**Reduction of Harmonics of Input Side Currents of a Three Phase Rectifier Combining Active and Passive Filters.**

Chapter 1

**1.1 Introduction **

Since most loads in modern electrical distribution systems are inductive, there is an ongoing interest in improving power factor [1]. The low power factor of inductive loads robs a system of capacity and can adversely affect voltage level. To improve input power factor of power converter, normally a power factor correction (PFC) circuit is designed and placed in front end of the converter, which in turn interfaced with the load. This power factor correction circuit may be an independent unit, by which the power supply followed, or an inseparable part of circuit incorporated into the power supply of the load. The line is a voltage source and will not be distorted if the line current is a sinusoidal one. Hence the basic idea of doing PFC is straightforward, by certain means, to force the line current to follow the waveform of the line voltage. However, there exists an unbalance of instantaneous power between the input powers of the PFC circuit, which is an alternative quantity with two times the line frequency, and its dc output power. Therefore, the operation principle of a PFC circuit is to process the input power in certain way that it stores the excessive input energy when the input power is larger than the dc output power, and releases the stored energy when the input power is less than the dc output power. To accomplish the above process, at least one energy storage element must be included in the PFC circuit. Various active and passive techniques are being carried out to meet the stander. To improve the power factor and to comply with various national and international line-harmonics regulations in line-operated electronic equipment, an active or passive power-factor-correction/line-harmonics-reduction circuit must be added to the capacitive filtered bridge or voltage-doublers front-end rectifier. Although it is straightforward to obtain negligible distortion (i.e. less than 5%) and high power factor (more than 99%) with active circuits operating at high frequency (above 20 kHz), the additional circuitry can significantly reduce the reliability and increase the complexity, EMI, and Cost of the equipment. Passive solutions (circuits without controlled switches) offer an attractive trade-off between cost and performance: they are simple, reliable, robust, generate no EMI, and still provide compliance with the norms

**1.2 Definiton**

Power factor correction is simply defined as the ratio of real power to apparent power,

or: PF = Real Power / Apparent Power

Where, the real power is the average, over a cycle, of the instantaneous product of current and voltage, and the apparent power is the product of the rms value of current times the rms value of voltage. If both current and voltage are sinusoidal and in phase, the power factor is 1.0. If both are sinusoidal but not in phase, the power factor is the cosine of the phase angle.

**1.3 Background**

The new European Norms EN 60555 and the international standard IEC555 will impose a limit on the harmonic content of the input current of mains supplied equipment. In practice this will require the addition of a Power Factor Corrector (PFC) at the input of many types of mains operated electronic equipment, for example electronic lamp ballasts, TV power supplies and motor drives. A correctly designed PFC draws a sinusoidal input current from the mains supply, in phase with the mains voltage, and meets the EN60555 norm. It may also provide additional functions, such as automatic mains voltage selection and a regulation of the voltage supplied to the attached equipment [2].

Passive techniques, which introduce a filtering stage consisting of inductor and/or capacitor, to reduce low frequency harmonics, are attractive for their simplicity and reliability. But size and weight are their major drawback. Active techniques on the other hand, use a high switching frequency converter that shapes the input currents almost sinusoidal with small harmonic contents.

That is why the use of active filter is getting increasing interest.

In most PFC circuits, an input inductor has been connected to the bridge rectifier. Because of the current continuity nature of inductor, we usually call such connection as “current driven”. The input inductor can operate in either continuous conduction mode (CCM) or discontinuous conduction mode (DCM). In DCM, the input inductor in no longer a state variable since its state in a given switching cycle is independent on the value in the previous switching cycle. The peak of the inductor current is sampling the line voltage automatically. This property of DCM input can be called “self-power factor correction” because no control loop is required from its input side.

Among the topologies shown in figure 2, the boost configuration operating in a continuous current mode (ie the value of the inductor at the input is calculated such that it conducts continuously throughout the switching cycle) applies the smallest amount of high frequency current to the input capacitor Ci . It is the only topology which allows the noise across the input capacitor to be reduced, which is the major factor defining the size and cost of the filter. Additionally, the boost inductor stores only a part of the transferred energy (because the mains still supplies energy during the inductor demagnetization) and so the inductor required is smaller in comparison with the other topologies. The boost topology thus leads to the cheapest PFC solution, but does not provide either in-rush current or short circuit protection. The buck/boost topology can also be used; its advantages are that it can provide output isolation and adjustable output voltage. This paper will take the cost as the most important consideration, and so will concentrate on the boost circuit topology.

**Figure 1.1 Active PFC topologies**

**1.4 Objective of the work**

The objective of this thesis is to make the input current of a three-phase rectifier circuit to be nearly sinusoidal and at the same time in phase with the supply potentials. This eliminates the harmonic contents in the input current and improves the power factor of the circuit. In doing so, the efficiency of the module is also improved. As a whole, the size and ratings of the equipments has been minimized. The aim of the study is to investigate an integrated power quality improvement by simultaneous active and passive filtering technique.

In this work, the appropriate switching frequency and solid-state switch has been selected to shape the input current. But this leads to introduce very high frequency harmonics in the wave. To eliminate these high frequency components in the input, a simple filter with very small rating inductor and capacitor is used to bypass these high frequency components. However, even after use of input filter low frequency components still exists in the input current.

