Dynamic Phasor Model for PMU Spectrum Leakage
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Solution Overview
Problem
Current phasor measurement technologies, particularly DFT-based methods, face challenges in accurately measuring dynamic power system conditions due to spectrum leakage and averaging effects, which can lead to incorrect control decisions and system breakdowns, as they assume constant signal parameters and fail to handle frequency deviations and modulation.
Innovation Solution
A synchrophasor measurement method that combines a low-pass digital filter with the DFT, using a dynamic phasor model based on a second-order Taylor series to eliminate spectrum leakage and calibrate measurement errors, ensuring accurate dynamic phasor estimation under changing conditions.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Device complexity
If DFT-based measurement method is used, then computational requirements are low and implementation is simple, but measurement precision deteriorates under dynamic conditions due to spectrum leakage and averaging effects
Solution Approach 1:
The patent transitions from static DFT-based phasor estimation to a dynamic phasor model that explicitly accounts for time-varying signal characteristics. The dynamic model incorporates time-dependent frequency, amplitude, and phase parameters, allowing the measurement system to adapt to changing system conditions rather than assuming stationary signals.
Solution Approach 2:
The patent changes the fundamental parameters of the measurement approach by moving from fixed-frequency DFT assumptions to time-varying parameter estimation. The dynamic phasor model allows frequency, amplitude, and phase to be estimated as time-dependent parameters, fundamentally changing how the measurement system processes dynamic signals.
2Measurement precision
If DFT is used for phasor estimation, then the method can extract nominal frequency components from corrupted waveforms, but spectrum leakage occurs due to frequency deviation and modulation in dynamic conditions
Solution Approach 1:
The dynamic phasor model captures frequency deviation and amplitude modulation by representing these parameters as time-varying quantities rather than constants. This dynamic representation prevents the spectral spreading caused by assuming fixed parameters when the actual signal is changing.
Solution Approach 2:
The patent creates an accurate temporal copy of the dynamic signal characteristics through the dynamic phasor model, which replicates the time-varying nature of frequency, amplitude, and phase. This copying approach preserves signal fidelity without introducing the spectral artifacts that arise from static analysis methods.
3Power
If static phasor model with DFT is used, then computational complexity is reduced, but averaging effect introduces significant errors under dynamic conditions
Solution Approach 1:
The dynamic phasor model replaces the static averaging assumption with time-varying parameter estimation. Instead of computing averages that mask dynamic variations, the model explicitly tracks how phasor parameters evolve over time, providing accurate estimates even during rapid system changes.
Solution Approach 2:
The patent changes the estimation approach from fixed-parameter averaging to time-varying parameter tracking. The dynamic model allows phasor magnitude, frequency, and phase to be estimated as changing parameters, fundamentally improving accuracy during transient and oscillatory conditions while maintaining computational feasibility.
4Ease of operation
If DFT-based measurement is used, then the method is widely applicable and easy to implement, but response speed is insufficient for tracking rapid power system dynamic responses
Solution Approach 1:
The dynamic phasor model inherently provides faster response to signal changes by explicitly modeling time-varying characteristics. The model's structure allows it to track rapid variations in frequency and phase without requiring longer analysis windows, thus improving response speed while maintaining implementation feasibility.
Data Source
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AI summary
This embodiment of the invention announced a synchrophasor measurement method applied to P class Phasor Measurement Unit (PMU). First, said measurement method is based on the dynamic phasor mathematic model. The low pass digital filter for phasor factors is designed, which is combined with DFT. It eliminates the spectrum leakage caused by the dynamic phasor inputs, and the raw phasor measurements after the spectrum leakage being eliminated can be obtained; the dynamic phasor is fitted by using the second order Taylor series. The linear relationship between the measurement errors caused the DFT averaging effect and the second order coefficients of the Taylor series is explored. And, the linear relationship is used to compensate the raw measurement errors under a dynamic condition. And, the accurate dynamic phasor measurements can be gotten. This measurement method can measure phasor accurately and rapidly under both static and dynamic conditions. The precision of the method not only meets the requirements in relevant standards, but also is an order of magnitude higher than the requirements of the standards.