EEE 302 Electrical Networks II

Dr. Keith E. Holbert Summer 2001 Lecture 10 1

Source/Load Connections • The equivalent load may be in an equivalent delta (  ) or wye (Y) configuration – the delta load configuration has no neutral line – the current is zero in the neutral line for a balanced wye load configuration • Source/Load connections can be connected in any of the possible combinations: Y source -Y load  source -Y load Y source  load  source  load – Analysis prefers the first connection (Y-Y) Lecture 10 2

Balanced Wye-Wye Connection

a

V

an

+ –

b

V

bn

+ –

c

V

cn

+ –

n

Lecture 10

Z

Y

Z

Y

Z

Y Load 3

Balanced Wye-Wye Connection • The

line-to-line voltages

V V

bc

V

ab ca (or

line voltages

) are = V P  3  30° =

V

ab  -120° =

V

ab  -240° where V P is the magnitude of the phasor voltage between any two lines • The magnitude of the line voltage is V L = V P  3 Lecture 10 4

Balanced Wye-Wye Connection • The line current for phase

a

is

I

a =

V

an /

Z

Y = V p  0° /

Z

Y – In a Y-Y connection the magnitude of the line current (I L ) equals the magnitude of the load current (

I

Y ) • The neutral current

I

n is

I

n =

I

a +

I

b +

I

c = 0 • Balanced Y-Y three-phase ac circuits may be analyzed on a per phase basis Lecture 10 5

Balanced Wye-Delta Connection

V

an a

V

bn

Z



b n

Z



V

cn

Z



c

Load Lecture 10 6

Summarizing • A very good summary appears on pages 568-9 of the textbook including a figure and table for explanation Lecture 10 7

Class Examples

• Extension Exercise E10.1

• Extension Exercise E10.2

Lecture 10 8

Three-Phase Power Relationships • The real and reactive power per phase are

P P



V P I L

cos 

V L I

3

L

cos  

Q P



V P I L

sin 

V L I

3

L

sin • The total real, reactive, and complex powers are

P T Q T

  3

P P

3

Q P

  3 3

V L V L I I L L

cos sin    

S

T

 3

V L I L

  Lecture 10 9

Class Examples

• Extension Exercise E10.8

• Extension Exercise E10.10

Lecture 10 10