Topic 7 resonance topic a7

Bài giảng ngành Điện: Giải các bài toán trong mạch điện điện thế thấp một pha và ba pha (Phần A) gồm các chủ đề sau Solve problems in single and threephase low voltage circuits Part A Content Topic 1 Sinusoidal Alternating Voltage and Current_Topic_A1 Topic 2 Phasors_Topic_A2.ppt Topic 3 Resistance in AC Circuits_Topic_A3 Topic 4 Inductance in AC Circuits_Topic_A4 Topic 5 Capacitance in AC Circuits_Topic_A5 Topic 6 AC Circuit Analysis_Topic_A6 Topic 7 Resonance_Topic_A7 Topic 9 Harmonics_Topic_B9

Solve problems in single and

three-phase low voltage circuits

Topic 7: Resonance Part A

Resonance in AC Circuits

 Since inductance and capacitance are

frequency-dependant devices, their reactances will vary with the frequency:

– Inductive reactance is directly proportional to the frequency

– Capacitive reactance is inversely proportional to the

frequency

 Therefore, for every R-L-C circuit, there must be one frequency at which XL will equal the XC When this occurs the circuit is said to have reached resonance.

Frequency and Reactance

Inductive Reactance XL

Capacitive Reactance XC

Frequency

Reactance

Resonant Frequency

XL = XC

 Resonance occurs in an R-L-C circuit when the capacitive reactance (XC) is equal to the inductive reactance (XL).

RESONANCE

XC = XL

This means ALL reactance in the circuit is cancelled, leaving the RESISTANCE as

the only opposition to current flow!

 For a given R-L-C circuit, resonance will

occur at a specific frequency This frequency can be found by:

ƒR = 1

(2π√(LC))LC))))

Where:

ƒR is the resonant frequency in Hertz (Hz) 2π is a constant

L is the Inductance in Henries (H)

C is the Capacitance in Farads (F)

Resonance: Parallel R-L-C Circuit

L=600mH

VS=230V ƒ= ?Hz

R = 100Ω

C = 68μF

Determine the following:

•Resonant Frequency ƒR

• XL and XC at resonance

•IR, IL and IC at resonance

•Draw a phasor diagram to determine Supply Current IS and Phase Angle Ø

•Impedance Z at resonance

Resonance: Parallel R-L-C Circuit

IR

IL

IS

IS is the same as IR

The phase angle (Ø) between IS and VS is zero (IN-PHASE)

IR+C

IC

 Answers

 R = 100 Ω

 XL = 93.93 Ω

 XC = 93.93 Ω

 IR = 2.30 A

 IL = 2.45 A

 IC = 2.45 A

 IS = 2.30 A

 Ø = 0oE In-Phase

 Z = 100 Ω

Effects of Resonance: Parallel Ccts

 IL and IC are equal and opposite

– cancel each other out

 Only current that flows from supply is through the

resistive branch

– Thus IS = IR (Impedance is at it’s highest value)

 Phase angle between VS and IS is 00 (IN-PHASE)

– load appears purely resistive to the supply

 Inductive and capacitive components may have very high circulating currents flowing between them

Effects of Resonance: Series Ccts

 VL and VC are equal and opposite

– cancel each other out

 Impedence triangle is a single horizontal line

– Represents Z as R because X is equal to zero

 Current that flows in the circuit is limited only by the value of R

– Impedance is at it’s lowest value

 The phase angle between the VS and IS is 00

– load appears purely resistive to the supply

 Inductive and capacitive components may have very high

voltage drops across them

– due to oscillating energy between the two components