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88 Rockwell Automation Publication 1412-UM001D-EN-P - September 2012
Appendix C Mathematical Formulas For Various Parameters
Distortion Factor Calculation
(DF)
Two global values giving the relative quantity of harmonics are computed: the
THD in proportion to the fundamental and the DF in proportion to the RMS
value.
Multiplying the voltage harmonic factor with the current harmonics factor gives
the power harmonic factor. Differentiating voltage harmonic phase angle with
current harmonic phase angle gives power harmonic phase angle.
• VAharm [3][51]
• VAph [3][51]
K Factor
Different Power Levels 1 Sec
W[3] = W[0] + W[1] + W[2] - Total Active Power
VA[3] = VA[0] + VA[1] + VA[2] - Total Apparent Power
VAR[3] = VAR[0] + VAR[1] + VA R [2] - Tota l Reac tive Power
[]
[][ ]
[][]
[]
[][ ]
[][]
[]
[][ ]
[][]
1
iAthd ,
1
i Uthd,
1
iVthd
50
2
2
50
2
2
50
2
2
iAharm
niAharm
iUharm
niUharm
iVharm
niVharm
nnn
∑∑∑
===
===
[]
[][ ]
[]
[]
[][ ]
[]
[]
[][ ]
[]
iArms
niAharm
iUrms
niUharm
iVrms
niVharm
nnn
∑∑∑
===
===
50
2
2
50
2
2
50
2
2
2
1
iAdf ,
2
1
i Udf,
2
1
iVdf
[]
[][
]
iAkf K factor for the i + 1 phase
n=50
1
2
n
2
niAharm
n
∑
=
[][ ]
n=50
1
2
niAharm
n
∑
=
=
[]
[][ ]
iW
VA[i] = Vrms[i] Arms[i] Apparent power i + 1 phase
VAR[i] =
ou VAR[i] = VA[i] – W[i] if computation method is with harmonics
Active power i + 1 phase
NSS-1
0
nVi
n
.
.
.
∑
=
[][ ]
nAi
=
1
NSS
[][ ]
Reactive power i + 1 phase
NSS-1
0
n - NSS / 4VF i
n
.
∑
=
[][ ]
nAF i
1
NSS
22