# American Institute of Mathematical Sciences

June  2020, 13(6): 1773-1790. doi: 10.3934/dcdss.2020104

## A new iterative identification method for damping control of power system in multi-interference

 1 School of Mechanical-electronic and Automobile Engineering, Beijing University of Civil Engineering and Architecture, Beijing 100044, China 2 Beijing Key Laboratory of Service Performance of Urban Rail Transit Vehicles, Beijing University of Civil Engineering and Architecture, Beijing 100044, China 3 School of Electrical Engineering, Computing and Mathematical Sciences, Curtin University, Perth, 6845, Australia

* Corresponding author: Miao Yu

Received  August 2018 Revised  October 2018 Published  September 2019

Fund Project: The first author is supported by the Scholarship for Young University Teachers granted by China Scholarship Council (201709960017); National Natural Science Foundation of China (No.51407201); Research Funds for Beijing University of Civil Engineering and Architecture (No.X18121); The second author is supported by BUCEA Post Graduate Innovation Project (No.PG2012085)

In this paper, we consider the closed-loop model of a power system in a multi-interference environment. For a multi-interference power system, the closed-loop identification is a difficult task. Yet, the model identification error can degrade the effect of the damping control. This could lead to instability of the power grid. Thus, for the closed-loop identification, we propose an iterative online identification algorithm based on the recursive least squares method and the v-gap distance. The convergence of the algorithm is proved by using direct method. The proposed algorithm is applied to the New England system, for which the results obtained are compared with those obtained using the prediction error method and the Runge-Kutta method. From the simulation study being carried out on the IEEE 39-bus New England system, we observe that by using the iterative identification algorithm proposed in this paper, the output response time is reduced by about half when compared with those obtained by using the prediction error method and the Runge-Kutta method. Also, the number of oscillations in the output response is less. These clearly indicate that the algorithm proposed can effectively suppress low frequency oscillation. As for the amplitudes of the output responses produced by the three methods, they are basically the same.

Citation: Miao Yu, Haoyang Lu, Weipeng Shang. A new iterative identification method for damping control of power system in multi-interference. Discrete and Continuous Dynamical Systems - S, 2020, 13 (6) : 1773-1790. doi: 10.3934/dcdss.2020104
##### References:
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show all references

