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Power Flow Solutions by Newton-Raphson Method with Approximated Second-Order Term of Taylor Series

Pornthep Panyakaew(1*)

(1) Rajamangala University of Technology Isan, Sakonnakhon Campus, Thailand
(*) Corresponding author


DOI: https://doi.org/10.15866/iree.v10i6.6994

Abstract


This paper presents a Newton-Raphson method with an approximated second-order term of the Taylor series for solving the power flow problem where the power flow equations are in polar form. The proposed method is to include the second-order derivative term of the Taylor series in the Newton-Raphson method and subsequently approximate it using the first-order differentiation of the central finite difference. To compare the proposed method’s capability of finding a solution, it is compared with the Newton-Raphson method both in the polar form and rectangular form of power flow equations. The proposed method and the comparative methods are applied to the ill-conditioned 13 bus, IEEE 14 bus and IEEE 30 bus systems. The results demonstrate that the proposed method is the only method that can satisfy in all systems and the ill-conditioned 13 bus systems with a high and highly reactive load at bus 11. While the Newton-Raphson method both in polar form and rectangular form can identify the solution in all systems, it cannot identify the solution in the ill-conditioned 13 bus with a highly reactive load at bus 11.
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Keywords


Approximated Second-Order Term of Taylor Series; Finite Difference Method; Ill-Conditioned System; Newton-Raphson Method; Power Flow Studies

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References


J.J. Grainger, W.D. Stevenson Jr., Power System Analysis (McGraw-Hill, Inc., 1994).

L.L. Grigsby, Power System Stability and Control (Taylor & Francis Group, LLC., 2006).

A.J. Wood, B.F. Wollenberg, Power Generation, Operation, and Control (John Wiley & Sons, Inc., 1996).

Gopal Sharma, K., Bhargava, A., Gajrani, K., Stability analysis of DFIG based wind turbines connected to electric grid, (2013) International Review on Modelling and Simulations (IREMOS), 6 (3), pp. 879-887.

Singhal, P., Agarwal, S.K., Kumar, N., Dube, A., Transient stability enhancement of a power system using unified power flow controller, (2013) International Review on Modelling and Simulations (IREMOS), 6 (5), pp. 1558-1569.

A. Elrayyah, Y. Sozer, M.E. Elbuluk, A Novel Load-Flow Analysis for Stable and Optimized Microgrid Operation, IEEE Transactions on Power Delivery, vol. 29 n. 4, August 2014, pp. 1709 –1717.
http://dx.doi.org/10.1109/tpwrd.2014.2307279

Moradi, M.H., Dehghan, S., Mirzaei, A., Improving congestion relief management as ancillary service in operation planning phase with demand side's presence, (2011) International Review of Electrical Engineering (IREE), 6 (3), pp. 1447-1454.

A. Street, A. Moreira, J.M. Arroyo, Energy and Reserve Scheduling under a Joint Generation and Transmission Security Criterion: an Adjustable Robust Optimization Approach, IEEE Transactions on Power Systems, vol. 29 n. 1, January 2014, pp. 3 – 14.
http://dx.doi.org/10.1109/tpwrs.2013.2278700

Chaiyabut, N., Damrongkulkamjorn, P., Optimal spinning reserve considering wind power reliability index by security-constrained unit commitment, (2014) International Review of Electrical Engineering (IREE), 9 (1), pp. 207-217.

A. Mao, M.R. Iravani, A Trend-Oriented Power System Security Analysis Method Based on Load Profile, IEEE Transactions on Power Systems, vol. 29 n. 3, May 2014, pp. 1279 – 1286.
http://dx.doi.org/10.1109/tpwrs.2013.2291400

D.I. Sun, B. Ashley, B. Brewer, A. Hughes, W.F. Tinney, Optimal Power Flow by Newton Approach, IEEE Transaction on Power Apparatus and System, vol. 103 n. 10, October 1984, pp. 2864 –2880.
http://dx.doi.org/10.1109/tpas.1984.318284

H. Wang, C.E. Murillo-Sanchez, R.D. Zimmerman, R.J. Thomas, On Computational Issues of Market-Based Optimal Power Flow, IEEE Transactions on Power Systems, vol. 22 n. 3, August 2007, pp. 1185 – 1193.
http://dx.doi.org/10.1109/tpwrs.2007.901301

Panyakaew, P., Damrongkulkamjorn, P., Hybrid computational method for step-bidding price optimal power flow, (2013) International Review of Electrical Engineering (IREE), 8 (1), pp. 369-378.

