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PF correction using SEPIC


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PF correction using SEPIC

  2. 2. 2 SIKSHA ‘O’ ANUSANDHAN UNIVERSITY: ORISSA BONAFIDE CERTIFICATE Certified that this project report “POWER FACTOR CORRECTION USING SEPIC CONVERTER” is the bonafide work of “SOUMYA DASH” who carried out the project work under my supervision. SIGNATURE: SIGNATURE: PROF. PRAVAT KUMAR ROUT ALOK KUMAR MISHRA HEAD OF DEPARTMENT SUPERVISOR Electrical and electronics engineering, Assistant professor, Department of EEE,ITER, Electrical and electronics engineering SOA University, Deaprtment of EEE, ITER Bhubaneswar-751030 SOA University, Bhubaneswar-751030
  3. 3. 3 ACKNOWLEDGEMENT I avail this opportunity to express my deep sense of gratitude and sincere thanks to Alok Kumar Mishra, Asst. Professor, Electronics and Electrical Engineering Department, Institute of Technical Education and Research for invaluable guidance rendered to me during the course of my work. His constant encouragement and painstaking efforts have been the sole endeavors to bring my dissertation work in present form. I thank all the teaching and non teaching staff members of the department who have contributed directly or indirectly in successful completion of my dissertation work. I am extremely grateful to friends and well-wishers for their candid help, meaningful suggestions and persistent encouragement given to me at different stages of my work. Finally, I would like to say that I am indebted to my parents for everything that they have given to me. I thank them for the sacrifices they made so that I could grow up in a learning environment. They have always stood by me in everything I have done, providing constant support, encouragement and love. Soumya Dash
  4. 4. 4 ABSTRACT Power electronic devices with front-end rectifier are widely used in industry, commerce and transportation, which generate current harmonics, produce power pollution and result in low power factor. Though there are several proposed solutions to this, SEPIC converter was the most successful one. But the conventional SEPIC converters suffer from high switching losses. Hence in this project, a new modified SEPIC converter is proposed to achieve unity power factor at the mains side with greater efficiency. The switching loss is reduced by applying soft switching topology i.e. zero voltage switching (ZVS). A prototype will be designed, analyzed and implemented along with required software simulations to establish the thought.
  5. 5. 5 LIST OF TABLES Table Table Description PageNo. 7.1 rule base for working of FIS
  6. 6. 6 LIST OF FIGURES Figure No. Description PageNo. 2.1 relation between voltage, current ,power and 10 average power. 2.2 relation between the three powers 10 2 peak current control scheme 12 2.3 average current control scheme 14 2.4 Hysterisis current control scheme 15 3.1 circuit describing the effect of harmonics on power 19 Factor 3.2 waveform describing the pulsed nature of input line 19 current 4.1 Schematic diagram of sepic converter 22 4.2 Circuit describing the mode 1 operation 24 Of sepic converter 4.3 Circuit describing mode 2 operation of 25 Sepic converter 5.1 (a) Basic buck boost type PFC 32 5.1 (b) Series connected buck-boost type PFC circuit 33 5.1 (c) Cuk topology 33 5.1 (d) Sepic topology 34 5.2 Operating sequences: electrical configuration 35 when Q is turned-on (a), when Q is turned-off while D in on (b), when Q and D arc both off(c). 5.3 Reactive component settings 39 5.4 circuit of closed loop control 41 6.1 simulation model of ideal sepic converter 47 6.2 & 6.3 Output 48
  7. 7. 7 6.4 Simulation model of sepic (open loop) converter 49 6.5 Output waveform - input current and voltage 50 6.6 Output waveform – output voltage 51 6.7 FFT analysis 51 6.9 Simulation model of sepic (closed loop) converter 52 6.10 output-output voltage 53 6.11 output current 53 6.12 waveform of input current and voltage 54 6.13 FFT analysis 54 6.14 closed loop control with load disturbance 55 6.16 waveform of input voltage and current 56 6.17 waveform of output voltage 57 6.18 FFT analysis 57 6.19 closed loop control with reference change 58 6.20 waveform of input voltage and current 59 6.21 waveform of output voltage 60 6.22 FFT analysis 60 6.23 Closed loop control with supply change 61 6.24 waveform of input voltage and current 62 6.25 waveform of output voltage 62 6,26 FFT analysis 63 6.27 circuit diagram of average current control 64 For power factor correction 6.28 waveform for average current control 64 6.29 simulation of average current control 66 6.30 waveform of input current and voltage 67 6.31 waveform of output voltage 67 6.32 FFT analysis 68 6.33 simulation of average current control by closed loop 69 6.34 waveform for input voltage and current 70 6.35 waveform for output voltage 70 6.36 FFT analysis 71 6.37 simulation model of power factor correction using 73 Sepic converter with three phase supply 6.38 waveform for input current and voltage 74
  8. 8. 8 6.39 waveform for output voltage 74 6.40 FFT analysis 75 7.1 diagram describing the fuzzy control system 77 7.2 diagram representing various membership functions 79 7.3 FIS editor 81 7.4 Membership Function for Voltage Error 82 7.5 Membership Function of Change in error 82 7.6 Membership function of change in frequency 83 7.7 (a) Rule editor 83 7.7(b) Rule viewer 84 7.8 simulation of the circuit for power factor correction 84 Using fuzzy logic controller 7.9 output waveform for input current and voltage 85 7.10 waveform for output voltage 85
  10. 10. 10
  11. 11. 11 CHAPTER-1 INTRODUCTION Power electronic devices with front-end rectifier are widely used in industry, commerce and transportation, which generate current harmonics, produce power pollution and result in low power factor. Therefore, there are international harmonic standards (such as: IEC-1000 and IEC-555) to confine power pollution. In order to meet the requirements of the standards, the input current waveforms of a device have to be shaped by a PFC to eliminate current harmonics and improve power factor. The PFCs can be briefly classified into two types. One is passive PFC, the other is active one. Passive- type PFC is mainly constructed by inductors and capacitors. Low efficiency, heavy weight and large volume are its major disadvantages. Besides, power factor merely is improved to around 0.8. For active type, active switch, diode and energy-stored component are used to achieve near unity power factor, of which topologies have Buck, Boost, Buck-Boost, Cuk, and SEPIC. The Buck-type PFC can obtain an output voltage smaller than ac input voltage. However, only a power factor of 0.95 is met. The Boost structure attains better power factor correction feature but its output voltage is higher than ac-side voltage and power components withstand high voltage stresses. The Buck-Boost PFC can obtain an output voltage magnitude either larger or smaller than the input. Nevertheless, there is a polarity reversal on the output and an isolation driver for active switch is required. Among the Cuk, and SEPIC PFC topologies, the SEPIC type possesses better performance in total harmonics distortion (THD), efficiency and power factor correction. In this project I have designed a SEPIC converter to improve the input power factor.
  12. 12. 12 CHAPTER-2 BASIC PRINCIPLES OF THE PROJECT There are several ways to define power factor of a load. It is the cosine of the phase angel (Φ) between the load voltage and load current. Fig 2.1 It is also the ratio of the real power or true power to the apparent power of the load. Fig 2.2
  13. 13. 13
  14. 14. 14 2.1 NEED FOR POWER FACTOR CORRECTION: The power drawn by a load from AC Mains depends not only on mains Voltage and current but also on the power factor of the load. Power drawn by a single phase load, W=VICosΦ Where, V = Mains Voltage across the load I =Load current CosΦ=Power factor of the load i.e. the Cosine of the phase angle between the load voltage and load current. As our supply mains voltage is maintained constant, power drawn by the load only depends on the load current and power factor from the above equation , it is clear that for a particular load if the power falls, the load current increases which results in higher current from supply mains and higher line loss. Higher line loss reduces the transmission efficiency. Power electronic devices with front end rectifier which is widely used in industry takes high pulsating current from mains and produces severe current harmonics. This causes line pollution and reduces the power factor. Hence in order to meet the international standards we must prevent the line harmonics and improve the power factor. That is why there always a need of power factor correction and power factor correction circuit. 3.3 VARIOUS METHODS FOR POWER FACTOR CORRECTION: There are two types of power factor correction (PFC) circuits. One is passive power factor correction circuit and the other is active power factor correction circuit. Passive-type PFC is mainly constructed by inductors and capacitors. Low efficiency, heavy weight and large volume are its major disadvantages. Besides, power factor merely is improved to around 0.8. For active type, active switch, diode and energy-stored component are used to achieve near unity power factor, of which topologies have Buck, Boost, Buck-Boost, Cuk, ZETA, SEPIC and Fly back.
