Power System Time-Delay Stability Margin Determination
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Solution Overview
Problem
Current methods for analyzing time-delay stability in power systems are inefficient due to the large number of variables required, especially in wide-area measurement systems, where time delays can lead to system instability, and existing simplification methods are not directly applicable to time-delay systems.
Innovation Solution
The method involves Jordan standardization, Taylor expansion, and Schur simplification to reduce the number of state variables in the time-delay power system model, allowing for a faster determination of the stability margin using the Lyapunov stability criteria.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If the direct method based on Lyapunov stability theory and LMI is used to determine time-delay stability margin, then the stability margin can be directly obtained, but the number of variables to be solved increases in an approximate square relationship with the number of state variables, resulting in too long calculation time
Solution Approach 1:
The patent segments the time-delay system model by separating state variables with time delay from state variables without time delay through Taylor expansion. This segmentation reduces the coupled variables in the LMI formulation, transforming a complex stability analysis problem into simpler sub-problems that can be solved more efficiently while maintaining accuracy.
Solution Approach 2:
The patent applies parameter changes by using Taylor expansion to approximate the transcendental terms in the characteristic equations of the time-delay system. This transforms the original complex stability criterion into a simplified LMI form with reduced variables, changing the mathematical parameters from exact transcendental expressions to polynomial approximations that are computationally tractable.
2Device complexity
If existing model simplification methods such as balanced reduction method or Hankel minimum approximant are applied, then model complexity is reduced, but these methods are not directly applicable to time-delay systems due to transcendental terms in characteristic equations
Solution Approach 1:
The patent transforms the time-delay system model by applying Taylor expansion to the transcendental terms, changing the mathematical parameters from exact delay expressions to polynomial approximations. This parameter transformation makes the system compatible with standard model reduction techniques like balanced reduction while preserving the essential time-delay characteristics.
Solution Approach 2:
The patent introduces an intermediary approach by first applying Taylor expansion to convert the time-delay system into an equivalent non-delay system form, then applying standard model reduction techniques. This intermediary transformation acts as a bridge between time-delay systems and conventional simplification methods, enabling the use of established techniques for time-delay problems.
Data Source
AI summary
The present disclosure discloses a method for fast determining a time-delay stability margin of a power system, which focuses on three steps, i.e., Jordan standardization, Taylor separation and Schur simplification, to reconstruct a new time delay system and reduce the system dimension. In this method, firstly, a time delay model is Jordan standardized; further, Taylor expansion is applied in a process for separating state variables with time delay from stage variables without time delay; then, balanced model reduction is realized by Schur simplification; and finally, a WSCC 3-generator-9-bus power system with multiple delays will be used to validate the proposed method via several typical criteria.