That is why another series LX filter has been set up at the input side. The component values of this input filter are modeled in such a way that they would resonate at the supply frequency so that power factor of the circuit remains near unity. All of this modeling has been done by using the simulation and the mathematical expression for the acceptable range of values of the components are found out.

**1.5 Thesis Layout**

Organization of this thesis includes seven chapters. Chapter one gives a general introduction followed by background & objective of the work.

Chapter two reviews basic concepts of power factor correction & classification of active, passive approach

In chapter three, different rectifier circuit with passive & active filters are analyzed to find out a perfect solution of our research. Simulation of each circuit is also provided.

Chapter four includesComparison of Basic Converter Topologies For Power Factor Correction.

Also include Cuk converter, Sepic converter and Zeta converter

Chapter five includes the proposed scheme that has to be implemented. It has four stages. First stage is a resonating low frequency filter, second stage has high frequency filter designed by high frequency transfer function, third stage is an IGBT switch that is driven by a separate switching module & the last & forth stage is load with capacitive filter for reducing the output voltage ripples.

Conclusive discussions & remarks are drawn in chapter six . Some suggestions leading to future scope of work are also presented here.

An appendix is included at the end. It describes Power Factor Controller.

Chapter 2

**BASIC CONCEPT OF POWER FACTOR CORRECTION**

**2.1 Power factor **

Power factor (pf) is defined as the ratio of the real power (P) to apparent power (S), or the cosine (for pure sine wave for both current and voltage) that represents the phase angle between the current and voltage waveforms (see Figure 1). The power factor can vary between 0 and 1, and can be either inductive (lagging, pointing up) or capacitive (leading, pointing down). In order to reduce an inductive lag, capacitors are added until pf equals 1. When the current and voltage waveforms are in phase, the power factor is 1 (cos (0°) = 1). The whole purpose of making the power factor equal to one is to make the circuit look purely resistive (apparent power equal to real power). Real power (watts) produces real work; this is the energy transfer component (example electricity-to-motor rpm). Reactive power is the power required to produce the magnetic fields (lost power) to enable the real work to be done, where apparent power is considered the total power that the power company supplies, as shown in Figure 1. This total power is the power supplied through the power mains to produce the required amount of real power.

** Figure 2.1 : Power Factor Triangle (Lagging)**

The previously-stated definition of power factor related to phase angle is valid when considering ideal sinusoidal waveforms for both current and voltage; however, most power supplies draw a non-sinusoidal current. When the current is not sinusoidal and the voltage is sinusoidal, the power factor consists of two factors:

1) the displacement factor related to phase angle and

2) the distortion factor related to wave shape.

5

Equation 1 represents the relationship of the displacement and distortion factor as it pertains to power factor.

* ………….*(1)

*Irms*(1) is the current’s fundamental component and *Irms *isthe current’s RMS value. Therefore, the purpose of the power factor correction circuit is to minimize the input current distortion and make the current in phase with the voltage. When the power factor is not equal to 1, the current waveform does not follow the voltage waveform. This results not only in power losses, but may also cause harmonics that travel down the neutral line and disrupt other devices connected to the line. The closer the power factor is to 1, the closer the current harmonics will be to zero since all the power is contained in the fundamental frequency.

**2.2 Harmonics**

Harmonics are currents or voltages with frequencies that are integer multiples of the fundamental power frequency. In the U.S., the fundamental frequency is 60Hz.

Harmonics are created by non-linear loads that draw current in abrupt pulses rather than in a smooth sinusoidal manner.The effects of harmonics can be overheating of transformers, cables, motors, generators and capacitors connected to the same power supply with the devices generating the harmonics. Electronic displays and lighting may flicker, circuit breakers can trip, computers may fail and metering can give false readings.

**2.3 Need of Power Factor Correction **

The current flow through the circuit is increased by the reactive component. Normally, loads are represented by a series combination of a resistance and a purely imaginary reactance. For this explanation, it is easier to contemplate it as an equivalent parallel combination. The diagram below illustrates a partially reactive load being fed from a real system with some finite resistance in the conductors, etc.

6

The current through the reactive component (Ireactive) dissipates no power, and neither does it register on the watt hour meter. However, the reactive current does dissipate power when flowing through other resistive components in the system, like the wires, the switches, and the lossy part of a transformer (Rline). Switches have to interrupt the total current, not just the active component. Wires have to be big enough to carry the entire current, etc. Correcting the power factor reduces the amount of over sizing necessary.

In elementary courses in electricity, this is sometimes taught as the definition of power factor, but it applies only in the special case, where both the current and voltage are pure sine waves. This occurs when the load is composed of resistive, capacitive and inductive elements and all are linear (invariant with current and voltage). Switched?mode power supplies present non?linear impedance to the mains, as a result of the input circuitry. The input circuit usually consists of a half?wave or full?wave rectifier followed by a storage capacitor. The capacitor maintains a voltage of approximately the peak voltage of the input sine wave until the next peak comes along to recharge it. In this case, current is drawn from the input only at the peaks of the input waveform, and this pulse of current must contain enough energy to sustain the load until the next peak. It does this by dumping a large charge into the capacitor during a short time, after which the capacitor slowly discharges the energy into the load until the cycle repeats. It is not unusual for the current pulse to be 10% to 20% of the cycle duration, meaning that the current during the pulse must be 5 to 10 times the average current in magnitude. Figure 2.2 and 2.3 illustrate this situation.

