Datasheet

Data Sheet ADE7758
Rev. E | Page 39 of 72
When using the line cycle accumulation mode, the RSTREAD
bit (Bit 6) of the LCYCMODE register should be set to Logic 0.
APPARENT POWER CALCULATION
Apparent power is defined as the amplitude of the vector sum of
the active and reactive powers. Figure 75 shows what is typically
referred to as the power triangle.
REACTIVE POWE
R
ACTIVE POWER
APPARENT
POWER
θ
04443-074
Figure 75. Power Triangle
There are two ways to calculate apparent power: the arithmetical
approach or the vectorial method. The arithmetical approach
uses the product of the voltage rms value and current rms value
to calculate apparent power. Equation 38 describes the arithmetical
approach mathematically.
S = VRMS × IRMS (38)
where S is the apparent power, and VRMS and IRMS are the
rms voltage and current, respectively.
The vectorial method uses the square root of the sum of the
active and reactive power, after the two are individually squared.
Equation 39 shows the calculation used in the vectorial approach.
22
QPS +=
(39)
where:
S is the apparent power.
P is the active power.
Q is the reactive power.
For a pure sinusoidal system, the two approaches should yield
the same result. The apparent energy calculation in the ADE7758
uses the arithmetical approach. However, the line cycle energy
accumulation mode in the ADE7758 enables energy accumula-
tion between active and reactive energies over a synchronous
period, thus the vectorial method can be easily implemented in
the external MCU (see the Line Cycle Active Energy
Accumulation Mode section).
Note that apparent power is always positive regardless of the
direction of the active or reactive energy flows. The rms value of
the current and voltage in each phase is multiplied to produce
the apparent power of the corresponding phase.
The output from the multiplier is then low-pass filtered to obtain
the average apparent power. The frequency response of the LPF
in the apparent power signal path is identical to that of the LPF2
used in the average active power calculation (see Figure 66).
Apparent Power Gain Calibration
Note that the average active power result from the LPF output
in each phase can be scaled by ±50% by writing to the phase’s
VAGAIN register ( AVAG, BVAG, or CVAG). The VAGAIN
registers are twos complement, signed registers and have a
resolution of 0.024%/LSB. The function of the VAGAIN
registers is expressed mathematically as
⎟
⎠
⎞
⎜
⎝
⎛
+×
=
12
2
12
RegisterVAGAIN
OutputLPF
PowerApparentAverage
(40)
The output is scaled by –50% by writing 0x800 to the VAR gain
registers and increased by +50% by writing 0x7FF to them.
These registers can be used to calibrate the apparent power (or
energy) calculation in the ADE7758 for each phase.
Apparent Power Offset Calibration
Each rms measurement includes an offset compensation register
to calibrate and eliminate the dc component in the rms value
(see the Current RMS Calculation section and the Vo lt ag e
Channel RMS Calculation section). The voltage and current
rms values are then multiplied together in the apparent power
signal processing. As no additional offsets are created in the
multiplication of the rms values, there is no specific offset
compensation in the apparent power signal processing. The offset
compensation of the apparent power measurement in each phase
should be done by calibrating each individual rms measurement
(see the Calibration section).