Accura 2300S/2350-1P3FSC User Guide
Chapter 5 Measurements
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Page 153
Measurement of Power Per Phase
There are two methods for calculating the reactive power(Q) and the apparent power(S) per phase.
1) Calculation with fundamental frequency components: Reactive power is calculated based on the
fundamental voltage and current values.
2) Calculation with RMS values: Reactive power is calculated based on the RMS voltage and current
values (including harmonics).
Reactive power and apparent power values can vary according to the method of calculating reactive
power. As the apparent power value changes, the power factor also changes.
Calculation with Fundamental Frequency Components
Active power for each phase is calculated by multiplying voltage and current.
𝑃
𝑘
=
1
𝑇
∫ 𝑣
𝑘
(𝑡)
𝑇
0
𝑖
𝑘
(𝑡)𝑑𝑡
where k=a,b,c
,
The reactive power for each phase is calculated by shifting the phase of the voltage by 90 degrees with
respect to the fundamental frequency.
𝑄
𝑘
=
1
𝑇
∫ 𝑣
𝑘
(𝑡 −
𝑇
4
)
𝑇
0
𝑖
𝑘
(𝑡)𝑑𝑡
where k=a,b,c
,
The apparent power for each phase is calculated based on the magnitude of the vector sum of the
active power and the reactive power.
𝑆
𝑘
= √𝑃
𝑘
2
+ 𝑄
𝑘
2
where k=a,b,c
,
Calculation with RMS Values
Active power for each phase is calculated by multiplying voltage and current.
𝑃
𝑘
=
1
𝑇
∫ 𝑣
𝑘
(𝑡)
𝑇
0
𝑖
𝑘
(𝑡)𝑑𝑡
where k=a,b,c
,
The apparent power for each phase is calculated by multiplying the RMS voltage by the RMS current.
The RMS values of voltage and current contain harmonic components.
𝑉
𝑘,𝑟𝑚𝑠
= √
1
𝑇
∫ 𝑣
𝑘
2
(𝑡)
𝑇
0
𝑑𝑡 ,
𝐼
𝑘,𝑟𝑚𝑠
= √
1
𝑇
∫ 𝑖
𝑘
2
(𝑡)
𝑇
0
𝑑𝑡
where k=a,b,c
𝑆
𝑘
= 𝑉
𝑘,𝑟𝑚𝑠
∙ 𝐼
𝑘,𝑟𝑚𝑠
where k=a,b,c
The magnitude of the reactive power for each phase is calculated based on the magnitude of the
vector difference between the apparent power and the active power. The sign of the reactive power is
the same as the sign of the reactive power calculated with fundamental frequency components.
𝑄
𝑘
= ±√𝑆
𝑘
2
− 𝑃
𝑘
2
where k=a,b,c
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