Download Chapter 14 Inductive Transients

Survey
yes no Was this document useful for you?
   Thank you for your participation!

* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project

Document related concepts

Pulse-width modulation wikipedia , lookup

Ground loop (electricity) wikipedia , lookup

Power engineering wikipedia , lookup

Immunity-aware programming wikipedia , lookup

Mercury-arc valve wikipedia , lookup

Switch wikipedia , lookup

Memristor wikipedia , lookup

Variable-frequency drive wikipedia , lookup

Transistor wikipedia , lookup

Stepper motor wikipedia , lookup

Ground (electricity) wikipedia , lookup

Power inverter wikipedia , lookup

Flexible electronics wikipedia , lookup

Three-phase electric power wikipedia , lookup

History of electric power transmission wikipedia , lookup

Islanding wikipedia , lookup

TRIAC wikipedia , lookup

Triode wikipedia , lookup

Distribution management system wikipedia , lookup

Rectifier wikipedia , lookup

Schmitt trigger wikipedia , lookup

Power electronics wikipedia , lookup

Electrical ballast wikipedia , lookup

Voltage regulator wikipedia , lookup

Power MOSFET wikipedia , lookup

Ohm's law wikipedia , lookup

Metadyne wikipedia , lookup

Electrical substation wikipedia , lookup

Voltage optimisation wikipedia , lookup

Resistive opto-isolator wikipedia , lookup

Current source wikipedia , lookup

Stray voltage wikipedia , lookup

Surge protector wikipedia , lookup

Switched-mode power supply wikipedia , lookup

Alternating current wikipedia , lookup

Mains electricity wikipedia , lookup

Opto-isolator wikipedia , lookup

Network analysis (electrical circuits) wikipedia , lookup

Buck converter wikipedia , lookup

Transcript
Chapter 14
Inductive Transients
C-C
Tsai
Source:
Circuit Analysis: Theory and Practice Delmar Cengage Learning
Transients

Voltages and currents during a transitional
interval


Capacitive circuit



Referred to as transient behavior of the circuit
Voltages and currents undergo transitional phase
Capacitor charges and discharges
Inductive circuit

C-C Tsai
Transitional phase occurs as the magnetic field builds
and collapses
2
1
Voltage Across an Inductor

Induced voltage across an inductor is proportional
to rate of change of current
vL  L

If inductor current could change instantaneously



i
t
Its rate of change would be infinite
Would cause infinite voltage
Infinite voltage is not possible


Inductor current cannot change instantaneously
It cannot jump from one value to another, but
must be continuous at all times
C-C Tsai
3
Transient due to Inductor
C-C Tsai
4
2
Inductor Voltage

Immediately after closing the switch on an RL circuit
Current is zero
Voltage across the resistor is zero



Voltage across resistor is zero
Voltage across inductor is source voltage


Inductor voltage will then exponentially decay to
zero
5
C-C Tsai
Open-Circuit Equivalent

After switch is closed (t=0+)


Inductor has voltage across it and no current through
it
Inductor with zero initial current looks like an
open circuit at instant of switching
C-C Tsai
6
3
Initial Condition Circuits

Voltages and currents in circuits immediately after
switching (t=0+)


By replacing inductors with opens


Determined from the open-circuit equivalent
We get initial condition circuit
Initial condition networks

Yield voltages and currents only at switching
7
C-C Tsai
Circuit Current and Circuit Voltages




Current i(t) in an RL circuit is an exponentially increasing
function of time
Current begins at zero and rises to a maximum value
Voltage across resistor VR is an exponentially
increasing function of time
Voltage across inductor VL is an exponentially
decreasing function of time
Rt




v R  E  1  e L 


C-C Tsai
vL  E  e  Rt / L
8
4
Time Constant


 = L/R , units are
seconds
The larger the inductance


The larger the resistance


The longer the transient
The shorter the transient
As R increases


Circuit looks more and
more resistive
If R is much greater than L,
the circuit looks purely
resistive
9
C-C Tsai
Example: RL Transients

Given E=50V, R=10, and L=2H, determine i(t).
 = L/R=0.2s
C-C Tsai
or
10
5
Example: RL Transients

Given E=50V, R=10, and L=2H, determine i(t).
 = L/R=0.2s
11
C-C Tsai
Interrupting Current in an
Inductive Circuit

When switch opens in an RL circuit




Energy is released in a short time
This may create a large voltage
Induced voltage is called an inductive kick
Opening of inductive circuit may cause voltage
spikes of thousands of volts
C-C Tsai
12
6
Interrupting a Circuit

Switch flashovers are generally undesirable


These large voltages can be useful


They can be controlled with proper engineering design
Such as in automotive ignition systems
It is not possible to completely analyze such a
circuit

Resistance across the arc changes as the switch opens
13
C-C Tsai
Example: Interrupting a Circuit
C-C Tsai
14
7
Inductor Equivalent at Switching

Current through an inductor


An inductance with an initial current


Same after switching as before switching
Looks like a current source at instant of switching
Its value is value of current at switching
15
C-C Tsai
De-energizing Transients

If an inductor has an initial current I0, equation for
current becomes
i  I 0e t /  '


 ' = L/R. R equals total resistance in discharge path
Voltage across inductor goes to zero as circuit deenergizes
v L  V0 e  t /  '

whereis product of current and
Voltage across any resistor
that resistor. Voltage across each of resistors goes to zero
C-C Tsai
V
v R0  RI0IR0 eT  t / τ '
16
8
De-energizing Transients
17
C-C Tsai
More Complex Circuits

For complex circuits




Determine Thévenin equivalent circuit using
inductor as the load
RTh is used to determine time constant
 = L/RTh
ETh is used as source voltage
C-C Tsai
18
9
Example1: More Complex Circuits
Switch is closed
19
C-C Tsai
Example1: More Complex Circuits
Switch is closed (Cont’d)
C-C Tsai
20
10
Example1: More Complex Circuits
Switch is opened
21
C-C Tsai
Example1: More Complex Circuits
C-C Tsai
22
11
Example2: More Complex Circuits
23
C-C Tsai
Transient Analysis Using Computers
C-C Tsai
24
12
Transient Analysis Using Computers
25
C-C Tsai
Problem: Determine iL and vL
C-C Tsai
26
13
Problem: Determine iL and vL
C-C Tsai
27
14