ee301 lesson 24 ac power and pwr triangle

7/25/2019 EE301 Lesson 24 AC Power and Pwr Triangle

1/23

Lesson 24

AC Power andPower Triangle


2/23

Learning Objectives

Define real (active) power, reactive power, average, andapparent power.

Calculate the real, reactive, and apparent power in ACseries parallel networks.

raph the real and reactive power of purel! resistive,inductive, or capacitive loads in AC series parallel networksas a function of ti"e.

Deter"ine when power is dissipated, stored, or released in

purel! resistive, inductive, or capacitive loads in AC seriesparallel networks.

#se the power triangle deter"ine relationships betweenreal, reactive and apparent power.


3/23

AC $ower

AC %"pedanceis a complex &uantit! "ade upof real resistanceand i"aginar! reactance.

ACApparent$ower is a complex &uantit! "ade

up of real activepower and i"aginar! reactive

power'

R jX= +Z ( )

jQ AP V= +S ( )


4/23

AC eal (Active) $ower ($)

he Active power is the power that is dissipatedin the resistance of the load.

%t uses the sa"e for"ula used for DC (* + % are

the "agnitudes, not the phasors)'22

[watts, W]P I R V

R= =

A-%- #1 mistake with AC power calculations!

he oltagein the above e&uation is the *oltage drop across the resistor, not

across the entire circuit

CA#%O-

/AL value of resistance () is used in /AL power calculations, not

%0$/DA-C/ (1)


5/23

AC %"aginar! (eactive) $ower (2)

he reactive power is the power that is e3changedbetween reactive co"ponents (inductors and capacitors)

he for"ulas look si"ilar to those used b! the active

power, but use reactance instead of resistances.

#nits' *olts4A"ps4eactive (*A)

2 is negative for a capacitor b! convention and positive

for inductor. 5ust like 6 is negative for a capacitor (46cj)

2

2 [VAR]Q I XXV= =

A-%- #1 mistake with AC power calculations!

he oltagein the above e&uation is the *oltage drop across the reactance, not

across the entire circuit


6/23

AC Apparent $ower (7)

he apparent power is the power that is8appears9 to flow to the load.

he "agnitude of apparent power can be

calculated using si"ilar for"ulas to those for

active or reactive power'

#nits' *olts4A"ps (*A)

* + % are the "agnitudes, not the phasors

22

[VA]V

S VI I Z

Z

= = =


7/23

AC $ower -otice the relationship between 1 and 7'

R j X= +Z ( )

P j Q VA= +S ( )

(ealpow

ercalculated

with(

(eactivep

owercalculate

dwith6

Apparentp

owercalculate

dwith1


8/23

$ower riangle

he power trianglegraphicall! shows therelationship between real (P), reactive (Q) and

apparent power (S).

2 2

LP jQ

QPS

S

= +

= +

=

S

S

v

v


9/23

Example Problem 1

Deter"ine the real and reactive power of eachco"ponent.

Deter"ine the apparent power delivered b! the

source.


10/23

eal and eactive $ower

he power trianglealso shows that we can findreal (P) and reactive (Q) power.

cos

sin

S IV

P S

Q S

=

=

=

(*A)

()

(*A)

-O/' he i"pedance angle and

the 8power factor angle9 are the

sa"e value


11/23

Example Problem 2

Deter"ine the apparent power, total real andreactive power using the following e&uations'

cos

sin

S VI

P S

Q S

=

=

=

(*A)

()

(*A)


12/23

otal $ower in AC Circuits

he total power real (PT) and reactive power

(QT) is si"pl! the su" of the real and reactive

power for each individual circuit ele"ents.

How elements are connected does not matterfor computation of total power.

1 2 3 4

1 2 3 4

T

T

P P P P P

Q Q Q Q Q

= + + +

= + + +


13/23

otal $ower in AC Circuits

7o"eti"es it is useful to redraw the circuit tos!"bolicall! e3press the real and reactive power loads


14/23

Example Problem 3

a. Deter"ine the unknown real ($:) and reactive powers

(2;) in the circuit below.

b. Deter"ine total apparent power

c. Draw the power triangled. %s the unknown ele"ent in Load


15/23

Example Problem 4

a. Deter"ine the value of , $and 2

b. Draw the power triangle and deter"ine 7.


16/23

#se of co"ple3 nu"bers in $ower calculations

AC power can be calculated using co"ple3 e&uations.

Apparent $ower can be represented as a co"ple3 nu"ber

he resultant can be used to deter"ine real and reactive power b!

changing it to rectangular for".

*

2

2

P j

= = +

= =

I

S VI

V

S I ZZ

v uvv

uv

v v uv

uv

is co"ple3 conjugate of %2

-O/

he co"ple3 conjugate of Current is used to "ake the power angle the sa"e as

the i"pedance angle


17/23

$ower >actor

Power actor(FP) tells us what portion of theapparent power(S) is actuall! realpower(P).

$ower factor is a ratio given b!

FP= P / S

$ower factor is e3pressed as a nu"ber

between ? to @.? (or as a percent fro" ? to

@??)


18/23

$ower >actor

>ro" the power triangle it can be seen that

FP= P / S = cos

Power actor angleis thus given

= cos-1(P / S)

>or a pure resistance, = 0

>or a pure inductance, = 90 >or a pure capacitance, = -90

-O/' B is the phase angle of 1, not the

current or voltage.


19/23

"nit power actor(FP @)

%"plies that allof a loads apparent power isreal power (S = P).

%f FP @, then = 0.

%t could also be said that the load looks purel!resistive.

Load current and voltage are in phase.


20/23

Lagging power actor(> 0)

he load current lags load voltage ELI %"plies that the load looks inductive.


21/23

Leading power actor(< 0)

he load current leads load voltage ICE %"plies that the load looks capacitive.


22/23

Example Problem 5

a. Deter"ine $,2,7 and the power factor for this circuit.

Draw the power triangle.

b. %s it a leading or lagging power factor=

c. %s the circuit inductive or capacitive=


23/23

Example Problem 6

a. Deter"ine total current, apparent power, and the power

factor for this circuit. %s it a leading or lagging power

factor=

b. Deter"ine total current, apparent power, and the power

factor if the capacitor reactance is decreased to E?

oh"s. hat kind of power factor does it have=

ee301 lesson 24 ac power and pwr triangle

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