage (or current), which varies as a sine function of angle, 2πƒ. The waveforms frequency, ƒ is determined by the number of cycles per second. In the United Kingdom this fundamental frequency is set at 50Hz while in the United States it is 60Hz. Harmonics are voltages or currents that operate at a frequency that is an integer (whole-number) multiple of the fundamental frequency. So given a 50Hz fundamental waveform, this means a 2nd harmonic frequency would be 100Hz (2 x 50Hz), a 3rd harmonic would be 150Hz (3 x 50Hz), a 5th at 250Hz, a 7th at 350Hz and so on. Likewise, given a 60Hz fundamental waveform, the 2nd, 3rd, 4th and 5th harmonic frequencies would be at 120Hz, 180Hz, 240Hz and 300Hz respectively.

So in other words, we can say that “harmonics” are multiples of the fundamental frequency and can therefore be expressed as: 2ƒ, 3ƒ, 4ƒ, etc. as shown.

3.3 Complex Waveforms Due To Harmonics

Fig. (23) Complex Waveforms Due To Harmonics

Note that the red waveforms above, are the actual shapes of the waveforms as seen by a load due to the harmonic content being added to the fundamental frequency. The fundamental waveform can also be called a 1st harmonics waveform. Therefore, a second harmonic has a frequency twice that of the fundamental, the third harmonic has a frequency three times the fundamental and a fourth harmonic has one four times the fundamental as shown in the left hand side column The right hand side column shows the complex wave shape generated as a result of the effect between the addition of the fundamental waveform and the harmonic waveforms at different harmonic frequencies. Note that the shape of the resulting complex waveform will depend not only on the number and amplitude of the harmonic frequencies present, but also on the phase relationship between the fundamental or base frequency and the individual harmonic frequencies. We can see that a complex wave is made up of a fundamental waveform plus harmonics, each with its own peak value and phase angle. For example, if the fundamental frequency is given as; E = Vmax(2πƒt), the values of the harmonics will be given as:

For a second harmonic:

E2 = V2(max)(2*2πƒt) = V2(max)(4πƒt), = V2(max)(2ωt)

For a third harmonic:

E3 = V3(max)(3*2πƒt) = V3(max)(6πƒt), = V3(max)(3ωt)

For a fourth harmonic:

E4 = V4(max)(4*2πƒt) = V4(max)(8πƒt), = V4(max)(4ωt)

and so on.Then the equation given for the value of a complex waveform will be:

Harmonics are generally classified by their name and frequency, for example, a 2nd harmonic of the fundamental frequency at 100 Hz, and also by their sequence. Harmonic sequence refers to the phasor rotation of the harmonic voltages and currents with respect to the fundamental waveform in a balanced, 3-phase 4-wire system. A positive sequence harmonic ( 4th, 7th, 10th, …) would rotate in the same direction (forward) as the fundamental frequency. Where as a negative sequence harmonic ( 2nd, 5th, 8th, …) rotates in the opposite direction (reverse) of the fundamental frequency. Generally, positive sequence harmonics are undesirable because they are responsible for overheating of conductors, power lines and transformers due to the addition of the waveforms. Negative sequence harmonics on the other hand circulate between the phases creating additional problems with motors as the opposite phasor rotation weakens the rotating magnetic field require by motors, and especially induction motors, causing them to produce less mechanical torque. Another set of special harmonics called “triplens” (multiple of three) have a zero rotational sequence. Triplens are multiples of the third harmonic ( 3rd, 6th, 9th, …), etc, hence their name, and are therefore displaced by zero degrees. Zero sequence harmonics circulate between the phase and neutral or ground. Unlike the positive and negative sequence harmonic currents that cancel each other out, third order or triplen harmonics do not cancel out. Instead add up arithmetically in the common neutral wire which is subjected to currents from all three phases. The result is that current amplitude in the neutral wire due to these

43 triplen harmonics could be up to 3 times the amplitude of the phase current at the fundamental frequency causing it to become less efficient and overheat.Then we can summarise the sequence effects as multiples of the fundamental frequency of 50Hz as:

Harmonic Sequencing

Note that the same harmonic sequence also applies to 60Hz fundamental waveforms.

3.4 Harmonics Summary Harmonics are higher frequency waveforms superimposed onto the fundamental frequency, that is the frequency of the circuit, and which are sufficient to distort its wave shape. The amount of distortion applied to the fundamental wave will depend entirely on the type, quantity and shape of the harmonics present. Harmonics have only been around in sufficient quantities over the last few decades since the introduction of electronic drives for motors, fans and pumps, power supply switching circuits such as rectifiers, power converters and thyristor power controllers as well as most non-linear electronic phase controlled loads and high frequency (energy saving) fluorescent lights. This is due mainly to the fact that the controlled current drawn by the load does not faithfully follow the sinusoidal supply waveforms as in the case of rectifiers or power semiconductor switching circuits. Harmonics in the electrical power distribution system combine with the fundamental frequency (50Hz or 60Hz) supply to create distortion of the voltage and/or current waveforms. This distortion creates a complex waveform made up from a number of harmonic frequencies which can have an adverse effect on electrical equipment and power lines. The amount of waveform distortion present giving a complex waveform its distinctive shape is directly related to the frequencies and magnitudes of the most dominant harmonic components whose harmonic frequency is multiples (whole integers) of the fundamental frequency. The most dominant harmonic components are the low order harmonics from 2nd to the 19th with the triplens being the worst [10].

