Grid Frequency Estimation via Complex Exponential Integration
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Solution Overview
Problem
Existing methods for estimating grid frequency or phase angle in AC power distribution systems are slow, computationally complex, and lack accuracy, especially during fault conditions, due to reliance on positive sequence decomposition.
Innovation Solution
A method involving sampling instantaneous voltages, applying Clarke transformation to derive α and β values, generating a complex variable, and integrating a chosen generating function to estimate grid frequency or phase angle without requiring positive sequence decomposition, thus reducing computational complexity and improving accuracy.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If positive sequence decomposition is used to estimate grid frequency or phase angle, then the estimation can be performed using conventional methods, but the computational complexity increases and the speed of estimation decreases
Solution Approach 1:
The patent extracts only the essential information needed for frequency and phase angle estimation by directly processing the complex exponential form of the signal. Instead of performing complete positive sequence decomposition, the method extracts the magnitude and phase angle directly from the complex exponential representation, eliminating unnecessary computational steps while maintaining estimation accuracy.
Solution Approach 2:
The patent inverts the conventional approach by representing the signal as a complex exponential from the beginning and deriving frequency and phase angle directly from this representation. Rather than decomposing into positive and negative sequences and then extracting information, the method starts with the complex exponential form and obtains the desired parameters through direct mathematical operations on this form.
2Reliability
If positive sequence decomposition is used to estimate grid frequency or phase angle, then conventional estimation techniques can be applied, but the response time during fault conditions deteriorates
Solution Approach 1:
The patent extracts only the critical components needed for reliable estimation during fault conditions by working directly with the complex exponential form. This extraction approach focuses computational effort on the essential signal characteristics that remain reliable during faults, rather than processing the entire positive sequence decomposition which includes components that may be corrupted during fault conditions.
Solution Approach 2:
The patent changes the mathematical parameters and representation of the signal from the conventional time-domain or positive sequence representation to a complex exponential form. This parameter change enables more direct and computationally efficient calculation of frequency and phase angle, improving response speed while maintaining reliability during fault conditions through the use of magnitude and phase angle extraction.
3Measurement precision
If more computational steps are performed to improve estimation accuracy, then measurement precision may improve, but the processing time increases
Solution Approach 1:
The patent extracts the essential phase angle information directly from the complex exponential form through a single mathematical operation. This extraction method achieves accurate phase angle estimation without requiring multiple iterative computational steps, thereby reducing processing time while maintaining high measurement precision.
Solution Approach 2:
The patent replaces complex mechanical-like computational processes (multiple steps of positive sequence decomposition and iteration) with a more direct mathematical approach using complex exponentials. This substitution eliminates unnecessary computational mechanics while preserving the essential information extraction, resulting in faster processing with equivalent or improved accuracy.
Data Source
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AI summary
The present disclosure relates to a method and system for estimating a grid frequency or grid phase angle of an electrical power distribution system in which instantaneous voltages output by the electrical power distribution system are sampled at a plurality of discrete sample times to generate a plurality of samples; α and β values are derived from the plurality of samples using a Clarke transformation; a complex variable is generated from the derived α and β values and is applied to a generating function; the generating function is integrated for the plurality of samples; and an estimate of the grid frequency or grid phase angle is generated based on the result of the integration of the generator function.