基于希尔伯特变换的电网络约束关系研究

Research on electric network constraint relationship based on Hilbert transform

为了研究电压波动条件下的电网络约束关系,文章基于希尔伯特变换,构建了供电电压存在波动下线性时不变负载上电压、电流的解析信号模型,推导出了以解析信号表征线性时不变电网络的拓扑约束和元件约束关系,将相量法思想拓展至对供电电压波动下线性时不变电网络响应特性的分析与求解。仿真验证结果表明,供电电压存在波动条件下,文中所建立的基于希尔伯特变换的电网络约束关系,不仅物理意义清晰、表征简明,而且正确、好用。文章所建立的电网络约束关系,能够为供电电压波动条件下电网络中线性时不变负载上电压电流关系的建模、仿真分析与计算提供指导。

In order to study the electric network constraint relationship under the condition of voltage fluctuation,this paper establishes the analytic signal models for the voltage and current of the linear time-invariant loads with supply voltage fluctuation based on the Hilbert transform.Then,the linear time-invariant electric network topology constraints and element constraints represented by analytic signals are derived,which are the generalization of phasor method extended to the analysis and solution of the response characteristics of linear time-invariant electric networks under supply voltage fluctuation.The simulation experiment results show that the electric network constraint relationship based on the Hilbert transform is not only clear in physical meaning and concise in characterization,but also correct and easy to use when the supply voltage fluctuates.The relationship established in this paper can provide guidance for the analysis and calculation of the voltage-current relationship on the linear time-invariant loads under the condition of supply voltage fluctuations.