**Figure 2.2 : Input Characteristic of a Typical Figure 2.3 : Harmonic Content of the Switched-Mode Power Supply without PFC Current Waveform without PFC**

Note that the current and voltage can be perfectly in phase, in spite of the severe distortion of the current waveform. Applying the “cosine of the phase angle” definition would lead to the erroneous conclusion that this power supply has a power factor of 1.0.

The input of a power supply with perfect power factor correction. It has a current waveform that mimics the voltage waveform, both in shape and in phase. Note that it’s input current harmonics are nearly zero.

**Figure 2.4 : Input Characteristic of a Power Supply with Near-Perfect PFC**

**2.4 Process of power factor Correction **

Given the reactive load component (Xload), you can calculate the capacitance that would be put in parallel to exactly match it using the equation:

Xc = 1/ (omega C) = 1/(2 *pi * f * C)

for 60 Hz: Xc = 1/( 2*pi * 60* C) =1/ (377*C) or, rearranging: C = 1/(377*Xc)

Power factor correction capacitors are often rated in kVar, instead of uF, because that is how the power company works. Say a factory has several thousand horsepower worth of motors at .85 power factor. They might have a reactive component of several hundred kVar. At a distribution voltage of 14,400 volts, this would require a capacitor with an impedance of a bit more than 1000 ohms, or about 2.5 microfarads, a reasonable sized and priced package. However, if you were crazy enough to try to compensate this at 230 volts, you would need about .01 Farads (i.e. 10,000 uF), a sizeable package.

For very large systems, even capacitors get unwieldy. One approach is to use large over excited synchronous motors which look like capacitors, electrically. Another approach is clever systems of thyristors and inductors which simulate the capactive reactance by drawing “displacement current”.

**2.5 Power Factor Correction vs. Harmonic Reduction**

It is clear from the previous illustrations that high power factor and low harmonics go hand?in?hand. There is not a direct correlation however, the following equations link total harmonic distortion to power factor.

Where K_{d} is the distortion factor and is equal to –

Therefore, when the fundamental component of the input current is in phase with the input voltage, K? = 1 and:

As illustrated, a perfectly sinusoidal current could have a poor power factor, simply by having its phase not in line with the voltage.

A 10% Total Harmonic Distortion (THD) corresponds then to a Power Factor approximately equal to 0.995. It is clear that specifying limits for each of the harmonics will do a better job of controlling the “pollution” of the input current, both from the standpoint of minimizing the current and reducing interference with other equipment. So, while the process of shaping this input current is commonly called “power factor correction,” the measure of its success in the case of the international regulations is the harmonic content.

**2.6 Loads that draw non-sinusoidal current**

Classic reactive loads, like transformers, lighting ballasts, and AC motors still have a sinusoidal current flow. The phase of the current is just shifted from that of the supply voltage. However, there are some loads which draw distinctly non-sinusoidal currents. The most recently notorious is the switching power supply in a PC. These power supplies start with a bridge rectifier feeding a capacitor, and so, particularly at part load, draw their current in little peaks, when the instantaneous line voltage is above the capacitor voltage, forward biasing the rectifier.

Another notorious non-sinusoidal current draw is the popular phase controlled light dimmer, which uses a TRIAC or SCR to reduce the RMS voltage to the load by turning on partway through the half cycle. Not only is the current waveform highly non-sinusoidal, but it is also out of phase with the voltage supply. Hence, these loads have a non-unity power factor, and draw reactive power.

However, to compensate these loads, you have to come up with a means to supply the reactive current at the appropriate times. A simple capacitor doesn’t do this. A capacitor only compensates nice sinusoidal power factor lags, like those from linear (non-saturating) inductors.

**2.7 Example of Power Factor Correction**

Let’s take an example. A 3/4 HP electric motor has a power factor of .85. The nameplate current is 10 Amps at 115 Volts, or 1150 Volt Amps.

- Apparent power = 1150 Volt Amps
- Active power (P) = .85 * 1150 = 977.5 Watts
- Reactive Power (Q) = sqrt(1150^2 – 977.5^2) = 605 VAR

So, we need about 600 var of power factor correction. I’m rounding to a couple digits, because, in reality, it’s unlikely that the power factor is known to more accuracy, nor will any of the PFC components be that precise. (10% accuracy would be quite good for a capacitor). Now, assume we want to put the capacitor in parallel with the motor: Calculating the required impedance from Q = E^2/X, where Q is the reactive power needed:

- 600 = 115^2/X => X = 115^2/600 = 22 ohms (rounding to 2digits)
- C = 1 /( 2 * pi * f *X) = 1/ (377 * 22) = 120 uF (again, rounding to 2 digits)

which is a fairly large capacitor in a constant duty environment (i.e. motor run, as opposed to motor start, where the capacitor is only in the circuit for a short time). We can calculate the RMS current through the capacitor either by dividing the VARs by the line voltage (600/115) or by dividing line voltage by reactance (115/22); both come out at around 5 1/4 Amps, so we’d want a capacitor rated at somewhat more current (e.g. 7-10 A). The capacitor’s series resistance should be pretty low, or it will dissipate a fair amount of energy. If the dissipation factor were 1%, we’d be dissipating about 6 Watts in the capacitor. One can also put the PFC capacitor in series with the load. In this case the capacitor would carry the entire load current of 10A, but, the required value is different.

