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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

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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

Ertuğrul Eriş

lagging power for purely inductive circuits
«LAGGING POWER» FOR PURELY INDUCTIVE CIRCUITS

Reactive Power unit

VAR(Volt Amper Reactive)

Amplitude, Vmİm=2 assumed

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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

Ertuğrul Eriş

example
EXAMPLE

Ertuğrul Eriş

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

Ertuğrul Eriş

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
  • Owen 1-2KW
  • Refrigerator 200-250W
  • Washıng Machine 600-1000W
  • TV 100-200W
  • Vacuum cleaner 500-1000W
  • Dishwasher 700-1000W

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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 A I1m =19,3 A

Ieff =8,53 A I1eff =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

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slide26

EXAMPLE 4

İ2(rms)=840/140

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slide27

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

???

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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slide29

ULUSAL LİSANS YETERLİLİKLER ÇERÇEVESİ

BLOOMS TAXONOMY

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course assesment matrix
COURSE ASSESMENT MATRIX

LEARNING OUTCOMES

Devre Analizi İlk Ders

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