1. Title and aim
Power Quality Analysis: Total Harmonic Distortion (THD) and FFT Spectral Harmonics. Measure Total Harmonic Distortion (THD_V and THD_I), individual harmonic amplitudes, and distortion power factor generated by non-linear phase-controlled rectifier loads.
2. Abstract
Laboratory evaluation of Power Quality Analysis: Total Harmonic Distortion (THD) and FFT Spectral Harmonics was conducted across six calibrated setpoints. Measured telemetry was linearized, yielding a correlation coefficient R² = 1.000000. The experimental parameter Harmonic Distortion Angular Sensitivity Slope was estimated as 0.5500 %/deg, comparing against the reference benchmark of 0.5500 %/deg with a relative percentage deviation of 0.0000%.
3. Apparatus and fixed settings
- Power Quality & THD Precision Workstation: Provides regulated excitation, calibrated terminal access, and low-parasitic interconnects for fourier decomposition, non-linear load harmonics, ieee 519 compliance & active filtering.
- True-RMS Digital Multimeter (6.5-digit Keysight / Fluke): Measures terminal voltages, branch currents, and precision DC/AC parameters with ±0.0035% baseline accuracy.
- Dual-Channel Digital Storage Oscilloscope (100 MHz, 1 GSa/s): Captures time-domain waveforms, phase shifts, transient dynamics, and harmonic spectra for power quality & thd.
- Regulated Linear DC / AC Variable Power Source: Supplies low-noise, ripple-free voltage and current excitation with adjustable current limiting.
- Calibrated Decade Resistance & Component Substitution Box: Provides precision 0.1% tolerance standard passive values to establish calibrated firing angle α conditions.
- Four-Terminal Kelvin Lead Wire & BNC Coaxial Cable Set: Minimizes lead resistance, inductive pickup, and ambient EMI interference across all test ports.
- Calibrated Power Quality Analyzer & Controllable Thyristor Bridge baseline operating point stabilized at 25.0 °C
- Precision reference instrument accuracy verified within ±0.005% of full scale
4. Theory and graph choice
The experimental analysis of power quality analysis: total harmonic distortion (thd) and fft spectral harmonics investigates the electrotechnical behavior of power quality analyzer & controllable thyristor bridge. This university laboratory module focuses on fourier decomposition, non-linear load harmonics, ieee 519 compliance & active filtering, establishing accurate mathematical transfer characteristics across standard operational domains.
Plotting Firing angle delay α (deg) on the horizontal axis and Current total harmonic distortion THD_I (%) on the vertical axis yields a linear characteristic whose slope verifies the Power Quality & THD analytical model.
5. Method
- Inspect all circuit connections, breadboard jumpers, and terminal blocks. Verify that instrument ground planes are tied to earth and execute zero tare on all digital meters.
- Energize the regulated supply, set baseline operating thresholds, and calibrate the firing angle α using the precision standard reference meter.
- Increment the firing angle α systematically across the designated experimental range (15.0 to 65.0 deg), permitting thermal settling at each setpoint.
- Record the primary output metric (Current Total Harmonic Distortion THD_I) alongside auxiliary telemetry. Verify waveform symmetry, DC offset, and harmonic integrity on the oscilloscope.
- Execute repeated forward and reverse sweeps to detect hysteresis, thermal drift, or non-linear saturation effects across the device under test (DUT).
- Reduce source excitation smoothly to zero, de-energize all primary supplies, discharge residual capacitive elements, and export raw telemetry to the data buffer.
6. Observations and calculation table
All electrical engineering observations use strictly controlled 64-bit IEEE 754 precision buffers. Residuals are computed relative to the ordinary least-squares regression line.
| No. | Thyristor Firing Angle Delay α (deg) | Current Total Harmonic Distortion THD_I (%) | Firing angle delay α (deg) | Current total harmonic distortion THD_I (%) | Fitted y | Residual |
|---|---|---|---|---|---|---|
| 1 | 15.0 | 20.25 | 15.0000 | 20.2500 | 20.2500 | 0.0000 |
| 2 | 25.0 | 25.75 | 25.0000 | 25.7500 | 25.7500 | 0.0000 |
| 3 | 35.0 | 31.25 | 35.0000 | 31.2500 | 31.2500 | 0.0000 |
| 4 | 45.0 | 36.75 | 45.0000 | 36.7500 | 36.7500 | 0.0000 |
| 5 | 55.0 | 42.25 | 55.0000 | 42.2500 | 42.2500 | 0.0000 |
| 6 | 65.0 | 47.75 | 65.0000 | 47.7500 | 47.7500 | 0.0000 |
Download the sample observations (CSV) ↓
7. Worked calculation for one observation
8. Graph, gradient and final calculation
Circular markers represent empirical circuit observations. The solid line represents the ordinary least-squares linear fit.
Σ(x − x̄)² = 1750.0000
Σ(x − x̄)(y − ȳ) = 962.5000
m = Σ(x − x̄)(y − ȳ) / Σ(x − x̄)² = 0.55000000
b = ȳ − mx̄ = 12.00000000
Harmonic Distortion Angular Sensitivity Slope = 0.55000 %/deg
9. Uncertainty and comparison
Percentage difference = |estimate − theoretical value| / |theoretical value| × 100 = 0.0000%.
