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Data Sheet

ADE7978/ADE7933/ADE7932

Rev. 0 | Page 65 of 120

POWER FACTOR CALCULATION AND TOTAL HARMONIC DISTORTION CALCULATION

POWER FACTOR CALCULATION

The ADE7978 provides a direct power factor measurement

simultaneously on all phases. Power factor in an ac circuit is

defined as the ratio of the total active power flowing to the load

to the apparent power. The absolute power factor measurement

is defined in terms of leading or lagging, referring to whether

the current waveform is leading or lagging the voltage waveform.

When the current waveform is leading the voltage waveform, the

load is capacitive and is defined as a negative power factor. When

the current waveform is lagging the voltage waveform, the load

is inductive and is defined as a positive power factor. Figure 83

illustrates the relationship of the current waveform to the

voltage waveform.

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 83. Capacitive and Inductive Loads

As shown in Figure 83, 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. The ADE7978 uses

the sign of the total reactive power as the sign of the absolute

power factor. If the total reactive power is in a no load state, the

sign of the power factor is the sign of the total active power.

Equation 48 shows the mathematical definition of power factor.

Power Factor = (Sign Total Reactive Power) ×

(48)

Power

Apparent

Power

Active

Total

The ADE7978 provides a power factor measurement on all phases

simultaneously. These readings are stored in three 16-bit signed

twos complement registers: APF (Address 0xE902) for Phase A,

BPF (Address 0xE903) for Phase B, and CPF (Address 0xE904)

for Phase C. The MSB of these registers indicates the polarity of

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

equates to a weight of 2−15. Therefore, the maximum register value

of 0x7FFF equates to a power factor value of 1, and the minimum

the power factor is outside the −1 to +1 range (because of offset

and gain calibrations), the result is set to −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; the registers are

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

taneous total phase reactive energy measurement on each phase.

If a power factor measurement with more averaging is required,

the ADE7978 can use 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.

To use the line cycle accumulation mode to determine the power

factor, the ADE7978 must be configured as follows:

•

Set the PFMODE bit (Bit 7) to 1 in the LCYCMODE

•

Enable line cycle accumulation mode on both the active

and apparent energies by setting the LWATT and LVA bits

to 1 in the LCYCMODE register. The update rate of the

power factor measurement is now an integral number of

half line cycles that can be programmed in the LINECYC

For complete information about configuring line cycle accumu-

lation mode, see the Line Cycle Active Energy Accumulation Mode

and Line Cycle Apparent Energy Accumulation Mode sections.

Note that the power factor measurement is affected by the no

load condition if no load detection is enabled (see the No Load

Condition section). If the apparent energy no load condition is

true, the power factor measurement is set to 1. If the no load

condition based on total active and reactive energies is true, the

power factor measurement is set to 0.

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