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A UKF-based approach to estimate parameters of a three-phase synchronous generator model

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Abstract

This paper proposes an approach based on the Unscented Kalman Filter to estimate the parameters of a three-phase synchronous generator model. The developed approach makes use of the trajectory sensitivity functions to assess the influence of the parameters in the model outputs and to classify the parameters into subgroups. Some of the parameters can only be estimated with the selection of a correct sampling window for the estimation process. This characteristic is taken into account to choose a set of windows for the application of the Unscented Kalman Filter. The covariance matrices of this filter, which are also important for the correct estimation of the parameters, are altered to obtain better results. The assessment of the impact of parameter initial values in the filter is also presented in this work. The signals used in the proposed approach are measured at the terminal bus of the synchronous generator, which eliminates the need of knowing the parameters of the grid. The accuracy of the approach is evaluated by comparing the mean squared error between the measured quantities and the responses of the model.

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Acknowledgements

The authors would like to thank Fundacao de Amparo a Pesquisa do Estado de Sao Paulo (FAPESP), which supported this work under Grant 2013/01340-0.

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Authors and Affiliations

  1. University of Sao Paulo, Sao Carlos, Brazil

    Edson L. Geraldi Jr. & Rodrigo A. Ramos

  2. Federal Institute of Education, Science and Technology of Sao Paulo, Piracicaba, Brazil

    Tatiane C. C. Fernandes

Authors
  1. Edson L. Geraldi Jr.
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  2. Tatiane C. C. Fernandes
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  3. Rodrigo A. Ramos
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Correspondence to Edson L. Geraldi Jr..

Appendix

Appendix

The synchronous generator considered in the test sytem has a rated power of 10 MVA, a nominal frequency of 60 Hz, 2 poles, rated voltage of \(20~kV_{LL}\), and \(I_{agline}\) is equal to 500 A. The parameter values of this generator are \(H = 0.71061~s\), \(D = 130~Nms\), \(r_a = 0.002~ pu\), \(L_d = 1.394~pu\), \(L_q = 1.353~ pu\), \(r_F = 0.0067~ pu\), \(L_F = 1.4426~ pu\) and \(M_{df} = 0.9847~ pu\).

The parameters of the automatic voltage regulator of the SG are \(K_a = 20\), \(T_a = 0.001~ s\), \(T_b = 1.0~ s\) and \(T_c = 0.6 ~s\). The value of the setpoint \(V_{REF}\) is \(0.6796\,pu\). The parameters of the speed governor are \(R_{SC} = 20\), \(T_1 = 0.5~ s\), \(T_2 =1.0~ s\), \(T_3 = 1.0~ s\) and \(D_t = 0\). The setpoint REF is equal to 0.14249 pu

The impedances of the three-phase load connected to the buses \({\mathrm {GB}}_{\mathrm {a}}\), \({\mathrm {GB}}_{\mathrm {b}}\) and \({\mathrm {GB}}_{\mathrm {c}}\) are \(Z_{L_a}=Z_{L_b}=Z_{L_c}=38.1 + j9.538~ \varOmega \). The elements of the matrix \(Z_{abc}\) of the distribution line are \(Z_{aa} = Z_{bb} = Z_{cc} = 14.70495 +j7.33127~ \varOmega \) and \(Z_{ab} = Z_{bc} = Z_{ca} = 0\). The voltage phasor of the buses \({\mathrm {IB}}_{\mathrm {a}}\), \({\mathrm {IB}}_{\mathrm {b}}\) and \({\mathrm {IB}}_{\mathrm {c}}\) are \(1.0\angle 0^{\circ }~ pu\), \(1.0\angle -120^{\circ }~ pu\) and \(1.0\angle 120^{\circ }~ pu\), respectively.

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Geraldi, E.L., Fernandes, T.C.C. & Ramos, R.A. A UKF-based approach to estimate parameters of a three-phase synchronous generator model. Energy Syst 9, 573–603 (2018). https://doi.org/10.1007/s12667-018-0280-1

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