Geometric Va Calculations; Arithmetic Va Calculations - Novatech Bitronics M87X Series Manual

In any connection type, the Total Watts and Total VARs is the arithmetic sum of the per-
element Watts and VARs. The sign conventions are shown in Figure 7 (pg. 33).
When used on 2-element systems, the reference phase voltage (typically phase B) input,
is connected to the Neutral voltage input, and effectively causes one of the elements to be
zero. See Figure 9 (pg. 89-96) and Section 7 for input connection information. It is not
required to use any particular voltage phase as the reference on 2-element systems.
When used on 2-element systems the per-element Watts, VARs, and VAs have no
direct physical meaning, as they would on 2-1/2 and 3 element systems where they
represent the per-phase Watts, VARs, and VAs.
When used on 2-1/2 element systems, one of the phase-to-neutral voltages is fabricated,
as described in Section 4.2. In all other respects, the 2-1/2 element connection is identical
to the 3 element connection.
The M87x may be configured to calculate Total VAs in one of several different ways. The
calculation method may be selected either by sending a command to the M87x via a
network and protocol (refer to the specific protocol manual for details) or by using the 70
Series Configurator. The three methods, Arithmetic, Geometric, and Equivalent (both for
WYE and DELTA), all yield the same results when used on balanced systems with no
harmonics present. The differences are illustrated below:

4.4.1 Geometric VA Calculations

 
2 2
GEOMETRIC VA Watts VARs
TOTAL TOTAL TOTAL
This is the traditional definition of Total VAs for WYE or DELTA systems, and is the default
method for Total VAs calculation. The value of Total VAs calculated using this method
does not change on systems with amplitude imbalance, relative to a balanced system.
There is also a relationship to the Total Power Factor which is described in Section 4.3.
Total Power Factor calculations using the Geometric VA method will still indicate a "1" on a
system with phase amplitude imbalance, or canceling leading and lagging loads.
For example, on a system with a lagging load on one phase and an equal leading load on
another phase, the Geometric VA result will be reduced relative to a balanced system but
the Total Power Factor will still be "1".

4.4.2 Arithmetic VA Calculations

     
     
ARITHMETIC VA V I V I V I
  
TOTAL A N A B N B C N C
The Arithmetic VA calculation is not applicable to DELTA connected systems. The value
of Total VAs calculated using this method also does not change on systems with amplitude
imbalance, relative to a balanced system. The value of Arithmetic VAs will not change on
a system with canceling leading and lagging loads.
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ML0021 August 15, 2018 Copyright 2018 Bitronics, LLC