Top

Published in:

2021 | OriginalPaper | Chapter

Analysis of Partial Differential Equations in Time Dependent Problems Using Finite Difference Methods and the Applications on Electrical Engineering

Authors : Hidir Duzkaya, Suleyman Sungur Tezcan, M. Cengiz Taplamacioglu

Published in: Numerical Methods for Energy Applications

Publisher: Springer International Publishing

Activate our intelligent search to find suitable subject content or patents.

search-config

AI-assisted search

Off

Abstract

Finite difference methods are used as a numerical method in the time-dependent and time-independent solution of partial differential equations commonly encountered in many engineering problems. In this chapter the theoretical basics and practical applications of these methods and limits their scope in terms of electrical engineer applications are examined. This numerical method, which are commonly used to solve problems of electromagnetic fields that cannot be solved by analytical methods are described in detail. Among these methods, the Finite Difference Time Domain (FDTD) method, which is widely used in the calculation of the electric and magnetic fields in electrical engineering applications is concentrated and the results, limitations and alternatives of this method for different applications are examined. Using this numerical method, nonlinear material and structural characteristics in engineering applications can be examined depending on time. Robust and accurate analysis results can be obtained by using this method, which can also be integrated with developed models and software.

Dont have a licence yet? Then find out more about our products and how to get one now:

Springer Professional "Wirtschaft+Technik"

Online-Abonnement

Mit Springer Professional "Wirtschaft+Technik" erhalten Sie Zugriff auf:

über 102.000 Bücher
über 537 Zeitschriften

aus folgenden Fachgebieten:

Automobil + Motoren
Bauwesen + Immobilien
Business IT + Informatik
Elektrotechnik + Elektronik
Energie + Nachhaltigkeit
Finance + Banking
Management + Führung
Marketing + Vertrieb
Maschinenbau + Werkstoffe
Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

inform now

Springer Professional "Technik"

Online-Abonnement

Mit Springer Professional "Technik" erhalten Sie Zugriff auf:

über 67.000 Bücher
über 390 Zeitschriften

aus folgenden Fachgebieten:

Automobil + Motoren
Bauwesen + Immobilien
Business IT + Informatik
Elektrotechnik + Elektronik
Energie + Nachhaltigkeit
Maschinenbau + Werkstoffe

Jetzt Wissensvorsprung sichern!

inform now

Springer Professional "Wirtschaft"

Online-Abonnement

Mit Springer Professional "Wirtschaft" erhalten Sie Zugriff auf:

über 67.000 Bücher
über 340 Zeitschriften

aus folgenden Fachgebieten:

Bauwesen + Immobilien
Business IT + Informatik
Finance + Banking
Management + Führung
Marketing + Vertrieb
Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

inform now

previous chapter Advanced Numerical Methods for Equations, Systems Equations and Optimization

next chapter Theoretical Approaches of Finite Elements Method (FEM)

Yee K (1966) Numerical solution of initial boundary value problems involving maxwell’s equations in isotropic media. IEEE Trans Antennas Propag 14(3):302–307. https://doi.org/10.1109/TAP.1966.1138693CrossRefMATH

Hu X, Siew WH, Judd MD, Reid AJ, Sheng B (2019) Modeling of high-frequency current transformer based partial discharge detection in high-voltage cables. IEEE Trans Power Delivery 34(4):1549–1556. https://doi.org/10.1109/TPWRD.2019.2910076CrossRef

Gedney SD (1996) The application of the finite-difference time-domain method to EMC analysis. In: Proceedings of symposium on electromagnetic compatibility, Santa Clara, CA, USA, pp 117–121. https://doi.org/10.1109/isemc.1996.561212

Musa BU, Siew WH, Judd MD, Wang T, Li QM (2013) Application of finite difference time domain method to high voltage substations: switching transient fields. Int J Eng Sci Innovat Technol (IJESIT) 2(5):20–29

Musa BU, Siew WH, Judd MD (2010) Computation of transient electromagnetic fields due to switching in high-voltage substations. IEEE Trans Power Delivery 25(2):1154–1161. https://doi.org/10.1109/TPWRD.2009.2034008CrossRef

Li T, Wang X, Zheng C, Liu D, Rong M (2014) Investigation on the placement effect of UHF sensor and propagation characteristics of PD-induced electromagnetic wave in GIS based on FDTD method. IEEE Trans Dielectr Electr Insul 21(3):1015–1025. https://doi.org/10.1109/TDEI.2014.6832244CrossRef

