High-Efficiency Pure Sine Wave Inverter PDF [PDF]

Zitiervorschau

Faculty of Engineering Department of Electrical Engineering

High-Efficiency Pure Sine Wave Inverter

Prepared for Dr. Natarajan Krishnamoorthy Final Year Degree Project Lakehead University Thunder bay, Ontario, Canada

Prepared by Mathais Mebratu (0648149), Imzan Khan (0646989) [email protected] [email protected] Electrical Engineering 15 April 2017

Abstract The purpose of the project was to design a high-power inverter to rival that of use in the market in terms of cost and efficiency. The efficiency was the key driving force in the project. The inverter consists of 3 stages: the boost stage, inverter stage, and filter/load stage. The boost stage consists of an isolated DC-DC converter which will take a low DC input supply and boost it to a regulated high DC output. (controlled by PWM signals). The inverter takes the high DC bus from the boost stage and inverts it to a chopped AC, which is filtered to output a pure sine wave. Load testing and efficiency calculations are done on the inverter.

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Acknowledgements We would like to acknowledge all our professors that have instructed us during our time at Lakehead University. It is due to their guidance that helped us in the successful completion of the project and in our studies. In special recognition; we would like to acknowledge Dr. Natarajan Krishnamoorthy for his support and willingness to always help when needed. In addition, our classmates, whom of which have helped us immensely in the completion of the degree project.

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Table of Contents Contents Abstract .................................................................................................................................................... 2 Acknowledgements ......................................................................................................................... 3 Table of Contents ................................................................................................................................ 4 Table of Figures .................................................................................................................................... 7 List of Tables ........................................................................................................................................ 10 List of Equations ................................................................................................................................. 11 Acronyms ............................................................................................................................................. 14 1. Introduction .................................................................................................................................... 15 1.1 Benefit to Society ................................................................................................................ 15 1.2 Project Duties ......................................................................................................................... 16 1.3 Project Scheduling ............................................................................................................. 17 2. Background ................................................................................................................................... 19 2.1 DC-DC Converter ................................................................................................................ 20 2.2 Isolated DC-DC Converter ............................................................................................ 21 2.2.1 Push-Pull Operation ................................................................................................... 23 2.3 Inverter....................................................................................................................................... 23 2.3.1 Pulse Width Modulation ......................................................................................... 24 3. Design Specifications and Procedure ........................................................................... 29 3.1 System Specifications ...................................................................................................... 29 3.2 Push-Pull Converter Design Procedure ................................................................. 29 3.2.1 High-Frequency Transformer Design .............................................................. 36 3.2.2 Output Filter Inductor Design .............................................................................. 44 3.2.3 Snubber Design ........................................................................................................... 50 3.2.4 Converter losses .......................................................................................................... 51 3.3 Inverter Low Pass Filter Design .................................................................................... 54 4. Implementation of Design .................................................................................................... 56 4.1 DC-DC converter implementation ........................................................................... 56 4.1a High-frequency transformer implementation ........................................... 56 4

4.2 Implementation of the three level SPWM ............................................................ 63 4.2.1 Internal Registers ......................................................................................................... 63 4.2.2 Fast PWM ......................................................................................................................... 66 4.2.3 Lookup Table................................................................................................................. 67 4.2.4 Arduino sPWM Implementation ........................................................................ 70 4.3 Inverter MOSFET Operation ........................................................................................... 73 4.3.1 MOSFET Gate Driver .................................................................................................. 73 4.3.2 MOSFET Consideration ............................................................................................ 76 4.3.3 Losses in MOSFET ......................................................................................................... 77 4.4 H-Bridge operation in Inverter .................................................................................... 78 4.5 Measurement and Protection Circuits ................................................................... 79 5. Results ................................................................................................................................................ 83 5.1 DC-DC converter testing ................................................................................................ 83 5.1.1 Unloaded Testing & Results .................................................................................. 83 5.1.2 Loaded Testing & Results ....................................................................................... 84 5.2 Inverter Testing & Results ................................................................................................ 89 5.2.2 Loaded Testing & Results ....................................................................................... 90 5.3 Full System Testing & Results......................................................................................... 93 5.4 Harmonic Content of sinusoidal output ................................................................ 97 6. Economic and Project Management Analysis ........................................................ 98 6.1 Bill of Materials....................................................................................................................... 98 7. Conclusion....................................................................................................................................101 7.1 Project Outcomes .............................................................................................................101 7.2 Future Work ...........................................................................................................................101 Bibliography ......................................................................................................................................103 Appendix ............................................................................................................................................108 A.1 PCB for DC-DC converter stage ..............................................................................108 A.2 PCB for Inverter stage ....................................................................................................109 A.3 Microcontroller Schematic ........................................................................................110 A.4 DC-DC Circuit Schematic ...........................................................................................111 A.5 Inverter Circuit Schematic..........................................................................................112 A.6 Lookup Table MATLAB Code.....................................................................................113 A.7 Microcontroller Code ....................................................................................................114 5

A.8 American Wire Gauge Table ....................................................................................119 Index ......................................................................................................................................................120

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Table of Figures Figure 1: Block diagram of power inverter ...................................................... 19 Figure 2: Basic topology for Boost Converter .................................................. 20 Figure 3: Basic Schematic of Push-Pull circuit ................................................. 22 Figure 4: Basic topology for inverter circuit ..................................................... 23 Figure 5: PWM with Different Duty Cycles ........................................................ 24 Figure 6: Output amplitude varied based on PWM duty cycle ................... 25 Figure 7: 2-Level PWM Output ........................................................................... 26 Figure 8: 3-Level PWM Output ........................................................................... 27 Figure 9: Sine PWM Output ................................................................................. 28 Figure 10: E-core transformer ............................................................................. 38 Figure 11: Arrangement of transformer ............................................................ 38 Figure 12: Core window area calculation ....................................................... 39 Figure 13: Skin effect ........................................................................................... 42 Figure 14: Core loss curve comparison ............................................................ 44 Figure 15: Kool Mu core selector chart ............................................................ 46 Figure 16: Kool Mu toroidal core ....................................................................... 46 Figure 17: Per unit permeability vs. DC bias .................................................... 48 Figure 18: Core dimensions ................................................................................ 49 Figure 19: Snubber design .................................................................................. 50 Figure 20: Series resistor ....................................................................................... 50 Figure 21: Distribution of converter losses ........................................................ 53 Figure 22: Distribution of losses with 4 parallel MOSFETs ................................. 53 Figure 23: Secondary winding turns .................................................................. 56 Figure 24: Centre tap primary windings ........................................................... 57 Figure 25: Complete transformer winded 1..................................................... 57 Figure 26: Complete transformer winded 2..................................................... 58 Figure 27: Reduced air gap transformer .......................................................... 58 Figure 28: Primary center-tap transformer ....................................................... 59 7

Figure 29: Inductance measurement............................................................... 59 Figure 30: Primary inductance........................................................................... 59 Figure 31: Secondary inductance measurement .......................................... 60 Figure 32: Turns ratio test ..................................................................................... 61 Figure 33: Measuring leakage inductance 1 .................................................. 61 Figure 34: Primary inductance with secondary open ................................... 62 Figure 35: Measuring leakage inductance 2 .................................................. 62 Figure 36: Primary inductance with secondary short..................................... 62 Figure 37: Testing of high-frequency transformer ........................................... 63 Figure 38: Timer/Counter1 Control Register A Bit Setup ................................ 64 Figure 39: Timer/Counter1 Control Register B Bit Setup ................................. 64 Figure 40: Timer/Coumter1 Interrupt Mask Bit Setup ...................................... 64 Figure 41: Fast PWM Timing Diagram................................................................ 66 Figure 42: Lookup Table Code .......................................................................... 68 Figure 43: Lookup Table Output Plots ............................................................... 69 Figure 44: Sample Lookup Table outputs ......................................................... 70 Figure 45: Arduino Code Segment-Gate Inputs ............................................. 70 Figure 46: Inverter Prototype .............................................................................. 71 Figure 47: H-Bridge Input (From microcontroller’s pins 11&12) ..................... 72 Figure 48: Unfiltered Output Response of H-Bridge @120Vpp ...................... 72 Figure 49: H-Bridge Output after LC lowpass filter @ 353Vpp ....................... 73 Figure 50: H-bridge .............................................................................................. 74 Figure 51: MOSFET Driver- connections (left) and pinout(right) ................... 74 Figure 52: Driver Specifications .......................................................................... 75 Figure 53: H-Bridge Operation ........................................................................... 79 Figure 54: Voltage and Current transducers ................................................... 80 Figure 55: DC-DC converter testing arrangement ......................................... 83 Figure 56: Unloaded regulation of output DC voltage ................................. 84 Figure 57: Input and output results of 147.3 ohm load .................................. 84 8

Figure 58: Duty cycle of loaded DC-DC converter ....................................... 85 Figure 59: Drain current waveform ................................................................... 85 Figure 60: Secondary Output voltage waveform .......................................... 86 Figure 61: Passive attenuator ............................................................................. 86 Figure 62: Output DC voltage in loaded condition ....................................... 87 Figure 63: Efficiency Vs. Various loads.............................................................. 88 Figure 64: Inverter testing arrangement........................................................... 89 Figure 65: Resistive load testing of inverter ...................................................... 90 Figure 66: Fan as inductive load ....................................................................... 91 Figure 67: Rating of fan ....................................................................................... 91 Figure 68: Measurement of low speed............................................................. 92 Figure 69: The whole system put together ....................................................... 93 Figure 70: Input voltage and current into the inverter .................................. 94 Figure 71: Output voltage of boost stage ....................................................... 94 Figure 72: Output current of inverter ................................................................ 95 Figure 73: Output voltage waveform and measurement ............................ 95 Figure 74: Harmonic content of output waveform ........................................ 97 Figure 75: PCB for DC-DC converter .............................................................. 108 Figure 76: Inverter PCB ...................................................................................... 109 Figure 77: μController Module ......................................................................... 110 Figure 78: DC-DC circuit schematic ............................................................... 111 Figure 79: Inverter circuit schematic .............................................................. 112

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List of Tables Table 1: Scheduling breakdown ....................................................................... 18 Table 2: Power Range of converter types ....................................................... 21 Table 3: System Specifications........................................................................... 29 Table 4: Push-pull Converter Specifications .................................................... 30 Table 5: High-Frequency Transformer Design Parameters ............................ 36 Table 6: Output inductor design parameters ................................................. 45 Table 7: Power MOSFET ....................................................................................... 51 Table 8: Diode parameters ................................................................................ 52 Table 9: Wave Generation Bits .......................................................................... 65 Table 10: Compare Output Mode for Fast PWM ............................................ 67 Table 11: Clock Select Bit Description .............................................................. 67 Table 12: MOSFET Specifications ....................................................................... 78 Table 13: Protection thresholds ......................................................................... 81 Table 14: Protection thresholds ......................................................................... 82 Table 15: Results for loaded DC-DC converter ............................................... 87 Table 16: Complete results for loaded DC-DC converter ............................. 88 Table 17: Load test of inverter ........................................................................... 90 Table 18: Spot testing of resistive load ............................................................. 94 Table 19: Full load testing of the overall system ............................................. 96 Table 20: Bill of materials..................................................................................... 98 Table 21: Salvaged/already available parts ................................................ 100

