Analyzing the internal resonances and energy exchange between modes of power system considering Frequency – Energy dependence using Pseudo-Arclength and shooting algorithm

Document Type : Research Article

Authors

Electrical Engineering Department, Shahid Rajaee Teacher Training University, Lavizan, Tehran, Iran.

Abstract

The power system nonlinearity and its profound impact on the individual states of power system is first evaluated and the interaction between their constituent modes during the occurrence of internal mode resonance (IMR) is discussed in this paper. A typical dynamical feature of nonlinear systems is the frequency-energy dependence of their states and their corresponding constituent modes which is also underlined in this paper. At first predominant state is identified which is defined as the one with highest energy level and the internal mode resonances and energy exchange between its constituent modes are explored accordingly. However, Perturbation Techniques such as Normal Form (NF) or Modal Series (MS) and several polynomial approximation are explored and it is demonstrated that such methodologies do not lead to the acceptable results and does not work well in near-resonant conditions. For this reason, the integrated algorithm consists of Shooting and Pseudo-Arclength is employed for obtaining Frequency-Energy Plot (FEP) to estimate and evaluate the involved modes behavior during the resonance and the energy level at which the internal resonance occurs. The studies are performed on 39-bus New England Test power System and the final results prove the accuracy and effectiveness of the proposed methodology and algorithm.

