In Part 2, we have seen how to combine MVAs connected in parallel. That is actually the easy part. In this part of the tutorial, we will be dealing with MVAs in series.

The calculation of MVAs in series is more complicated than those connected in parallel. However, in order to make life much easier, we will be dealing with two methods.

  1. Approximation Method
  2. Exact Method

In the approximation method, the X/R margin of error is about 2-12% depending on the magnitude of angle between the two MVAs.

S right MVA
P right MW
Q right MVAR
theta right {{tan^{-1}}{X/R}}

Approximation Method
{1/P_TOTAL}={1/P_1}+{1/P_2}+{1/P_3}+ ... + {1/P_n} - (1)

{1/Q_TOTAL}={1/Q_1}+{1/Q_2}+{1/Q_3}+ ... + {1/Q_n} - (2)

{1/S_TOTAL}={1/S_1}+{1/S_2}+{1/S_3}+ ... + {1/S_n} - (3)

{X/R}={{Q_TOTAL}/{P_TOTAL}} - (4)

Exact Method
In this method, we will only be calculating two(2) MVA values at a time.

{S_TOTAL}={S_1}*{S_2}/{{S_1}+{S_2}} - (5)

Please note that these are vector quantities and not planar quantities.

{S_1}*{S_2} = ({P_1+j{Q_1}})*({P_2+j{Q_2}}) - (6)

{S_1} + {S_2} = ({P_1} + {P_2}) + j({Q_1+Q_2}) - (7)

For purposes of this tutorial, we will only be dealing with the approximation method of calculation. The exact method is only presented to provide some comparative presentation.

In Part 4, I will be presenting examples on the Complex MVA Method.


  • A Filipino Engineer, Registered Professional Engineer of Queensland (RPEQ) - Australia, and Professional Electrical Engineer (PEE 2574 - 1st Place April 1991) - Philippines with extensive experience in concept selection, front-end engineering, HV & LV detail design, construction, and commissioning of Hazardous and Non-Hazardous Area electrical installations in water and wastewater pipeline and pumping facilities, offshore platforms, hydrocarbon process plants and pipelines including related facilities. Hazardous area classification and design certification (UEENEEM015B, UEENEEM016B, UEENEEM017B).