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List of Equations Equation 1: Input to output voltage transfer function ................................... 29 Equation 2: Switching period ............................................................................. 31 Equation 3: Maximum duty cycle ..................................................................... 31 Equation 4: Maximum duty cycle for each phase ........................................ 31 Equation 5: Input power ..................................................................................... 31 Equation 6: Max. average input current ......................................................... 31 Equation 7: Max. Equivalent flat topped input current ................................. 32 Equation 8: Max. input RMS current ................................................................. 32 Equation 9: Max. MOSFET RMS current ............................................................. 32 Equation 10: Min. MOSFET breakdown voltage .............................................. 32 Equation 11: Transformer turns ratio.................................................................. 32 Equation 12: Min. duty cycle ............................................................................. 33 Equation 13: Nominal duty cycle ...................................................................... 33 Equation 14: Average output current .............................................................. 33 Equation 15: Secondary max. RMS current ..................................................... 33 Equation 16: Rectifier diode voltage................................................................ 33 Equation 17: Min. output filter inductor ............................................................ 34 Equation 18: Output filter inductor ................................................................... 34 Equation 19: Min. output current ...................................................................... 34 Equation 20: Max. output ripple ........................................................................ 34 Equation 21: Output filter capacitor value ..................................................... 35 Equation 22: Equivalent Series Resistance ....................................................... 35 Equation 23: RMS capacitor current ................................................................ 35 Equation 24: Ripple input voltage .................................................................... 35 Equation 25: Input capacitor............................................................................. 35 Equation 26: Apparent power ........................................................................... 37 Equation 27: Ke parameter ................................................................................ 37 11

Equation 28: Core geometry parameter ......................................................... 37 Equation 29: Kg relation to core ....................................................................... 37 Equation 30: Core window area ....................................................................... 39 Equation 31: Primary turns calculation ............................................................. 39 Equation 32: Bmax check .................................................................................. 39 Equation 33: Primary inductance value .......................................................... 40 Equation 34: Secondary turns calculation ...................................................... 40 Equation 35: Skin depth ...................................................................................... 40 Equation 36: Wire diameter ............................................................................... 40 Equation 37: Conductor section ....................................................................... 41 Equation 38: Wire diameter for AWG21 ........................................................... 41 Equation 39: Wire area for AWG21 ................................................................... 41 Equation 40: Wire resistance for AWG21 ......................................................... 41 Equation 41: Number of primary wires ............................................................. 42 Equation 42: Total area of primary side ........................................................... 42 Equation 43: Primary resistance ........................................................................ 42 Equation 44: Primary resistance value ............................................................. 43 Equation 45: Total area of secondary side...................................................... 43 Equation 46: Number of secondary wires........................................................ 43 Equation 47: Secondary resistance .................................................................. 43 Equation 48: Secondary resistance value ....................................................... 43 Equation 49: Total copper losses ....................................................................... 43 Equation 50: Transformer regulation ................................................................. 44 Equation 51: Inductor Peak current value ....................................................... 45 Equation 52: LI^2 product .................................................................................. 45 Equation 53: Minimum nominal inductance ................................................... 47 Equation 54: Number of turns ............................................................................ 47 Equation 55: DC bias........................................................................................... 47 Equation 56: Adjusted number of turns ............................................................ 48 12

Equation 57: Circumference of inner core ...................................................... 49 Equation 58: Width of AWG21 ........................................................................... 49 Equation 59: number of turns/layer .................................................................. 49 Equation 60: Total layers ..................................................................................... 49 Equation 61: Stored energy in a capacitor ..................................................... 50 Equation 62: Estimate of power dissipation ..................................................... 51 Equation 63: Capacitor in snubber .................................................................. 51 Equation 64: Dissipated power.......................................................................... 51 Equation 65: Power dissipated in Rs ................................................................. 51 Equation 66: Conduction loss in MOSFET ......................................................... 52 Equation 67: MOSFET gate loss .......................................................................... 52 Equation 68: Switching losses in MOSFET .......................................................... 52 Equation 69: Conduction losses in diode ........................................................ 52 Equation 70: Switching losses in diode ............................................................. 52 Equation 71: Filter cut-off frequency ................................................................ 54 Equation 72: Capacitive reactance ................................................................ 54 Equation 73: Filter capacitor value................................................................... 55 Equation 74: Resonant frequency of filter ....................................................... 55 Equation 75: Actual filter capacitor value ...................................................... 55 Equation 76: Measured turns ratio .................................................................... 60 Equation 77: Measured total inductance ....................................................... 62 Equation 78: Leakage inductance value........................................................ 63 Equation 79: Input compare register................................................................ 68 Equation 80: Sample number ............................................................................ 69 Equation 81: AC voltage reading ..................................................................... 81 Equation 82: Sample voltage calculation ...................................................... 81 Equation 83: AC voltage reading at the LCD................................................. 81

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Acronyms PWM – Pulse Width Modulation SPWM – Sinusoidal PWM THD – Total Harmonic Distortion PSW – Pure Sine Wave CCM – Continuous Conduction Mode D – Duty Cycle DCM – Discontinuous Conduction Mode MOSFET – Metal-Oxide-Semiconductor Field-Effect Transistor ICR – Input Compare Register RMS – Root Mean Square MGD – MOSFET Gate Driver UPS – Uninterruptible Power Supply PCB – Printed Circuit Board EMF – Electromotive Force ISR – Interrupt Service Routine AWG – American Wire Gauge LCR – Inductance, Capacitance and Resistance meter

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1. Introduction A power inverter is simply an electronic circuit that uses a DC voltage as an input and converts that to an AC voltage (Output). For this process to be successful, the DC input source must be stable and have enough current supply. There are several types of inverters that give various types of output. These include square wave, modified sine wave, pulsed sine wave and pure sine wave (PSW). They all have different uses in the industry but the PSW is mostly used since they can power many common electronic devices. The PSW inverter is considered in this project. PSW can also be used in solar powered systems in which a low DC voltage input supplied from the solar panels is inverted to high power AC output which can be used to power AC appliances. Another use of PSW is in Uninterruptible power supply (UPS) which are used to provide a constant flow of power in sensitive loads that require as such, PSW find their use in such power supplies. The use of PSW inverter also allows a user to have access to an AC power if they might be in an area with only DC power available such as at work sites or in camping sites.

1.1 Benefit to Society A high efficiency single-phase inverter at a low cost is not only a benefit for industrial applications, but also to residential applications. Having a single-phase inverter in conjunction with an existing solar powered system tied to the grid is not new concept; however, in terms of efficiency and money it is not feasible. Therefore, having a high efficiency, single-phase inverter at a comparatively low cost in comparison to current market inverters; not only makes the renewable energy more enticing money wise, but also promotes renewable energy.

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1.2 Project Duties Farrukh Gill – PCB design, ordering of parts, schematic drawing, inverter design. Mathais Mebratu – Specification of parts, safety & protection devices, and DC-DC converter design. Imzan Khan – Programming of the Microcontroller, feedback and interfacing circuity design, inverter design. Simardeep Gill - DC-DC converter design, main converter design and economic/project management analysis.

All group members will be involved in design and testing of the PWM programming, DC-DC converter & Inverter circuits. Project management duties will be rotated amongst the group; thus, all group members will have a good understanding of every aspect of the project, as well as a leadership role in a project based environment.

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1.3 Project Scheduling

Task Name

Start

Finish

Project Manager

Degree Project 2016/17

Mon 9/12/16

Mon 4/10/17

Imzan Khan

Weekly Meetings with Supervisor

Mon 9/12/16

Sat 4/1/17

Develop Final Presentation

Mon 9/12/16

Mon 9/12/16

Final Report

Sat 11/5/16

Sat 4/8/17

Initiating & Research

Mon 9/12/16

Fri 11/4/16

Topic Research & Selection

Mon 9/12/16

Sat 10/29/16

Develop Project Proposal

Sat 10/29/16

Fri 11/4/16

Prepare Preliminary Project Scope

Mon 10/31/16

Mon 10/31/16

Develop System Block Diagram

Mon 10/31/16

Mon 10/31/16

Identify Goals and Objectives

Mon 10/31/16

Mon 10/31/16

Document Project Costs and Benefits

Tue 11/1/16

Tue 11/1/16

Develop Strategies and Plans

Tue 11/1/16

Wed 11/2/16

Distribute Roles & Responsibilities

Wed 11/2/16

Fri 11/4/16

Fri 11/4/16

Sun 1/8/17

Fri 11/4/16

Sun 1/8/17

Microcontroller Selection

Mon 9/12/16

Mon 9/12/16

Acquire Programming Software

Wed 11/2/16

Wed 11/2/16

Develop Arduino code

Mon 12/19/16

Sun 1/8/17

Sat 11/5/16

Sat 12/3/16

DC-DC Converter build

Sat 11/5/16

Thu 11/17/16

Testing of converter

Sat 11/5/16

Tue 11/22/16

Optimization of Circuits (Software)

Wed 11/23/16

Wed 11/30/16

PCB Design

Wed 11/30/16

Sat 12/3/16

Wed 11/30/16

Fri 3/24/17

Authorize Work

Wed 11/30/16

Wed 11/30/16

Order Parts

Wed 11/30/16

Fri 1/6/17

Circuit Development

Wed 11/30/16

Thu 3/23/17

Construction of Circuits

Wed 11/30/16

Mon 3/20/17

Manage Requirements

Tue 3/21/17

Tue 3/21/17

Efficiency Test

Wed 3/22/17

Wed 3/22/17

Programming & Implementation Process Software Setup

Implementation

Execution

Mathais Mebratu

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Optimization of Circuitry (Hardware)

Thu 3/23/17

Thu 3/23/17

Fri 3/24/17

Mon 4/10/17

Enclosure of Circuits

Fri 3/24/17

Fri 4/7/17

Close Project

Fri 3/24/17

Mon 4/10/17

Assess Satisfaction

Fri 3/24/17

Fri 3/24/17

Final Presentation Rehearsal

Mon 3/27/17

Thu 4/6/17

Final Presentation

Fri 4/7/17

Fri 4/7/17

Closing

Table 1: Scheduling breakdown

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2. Background In this section, background information on the various parts used in constructing the PSW is discussed. A PSW inverter consists of an input power supply, a DCDC converter, a DC-AC inverter and an low pass filter at the output. An overall operation of a PSW inverter is as:

1. Low-voltage DC is inputted, which is provided, for example, from a car battery or solar panel 2. A DC-DC converter will step-up the low voltage DC to a higher DC voltage 3. Next, the Arduino microcontroller will generate the sPWM and PWM signals to convert this high DC voltage to an high voltage AC output

An block overview of the operation:

Figure 1: Block diagram of power inverter

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2.1 DC-DC Converter The DC-DC converter is a specific type of switching converter that converts one level of DC input voltage to another DC output voltage. A DC-DC converter that converts a low voltage DC to a higher DC voltage is called a boost converter and a buck converter is the opposite of this.

