Presented by Byoung-Kuk Lee, Ph. D., Senior IEEE

Presented by Byoung-Kuk Lee, Ph. D., Senior IEEE

Energy Mechatronics Lab.

College of Information and Communication Eng.

Sungkyunkwan University Tel: +82-31-299-4581 Fax: +82-31-299-4612 http://seml.skku.ac.kr EML: bkleeskku@skku.edu

11.1 Balanced Three-Phase Voltages

Three-Phase

A basic three-phase circuit

11.1 Balanced Three-Phase Voltages

Three-Phase

Phasor diagrams of a balanced set of three-phase voltages The abc

(positive) sequence

The acb

(negative) sequence

a b c

V 0

V 120

V 120

m m m

V V V

 

  

  

a b c

V 0

V 120

V 120

m m m

V V V

 

  

  

11.1 Balanced Three-Phase Voltages

Three-Phase

a b c

a b c

V V V 0 0

v v v

  

   

V_a: phasor representation of a-phase voltage v_a: a-phase instantaneous voltage

If V_a or v_a (I_a or i_a) is obtained,

remaining other phase voltages (V_b, V_c, v_b, v_c) can also be found using the sequence !!

11.1 Balanced Three-Phase Voltages

Three-Phase

A sketch of a three-phase voltage source

 Generated phase voltages have the same amplitudes

 Their phases are different by 120

11.2 Three-Phase Voltage Sources

Three-Phase

Y-connected source ∆-connected source

• The two basic connections of an ideal three-phase source

11.1 Balanced Three-Phase Voltages

Three-Phase

A model of a three-phase source with winding impedance:

(a) A Y-connected source (b) A ∆-connected source

11.3 Analysis of the Wye-Wye Circuit

Three-Phase

A three-phase Y-Y system

11.3 Analysis of the Wye-Wye Circuit

Assume n is ground node

▶ 9

N N a n N b n N c n

0 ga la A gb lb B gc lc C

V V V V V V V

+ + 0

Z Z Z Z Z Z Z Z Z Z

  

  

 

     

In a balanced three-phase circuit,

(1) V_a'n, V_b'n, and V_c'n comprise a set of balanced three-phase voltages.

(2) Same source impedances: Z_ga = Z_gb = Z_gc (3) Same line impedances: Z_la = Z_lb = Z_lc (4) Same load impedances: Z_A = Z_B = Z_C

 

N a n b

N

0

N

n c n

N 0

3V V V V V

V 1 3

+ 0 + V 0 0

Z Z

Z Z

  

 

  

          

ga la A gb lb B gc lc C

Z

 Z  Z  Z  Z  Z  Z  Z  Z  Z

11.3 Analysis of the Wye-Wye Circuit

balanced three-phase circuit

In a balanced three-phase circuit,

a n N a n

aA

ga la A

b n N b n

bB

gb lb B

c n N c n

cC

gc lc C

a n b n c n

aA bB

0 cC

V -V V

I =

V -V V

I =

V -V V

I =

V V V

I I I I 0

Z Z Z Z

Z Z Z Z

Z Z Z Z

Z









 

 

 

  

  

  

  

 

  

 

11.3 Analysis of the Wye-Wye Circuit

balanced three-phase circuit

A single-phase equivalent circuit

A single-phase equivalent circuit is used to calculate the line current and the phase voltage in one phase of the Y-Y structure.

[Caution] Current flowing through neutral line (n-N), I₀, is 0 not I_aA.

11.3 Analysis of the Wye-Wye Circuit

balanced three-phase circuit

AN BN

B AB

BC N CN

CN N

CA A

V V V V V V

V

V V

 

 

 

Line-to-line and line-to-neutral voltages 선(간) 전압 상전압

Line voltage

Phase voltage

Line current is the same as phase current in a Y load

11.3 Analysis of the Wye-Wye Circuit

balanced three-phase circuit

• Phasor diagrams showing the relationship between line-to-line and line-to-neutral voltages in a balanced system.

The abc sequence

 

AB

BC

C

AN BN CN

AN BN

AN

BN CN BN

30

30

1

CN AN CN

0

0

A

2

3

0 120 1

3 3 3 1

V 0 , V 120 , V

3 3 30

2 2 2 2

V

V V

120

V V

V

V V V

V V V

3

3 3 ^j

j

j

V V V e j

V j V j V

e

e e

V V V

  

  

  

         

   

         



  

 

     