  15. 15. 15 2.2 REVIEW OF PFC CONTROL TECHNIQUES: 2.2.1 peak current control: The basic scheme of the peak current controller is shown in Fig.2, together with a typical input current waveform. As we can see, the switch is turned on at constant frequency by a clock signal, and is turned off when the sum of the positive ramp of the inductor current (i.e. the switch current) and an external ramp (compensating ramp) reaches the sinusoidal
  16. 16. 16 current reference. This reference is usually obtained by multiplying a scaled replica of the rectified line voltage v g times the output of the voltage error amplifier, which sets the current reference amplitude. In this way, the reference signal is naturally synchronized and always proportional to the line voltage, which is the condition to obtain unity power factor. As Fig.2 reveals, the converter operates in Continuous Inductor Current Mode (CICM); this means that devices current stress as well as input filter requirements are reduced. Moreover, with continuous input current, the diodes of the bridge can be slow devices (they operate at line frequency). On the other hand, the hard turn-off of the freewheeling diode increases losses and switching noise, calling for a fast device. Advantages and disadvantages of the solution are summarized hereafter. Advantages:  Constant switching frequency;  Only the switch current must be sensed and this can be accomplished by a current transformer, thus avoiding the losses due to the sensing resistor;  No need of current error amplifier and its compensation network;  Possibility of a true switch current limiting. Disadvantages:  Presence of sub harmonic oscillations at duty cycles greater than 50%, so a compensation ramp is needed;  Input current distortion which increases at high line voltages and light load and is worsened by the presence of the compensation ramp [4-5];  Control more sensitive to commutation noises 2.1.2 Average current control: Another control method, which allows a better input current waveform, is the average current control represented in Fig.2.3 [4,7-10]. Here the inductor current is sensed and filtered by a current error amplifier whose output drives a PWM modulator. In this way the inner current loop tends to minimize the error between the average input current ig and its reference. This latter is
  17. 17. 17 obtained in the same way as in the peak current control. The converter works in CICM, so the same considerations done with regard to the peak current control can be applied. Fig 2.3 Advantages:  Constant switching frequency;  No need of compensation ramp;  Control is less sensitive to commutation noises, due to current filtering;  Better input current waveforms than for the peak current control since, near the zero crossing of the line voltage, the duty cycle is close to one, so reducing the dead angle in the input current.
  18. 18. 18 Disadvantages:  A current error amplifier is needed and its conpensation network design must take into account the different converter operating points during the line cycle.  Inductor current must be sensed; 2.1.3 Hysteresis control: This type of control in which two sinusoidal current references IP,ref, IV,ref are generated, one for the peak and the other for the valley of the inductor current.According to this control technique, the switch is turned on when the inductor current goes below the lower reference IV,ref and is turned off when the inductor current goes above the upper reference IP,ref, giving rise to a variable frequency control .Also with this control technique the converter works in CICM. Fig 2.4
  19. 19. 19 Advantages:  No need of compensation ramp;  Low distorted input current waveforms. Disadvantages:  Variable switching frequency;  Inductor current must be sensed;  Control sensitive to commutation noises
  20. 20. 20 CHAPTER-3 HARMONIC DISTORTION AND POWER FACTOR CORRECTION 3.1 INTRODUCTION: One of the causes of low power factor is also related to the total harmonic distortion that is caused by the non linear loads like rectifiers or in other words when we draw current from the A.C mains , the line current that is drawn has some harmonic components in it. Due to this the net power factor of the resultant is very low due to which many problems arise. In case of the electrical power system, loads with low power factor draws more current than loads with high power factor for the same amount of useful power transferred. The higher currents increase the energy lost in the distribution system, and require larger wires and other equipment. Because of the costs of larger equipment and wasted energy, electrical utilities will usually charge a higher cost to industrial or commercial customers where there is a low power factor. Power factors below 1.0 require a utility to generate more than the minimum volt-amperes necessary to supply the real power (watts). This increases generation and transmission costs. For example, if the load power factor were as low as 0.7, the apparent power would be 1.4 times the real power used by the load. Line current in the circuit would also be 1.4 times the current required at 1.0 power factor, so the losses in the circuit would be doubled (since they are proportional to the square of the current). Alternatively all components of the system such as generators, conductors, transformers, and switchgear would be increased in size (and cost) to carry the extra current. 3.2 Some of the important definitions related to this topic are:  HARMONICS: A harmonic is a sinusoidal component of the periodic wave or quantity having a frequency that is an integral multiple of the fundamental frequency. An A.C periodic voltage or current can be represented by a fourier series of the pure sinusoidal waves which contains the basic or fundamental frequency and iots multiples called harmonics.
  21. 21. 21  HARMONIC DISTORTION: It refers to the distortion factor of the voltage or current waveform with respect to the pure sine wave.  DISTORTION FACTOR: It is the ratio of the root mean square of the harmonic component to the root mean square value of the fundamental quantity, expressed as a percentage of the fundamental.  TOTAL HARMONIC DISTORTION: This term is commonly used to define the voltage or the current distortion factor. 3.3 TOTAL HARMONIC DISTORTION: Harmonic distortion is divided into two classes, voltage distortion and current distortion. Since the voltage is common to all the loads in the system, any voltage distortion will result in a corresponding current distortion assuming the source impedance is very low. On the other hand current distortion results in voltage distortion only to the extent that the source impedance provides a common coupling impedance. The effects of the harmonic currenst from non linear loads are not widely understood. Due to the low impedance of most power systems, the power system can generally absorb significant amount of harmonic currents without converting then into unacceptable voltage distortion levels. 3.4 SOURCES OF NON UNITY POWER FACTOR AND HARMONIC DISTORTION: Linear reactive loads draw power from the reactive source which is at the same frequency of the power system. For the general linear passive network having voltage v=Vm sinwt and resulting current i= Im sin(wt+Ө) then the instantaneous power is defined by P=vi and the average value of power is P=0.5 Vm Im cos Ө. Here phase angle Ө defines the power factor in linear systems.
  22. 22. 22 Non linear loads generally do not cause reactive power to flow at the fundamental line frequency. They can however draw high RMS current and can add to distribution system losses for a given load. The non linear nature of these loads then draws non pure sine wave currents thus causing harmonics of the fundamental current to be present. Since harmonics distortion is caused by non linear elements connected to the power system, any device with non linear characteristics will cause harmonic distortion. Switched mode power supplies, uninterruptible power supplies and electronic light ballasts may have low power factor and can generate harmonic distortion. This is not because they are high frequency switching converters but rather because the input stage is usually a low cost rectifier/ capacitor filter. Fig 3.1 In this type of loads, causes current to be drawn from the AC line when the AC voltage is higher than the rectified voltage of the input filter capacitor. Fig 3.2
  23. 23. 23 The input filter capacitor is then charged to the peak of the line minus some voltage drop from semi from the semiconductors and internal and external source impedances. The non linear loads reduce power factor not because of the phase shift of the fundamental current with respect to the voltage but because higher RMS current caused by the pulsed nature of the input current. That is, the power is taken from the source only during a short period of time near the peak of the voltage wave. Since total power factor is defined as the real power divided by the product of the rms line voltage and current, the higher line current reduces power factor. Harmonic power factor is related to harmonic distortion and can be calculated by the equation : 𝑃𝑜𝑤𝑒𝑟 𝑓𝑎𝑐𝑡𝑜𝑟 = 1/(1 + 𝑇𝐻𝐷)2 The total harmonic distortion can be calculated by the following formula: THD= (𝐼1 2 + 𝐼2 2 + ⋯+ 𝐼 𝑛 2 )/𝑛 So more the total harmonic distortion, less will be the total power factor. 3.4EFFECT ON POWER FACTOR NETWORK AND CONNECTED EQUIPMENTS: The effects of harmonic distortion vary with the application. The degree to which the harmonics can be tolerated is determined by the susceptibility of the load to them. The presence of harmonic currents or voltages produces magnetic and electric fields that may impair the satisfactory performance of communication systems susceptible to the disturbance by virtue of their proximity. The disturbance is a function of both amplitude and frequency of the harmonic components. Metering and instrumentation are affected by the harmonic components. Induction disk devices such as watt hour meters normally see only the fundamental current, but erroneous operation resulting in positive and negative errors are possible with harmonic distortion present , depending on the type of meters and harmonics involved. Power systems are affected in various ways and the extent of the influence is application and configuration dependent. Three common configurations to power load are a) Single phase (120V AC or 220 V AC phase to neutral)
  24. 24. 24 b) Single phase loads connected phase to phase c) Three phase connected loads It is possible to eliminate harmonics in the design of the product using active or passive means and products are available with power factor correction . passive harmonic distortion correction filters are available also which remove the harmonics. This can be done by the inductor-capacitor filters. The drawback with this technique is they require large reactive components and the filters are tuned to filter a specific frequency ad hence become less effective as component values change over time.