Figure 2: Basic topology for Boost Converter From Fig. 2, the switch is usually a MOSFET or IGBT, as fast switching is required. When a high frequency square wave is applied to the gate, the switch will repeatedly turn ON and OFF. When the switch will be ON, the inductor will begin to store energy in its magnetic field, and when the switch is OFF, the back EMF from the inductor is produced with a reverse polarity than when the switch was ON. Due to this, the Vs (supply voltage) and VL (back EMF) will be in series. The diode is forward biased in this stage, and a capacitor at the load charges to (Vs + VL) minus the voltage drop across the diode. Therefore, the output always sees a steady output voltage of (Vs + VL), because during the ON stage the capacitor charges, and during OFF stage it discharges through the load. At steady-state operation, the output voltage is found as: 𝑉𝑜𝑢𝑡 =

𝑉𝑖𝑛 1 − 𝐷𝑢𝑡𝑦 𝐶𝑦𝑐𝑙𝑒

This equation is assuming continuous operation mode, which is also the mode used for this project. Fig. 2 is a basic boost converter switching circuit, in this report a high turns ratio (24 V to 180 VRMS) is required so a transformer isolated switching circuit is preferred as opposed to an inductor or non-isolated DC-DC converter. 20

2.2 Isolated DC-DC Converter In these circuits, the duty cycle of the square wave input is adjusted, which will in turn allow control of the power transferred to the load. Circuit

Power Range

Fly-back

1 W – 100 W

Forward

1 W – 200 W

Push-Pull

200 W – 500 W

Half Bridge

200 W – 500 W

Full Bridge

500 W – 2000 W

Table 2: Power Range of converter types In addition, in the transformer isolated converters, the load side is isolated from the AC lines. There are several topologies of transformer isolated converters given in Table 1. The half or full bridge configurations are more suitable for higher DC input voltages, but the gate circuitry for the switches are more complex. In this project, the push-pull topology is used. This topology is used due its efficient operation at low input voltages and at higher power applications. The breakdown voltage of the power transistors should be greater than twice the input DC voltage and due to this reason push-pull converter are not suitable for high DC input voltages. In contrast to half bridges, where the switches must withstand voltage equal to input voltage. This topology also allows to have multiple outputs. An advantage the push-pull has over half bridge is that neither switch requires an isolated driver. This design also used the current mode PWM control like the nonisolated converters. In push-pull converters, eight transistors are used on the primary side with a center-tapped high frequency transformer.

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Figure 3: Basic Schematic of Push-Pull circuit

An H-Bridge is on the primary side of high-frequency transformer. These switches are open and closed 180 degrees out of phase. These 4 MOSFETs correspond to high side left, high side right, low side left and low side right. The selection of these MOSFETs whether NPN or PNP depend on parameters such as the RDS (on) resistance, which should be very low as to reduce power losses. Since the switches conduct alternately to each other a bipolar output voltage is seen at the primary transform thus a full wave rectifier bridge is at the secondary. In addition, note that the freewheeling diode could also be added to the primary transformer to control the voltage present on the secondary when the switches open. The duty cycle of the PWM modulator must be less than 0.5 or 50% to avoid conduction of the alternate switches at the same time. In this project, the PWM duty cyle is set to 0.45 or 45%.

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2.2.1 Push-Pull Operation The basic operation is similar to the forward converter. When the high side left and low side right switches are ON, the current will flow through the rectifier diodes and charge the output inductor with a positive voltage across the load, likewise during the ON state of the high side right and low side left switches the voltage across the load is negative. The drivers for the switches doubles the effective duty cycle; therefore, the operating frequency at the output filter is double the switching frequency. The drivers should have an appropriate amount of dead time between the alternating phases, as to ensure one switch is completely off before another switch conducts.

2.3 Inverter The Inversion process is explained and comprised of the following sections: the conversion of DC to AC by the H-Bridge, which is controlled by a MOSFET driver. The MOSFET driver is controlled by the SPWM and PWM signals of the Arduino ATMEGA 2560 microcontroller.

Figure 4: Basic topology for inverter circuit 23

2.3.1 Pulse Width Modulation A ‘level’ is based on the amplitude levels of the varying pulses, which also includes the zero-crossing level.

2.3.1a Two-level PWM A ‘level’ is based on the amplitude levels of the varying pulses, which also includes the zero-crossing level.

The 2-level PWM is normally referred to as PWM (Pulse Width Modulation) and refers to the concept of rapidly pulsing a digital signal between the positive (or negative) peak value and zero. The duty cycle of a PWM waveform determines how long the pulse remains ON or HIGH, or in other words the percentage in which the waveform is at its peak value (Figure 5).

Figure 5: PWM with Different Duty Cycles (Source: “Arduino - PWM,” Arduino - PWM. [Online]. Available: https://www.arduino.cc/en/Tutorial/PWM)

The use of PWM in an inverter circuit is crucial as it provides a means of decreasing the total harmonic distortion of the load current. In addition, using a PWM signal to control the inputs of switches (Figure 4) allows for more efficiency

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as you can turn the load fully OFF and fully ON; thus, reducing the amount of power wasted compared to a linear switch controller.

Figure 6: Output amplitude varied based on PWM duty cycle (Source: “ermicroblog,” Microcontrollers and Electronics Parts e-Shop. [Online]. Available: http://www.ermicro.com/blog/?p=706 )

PWM is comparable to an AM signal, as the duty cycle (analogous to a human’s varying vocal level) of the PWM signal determines the amplitude of the output signal. as when a voltage in between ON and OFF is required, this can be achieved easily by modifying the duty cycle (Figure 5). Whereas, the carrier frequency of an AM signal is analogous to the ON/OFF frequency of a PWM and is known as the switching frequency, which is essential to reproducing an efficient (low power loss) output signal, and will be discussed in later sections with regards to switching losses. This amplitude modulation idea can be further modified to achieve a Sinusoidal waveform (Figure 6). 25

Figure 7: 2-Level PWM Output (Source: “Delta modulation,” Wikipedia, 15-Mar-2017. [Online]. Available: https://en.wikipedia.org/wiki/Delta_modulation)

The output waveform in figure 7, illustrates the filtered response of a 2-Level PWM with reference of a sinusoidal waveform. The output response is not desirable for the specifications of the project, as it is would result in a higher harmonic distortion; thus, reducing the efficiency of the inverter.

2.3.1b Three-level PWM To improve the efficiency, the number of levels the PWM waveform contains is increased, as the more levels a PWM waveform has, the better an approximation of a pure sine wave can be achieved (after passing through a filter).

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Figure 8: 3-Level PWM Output (Source: “Pulse-width modulation,” Wikipedia, 24-Mar-2017. [Online]. Available: https://en.wikipedia.org/wiki/Pulse-width_modulation)

Referenced to a sine wave, the pulsing waveforms are segmented into 3-levels: the positive peak to 0, the zero-crossing level, and 0 to the negative peak. Whilst another level was introduced, the output waveform is still not usable for a high efficiency inverter system.

2.3.1c Sinusoidal PWM Sinusoidal PWM (sPWM), is the varying and combination of pulse widths in such that they are proportional to the amplitudes of a sinusoidal waveform at the sample time set by the switching frequency.

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Figure 9: Sine PWM Output (Source: Terbytes, “Terbytes/Arduino-Atmel-sPWM,” GitHub, 14-Mar-2016. [Online]. Available: https://github.com/Terbytes/Arduino-Atmel-sPWM)

This method will be used in the project as its filtered output more clearly resembles that of a sine wave, and will be discussed in further detail in section 4.2.

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3. Design Specifications and Procedure The design procedure used for this project are found in references [27] to [32]. These textbooks contain the equations to use for designing switching power supplies.

3.1 System Specifications The system specification is listed below:

Specification

Value

Nominal Voltage Input

24 Vdc

Output Voltage

120 Vrms at 60 Hz

Output Power

500 W

Efficiency

80%

Switching Frequency

30 KHz (DC-DC); 100 KHz (DC-AC)

Table 3: System Specifications The relationship between the input and output voltage is given by:

𝑁2 𝑉𝑜𝑢𝑡 = 2 ( ) 𝐷𝑉𝑖𝑛 𝑁1

(1)

Equation 1: Input to output voltage transfer function

3.2 Push-Pull Converter Design Procedure As per the table 1, a proper gate driver is needed which can switch at the required frequency and also maintain the duty cycle needed. The SG3525A Pulse Width Modulator Control Circuit was chosen for this for several reasons. Firstly, it 29

provides a wide range of switching frequency (100 Hz to 400 kHz). Secondly it has built in soft-start circuitry to ensure no fast build up of charge. Thirdly, deadtime is simply arranged by connecting a single resistor between the CT and Discharge pins. The driver will be used as a voltage mode control as the input voltage is not a constrained source and will vary. Voltage mode is also advantageous in applications where high power is needed such as in this project. Also, as stated in section 2.2, in practice; leakage inductance from the high frequency transformer causes significant over-voltages across the transistor and thus the breakdown voltage of these devices should be higher than twice the input voltage. The STP160N75F3 N-Channel Power MOSFET’s were selected for the DC-DC converter design. These MOSFET’s provide an ultra low on-resistance, can handle up to 75 Volts with 120 Amps at 25 degrees Celsius. These switches provide extremely fast switching and can be operated normally up to 175 degrees Celsius. From Table 3, the DC-DC converter specifications are listed. In the procedure, calculations are based upon a power output of 700 Watts as a gross overload for the converter. Specification

Value

Nominal Voltage Input (Vin)

24 V

Maximum Voltage Input (Vin,max)

28 V

Minimum Voltage Input (Vin,min)

20 V

Nominal Power Output (Pout)

500 W

Nominal Output Voltage (Vout)

180 V

Target Efficiency (η)

90 %

Switching Frequency (f)

30 kHz

Table 4: Push-pull Converter Specifications 30

The switching period is given by:

𝑇=

1 1 = = 33.33 𝜇𝑠 𝑓 30 𝑘𝐻𝑧

(2)

Equation 2: Switching period Maximum duty cycle:

∗ 𝑡𝑜𝑛 = 0.5𝑇 = 16.67 𝜇𝑠

(3)

Equation 3: Maximum duty cycle Maximum duty cycle of each phase:

