User manual

PQM-702, PQM-703 Operating Manual
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The ideal integrator has infinite gain for DC signals which descends at a rate of 20 dB/frequency
decade. The phase shift is constant over the entire frequency range and is equal to 90°.
Theoretically infinite gain for DC signal, when present at integrator input, causes the input sat-
uration close to the supply voltage and prevents its further work. In practical systems, a solution is
introduced to limit the gain for DC signals to some fixed value. Additionally, periodic reset of the
output is performed. There are also techniques for active cancellation of DC voltage, based on its
measuring and feeding it back to the input, but with the opposite sign, effectively cancelling it. In
such case professionals use term "leaky integrator". Analog "leaky integrator" is simply an integrator
with shunted capacitor (by resistor with high resistance). Such a system operates in the same man-
ner as a low-pass filter with a very low cut-off frequency.
Digital implementation of the integrator ensures excellent long-term parameters - the whole
procedure is performed by computing, there is no issue of component ageing, drifts etc. However,
similarly to the analog version, the saturation problem may also occur and without adequate pre-
vention it may cause the failure of digital integration. Please note that input amplifiers and analog-
to-digital converters have some limited and undesirable offset, which must be removed before the
integration process. The analyzer software includes a digital filter whose task is to completely re-
move the DC component. The filtered signal is subject to digital integration. The resulting phase
characteristics are excellent and the phase shift for the most critical frequencies (50 Hz and 60 Hz)
is minimal.
Ensuring the smallest phase shift between current and voltage signals is extremely important
to achieve small power measurement errors. It can be shown that approximate power measurement
error may be expressed in relation
1
:
Power measurement error ≈ phase error (in radians) × tan(φ) × 100%
where tan(φ) is the tangent of the angle between the current and its voltage fundamental compo-
nents. The above formula indicates that measurement errors increase with decreasing displace-
ment power factor, e.g. with the phase error of 0.1° and cosφ=0.5 the error is 0.3%. Anyway, to
ensure accurate power measurements, the phase coincidence of voltage and current circuits must
be the highest.
3.4 Signal sampling
The signal is sampled simultaneously in all eight channels with a frequency synchronized with
the frequency of power supply voltage in the reference channel. This frequency is 10.24 kHz for
50 Hz and 60 Hz.
Thus, the single period contains 204.8 samples for 50 Hz and 170.67 for 60 Hz. 16-bit analog-to-
digital converter was used to ensure 64-times oversampling.
3-decibel analog attenuation has been specified for frequency approx. 20 kHz, and the ampli-
tude error for the maximum usable frequency 3 kHz (i.e. the frequency of the 50th harmonic for
60 Hz network) is approximately 0.1 dB. The phase shift for the same frequency is less than 15°.
Attenuation in the stop band is above 75 dB.
It should be noted that for the correct measurement of phase shift between the voltage harmon-
ics in relation to current harmonics and power of these harmonics, the important factor is not abso-
lute phase shift in relation to the basic frequency, but the phase coincidence of voltage and current
circuits. Maximum phase difference error is f = 3 kHz, max. 15°. This error decreases with the de-
creasing frequency. When estimating measurement errors in power harmonics, also take into ac-
count additional error introduced by the clamps and transformers.
3.5 PLL synchronization
The synchronization of sampling frequency is implemented by hardware. After passing through
the input circuits, the voltage signal is sent to a band-pass filter which is to reduce the harmonics
level and pass only the voltage fundamental component. Then, the signal is routed to the Phase
1
Current sensing for energy metering, William Koon, Analog Devices, Inc.