  25. 25. 25 CHAPTER-4 BASIC SEPIC Converter 4.1 INTRODUCTION: Single-ended primary-inductor converter (SEPIC) is a type of DC-DC converter that allows the electrical potential (voltage) at its output to be greater than, less than, or equal to that at its input; the output of the SEPIC is controlled by the duty cycle of the control transistor. A SEPIC is similar to a traditional buck-boost converter, but has advantages of having non- inverted output (the output voltage is of the same polarity as the input voltage), the isolation between its input and output (provided by a capacitor in series), and true shutdown mode: when the switch is turned off, its output drops to 0 V. SEPICs are useful in applications in which a battery voltage can be above and below that of the regulator's intended output. For example, a single lithium ion battery typically discharges from 4.2 volts to 3 volts; if other components require 3.3 volts, then the SEPIC would be effective. Figure 4.1: Schematic of SEPIC
  26. 26. 26 4.2 Circuit operation: The schematic diagram for a basic SEPIC is shown in Figure2. 1. As with other switched mode power supplies (specifically DC-to-DC converters), the SEPIC exchanges energy between the capacitors and inductors in order to convert from one voltage to another. The amount of energy exchanged is controlled by switch S1, which is typically a transistor such as a MOSFET; MOSFETs offer much higher input impedance and lower voltage drop than bipolar junction transistors (BJTs), and do not require biasing resistors (as MOSFET switching is controlled by differences in voltage rather than a current, as with BJTs). A SEPIC is said to be in continuous-conduction mode ("continuous mode") if the current through the inductor 𝐿1 never falls to zero. During a SEPIC's steady-state operation, the average voltage across capacitor 𝐶1 (𝑉𝑐1) is equal to the input voltage (Vin). Because capacitor 𝐶1 blocks direct current (DC), the average current across it (𝐼𝑐1) is zero, making inductor 𝐿2 the only source of load current. Therefore, the average current through inductor 𝐿2 (𝐼𝐿2 ) is the same as the average load current and hence independent of the input voltage. Looking at average voltages, the following can be written Vin = 𝑉𝐿1 + 𝑉𝑐1 + 𝑉𝐿2 The average currents can be summed as follows: 𝐼 𝐷1 = 𝐼𝐿1 − 𝐼𝐿2 MODE-I
  27. 27. 27 When switch S1 is turned on, current 𝐼𝐿1 increases and the current 𝐼𝐿2increases in the negative direction. (Mathematically, it decreases due to arrow direction.) The energy to increase the current 𝐼𝐿1comes from the input source. Since 𝑆1 is a short while closed, and the instantaneous voltage 𝑉𝑐1 is approximately Vin, the voltage 𝑉𝐿2 is approximately − Vin. Therefore, the capacitor 𝐶1 supplies the energy to increase the magnitude of the current in𝐼𝐿2 and thus increase the energy stored in 𝐿2 . Figure 4.2: With S1 closed current increases through L1 (green) and C1 discharges Increasing current in L2 (red) 𝑆1 is on at t=0 𝑉𝐿1 = 𝑉𝑖𝑛 𝐿1 𝑑𝑖 𝐿1 𝑑𝑡 = 𝑉𝑖𝑛 𝑖 𝐿1 (t) = 𝑉𝑖𝑛 𝐿1 t + 𝐼 𝐿1 (0) At t = DT 𝑖 𝐿1 (t) = 𝐼𝐿1 (DT)
  28. 28. 28 ⇒ 𝐼𝐿1 (DT) = 𝑉𝑖𝑛 𝐿1 𝐷T + 𝐼𝐿1 (0) ………………(2.1) If we assume average voltage across 𝐶1 has no ripple then its average value is 𝑉𝑖𝑛 = 𝑉𝐿1 + 𝑉𝐶1 + 𝑉𝐿2 ⇒ 𝑉𝐶1 = 𝑉𝑖𝑛 ⇒ 𝑉𝐿2 = 𝑉𝐶1 = 𝑉𝑖𝑛 𝐿2 𝑑𝑖 𝐿2 𝑑𝑡 = 𝑉𝑖𝑛 𝑖 𝐿2 (t) = 𝑉𝑖𝑛 𝐿2 t + 𝐼𝐿2 (0) at t=DT 𝐼𝐿2 (DT) = 𝑉𝑖𝑛 𝐿2 𝐷T + 𝐼𝐿2 (0) ………………(2.2) MODE-II When switch 𝑆1 is turned off, the current 𝐼𝑐1becomes the same as the current 𝐼𝐿1, since inductors do not allow instantaneous changes in current. The current 𝐼𝐿2 will continue in the negative direction, in fact it never reverses direction. It can be seen from the diagram that a negative 𝐼𝐿2 will add to the current 𝐼𝐿1 to increase the current delivered to the load. Using Kirchoff's Current Law, it can be shown that 𝐼 𝐷1 = 𝐼𝑐1 − 𝐼𝐿2. It can then be concluded, that while 𝑆1 is off, power is delivered to the load from both 𝐿2 and 𝐿1., however 𝐶1 is being charged by 𝐿1 during this off cycle, and will in turn recharge 𝐿2during the on cycle.
