Phase Ratio Determination for Cable Loss Factor Diagnosis
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Solution Overview
Problem
Existing methods for determining the relationship between periodically changing variables, such as voltage and current in medium or high-voltage cables, suffer from precision issues due to uncertainties in fundamental frequency and measurement timing, leading to measurement errors and loss of precision.
Innovation Solution
The method involves calculating the ratio of complex numbers representing voltage and current without initial transformation by the factor e^(-jωt, which allows for accurate representation of the absolute phase relationship, thereby reducing the impact of frequency and timing deviations, and using arithmetic mean to enhance precision.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Device complexity
If the complex numbers are transformed by multiplying with e^(-jωt) to eliminate time dependence, then the representation becomes simpler, but the absolute phase relationship is lost and precision deteriorates
Solution Approach 1:
Instead of transforming the complex numbers by multiplying with e^(-jωt) to eliminate time dependence (conventional approach), the patent inverts this approach by keeping the time-dependent complex numbers in their original form and directly calculating ratios. This preserves the absolute phase relationship information while avoiding the precision loss introduced by the transformation.
2Adaptability or versatility
If measurements are taken at irregular time points due to frequency deviations, then adaptability to real-world conditions improves, but phase relationship precision deteriorates
Solution Approach 1:
The patent uses feedback by continuously tracking the instantaneous frequency and adjusting the measurement process accordingly. By calculating the ratio of complex numbers at each time point and then averaging, the system adapts to frequency variations while maintaining precision through the mathematical properties of the complex ratio calculation.
Solution Approach 2:
The patent employs periodic sampling of voltage and current at multiple time points within a period, then averages the resulting complex ratios. This periodic action with subsequent averaging provides robustness against frequency variations and timing irregularities while maintaining measurement precision.
3Reliability
If averaging of complex ratios is performed to reduce noise impact, then measurement reliability improves, but computational complexity increases
Solution Approach 1:
The patent replaces complex signal processing mechanisms with a straightforward mathematical approach: calculating the ratio of complex numbers at each time point and then performing arithmetic averaging. This substitution of complex mechanical/signal processing with simple mathematical operations achieves noise reduction while keeping computational complexity manageable.
Data Source
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AI summary
In order to determine a phase ratio between two predominantly sinusoidally varying variables, respective measurement values for the two variables are expanded into complex numbers, then a ratio variable c[k] is calculated directly from these complex numbers, the average c of all ratio variables is determined, and then a statement about the ratio between the two variables can be made on the basis of this average. The invention is particularly suitable when the loss factor for a medium or high-voltage cable is to be determined.