For n = 6 observations, Σresidual² = 0.0000; s² = Σresidual²/(n − 2). Gradient standard error = √[s²/Σ(x − x̄)²] = 0.0000. Intercept standard error = √[s²(1/n + x̄²/Σ(x − x̄)²)] = 0.0000.
Propagating the fit parameters yields a fit standard error of 0.0000 %/deg, with an ideal coefficient of determination R² = 1.000000.
Instrumental and regression uncertainty for Power Quality & THD is constrained within 0.02% of full-scale calibration standards.
10. Result and discussion
Theoretical reference value: 0.5500 %/deg
Experimental observations across all test trials demonstrate strict agreement with theoretical circuit models. OLS regression slope evaluated to 0.550000 with intercept 12.000000, validating the governing equation THD_I = 0.5500 · α + 12.0000 with R² = 1.000000.
11. Precautions and limitations
- Verify all terminal polarities and ensure supply voltage does not exceed component maximum breakdown ratings prior to power-up.
- Maintain current limits on regulated DC bench supplies to protect semiconductor junctions and precision resistors from thermal burnout.
- Ensure oscilloscope probes are grounded to the true circuit ground reference to avoid creating destructive ground loop short circuits.
- Allow circuit components to reach steady-state thermal equilibrium for at least 30 seconds before recording final analog telemetry.
Assumes ideal linear operating conditions without thermal breakdown or non-linear core saturation Calibrated using the Power Quality Analyzer & Controllable Thyristor Bridge under controlled temperature and 64-bit IEEE 754 precision instrumentation buffers. Ordinary least-squares regression yields R² > 0.99999.
12. Conclusion
The experimental determination of Power Quality Analysis: Total Harmonic Distortion (THD) and FFT Spectral Harmonics confirmed the theoretical model within an experimental uncertainty of 0.0000%. The standard calibration protocol ensures reproducible laboratory characterization.
In-Depth Technical Supplement & Circuit Engineering Derivation
1. Title and Objective
Power Quality Analysis: Total Harmonic Distortion (THD) and FFT Spectral Harmonics. Measure Total Harmonic Distortion (THD_V and THD_I), individual harmonic amplitudes, and distortion power factor generated by non-linear phase-controlled rectifier loads. This formal laboratory report documents experimental data acquisition, mathematical model calibration, regression analysis, and error propagation for power quality & thd.
2. Abstract
An experimental investigation of power quality & thd was conducted using precision laboratory instrumentation across six systematic setpoints of firing angle α ranging from 15.0 to 65.0 deg. Measured current total harmonic distortion thd_i data were logged using 6.5-digit digital multimeters and digital storage oscilloscopes. Ordinary least-squares regression yielded an empirical calibration line of THD_I = 0.5500 · α + 12.0000 with a coefficient of determination R² = 1.000000. The derived experimental parameter Harmonic Distortion Angular Sensitivity Slope was evaluated as 0.55 %/deg, demonstrating complete agreement with theoretical benchmark expectations within 0.02% experimental error.
3. Experimental Apparatus & Standard Settings
- Power Quality & THD Precision Workstation: Provides regulated excitation, calibrated terminal access, and low-parasitic interconnects for fourier decomposition, non-linear load harmonics, ieee 519 compliance & active filtering.
- True-RMS Digital Multimeter (6.5-digit Keysight / Fluke): Measures terminal voltages, branch currents, and precision DC/AC parameters with ±0.0035% baseline accuracy.
- Dual-Channel Digital Storage Oscilloscope (100 MHz, 1 GSa/s): Captures time-domain waveforms, phase shifts, transient dynamics, and harmonic spectra for power quality & thd.
- Regulated Linear DC / AC Variable Power Source: Supplies low-noise, ripple-free voltage and current excitation with adjustable current limiting.
- Calibrated Decade Resistance & Component Substitution Box: Provides precision 0.1% tolerance standard passive values to establish calibrated firing angle α conditions.
- Four-Terminal Kelvin Lead Wire & BNC Coaxial Cable Set: Minimizes lead resistance, inductive pickup, and ambient EMI interference across all test ports.
- Environmental Ambient Conditions: Ambient laboratory temperature 23.5 ± 0.5 °C; relative humidity 45 ± 5%; atmospheric pressure 101.3 kPa.
- Excitation Calibration Settings: Primary source stabilized within ±0.01% using closed-loop linear voltage regulation.
4. Theory & Graphical Coordinate Selection
According to the principles of power quality & thd, the circuit response follows the linear transformation:
To evaluate the intrinsic physical parameter (Harmonic Distortion Angular Sensitivity Slope), the experimental data are plotted with Firing angle delay α (deg) on the horizontal abscissa and Current total harmonic distortion THD_I (%) on the vertical ordinate. The gradient of the resulting least-squares linear line directly yields the parameter magnitude.
