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Abstract

The eigenvalues assignment problems for descriptor linear systems with state and its derivative feedbacks are considered herein. Necessary and sufficient conditions for the existence of solutions to the problems are established. The Euler and Tustin approximations of the continuous-time systems are analyzed. Procedures for computation of the feedbacks are given and illustrated by numerical examples.
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Authors and Affiliations

Tadeusz Kaczorek
1
ORCID: ORCID

  1. Bialystok University of Technology, Faculty of Electrical Engineering, Wiejska 45D, 15-351 Bialystok, Poland
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Abstract

It is shown that in uncontrollable linear system = Ax + Bu it is possible to assign arbitrarily the eigenvalues of the closed-loop system with state feedbacks u = Kx, K ∈ ℜnm if rank [A B] = n. The design procedure consists in two steps. In the step 1 a nonsingular matrix  M ∈ ℜnm is chosen so that the pair (MA,MB) is controllable. In step 2 the feedback matrix K is chosen so that the closed-loop matrix Ac = A  − BK has the desired eigenvalues. The procedure is illustrated by simple example.

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Authors and Affiliations

Tadeusz Kaczorek
1
ORCID: ORCID

  1. Białystok University of Technology, ul. Wiejska 45A, 15-351 Białystok, Poland
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Abstract

A new approach to the transformations of the matrices of linear continuous-time systems to their canonical forms with desired eigenvalues is proposed. Conditions for the existence of solutions to the problems were given and illustrated by simple numerical examples.
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Authors and Affiliations

Tadeusz Kaczorek
1
ORCID: ORCID

  1. Bialystok University of Technology, Białystok, Poland
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Abstract

The software for co-ordinate measuring machine (CMM) is used for approximating geometric elements in plane (2d) and in space (3d) by approximation algorithms when number of measuring points obtained is larger than the minimum number of points necessary for element definition. Orthogonal regression methods are discussed in this paper. For 2d and 3d cases and they are compared with methods for defining straight line using linear regression. The advantage of orthogonal regression over linear regression is shown by comparing variance of measuring point displacement from both approximation line types.Algorithms for orthogonal regression make it possible to determine optimum position of a straight line for which value of variance of point distance from the line is the lowest possible. The tests have been performed on the Carl Zeiss CMM.
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Authors and Affiliations

Ryszard Filipowski
Lucjan Dąbrowski
Józef Zawora
Ryszard Kossowski
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Abstract

In the paper, the results of investigations on the location of generating units most affecting the angular stability of a large power system (PS) are presented. For their location, the eigenvalues of the PS model state matrix associated with electromechanical phenomena (electromechanical eigenvalues) were used. The eigenvalues were calculated on the basis of the analysis of the disturbance waveforms of instantaneous power of the generating units operating in the PS. The used method of calculating eigenvalues consists in approximation of the disturbance waveforms of generating units by the waveforms being the superposition of modal components. The parameters of these components depend on the sought eigenvalues and their participation factors. The objective function was defined as the mean square error between the approximated and approximating waveforms. To minimize it, a hybrid algorithm, being a combination of genetic and gradient algorithms, was used. In the instantaneous power waveforms of generating units most affecting the PS angular stability, the least damped or undamped modal components dominate. They are related to eigenvalues with the largest values of real parts. The impact of individual modal components on the disturbance waveforms of subsequent generating units was determined with the use of participation factors and correlation coefficients of electromechanical eigenvalues.

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Authors and Affiliations

Piotr Pruski
ORCID: ORCID
Stefan Paszek
ORCID: ORCID
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Abstract

The grid integration of large-scale wind and solar energy affects the power flow of wind-PV-thermal-bundled power transmission systems and may introduce an unpredicted threat to the power system’s small signal stability. Meanwhile, a power system stabilizer (PSS) and static synchronous series compensator (SSSC) play an important role in improving the static and dynamic stability of the system. Based on this scenario and in view of the actual engineering requirements, the framework of wind-PV-thermal-bundled power transmitted by an AC/DC system with the PSS and SSSC is established considering the fluctuation of wind and photovoltaic power output and the characteristics of the PSS and SSSC. Afterwards, the situation model is constructed in the IEEE 2-area 4-unit system, and the influence of the PSS and SSSC on the system stability under different operating conditions is analyzed in detail through eigenvalue analysis and time-domain simulation. Finally, an index named the gain rate is defined to describe the improvement of the stability limitations of various wind-PV-thermal operating conditions with the PSS and SSSC. The results indicate (K) that the damping characteristics, dynamic stability and stability limitations for various wind-PV-thermal operating conditions of the wind-PV-thermal-bundled power transmission system can be significantly improved by the interaction of the PSS and SSSC.