##### References:
 [1] H. K. Abdulkhader, J. Jacob and A. T. Mathew, Fractional-order lead-lag compensator-based multi-band power system stabiliser design using a hybrid dynamic GA-PSO algorithm, IET Gener. Tran. and Distr., 12 (2018), 1515-1521. [2] P. Albertos and A. Sala, Iterative Identification and Control: Advances in Theory and Applications, Springer-Verlag, New York, 2002. [3] X. H. Bu and Z. S. Hou, Adaptive iterative learning control for linear systems with binary-valued observations, IEEE Trans. on Neur. Net. and Lear. Syst., 29 (2018), 232-237.  doi: 10.1109/TNNLS.2016.2616885. [4] X. M. Chen and G. R. Guo, The convergence analysis of the WCE iterative algorithm, J. Natl. Univ. of Def. Tech., 3 (1986), 16-25. [5] M. Darabian and A. Jalilvand, Designing a wide area damping controller to coordinate FACTS devices in the presence of wind turbines with regard to time delay, IET Rene. Power Gener., 12 (2018), 1523-1534.  doi: 10.1049/iet-rpg.2017.0602. [6] Z. L. Deng, X. H. Qin and M. B. Zhang, Frequency-domain analysis of robust monotonic convergence of norm-optimal iterative learning control, IEEE Trans. on Contr. Syst. Tech., 26 (2018), 637-651. [7] L. Q. Dou, Q. Zong, Z. S. Zhao and Y. H. Ji, Iterative identification and control design with optimal excitation signals based on v-gap, Sci. in China, 52 (2009), 1120-1128. [8] R. Goldoost-Soloot, Y. Mishra and G. Ledwich, Wide-area damping control for inter-area oscillations using inverse filtering technique, IET Gener. Tran. and Distr., 9 (2015), 1534-1543.  doi: 10.1049/iet-gtd.2015.0027. [9] Q. Guo, The Iterative Methods to Solve Systems of Nonlinear Equations, Ph.D thesis, Hefei University of Technology in Anhui Province, 2015. [10] Z. X. Liu, Y. Z. Sun, X. Li, B. Song, Z. S. Liu and F. M. Feng, Wide-area damping control system in China Southern Power Grid and its operation analysis, Auto. Electric. Power Syst., 38 (2014), 152–159 and 183. [11] K. Liu, Y. M. Zhang, X. Y. Li, R. Jiang and Q. Zeng, Design of VSC-HVDC bilateral fuzzy logic reactive power damping controller based on oscillation transient energy decrease, Power Syst. Tech., 40 (2016), 1030-1036. [12] W. C. Meng, X. Y. Wang, B. Fan, Q. M. Yang and I. Kamwa, Adaptive nonlinear neural control of wide-area power systems, IET Gener. Tran. and Distr., 11 (2017), 4531-4536. [13] D. H. Owens and K. Feng, Parameter optimization in iterative learning control, Int. J. Contr., 76 (2003), 1059-1069.  doi: 10.1080/0020717031000121410. [14] D. Rimorov, A. Heniche, I. Kamwa, S. Babaei, G. Stefopolous and B. Fardanesh, Dynamic performance improvement of New York state power grid with multi-functional multi-band power system stabiliser-based wide-area control, IET Gener. Tran. and Distr., 11 (2017), 4537-4545.  doi: 10.1049/iet-gtd.2017.0288. [15] X. Ruan, Z. Z. Bien and Q. Wang, Convergence characteristics of proportional-type iterative learning control in the sense of Lebesgue-p norm, IET Contr. Theory and Appl., 6 (2012), 707-714.  doi: 10.1049/iet-cta.2010.0388. [16] G. Sebastian, Y. Tan, D. Oetomo and I. Mareels, Feedback-based iterative learning design and synthesis with output constraints for robotic manipulators, IEEE Contr. Syst. Lett., 2 (2018), 513-518.  doi: 10.1109/LCSYS.2018.2842186. [17] Y. Shen, W. Yao, J. Y. Wen and H. B. He, Adaptive wide-area power oscillation damper design for photovoltaic plant considering delay compensation, IET Gener. Tran. and Distr., 11 (2017), 4511-4519.  doi: 10.1049/iet-gtd.2016.2057. [18] T. D. Son, G. Pipeleers and J. Swevers, Robust monotonic convergent iterative learning control, IEEE Trans. on Automat. Contr., 61 (2016), 1063-1068.  doi: 10.1109/TAC.2015.2457785. [19] F. Z. Song, Y. Liu, J. X. Xu, X. F. Yang, P. He and Z. L. Yang, Iterative learning identification and compensation of space-periodic disturbance in PMLSM systems with time delay, IEEE Trans. on Ind. Electron., 65 (2018), 7579-7589.  doi: 10.1109/TIE.2017.2777387. [20] C. Wu, Identification of Dominant Dynamic Characteristics of Power System Based on Ambient Signals, Ph.D thesis, Tsinghua University in Beijing, 2010. [21] C. Zhang and D. Shen, Zero-error convergence of iterative learning control based on uniform quantisation with encoding and decoding mechanism, IET Contr. Theory and Appl., 12 (2018), 1907-1915.  doi: 10.1049/iet-cta.2017.0919. [22] S. Zhu, X. J. Wang and H. Liu, Observer-based iterative and repetitive learning control for a class of nonlinear systems, IEEE/CAA J. Autom. Sinica, 5 (2018), 990-998.  doi: 10.1109/JAS.2017.7510463. [23] H. Zhang and M. Gou, Convergence analysis of compressive sensing based on SCAD iterative thresholding algorithm, Chinese J. Eng. Math., 33 (2016), 243-258.
Closed-loop Power System Model
Closed-loop Power System Identification Model
The flow chart of iterative identification algorithm based on RLS and $v$-gap
IEEE 39-bus New England test system
The optimal parameters of the New England system being identified by the RLS parameter estimation
The Bode diagrams of the identified model and the initial model for New England system
Comparison of output responses for New England system
The $v$-gap distance between $G$ and $B_i$ for New England system
The output responses obtained by different identification methods for New England system
 Runge-Kutta Iterative identification Prediction Error Time/s 70 29 39 Amplitude/dB 0.912 0.984 0.883
 Runge-Kutta Iterative identification Prediction Error Time/s 70 29 39 Amplitude/dB 0.912 0.984 0.883
The frequency stability margin and the $v$-gap distance corresponding to each identified data for New England system
 Group 1 Group 2 Group 3 Group 4 Group 5 Group 6 The frequency stability margin 0.0447 0.0269 0.0325 0.0622 0.1272 0.1257 v-gap distance 0.5899 0.5660 0.4151 0.1462 0.1099 0.1048 Group 7 Group 8 Group 9 Group 10 Group 11 Group 12 The frequency stability margin 0.1258 0.1178 0.1177 0.1191 0.1193 0.1192 v-gap distance 0.1041 0.0645 0.0589 0.0590 0.0610 0.0645
 Group 1 Group 2 Group 3 Group 4 Group 5 Group 6 The frequency stability margin 0.0447 0.0269 0.0325 0.0622 0.1272 0.1257 v-gap distance 0.5899 0.5660 0.4151 0.1462 0.1099 0.1048 Group 7 Group 8 Group 9 Group 10 Group 11 Group 12 The frequency stability margin 0.1258 0.1178 0.1177 0.1191 0.1193 0.1192 v-gap distance 0.1041 0.0645 0.0589 0.0590 0.0610 0.0645
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