A Closed-form Formulation of Eigenvalue Sensitivity Based on Matrix Calculus for Small-signal Stability Analysis in Power System

With the rapid development of power-electronicsenabled power systems,the new converter-based generators are deteriorating the small-signal stability of the power system.Although the numerical differentiation method has been widely used for approximately calculating the eigenvalue sensitivities,its accuracy has not been carefully investigated.Besides,the element-based formulation for computing closed-form eigenvalue sensitivities has not been used in any commercial software due to the average efficiency,complicated formulation,and errorprone characteristics.Based on the matrix calculus,this paper proposes an easily manipulated formulation of the closed-form eigenvalue sensitivities with respect to the power generation.The distinguishing feature of the formulation is that all the formulas consist of vector and matrix operations,which can be performed by developed numerical algorithms to take full advantages of architectural features of the modern computer.The tests on WSCC 3-machine 9-bus system,New England 10-machine 39-bus system,and IEEE 54-machine 118-bus system show that the accuracy of the proposed formulation is superior to the numerical differentiation method and the efficiency is also greatly improved compared to the element-based closed-form formulation.The proposed formulation will be helpful to perform a more accurate and faster stability analysis of a power grid with converter-based devices.

Time-domain Dynamic-performanceimprovement Method for Pulse-width-modulated DC-DC Converters Based on Eigenvalue and Eigenvector Sensitivity

For pulse-width modulated(PWM)DC-DC converters,the input voltage fluctuation and load variation in practical applications make it necessary for them to have better dynamic performance to meet the regulation requirements of the system.The dynamic-performance-improvement method for PWM DC-DC converters is mainly based on indirect dynamic performance indices,such as the gain margin and phase margin.However,both settling time and overshoot in the time domain are important in practical engineering.This makes it difficult for designers to obtain a clear understanding of the time-domain dynamic performance that can be achieved with improved control.In this study,a direct analysis of the time-domain dynamic characteristic of PWM DC-DC converters is performed.A dynamic-performance-improvement method based on eigenvalues and eigenvector sensitivity(E2S-based DPIM)is proposed to directly improve the time-domain dynamic performance index of PWM DC-DC converters.By considering a boost converter with proportional-integral control as an example,an additional virtual inductor current feedback control was designed using the proposed dynamic-performance-improvement method.Simulation and experimental results verify the validity and accuracy of the proposed dynamic-performance-improvement method.

A Novel Perturbative Iteration Algorithm for Effective and Efficient Solution of Frequency-Dependent Eigenvalue Problems

Many engineering structures exhibit frequency dependent characteristics and analyses of these structures lead to frequency dependent eigenvalue problems.This paper presents a novel perturbative iteration(PI)algorithm which can be used to effectively and efficiently solve frequency dependent eigenvalue problems of general frequency dependent systems.Mathematical formulations of the proposed method are developed and based on these formulations,a computer algorithm is devised.Extensive numerical case examples are given to demonstrate the practicality of the proposed method.When all modes are included,the method is exact and when only a subset of modes are used,very accurate results are obtained.

Stability-improvement Method of Cascaded DC-DC Converters with Additional Voltage-error Mutual Feedback Control

The interaction between the source and load converters in cascaded DC-DC converters may cause instability.Thus,improving the stability of cascaded DC-DC converters is important.To solve the above-mentioned problem,a flowchart to improve the control method is established by calculating the eigenvalue sensitivity of a time-domain model of cascaded DC-DC converters.Further,an additional voltage-error mutual feedback control method is firstly proposed based on the flowchart provided in this study to improve the stability of cascaded DC-DC converters.Subsequently,the influence of the proposed mutual feedback control on the stability of cascaded DC-DC converters is analyzed.Finally,the effectiveness of the proposed control method is verified by simulation and experiment.