# Review of Basic Electrical and Magnetic Circuit Concepts

## Presentation on theme: "Review of Basic Electrical and Magnetic Circuit Concepts"— Presentation transcript:

Review of 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 Electrónica de Potência © 2008 José Bastos Chapter 3 Basic Electrical and Magnetic Circuit Concepts

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

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

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

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. Electrónica de Potência © 2008 José Bastos Chapter 3 Basic Electrical and Magnetic Circuit Concepts

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

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 (f1) The current signal has many harmonics (multiples) of the fundamental The harmonics can be calculated by Fourier Analysis Electrónica de Potência © 2008 José Bastos Chapter 3 Basic Electrical and Magnetic Circuit Concepts

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

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

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

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

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

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

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

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

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

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

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

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

Chapter 3 Basic Electrical and Magnetic Circuit Concepts
Ampere’s Law Electrónica de Potência © 2008 José Bastos Chapter 3 Basic Electrical and Magnetic Circuit Concepts

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

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

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

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

Chapter 3 Basic Electrical and Magnetic Circuit Concepts
Faraday’s Law Electrónica de Potência © 2008 José Bastos Chapter 3 Basic Electrical and Magnetic Circuit Concepts

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

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

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

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

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

Transformer Equivalent Circuit
Lm N2/N1 Lm Electrónica de Potência © 2008 José Bastos Chapter 3 Basic Electrical and Magnetic Circuit Concepts

Chapter 3 Basic Electrical and Magnetic Circuit Concepts
Ideal Transformers R1=R2=0 Ll1=Ll2=0 Core permeability = Electrónica de Potência © 2008 José Bastos Chapter 3 Basic Electrical and Magnetic Circuit Concepts