𝐷𝑚𝑎𝑥 =

∗ 0.9𝑡𝑜𝑛 = 0.45 = 45% 𝑇

(4)

Equation 4: Maximum duty cycle for each phase Input power:

𝑃𝑖𝑛 =

𝑃𝑜𝑢𝑡 700 = = 778 𝑊 𝜂 0.9

(5)

Equation 5: Input power Maximum average input current:

𝐼𝑖𝑛 =

𝑃𝑖𝑛 𝑉𝑖𝑛,𝑚𝑖𝑛

=

778 = 38.9 𝐴 20

(6)

Equation 6: Max. average input current

31

Maximum equivalent flat topped input current:

𝐼𝑝𝑓𝑡 =

𝐼𝑖𝑛 38.9 = = 43.22 𝐴 2𝐷𝑚𝑎𝑥 2 ∗ 0.45

(7)

Equation 7: Max. Equivalent flat topped input current Maximum input RMS current:

𝐼𝑖𝑛,𝑅𝑀𝑆 = 𝐼𝑝𝑓𝑡 √2𝐷𝑚𝑎𝑥 = 43.22√0.9 = 41 𝐴

(8)

Equation 8: Max. input RMS current Maximum MOSFET RMS current:

𝐼𝑚𝑜𝑠,𝑅𝑀𝑆 = 𝐼𝑝𝑓𝑡 √𝐷𝑚𝑎𝑥 = 29 𝐴

(9)

Equation 9: Max. MOSFET RMS current

Minimum MOSFET breakdown voltage:

𝑉𝐵𝑟𝑘,𝑀𝑜𝑠 = 1.3 ∗ 2 ∗ 𝑉𝑖𝑛.𝑚𝑎𝑥 = 72.8 𝑉

(10)

Equation 10: Min. MOSFET breakdown voltage Transformer turns ratio:

𝑁=

𝑁2 𝑉𝑜𝑢𝑡 = = 10 𝑁1 2𝑉𝑖𝑛,𝑚𝑖𝑛 𝐷𝑚𝑎𝑥

(11)

Equation 11: Transformer turns ratio

32

Minimum duty cycle value:

𝐷𝑚𝑖𝑛 =

𝑉𝑜𝑢𝑡 = 0.32 2𝑁𝑉𝑖𝑛,max

(12)

Equation 12: Min. duty cycle Duty cycle at nominal input voltage:

𝐷𝑛𝑜𝑚𝑖𝑛𝑎𝑙 =

𝑉𝑜𝑢𝑡 = 0.38 2𝑁𝑉𝑖𝑛

(13)

Equation 13: Nominal duty cycle Maximum average output current:

𝐼𝑜𝑢𝑡 =

𝑃𝑜𝑢𝑡 = 3.9 𝐴 𝑉𝑜𝑢𝑡

(14)

Equation 14: Average output current Secondary maximum RMS current:

𝐼𝑠𝑒𝑐,𝑅𝑀𝑆 = 𝐼𝑜𝑢𝑡 √𝐷𝑚𝑎𝑥 = 2.62 𝐴

(15)

Equation 15: Secondary max. RMS current Rectifier diode voltage:

𝑉𝑑𝑖𝑜𝑑𝑒 = 𝑁𝑉𝑖𝑛,max = 280 𝑉

(16)

Equation 16: Rectifier diode voltage

33

Output filter inductor value: Assuming a ripple current value 15% of output current (𝛥𝐼 = 0.15𝐼𝑜𝑢𝑡 = 0.585).

𝐿𝑚𝑖𝑛 ≥

𝑁 (𝑁2 𝑉𝑖𝑛 − 𝑉𝑜𝑢𝑡 ) 𝑡𝑜𝑛,max 1

Δ𝐼

= ((10)(24) − 180)

15𝜇 = 1.5 𝑚𝐻 0.585

(17)

Equation 17: Min. output filter inductor Based on equation 17, the output filter inductor is chosen as:

𝐿𝑓𝑖𝑙𝑡𝑒𝑟 = 2 𝑚𝐻

(18)

Equation 18: Output filter inductor The converter is used in Continuous Conduction Mode (CCM). This means that current in the output inductor does not drop to zero during switching cycles. CCM gives higher efficiencies as compared to Discontinuous Conduction Mode (DCM).

This output filter inductor value will ensure a CCM operation for a minimum output current of: 𝐼𝑜𝑢𝑡,min =

Δ𝐼 0.585 = = 0.293 𝐴 2 2

(19)

Equation 19: Min. output current Maximum output voltage ripple value:

Δ𝑉𝑜 = 0.1%𝑉𝑜𝑢𝑡 = 0.180 𝑉

(20)

Equation 20: Max. output ripple

34

Output filter capacitor value:

𝐶𝑚𝑖𝑛 =

1 Δ𝐼𝐿 1 0.585 𝑇𝑠 = ∗ ∗ 33.33𝜇 = 13.6 𝜇𝐹 8 Δ𝑉𝑜 8 0.180

(21)

Equation 21: Output filter capacitor value

The Equivalent Series Resistance (ESR) must be lower than:

𝐸𝑆𝑅𝑚𝑎𝑥 =

Δ𝑉𝑜 0.180 = = 0.31 Ω Δ𝐼𝐿 0.585

(22)

Equation 22: Equivalent Series Resistance RMS capacitor current:

2 2 𝐼𝐶,𝑟𝑚𝑠 = √𝐼𝐼𝑛,𝑟𝑚𝑠 − 𝐼𝑖𝑛 = √412 − 38.92 = 12.95 ≅ 13 𝐴

(23)

Equation 23: RMS capacitor current Ripple input voltage:

Δ𝑉𝑖𝑛 = 0.1%𝑉𝑖𝑛,max = 0.028 𝑉

(24)

Equation 24: Ripple input voltage Input capacitor:

𝐶𝑖𝑛 = 𝐼𝐶,𝑟𝑚𝑠

Δ𝑇𝑜𝑛,max 15𝜇𝑠 = 13 ∗ = 7 𝑚𝐹 Δ𝑉𝑖𝑛 0.028

(25)

Equation 25: Input capacitor The high voltage conversion ratio needed from system specifications is achieved by proper high-frequency transformer turns ratio design. The high-frequency 35

transformer must be designed in order to minimize the leakage inductance. Furthermore, the winding of the transformer must be symmetrical to minimize the imbalance of the primary inductance values. Special care of the PCB design is needed as well to have proper balance of the inductances values. There is also the challenge of saturating the transformer through difference of peak current values in the transistors.

3.2.1 High-Frequency Transformer Design

Specification

Value

Nominal Voltage Input (Vin)

24 V

Maximum Voltage Input (Vin,max)

28 V

Minimum Voltage Input (Vin,min)

20 V

Nominal Output Voltage (Vout)

180 V

RMS Input Current (Iin)

41 A

Output Current (Iout)

3.9 A

Switching Frequency (f)

30 kHz

Efficiency (η)

98 %

Regulation (α)

0.05 %

Maximum Operating Flux Density (Bm) 0.05 T Window Utilization (Ku)

0.3

Duty Cycle (Dmax)

0.45

Temperature Rise (Tr)

30 degrees Celsius

Table 5: High-Frequency Transformer Design Parameters

36

Apparent power:

𝑃𝑡 =

𝑃𝑜 1 1 + 𝑃𝑜 = ( + 1) 𝑉𝑜 𝐼𝑜 = ( + 1) ∗ 180 ∗ 4 = 1.455 𝑘𝑊 𝜂 𝜂 0.98

(26)

Equation 26: Apparent power Electrical condition parameter calculation Ke:

2 (10−4 ) 𝐾𝑒 = 0.145𝐾𝑓2 𝑓 2 𝐵𝑚 = 0.145(4)2 (30 𝑘𝐻𝑧)2 (0.05)2 (10−4 ) = 522

(27)

Equation 27: Ke parameter Note Kf = 4 is the waveform coefficient for square waves.

Core geometry parameter:

𝐾𝑔 =

𝑃𝑡 1.455 𝑘𝑊 = = 2.787 𝑐𝑚5 2𝐾𝑒 𝛼 2 ∗ 522 ∗ 0.05 100

(28)

Equation 28: Core geometry parameter Kg is related to the transformer core through:

𝑊𝑎 𝐴2𝑐 𝐾𝑢 (5.7 ∗ 5.292 ∗ 0.3) 𝐾𝑔 = = = 3.57 𝑀𝐿𝑇 13.4

(29)

Equation 29: Kg relation to core Where Wa is the core window area, Ac is the cross-sectional area and MLT is the mean length per turn.

37

In this project, the E65/32/27 core with N27 ferrite was chosen due to its high saturation flux density (320 mT) and a high AL of 7200 nH. These parameters allow us to have the fewest turns while still getting the required inductance.

Figure 10: E-core transformer Two of these cores are arranged as such:

Figure 11: Arrangement of transformer

38

The values used in equation (29) are found as:

Figure 12: Core window area calculation 𝑊𝑎 = 12.7 ∗ 45 = 571.5 𝑚𝑚2 = 5.715 𝑐𝑚2

(30)

Equation 30: Core window area The cross-sectional area and the MLT is found from the data sheet.

From datasheet, Bs = 320 mT = 3200 Gauss so assuming Bmax = 1500 Gauss to ensure no saturation. The number of primary turns is found as:

𝑁1 =

𝑉𝑛𝑜𝑚𝑖𝑛𝑎𝑙 ∗ (108 ) 108 = 24 ∗ ≅ 3 𝑡𝑢𝑟𝑛𝑠 (4 ∗ 𝑓𝑜 ∗ 𝐴𝑐 ∗ 𝐵𝑚𝑎𝑥 ) 4 ∗ 30 𝑘𝐻𝑧 ∗ 5.29 ∗ 1500

(31)

Equation 31: Primary turns calculation Check Bmax with the N1 calculated by re-arranging equation (31):

𝐵𝑚𝑎𝑥

24 ∗ 108 = = 1260 𝐺𝑎𝑢𝑠𝑠 4 ∗ 30 𝑘𝐻𝑧 ∗ 5.29 ∗ 3

(32)

Equation 32: Bmax check 39

With the approximation for N1 = 3 turns, the Bmax is below the 1500 Gauss designed for so the approximation is good.

The primary inductance value is:

𝐿𝑝 = 𝑁 2 𝐴𝐿 = 32 ∗ 7200 = 65 𝜇𝐻

(33)

Equation 33: Primary inductance value The number of secondary turns is:

𝑁2 = 𝑁𝑁1 = 10 ∗ 3 = 30 𝑡𝑢𝑟𝑛𝑠

(34)

Equation 34: Secondary turns calculation

3.2.1a Wire selection for high-frequency transformer In this section, the magnetic wire to be used for winding the transformer are found.