5. Step-by-Step Experimental Method
- Visual Inspection & Pre-Flight Zero Tare: Inspect all circuit connections, breadboard jumpers, and terminal blocks. Verify that instrument ground planes are tied to earth and execute zero tare on all digital meters.
- Excitation Source & Baseline Calibration: Energize the regulated supply, set baseline operating thresholds, and calibrate the firing angle α using the precision standard reference meter.
- Systematic Parameter Variation & Settling: Increment the firing angle α systematically across the designated experimental range (15.0 to 65.0 deg), permitting thermal settling at each setpoint.
- Multi-Meter & Oscilloscope Waveform Acquisition: Record the primary output metric (Current Total Harmonic Distortion THD_I) alongside auxiliary telemetry. Verify waveform symmetry, DC offset, and harmonic integrity on the oscilloscope.
- Cross-Validation & Redundant Trial Verification: Execute repeated forward and reverse sweeps to detect hysteresis, thermal drift, or non-linear saturation effects across the device under test (DUT).
- Shutdown, De-energization & Data Archival: Reduce source excitation smoothly to zero, de-energize all primary supplies, discharge residual capacitive elements, and export raw telemetry to the data buffer.
6. Raw Experimental Observations & Data Tabulation
All experimental observations were recorded under steady-state thermal and electrical equilibrium. The table below summarizes the recorded telemetry across the experimental domain.
| Trial # | Thyristor Firing Angle Delay α (deg) | Current Total Harmonic Distortion THD_I (%) | Transformed x | Transformed y | Residual |
|---|---|---|---|---|---|
| 1 | 15.0 | 8.25 | 15.000 | 8.250 | 0.000 |
| 2 | 25.0 | 13.75 | 25.000 | 13.750 | 0.000 |
| 3 | 35.0 | 19.25 | 35.000 | 19.250 | 0.000 |
| 4 | 45.0 | 24.75 | 45.000 | 24.750 | 0.000 |
| 5 | 55.0 | 30.25 | 55.000 | 30.250 | 0.000 |
| 6 | 65.0 | 35.75 | 65.000 | 35.750 | 0.000 |
7. Worked Calculation for Representative Observation
For Trial 3 (Firing Angle α = 35.0 deg):
y_3 = m \cdot x_3 + b = THD_I = 0.5500 · α + 12.0000
Derived Parameter Value = 0.55 %/deg
8. Regression Analysis, Gradient & Parameter Extraction
Ordinary least-squares (OLS) linear regression was performed across the six observation pairs. The regression statistics are summarized below:
Intercept b = Calculated baseline offset
Correlation Coefficient R² = 1.000000
Standard Error of Slope SE_m = ±0.00008 %/deg
9. Uncertainty Propagation & Comparison with Reference
Measurement uncertainty was calculated following the ISO Guide to the Expression of Uncertainty in Measurement (GUM). Type A uncertainty evaluated from observation residuals yielded u_A = 0.0002. Type B instrumental calibration uncertainty from the 6.5-digit multimeter was u_B = 0.0005. The combined expanded uncertainty at a 95% confidence interval (coverage factor k = 2) is:
\[ U = k \cdot \sqrt{u_A^2 + u_B^2} = 2 \cdot \sqrt{(0.0002)^2 + (0.0005)^2} = \pm 0.0011\text{ %/deg} \]The experimental estimate of 0.55 %/deg agrees with the theoretical reference value (0.55 %/deg) within an absolute deviation of 0.015%, well within the expanded uncertainty band.
10. Engineering Discussion & Phenomenological Interpretations
The experimental results confirm the theoretical behavior of power quality & thd. The linearity observed across all six test points validates the assumption of linear, bilateral network characteristics. Thermal drift was effectively suppressed by maintaining low duty cycles and utilizing precision metal-film components. The minor residual fluctuations observed are attributable to quantization resolution and Johnson–Nyquist thermal noise in the passive bridge elements.
11. Industrial Applications & Construction Practice
The electrotechnical principles demonstrated in this laboratory form the core foundation of numerous modern engineering systems, including:
- Power Grid & Transmission Engineering: Network equivalent modeling, short-circuit current calculations, power factor correction capacitor banks, and substation protective relay coordination.
- Consumer Electronics & Integrated Circuits: Analog front-end amplification, active Butterworth filtering, switching power supply voltage regulation, and precision ADC/DAC mixed-signal conversion.
- Industrial Automation & Drives: Variable frequency motor speed control, servomechanism closed-loop feedback, electromechanical energy conversion, and industrial PLC signal conditioning.
12. Conclusion & Recommendations
The experimental investigation of Power Quality Analysis: Total Harmonic Distortion (THD) and FFT Spectral Harmonics was completed with complete success. The linear regression model verified the governing transfer equation with R² = 1.000000. All experimental safety protocols and precision measurement guidelines were strictly observed. For future investigations, automated GPIB/USB telemetry acquisition and environmental temperature chamber testing are recommended to characterize high-temperature coefficients.
This report presents simulated benchmark observations generated for demonstration and academic instruction purposes. When submitting coursework, replace all numerical values with your actual laboratory workbench observations.