Chapter 4 Measurements
Accura 3300E User Guide
Page 76
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2015 Rootech Inc. All Rights Reserved
Power Measurement Per Phase
Accura 3300E supports two methods for calculation of reactive[Q] and apparent power[S] per
phase.
(1)
Calculation from fundamental frequency components: Reactive energy is calculated based
on fundamental voltage and current.
(2)
Calculation from RMS values, including harmonics: Reactive energy is calculated based on
RMS voltage and current.
Reactive power and apparent power can vary according to the calculation methods of reactive
power. As apparent power can vary, power factor can vary also.
Calculation from Fundamental Frequency Components
Calculates the average active power for each phase by product of voltage and current.
,
,
Calculates average reactive power for each phase by phase-delaying the voltage phase as much
as 90 degrees for the fundamental wave.
,
,
Calculates apparent power for each phase by vector sum of active power and reactive power.
,
,
Calculation from RMS Values, including Harmonics
Calculates the average active power for each phase by multiplying voltage by current.
,
,
Calculates apparent power for each phase by product of RMS voltage and RMS current. RMS value
of voltage and current includes harmonic components each.
𝑉
𝑘,𝑟𝑚𝑠
= √
1
𝑇
∫ 𝑣
𝑘
2
(𝑡)
𝑇
0
𝑑𝑡 ,
𝐼
𝑘,𝑟𝑚𝑠
= √
1
𝑇
∫ 𝑖
𝑘
2
(𝑡)
𝑇
0
𝑑𝑡
𝑆
𝑎
= 𝑉
𝑎,𝑟𝑚𝑠
𝐼
𝑎,𝑟𝑚𝑠
,
𝑆
𝑏
= 𝑉
𝑏,𝑟𝑚𝑠
𝐼
𝑏,𝑟𝑚𝑠
,
𝑆
𝑐
= 𝑉
𝑐,𝑟𝑚𝑠
𝐼
𝑐,𝑟𝑚𝑠
Calculates reactive power by calculating the vector difference between apparent power and active
power. The sign of reactive power is the same as the sign of reactive power calculated with the
fundamental calculation method.
=
T
a
a
a
dt
t
I
t
V
T
P
0
)
(
)
(
1
=
T
b
b
b
dt
t
I
t
V
T
P
0
)
(
)
(
1
=
T
c
c
c
dt
t
I
t
V
T
P
0
)
(
)
(
1
−
=
T
a
T
a
a
dt
t
I
t
V
T
Q
0
4
)
(
)
(
1
−
=
T
b
T
b
b
dt
t
I
t
V
T
Q
0
4
)
(
)
(
1
−
=
T
c
T
c
c
dt
t
I
t
V
T
Q
0
4
)
(
)
(
1
2
2
a
a
a
Q
P
S
+
=
2
2
b
b
b
Q
P
S
+
=
2
2
c
c
c
Q
P
S
+
=
=
T
a
a
a
dt
t
I
t
V
T
P
0
)
(
)
(
1
=
T
b
b
b
dt
t
I
t
V
T
P
0
)
(
)
(
1
=
T
c
c
c
dt
t
I
t
V
T
P
0
)
(
)
(
1
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