Chapter Four (Results and Discussion).

4.1 Single phase rectifier As it was explained in the literature review section of this report, single phase rectifier can be designed in the PSIM software as shown in the figure (24).

Figure (24) single phase bridge diode rectifier

As it clear from its name rectifier can convert AC signal to DC signal, therefore the input waveform which is an AC signal is depicted in the figure (25).

Figure (25) input DC waveform.

Then the output waveform is measured accordingly in the figure (26).

Fig. (26) Output waveform

Considerable amount of ripple is seen in the output waveform, which is undesirable, to reduce that filter is required which is discussed in the later section of this chapter.

4.2 Three-phase bridge diode rectifier Detailed explanation of three-phase diode rectifier is given in the literature review, and then its designed in the PSIM software as shown in the figure (27).

Figure (27) three-phase diagram of the bridge diode rectifier.

The three-phase input AC signal is fed to the above rectifier circuit, which is shown in the figure (28).

Figure (28) three-phase input AC signal.

As it has been explained in the introduction and literature review, harmonic distortion is one of the major issues with the DC load, therefore considerable amount of harmonics is seen in the input current waveform as depicted in the figures (29) , (30) and (31).

Figure (29) input current phase Ia waveform.

Figure (30) input current phase Ic waveform.

Accordingly, the output waveform which is a generated DC signal is shown in the figure (31), which included a considerable amount of ripple.

Figure (31) output waveform DC.

4.3 12-pulse diode bridge harmonic cancellation In order to cancel out the harmonics 12-pulse diode bridge is designed in the PSIM for the sake of harmonics cancellation, two transformers are used, the phase angle of the first transformer is 0o, while the second transformer phase angle is 30 o this circuit diagram is shown in the figure (32).

Figure (32) circuit diagram of 12-pulse diode bridge rectifier.

Moderate number of harmonics were seen in the input AC waveform due to the nonlinearities of DC load, details of that can be seen in the figure (33).

Figure (33) three-phase AC input current primary and secondary side current of transformer are shown in the figures of (34) and (35), respectively

Figure (34) primary side current of transformer.

Figure (35) secondary side current of transformer.

Finally output waveform of the inverter is measured and shown in the figure (38).

Figure (36) DC output waveform of 12-pulse diode bridge diode rectifier.

4.4 Harmonic Cancellation of 24-pulse Rectifier Using Phase-Shifting Transformers.

Figure (37) circuit diagram of 24-pulse Rectifier Using Phase-Shifting Transformers.

Extremely low of harmonics were seen in the input AC waveform due to harmonics cancellation, details of that can been seen in the figure (38).

Figure (38) three-phase AC input current

Figure (39) secondary side current of transformer.

Finally output waveform of the inverter is measured and shown in the figure (40).

Figure (40) DC output waveform of 12-pulse diode bridge diode rectifier.

To sum up, the harmonics can bee minimized to the minimum value via using phase shift transformer.

CONCLUSIONS

This paper present the comparison between 12- pulse and 24-pulse rectifier. After finishing necessary calculation we have seen 24-pulse contain less harmonic content in input current. It improves power factor with inductive and capacitive load. Although detail analysis has not been described in this paper, but every inevitable information are given. The desirable features of the modified diode rectifier, such as compact, economical, efficient and reliable are added with the new 24-pulse rectifier. Some new features are joined with this configuration such as lower Ripple component and higher power factor.

List of references

[1] Owen, E.L., 1996. History [origin of the inverter]. IEEE Industry Applications Magazine, 2(1), pp.64-66.

[2] E.F.W Alexanderson, ‘The Thyratron Con- verter,” Camp Engzneerzng, 1925 Alexandersgn paper from Special Collection, Schaffer Library, Union College, Schenectady, N Y

[3] Shabbir, M.N.S.K., Jannat, F.T., Rahman, M.A. and Rana, M.S., 2016. Harmonics Cancellation and Alleviation of Ripple Content from AC-DC Uncontrolled Rectifier by Pulse-Multiplication Technique using Phase-Shifting Transformer. Global Journal of Research In Engineering.

[4] Rashid, M.H., 2009. Power electronics: circuits, devices, and applications. Pearson Education India.

[5] M Kiran, L Phani Kumar and N Srinivasa Rao ‘Design And Analysis of a 24- pulse AC-DC Power Converter By Employing a Pulse Doubling Technique for Asynchronous Drive.’, vol. 3, Issue,1, April 2015,ISSN: 2345-9603.

[6] Yasuyuki NISHIDA, Hiromichi. OHYAMA, Predrag PEJOVIC and Johann W. KOLAR’ Three Phase Harmonic reducing diode rectifier’ conf. EPE-PEME 2012 ECCE Europe.

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[9] [online] Available at: https://www.electronics- tutorials.ws/accircuits/harmonics.html [Accessed 5 May 2021].