PRACTICAL MATLAB® FOR ENGINEERS PRACTICAL MATLAB

Alternating Current Analysis 265

R.3.86 The example shown in Figure 3.47 illustrates the general approach employed to

solve for all the currents (load and line) in a typical polyphase balanced network.

The voltage specs are

V 12 = 120 ∠0°

V 23 = 120 ∠−120°

V 31 = 120 ∠120° (in volts)

The analysis shown in the following is for the load specs for the following

structures:

a. A ∆ impedance confi guration shown in Figure 3.47 with

Z 12 = Z 23 = Z 31 = j 10 

b. A Y impedance confi guration shown in Figure 3.48 with

Z 1 = Z 2 = Z 3 = j 10 

ANALYTICAL Solution

Part a

Applying Ohm’s law to the circuit shown in Figure 3.47, the following currents can be

evaluated by

I V

(^12) Zj
12
12
120 0
10
120 0
10 90


12 90







∠∠
∠
∠ A
I V
(^23) Z
23
23
120 120
10 90


12 120 90 12 210





∠
∠
∠∠() A
I 23 = 12 ∠150°
I V
(^31) Z
31
31
120 120
10 90


12 120 90 12 30





∠
∠
∠∠() A
FIGURE 3.47
3 Φ system connected to a ∆ load with Z 12 = Z 23 = Z 31 = j10.

• V 23 −
  V 31
  V 12
  Z 12
  Z 13
  Z 32
  I 1
  I 3
  I 31
  I 12
  I 23
  I (^22)
  3


• 
  

  −
  −

  
  


• 
  

  1