class #04 approximate method of analysis 1 1-27-04

7/28/2019 Class #04 Approximate Method of Analysis 1 1-27-04

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EE 494/544

Class 4

Chapter 3 (1)Approximate Method of Analysis


2/31

Chapter 2 Summary

What is demand?

What is energy in kWH?

How does diversity factor work?

Methods of voltage drop analysis

Max demand from metered readings

Max demand from diversity factors


3/31

Load Allocation Methods

Max metered kVA proportioned out equally

to each customer

Max metered kVA current proportioned out

equally to each customer

Max metered kVA proportioned out to each

transformer based upon transformer kVArating


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Conclusions from Chapter 2

The best way to compute voltage drop requires

metered demand data for every customer. That is

never the case. An OK method is to compute voltage drop using

diversity factors. This requires a table of diversity

factors, which usually is not known.

Very little error is made in allocating loads based

upon transformer kVA ratings. This is what will

be used throughout the course


5/31

Line-to-Neutral Eq. Circuit

R jX

Load

+

-

VS

+

VL

-

I

S L LV V R jX I V R I jX I


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Phasor Diagram

I

RI

VS

VL jXI

ZI

0

Im(ZI)

Real(ZI)

S L LV V R jX I V R I jX I


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Voltage Drop

Re

% _ 100%Nominal _ _

drop S L

drop

drop

V V V

V Z I

Vdrop

LN Voltage


8/31

Three-Phase Line Impedance

Dab Dbc

a b c

n

Dca

3

0.12134lneq

positive

eq ab bc ca

Dz r j

GMR

D D D D


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Show Appendix A Conductor Data


10/31

Z Calculation and

Voltage Drop Example


11/31

K Drop Factor

1. 0 miles of line0.9 PF1.0 kVA

% _ _

_drop

voltage dropK

kVA mile

% _ Re( )dropNOMINAL

Z IVVLN


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Continue Example Using K Drop

Factor


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Capacitor Load Circuit

R jX

+

-VS

+

VL-

S L cap L cap capV V R jX I V R I jX I

I

Icap

cap


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Voltage Rise Phasor Diagram

VL

I cap

RI

VS

cap

jXIcap

ZI

Real(ZI)

Im(ZI)

Re( ) ReRe( )

rise cap cap

rise cap cap cap

V Z I R jX jI

V jR I X I X I


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K Rise Factor

1. 0 miles of line

1.0 kvar

% _Re( )

riseNOMINAL

Z IV

VLN

% _ _var_

rise voltage riseKk mile


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Load + Capacitor Circuit

R jX

Load

+

-

VS

+

VL

-

S L cap L cap capV V R jX I I V R I jX I R I jX I

I

I

I line

cap


17/31

Load + Cap Phasor Diagram

I

RI

VL jXI

ZI

0

Im(ZI)

Real(ZI)

S L cap L cap capV V R jX I I V R I jX I R I jX I

Icap

Real(ZIcap)

Im(ZIcap)VS

Re( ) Re( )drop capV Z I Z I


18/31

Continue Example with Shunt

Capacitor


19/31

Application of K Factors

2 3 41

Qc

S1 S2 S3

L-3L-1 L-2

S1+S2+S3 S2+S3 S3

Qc

4 1 2 3 1 2 3 2 3 3

4 1 2

4 4 4

% _

% __ % _ % _

drop

rise c

Drop K S S S L S S L S L

Rise K Q L LNet Drop Drop Rise


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Uniformly Distributed Loads

1 2 3 45

di di di di di di

dxdx

dxdx dx

S

IT

n

length


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Work Uniformly Distributed

Load Example


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Circuit for Voltage Drop

S

IT

n

length

IT

length/2


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OR:

S

IT

n

length

IT /2


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Circuit for Power Loss

S

IT

n

length

length/3

IT


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OR:

S

IT

n

length

IT /3


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Desired Exact Model for

Uniformly Distributed Loads

S

IT

n

T

I

x

lk

l

(1-k) l

c I


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28/31

S

IT

n

TI

lk

l

(1-k) l

c I

22 2

2

2 2 2 2

11

3

1

13

11

3

total T T T Ploss R I k R I k R c I

k k c

k c k c k c c

x


29/31

22 2

2

2 2 2 2

2 2

11

3

1 13

11

3

0.51

1 0.51

3 1

1

3

1

4

total T T T Ploss R I k R I k R c I

k k c

k c k c k c c

ckc

cc c

c

c

k


30/31

Exact Model

S

IT

n

IT

l

l

14_ 3

4_

l

23_

TI1

3_


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Class 4 Homework

Chapter 3 -1,2,3,4

class #04 approximate method of analysis 1 1-27-04

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