For a series compensation, we’d determine the series equivalent of the load (we used a parallel model, above). For the series model, you use currents, instead of voltages:

600 VAR = I^2 * X => 600 = 10*10 * X => X = 6 ohms

And converting an impedance to a capacitance: C=1/(377*6) = 440 uF.

So, not only would the capacitor be larger, but it would need to carry the entire load current. For this example, at least, parallel PFC seems to be a better approach. Only if the power factor were very poor, so the reactive impedance was quite large (and the corresponding capacitance low) would series compensation seem to be useful.

If the line voltage were higher, the correction impedance would be increased as the square of the line voltage. The capacitance would be reduced as the square of the line voltage. That is, if the same motor were run off 230 Volts, the capacitor would only need to be about 30 uF. And if we were to do power factor compensation at the distribution voltage of 4160 volts (for example), we would only need about .1 uF. This is why power factor correction is usually done in the distribution network at MV or HV, and not at the end voltage.

**2.8 Classification of Power Factor Correction Approaches **

The general approaches to improve power factor can be widely classifieds as passive and active approaches[3]. The passive approaches use capacitive inductive filters to achieve PCF, while the active approaches use a switched mode power supply to shape the input current. However, there are no rules demanding that the PFC be accomplished by active circuits (transistors, ICs, etc.). Any method of getting the harmonics below the regulatory limits is fair game. It turns out that one inductor, placed in the same location as the active circuit, can do the job.

Waveforms:

1. Input current with no PFC

2. Input current with passive PFC

3. Input current with active PFC

4. Input voltage

**Figure 2.5 : Input Characteristics of PC Power Supplies with Different PFC Types (None, Passive, and Active)**

**2.8.1 Passive Approaches**

In the passive approaches, a full bridge rectifier with an LC filter is used to reduce the line current harmonic limits. Generally the LC filter can be placed in either the AC-side or the DC-side of the rectifier as shown in Figure 2.6. Placing the LC filter in the AC-side will result in more pure sinusoidal input current. Passive PFC can meet the regulation with high efficiency, superior reliability, low cost, and low EMI [4-5]. On the other hand, the filter capacitor voltage vanes with the line voltage, which has a detrimental effect on the performance and efficiency of the DC-DC converter. When considering a hold-up time for the power supply, the bulk capacitance has to be increased and becomes very bulky compared to what it would be without this varying voltage.

As a result, the passive approaches seem to be more attractive in low-power applications, up to 300Watts, and are more suitable for narrow line voltage range. Other drawbacks are the size and weight of the filter choke inductor.

However, the majority of power supplies manufactured in low-power and cost-sensitive applications have adopted the passive PFC approaches.

**Figure 2.6 : General Structures of the Passive PFC Approaches**

**2.8.2 Active Approaches**

In active PFC approaches, a switched mode converter is employed to overcome the limitations of the passive approaches. Assuming unity power factor, the line current should be sinusoidal and in phase with the line voltage. That will result in pulsating output power than contains – in addition to the real (average power) – an alternating component with double-line frequency.

Since the power demanded by most loads is constant, an energy storage element is needed. Since the inductor-stored energy cannot match this excessive energy, another storage component isneeded. This storage capacitor is normally located between the two stages and should handle the double-line frequency ripple component, which make it bulky. This second, harmonic problem that presents itself on the output of the PCF stage cannot be internally solved. Usually, a compromise between PFC and output voltage ripple should be made, but most of the time thisoutput voltage is not good enough to supply the load. As a result, another DC-DC converter is needed, or what is so called post regulator, to solve this problem and achieve tight output regulation. The result in the most powerful PFC configuration and is the active two-stage PFC shown in Figure 2.7.

**2.8.2 (A) Two-Stage PFC converter**

This configuration implies the use of *two *converters to achieve both power factor correction and output regulation in addition to the rectification circuit and the input EMI filter. These converters are independent, which means each one has its own switches and control circuit. The PFC converter performs the input current shaping using one of the popular converter topologies (buck, boost, buck-boost, flyback, SEPIC, Cuk*, *ZETA) in addition to one of the PFC controlling techniques. The boost converter iswidely used due to its advantages, which include good power factor, grounded switch, input inductor and simplicity. However, this PFC converter normally has a low bandwidth control, which implies a loosely regulated output voltage across the storage capacitor. In universal line voltage applications, the DC bus voltage may vary between 380-400V**. **Because of the relative high voltage on the storage capacitor, the value of the capacitance can be optimized to provide the necessary hold up time. The DC-DC converter is connected to the storage capacitor to provide the necessary tight output voltage regulation with the appropriate gain and, most of the time, provides isolation.