Keywords

Main Subjects


 Y. Ni, V. Vittal and W. Kliemann, “Analysis of structural properties responsible for nonlinear modal behavior of a stressed power system using the normal form technique,” in Proc. IEEE, 39th Midwest symposium., Circuits and Systems ., Aug, 1996, vol.3, pp. 1029-1033
Cheng Liu, Guowei Cai, Weichun Ge, Deyou Yang, Chuang Liu, Zhenglong Sun, “Oscillation Analysis and Wide-Area Damping Control of DFIGs for Renewable Energy Power Systems Using Line Modal Potential Energy” DOI 10.1109/TPWRS.2018.2791543, IEEE Transactions on Power Systems, 2018
Bin Wang, Student Member, IEEE, and Kai Sun, Senior Member, IEEE, “Formulation and Characterization of Power System Electromechanical Oscillations”, IEEE Transactions on Power Systems, 2018 Digital Object Identifier 10.1109/TPWRS.2016.2535384
Wenjuan Du, Member, IEEE, Jingtian Bi and H.F.Wang, SeniorMember, IEEE, “Damping Degradation of Power System Low-frequency Electromechanical Oscillations Caused by Open-Loop Modal Resonance” DOI 10.1109/TPWRS.2018.2805187, IEEE Transactions on Power Systems
Hadi Lomei, Mohsen Assili, Danny Sutanto and Kashem Muttaqi, “A New Approach to Reduce the Non-Linear Characteristics of a Stressed Power System by Using the Normal Form Technique in the Control Design of the Excitation System,” IEEE Transactions on Industry Applications, vol. PP, no. 11, pp. 1–8, 2016
A.H. Nayfeh, on direct methods for constructing nonlinear normal modes of continuous systems, Journal of Vibration and control 1 (1995), 389-430
A. R. Messina, Inter-Area Oscillations in Power Systems. New York, NY, USA: Springer, 2009.
L. Jezequel, C.H. Lamarque, Analysis of nonlinear dynamic systems by the normal form theory, Journal of Sound and Vibration, 149 (1991), 429-459
H. Shayeghi, A. Ahmadpour, E. Mokaramian, Alleviating the Small-Signal Oscillations of the SMIB Power System with the TLBO–FPSS and SSSC Robust Controller. Electrical and Computer Engineering Innovations (JECEI), volume. 5, issue 2, pages: 163-170, 2017
R. Hajmohammadi, H. Nasirisoloklo, M. M. Farsangi, The Sine-Cosine Wavelet and Its Application in the Optimal Control of Nonlinear Systems with Constraint,  Electrical and Computer Engineering Innovations (JECEI), volume. 1, issue 1, pages 51-55, 2013
C. M. Lin, V. Vittal, W. Kliemann, and A. A. Fouad, “Investigation of modal interaction and its effects on control performance in stressed power systems using normal forms of vector fields,” IEEE Trans. Power Syst., vol. 11, no.2, pp: 781–787, May 1996
R.Z. Davarani, R. Ghazi, N. Pariz, “Normal Form Analysis of the Sub synchronous Torsional Interaction with SVC in the Complex Power Systems,” Arabian Journal for Science & Engineering, vol.39, no.5 pp:4231-4240, May 2014
E. Barocio, A. R. Messina, and J. Arroyo, “Analysis of factors affecting normal form results,” Elect. Power Syst. Res., vol. 45, pp. 2349–1234, Dec. 2004
Z. Wang, Q. Huang, “A Closed Normal Form Solution under Near-Resonant Modal Interaction in Power Systems,” IEEE Trans. Power Syst., DOI 10.1109/TPWRS.2017.2679121
R. J. Betancourt, E. Barocio, J. Arroyo, and A. R. Messina, “A Real Normal Form Approach to the Study of Resonant Power Systems,” IEEE Trans. Power Syst., vol. 21, no. 1, pp. 431–432, Feb. 2006
H.M. Shanechi, N. Pariz, E. Vaahedi, “General Nonlinear Modal Representation of Large Scale Power Systems,” ,” IEEE Trans. Power Systems, vol.18, no.3, pp.1103-1109, Aug. 2003
N. Pariz, H.M. Shanechi, E. Vaahedi, “Explaining and Validating Stressed Power Systems Behavior using Modal Series,” IEEE Trans. Power Systems, vol.18, pp.778-785, May. 2003
O. Rodriguez, A. Medina, A.R. Messina, and C.R. Fuerte-Esquivel, “The Modal Series Method and Multi-Dimensional Laplace Transforms for the Analysis of Nonlinear Effects in Power Systems Dynamics,” in Proc. IEEE Power & Energy Society General Meeting, Calgary, Alberta, Canada, July 2009
H.M. Shanechi, N. Pariz, E. Vaahedi, “General Nonlinear Modal Representation of Large Scale Power Systems,” IEEE Trans .Power. Syst, vol.18, no.3, pp: 1103-1109, Aug. 2003
Yongzhi Zhou, Hao Wu, Member, IEEE, Chenghong Gu, Member, IEEE, and Yonghua Song, Fellow, IEEE, “A Novel Method of Polynomial Approximation for Parametric Problems in Power Systems” DOI 10.1109/TPWRS.2016.2623820, IEEE Transactions on Power Systems, 2018
L. Chen , Y. Min, and W. Hu, “An energy-based method for location of power system oscillation source,” IEEE Trans. Power Syst., vol. 28, no. 2, pp. 826– 836, May 2013
V. Vittal, N. Bhatia, and A. A. Fouad, “Analysis of the inter-area mode phenomenon in power systems following large disturbances,” IEEE Trans. Power Syst., vol. 6, no. 4, pp. 1515–1521, Nov. 1991
Identification of Electromechanical Modes in Power Systems, IEEE Task Force Rep. TP462, 2012.
Qi Huang, Zhouqiang Wang, Changhua Zhang, “Evaluation of the Effect of Modal Interaction Higher than 2nd Order in Small-signal Analysis,” in Proc. 2009 IEEE Power & Energy Society General Meeting, Calgary, Alberta, Canada, July 2009
L. Xiea, S. Bagueta, B. Prabelb, R. Dufoura, “Bifurcation tracking by Harmonic Balance Method for performance tuning of nonlinear dynamical systems” , Mechanical Systems and Signal Processing, 0888-3270/ © 2016 Elsevier Ltd.
Malte Krack n, LarsPanning-vonScheidt, JörgWallaschek, “A high-order harmonic balance method for systems with distinct states”, Journal of Sound and Vibration332 (2013)5476–5488
Zhengshuo Li  Qinglai Guo  Hongbin Sun  Jianhui Wang  Yinliang Xu  Miao Fan, “A Distributed Transmission-Distribution-Coupled Static Voltage Stability Assessment Method Considering Distributed Generation” IEEE Transactions on Power Systems ( Volume: 33 , Issue: 3 , May 2018
Hongcai ZhangScott J. MouraZechun Hu  Yonghua Song, “PEV Fast-Charging Station Siting and Sizing on Coupled Transportation and Power Networks”, IEEE Transactions on Smart Grid Volume: 9 , Issue: 4 , July 2018