Multi-Sampling Techniques for Harmonic Power

The proliferation of nonlinear loads on electrical power systems has led to an increase in harmonic distortions. Harmonics can reduce system efficiency, cause equipment overheating, and lead to premature failures. Therefore, accurate calculation of harmonic power quantities is essential for power quality analysis and mitigation. Traditional techniques use a single sampling frequency, but this can result in notable errors due to spectral leakage. Multi-sampling approaches can improve calculation accuracy by capturing a wider range of harmonic components.

Spectral Leakage and Aliasing

Spectral leakage refers to the spreading of power from a harmonic frequency across adjacent frequencies when using discrete Fourier transforms. This phenomenon occurs because signals are truncated within a finite window. When a signal is sampled, it is effectively multiplied by a rectangular window, leading to the loss of information about its true frequency content. The mathematical representation of the Discrete Fourier Transform (DFT) highlights this process:

X_k = \sum_{n=0}^{N-1} x[n] e^{-j \frac{2\pi}{N}kn}

In this formula, \displaystyle X_k represents the frequency component at index \displaystyle k, with \displaystyle x[n] being the sampled time-domain signal. The summation captures the contributions of all samples \displaystyle n from 0 to \displaystyle N-1. However, when the signal is truncated, energy from the true frequency can "leak" into adjacent frequencies, causing inaccuracies in harmonic measurements.

Aliasing is another critical issue that arises when higher frequency components are inadequately sampled, causing them to appear as lower frequencies in the measurement. This misrepresentation can lead to further inaccuracies in harmonic analysis, especially in systems with strong harmonic distortion.

Multi-sampling captures power system signals using two or more different sampling frequencies. This approach widens the observable spectrum, effectively reducing both spectral leakage and aliasing errors. By employing multiple sampling rates, it enables better detection of higher frequency harmonic components that may otherwise be obscured in a single-sampling scenario.

Common Multi-Sampling Techniques

Several techniques have been developed to leverage multi-sampling for power system analysis. These include the following:

Multiple Coherent Sampling (MCS)
This uses sampling frequencies with integer relationships, allowing alignment of the frequency bins. It improves leakage performance.
Randomly Interleaved Sampling (RIS)
Samples are taken randomly within the fundamental cycle. Spectral leakage is diversified over a wider band.
Multicycle Sampling (MS)
Samples at different sampling rates are collected over multiple cycles. This enhances the resolution.
Polyphase Decimator Sampling (PDS)
Sampling at various decimation factors filters out-of-band components before downsampling. This prevents aliasing.

Estimating Harmonic Powers

Once multi-sample data is acquired, it can be processed to calculate harmonic powers. Common estimation methods include:

Discrete Fourier Transform (DFT)
This finds frequency components in the data. Leakage effects are minimized by the diverse sampling.
Interpolation
Data points from different sampling sets can be interpolated to reconstruct waveforms at higher resolutions. This improves DFT performance.
Windowing
Applying appropriate window functions (like Hanning or flat-top) on signals further reduce leakage during DFT.
Prony's Method
This fits sampled data using exponential functions. Harmonic powers are derived from the curve parameters. It is robust against noise.

The estimated powers for individual frequencies are aggregated to determine total harmonic distortion. Multi-sampling provides cleaner detection of harmonics for more accurate results.

Key Benefits of Multi-Sampling

Applying multi-sampling best practices provides the following advantages for power quality assessments:

Reduced leakage and aliasing errors – More accurate harmonic measurement with less spreading between frequency bins.
Detection of higher frequency components – Ability to capture higher order harmonic signatures that may be missed by single sampling rates.
Increased observable bandwidth – Fundamental and interharmonics can be measured simultaneously with reduced aliasing.
Noise mitigation – Aggregating multiple diverse sample sets smooths out random noise components in the data.
Higher resolution – Interpolation techniques using multi-rate data can reconstruct waveforms at finer resolutions.
Validation of results – Consistent outcomes from different sampling sets increases confidence in the measurement accuracy.

Overall, multi-sampling gives greater precision in determining harmonic indices like total harmonic distortion (THD), total demand distortion (TDD), telephone influence factor (TIF), etc. Proper harmonic power quantification aids in tackling issues like transformer heating, neutral conductor overload, and low system efficiency. It also enables compliance with power quality standards like IEEE 519.

Practical Implementation

For the best results, certain considerations should be kept in mind when implementing multi-sampling:

Sample rates should be mutually prime to diversify leakage spreading.
Sampling windows need to cover at least one fundamental cycle to allow harmonic power calculations.
Synchrophasor technology can accurately timestamp readings from different samplers.
Careful recorder configuration is required to coordinate multi-rate sampling.
Harmonic cancellation effects should be accounted for when aggregating results.
Sampling rates should encompass up to 50th order harmonics for comprehensive analysis.

With modern on-site testPortable Calibrator RS350 equipment and sophisticated algorithms, multi-sampling techniques have become more feasible for wider usage.

Takeaway

As nonlinear loads proliferate, managing harmonic distortions is an increasing challenge. Multi-sampling strategies provide a comprehensive solution by capturing a wide spectrum of frequency components. This gives greater accuracy in determining vital harmonic power indices. Integrating these techniques can significantly improve power quality assessments and inform mitigation approaches. Continued advancements in measurement equipment, synchrophasor technology, and analytical algorithms will further unlock the benefits of multi-sampling for power system operators.