Logarithmic Power Feedback for Wind Turbine ESC Stability
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Solution Overview
Problem
The extremum seeking control (ESC) algorithm for fluid dynamic systems, such as wind turbines, is highly sensitive to variations in wind speed due to the cubic relationship between power and wind speed, leading to inconsistent and unpredictable performance optimization.
Innovation Solution
Applying a logarithmic transformation to the measured power signal before inputting it into the ESC algorithm, decoupling the power coefficient from the power signal and making the algorithm insensitive to wind speed variations.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Power
If the ESC algorithm uses the power signal directly for feedback control, then the power maximization function is achieved, but the control performance becomes highly sensitive to wind speed variations and inconsistent
Solution Approach 1:
The patent transforms the feedback signal from raw power (P) to the natural logarithm of power (ln P). This parameter transformation changes the relationship between the feedback signal and wind speed, converting the cubic relationship into a linear relationship with the cube root of wind speed. This makes the gradient of the transformed performance index less sensitive to wind speed variations, thereby improving control consistency while maintaining power maximization capability.
2Productivity
If the ESC algorithm uses power signal feedback, then optimal performance is tracked, but settling time varies dramatically with wind speed changes
Solution Approach 1:
By applying the natural logarithm transformation to the power signal, the patent creates a new performance index whose gradient varies more slowly with wind speed changes. This transformation ensures that the ESC algorithm's settling time remains relatively constant across different wind speed conditions, preventing the dramatic variations that occur with direct power feedback.
3Ease of operation
If the ESC algorithm operates with direct power feedback, then the control system responds to power variations, but the behavior becomes extremely sensitive to wind speed changes
Solution Approach 1:
The natural logarithm function serves as a mathematical intermediary between the raw power signal and the ESC algorithm. This intermediary transformation decouples the direct cubic relationship between power and wind speed, creating a more stable feedback signal that allows the ESC algorithm to operate consistently across varying wind conditions without requiring manual recalibration.
Data Source
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AI summary
The present disclosure provides a method and system for optimizing a control process. The method and system comprise using a sensor to generate a feedback signal that represents a measured performance index for an extremum seeking control (ESC) method and sending the feedback signal to an ESC conditioning circuit that applies a logarithmic transformation to the feedback signal to obtain a modified feedback signal. An ESC controller applies the modified feedback signal to the ESC method to generate an output value that is used to control an actuator to maximize the performance of a machine or process.