Current penetration depth (Skin depth):

𝛿=

6.62 √𝑓

=

6.62 √30 𝑘𝐻𝑧

= 0.0382 𝑐𝑚 ≅ 0.4 𝑚𝑚

(35)

Equation 35: Skin depth The wire diameter: 𝑑 = 2𝛿 = 0.7644 𝑚𝑚

(36)

Equation 36: Wire diameter

40

Conductor section:

𝜋𝑑 2 𝐴𝑤 = = 0.4589 𝑚𝑚2 4

(37)

Equation 37: Conductor section From the electrical lab, AWG21 is available and according to the American Wire Gauge Conductor Size Table; this wire is able to withstand a maximum current of 1.2 A at a maximum frequency of 33 kHz for 100% skin depth. The table can be found in appendix A.8. The AWG21 wire has the following specifications:

𝑊𝑖𝑟𝑒 𝑑𝑖𝑎𝑚𝑒𝑡𝑒𝑟 = 𝑑𝐴𝑊𝐺21 = 0.7239 𝑚𝑚

(38)

Equation 38: Wire diameter for AWG21 𝑊𝑖𝑟𝑒 𝑎𝑟𝑒𝑎 = 𝐴𝑤 𝐴𝑊𝐺21 = 0.41 𝑚𝑚2

(39)

Equation 39: Wire area for AWG21 𝑊𝑖𝑟𝑒 𝑟𝑒𝑠𝑖𝑠𝑡𝑎𝑛𝑐𝑒 = 𝑅𝐴𝑊𝐺21 = 41.984

𝛺 𝑘𝑚

(40)

Equation 40: Wire resistance for AWG21 A current density, J, was chosen as 4.5 A/mm2 from the plot of current density versus frequency. Since J is dependent on the frequency, its value drops considerably at high frequency called the “Skin effect”. If reached at this point, the high-frequency alternating current only flows through the top layer of the conductor as pictured in Fig. 7. Due to these reasons, the current density was chosen as such to avoid these issues.

41

Figure 13: Skin effect (Source: [Online]. Available: https://www.solo-labs.com/cabling-effects-selecting-rightcable/. [Accessed: 05- Apr- 2017].

The AWG21 magnetic wires need to be bundled appropriately as to handle the high input current of 38.9 A.

Number of primary wires: 𝑆𝑛𝑝 =

𝐴𝑤𝑝 𝐴𝑤𝐴𝑊𝐺21

=

8.9 ≅ 22 𝑏𝑢𝑛𝑑𝑙𝑒𝑠 0.41

(41)

Equation 41: Number of primary wires Where, 𝐴𝑤𝑝 =

𝐼𝑖𝑛 38.9 40 = ≅ = 8.9 𝑚𝑚2 𝐽 450 450

(42)

Equation 42: Total area of primary side Note that the input current is rounded to 40 A as to over-compensate the requirement. The primary resistance is:

𝛺 −5 𝑅𝐴𝑊𝐺21 (4.1984 ∗ 10 ) 𝑚𝑚 𝜇𝛺 𝑟𝑝 = = = 1.91 𝑆𝑛𝑝 22 𝑚𝑚

(43)

Equation 43: Primary resistance 42

Value of resistance for the primary winding:

𝑅𝑝 = 𝑁1 ∗ 𝑀𝐿𝑇 ∗ 𝑟𝑝 = (3)(13.4)(1.91) = 767.82 𝜇𝛺

(44)

Equation 44: Primary resistance value Total area of secondary side: 𝐴𝑤𝑠 =

𝐼𝑜𝑢𝑡 4 = = 0.89 𝑚𝑚2 𝐽 4.5

(45)

Equation 45: Total area of secondary side Number of secondary wires:

𝑆𝑛𝑠 =

𝐴𝑤𝑠 𝐴𝑤𝐴𝑊𝐺21

=

0.89 ≅ 3 𝑏𝑢𝑛𝑑𝑙𝑒𝑠 0.41

(46)

Equation 46: Number of secondary wires The secondary resistance: 𝑅𝐴𝑊𝐺21 4.1984 ∗ 10 𝑟𝑠 = = 𝑆𝑛𝑠 3

−5

𝛺 𝑚𝑚 = 14 𝜇𝛺 𝑚𝑚

(47)

Equation 47: Secondary resistance Value of resistance for the secondary winding:

𝑅𝑠 = 𝑁2 ∗ 𝑀𝐿𝑇 ∗ 𝑟𝑠 = (30)(134)(14) = 0.0563 = 56.3 𝑚𝛺

(48)

Equation 48: Secondary resistance value

3.2.1b Losses in HF transformer Total copper losses:

2 𝑃𝑐𝑢 = 𝑃𝑝 + 𝑃𝑠 = 𝑅𝑝 𝐼𝑖𝑛 + 𝑅𝑠 𝐼𝑠2 = (767.82 𝜇𝛺)(29 𝐴)2 + (56.3 𝑚𝛺)(4 𝐴)2 = 1.546 𝑊 (49)

Equation 49: Total copper losses 43

Transformer regulation:

𝛼=

𝑃𝑐𝑢 1.546 100 = ∗ 100 = 0.221 % 𝑃𝑜𝑢𝑡 700

(50)

Equation 50: Transformer regulation

3.2.2 Output Filter Inductor Design In this project, the Kool Mu toroidal core is chosen as the output inductor. The reason for this is due to Kool Mu’s core having high saturation level (up to 10 500 Gauss) and core loss being significantly less in high frequency application. The procedure used to design the inductor is found in “Magnetics Power Core Catalog”. Two design parameters are needed to determine the core size and number of turns. They are the inductance needed with DC bias and the DC current. Table 5 lists the specification needed on the output filter inductor.

Figure 14: Core loss curve comparison

44

Specification

Value

Minimum inductance value (Lmin)

2 mH

Calculated inductance value (Lcalc)

1.538 mH

DC current (Io)

3.9 A

AC current (ΔI)

0.585 A

Output power (Po)

700 W

Ripple frequency (fr)

2*30 kHz = 60 kHz

Table 6: Output inductor design parameters

Peak current value across the inductor:

𝐼𝑝𝑘 = 𝐼𝑜 +

Δ𝐼 0.585 = 3.9 + = 4.1925 𝐴 2 2

(51)

Equation 51: Inductor Peak current value The product of LI2:

2 𝐿𝑐𝑎𝑙𝑐 𝐼𝑝𝑒𝑎𝑘 = (1.538)(4.1925)2 = 27.03 𝑚𝐻 ∗ 𝐴2

(52)

Equation 52: LI^2 product

45

Figure 15: Kool Mu core selector chart From the LI2 product in equation (52) and from Fig. 9, a Kool Mu core having a permeability of 60μ is needed and the Kool Mu core part number is: 77716AC. The core that lies above the diagonal permeability line is chosen.

Figure 16: Kool Mu toroidal core

46

For winding this core, the core size and dimension are needed. From the datasheet, the specifications of this core are:

𝑀𝑎𝑥 𝑂𝐷 (𝐴) 𝑑𝑖𝑚𝑒𝑛𝑠𝑖𝑜𝑛 = 72.4 𝑚𝑚

𝑀𝑎𝑥 𝐻𝑇 (𝐶) 𝑑𝑖𝑚𝑒𝑛𝑠𝑖𝑜𝑛 = 40.6 𝑚𝑚

73 𝑛𝐻 ± 8% 𝑇𝑢𝑟𝑛𝑠 2 67.16 𝑛𝐻 = (73)(0.92) = 𝑇𝑢𝑟𝑛𝑠 2 𝐴𝐿 =

𝐴𝐿𝑚𝑖𝑛

(53)

Equation 53: Minimum nominal inductance The number of turns is found as:

𝐿 2 𝑚𝐻 𝑁=√ =√ = 172.56 𝑡𝑢𝑟𝑛𝑠 67.16 𝑛𝐻 𝐴𝐿 𝑇𝑢𝑟𝑛𝑠 2

(54)

Equation 54: Number of turns The resulting magnetic force (DC bias) in oersteds:

𝐻=

0.4𝜋𝑁𝐼 (0.4𝜋)(172.56)(3.9) = = 66.56 𝑜𝑒𝑟𝑠𝑡𝑒𝑑𝑠 𝐿𝑒 127

(55)

Equation 55: DC bias Where, Le is the path length which is 127 mm from datasheet.

47

Figure 17: Per unit permeability vs. DC bias From Fig. 11 at 66.56 oersteds, there is a roll-off of 0.65 in per unit of initial permeability (μpu). Therefore, the number of turns must be increased to take into the account of reduction of initial permeability.

Adjusted number of turns:

𝑁=

172.56 = 265.47 ≅ 266 𝑡𝑢𝑟𝑛𝑠 0.65

(56)

Equation 56: Adjusted number of turns Due to availability of parts, the Kool Mu core chosen is the part number 77192A7 rather than the 77716A7. This core is slightly larger than the 77716AC and has a higher nominal inductance (138 nH/Turns2).

48

3.2.2a Wire selection for output inductor

Figure 18: Core dimensions The AWG21 magnetic wire is also selected for this section.

26 𝐶𝑖𝑟𝑐𝑢𝑚𝑓𝑒𝑟𝑒𝑛𝑐𝑒 = 2𝜋𝑅 = (2𝜋) ( ) = 81.68 𝑚𝑚 2

(57)

Equation 57: Circumference of inner core 𝑊𝑖𝑑𝑡ℎ 𝑜𝑓 𝐴𝑊𝐺21 = (0.8)(3) = 2.4 𝑚𝑚

(58)

Equation 58: Width of AWG21 𝑡𝑢𝑟𝑛𝑠 81.68 = = 34.03 𝑙𝑎𝑦𝑒𝑟 2.4

(59)

Equation 59: number of turns/layer 𝑇𝑜𝑡𝑎𝑙 𝑙𝑎𝑦𝑒𝑟𝑠 =

266 = 7.82 ≅ 8 𝑙𝑎𝑦𝑒𝑟𝑠 24.03

(60)

Equation 60: Total layers This core will have the inductance equal to or greater than the one needed when biased with the specified DC current.

49

3.2.3 Snubber Design The snubber is placed across the switches on the primary side in the DC-DC converter. It is used to reduce the peak voltage at turn-off and to damp the ringing. A quick snubber design procedure is outlined in this section. [32] contains this procedure.

Figure 19: Snubber design (Source: http://www.cde.com/resources/technical-papers/design.pdf)

In this project: Io is the primary DC current and Eo is the source voltage.

