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ADE7753 Datasheet(PDF) 34 Page - Analog Devices |
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ADE7753 Datasheet(HTML) 34 Page - Analog Devices |
34 / 60 page ADE7753 Rev. C | Page 34 of 60 90°. The resulting waveform is called the instantaneous reactive power signal. Equation 25 gives an expression for the instanta- neous reactive power signal in an ac system when the phase of the current channel is shifted by +90°. The average reactive power over an integral number of lines (n) is given in Equation 26. v(t) = ) sin( 2 θ + ωt V (23) ∫ = = nT VI dt t Rp nT RP 0 ) sin( ) ( 1 θ (26) i(t) = ) sin( 2 t I ω ⎟ ⎠ ⎞ ⎜ ⎝ ⎛ π + ω = ′ 2 sin 2 ) ( t I t i (24) where: T is the line cycle period. RP is referred to as the reactive power. Note that the reactive power is equal to the dc component of the instantaneous reactive power signal Rp(t) in Equation 25. This is the relationship used to calculate reactive power in the ADE7753. The instantaneous reactive power signal Rp(t) is generated by multiplying Channel 1 and Channel 2. In this case, the phase of Channel 1 is shifted by +90°. The dc component of the instantaneous reactive power signal is then extracted by a low-pass filter in order to obtain the reactive power informa- tion. Figure 71 shows the signal processing in the reactive power calculation in the ADE7753. where: θ is the phase difference between the voltage and current channel. V is the rms voltage. I is the rms current. Rp(t) = v(t) × i’(t) (25) Rp(t) = VI sin (θ) + VI sin(2ωt + θ) ZERO-CROSSING DETECTION MULTIPLIER + + LVARENERGY [23:0] ACCUMULATE REACTIVE ENERGY IN INTERNAL REGISTER AND UPDATE THE LVARENERGY REGISTER AT THE END OF LINECYC HALF LINE CYCLES INSTANTANEOUS REACTIVE POWER SIGNAL (Rp(t)) 23 0 49 0 02875-0-070 LPF1 FROM CHANNEL 2 ADC LINECYC [15:0] LPF2 CALIBRATION CONTROL π 2 V I 90 DEGREE PHASE SHIFT Figure 71. Reactive Power Signal Processing |
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