Both power flow states and sensitivities between variables are important information in power system analysis and should be kept consistent before and after equivalence. The general sufficient and necessary condition for sensitivity consistency in equivalent methods is derived. Based on the proposed general condition, it is further derived that Thevenin equivalent method can keep sensitivity consistent before and after equivalence, whereas the specific preconditions for sensitivity consistency are required for the traditional Ward equivalent method and extended Ward equivalent method. These two Ward equivalent methods cannot meet the preconditions in general cases and may lead to significant errors. This conclusion is confirmed by simulation results of the IEEE 39-bus system and an actual power system with 661 buses.

References

1. 1)
  - 5. Annakkage, U.D., Nair, N.K.C., Liang, Y., et al: ‘Dynamic system equivalents: a survey of available techniques’, IEEE Trans. Power Syst., 2012, 27, (1), pp. 411–420 (doi: 10.1109/TPWRD.2011.2167351).
2. 2)
  - 12. van Amerongen, R.A.M., van Meeteren, H.P.: ‘A generalised ward equivalent for security analysis’, IEEE Trans. Power Appar. Syst., 1982, 101, (6), pp. 1519–1526 (doi: 10.1109/TPAS.1982.317200).
3. 3)
  - 14. Kai, S., Lee, S.T., Pei, Z.: ‘An adaptive power system equivalent for real-time estimation of stability margin using phase-plane trajectories’, IEEE Trans. Power Syst., 2011, 26, (2), pp. 915–923 (doi: 10.1109/TPWRS.2010.2055900).
4. 4)
  - 9. Dobrijević, Đ.M., Popvić, D.P.: ‘An unified external network equivalent in steady-state security assessment’, Facta universitatis-series: Electron. Energ., 2010, 23, (2), pp. 179–189 (doi: 10.2298/FUEE1002179D).
5. 5)
  - A.J. Conejo , N. Alguacil , G. Fernandez-Ruiz . Allocation of the cost of transmission losses using a radial equivalent network. IEEE Trans. Power Syst. , 4 , 1353 - 1358
6. 6)
  - 1. Poon, K.K.Y., Emami, R., Bose, A., Abur, A.: ‘External data exchange issues for state estimation in power systems’, IEEE Trans. Power Syst., 2012, 27, (2), pp. 849–856 (doi: 10.1109/TPWRS.2011.2176150).
7. 7)
  - 13. Yu, J., Zhang, M., Li, W.: ‘Static equivalent method based on component particularity representation and sensitivity consistency’, IEEE Trans. Power Syst., 2014, 29, (5), pp. 2400–2408 (doi: 10.1109/TPWRS.2014.2300868).
8. 8)
  - 6. Ghassemi, F., Koo, K.L.: ‘Equivalent network for wind farm harmonic assessments’, IEEE Trans. Power Deliv., 2010, 25, (3), pp. 1808–1815 (doi: 10.1109/TPWRD.2009.2037909).
9. 9)
  - F.F. Wu , A. Monticelli . Critical review of external network modelling for online security analysis. Int. J. Electr. Power Energy Syst. , 4 , 222 - 235
10. 10)
  - 4. Lin, X., Gole, A.M., Yu, M.: ‘A wide-band multi-port system equivalent for real-time digital power system simulators’, IEEE Trans. Power Syst., 2009, 24, (1), pp. 237–249 (doi: 10.1109/TPWRS.2008.2007000).
11. 11)
  - S. Deckmann , A. Pizzolante , A. Monticelli , B. Stott , O. Alsac . Studies on power system load flow equivalencing. IEEE Trans. Power Appar. Syst. , 6 , 2301 - 2310
12. 12)
  - 14. Ward, J.B.: ‘Equivalent circuits for power flow studies’, Electr. Eng., 1949, 68, (9), pp. 794–794 (doi: 10.1109/EE.1949.6444973).
13. 13)
  - 11. Wang, P., Billinton, R., Goel, L.: ‘Unreliability cost assessment of an electric power system using reliability network equivalent approaches’, IEEE Trans. Power Syst., 2002, 17, (3), pp. 549–556 (doi: 10.1109/TPWRS.2002.800873).
14. 14)
  - 2. Neto, A.C., Rodrigues, A.B., Prada, R.B., da Guia da Silva, M.: ‘External equivalent for electric power distribution networks with radial topology’, IEEE Trans. Power Syst., 2008, 23, (3), pp. 889–895 (doi: 10.1109/TPWRS.2008.922250).

Sufficient and necessary condition of sensitivity consistency in static equivalent methods

References

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