𝑅𝑠 =

𝐸𝑜 48 = = 1.23 ≅ 1.2 𝛺 𝐼𝑜 38.9

(61)

Figure 20: Series resistor Due to availability of parts in lab, a 10 Ω power resistor was used for the snubber. The initial voltage step due to the current flowing in 𝑅𝑠 is no greater than the clamped output voltage. The power dissipated in 𝑅𝑠 is estimated from peak energy stored in Cs:

𝐶𝑠 𝐸𝑜2 𝑈𝑝 = 2

(62)

Equation 61: Stored energy in a capacitor 50

The average power dissipation at a switching frequency:

𝑃𝑑𝑖𝑠𝑠 = 𝐶𝑠 𝐸𝑜2 𝑓𝑠

(63)

Equation 62: Estimate of power dissipation A good choice to make 𝐶𝑠 to be equal to twice the sum of the output capacitance of the switch and estimated mounting capacitance. From STP160N75F3 datasheet, the output capacitance is 1080 pF and the mounting capacitance is a typical value estimated at 40 pF.

(64)

𝐶𝑆 = 2(1080 + 40) = 2.24 𝑛𝐹 Equation 63: Capacitor in snubber 𝑃𝑑𝑖𝑠𝑠 = (2.24 𝑛𝐹)(48)2 (30 𝑘𝐻𝑧) = 0.154 𝑊

(65)

Equation 64: Dissipated power

𝑈𝑝 =

(2.24)(48)2 = 2.58 𝜇𝑊 2

(66)

Equation 65: Power dissipated in Rs

3.2.4 Converter losses The losses for the power MOSFET and the output diodes is considered in this section.

Device

RDS(ON)

tr+tf

Vbr

Id at 100 °C

STP160N75F3

4 mΩ

65 ns + 15 ns

75 V

120 A

Table 7: Power MOSFET

51

The diodes chosen for this project are the STTH8R06 “Ultrafast diode”. The reason for this selection of diodes is due to its ultrafast switching and lower switching losses.

Device

VF at 175 °C

trrMax

VRRM

IF at 100 °C

IRM

STTH8R06

1.4 V

25 ns

600 V

8A

5.5 A

Table 8: Diode parameters For the conduction and switching losses, it is assumed that circuit operates in worst case condition.

2 𝑃𝑐𝑜𝑛𝑑 = 1.6𝑅𝑑𝑠,𝑂𝑁 𝐼𝑀𝑜𝑠,𝑅𝑀𝑆 = (1.6)(0.004)(41)2 = 10.76 𝑊

(61)

Equation 66: Conduction loss in MOSFET 𝑃𝑔𝑎𝑡𝑒 = 𝑄𝑔 𝑉𝑔𝑠 𝑓 = (85 𝑛𝐶)(20 𝑉)(30 𝑘𝐻𝑧) = 0.051 𝑊

(62)

Equation 67: MOSFET gate loss

𝑃𝑆𝑊,(𝑂𝑁+𝑂𝐹𝐹) =

𝑉𝑏𝑟 𝐼𝑑 (𝑡𝑟 + 𝑡𝑓 ) (75)(120)(65𝑛 + 15𝑛) = = 10.8 𝑊 (2)(33.33𝜇) 2𝑇

(63)

Equation 68: Switching losses in MOSFET 𝑃𝑐𝑜𝑛𝑑,𝐷𝑖𝑜𝑑𝑒 = 𝑉𝐹 𝐼𝑠𝑒𝑐,𝑅𝑀𝑆 = (1.4) (

3.9 ) = 3.86 𝑊 √2

(64)

Equation 69: Conduction losses in diode From diode datasheet, VRRM = 600 V however VRRM = 350 V is considered.

𝑃𝑑𝑖𝑜𝑑𝑒,𝑆𝑊 =

((350)(5.5)(25)(30 𝑘𝐻𝑧)) 𝑉𝑅𝑅𝑀 𝐼𝑅𝑀 𝑡𝑟𝑟𝑀𝑎𝑥 𝑓= = 0.72 𝑊 2 2

(65)

Equation 70: Switching losses in diode 52

CONVERTER LOSSES Diode Conduction Losses: 14.73%

Diode Switching Losses: 2.75%

Mosfet Switching Losses: 41.23%

Mosfet Conduction Losses: 41.27%

Figure 21: Distribution of converter losses To reduce the conduction losses, 4 power MOSFET are in parallel connection. The conduction power loss is simply divided by four.

Diode Switching Losses: 4%

Diode Conduction Losses: 21.3%

CONVERTER LOSSES Mosfet Conduction Losses: 15%

Mosfet Switching Losses: 59.72%

Figure 22: Distribution of losses with 4 parallel MOSFETs 53

3.3 Inverter Low Pass Filter Design The low-pass filter design is needed to remove the high frequency sPWM switching leaving a smooth 60 Hz sine wave. The filter should not attenuate the 60 Hz fundamental frequency.

As a rule of thumb, the cut-off frequency must be 10 times away from the fundamental to avoid attenuation. But to have more ideal filter, the cut-off frequency must be logarithmically equally far away from the switching and fundamental frequency. 𝐹𝑐 = √𝑓0 𝑓𝑠𝑃𝑊𝑀 = √(60)(20000) = 1095 𝐻𝑧

(66)

Equation 71: Filter cut-off frequency The capacitor should be a suitable value in order not to add reactive current through the inductor thereby immaturely saturating the inductor. Therefore, the capacitor was chosen based upon an additional 250 mA reactive current on top of the load current flowing through the inductor in order to provide the filtering action.

Now, 𝑉 = 120 𝑉 and 𝐼𝑐 = 250 𝑚𝐴 so the following can be found.

𝑋𝑐 =

𝑉 120 = = 480 𝛺 𝐼𝑐 0.25

(67)

Equation 72: Capacitive reactance

54

Then the capacitance value is found using 𝑋𝑐 = (𝜔𝑐)−1:

𝐶≤

1 1 = = 5.526 ≅ 5.6 𝜇𝐹 2𝜋𝑓0 𝑋𝑐 (2𝜋)(60)(480)

(68)

Equation 73: Filter capacitor value

Therefore, the capacitor must be equal or less than 5.6 μF. The inductor is predetermined to be 100 mH from already available parts. So the inductive reactance is found as: 𝐹𝑐 =

1

(69)

2𝜋√𝐿𝐶

Equation 74: Resonant frequency of filter Solving for C: 𝐶=

1 4𝜋 2 𝐹𝑐2 𝐿

=

1 4𝜋 2 (1095)2 (0.1)

= 211.2 𝑛𝐹

(70)

Equation 75: Actual filter capacitor value

Capacitor chosen as a standard value of 220 nF.

55

4. Implementation of Design The implementation of the PSW is done through two stages: implementation and testing of DC-DC converter and implementation and testing of the inverter.

4.1 DC-DC converter implementation Before the entire topology of the push-pull converter could be implemented on a test board and the PCB, the high-frequency transformer and the output inductor need to be winded and tested.

4.1a High-frequency transformer implementation The winding of the secondary side(HV) includes 22 bundles of 3 turns around the bobbin. Secondary side was winded first to accommodate the thick wires for the centre tap primary windings.

Figure 23: Secondary winding turns 56

Similarly, the primary is winded along with centre tap wires terminated at the bobbin. Fig. 22 shows the arrangement of the centre tap windings.

Figure 24: Centre tap primary windings

The finished primary and secondary windings with the core included are shown Fig 23 and 24.

Figure 25: Complete transformer winded 1 57

Figure 26: Complete transformer winded 2 In order to reduce the air gaps, a zip tie is used through the bobbin and clasping the two e-core as much as possible.

Figure 27: Reduced air gap transformer Now measurements will be conducted using an LCR meter to confirm the primary inductance, secondary inductance, turns ratio and leakage inductance. 58

Figure 28: Primary center-tap transformer

Figure 29: Inductance measurement

Figure 30: Primary inductance

59

Note that this value is taken from the positive primary wire to the center tap which is common to both primaries. From equation (33), the calculated primary inductance is 65 μH and this closely matches the measured one at 67.1 μH. Similarly, for the second primary; a similar value to 67.1 μH which confirms the polarity dot connection from Fig. 19. The secondary inductance was measured and shown in Fig. 20.

Figure 31: Secondary inductance measurement The turns ratio:

𝑁𝑠 7.417 𝑚𝐻 = √𝐼𝑛𝑑𝑢𝑐𝑡𝑎𝑛𝑐𝑒 𝑟𝑎𝑡𝑖𝑜 = √ = 10.5 𝑁𝑝 67.1 𝜇𝐻

(66)

Equation 76: Measured turns ratio Compared to equation (11), the measured turns ratio is similar to calculated turns ratio. To confirm the above calculations a voltage signal was injected into the

60

primary winding and a reading was taken from the secondary. Fig. 29 illustrates the procedure.

Figure 32: Turns ratio test

Leakage inductance is result due to the imperfect magnetic linking from one winding to another. This leakage inductance is shown as an inductor in parallel with the primary. To measure leakage inductance, the secondary is left open and LCR is measures the inductance of the primary winding. The value measured is the primary inductance plus the leakage inductance.

Figure 33: Measuring leakage inductance 1

61

Figure 34: Primary inductance with secondary open

𝐿𝑡𝑜𝑡𝑎𝑙 = 𝐿𝑝 + 𝐿𝑙𝑒𝑎𝑘𝑎𝑔𝑒 = 280.19 𝜇𝐻

(67)

Equation 77: Measured total inductance Now, the secondary side is shorted and inductance is measured again from the primary. Due to the short, only the leakage inductance should be measured.

Figure 35: Measuring leakage inductance 2

Figure 36: Primary inductance with secondary short

62

Therefore: 𝐿𝑙𝑒𝑎𝑘𝑎𝑔𝑒 = 1.5 𝜇𝐻

(68)

Equation 78: Leakage inductance value

Figure 37: Testing of high-frequency transformer

From Fig. 33, the output is regulated at 180 V from a 24.2 V input.

4.2 Implementation of the three level SPWM 4.2.1 Internal Registers The 3-level PWM signal is produced using internal registers of the Arduino microcontroller (ATMEGA 2560). The registers are setup to produce a PWM waveform suitable for controlling the power MOSFET’s of the inverter.

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The internal registers are manipulated as follows:

Figure 38: Timer/Counter1 Control Register A Bit Setup In Control Register A, TCCR1A is used to enable the wave generate mode (WGM) of the Arduino. For 0b10100010: WGM11, COM1B1, COM1A1 are enabled.

Figure 39: Timer/Counter1 Control Register B Bit Setup In Control Register B, TCCR1B is used to enable the wave generation mode (WGM). For 0b00011001: CS10, WGM12, WGM13 are enabled.

Figure 40: Timer/Coumter1 Interrupt Mask Bit Setup

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In Interrupt Mask Register, 0b00000001 enables TOIE1 Bit 0 – TOIEn: Timer/Countern, Overflow Interrupt Enable Interrupt Service Routine (ISR) defines what code is to be run continuously and sets the timer to be used by that segment of code. When this bit is written to one, and the I-flag in the Status Register is set (interrupts globally enabled), the Timer/Countern Overflow interrupt is enabled. The above-mentioned registers are used in conjunction to enable Mode 14 of the Waveform Generation Mode Bit table, shown below. In this mode, Fast PWM mode of the Arduino is initialized.

