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3-1 Electrónica de Potência © 2008 José Bastos Chapter 3 Basic Electrical and Magnetic Circuit Concepts Chapter 3 Review of Basic Electrical and Magnetic Circuit Concepts Electric Circuits Phasors Power, Power Factor Fourier Analysis Inductors and Capacitors Magnetic Circuits Transformers

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3-2 Electrónica de Potência © 2008 José Bastos Chapter 3 Basic Electrical and Magnetic Circuit Concepts AVERAGE POWER AND RMS CURRENT

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3-3 Electrónica de Potência © 2008 José Bastos Chapter 3 Basic Electrical and Magnetic Circuit Concepts Sinusoidal Steady State

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3-4 Electrónica de Potência © 2008 José Bastos Chapter 3 Basic Electrical and Magnetic Circuit Concepts Phasor Representation R j L Z

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3-5 Electrónica de Potência © 2008 José Bastos Chapter 3 Basic Electrical and Magnetic Circuit Concepts Power, Reactive Power, Power Factor Complex power S Real power is Reactive power is Power Factor Ideally power factor should be 1.0

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3-6 Electrónica de Potência © 2008 José Bastos Chapter 3 Basic Electrical and Magnetic Circuit Concepts Example An inductive load connected to a 120V, 60Hz ac source draws 1 kW at a power factor of 0.8. Calculate the capacitance required in parallel with the load in order to bring the power factor to 0.95.

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3-7 Electrónica de Potência © 2008 José Bastos Chapter 3 Basic Electrical and Magnetic Circuit Concepts Example (end)

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3-8 Electrónica de Potência © 2008 José Bastos Chapter 3 Basic Electrical and Magnetic Circuit Concepts Non-sinusoidal waveforms in steady state

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3-9 Electrónica de Potência © 2008 José Bastos Chapter 3 Basic Electrical and Magnetic Circuit Concepts Non-sinusoidal waveforms in steady state (cont.) -current drawn from power electronic equipment is highly distorted -However -In steady state waveforms repeat with period T=1/f -f is the fundamental frequency (f 1 ) -The current signal has many harmonics (multiples) of the fundamental -The harmonics can be calculated by Fourier Analysis

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3-10 Electrónica de Potência © 2008 José Bastos Chapter 3 Basic Electrical and Magnetic Circuit Concepts Fourier Analysis -a non sinusoidal waveform f(t) repeating with angular frequency can be expressed as

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3-11 Electrónica de Potência © 2008 José Bastos Chapter 3 Basic Electrical and Magnetic Circuit Concepts Fourier Analysis

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3-12 Electrónica de Potência © 2008 José Bastos Chapter 3 Basic Electrical and Magnetic Circuit Concepts Distortion in the Input Current Voltage is assumed to be sinusoidal Subscript 1 refers to the fundamental The phase 1 is between the voltage and the current fundamental

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3-13 Electrónica de Potência © 2008 José Bastos Chapter 3 Basic Electrical and Magnetic Circuit Concepts Line-Current Distortion(1)

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3-14 Electrónica de Potência © 2008 José Bastos Chapter 3 Basic Electrical and Magnetic Circuit Concepts Total Harmonic Distortion -THD

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3-15 Electrónica de Potência © 2008 José Bastos Chapter 3 Basic Electrical and Magnetic Circuit Concepts POWER FACTOR - PF -starting with the definition of average power

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3-16 Electrónica de Potência © 2008 José Bastos Chapter 3 Basic Electrical and Magnetic Circuit Concepts Inductor and Capacitor Phasors (1)

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3-17 Electrónica de Potência © 2008 José Bastos Chapter 3 Basic Electrical and Magnetic Circuit Concepts Inductor and Capacitor Phasors (2)

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3-18 Electrónica de Potência © 2008 José Bastos Chapter 3 Basic Electrical and Magnetic Circuit Concepts Phasor Representation

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3-19 Electrónica de Potência © 2008 José Bastos Chapter 3 Basic Electrical and Magnetic Circuit Concepts ** Inductor and Capacitor Response

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3-20 Electrónica de Potência © 2008 José Bastos Chapter 3 Basic Electrical and Magnetic Circuit Concepts Response of L and C

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3-21 Electrónica de Potência © 2008 José Bastos Chapter 3 Basic Electrical and Magnetic Circuit Concepts Average v L and i C in steady state -steady-state condition implies that voltage and current waveforms repeat with a time period T:

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3-22 Electrónica de Potência © 2008 José Bastos Chapter 3 Basic Electrical and Magnetic Circuit Concepts Inductor Voltage and Current in Steady State Volt-seconds over T equal zero.

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3-23 Electrónica de Potência © 2008 José Bastos Chapter 3 Basic Electrical and Magnetic Circuit Concepts Capacitor Voltage and Current in Steady State Amp-seconds over T equal zero.

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3-24 Electrónica de Potência © 2008 José Bastos Chapter 3 Basic Electrical and Magnetic Circuit Concepts Amperes Law Direction of magnetic field due to currents Amperes Law: Magnetic field along a path

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3-25 Electrónica de Potência © 2008 José Bastos Chapter 3 Basic Electrical and Magnetic Circuit Concepts Amperes Law

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3-26 Electrónica de Potência © 2008 José Bastos Chapter 3 Basic Electrical and Magnetic Circuit Concepts Direction of Magnetic Field

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3-27 Electrónica de Potência © 2008 José Bastos Chapter 3 Basic Electrical and Magnetic Circuit Concepts Flux Lines

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3-28 Electrónica de Potência © 2008 José Bastos Chapter 3 Basic Electrical and Magnetic Circuit Concepts Magnetic Flux

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3-29 Electrónica de Potência © 2008 José Bastos Chapter 3 Basic Electrical and Magnetic Circuit Concepts Concept of Magnetic Reluctance

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3-30 Electrónica de Potência © 2008 José Bastos Chapter 3 Basic Electrical and Magnetic Circuit Concepts Faradays Law

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3-31 Electrónica de Potência © 2008 José Bastos Chapter 3 Basic Electrical and Magnetic Circuit Concepts Definition of Self-inductance L

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3-32 Electrónica de Potência © 2008 José Bastos Chapter 3 Basic Electrical and Magnetic Circuit Concepts Inductance L A l

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3-33 Electrónica de Potência © 2008 José Bastos Chapter 3 Basic Electrical and Magnetic Circuit Concepts Analysis of a Transformer (1) Very simple case:

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3-34 Electrónica de Potência © 2008 José Bastos Chapter 3 Basic Electrical and Magnetic Circuit Concepts Analysis of a Transformer (2)

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3-35 Electrónica de Potência © 2008 José Bastos Chapter 3 Basic Electrical and Magnetic Circuit Concepts Analysis of a Transformer (3)

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3-36 Electrónica de Potência © 2008 José Bastos Chapter 3 Basic Electrical and Magnetic Circuit Concepts Transformer Equivalent Circuit LmLm N 2 /N 1 L m

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3-37 Electrónica de Potência © 2008 José Bastos Chapter 3 Basic Electrical and Magnetic Circuit Concepts Ideal Transformers 1.R 1 =R 2 =0 2.L l1 =L l2 =0 3.Core permeability =

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