Dynamic Voltage Stability Evaluation of Power Systems Considering Industrial Electrical Loads

  • Mohammad reza Ansari University of Shahreza
Keywords: Voltage stability, Dynamic Simulation, Hopf Bifurcation, Industrial Electrical Loads


   This paper presents a simulation of the dynamic voltage stability in power system. In application of modern power system, dynamic assessment of voltage stability is known as basic concept. In order to study dynamic voltage stability in a power system, different dynamic boundaries are defined such as, Hopf bifurcation (HB) boundary. HB point is an oscillatory boundary in power system. For recognition of the bifurcations, it is unavoidable to study the eigenvalues of power system. In spite of this, determination of these eigenvalues need to dynamic Jacobian matrix of power system and modal analysis that is very time consuming and complex in large systems. Also, different industrial loads (static and dynamic) e.g. induction motors can effect on dynamic voltage stability boundaries. In this paper, we proposed a solution method based on analysis the eigenvalues of reduced Jacobian matrix and time domain simulation for assessment of dynamic voltage stability. In addition, effects of industrial electrical loads on the small disturbance voltage stability are evaluated by the proposed method. To show the effectiveness of the proposed solution method, it is tested on IEEE 14 bus and New England test systems.


[1] N. Amjady, M. R. Ansari “Small Disturbance Voltage Stability Assessment of Power Systems by Modal Analysis and Dynamic Simulation”. Energy Conversion and Management, vol. 49(10), pp. 2629-2641, 2008.
[2] S. Repo, On-line Voltage Stability Assessment of Power Systems-An Approach of Black Box Modeling, Tampere University of Technology Publications 344, 2001.
[3] N. Amjady, M. R. Ansari, “Small disturbance voltage stability evaluation of power systems”, Transmission and Distribution Conference and Exposition, 2008
[4] P. Kundur, J. Paserba, V. Ajjarapu, G. Anderson, A. Bose, C. Canizares, N. Hatziargyriou, D. Hill, A. Stankovic, C. Taylor, T.V. Cutsem, and V. Vittal. “Definition and Classification of Power System Stability”, IEEE Trans. on Power Systems, vol. 19(3), pp. 1387-1401, Aug. 2004.
[5] T. V. Cutsem, C. Vournas, “Voltage Stability of Electric Power Systems”, Kluwer Academic Publishers, Boston, USA, 1998.
[6] F. Zhihong., “The static voltage stability analysis methods for many generators power system–singularity decoupled method”, Proceedings of CSEE., vol. 12(3): pp. 10-18, 1992.
[7] H. Chen., Y. Wang, R. Zhou “Transient and voltage stability enhancement via coordinated excitation and UPFC control”, IEE Proc. Gener Transm Distrib. vol. 148(3), pp. 201-208, 2001.
[8] N. Amjady, M. H. Velayati, “Evaluation of Hopf Bifurcation Considering the Effect of Load Models and Excitation System Parameters”, International Review of Electrical Engineering, vol. 6(5), pp. 2419-2427, 2011.
[9] N. Amjady, M. H. Velayati, “Evaluation of the Maximum Loadability Point of Power Systems Considering the Effect of Static Load Models”, Energy Conversion and Management, vol. 50(12), pp. 3202-3210, 2009.
[10] GM. Huang, L. Zhao, X. Song, “new bifurcation analysis for power system dynamic voltage stability studies”, In: Proc. IEEE power eng. Soc. winter meeting. 2002, pp. 882-887, 2002.
[11] J. Hongjie., Y. Xiaodan, Y. Yixin, “An improved voltage stability index and its application”, Electrical power and energy systems, vol. 27, pp. 567-574, 2005.
[12] A. P. Lerm, “Control of Hopf Bifurcation in Multi Area Power Systems via a Secondary Voltage. Regulation Scheme”. IEEE Trans. Power Syst., vol. 23(3), pp. 245-254, 2002.
[13] C. F. Yang, G. G. Lai, C. H. Lee, C. T. Su, G. W. Chang, “Optimal Setting of Reactive Compensation Devices with an Improved Voltage Stability Index for Voltage Stability Enhancement”. Electrical Power and Energy Systems, vol. 37(1). pp. 50-57, 2012.
[14] H. Raoufi, M. Kalantar, “Reactive Power Rescheduling with Generator Ranking for Voltage Stability Improvement”. Energy Conversion and Management, vol. 50(4), pp. 1129-1135, 2009.
[15] A. Kargarian, M. Raoofat, M. Mohammadi, “Reactive Power Market Management Considering Voltage Control Area Reserve and System Security”, Applied Energy, vol. 88(11), pp. 3832-3840, 2011.
[16] N. Amjady, M. Esmaili, “Improving voltage security assessment and ranking vulnerable bus with consideration of power system limits,” Elect. Power Energy Syst., vol. 25(9), pp. 705–715, Nov. 2003.
[17] H. Chen, Y. Wang, R. Zhou, “Transient and voltage stability enhancement via coordinated excitation and UPFC control,” IEE Proc. Gener. Transm. Distrib., vol. 148(3), pp. 201-208, May 2001.
[18] R. J. Avalos, C. Canizares, F. Milano, A. j. Conejo, “Equivalency of Continuation and Optimization Methods to Determine Saddle-node and Limit-induced Bifurcations in Power Systems”. IEEE Trans. Circuits and Systems–I: Regular Paper., vol. 56(1), pp. 210-223, 2009.
[19] P. W. Sauer and M. A. Pai, Power System Dynamics and Stability, Upper Saddle River, NJ: Prentice-Hall, 1998.
[20] W. Marszalek, Z. W. Trzaska, “Singularity-Induced Bifurcations in Electrical Power Systems,” IEEE Trans. on Power Systems, vol. 20(1), pp. 312-320, Feb. 2005.
[21] N. Amjady, “Dynamic voltage security assessment by a neural network based method,” Elect. Power Syst. Res., vol. 66(3), pp. 215–226, Sep. 2003.
[22] K. Hongesombut, Y. Mitani, and K. Tsuji, “Power System Stabilizer Tuning in Multimachine Power System Based on a Minimum Phase Control Loop Method and Genetic Algorithm”, 14th PSCC, Sevilla, pp. 1-7, June 2002.
[23] M. A. Pai, Energy Function Analysis for Power System Stability, Kluwer, Boston, 1989.
[24] http://www.ee.washington.edu/research/pstca/.
[25] DIgSILENT User Manual Toolbox, Available: http:// www.digsilent.de/.
[26] H. K. Nam, Y. K. Kim, K. S. Shim, and K. Y. Lee, “A new Eigen-sensitivity theory of augmented matrix and its applications to power system stability analysis,” IEEE Trans. Power Syst., vol. 15(1), pp. 363–369, Feb. 2000
How to Cite
Ansari, M. reza. (2018). Dynamic Voltage Stability Evaluation of Power Systems Considering Industrial Electrical Loads. Majlesi Journal of Electrical Engineering, 12(1), 79-86. Retrieved from http://mjee.iaumajlesi.ac.ir/index/index.php/ee/article/view/2495