Table 9: Wave Generation Bits (Source of Figures and Tables: ATMEL, “Atmel ATmega640/V-1280/V 1281/V-2560/V-2561/V,” 8-bit Atmel Microcontroller with 16/ 32/64KB In-System Programmable Flash, Feb-2014. [Online]. Available: http://www.atmel.com/Images/Atmel-2549-8-bit-AVR-Microcontroller-ATmega640-1280-12812560-2561_datasheet.pdf)

65

4.2.2 Fast PWM The fast PWM mode provides a high frequency PWM waveform generation option. The fast PWM differs from the other PWM options by its single-slope operation. The counter counts from BOTTOM to TOP then restarts from BOTTOM. The TOP value is set by the Input Compare Register (ICRn), which will be explained in detail in the subsequent sections. Due to the single- slope operation, the operating frequency of the fast PWM mode can be twice as high as the phase correct and phase and frequency correct PWM modes that use dual-slope operation. This high frequency makes the fast PWM mode well suited for power regulation, rectification, and DAC applications. High frequency allows physically small sized external components (coils, capacitors), hence reduces total system cost.

Figure 41: Fast PWM Timing Diagram

66

Table 10: Compare Output Mode for Fast PWM The table above shows how Fast PWM utilizes Compare Output Mode; COM1A1 & COM1B1 are both set to 1 and COM1A0 & COM1B0 are set to 0, when configuring TCCR1A, which means the output compare registers are in non-inverting mode.

Table 11: Clock Select Bit Description The table above shows Clock Select Bit Description, CS10 is initialized while initializing TCCR1B and sets our clock to 16MHz with no pre-scaling.

4.2.3 Lookup Table The value of ICR1 is decided per the Arduino’s internal clock and the carrier frequency.

67

𝐼𝐶𝑅1 =

𝐼𝑛𝑡𝑒𝑟𝑛𝑎𝑙 𝐶𝑙𝑜𝑐𝑘 𝐹𝑟𝑒𝑞𝑢𝑒𝑛𝑐𝑦 16𝑀𝐻𝑧 = = 800 𝐷𝑒𝑠𝑖𝑟𝑒𝑑 𝑆𝑤𝑖𝑡𝑐ℎ𝑖𝑛𝑔 𝐹𝑟𝑒𝑞𝑢𝑒𝑛𝑐𝑦 20𝑘𝐻𝑧

(69)

Equation 79: Input compare register In the project, a switching frequency of 20kHz set for MOSFET’s, due to suggestions in most Power Electronic textbooks, and based on the components designed in the DC-DC portion. This value (800) is compared with the output compare register values (OCR1A & OCR1B) set by the lookup table generator in MATLAB. The lookup table is generated using the following code:

Figure 42: Lookup Table Code In section 2.3.1a, the PWM waveform was described as being like an AM waveform, this idea will be revisited and compared with the MATLAB code in Figure 40. The desired output frequency of the inverter is 60Hz. It is designed to be able to power common electrical and electronic devices. The 60Hz will be the modulating signal of the sPWM. This will be the signal amplitude of the duty cycle of the pulse widths will be based upon.

68

In the development of the sPWM waveform, each full waveform will be comprised of a certain number of pulse widths, which is calculated via MATLAB based on the desired switching frequency and the required output frequency. 𝑆𝑎𝑚𝑝𝑙𝑒 =

𝐷𝑒𝑠𝑖𝑟𝑒𝑑 𝑆𝑤𝑖𝑡𝑐ℎ𝑖𝑛𝑔 𝐹𝑟𝑒𝑞𝑢𝑒𝑛𝑐𝑦 20𝑘𝐻𝑧 = ≅ 332 𝑂𝑢𝑡𝑝𝑢𝑡 𝑆𝑖𝑔𝑛𝑎𝑙 𝐹𝑟𝑒𝑞𝑢𝑒𝑛𝑐𝑦 60𝐻𝑧

(70)

Equation 80: Sample number

The 60Hz sine wave will be sampled at 20kHz, which resulted in approximately 332 points (referred to as ‘samples’ in the code). The Arduino cannot produce a negative voltage; thus, only the amplitudes of the positive half of the waveform is required, and as such, the sample values is divided by two. To sample the signal at the correct times, the output signal period is divided by the number of samples, and is also divided by two; this value is referred to as ‘StopTime’ in the code, and will set the run time of program.

Figure 43: Lookup Table Output Plots Lastly, the lookup table values (Figure 41) are generated via the sine wave function 69

in MATLAB. Then this is plotted with each value multiplied by the ICR value to normalize to meet the compare register requirements of the Arduino microcontroller. For example: If the output compare register value is outputs 403 then the duty cycle of that pulse would be 0.503 (≃50%), and occurs at approximately 1.4ms (≃ 1.38)

Figure 44: Sample Lookup Table outputs: Amplitude(Left) and Time (Right) As stated prior, the Arduino is incapable of outputting negative values (negative voltages); thus, two positive waveforms are produced with the 2nd half being identical to the first, but 180 degrees out of phase. Therefore, two output registers are required, acting as the HIGH inputs to MOSFET drivers

4.2.4 Arduino sPWM Implementation

Figure 45: Arduino Code Segment-Gate Inputs 70

The lookup table values are used in the Arduino code (full code attached to the Appendix A.5) as the OCRn values (Figure 39). Note: The above code is ran continuously using global interrupts at the internal clock frequency. The application of the sPWM and PWM pins in the circuit will be discussed later in the report.

4.2.4a SPWM Waveforms Test

Figure 46: Inverter Prototype A prototype of the inverter was built as a means of testing the SPWM inputs on the driver in conjunction with the driver and H-Bridge. The drain voltage was tested at approximately 120Vpp and 150Vpp and was passed through the LC filter at the output of the inverter.

71

Figure 47: H-Bridge Input (From microcontroller’s pins 11&12)

Figure 48: Unfiltered Output Response of H-Bridge @120Vpp

72

Figure 49: H-Bridge Output after LC lowpass filter @ 353Vpp

4.3 Inverter MOSFET Operation 4.3.1 MOSFET Gate Driver The output from Arduino pin is 5V at 40mA. This source doesn’t have enough drive to run the H-Bridge on its own. Therefore, the use of MOSFET gate drivers (MGD) is essential to the proper operation of the circuit. To choose the MGD, the following specifications were considered.

The H-Bridge had to work to at least peak voltage of 180V, which comes from the boost stage of the inverter. The gate driver supply voltage had to be at least 10V or higher to operate N-Channel MOSFET IRFP460. Also, to make sure that either 𝑄1 & 𝑄2 or 𝑄3 & 𝑄4 (Fig. 48) are not turned on at the same time, there had to be built in protection.

73

Figure 50: H-bridge

To meet the above criteria, the IR2010 part was selected from Digi-Key® as the MGD.

Figure 51: MOSFET Driver- connections (left) and pinout(right)

74

Figure 52: Driver Specifications (Source of Figures 49-50: I. T. AG, “Products,” Infineon Technologies. [Online]. Available: http://www.infineon.com/cms/en/product/power/gate-driver-ics/level-shift-gate-drivers/high-andlow-side-drivers/IR2010/productType.html?productType=5546d462533600a401533d22608a563b.)

The capacitors between 𝑉𝑑𝑑 − 𝑉𝑠𝑠 , 𝑉𝑐𝑐 − 𝐶𝑂𝑀 are decoupling capacitors. Decoupling capacitors in practice are used to compensate for the inductance of the supply lines. The capacitor between 𝑉𝑏 & 𝑉𝑠 is the bootstrap capacitor, the only voltage seen by the bootstrap capacitor is 𝑉𝑐𝑐 − 𝐷𝑖𝑜𝑑𝑒 𝐷𝑟𝑜𝑝. The gate charge for the highside MOSFET is provided by the bootstrap capacitor which is charged by the 15 V supply through the bootstrap diode during the time when the device is off. Since the capacitor is charged from a low voltage source the power consumed to drive the gate is small. There are two ways of calculating bootstrap capacitance, using the formula or using the graph. Both methods are explained in the application note AN-978 from International Rectifier. Here the bootstrap diode blocks the voltage seen at the 𝑉𝑠 terminal of IR2010 from 𝑉𝑐𝑐 . The bootstrap diode is between 𝑉𝑏 & 𝑉𝑐𝑐 of the IR2010.

The IR2010 is a high power, high voltage, and high-speed power MOSFET and IGBT driver with independent high and low side referenced output channels. Logic inputs are compatible with standard CMOS or LSTTL output, down to 3.0V

75

logic. Project requirement for 𝑉𝑂𝐹𝐹𝑆𝐸𝑇 (𝑚𝑎𝑥) 𝑖𝑠 180𝑉, this MOSFET driver can go up to 200V.

Switching time had to be as low as possible, while maintaining the specifications. 𝑡𝑜𝑛 and 𝑡𝑜𝑓𝑓 for this driver is 95ns and 65ns respectively. The gate driver supply range is from 10 to 20V. The MOSFET used is an N-Channel MOSFET (IRFP460) which has a 𝑉𝐺𝑆 of ±20V. A gate driver is a power amplifier that accepts a low power input from the microcontroller (Arduino) and produces a high current drive input for the gate of high power transistor, such as the power MOSFET used in this project. The max current on the Arduino output pin is 40mA, which is not enough to run the MOSFET; therefore, the 𝐼𝑜 of the MOSFET driver is essential to the working of the inverter efficiently. Input capacitance of the MOSFET (IRFP460) is 1300pF; microcontrollers are usually designed to drive loads of less than a 100pF. The maximum 𝐼𝑜 rating of the MGD is 3A; this current is used to charge the gate capacitor of the MOSFET, the higher the current the faster the gate capacitor charges reducing switching losses. The cross-conduction prevention logic prevents the MOSFETs from turning on at the same time, specifically 𝑄1 & 𝑄2 or 𝑄3 & 𝑄4 (see Fig. 48).

4.3.2 MOSFET Consideration MOSFETs are the preferred power transistors over power BJTs because of their fast switching times and their stability over wide operating conditions. Second, because of the high input impedance of the device, the drive circuitry can be of low power, and compact and simple. Two or more MOSFETS can be connected in parallel with ease to supply high-power loads. This is possible because of the positive temperature coefficient of the device; when the MOSFET conducting the 76

higher current heats up it is forced to share its current with the other parallel MOSFETS.