  29. 29. 29 Figure 4.3: With S1 open current through L1 (green) and current through L2 (red) When switch is open at t = DT 𝑉𝐿1 = −𝑉0 (&𝑉𝐶1 𝑎𝑣𝑔 = 𝑉𝑖𝑛 ) 𝐿1 𝑑𝑖 𝐿1 𝑑𝑡 = −𝑉0 ⇒ 𝑖 𝐿1 (t) = −𝑉0 𝐿1 (t-DT) + 𝐼𝐿1 (DT) At t = T 𝑖 𝐿1 (t) = 𝐼𝐿1 (0) ⇒ 𝐼𝐿1 (0) = −𝑉0 𝐿1 (1 − 𝐷)T + 𝐼𝐿1 (DT) ………………(2.3) 𝑉𝐿2 = −𝑉0 𝐿2 𝑑𝑖 𝐿2 𝑑𝑡 = −𝑉0 𝑖 𝐿2 (t) = −𝑉0 𝐿2 (t-DT) + 𝐼𝐿2 (DT) at t = T 𝑖 𝐿2 (t) = 𝐼𝐿2 (0) 𝐼𝐿2 (0) = −𝑉0 𝐿2 (1 − 𝐷)T + 𝐼𝐿2 (DT) ………………(2.4)
  30. 30. 30 From equation (2.1) & (2.3) 𝐼𝐿1 ( 𝐷𝑇) − 𝐼𝐿1 (0) = 𝑉𝑖𝑛 𝐿1 𝐷T 𝐼𝐿1 ( 𝐷𝑇) − 𝐼𝐿1 (0) = 𝑉0 𝐿1 (1 − 𝐷)T Equating the above equation 𝑉0 𝑉𝑖𝑛 = 𝐷 1−𝐷 or from equation (2.2) & (2.4) 𝐼𝐿2 ( 𝐷𝑇) − 𝐼𝐿2 (0) = 𝑉𝑖𝑛 𝐿2 𝐷T 𝐼𝐿2 ( 𝐷𝑇) − 𝐼𝐿2 (0) = 𝑉0 𝐿2 (1 − 𝐷)T Equating the above equation 𝑉0 𝑉𝑖𝑛 = 𝐷 1−𝐷 Average input current is same as average inductor current 𝐿1 as average current across the capacitor 𝑖 𝑐1 is zero. 𝐼𝑖𝑛𝑎𝑣𝑔 = 1 𝑇 [𝑇 × 𝐼𝐿1 (0)+ 1 2 × 𝑇 × (𝐼𝐿1 ( 𝐷𝑇) − 𝐼𝐿1 (0))] 𝐼𝑖𝑛𝑎𝑣𝑔 = 𝐼 𝐿1 ( 𝐷𝑇)+𝐼 𝐿1 (0) 2 Average output current is same as average inductor current 𝐿2 𝐼0 = 1 2 [𝐼𝐿2 ( 𝐷𝑇)+ 𝐼𝐿2 (0)]
  31. 31. 31 Average input power is same as average output power 𝑃0 = 𝑃𝑖𝑛 𝑉0 𝐼0 =𝑉𝑖𝑛 𝐼𝑖𝑛 ⇒ 𝐼𝑖𝑛 𝐼0 = 𝐷 1−𝐷 From equation (2.1) & (2.5) 𝐼𝐿1 ( 𝐷𝑇) − 𝐼𝐿1 (0) = 𝑉𝑖𝑛 𝐿1 𝐷T 𝐼𝐿1 ( 𝐷𝑇) + 𝐼𝐿1 (0) = 2𝐼𝑖𝑛 = 2 𝐷 𝐼0 1−𝐷 = 2𝐷 𝑉0 𝑅(1−𝐷) = 2𝑉𝑖𝑛 𝐷2 𝑅(1−𝐷2 ) Solving 𝐼𝐿1 ( 𝐷𝑇) = [ 𝐷2 (1−𝐷)2𝑅 + 𝐷𝑇 2𝐿1 ] 𝑉𝑖𝑛 𝐼𝐿1 (0) = [ 𝐷2 (1−𝐷)2𝑅 − 𝐷𝑇 2𝐿1 ] 𝑉𝑖𝑛 To calculate 𝐿 𝑐𝑟𝑖𝑡 𝐼𝐿1 (0) = 0 𝐿1𝑐𝑟𝑖𝑡 = (1−𝐷)2 𝑅𝑇 2𝐷 𝐼𝐿2 ( 𝐷𝑇) + 𝐼𝐿2 (0) = 2𝐼0 = 2 𝑉0 𝑅 = 2𝑉𝑖𝑛 𝐷 (1−𝐷) 𝐼𝐿2 ( 𝐷𝑇) − 𝐼𝐿2 (0) = 𝑉𝑖𝑛 𝐿2 𝐷T Solving 𝐼𝐿2 ( 𝐷𝑇) = 𝑉𝑖𝑛 [ 𝐷 𝑅(1−𝐷) + 𝐷𝑇 2𝐿2 ] 𝐼𝐿2 (0) = 𝑉𝑖𝑛 [ 𝐷 𝑅(1−𝐷) − 𝐷𝑇 2𝐿2 ]
  32. 32. 32 To find 𝐿2𝑐𝑟𝑖𝑡 𝐼𝐿2 (0)= 0 𝐿2𝑐𝑟𝑖𝑡 = (1−𝐷) 𝑅𝑇 2 Voltage and current across 𝐶1 are given by: y = −∆𝐼 𝐿2 𝐷𝑇 𝑡 − 𝐼 𝐿2 (0) ∆𝐼𝐿2 = 𝐼𝐿2 ( 𝐷𝑇) − 𝐼𝐿2 (0) = inductor current ripple 𝑣𝑐1 ( 𝑡) = 1 𝑐1 ∫ 𝑦𝑑𝑡 + 𝑡 0 𝑣𝑐1 (0) = 1 𝑐1 ∫ [ −∆𝐼 𝐿2 𝐷𝑇 𝑡 − 𝐼𝐿2 (0)] 𝑑𝑡 + 𝑡 0 𝑣𝑐1 (0) = −1 𝑐1 [ ∆𝐼 𝐿2 𝐷𝑇 𝑡2 2 + 𝐼𝐿2 (0) 𝑡] 0 𝑡 + 𝑣𝑐1 (0) at t = DT 𝑣𝑐1 ( 𝑡) = 𝑣𝑐1 ( 𝐷𝑇) 𝑣𝑐1 ( 𝐷𝑇) = −1 𝑐1 [ ∆𝐼 𝐿2 𝐷𝑇 ( 𝐷𝑇)2 2 + 𝐼𝐿2 (0) 𝐷𝑇] 0 𝑡 + 𝑣𝑐1 (0) 𝑣𝑐1 (0)− 𝑣𝑐1 ( 𝐷𝑇) = ∆ 𝑉𝑐1 = 1 𝑐1 𝐷𝑇 [ 𝐼 𝐿2 ( 𝐷𝑇)− 𝐼 𝐿2 (0) 2 + 𝐼𝐿2 (0) ] ∆ 𝑉𝑐1 = 𝐷𝑇 𝐶1 𝐼0 ∆ 𝑉𝑐1 = 𝐷𝑇 𝐶1 𝑉0 𝑅 ⇒ ∆ 𝑉𝑐1 𝑉0 = 𝐷𝑇 𝑅𝐶1
  33. 33. 33 Voltage and current across 𝐶2 is 𝑖 𝑐2 = −𝐼0 0 < t < DT 𝑖 𝑐2 = 𝑖 𝐿1 + 𝑖 𝐿2 −𝐼0 DT < t < T 𝑣𝑐2 ( 𝑡) = 1 𝑐2 ∫ 𝑖 𝑐2 𝑡 −∞ ( 𝑡) 𝑑𝑡 𝑣𝑐2 ( 𝑡) = 1 𝑐2 ∫ 𝑖 𝑐2 ( 𝑡) 𝑡 0 𝑑𝑡 + 𝑣𝑐2 (0) = 1 𝑐2 −𝐼0 𝑡 + 𝑣𝑐2 (0) at t= DT 𝑣𝑐2 ( 𝑡) = 𝑣𝑐2 ( 𝐷𝑇) ∆𝑉𝐶2 = 𝑣𝑐2 (0)− 𝑣𝑐2 ( 𝐷𝑇) = 𝐼0 𝐶2 𝐷𝑇 = 𝑉0 𝐷𝑇 𝑅𝐶2 ⇒ ∆ 𝑉𝑐2 𝑉0 = 𝐷𝑇 𝑅𝐶2 → output voltage ripple. Because the potential (voltage) across capacitor 𝐶1 may reverse direction every cycle, a non-polarized capacitor should be used. However, a polarized tantalum or electrolytic capacitor may be used in some cases, because the potential (voltage) across capacitor 𝐶1will not change unless the switch is closed long enough for a half cycle of resonance with inductor 𝐿2, and by this time the current in inductor 𝐿1 could be quite large.The capacitor 𝐶𝐼𝑁 is required to reduce the effects of the parasitic inductance and internal resistance of the power supply. The boost/buck capabilities of the SEPIC are possible because of capacitor 𝐶1 and inductor 𝐿2. Inductor 𝐿1 and switch 𝑆1create a standard boost converter, which generate a voltage (𝑉𝑠1) that is higher than 𝑉𝑖𝑛, whose magnitude is determined by the duty cycle of the switch S1. Since the average voltage across 𝐶1 is 𝑉𝑖𝑛, the output voltage (𝑉0) is 𝑉𝑠1 - 𝑉𝑖𝑛. If 𝑉𝑠1 is less than double 𝑉𝑖𝑛, thenthe output voltage will be less than the input voltage. If 𝑉𝑠1
  34. 34. 34 is greater than double 𝑉𝑖𝑛, then the output voltage will be greater than the input voltage. CHAPTER-5 PRACTICAL DESIGN OF A SEPIC POWER CORRECTOR 5.1 Introduction: Compared to conventional buck or boost converters, SEPIC topology allows a low current ripple at the input for a relatively low level of the DC-bus voltage. Consequently, the high frequency filter needed at the AC-side of a buck converter is avoided, and the high voltage stresses applied on the switches are significantly reduced with respect to the boost converter. The converter is integrated as a power factor correction circuit at the DC-end of a single- phase diode bridge. Based on the averaged model of the converter, a Pulse-Width- Modulated (PWM) control algorithm is developed in order to ensure a unity power factor at the AC- source side and a regulated voltage at the DC-load side. High power quality achievement is increasingly required for the power supply systems in order to comply with the international standards. For this purpose, and especially for single-phase low power applications, switch-mode DC-DC converters, commonly known as Power Factor Correction (PFC) circuits, are designed in order to ensure a high power factor at the mains side, and to emulate a purely resistive operation of the diode-bridge-based frontend rectifier.