Lakdja, F., Ould Abdeslam, D., Gherbi, F.Z., Optimal location of thyristor-controlled series compensator for optimal power flows, (2013) International Review on Modelling and Simulations (IREMOS), 6 (2), pp. 465-472.

X.F. Wang, Y. Song, M. Irving, Modern Power Systems Analysis (Springer Science+Business Media, LLC., 2008).

M.S. Sachdev, T.K.P. Medicherla, A Second Order Load Flow Technique, IEEE Transactions on Power Apparatus and Systems, vol. 96 n. 1, January/February 1977, pp. 189 – 197.
http://dx.doi.org/10.1109/t-pas.1977.32323

C.A. Ferreira, V.M. Da Costa, A Second Order Power Flow Based on Current Injection Equations, International Journal of Electrical Power and Energy Systems, vol. 27, May 2005, pp. 254 – 263.
http://dx.doi.org/10.1016/j.ijepes.2004.10.005

V.H. Quintana, N. Muller, Studies of Load Flow Methods in Polar and Rectangular Coordinates, Electric Power Systems Research, vol. 20, March 1991, pp. 225 – 235.
http://dx.doi.org/10.1016/0378-7796(91)90067-w

T. Kulworawanichpong, Simplified Newton-Raphson Power-Flow Solution Method, International Journal of Electrical Power and Energy Systems, vol. 32, July 2010, pp. 551 – 558.
http://dx.doi.org/10.1016/j.ijepes.2009.11.011

S. Kamel, M. Abdel-Akher, F. Jurado, Improved NR Current Injection Load Flow Using Power Mismatch Representation of PV Bus, International Journal of Electrical Power and Energy Systems, vol. 53, December 2013, pp. 64 – 68.
http://dx.doi.org/10.1016/j.ijepes.2013.03.039

S. Iwamoto, Y. Tamura, A Load Flow Calculation Method for Ill-Conditioned Power Systems, IEEE Transactions on Power Apparatus and Systems, vol. 100 n. 4, April 1981, pp. 1736 – 1743.
http://dx.doi.org/10.1109/tpas.1981.316511

L.M.C. Braz, C.A. Castro, C.A.F. Murari, A Critical Evaluation of Step Size Optimization Based Load Flow Methods, IEEE Transactions on Power Systems, vol. 15 n. 1, February 2000, pp. 202 – 207.
http://dx.doi.org/10.1109/59.852122

J.E. Tate, T.J. Overbye, A Comparison of the Optimal Multiplier in Polar and Rectangular Coordinates. IEEE Transactions on Power Systems, vol. 20 n. 4, November 2005, pp. 1667 – 1674.
http://dx.doi.org/10.1109/tpwrs.2005.857388

A.G. Exposito, E.R. Ramos, Augmented Rectangular Load Flow Model, IEEE Transactions on Power Systems, vol. 17 n. 2, May 2002, pp. 271 – 276.
http://dx.doi.org/10.1109/tpwrs.2002.1007892

Wikipedia, The Free Encyclopedia, Available Online: http://en.wikipedia.org/wiki/Newton's_method.

Department of Electrical Engineering at University of Washington, Available Online: http://www.ee.washington.edu/research/pstca/.

S.C. Tripathy, G.D. Prasad, O.P. Malik, G.S. Hope, Load-Flow Solutions for Ill-Conditioned Power Systems by a Newton-Like Method, IEEE Transactions on Power Apparatus and Systems, vol. 101 n. 10, October 1982, pp. 3648 – 3657.
http://dx.doi.org/10.1109/tpas.1982.317050


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