31.MET January 2019 Q.7(B)

Two 10 MVA 3 phase alternators operate in parallel to supply at 0.8 power factor with lagging load of 15 MVA. If output of one alternator is 8 MVA at 0.9 lagging.
1) Calculate the output of second alternator
2) Calculate the value of power factor of second alternator

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Given

MVAtotal = 15 MVA
Φtotal = 0.8 ; sin Φtotal = 0.6
For Alternator 1
MVA1 = 8 MVA
Φ1 = 0.9 ; SinΦ1 = 0.436

To find

1. MVA2
2. Φ2

Solution

Total load MWtotal = MVAtotal x cos Φtotal
                               = 15 x 0.8
                               = 12 MW

Total Reactive load MVARtotal = MVAtotal x sin Φtotal
                                                  = 15 x 0.6
                                                  = 9 MVA

Alternator 1 load MW1 = MVA1 x cos Φ1
                                     = 8 x 0.9
                                     = 7.2 MW

Alternator 1 Reactive load MVAR1 = MVA1 x sin Φ1
                                                        = 8 x 0.436
                                                        = 3.49 MVAR

For Alternator 2 Load MW2 = MWtotal - MW1
                                             = 12 - 7.2
                                             = 4.8 MW

Alternator 2 Reactive load MVAR2 = MVARtotal - MVAR1
                                                        = 9 - 3.49
                                                        = 5.51 MVAR

1. MVA2²  = MW2² + MVAR2²
    MVA2    = Square root of (MW² + MVAR²)
                 =  Square root of (4.8² + 5.51²)
    MVA2    =  7.3 MVA             

2.  Cos Φ2 = MW2 / MVA2
                  = 4.8 / 7.3
     Cos Φ2 = 0.66 (lag)