  35. 35. 35 5.1.1 Buck-Boost Converters  There are some typical applications, which require buck and boost operations in the same converter, therefore, an additional classification of buck–boost converter is made.  It is a combination of diode rectifier with buck–boost dc–dc converters.  Since buck–boost converters are developed in non-isolated and isolated topologies, a large number of configurations is also reported, such as a combination of buck and boost or vice versa, buck–boost, SEPIC, Cuk, etc. Fig.5.1(a) Basic buck-boost type PFC circuit  In the basic topology given in Fig. 3.1(a), shown above the inverted DC voltage delivered at the output can vary theoretically between zero and an infinite value.  Similar to buck converter the presence of the switch in series with the DC source induces a commutated current at the input and a discontinuous current mode operation of the diode bridge when the circuit is used for PFC.  A high frequency shunt filter is to be inserted between the source and the diode bridge. In order to avoid such problem, the configuration of Fig.3.1.(b)shown below that consists of a series connection of a Buck and a Boost converters can be considered.  However, a smooth input current is obtained at the expense of a twice number of switches.
  36. 36. 36 Fig.5.1 (b) Series connected buck-boost type PFC circuit  A more convenient solution that ensures a smooth input current by using a single switch is shown either in Fig. 5.1(c) or Fig.5.1(d).  The Cuk converter (Fig.5.1(c)) and the Single Ended Primary Inductance Converter (SEPIC) (Fig. 5.1(d))differ from each other at the output stage, where the free-wheel diode and the output inductor are permutated, and the polarity of the output voltage is inverted.
  37. 37. 37 Fig.5.1(c) Cuk topology  In case of buck-boost, Cuk there is a polarity reversal on the output and an isolation driver for active switch is required.  Among buck-boost, Cuk and Sepic, the Sepic type possesses better performance in total harmonic distortion (THD), efficiency and power factor correction. Fig.5.1(d) Sepic topology These IPQCs are extensively used in SMPSs, railway signalling, battery chargers, UPSs; small-rating brushless ac motor drives, etc. 5.2 Operation Sequences and Switching-Function-Based Model:
  38. 38. 38 The operating sequences of the SEPIC converter in the most general case of a Discontinuous Current Mode (DCM) are given in Fig. 3.2. The circuit has three possible configurations, depending on the state of the main switch Q and diode D. The third configuration, where both Q and D are at their off-state, appears only when the current (iL1 + iL2 )crosses zero, Otherwise, i.e. if the condition (iL1 + iL2 )> 0 always stands, only the first two configurations exit in a switching period. In that case, the converter is said to operate in a Continuous Current Mode (CCM), and the diode D will always conducts whenever the switch Q is turned-off. : Fig. 5.2: Operating sequences: electrical configuration when Q is turned-on (a), when Q is turned-off while D in on (b), when Q and D arc both off(c). Following these considerations, we may describe analytically the operation of the converter in the more general case by writing the equations (5.1) L1 diL1 dt =sQ ∙ vin + sQ̅̅̅ ∙ θ(iL1 + iL2 ) ∙ (vin − vc − v0 ) + sQ̅̅̅ ∙ θ(iL1 + iL2 )̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅ ∙ L1 L1 +L2 ∙ (vin − vc )
  39. 39. 39 L2 diL2 dt =sQ ∙ vc − sQ̅̅̅ ∙ θ(iL1 + iL2 ) ∙ v0 − sQ̅̅̅ ∙ θ(iL1 + iL2 )̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅ ∙ L2 L1+L2 ∙ (vin − vc ) C dvc dt = sQ̅̅̅ ∙ iL1 − sQ ∙ iL2 (5.1) C0 dv0 dt = sQ̅̅̅ ∙ θ(iL1 + iL2 ) ∙ (iL1 + iL2 ) − i0 where sQ denotes the switching function of switch Q, defined as: sQ ={ 0 if Qis turned− off 1 if Qis turned − on (5.2) θ is the threshold function defined as: θ(z) = { 0 if z ≤ 0 1 if z > 0 (5.3) sQ̅̅̅ and θ̅ their respective complements. Note that in CCM the θ(iL1 + iL2 ) term is always equal to unity, and the mode(1) becomes simpler. Moreover, the switching frequency of switch Q is either time-varying (if a hysteresis flip-flop controller is used for the line current shaping) or fixed (if a saw-tooth-carrier-based pulse-width modulator is used along with a continuous current controller). However, it will be assumed in both cases, especially as far as the calculation of the reactive components 𝐿1, 𝐿2, C and 𝐶0. 3.3 Steady-State Operation for a Unity Power Factor Condition: In a Unity Power Factor (UPF) operating condition, the converter and its control circuit emulate a purely resistive load. The line current has, in this case, a sine-wave shape, in phase with the AC source voltage. The DC current 𝑖 𝐿1delivered by the diode bridge is a rectified sine-wave signal and, thus, has the following expression: iL1 ∗ (t) = Is√2⃒sin ω0 t⃒ (5.4)
  40. 40. 40 Where Is represents the line current RMS-value and ω0the angular frequency of the mains source. The asterisk (*) denotes that we are placed in the desired steady-state operating regime. In addition, by neglecting the voltage ripple at the capacitors (which is justified by choosing high enough values for C and𝐶0 ) we may aIso write: v0 ∗(t) ≅ v0 ∗ (5.5) and: vc ∗(t) ≅ vc ∗ = 〈vin〉 = 2√2 π Vs (5.6) Where V0 ∗ and VC ∗ designate respectively the static values of 𝑣0 ∗( 𝑡)and 𝑉𝑐 ∗ ( 𝑡). In (5.6) vin, is the voltage at the DC-side of the diode rectifier. It is expressed by: vin(t) = Vs√2⃒sin ω0 t⃒ (5.7) Where Vs denotes the mains voltage RMS-value. Moreover, applying the state-space averaging technique in CCM mode (it is assumed here that the condition (iL1 + iL2 ) > 0 always stands; this assumption will be justified later by a suitable choice of inductor L2) yields the following low-frequency model of the converter, given by(5.8) L1 diL1 dt = vc − (1 − d) ∙ (vc + v0) L2 diL2 dt = 𝑑 ∙ vc − (1 − d) ∙ v0 (5.8) C dvc dt = (1 − d) ∙ iL1 − 𝑑iL2 C0 dv0 dt = (1 − d) ∙ (iL1 + iL2 ) − i0 Where d(t) is the duty cycle of the switch Q. Replacing iL1, v0, vc 𝑎𝑛𝑑 vcby their desired expressions given respectively in (5.4), (5.5), (5.6) and (5.7) into the system (5.8) yields expressions (5.9) and (5.l0)
  41. 41. 41 d∗ ≅ 1 − ε Vs√2 sin(2ω0t)− L1ω0Is√2 cos(ω0t) V0 ∗ +VC ∗ (5.9) iL2 ∗ (t) = I0 ∗ + 2√2 π ∑ Vs k(4k2 −1) L2ω0 ∞ k=1 sin(2kω0t) − L1 L2 ∙ 2Is 4k2−1 cos(2kω0t) (5.10) Where ϵ = { +1 for 2kπ < ω0 𝑡 < (2k + 1)π −1 for (2k + 1)π < ω0 𝑡 < 2(2k + 1)π, k ϵ Z (5.11) and I0 ∗ is the desired steady-state value of the DC load current i0. in the derivation of expression (10), the Fourier series development of εsin(ω0 𝑡) and ε cosω0 𝑡 has been used. ε ∙sin(ω0 𝑡) = 2 π − 4 π ∑ 1 4k2 −1 ∞ k=1 cos(2kω0t) (5.12) ε ∙ cosω0 𝑡 = 8 π ∑ 1 4k2−1 ∞ k=1 sin(2kω0t) (5.13) Considering that we have in practice L1ω0Is ≪ Vs, and that: k(4k2 − 1) ≫ 3 for k ≥ 2 (5.14) we may write approximately: iL2 ∗ (t) ≅ I0 ∗ + 2√2 Vs 3π L2ω0 sin(2ω0t) (5.15) and it appears clearly that, for an increased value of L2 , the validity of the assumption (iL1 ∗ (t)+ iL2 ∗ (t))> 0 also increases, and the converter tends to operate in CCM. Furthermore, the low-frequency expressions of and vc ∗ and v0 ∗ are given approximately by expressions (5.16) and (5.17) vc ∗(t) ≅ Vc ∗ + Vc ∗ 90L2Cω0 2 ∙ 15V0 ∗ −VC ∗ V0 ∗ +VC ∗ cos(2ω0t) − I0 ∗ 6Cω0 ∙ 3V0 ∗ +2VC ∗ V0 ∗ +VC ∗ sin(2ω0t) (5.16)
  42. 42. 42 v0 ∗(t) ≅ V0 ∗ − 8Vc ∗ 45L2C0ω0 2 ∙ VC ∗ V0 ∗ +VC ∗ cos(2ω0t) − I0 ∗ 6C0ω0 ∙ 3V0 ∗ +2VC ∗ V0 ∗ +VC ∗ sin(2ω0t) (5.17) 3.4 Reactive Components Settings: In order to choose the inductor, we have to evaluate first the current ripple at the switching frequency in each inductor. For inductor L1, the current ripple is given in fig.5.3 fig.5.3 ∆iL1,HF(t) = [tan(β) − tan(α)] ∙ d∗ (t) fs(t) (5.18) with: tan(α) = 𝑑 𝑑𝑡 (iL1 ∗ ) tan(α) = vin L1 and 𝑓𝑠( 𝑡) is the switching frequency. Combining expressions (5.4),(5.7) and (5.9) with (5.18) we get equation(5.19). ∆iL1,HF( 𝑡)
