Distributed Power Stability Regions Under Multiple Time Delays
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Solution Overview
Problem
Distributed cyber-physical power systems with multiple time delays face challenges in maintaining stability, as existing methods are inefficient in characterizing and controlling the stable region, leading to potential system instability.
Innovation Solution
A method is developed to determine the stable region for distributed cyber-physical power systems by establishing a state space expression, converting it to the frequency domain, and solving for marginally stable characteristic equations with unified time delays, which allows for the identification of stable boundaries in each time delay direction, ultimately generating a stable domain for multiple time delays.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Adaptability or versatility
If distributed control architecture is used in cyber-physical power systems, then system adaptability and scalability are improved, but time delays in measurement, communication, and control links increase, leading to system instability
Solution Approach 1:
The patent transforms the stability analysis problem from time domain to frequency domain by changing the parameter representation. It uses Laplace transform to convert differential equations with time delays into algebraic equations in the s-domain, where stability can be analyzed through characteristic equations and eigenvalue distribution, avoiding direct time-domain simulation complexity
Solution Approach 2:
The patent introduces an intermediary computational framework that uses state-space representation and characteristic equation analysis as a mediator between the distributed control architecture and stability assessment. This intermediary method systematically handles multiple time delays by formulating a unified characteristic equation that captures the combined effect of all delay sources without requiring direct time-domain integration
2Measurement precision
If existing frequency domain methods such as Pade approximation are used to analyze time delay stability, then analysis can be performed, but computational efficiency is low and accurate characterization of stable region is difficult
Solution Approach 1:
The patent replaces traditional mechanical approximation methods (Pade approximation) with a direct frequency domain transformation approach. Instead of approximating time delay effects through rational function expansions, the method uses exact Laplace transform to convert the delayed differential equations into algebraic equations, eliminating the need for approximation and improving both accuracy and efficiency
Solution Approach 2:
The patent changes the analysis parameter from time-domain delay values to frequency-domain characteristic roots. By transforming the problem into the s-domain and analyzing the distribution of eigenvalues of the characteristic equation, the method achieves precise stable region characterization without the computational burden of time-domain simulation or iterative approximation methods
Data Source
AI summary
The present disclosure provides a stable region determining method for distributed cyber-physical power systems with multiple time delays, including: first establishing a state space expression of the cyber-physical power systems under distributed control with multiple time delays; converting the state space expression to frequency domain through Laplace transform to obtain a characteristic equation for multiple time delays of the cyber-physical power systems under distributed control, and establishing a marginally stable characteristic equation with unified time delay to obtain a marginally stable characteristic equation for multiple time delays of the cyber-physical power systems under distributed control with unified time delay; in each time delay direction, solving a stable boundary for time delay of the cyber-physical power systems under distributed control; connecting the stable boundaries for time delays in all time delay directions, and generating a stable domain for time delays of the cyber-physical power systems under distributed control.