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APPENDIX A
A.1 Mathematical Formulas for Various Parameters
NOTE the following abbreviations used in this section:
NSHC = number of samples per half cycle (between two consecutive zeros)
NSC = number of samples per cycle
NSS = number of samples in a second (multiple of NSC)
V = voltage phase to neutral
U = voltage phase to phase
A.1.1 Network Frequency and Sampling
Sampling is controlled by (locked to) the network frequency to deliver 256 samples per cycle from 40 to 70Hz. This locking
is essential for many calculations, including reactive power, distorting power, fundamental power factor, unbalance, and
harmonic factors and angles.
Instantaneous frequency is measured by analyzing eight consecutive positive-going zero crossings on the signal in
question after digital low-pass filtering and digital suppression of the DC component (i.e. seven periods filtered). The time
of the zero crossing is determined precisely by linear interpolation between two samples to achieve resolution better than
0.002%.
The device is capable of calculating an instantaneous frequency simultaneously on each of the three phases in voltage
(phase-to-neutral for distribution systems with neutral and phase-to-phase for distribution systems without neutral) or in
current. It then chooses one from among two or three of them as the official instantaneous frequency.
The network frequency over one second is determined (approximately) as the reciprocal of the arithmetic mean of the
instantaneous periods.
The signals are acquired using a 16-bit converter and (for current acquisition) dynamic gain switches.
A.1.2 Waveform Mode
A.1.2.1 RMS VALUES OF HALF-CYCLE VOLTAGE AND CURRENT (EXCLUDING NEUTRAL)
Half-cycle RMS phase-to-neutral voltage of phase (i+1) with i X [0; 2].
Half-cycle RMS phase-to-phase voltage of phase (i+1) with i X [0; 2].
109
Power Quality Analyzer PowerPad
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