**Figure 2.7 : System Configuration of Two-Stage PFC Power Supply**

** (B) Single-Stage PFC converter**

The single-stage PFC configuration came about to reduce the cost and complexity of the two-stage structure, and it can be viewed more as a modification on the two stage PFC rather than a class by itself. As can be seen from Figure 2.8, the PFC and the DC-DC cell share the control circuit and can also share the switches in this configuration. The energy storage capacitor between the two stages serves as a buffer for frequency isolation and to provide the converter with the necessary hold up time. However, in single stage configuration, the voltage across the storage capacitor is not regulated, -because the controller isused to regulate the output voltage. As a result, this voltage can vary greatly, usually between 130-500V in universal line application. This will have a negative impact on the design and cost of the PFC converter.

**Figure 2.8 : System Configuration of Single-Stage PFC Power Supply**

**2.9 Approach Comparisons**

Generally, the passive approach should be considered in low power applications, especially when designing to meet the minimum regulation requirements with a narrow line voltage range. At low power levels (<300W),the active single-stage approach offers a great advantage over the passive approaches due to its simple structure, low cost, minimum weight and better PFC performance.

Unity power factor and tight output regulation for any power range can be achieved through the two-stage active PFC. This structure can guarantee compliance with any regulation and is compatible with universal line voltage applications. Some negative factors of the two-stage scheme include cost, size, and sometimes its lower efficiency.

**Table-1** Provides a general relative performance comparison for the passive and active single- and two stage approaches [6] .

Performance Review | Passive Scheme | Active Two- Stage | Active Single- Stage |

THD | High | Low | Medium |

Power Factor | Low | High | Medium |

Efficiency | High | Medium | Low |

Size | Large | Medium | Medium Small |

Bulk-Cap Voltage | Variation | Constant | Variation |

Control | Simple | Complex | Medium |

Component Count | Least | Medium | Medium-Low |

Power Range | <300 W | Any | <300 w |

Chapter 3

**IMPROVEMENT OF THD RECTIFIER**

**3.1 Analysis of 3-Phase rectifier circuit**

Three phase diode rectifier circuits are extensively used in many high power low cost applications leading the degradation in the power quality due to the current distortion. A simple three phase rectifier circuit and its input current and harmonics are shown in the figure 3.1, 3.2, 3.3 respectively.

**Figure 3.1: A simple diode bridge rectifier without capacitor**

Here input voltage V1, V2, V3 peak value 300v with phase difference 120 deg. Frequency 50Hz, R1 100?.

**Figure 3.2a: Input voltages of the three phases of the rectifier for Phase A, B, C**

**Figure 3.2b: Input currents of the three phases of the rectifier for Phase A, B, C**

**Figure 3.3: Harmonic content of the three phases A, B, C**

**Table 3.1**: Harmonic content of Current in the phase A without capacitor

Harmonics | Values (mA) | Harmonics | Values (mA) |

I-1(50Hz) | 5500 | I-11(550Hz) | 300 |

I-2(100Hz) | 45 | I-12(600Hz) | 38 |

I-3(150Hz) | 20 | I-13(650Hz) | 75 |

I-4(200Hz) | 44 | I-14(700Hz) | 45 |

I-5(250Hz) | 1100 | I-15(750Hz) | 12 |

I-6(300Hz) | 55 | I-16(800Hz) | 38 |

I-7(350Hz) | 500 | I-17(850Hz) | 100 |

I-8(400Hz) | 48 | I-18(900Hz) | 18 |

I-9(450Hz) | 6 | I-19(950Hz) | 52.5 |

I-10(500Hz) | 42 | I-20(1000Hz) | 36 |

?? (Mh ) 2

THD% =———— * 100%

M1

Where Mh is the magnitude of either voltage or current harmonic component and M1is the magnitude of either the fundamental voltage or current.

Putting the values in the equation we have got the THD values for a simple rectifier is 22.9%.

18

**Figure 3.4:Output voltage of this rectifier without capacitor**

**Figure 3.5: Phase relation of input current and output voltage without capacitor**

**3.2 A three diode bridge rectifier with capacitor**

**Figure 3.6: A simple diode bridge rectifier with capacitor**

**Figure 3.7: Input currents of the three phases of the rectifier with capacitor**

**Table 3.2:** Harmonic content of Current in the phase A with capacitor

Harmonics | Values (mA) | Harmonics | Values (mA) |

I-1(50Hz) | 5500 | I-11(550Hz) | 1175 |

I-2(100Hz) | 50 | I-12(600Hz) | 43 |

I-3(150Hz) | 33.6 | I-13(650Hz) | 1050 |

I-4(200Hz) | 32 | I-14(700Hz) | 16.5 |

I-5(250Hz) | 3450 | I-15(750Hz) | 75 |

I-6(300Hz) | 16 | I-16(800Hz) | 47 |

I-7(350Hz) | 2150 | I-17(850Hz) | 750 |

I-8(400Hz) | 35 | I-18(900Hz) | 53 |

I-9(450Hz) | 77.5 | I-19(950Hz) | 590 |

I-10(500Hz) | 60 | I-20(1000Hz) | 21 |

The THD value obtained from this rectifier is 83.23%. This is an extremely large value. Because of the insertion of the capacitor at the o/p to make the o/p volt. Ripple free the i/p current becomes too much distorted and harmonic content has increases a lot