4.3.3 Losses in MOSFET The on-resistance (𝑅𝐷𝑆_𝑂𝑁 ) of a Power MOSFET is a very important parameter because it determines how much current the device can carry for low to medium switching frequencies. For example, a switching frequency of 20kHz used in this project. Paralleling the MOSFETS also reduces the 𝑅𝐷𝑆_𝑂𝑁 of the devices there by reducing conduction losses. During continuous conduction at constant drain current, the MOSFET conduction loss is found simply by calculating 𝐼𝐷2 𝑅𝐷𝑆_𝑂𝑁 . The other source of power loss is through switching losses. As the MOSFET switches on and off, its intrinsic parasitic capacitance (gate capacitance) stores and then dissipates energy during each switching transition. The losses are proportional to the switching frequency and the values of the parasitic capacitances. As the physical size of the MOSFET increases, its capacitance also increases; thus, increasing MOSFET size also increases switching loss.

In

general, a higher switching frequency and a higher input voltage require a lower 𝑄𝐺 , therefore the lower the 𝑄𝐺 the lower the switching losses. To build the H-Bridge per the project requirements the appropriate MOSFET had to be selected. Based on the criteria mentioned above, the least amount of losses had to be taken in to account. In addition, the voltage of 170V on the H-Bridge and the current requirement of 4.2A had to be met. The IRFP460 exceeded the project requirements, as it has the following characteristics;

77

Table 12: MOSFET Specifications (Source: alldatasheet.com, “IRFP460 Datasheet(PDF) - International Rectifier,” IRFP460 Datasheet(PDF) - International Rectifier. [Online]. Available: http://www.alldatasheet.com/datasheet-pdf/pdf/68529/IRF/IRFP460.html. [Accessed: 05-Apr-2017])

Therefore, the IRFP460 is used in conjunction with IR2010 MGD’s to develop the H-Bridge circuit.

4.4 H-Bridge operation in Inverter The sPWM from the Arduino is outputted on to Pins 11 and 12 in conjunction with the alternating digital high and digital low signals on Pins 9 and 10. In the project, two MGDs are used: one to control the switching of MOSFET 𝑆1 and 𝑆2 (Fig. 51) the other MGD controls MOSFET 𝑆3 and 𝑆4 . Pin 11 and 12 are connected to 𝑀𝐺𝐷1 and 𝑀𝐺𝐷2 high input respectively. Also, Pin 9 and 10 are connected to 𝑀𝐺𝐷1 and 𝑀𝐺𝐷2 low input respectively. To operate the H-Bridge 𝑆1 and 𝑆3 are supplied with sPWM from each of the MGD’s 𝐻𝑜 Pin. 𝑆2 and 𝑆4 are used to control the output of the H-Bridge. When 𝑆2 is high the output flows through the load from 𝑆3 and 𝑆2 for one cycle, and for the other half it flows through 𝑆1 to 𝑆2 completing one cycle. This output from the H-Bridge is also an sPWM but much higher magnitude, resembles a sine wave after lowpass LC filter.

78

Figure 53: H-Bridge Operation (Source: “multiple motor h bridge,” Electrical Engineering Stack Exchange. [Online]. Available: https://electronics.stackexchange.com/questions/207319/multiple-motor-h-bridge.)

4.5 Measurement and Protection Circuits When dealing with high powered applications proper caution must be taken when performing measurements. In the full code of the Arduino, sensor values were read via the analog inputs from HV DC bus voltage, HV AC output voltage and AC current of the load and temperature of boost stage transistors. An AC voltage and current transducer was used to measure the AC quantities while a simple voltage divider circuit was used to measure the HV DC bus voltage. transducers are shown in Fig. 52 and Fig 53. The voltage transducer is rated

The as

0-150 VAC with an output DC current of 0-1 mA and should be terminated with a load resistor of 4.99 kΩ (1%) to produce 0-5 VDC that can be inputted in to the microcontrollers analog pins. Similarly, the current transducer is rated as 0-5 A AC and outputs 0-1 mA DC current and should also be terminated with a load resistor of 4.99 kΩ (1%).

79

To test the noise performance and accuracy of the transducers, a test was performed injecting a rated voltage of 120 VAC and 5 AC to terminals 2 and 4 with 10 kΩ terminating resistor at terminals 1 and 2. See figure below.

Figure 54: Voltage and Current transducers with 10 kΩ terminating resistors between 1 and 2

Prior to reading the values directly at the inputs of the microcontroller they must be first stepped down to a safe level acceptable by the Arduino (0-5V). The analog values read from the pins vary from [0,1023] due to their 10-bit resolution; thus, before any conversion takes place in the code, the analog input is multiplied by 1023 to normalize the value back to the [0,5] VDC range. However, for the DC Bus regulation voltage, the [0,170] VDC is stepped down to [0,2.5] VDC as a means of protecting the Arduino. Next, a specific conversion factor (CF) is applied to each analog input value (as show in Table 13) depending the measurement being performed.

80

Measurement

Analog

Conversion factor(CF)

Threshold

Pin AC voltage

1

Overcurrent

3

DC Bus Regulation

5

Digital Pin

𝐶𝐹 =

150𝑉𝑟𝑚𝑠 𝑉𝑟𝑚𝑠 = 30 5𝑉𝐷𝐶 𝑉𝐷𝐶

5𝐴 𝐴 =1 5𝑉 𝑉 180𝑉𝑑𝑐 𝐶𝐹 = = 72 2.5𝑉𝐷𝐶 𝐶𝐹 =

< 106 Vrms

21

= 180 || busOutput 180V then turn on the relay // to shutdown the Inverter digitalWrite(Error, HIGH); flag = 1; } if (currentOutput >= 4) { // If the current is > 4A then pin26 set to HIGH // to the over current protection circuit digitalWrite(OverCurrent, HIGH); digitalWrite(Error, HIGH); flag = 2; } // Temperature reading lcd.setCursor(0, 1); lcd.print(" Temp: "); lcd.print(sensors.getTempCByIndex(0)); // You can have more than one DS18B20 on the same bus; // 0 refers to the first IC on the wire lcd.print("C"); delay(1000); lcd.clear(); float Power = voltageOutput * currentOutput; lcd.print(" Power: "); lcd.print(Power); lcd.print("W"); delay(1000); lcd.clear(); } if (flag == 1) { lcd.setCursor(0, 0); lcd.print("Error"); lcd.setCursor(0, 1); lcd.print("Check Bus O/P"); } if (flag == 2) { lcd.setCursor(0, 0); lcd.print("Error"); lcd.setCursor(0, 1); lcd.print("Check Current"); } }//end of void setup

117

167 168 169 170 180 190 191 192 193 194 195 196 197 198 199 200 201

void loop() {} ISR(TIMER1_OVF_vect) { static int num; OCR1A = lookUp1[num]; if (num < 166) { digitalWrite(pin9, LOW); digitalWrite(pin10, HIGH); } else if (num > 166) { digitalWrite(pin9, HIGH); digitalWrite(pin10, LOW); } OCR1B = lookUp2[num]; if (++num >= 332) { num = 0; // Reset num } }

118

A.8 American Wire Gauge Table

Table 22: American Wire Gauge (AWG)

119

Index 3 3-level, 66 A adjustable feedback resistor, 95 alternate phases, 25

core window area, 39 cross-conduction, 78 current density, 43 Current penetration depth, 42 current transducer, 81, 101 D

amplitude, 25, 26, 27

DC Bus Regulation, 83, 84

Arduino, 20, 25, 26, 29, 66, 67, 70,

DC-DC converter, 20, 21, 22, 32,

71, 72, 73, 76, 78, 80, 99, 103, 105, 113

58, 76, 108 Decoupling, 77

Arduino microcontroller, 20, 66

digital high and digital low, 80

attenuation, 56

drain current, 79

B bipolar output voltage, 24 boost converter, 21 bootstrap capacitance, 78 bootstrap diode, 77 breakdown, 23, 32, 34 C center tap wires terminated, 59 center-tapped, 23

driver, 23, 25, 31, 74, 76, 78 dual-slope operation, 68 duty cycle, 23, 24, 26, 27, 31, 33, 34, 35 E efficiency, 23, 26, 28, 29 Equivalent Series Resistance (ESR), 36 F

compare registers, 69

fast PWM mode, 68

conduction, 24, 54, 55, 79

fast switching, 21, 32, 79

Continuous Conduction Mode, 36

filtered response, 28

Control Register, 66

filtering action, 56

Converter losses, 53

flat topped, 34 120

forward converter, 24 freewheeling diode, 24

K Kool Mu toroidal core, 46, 48

frequency, 24, 25, 27, 31, 37, 42, 43, 47, 58, 65, 68, 70, 73, 79

L

frequency correct, 68

LCR meter, 61

full load, 91, 98, 102

leakage inductance, 32, 37, 61,

fundamental frequency, 56 G Gate capacitor, 78

63, 64 linear switch controller, 26 Logic, 78 low side, 24, 78

gate driver, 78 M H

magnetic field, 21

half bridge, 23

MATLAB, 70

H-Bridge, 24, 25, 74, 75, 76, 80, 81

Maximum input RMS current, 34

high frequency, 21, 23, 32, 43, 46,

Maximum Operating Flux Density,

68

38

high power, 16, 32, 78

modulator, 24

high side, 24

MOSFET, 21, 25, 32, 34, 53, 54, 55,

high-power loads, 79 I implementation, 58 inductive loads, 92

66, 70, 76, 77, 78, 79, 80, 105 mounting capacitance, 53 N N-Channel, 32, 76, 78

initial, 50 internal registers, 66

O

Interrupt Service Routine (ISR), 67

oersteds, 49, 50

intrinsic, 79

output diodes, 53

Inversion, 25

Output filter capacitor, 36 Output Power, 31 121

output signal, 27

S

Overcurrent, 83, 84

saturation, 39, 41, 46

over-voltages, 32

Secondary maximum RMS current, 35

P parallel connection, 55 parasitic capacitances, 79 Passive, 9, 88 PCB, 37, 58, 108, 109 peak current values, 38 permeability, 48, 50 phase correct, 68 polarity dot, 62 power dissipated, 52 power factor, 93 power inverter, 16, 20 prototype, 74 pulsing waveforms, 29 pure sine wave, 16, 28

shorted, 64 sine wave, 16, 29, 30, 81 Sinusoidal waveform, 27 Skin effect, 43, 44 snubber, 13, 52, 53 soft-start circuitry, 31 SPWM, 25, 29, 68, 74, 80 steady-state operation, 21 switching converter, 21 switching losses, 27, 53, 54, 79 switching period, 33 T the Input Compare Register (ICRn), 68

push-pull topology, 23

Total copper losses, 46

PWM control, 23

total harmonic distortion, 26

R RDS (on) resistance, 24 reactive current, 56 rectifier diodes, 25 Regulation, 38 ripple current, 35

transformer, 22, 23, 24, 32, 37, 38, 39, 40, 42, 46, 58, 59, 60, 61, 65 transformer isolated, 22, 23 Transformer turns ratio, 34 U Uninterruptible power supply, 16 unload test, 85 122

V Voltage mode, 32 voltage transducer, 81

Wire selection, 42, 51 Z zero-crossing level, 25, 26, 29

W waveform coefficient, 39

123