  43. 43. 43 ≅ 𝜀∙⃒Vs√2 sin(2ω0t)− L1ω0Is√2 cos(ω0 t) ⃒∙ ⃒V0 ∗ +VC ∗ −εVs√2 sin(2ω0t)+εL1ω0Is√2 cos(ω0t)⃒ L1∙𝑓𝑠( 𝑡)∙(V0 ∗ +VC ∗ ) (5.19) The maximum value of the product [𝑓𝑠( 𝑡) ∙ ∆iL1,HF(t)] appears when: 𝑣𝑖𝑛( 𝑡) − L1 d dt [iL1 ∗ (t)] = V0 ∗ +VC ∗ 2 (5.20) In this case we gate: [𝑓𝑠( 𝑡) ∙ ∆iL1,HF(t)] max = V0 ∗ +VC ∗ 4L1 (5.21) which must be lower than [𝑓𝑠( 𝑡) ∙ ∆iL1,HF(t)] admissible . This leads to the setting of L1: L1 > V0 ∗ +VC ∗ 4[ 𝑓𝑠( 𝑡)∙ ∆iL1,HF (t)] admissible ≜ L1,min (5.22) For the setting of inductor L2 , we refer to expression (5.15). The required value of L2 must guarantee a CCM operation of the converter, i.e. [iL1 ∗ (t) + iL2 ∗ (t)] > 0, ∀ t. Using expressions (5.4) and (5.15), a sufficient condition for CCM is to have: L2 > VC ∗ 3ω0 I0 ∗ ≜ L2,min (5.23) Concerning the capacitors C and, C0their determination is based on equations (5.16) and (5.17) respectively. For L2 ≅ L2,min , we obtain after some mathematical manipulations: C > 0.66I0 ∗ ω0(∆𝑣 𝑐)admissible √1 + ( 1.91V0 ∗ +0.21VC ∗ V0 ∗ +VC ∗ ) 2 ≜ Cmin (5.24)
  44. 44. 44 and: C0 > 0.95I0 ∗ ω0 (∆𝑣0)admissible √1 + ( 0.31V0 ∗ −0.86VC ∗ V0 ∗ +VC ∗ ) 2 ≜ C0,min (5.25) 3.5 Control System Design: The control circuit is given in Fig. 5.4. It consists of two successive loops: the inner or current one is designed to ensure the wave-shaping of the DC input current iL1and, consequently, the improvement of the input power factor, while the outer or voltage loop is aimed to regulate the DC load voltage and to stabilize it around a desired set-point. The inner controller is chosen to be a hysteresis flip-flop with a 0.4A width, and the outer regulator is a linear Proportional-integral (PI) one represented by the transfer function Hv(s), 𝐾𝑖 and 𝐾𝑣 are scaIing gains. To ensure high stability of the control system, the outer loop is designed to be enough slower than the inner one. The input to the PI controller is the difference of the actual output voltage and the reference voltage as set by the user. As this difference changes , required change is carried out by the PI controller which helps to set the =output
  45. 45. 45 Fig 5.4 Numerical values are given as Mains voltage RMS-value 𝑉𝑠 = 120V Rated load power 𝑃0 = 1kW Voltage reference 𝑉𝑜 ∗ = 100V Main frequency 𝑓𝑜 = 60Hz DC inductors 𝐿1= 1mH, 𝐿2 = 10mH Series inductors’ resistors 𝑅 𝐿1=0.1Ω, 𝑅 𝐿2=0.1Ω DC Capacitors C=10mF, 𝐶0=10mF Scaling Gains 𝐾𝑖=1Ω, 𝐾𝑣=1/1008 Hysteresis width for current regulator h=0.4A
  46. 46. 46 DC voltage regulator 𝐻 𝑣(s)=(4s+0.1)/3s Voltage Filter 𝐹𝑣(s)=300/(𝑠2 +40.426s+900) CHAPTER-6 SOFTWARE DEVELOPMENT 6.1 SOFTWARE SIMULATION: Software Simulation is based on the process of imitating a real phenomenon with a of mathematical formulas. It is, essentially, a program that allows the user to observe an operation through simulation without actually performing that operation. Simulation software is used widely to design equipment so that the final product will be as close to design specs as possible without expensive in process modification. Electronics simulation software utilizes mathematical models to replicate the behavior of an actual electronic device or circuit. Essentially, it is a software program that converts a computer into a fully functioning electronics laboratory.
  47. 47. 47 Electronics simulators such as Circuit Logix integrate a schematic editor MATLAB simulator and on-screen waveforms and make “what-if” scenarios easy and instant. By simulating a circuit’s behavior before actually building it greatly improves efficiency and provides insights into the behavior and stability of electronics circuit designs. Most simulators use a MATLAB engine that simulates analog, digital and mixed A/D circuits for exceptional power and accuracy. They also typically contain extensive model and device libraries. While these simulators typically have printed circuit board (PCB) export capabilities, they are not essential for design and testing of circuits, which is the primary application of electronic circuit simulation.The software simulation of the proposed PFC was one of the objective our project and we have tried our level best to achieve the correct simulation result. 6.1.1 Simulation Model of ideal SEPIC converter
  48. 48. 48 Fig 6.1 D= 0.52, 𝑉𝑖𝑛 = 112 𝑉 , 𝑓𝑠=110 kHz R=12 Ω , 𝐿1 = 𝐿2 = 50µ𝐻 , 𝐶1 = 𝐶2 =147µ𝐹 Output :
  49. 49. 49 Fig 6.2 Fig 6.3 6.1.2 Simulation of SEPIC (open loop) PFC converter:
  50. 50. 50 Fig 6.4 In case of open loop control for power factor correction after a AC to DC converter we connect a sepic converter that is utilising the active power factor correction method to bring the reduced power factor near to unity and to reduce the net T.H.D ( total harmonic distortion) of the input line current. In case of open loop control as designed above we use hysteresis control. In this type of control two sinusoidal current references Ipref and Ivref are generated, one for the peak and other for the valley of the inductor current. According to the hysteresis technique, the switch is turned on when the inductor current goes below the lower reference Ivref and is turned off when the inductor current goes above the upper reference Ipref giving rise to variable frequency control. Advantage:  It gives rise to low distorted input current waveforms. Disadvantage:
  51. 51. 51  It has variable switching frequency.  inductor current must be sensed Output: a> Input current and voltage: Fig 6.5 b> Output voltage:
  52. 52. 52 Fig 6.6 c> FFT analysis: Fig 6.7
  53. 53. 53 The main problem that arises in case of open loop control is that when we change the constant given at the input side (0.38) in this case, the input current waveform as well as the value of the output current changes. So to avoid this we have designed a closed loop control for power factor correction. 6.1.3 Simulation of SEPIC (closed loop) PFC converter: In case of closed loop control here we use PI controller as the controller feedback. The output voltage is sensed and is compared with a reference voltage. The error from among the two is fed to a PI controller which acts as an error amplifier here. The PI controller in voltage feedback is slow in action because any change in output voltage is sensed and compared with the reference voltage. The basic purpose of closed loop control is to keep the output voltage regulated irrespective of variation in load, in input supply or in the reference set point. Fig 6.9
  54. 54. 54 Output: a> Output voltage: Fig 6.10 b> Output current: Fig 6.11
  55. 55. 55 c> Input current and voltage: Fig 6.12 d> FFT analysis: Fig 6.13
  56. 56. 56 6.1.4 closed loop control with load disturbance: Closed loop control is designed to get a regulated output. Or in other words if we change any of the parameters of the circuit then the output voltage remains the same. We have designed some of the circuits to ensure it. Fig 6.14 In the previous closed loop circuit, the output resistance is taken to be 10 ohm. So to check the load disturbance factor, we have connected another resistance of value 10 ohm in parallel to it, with a switch connected to it that is controlled by a pulse generator. Initially when there is no pulse, the switch is open and thus the output resistance is 10 ohms. After the given time period when a pulse is given to the switch, it closes and so another parallel resistance of value 10 ohms comes to the picture. so the overall resistance becomes 5 ohms. The change is fed to the PI controller which readjusts itself and thus the output is maintained at 100 volts.