**Figure 3.9: Output voltage of the rectifier with capacitor**

**Figure 3.10: Phase relation of i/p current and o/p Volt. with capacitor**

**3.3 Harmonic reduction with passive filter **

By observing the input current wave shape of these filters we can say about the harmonic contents of them. There is no even harmonics as the waveforms are symmetrical about the X-axis. Another noteworthy fact is balanced three phase rectifier type loads do not produce a third harmonic component. Nor do they produce any triplet harmonic component. Again the 11^{th} harmonic & higher is a point where the magnitude diminishes to a very low level. Thus 5^{th} & 7^{th} orders are the problem child harmonics for AC drives.

**Table 3.3:** Harmonic spectrums Analysis

Harmonic | Value/unit | Frequency(Hz) |

fundamental | 1 | 50 |

5^{th} |
0.2 | 300 |

7^{th} |
0.14 | 350 |

11^{th} |
0.09 | 550 |

13^{th} |
0.07 | 650 |

17^{th} |
0.06 | 850 |

19^{th} |
0.05 | 950 |

Passive filters may be used for reducing the harmonics content of the output currents. But they do not allow the regulation of the output voltage & also decreases the output voltage levels in comparison with the unfiltered rectifiers.

Taking the harmonic limits as a quality index, the resulting inductors are typically larger than the ones used in high quality using circuits[7-8].

**3.4 Effect of input inductance **

**Figure 3.11: Three-phase rectifier with input inductance**

**Figure 3.12: Input current with 1mH inductance**

**Figure 3.13: Output voltage with 1mH inductor **

**Figure 3.14: Input current with L1=L2=L3=100mH **

**Figure 3.15: Output voltage with L1=L2=L3=100mH**

**Figure 3.16: Input current with L1=L2=L3=1H **

**Figure 3.17: Output voltage with L1=L2=L3=1H**

As we can see with increasing the inductive value of the i/p inductor the current wave shape improves but the o/p voltage decreases.

**3.5 Rectifier Analysis with passive filter**

**Figure 3.18: Rectifier with i/p passive filter**

**Figure 3.19: Input current & Output voltage **

**L1=L2=L3=100mH, C1=C2=C3=100uF**

**Figure 3.20: Input current & Output voltage**

**L1=L2=L3=1H, C1=C2=C3=10uF**

**Figure 3.21: Input current & Output voltage**

**L1=L2=L3=10mH, C1=C2=C3=100uF**

**Figure 3.22: Input current & Output voltage**

**L1=L2=L3=10mH, C1=C2=C3=10uF**

**Figure 3.23: Input current & Output voltage**

**L1=L2=L3=10H, C1=C2=C3=100uF**

**Figure 3.24: Input current & Output voltage**

**L1=L2=L3=100mH, C1=C2=C3=10uF**

From the wave shapes shown above, we see that the value of the inductor increases the input wave shapes is improving a lot but output voltage level decreases & decreasing the value of inductor given more output voltage but input current distortion increases.

The best model for the passive filter has obtained when L=100mH & C=100uF. Actually the filter can be modeled by calculating the resonating values as X_{L}=X_{C}.

Calculation is done by considering the fundamental component as 50Hz. The product of LC should be 1*10^{-5 }. So in a passive input filter the component values are very large & regulation of the output voltage is not possible.

**3.6 Introduction of switching in Boost Rectifier **

Active wave shaping means to introduce switching in the rectifier circuit. In a boost rectifier if switching is introduced without having any input filter the input current start to conduct in Discontinuous Conduction Mode (DCM) & the wave shape follows the input voltage but have high frequency switching components. The output cannot reach to a desired level as expected by the boost converter. So, though the input current wave shape has improved a lot, the efficiency of this module is not good at all. In Figure 3.26 the input current & output voltage wave shapes are given that we got from simulation.

**Figure 3.25: A single switch boost rectifier**

**Figure 3.26: PWM circuit.**

31

**Figure 3.27: The input voltage (Vpulse) of the OpAmp at pin#3**

A 4kHz saw tooth wave varying from 15V to 0V.

**Figure 3.28: Input current & Output voltage with switching **

With the introduction of EMI filter at the input can make better the performance. The circuit model for switching with input filters where L1, L2, & L3 are of 500uH. Here we can see the output voltage has got to an acceptable high value as expected by boost rectifier.

