ADE7880 datasheet(56/104 Pages) AD

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ADE7880

Data Sheet

Rev. A | Page 56 of 104

ACTIVE (–)

REACTIVE (–)

PF (+)

CAPACITIVE:

CURRENT LEADS

VOLTAGE

INDUCTIVE:

CURRENT LAGS

VOLTAGE

ACTIVE (+)

REACTIVE (–)

PF (–)

ACTIVE (–)

REACTIVE (+)

PF (–)

ACTIVE (+)

REACTIVE (+)

PF (+)

θ = +60°

PF = –0.5

θ = –60°

PF = +0.5

Figure 81. Capacitive and Inductive Loads

As shown in Figure 81, the reactive power measurement is

negative when the load is capacitive, and positive when the load

is inductive. The sign of the reactive power can therefore be

used to reflect the sign of the power factor. Note that the ADE7880

computes the fundamental reactive power, so its sign is used as

the sign of the absolute power factor. If the fundamental

reactive power is in no load state, then the sign of the power

factor is the sign of the total active power.

The mathematical definition of power factor is shown in

Equation 47:

Power Factor = (Sign Fundamental Reactive Power) ×

Power

Apparent

Power

Active

Total

(47)

As previously mentioned, the ADE7880 provides a power factor

measurement on all phases simultaneously. These readings are

provided into three 16-bit signed registers, APF (Address

0xE609 ) for Phase A, BPF (Address 0xE60A) for Phase B, and

CPF (Address 0xE60B) for Phase C. The registers are signed

twos complement register with the MSB indicating the polarity

of the power factor. Each LSB of the APF, BPF, and CPF

registers equates to a weight of 2−15, hence the maximum

The minimum register value of 0x8000 corresponds to a power

factor of −1. If because of offset and gain calibrations, the power

factor is outside the −1 to +1 range, the result is set at −1 or +1

depending on the sign of the fundamental reactive power.

By default the instantaneous total phase active and apparent

powers are used to calculate the power factor and the registers

are updated at a rate of 8 kHz. The sign bit is taken from the

instantaneous fundamental phase reactive energy measurement

on each phase.

Should a measurement with more averaging be required, the

ADE7880 provides an option of using the line cycle accumulation

measurement on the active and apparent energies to determine

the power factor. This option provides a more stable power

factor reading. This mode is enabled by setting the PFMODE

bit (Bit 7) in the LCYCMODE register (Address 0xE702). When

this mode is enabled the line cycle accumulation mode must be

enabled on both the active and apparent energies. This is done

by setting the xLWATT and xLVA bits in the LCYCMODE

measurement is now an integral number of half line cycles that

can be programmed into the LINECYC register (Address 0xE60C).

For full details on setting up the line cycle accumulation mode

see the Line Cycle Active Energy Accumulation Mode and Line

Cycle Apparent Energy Accumulation Mode sections.

Note that the power factor measurement is effected by the no

load condition if it is enabled (see the No Load Condition

section). If the apparent energy no load is true, then the power

factor measurement is set to 1. If the no load condition based

on total active and apparent energies is true, the power factor

measurement is set at 0.

The ADE7880 also computes the power factor on the

fundamental and harmonic components based on the

fundamental and harmonic active, reactive and apparent

powers. See the Harmonics Calculations section for details.

HARMONICS CALCULATIONS

The ADE7880 contains a harmonic engine that analyzes one

phase at a time. Harmonic information is computed with a no

attenuation pass band of 2.8 kHz (corresponding to a −3 dB

bandwidth of 3.3 kHz) and it is specified for line frequencies

between 45 Hz and 66 Hz. Neutral current can also be analyzed

simultaneously with the sum of the phase currents. Figure 82

presents a synthesized diagram of the harmonic engine, its

settings and its output registers.

Theory of Operation

Consider an nonsinusoidal ac system supplied by a voltage, v(t)

that consumes the current i(t). Then

sin

)

(

∑

∞

(kωt + φk)

(48)

()

ω +

∑

∞

sin

)

(

where:

Vk, Ik are rms voltage and current, respectively, of each

harmonic.

Φk, γk are the phase delays of each harmonic.

ω is the angular velocity at the fundamental (line) frequency f.

The ADE7880 harmonics calculations are specified for line

frequencies between 45 Hz and 66 Hz. The phase nominal

voltage used as time base must have an amplitude greater than

20% of full scale.

The number of harmonics N that can be analyzed within the

2.8 kHz pass band is the whole number of 2800/f. The absolute

maximum number of harmonics accepted by the ADE7880

is 63.

⎥

⎦

⎤

⎢

⎣

⎡

2800

, N≤63

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