  57. 57. 57 Output: a> Input voltage and current: Fig 6.15
  58. 58. 58 b> Output voltage: Fig 6.16 c> FFT analysis: Fig 6.17
  59. 59. 59 6.1.5 closed loop control with reference change: Previously in case of closed loop , we have considered a reference value of 4.268 which we have compared with the voltage across the load and the error has been fed into the PI controller. So basically, we conclude that the output voltage required (i.e. 100 V) is set by this reference. So now if we change this reference, the output voltage also changes therewith. Fig 6.18 In case of this circuit, the reference given before the PI controller is changes to a unit step signal where the initial value is set at 100 V and after a time difference of 2 sec the value is change to 120 V. So the output voltage changes according to this reference.
  60. 60. 60 Output: a> Input voltage and current: Fig 6.19
  61. 61. 61 b> Output voltage : Fig 6.20 c> FFT analysis: Fig 6.21
  62. 62. 62 6.1.6 closed loop control with supply change: Fig 6.22 In case of this circuit, two input supplies of different values are connected to the circuit. The two supplies have two switches connected to them. These switches are provided pulses with the help of a step. When the step is high, the supply with RMS value 100 V is activated. At the same time, the other switch is connected to the unit step through a NOT gate, which means that if the first switch is ON, the second will be OFF. So at a time only one supply will be activated. Initially the value of unit step is LOW. So the first supply will be OFF, and after passing through the NOT gate, the second supply is ON. After a time duration of 2 seconds, a high input is given to the first switch, making the first supply ON and the second OFF.
  63. 63. 63 Output: a> Input current and voltage: Fig 6.23 b> Output voltage: Fig 6.24
  64. 64. 64 c> FFT analysis: Fig 6.25
  65. 65. 65 6.2 AVERAGE CURRENT CONTROLFOR POWER FACTOR CORRECTION: Average current control method for power factor correction is a control method which allows a better current input waveform. It is one of the other methods for power factor correction which we have implemented here. Fig 6.26 In case of this circuit, the inductor current is sensed and filtered by a current error amplifier whose output drives a PWM modulator. In this way the inner current loop tends to minimise the error between the average input current Ig and its reference. Fig 6.27
  66. 66. 66 The converter works in CICM (continuous inductor current mode). Advantages: The advantages under this technique are: 1> Constant switching frequency. 2> No need of compensation Ramp. 3> Control is less sensitive to commutation noises, due to current filtering. 4> Better input current waveforms . Disadvantages: The disadvantages of this technique are listed below: 1> In this case the inductor current must be sensed. 2> A current error amplifier is needed .
  67. 67. 67 6.2.1 Simulation of average current control (open loop): Fig 6.28
  68. 68. 68 Output: a> Input voltage and current: fig 6.29 b> Output voltage: fig 6.30
  69. 69. 69 c> FFT analysis: Fig 6.31
  70. 70. 70 6.2.2 Simulation of average current control (closed loop): Similar to that of the hysteresis current control technique, in case of average current control technique closed loop control is employed for regulated output voltage. Fig 6.32
  71. 71. 71 Output: a> Input voltage and current: Fig 6.33 b> Output voltage: Fig 6.34
  72. 72. 72 c> FFT analysis: Fig 6.35
  73. 73. 73 6.3 POWER FACTOR CORRECTION USING SEPIC CONVERTER PROVIDED WITH THREE PHASE SUPPLY: Previously we have implemented the SEPIC converter for power factor correction with single phase supply. Here we have implemented the same SEPIC converter, but with a three phase supply. Fig 6.36 For the three phase supply: 1. Phase to phase RMS voltage=200 V 2. Phase angle of phase A = 0 degrees 3. 3 phase short circuit level at base voltage (VA)=800e3 4. Base voltage(Vrms ph-ph)=200 5. X/R ratio=7
  74. 74. 74 Output: a> Input voltage and current: Fig 6.37 b> Output voltage: Fig 6.38
  75. 75. 75 c> FFT analysis: Fig 6.39
  76. 76. 76 CHAPTER 7 FUZZY CONTROL IMPLEMENTATION FOR POWER FACTOR CORRECTION 7.1 Fuzzy Logic Controller(FLC): In mid 1960’s, a new theory called “Fuzzy Logic” or fuzzy set theory was propounded by L.A.Zadeh. He the originator of this theory, argued that nost of the human thinking id fuzzy or imprecise in nature, and therefore, Boolean logic which is represented by crisp 0 and 1cannot adequately emulated the thinking process. In recent years, fuzzy logic has emerged as an important tool to characterise and control a system whose model is not known or is ill defined. The advantages of fuzzy logic controller are given below:  Fuzzy controllers are more robust than PID controllers because they cover a much wider range of operating conditions that PID can, and can operate with noise and disturbances of different nature.  Developing a fuzzy controller is cheaper than developing a model based or other controller to do the same thing,  Fuzzy controller are customisable, since it is easier to understand and modify their rules, which not only use a human operator’s strategy but also are expressed in natural linguistic terms.  It is easy to learn how fuzzy controllers operate and how to design and apply them in concrete applications. 7.1.1 FUZZY LOGIC PRINCIPLE: In fuzzy set theory a particular object has a degree of membership in a given set that may be anywhere in the range of 0 to 1. This property allows the fuzzy logic to deal with situations in a fairly natural way. Although Fuzzy logic deals with imprecise information, it is based on sound quantitative mathematical theory. Figure 4.1 shows the basic configuration of FLC.