**3.7 Boost Rectifier with EMI filter and Switching**

**Figure 3.29: A three phase boost rectifier with single switch and i/p filter**

**Figure 3.30: Duty Cycle of PWM**

Duty Cycle 0.17 V1 =V2=V3= 300volt.(peak)

**Figure 3.31: Input current for boost rectifier with i/p filter and switching**

**Figure 3.32: Output voltage for boost rectifier with i/p filter and switching **

**Figure 3.33: Input current Harmonics content of the phases A for boost rectifier with i/p filter & switching**

**Table 3.4:** Harmonic content of Current in the phase A with switching & EMI filter

Harmonics | Values (mA) | Harmonics | Values (mA) |

I-1(50Hz) | 820000 | I-11(550Hz) | 6250 |

I-2(100Hz) | I-12(600Hz) | ||

I-3(150Hz) | I-13(650Hz) | 3125 | |

I-4(200Hz) | I-14(700Hz) | ||

I-5(250Hz) | 50000 | I-15(750Hz) | 1562.5 |

I-6(300Hz) | I-16(800Hz) | ||

I-7(350Hz) | 25000 | I-17(850Hz) | 7811 |

I-8(400Hz) | I-18(900Hz) | ||

I-9(450Hz) | 12500 | I-19(950Hz) | 390 |

I-10(500Hz) | I-20(1000Hz) |

A THD of a three-phase rectifier with capacitor can be reduced from 83.23% to 17.61% with the introduction of active filter or switching in the rectifier. Even at this value of the THD is not acceptable as recommended by different regulations & standards. Some application requires the THD to be less than 10% & even some other application have set the limit to be less than 5%. That is why research is still going on to improving the THD level. In our work, we tried to reduce the value to be less than 5%.

Duty Cycle 0.435 V1 =V2=V3= 17volt.(peak)

**Figure 3.34: Input current for boost rectifier with i/p filter and switching**

**Figure 3.35: Output voltage for boost rectifier with i/p filter and switching **

**Figure 3.36: Input current Harmonics content of the phases A for boost rectifier with i/p filter & switching**

**Table 3.5:** Harmonic content of Current in the phase A with switching & EMI filter

Harmonics | Values (mA) | Harmonics | Values (mA) |

I-1(50Hz) | 3250 | I-11(550Hz) | 50 |

I-2(100Hz) | I-12(600Hz) | ||

I-3(150Hz) | I-13(650Hz) | 25 | |

I-4(200Hz) | I-14(700Hz) | ||

I-5(250Hz) | 200 | I-15(750Hz) | 12.2 |

I-6(300Hz) | I-16(800Hz) | ||

I-7(350Hz) | I-17(850Hz) | 6.25 | |

I-8(400Hz) | I-18(900Hz) | ||

I-9(450Hz) | 100 | I-19(950Hz) | 3.125 |

I-10(500Hz) | I-20(1000Hz) |

**Chapter 4**

**Comparison of Basic Convertor Topologies For Power Factor Correction**

**4.1 Input Voltage-Current Characteristics of Basic Converter Topologies**

Inorder to examine the self-PFC capabilities of the basic converters, we first investigate their input characteristics. Because the input currents of these converters are discrete when they are operating in DCM, only averaged input currents are considered. Since switching frequency is much higher than the line frequency, let’s assume the line voltage is constant in a switching cycle. In steady state operation, the output voltage is nearly constant and the variation in duty ratio is slight. Therefore, constant duty ratio is considered in deriving the input characteristics. During the analysis, the following nomenclatures are used :

*v _{l}(t)=V_{im} sin?_{i}t *— line voltage;

i_{l}(t) — line current;

v_{l}(t) — rectified line voltage;

*i _{l}(t) *— rectified line current;

i_{l},avg(t) — average value of rectified line current,

(assume *i _{l}(t) = i_{l},avg(t));*

*V _{0} *— output dc voltage;

*? _{l}*— line angular frequency;

T_{l}— line period;

T_{s} — switching period;

D — duty ratio;

D_{l} — input inductor discharging time ratio.

**Buck converter**

The basic buck converter topology and its input current waveform when operating in DCM are shown in Figure 4.1(a) and 4.1(b), respectively. It can be shown that the average input current in one switching cycle is given by,

38

Figure 4.1(c) shows that the input voltage-input current V-I characteristics is a straight line. It should be note that this straight line does not go through the original. When the rectified line voltage v_{l}(t) is less than the output voltage *V _{o} *negative input current would occur. This is not allowed because the bridge rectifier will block the negative current. As a result, the input current is zero near the zero cross point of the line voltage, as shown in Figure 4.1(c). Actually, the input current is distorted simply because the buck converter can work only under the condition that the input voltage is larger than the output voltage. Therefore the basic buck is not a good candidate for DCM input power factor correction.

**Figure 4.1: Input V-I Characteristic of basic buck Converter operating in DCM**

**Boost converter**

The basic boost converter and its input current waveform are shown in Figure 4.2(a) and 4.2(b), respectively. The input V-I characteristic can be found as follows:

By plotting Eq. (2), we obtain the input V-I characteristic curve as given in Figure 4.2(c). As we can see that as long as the output voltage is larger than the peak value of the line voltage in certain extent (depending on *D _{l}), *the relationship between

*v*and

_{l}(t)*i*is nearly linear. When the boost converter connected to the line, it will draw almost sinusoidal average input current from the line, when the output voltage is higher than its input shown as in Figure 4.2(c).

_{l},avg(t)**Figure 4.2: Input V-I Characteristic of basic boost converter operating in DCM**

As one might notice from Eq. (2) that the main reason to cause the non-linearity is the existence of *D _{l}. *Ideally, if

*D*= 0, the input V-I characteristic will be a linear one. In practice, to reduce the discharge period

_{l}*D*by properly configuring the circuit topology, a higher voltage, instead of

_{l},*V*can be created to be applied to the inductor during

_{0},*D*to discharge the inductor[11].

