Sinusoidal steady state power calculations
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SINUSOIDAL STEADY-STATE POWER CALCULATIONS. Prepared by: Ertuğrul Eriş Reference textbook: electric Circuits, Nilsson/Riedel. Updated: November 2011. INSTANTANEOUS POWER. Zero time: the instant the current passing through a positive maximum. This reference system requires

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Sinusoidal steady state power calculations

SINUSOIDAL STEADY-STATE POWER CALCULATIONS

Prepared by: Ertuğrul Eriş

Reference textbook: electric Circuits, Nilsson/Riedel

Updated: November 2011

Ertuğrul Eriş


Instantaneous power

INSTANTANEOUS POWER

Zero time: the instant the current

passing through

a positive maximum.

This reference system requires

a negative phase shift of both

the voltage and current by θi.

Ertuğrul Eriş


Sinusoidal source

SINUSOIDAL SOURCE

Cos(ωt+Φ)

Cos ωt

Phase shift

+→Left

_ - →Right

Ertuğrul Eriş


Instantaneous power average and reavtive power

INSTANTANEOUS POWER, AVERAGE AND REAVTIVE POWER

Ertuğrul Eriş


Power

POWER

First term in instantaneus Power, average Power (Real Power),

constant, transformed to non electrical energy(light, heat) this energy is charged by the power companies

Second and third terms in instantaneus Power, frequency doubled, related average energy over a period is zero

Power factor (güç faktörü) = 0 max power

cos(φ), φ=θv-θi= π/2 power (0)

Ertuğrul Eriş


Power for purely resistive circuits

POWER FOR PURELY RESISTIVE CIRCUITS

ω=377 rad/sn, f=60 hz

Amplitude, Vmİm=2 assumed

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Lagging power for purely inductive circuits

«LAGGING POWER» FOR PURELY INDUCTIVE CIRCUITS

Reactive Power unit

VAR(Volt Amper Reactive)

Amplitude, Vmİm=2 assumed

Ertuğrul Eriş


Leading power for purely conductive circuits

«LEADING POWER» FOR PURELY CONDUCTIVE CIRCUITS

Reactive Power unit

VAR(Volt Amper Reactive)

Amplitude, Vmİm=2 assumed

Genlik, Vmİm=2 düşünülmüştür

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Example

EXAMPLE

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Rms root mean square voltage current values

RMS(ROOT MEAN SQUARE) VOLTAGE/CURRENT VALUES

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Power delivered to a resistor r for ac and dc sources

POWER DELIVERED TO A RESISTOR «R» FOR AC AND DC SOURCES

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Example1

EXAMPLE

Ip=180mA

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Complex power phasors

COMPLEX POWER /PHASORS

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Example2

EXAMPLE

P=8 kW

V=240 V rms

Pf=0.8

Complex S?

Load empedance?

S=8+j6 KVA

Z= 5.76ej36.87=4.608+j3.456

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Various power calculations

VARIOUS POWER CALCULATIONS

S= VeffI*eff= (1/2)VI*

Veff=Veffejθv

Ieff=Ieffejθi

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Power consumptions for some home appliances

POWER CONSUMPTIONS FOR SOME HOME APPLIANCES

  • Heater 1-2KW

  • Owen1-2KW

  • Refrigerator200-250W

  • Washıng Machine600-1000W

  • TV100-200W

  • Vacuum cleaner500-1000W

  • Dishwasher700-1000W

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Alternate forms for complex power

ALTERNATE FORMS FOR COMPLEX POWER

S=ZIeffI*eff

P=|Ieff|2R=(1/2) im2 R

Q=|Ieff|2X=(1/2) im2 X

P= =|Veff|2/R

Q= =|Veff|2/X

Ertuğrul Eriş


Example 1 power compensation

EXAMPLE-1: POWER COMPENSATION

precompensatıon

Vm=(R2+ω2L2)1/2 I1m

φ= φv- φi=atctg(ωL/R)

φ=530

cos φ=0,6

I1m =19,3 A

I1eff =13,7 A

Pave = 1876 Watt

Preactive=2409 VAR

aftercompensation

C=155μF

Vm=(R2+ω2L2)1/2 I1m

φ=00

Cos φ=cos( φv- φ ) =1; Sin φ=0

ZL= | ZL |e j φ= | ZL |= R / (1-ω2LC)2+ ω2R2C2=25.8

Resistive!

Im =12 AI1m =19,3 A

Ieff =8,53 AI1eff =13,7 A

Pave = 1876 Watt

Preactive=0 VAR

Ertuğrul Eriş


Example 2

EXAMPLE 2

SLoad=975+j650; Sline=25+j100; delivered power: Ss=-(1000+j750)

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Example 21

EXAMPLE 2

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Maximum power transfer

MAXIMUM POWER TRANSFER

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Maximum power transfer1

MAXIMUM POWER TRANSFER

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Example 1

EXAMPLE 1

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Example 22

EXAMPLE 2

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Example 3

EXAMPLE 3

a. What impedance should be connected across terminals a,b for a maximum power transfer

b. What is the maximum power transferred to the impedance in (a)?

c. Assume that the load is restricted to pure resistance. What size resistor connected across a,b will result in the maximum aserage power transfer?

d. What is the maximum power transferred to the resistor in (c)?

ig=3cos5000t A

a. 20-j10; b.18W; c. 22.36Ω; d.17W

Ertuğrul Eriş


Sinusoidal steady state power calculations

EXAMPLE 4

İ2(rms)=840/140

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Sinusoidal steady state power calculations

PROGRAM DESIGN

DEPT, PROGRAM

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STUDENT

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PROGRAM OUTCOMES

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STATE, ENTREPRENEUR

FIELD

QALIFICATIONS

EU/NATIONAL QUALIFICATIONS

KNOWLEDGE

SKILLS

COMPETENCES

NEWCOMERSTUDENT

ORIENTIATION

GOVERNANCE

Std.

questionnaire

ALUMNI, PARENTS

ORIENTIATION

STUDENT

PROFILE

Std.

questionnaire

FACULTY

NGO

STUDENT,

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CIRCICULUM

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INTRERNAL CONSTITUENT

Std.

questionnaire

EXTRERNAL CONSTITUENT

EXTRERNAL CONSTITUENT

REQUIREMENTS

EU/NATIONAL

FIELD QUALIFICATIONS

PROGRAM OUTCOMES

QUESTIONNAIRES

QUALITY IMP. TOOLS

GOAL: NATIONAL/INTERNATIONAL ACCREDITION


Bloom s taxonomy anderson and krathwohl 2001

BLOOM’S TAXONOMYANDERSON AND KRATHWOHL (2001)

!!Listening !!

Doesn’t exits in the original!!!

http://www.learningandteaching.info/learning/bloomtax.htm

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Sinusoidal steady state power calculations

ULUSAL LİSANS YETERLİLİKLER ÇERÇEVESİ

BLOOMS TAXONOMY

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Course assesment matrix

COURSE ASSESMENT MATRIX

LEARNING OUTCOMES

Devre Analizi İlk Ders


Abet engineering outcomes

‘ABET’ ENGINEERING OUTCOMES

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