[email protected] ENGR-43_Lec-09-3_1-Ph_3W_Power.ppt 1 Bruce Mayer, PE Engineering-43: Engineering Circuit Analysis Bruce Mayer, PE Licensed Electrical.

[email protected] • ENGR-43_Lec-09-3_1-Ph_3W_Power.ppt1

Bruce Mayer, PE Engineering-43: Engineering Circuit Analysis

Bruce Mayer, PELicensed Electrical & Mechanical Engineer

[email protected]

Engineering 43

Chp 9 [8-9]Chp 9 [8-9]House House PowerPower



Outline – AC Steady State PowerOutline – AC Steady State Power

Instantaneous Power Concept• For The Special Case Of Steady State

Sinusoidal Signals

Average Power Concept• Power Absorbed Or Supplied During in

Integer Number of Complete Cycles

Maximum Average Power Transfer• When The Circuit Is In Sinusoidal Steady

State



Outline – AC SS Power cont.Outline – AC SS Power cont. Effective or RMS Values

• Heating Value for Sinusoidal Signals

Power Factor• A Measure Of The Angle Between Current

And Voltage Phasors

Power Factor Correction• Improve Power Transfer To A Load By

“Aligning” Phasors

Single Phase Three-Wire Circuits• Typical HouseHold Power Distribution



Single Phase, 3Wire CircuitsSingle Phase, 3Wire Circuits Power Supplied to Most

Houses And Other Residences Takes This form

For residential Electrical Power Service

115V → Lights and convenience (3-prong) Outlets• Powered from

“Line” to Neutral

230V → Large Appliances, e.g; Electric Ovens, Air Cond, Dryers• Run “Line-to-Line”

02302

0115

Vrms

then

Vrms

ab

nban

VV

VVV

Neutral Wire



Residential Electrical ServiceResidential Electrical Service

PG&E Electrical Service

Utility Connection

110/115/120 Vac Circuits Run Line→Neutral

220/230/240 Vac Circuits Run Line→Line



Actual Residential WiringActual Residential Wiring

WattHour Meter Main Service

Disconnect CB• 200 Arms Service

Circuit Breaker Power Distribution Panel

Two,100 AmpCBs



Distrib

utio

n P

anel

Distrib

utio

n P

anel

• 115Vrms15Arms GFICB– BathRooms

• 230Vrms 30A/2Pole CBs– Clothes Dryer– Oven

• 115Vrms20Arms CBs– Appliances

• 115Vrms15Arms CBs– Convenience

OutLets



Single-Single-, 3W Electrical Power, 3W Electrical Power In A “Balanced”

Condition, The Loads across the two Sources are EQUAL

In the N-n Branch for Equal Loads by KCL

Thus the Current in the Neutral Wire is ZERO• This is the Ideal Condition

• And the Neutral Wire is (theoretically) NOT NEEDED

Next, Account for• Line Impedances

• Line-to-Line Loads

0

LLbBaAnN Z

V

Z

VIII



1-1-, 3W Pwr cont, 3W Pwr cont A more Realistic

230Vac, 1 Ckt Model

Analyze Ckt by Superposition

+

If Any Line or Load Z’s are Unequal, Then Ineutral 0



Example – Unbalanced LoadExample – Unbalanced Load Given a 1, 3Wire Household Power Load

aAI A31

A1

By KCL at A, B, N

LSnN

RSbB

RLaA

III

III

III

Assuming Resistive Loads

rmsRR

rmsSS

rmsLL

AVPI

AVPI

AVPI

302407200

2.012024

1120120



Example – Unbalanced Load contExample – Unbalanced Load cont Then The ENERGY use

TimePdttpEnergy average)(

For Each Load, DailykWhHrkWHrkWElights 8.1712.0812.0

kWhHrkWErange 8.28)112(2.7

kWhHrkWEstereo 192.0)35(024.0

The Total Daily Energy Usage

kWhEEkdaily 792.30

month

dayCost

kWhkWhCost

/$

/.$

/.$.

139

624

1507930

Then The Total Cost at 15¢/kWh



Electrical SafetyElectrical Safety Globally, Electrical Power

Systems Run at Frequencies of either • 60 Hz

– USA, Most Asia

• 50 Hz– Most of Europe

The Danger From Electricity is not the Voltage, but the CURRENT Thru the Human body



Grounded NeutralGrounded Neutral Typical 1, 110/115/120 Vrms Household Power Wiring

Note The Neutral Wire is Tied To the Ground Wire• The Neutral and GND wire are Run in Tandem to all Loads

But, The GROUND conductor Does NOT Carry any Working Current; so Why is it there?• As a Safety PreCaution; Illustrate Function by Way of Example



Example – Grounded CaseExample – Grounded CaseWhen switched-on the tool-case is energized

without the ground connector theuser can be exposed to the fullsupply voltage!

Conducting due to wet floor

If the case is grounded then “Joe” is at the Case, i.e. GND, Potential, and Cannot Receive A Shock. Essentially the supply is shorted Around Joe, and the Circuit Breaker Trips to open the circuit. •The Tripped CB Alerts Joe that Something is Wrong Somewhere.

CB

DrillCase



Numerical Example Numerical Example Another Shorted Drill; Ground Prong Removed

Ground prong REMOVED

R(dry skin) 15kOhmR(wet skin) 150OhmR(limb) 100OhmR(trunk) 200Ohm

Suggested resistancesfor human body

150150

Wet skin

400

Limbstrunk

1

mAIbody 171701

120

Can cause ventricular fibrillation



Numerical ExampleNumerical Example A 7.2 kV Power-Line Falls on Car. The Driver can Get Out or Stay in. Which is

better?

Wet Road

Option 1.Driver opens door and steps down.Conduction Path = ARM + TRUNK +LEG

Option 2: Driver stays inside the car• No Path to GND

7200V

Car body is good conductor

Tires are insulators

R(dry skin) 15kOhmR(wet skin) 150OhmR(limb) 100OhmR(trunk) 200Ohm

Suggested resistancesfor human body

trunklimbskindry body RRRI

2

7200 0bodyI

dangerous! Very mAI 460



WhiteBoard WorkWhiteBoard Work Let’s Work Text

Problems• 9.79

• 9.80

• 9.78

• 9.32

R arm R armR t ru n k

1 0 0 1 0 02 0 0

I7 2 0 0 V

7 2 0 0 V rm s

[email protected] ENGR-43_Lec-09-3_1-Ph_3W_Power.ppt 1 Bruce Mayer, PE Engineering-43: Engineering Circuit Analysis Bruce Mayer, PE Licensed Electrical.

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