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Authors and Affiliations

Ping He
ORCID: ORCID
Xinxin Wu
Congshan Li
ORCID: ORCID
Mingming Zheng
Zhao Li
ORCID: ORCID
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Abstract

The static series synchronous compensator (SSSC) has demonstrated its capability in providing voltage support and improving power system stability. The objective of this paper is to analyze the dynamic interaction stability mechanism of a hybrid renewable energy system connected with doubly-fed induction generators (DFIGs) and solid oxide fuel cell (SOFC) energy with the SSSC. For this purpose, a linearized mathematical model of this modified hybrid single-machine infinite-bus (SMIB) power system is developed to analyze the physical mechanism of the SSSC in suppressing oscillations and the influence on the dynamic stability characteristics of synchronization. Typical impacting factors such as the series compensation level, the SOFC penetration and tie-line power are considered in the SMIB and two-area systems. The impact of dynamic interactions on enhancing damping characteristics and improving transient performance of the studied systems is demonstrated using eigenvalue analysis and dynamic time-domain simulations, which validates the validity of the proposed physical mechanism simultaneously.
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Bibliography

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Authors and Affiliations

Ping He
1
ORCID: ORCID
Pan Qi
1
ORCID: ORCID
Yuqi Ji
1
ORCID: ORCID
Zhao Li
1
ORCID: ORCID

  1. Zhengzhou University of Light Industry, No.5 Dongfeng Road, Jinshui District, Zhengzhou, 450002, China
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Abstract

In this paper, a new application of the Numerical Assembly Technique is presented for the balancing of linear elastic rotor-bearing systems with a stepped shaft and arbitrarily distributed mass unbalance. The method improves existing balancing techniques by combining the advantages of modal balancing with the fast calculation of an efficient numerical method. The rotating stepped circular shaft is modelled according to the Rayleigh beam theory. The Numerical Assembly Technique is used to calculate the steady-state harmonic response, eigenvalues and the associated mode shapes of the rotor. The displacements of a simulation are compared to measured displacements of the rotor-bearing system to calculate the generalized unbalance for each eigenvalue. The generalized unbalances are modified according to modal theory to calculate orthogonal correction masses. In this manner, a rotor-bearing system is balanced using a single measurement of the displacement at one position on the rotor for every critical speed. Three numerical examples are used to show the accuracy and the balancing success of the proposed method.
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Bibliography

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Authors and Affiliations

Georg Quinz
1
Marcel S. Prem
1
Michael Klanner
1
ORCID: ORCID
Katrin Ellermann
1

  1. Graz University of Technology, Institute of Mechanics, Kopernikusgasse 24/IV, 8010 Graz, Austria
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Abstract

Wind power integration through the voltage source converter-based high-voltage direct current (VSC-HVDC) system will be a potential solution for delivering large-scale wind power to the “Three-North Regions” of China. However, the interaction between the doubly-fed induction generator (DFIG) and VSC-HVDC system may cause the risk of subsynchronous oscillation (SSO). This paper establishes a small-signal model of the VSC based multi-terminal direct current (VSC-MTDC) system with new energy access for the problem, and the influencing factors causing SSO are analyzed based on the eigenvalue analysis method. The theoretical analysis results show that the SSO in the system is related to the wind farm operating conditions, the rotor-side controller (RSC) of the DFIG and the interaction of the controller in the VSC-MTDC system. Then, the phase lag characteristic is obtained based on the signal test method, and a multi-channel variable-parameter subsynchronous damping controller (SSDC) is designed via selecting reasonable parameters. Finally, the correctness of the theoretical analysis and the effectiveness of the multi-channel variable-parameter SSDC are verified based on time-domain simulation.
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Bibliography

[1] Tang G.F., HVDC based on voltage source converter, China Electric Power Press (2010).
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[3] Liu T.Q., Tao Y., Li B.H., Critical problems of wind farm integration via MMC-MTDC system, Power System Technology, vol. 41, no. 10, pp. 3251–3260 (2017).
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[10] Wang L., Yang Z.H., Lu X.Y., Prokhorow A.V., Stability analysis of a hybrid multi-infeed HVDC system connected between two offshore wind farms and two power grids, IEEE Transactions on Industry Applications, vol. 53, no. 3, pp. 1824–1833 (2017).
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[15] Lyu J., Dong P., Shi G., Cai X., Li X.L., Subsynchronous oscillation and its mitigation of MMC-based HVDC with large doubly-fed induction generator-based wind farm integration, Proceedings of the CSEE, vol. 35, no. 19, pp. 4852–4860 (2015).
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Authors and Affiliations

Miaohong Su
1
ORCID: ORCID
Haiying Dong
1 2
Kaiqi Liu
1
Weiwei Zou
1

  1. School of Automatic and Electrical Engineering, Lanzhou Jiaotong University, China
  2. School of New Energy and Power Engineering, Lanzhou Jiaotong University, China

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