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MSO5000 Live Power Analysis

Project: MSO5000 Liveview Power Analyzer
Goal: Scientifically transparent, repeatable, and defensible computation of power quantities (P, S, Q₁, PF, φ₁) from oscilloscope waveforms.

1) Physical-to-Digital Signal Path

Signals pass through the scope’s analog front-end (attenuation, coupling, offset, BW limit), are sampled by the ADC, then retrieved via SCPI with scaling metadata (:WAV:PRE?). The software decodes raw bytes into calibrated voltage/current arrays using probe factors and channel units; each sample has a known time step \( \Delta t \). These arrays are the basis for RMS, power, energy, and spectral/phasor analysis.

2) Acquisition

  • Instrument: Rigol MSO5000 (SCPI over TCP/IP)
  • Channels: any pair (e.g., CH3 = voltage, CH4 = current)
  • Waveform mode: RAW/NORM via :WAV:DATA?
  • Record length: configurable; choose windows covering ≥ 5–10 fundamental cycles (e.g., ~200 ms at 50 Hz) for stable \(f_0\) and phasors
  • Scope settings: vertical scales, offsets, inversion (:CHANx:INVert), and BW limit are honored

3) Current Measurement Models

a) Shunt Resistor

\( I(t) = \frac{V_\text{shunt}(t)}{R_\text{shunt}} \) - Example: R010 \(= 0.01\ \Omega\) low-side; use Kelvin sensing if possible.

b) Current Clamp / Probe

If the clamp outputs voltage proportional to current (typical datasheet sensitivity in mV/A): \( I(t) = V_\text{clamp}(t)\times \underbrace{\left(\frac{\mathrm{A}}{\mathrm{V}}\right)}_{\text{Probe value in software}} \) - Example: 100 mV/A ⇒ \(0.1\ \mathrm{V/A}\) ⇒ A/V = 10. Enter 10.0 as the probe value.

If the channel already reports AMP (rare, via dedicated interface), set the software probe value to 1.0 to avoid double scaling.

Clarification: We express the software’s clamp value as A/V (amps per volt). Avoid “× attenuation” wording for clamps; use A/V sensitivity.

4) Power & RMS Computation (corrected)

Given scaled arrays \( v(n] \) (volts) and \( i(n] \) (amps) with \( n=1..N \):

  • RMS \( V_\mathrm{rms}=\sqrt{\tfrac1N\sum_n v[n]^2},\quad I_\mathrm{rms}=\sqrt{\tfrac1N\sum_n i[n]^2} \)

  • Instantaneous & Real Power \( p[n]=v[n]\cdot i[n],\qquad P=\tfrac1N\sum_n p[n] \) (valid for any waveform)

  • Apparent Power \( S = V_\mathrm{rms}\,I_\mathrm{rms} \)

  • Fundamental Phasors (for \(Q_1,P_1,\varphi_1\))
    Estimate \( f_0 \) in the window; form RMS phasors \(U_1,I_1\) by orthogonal projection at \( f_0 \) (DC removed for the phasor step). Then: \( S_1 = U_1\,I_1^*,\quad P_1=\Re\{S_1\},\quad Q_1=\Im\{S_1\} \) with the sign convention \(Q_1>0\) inductive (current lags), \(Q_1<0\) capacitive (current leads).

  • Power Factor \( \mathrm{PF}=\frac{P}{S}\quad(\text{signed by }P),\qquad \mathrm{PF}_1=\frac{P_1}{|S_1|} \)
  • Phase Angle (reported) \( \varphi_1=\arg(S_1)=\arctan2(Q_1,P_1) \)

    Important: We do not use \(Q=\sqrt{S^2-P^2}\); it is signless and invalid under distortion. \(Q_1\) from fundamental phasors is IEEE-1459-consistent and ensures correct sign.

5) Energy Integration

Integrate over elapsed time (window-averaged values):

  • Real energy (Wh): \( E_P = \sum P_\text{avg}\,\Delta t \)
  • Apparent energy (VAh): \( E_S = \sum S_\text{avg}\,\Delta t \)
  • Reactive energy (varh): \( E_Q = \sum Q_{1,\text{avg}}\,\Delta t \) (reactive energy of the fundamental)

6) Scientific Validity & Standards Alignment

  • IEEE Std 1459-2010: \(P\) from time-domain average of \(v\cdot i\); \(Q_1\), \(P_1\), \(\varphi_1\) from fundamental phasors; \(S=V_\mathrm{rms}I_\mathrm{rms}\); PF definitions as above.
  • IEC 61000-4-30 (method compatibility): Use cycle-based windows (e.g., 10 cycles @ 50 Hz) for stable aggregation; preserve raw waveforms & metadata for traceability.
  • Valid for sinusoidal and distorted waveforms; sign of \(P\) supports reverse power; sign of \(Q_1\) distinguishes inductive vs capacitive behavior.

7) Known Limitations

  • Accuracy depends on probe/shunt tolerances, clamp phase/magnitude vs frequency, vertical resolution, ADC pairing, and scope BW.
  • Fixed inter-channel delays (probe/filter) are not automatically de-embedded; keep voltage/current on the same ADC pair when possible and use BW limit for stability.
  • Harmonic KPIs (IEC 61000-4-7), flicker (-4-15), dips/swells/RVC are out of scope unless enabled by separate workflows.

8) Data Logging

Each CSV row contains timestamped metrics: - \(P\) (W), \(S\) (VA), \(Q_1\) (var), PF (signed), \(\varphi_1\) (deg), \(V_\mathrm{rms}\), \(I_\mathrm{rms}\), \(f_0\) (Hz), and energies \(E_P, E_S, E_Q\) (Wh/VAh/varh).

Example Timestamp,P,S,Q1,PF,phi1_deg,Vrms,Irms,f0,EP,ES,EQ 2025-07-21T09:21:44.049118,0.303,1.069,1.023,0.284,73.7,42.894,0.024861,50.00,10.740e-3,3.923e-3,42.583e-3

9) Practical Tips

  • Shunt (low-side): Kelvin wiring; CH3=voltage (10×), CH4=shunt drop (1×); enable 20 MHz BW limit on both; verify polarity (invert if \(P<0\) for a known consumer).
  • Clamp: Enter A/V sensitivity (e.g., 10.0 for 100 mV/A). If the scope channel is already in AMP, use 1.0 in software.
  • Windows: Prefer ≥5–10 cycles; for fluctuating \(f_0\), estimate \(f_0\) per window; use rectangular windows for final power averages (cycle-exact) and Hann only for estimation when needed.

Conclusion

The revised method delivers: - Time-domain \(P\) (general, distortion-proof)
- IEEE-1459 \(Q_1\) with correct sign, \(P_1\), \(\varphi_1\), and PF/PF₁
- Transparent scaling for shunt and clamp (A/V)
- Windowing and logging that support traceable, reproducible results

This brings the MSO5000 Liveview Power Analyzer in line with best-practice definitions for modern PQ analysis while staying fully auditable and open.