Compressor Protection via Polar Coordinate Transformation
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Solution Overview
Problem
Existing compressor protection methods fail to accurately determine the operating point's position relative to both surge and choke limits in dynamic compressors, limiting efficient operation and stability.
Innovation Solution
The method involves converting compressor performance maps from rectangular to polar coordinates, allowing for precise calculation of controlled variables for PID controllers, enabling accurate positioning of the operating point within the surge and choke limits.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Device complexity
If rectangular coordinate methods are used to determine operating point position, then the method is simple to implement, but it cannot simultaneously determine the position relative to both surge and choke lines
Solution Approach 1:
The patent transforms the compressor performance map from rectangular coordinates (mass flow vs. pressure ratio) to polar coordinates (radius vs. angle). This dimensional transformation enables simultaneous representation of both surge and choke limits, allowing the operating point position to be determined relative to both boundaries in a single coordinate system, thereby resolving the contradiction between method simplicity and measurement precision.
2Ease of operation
If conventional PID control is used with rectangular coordinates, then the control system is straightforward, but it cannot accurately protect against both surge and choke conditions
Solution Approach 1:
By converting the performance map to polar coordinates, the patent enables PID control to simultaneously account for both surge and choke conditions. The radial coordinate represents the distance from the surge line while the angular coordinate represents the position relative to the choke line, allowing the control system to accurately determine protection requirements for both conditions using a single control algorithm, thus improving reliability without significantly complicating operation.
3Adaptability or versatility
If the full operating range from surge to choke is represented in rectangular coordinates, then the representation is geometrically limited, but it cannot accurately reproduce the operating range
Solution Approach 1:
The patent applies polar coordinate transformation to represent the full operating range from surge to choke limits. In the polar coordinate system, the surge line corresponds to a constant angle while the choke line corresponds to another constant angle, allowing the entire operating range to be accurately reproduced. This transformation eliminates the geometric limitations of rectangular coordinates and enables precise positioning of operating points across the full range.
Data Source
AI summary
This disclosure describes a novel methodology for anti-surge and anti-choke control systems protecting centrifugal and axial compressors. The methodology, based on Buckingham's π-theorem for compressors, presents compressor performance maps in dimensionless rectangular π-term coordinates that are independent of compressor inlet conditions, fluid molecular weight and rotational speed. The full range of compressor operating points from surge to choke is monitored and controlled when surge and choke limits are available. This is accomplished by converting rectangular coordinates presented in π-terms to polar coordinates, and then converting them to a controlled variable used in the closed-loop controllers. The methodology provides control algorithms for variable speed compressors, variable geometry compressors equipped with inlet guide vanes or stator vanes that exhibit displacement of surge and choke limits. The methodology most accurately estimates the location of the operating point relative to its limit in polar coordinates if only the surge or choke limit is available. The presented protection methods are applicable to any known types of dynamic compressors for industrial, commercial, jet engines, turbochargers.