  77. 77. 77 Fig 7.1 The classical design scheme contains the following steps:  Define the input and control variables-determine which states of the process shall be observed and which control actions are to be considered.  Define the condition interface-fix the way in which observations of the processes are expressed as fuzzy sets.  Design the rule base-determine which rules are to be applied under which conditions.  Design the computational unit – supply algorithms to perform fuzzy computations. Those will generally lead to fuzzy outputs.  Determine rules according to which fuzzy control statements can be transformed into crisp control actions. 7.1.2 Fuzzy Membership functions The shape of membership functions can also be trapezoidal or Gaussian etc depending on the applications and can be symmetrical or asymmetrical. In fuzzy set terminology the possible values that voltage error can assume are named universe of discourse and the fuzzy sets (characterised by membership functions) cover the whole universe of discourse. A fuzzy variable has values, which are expressed by natural English language. For example, the voltage error of a power converter as indicated in figure 4.3 can be defined by linguistic
  78. 78. 78 variables (fuzzy sets or fuzzy subsets) negative big (NB), negative medium (NM), negative small(NS), zero( ZE), positive small(PS), positive medium (PM) where each variable is defined by a gradually varying triangular membership function. 7.1.3 Fuzzification Seven fuzzy levels or sets are chosen and defined by the following library of fuzzy set value for the error e and change in error de The number of fuzzy levels in not fixed and depends on the input resolution needed in an application. The larger the number of fuzzy levels, the higher is the input resolution. The inputs are not quantizes in the classical sense that each input is assigned to exactly ne level. Instead, each input is assigned a “membership function” µ to each fuzzy set. The fuzzy set controller implemented here uses triangular fuzzy set values. Trapezoidal or bell shaped sets may also be employed. The triangular functions are used to reduce complexity in calculations. Hence, the fuzzy representation of quantized values of e and de are the fuzzy sets and degree to which they belong to each fuzzy set. 7.1.4 Fuzzy Control rules and Composition Fuzzy control is described by a set of IF.....THEN.....rules(called implications), where the rule has the following structure: IF i is A AND B is j THEN y is C. Where i,j,y are the fuzzy variables and A,B,C are the fuzzy sets in the universe of discourses X,Y,Z respectively. In general the rule is in n dimensional where n is the number of variables included in the rule. The individual rules are combined to give an overall rule R which is computed by the union operator as follows: R=R1 U R2 U R3 .....U Rn For the given rule base of a control system, the fuzzy controller determines the rules to be fired for the specific input and then computes the effective control action. The compensation method is one by which such control output can be generated. The most commonly used composition method is MAX-MIN which is illustrated in figure 4.4.
  79. 79. 79 Fig 7.2 7.1.5 Defuzzification The most preferred interference method is Mamdani mini fuzzy Interference method. The interference result of each rule using Mamdani mini fuzzy implication consists of 2 parts, the weighing factor wi of the individual rule and degree of output Ci according to the control table. Therefore the inferred output of each rule using Mamdani mini fuzzy implication is written as: Yi=min {µinput(i) , µinput(j)}Ci Yi=wiCi When yi denotes the fuzzy representation of output inferred by the ith rule. Since the output result is linguistic result, a defuzzification operation is performed next to obtain a crisp result. The crisp value for the final output is calculated using the centre of gravity method. The product of centroid Ci(obtained from control rules) and the weighting factor wi gives the contribution of ith inference result to the crisp value of the final output. The resultant output can therefore be represented as Final output= ∑ 𝑤𝑖 𝑚𝑖4 𝑖=1 ∑ 𝑤𝑖𝑢4 𝑖=1 The basic structure of the fuzzy controller is given in this chapter. Each block of the controller has been discussed in brief. Steps for designing the controller are also discussed. 7.2 Fuzzy Control Algorithm for DC-DC Converter
  80. 80. 80 The entire PWM controller has very simple linear transfer function but the non linear transfer function of multiple output converters requires a corresponding non-linear control algorithm to utilise full capabilities of the converter. Most multiple output converters experience a high degree of nonlinearity in their control characteristics. All the traditional control methods have used linear controller while scarifying potential electrical performance of the converters. Other approaches use complex nonlinear controls to obtain better performance; this often requires expensive current and voltage sensor to monitor electrical state variables within a given multiple output converters. The Fuzzy Logic Controller (FLC) provides a solution to the entire above problem. FLC provides an inexpensive nonlinear control (14-17) for obtaining a good electrical performance. Such a controller exhibit increased robustness in the face of changing circuit parameters, saturation effect and external disturbances. The basic purpose of closed loop control of converter is to keep output voltage regulated irrespective of variation in load, in input supply or in the reference set point. The implement this output voltage of the converter is sensed and then compared with reference voltage, the result is error given as: e(k) = Vref – Vo and then change in error is calculated as de(k) = e(k) – e(k-1) where, Vref = reference voltage, Vo = output voltage e(k) = voltage error at Kth instant, de(k) = change in voltage error at Kth instant e(k-1) = voltage error at (k-1)th instant Therefore two inputs to the FLC are voltage error e(k) and change in voltage error de(k) and according to control law implemented; it produces the output which is change duty cycle. The duty cycle at kth sampling time is determined by adding the previous cycle to the calculated change in the duty cycle. Change in duty cycle δ(k) = δ (k-1) + dδ Where δ (k) = duty cycle at kth instant , δ (k-1) = duty cycle at (k-1)th instant dδ = change in duty cycle The duty cycle at the kth instant is used for the switching of the switches SWm
  81. 81. 81 And SW(k+1) at constant frequency and the remaining two switches with a delay of half of the time period. Table 4.1 gives the change in duty cycle(dδ). de e NB NM NS ZE PS PM PB NB NB NB NB NB NM NS ZE NM NB NB NB NM NS ZE PS NS NB NB NM NS ZE PS PM ZE NB NM NS ZE PS PM PB PS NM NS ZE PS PM PB PB PM NS ZE PVS PM PB PB PB PB ZE PS PS PB PB PB PB Table 7.1 7x7 Rule The fuzzy control rules are derived keeping in mind the positive slope region of the DC characteristics of converter. Following are the main points considered;  When the output of converter is far from the set point, the change in duty cycle must be small so as to bring the output to the set point quickly.  When the output of converter is approaching the set point, a small change in duty cycle is necessary.  When the output of the converter is near the set point and is approaching it rapidly, the duty cycle must be kept constant so as to prevent overshoot.  when the set point is reached and output is still changing, the duty cycle must be changed a little bit to prevent the output from moving away.  When the set point is reached and the output is steady, the duty cycle should remain unchanged.  When the output is above the set point, the sign of the change of duty cycle must be negative and vice versa. FLC tool box The FIS Editor, the Membership Function Editor, the Rule Editor, and the Rule Viewer of fuzzy controller used here are shown in Figures 4.5, 4.6, 4.7, 4.8, 4.9(a) and 4.9(b).
  82. 82. 82 The FIS editor handles the high level issues for the system: how many input and output variables and what are their names? The fuzzy logic tool box does not limit the number of inputs. However, the number of inputs is limited by the available memory of the system. The membership function editor is used to define the shapes of all the membership functions associated with each variable. The rule editor is for editing the list of rules that defines the behaviour of the system. The rule viewer and surface viewer are used for looking at, as opposed to editing the FIS. They are strictly read only tools. The rule viewer is a MATLAB based display of the fuzzy inference diagram. Used as a diagnostic it can show which rules are active, or how individual membership function shapes are influencing the results. Figure 7.3 FIS Editor
  83. 83. 83 Figure 7.4 Membership Function for Voltage Error Figure 7.5 Membership Function of Change in error
  84. 84. 84 Figure 7.6 Membership function of change in frequency Figure 7.7(a) Rule Editor
  85. 85. 85 Figure 7.7(b) Rule Viewer Simulation results of powerfactorcorrectioncircuit using fuzzy logic: Fig 7.8
  86. 86. 86 Output: a> Input voltage and current: Fig 7.9 b> Output voltage: Fig 7.10
  87. 87. 87 c> FFT Analysis:
  88. 88. 88 CHAPTER 8 SUMMARY AND CONCLUSION In this project we have presented various ways for power factor correction using a SEPIC converter, including its closed loop and open loop. The main focus of this thesis was to present various ways for power factor correction using active power factor correction method Apart from SEPIC converter, this thesis also focuses on some other methods and instruments which could be used instead of SEPIC converter for improving the power factor around unity. The focus is fixed mainly on power factor correction using FUZZY LOGIC CONTROLLER, AVERAGE CURRENT CONTROL METHOD. Apart from single phase connection, we have concentrated upon designing the circuit using three phase connection also in this thesis.
  89. 89. 89 REFERENCES 1.H. Endo, T. Yamashita and T. Sugiura, “A high powerfactor buck converter”, in Proc. IEEE PESC’92, 1992, pp. 107 1-1 076. 2.C. Zhou, R. B. Ridley and F. C. Lee, “Design and analysis of a hysteretic boost power factor correction circuit”, in PUW. IEEE PESC’90, 1990, pp. 800-807. 3.S. Funabiki, N. Toita and A. Mechi, “A single-phase PWM AC to DC converter with a step up/down and sinusoidal source current”, in Con$ Rec. IEEE-IAS Annual Meeting, 1991,pp. 1017-1022.