_{l}Because of the above reasons, boost converter is comparably superior to most of the other converters when applied to do PFC[11-13]. However, it should be noted that boost converter can operate properly only voltage. When low voltage output is needed, a step-down dc-dc converter must be cascaded.

**Buck-boost converter**

Figure 4.3(a) shows a basic buck-boost converter. The averaged input current of this converter can be found according to its input current waveform, shown in Figure 4.3(b).

**Figure 4.3 Input V-I Characteristic and input waveforms.**

Equation (3) gives a perfect linear relationship between *i _{l}.avg(t) *and

*v*which proves that a buck-boost has excellent self-PFC property. This is because the input current of buck-boost converter does not related to the discharging period

_{l}(i),*D*Its input V-I characteristics and input voltage and current waveforms are shown in Figure 4.3(c). Furthermore, because the output voltage of buck-boost converter can be either larger or smaller than the input voltage, it demonstrates strong availability for DCM input technique to achieve power factor correction. So, theoretically buck-boost converter is a perfect candidate. Unfortunately, this topology has two limitations: 1) the polarity of its output voltage is reversed, i.e., the input voltage and the output voltage don’t have a common ground; and 2) it needs floating drive for the power switch. The first limitation circumscribes this circuit into a very narrow scope of applications. As a result, it is not widely used.

_{l}.** D. Flyback converter**

**Figure 4.4 Input V-I Characteristic of basic flyback converter operating in DCM**

42

Flyback converter is an isolation converter. Its topology is shown in Figure 4.4(a). Figure 4.4(b) shows its input current waveform. The input voltage-input current relationship is similar to that of buck-boost converter:

Where, Lm is the magnetizing inductance of the output transformer. Therefore, it has the same input V-I characteristic, and hence the same input voltage and input current waveforms as those the buck-boost converter has, shown in Fig. 4(c). Comparing with buck-boost converter, flyback converter has all the advantages of the buck-boost converter without any limitation. What’s more, input-output isolation can be provide by flyback converter. These advantages make flyback converter most preferable in power factor correction with DCM input technique [14-16].

** E. Forward converter**

**Figure 4.5 Forward converter and its input current waveform**

The circuit shown in Figure 4.5 is a forward converter. In order to avoid transformer saturation, it is well know that forward converter needs the 3^{rd} winding to emagnetize (reset) the transformer. When a forward converter is connected to the rectified line voltage, the demagnetizing current through the 3 rd winding is blocked by the rectifier diodes. Therefore, forward converter is not available for PFC purpose.

** F. Cuk converter, Sepic converter and Zeta converter**

It can be shown that Cuk converter, Sepic converter and Zeta converter given in Figure 4.6(a), (b) and (c), respectively, have the same input V-I characteristic. Each of these converter topologies has two inductors, with one located at its input and the other one at its output. Let’s consider the case when the input inductor operates in DCM while the output inductor operates in CCM. To investigate the input characteristic of these converters, let’s take the Cuk converter as an example. One should note that the results from the Cuk converter are also suitable for Sepic converter and Zeta converter.

**Figure 4.6 : Basic topologies of Cuk, Sepic and Zeta converters**

The waveforms of the Cuk converter, shown in Figure 4.6(a), for input inductor current (=input current), output inductor current and the current through the capacitor C are depicted in Figure 4.7(a). Assume that the output current is I_{0}. Then the average output inductor current is I_{0}. In steady state, employing charge equilibrium principle, we obtain

44

Then the averaged input current can be found as

**Figure 4.7 : Input V-I Characteristic of basic Cuk converter operating in DCM input**

From Eq.(6), the input V-I characteristic of Cuk converter is plotted in Fig. 7(b). According to this input V-I chart, the input current waveform corresponding to a sinusoidal input voltage is sketched. As we can see that the input current waveform is a distorted one. Therefore, Cuk converter does not have a good self-PFC property. This conclusion can be also extended to the Sepic and Zeta converters.

**4.2 Conclusions**

According to the above discussion, we may conclude that the basic boost converter, flyback converter and buck-boost converter have excellent self-PFC capability naturally. Among them, boost converter and flyback converter are especially suitable for DCM PFC usage. Hence, these two converters are most preferable by the designers for power factor topologies purpose. Other converters may be used only if their input V-I characteristics have been modified (linearized), or when they operate in continuous conduction mode. The characteristics of the above eight basic converter topologies are summarized as in Table I.

**Table 4.1 Comparison of various kinds of Topology**

#### Chapter 5

**ANALYSIS OF THE PROPOSED MODEL**

#### 5.1 Introduction

The Buck and Boost inductors are most commonly used in “switchmode” or feedforwardtype of converter configurations. A forward type converter is said to beoperating in “continuous mode” as long as the current through the inductorremains above zero for the entire switching cycle. If, at minimum output current,the current through the inductor drops to and remains at zero during someportion of the cycle, the converter is being operated in the “discontinuous mode.”A real world example of this application would be in a battery charger for yourlaptop.