基于谱离散化和特征值优化的大规模多时滞电力系统广域阻尼协调控制方法研究

In the past years, the wide-area damping control studies for large power systems considering time delay effects mainly concentrated on damping controller design based on model reduction and delay approximation. There exist several shortcomings in these studies, including biased errors in system modeling, inherent conservation and lack of coordination between multiple controllers. To deal with these challenges, three core techniques are used in this project. Firstly, the spectrum of the time-delayed power system is mapped into that of an infinite-dimensional operator. Secondly, the infinite-dimensional operator is discretized into a finite-dimensional one. Lastly, an eigenvalue-based optimization method is presented to design wide-area damping controllers in a coordinated manner. . This project contains three parts. Firstly, the spectral mapping property of the integral operator of time-delayed systems, i.e., solution operator is studied, which can transform the rightmost eigenvalues of time-delayed power systems into critical eigenvalues of itself with largest moduli. Based on which, a solution operator discretization (SOD)-based method is presented for efficient computing critical eigenvalues and fast determining the small signal stability of time-delayed power systems. Secondly, the computation of H∞ norm of power system is firstly mapped and decoupled into eigenvalue computation of two induced operators. Then, an efficient and indirect method for computing H∞ norm is presented based on spectral discretization and iterative eigenvalue computation of the two operators. Lastly, based on accurate computation of critical eigenvalues and H∞ norm, coordinated methods for design multiple wide-area power system stabilizers (PSSs) and H∞ robust damping controllers are proposed by utilizing non-smooth eigenvalue optimization. The research outcomes of this project will provide a brand new method for power system wide-area damping control which takes time delay effects into consideration. Therefore, it is of great significance and value in both theory and practical application.

以往考虑时滞影响的电力系统广域阻尼控制研究，主要是在模型降阶和时滞近似基础上设计阻尼控制器，存在降阶和近似误差、固有保守性和多控制器难以协调的不足。对此，本项目用无限维算子对时滞电力系统的谱进行映射，用离散化将无限维算子转化为有限维算子，用特征值优化实现广域阻尼协调控制。包括3方面工作：(1)利用解算子将电力系统最右侧的关键特征值映射为其模值最大的部分特征值的特性，提出了基于解算子离散化的时滞电力系统关键特征值高效计算和稳定性快速判别方法；(2)将H∞范数计算映射和分解为两个导出算子特征值的交替求解，进而提出了基于算子离散化和特征值交替求解的H∞范数的高效和间接求解方法；(3)在关键特征值和H∞范数精确计算的基础上，提出了基于非光滑特征值优化的广域PSS和H∞鲁棒阻尼控制器协调设计方法。本项目研究成果将为考虑时滞影响的电力系统广域阻尼控制提供全新的思路和方法，具有重要的理论意义和应用价值。

项目突破了大规模时滞电力系统低复杂度高精度建模、关键特征值高效计算、区间低频振荡的广域协调阻尼控制等关键技术，建立了大规模时滞电力系统的振荡分析和控制技术体系。. （1）提出了基于时滞合并原理的低复杂度建模方法，首创了无穷维时滞电力系统的低阶高精度部分谱离散化理论，解决了时滞电力系统特征值精确计算的可行性问题，将系统总时滞个数减少50%，降低了系统模型的复杂度，保证特征值具有谱精度。. （2）提出了快速求取系统部分关键特征值的稀疏计算和收敛加速技术，突破了大规模时滞电力系统特征值计算效率低的瓶颈，实现了关键特征值的高效、准确求取，开发了目前国际上唯一的时滞电力系统特征值计算商用软件，适用于5万阶数级实际大规模电力系统，处理规模、计算精度和求解效率等指标国际领先。. （3）提出了基于算子离散化的大规模多时滞电力系统H-inf范数计算方法，攻克了考虑时滞影响的发电机组励磁系统附加广域PSS和广域H-inf鲁棒控制器参数设计的非凸、非光滑优化难题，提出了基于特征值优化的广域PSS和H-inf鲁棒阻尼控制器的协调设计方法。

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