Ghania SM (2019) Grounding systems under lightning surges with soil ionization for high voltage substations by using two layer capacitors (TLC) model. Electric Power Syst Res 174(105871). https://doi.org/10.1016/j.epsr.2019.105871

Noda T (2018) A study of an FDTD-based frequency-dependent line model for electromagnetic transient simulations. Electr Eng Jpn 202(2):33–42. https://doi.org/10.1002/eej.23038CrossRef

Ametani A, Xue H, Natsui M, Mahseredjian J (2018) Electromagnetic disturbances in gas-insulated substations and VFT calculations. Electr Power Syst Res 160:191–198. https://doi.org/10.1016/j.epsr.2018.02.014CrossRef

10.

DuChateau P, Zachmann DW (2002) Applied partial differential equations. Dover Publications, New York. ISBN: 978-0-486-41976-3

11.

Sheikh MAA, Andallah LS, Kowser MA (2014) A comparative study of finite difference scheme for Burger’s equation. Gazi Univ J Sci GU J Sci 27(4):1045–1052

12.

Versteeg HK, Malalasekera W (2007) An introduction to computational fluid dynamics, 2nd edn. Pearson Education Limited. ISBN: 978-0-13-127498-3

13.

Zhang X, MA615 numerical methods for PDEs, spring 2020 lecture notes. Math Dept, Purdue University

14.

Shampine L (2009) Stability of the leapfrog/midpoint method. Appl Math Comput 208(1):293–298. https://doi.org/10.1016/j.amc.2008.11.029MathSciNetCrossRefMATH

15.

Sun C, Trueman CW (2003) Unconditionally stable Crank-Nicolson scheme for solving two-dimensional Maxwell’s equations. Electron Lett 39(7):595–597. https://doi.org/10.1049/el:20030416CrossRef

16.

Käppeli R, Balsara DS, Chandrashekar P, Hazra A (2020) Optimal, globally constraint-preserving, DG(TD)2 schemes for computational electrodynamics based on two-derivative Runge-Kutta time stepping and multidimensional generalized Riemann problem solvers—a von Neumann stability analysis. J Comput Phys 408:109238. https://doi.org/10.1016/j.jcp.2020.109238MathSciNetCrossRef

17.

Angus DA (2014) The one-way wave equation: a full-waveform tool for modeling seismic body wave phenomena. Surv Geophys 35:359–393. https://doi.org/10.1007/s10712-013-9250-2CrossRef

18.

Mulder WA, Plessix RE (2004) A comparison between one-way and two-way wave-equation migration. Geophysics 69(6):1491–1504. https://doi.org/10.1190/1.1836822CrossRef

19.

Ching MH, Deiwert GS, Inouye M (2002) The MacCormack method—historical perspective. Front Computat Fluid Dyn 45–59. https://doi.org/10.1142/9789812810793_0003

20.

Fontana F, Bozzo E, Novello M (2015) Decimation in time and space of finite-difference time-domain schemes: standard isotropic lossless model. IEEE Trans Signal Process 63(20):5331–5341. https://doi.org/10.1109/TSP.2015.2453139MathSciNetCrossRefMATH

21.

Nagarjuna K, Chandrasekaran K (2019) Analysis of horizontal grounding electrode in transmission line approach. In: 2019 international conference on communication and electronics systems (ICCES). Coimbatore, India, pp 267–272

22.

Ishak AM, Ishak MT, Jusoh MT, Syed Dardin SF, Judd MD (2017) Design and optimization of UHF partial discharge sensors using FDTD modeling. IEEE Sens J 17(1):127–133. https://doi.org/10.1109/jsen.2016.2628035

23.

Laour M, Tahmi R, Vollaire C (2017) Experimental evaluation and FDTD method for predicting electromagnetic fields in the near zone radiated by power converter systems. Turk J Elec Eng Comp Sci 25:1460–1471. https://doi.org/10.3906/elk-1506-278CrossRef

24.

Aodsup K, Kulworawanichpong T (2017) Analysis of surge propagation with lightning arrester using FDTD for 25 kV-AC transmission line. Int J Eng Appl Sci 4(4):66–70

25.

Shakeri J, Abbasi AH, Shayegani AA, Mohseni H (2010) FDTD simulation of voltage distribution in transformer winding under VFTO Phenomena. Int Rev Electr Eng 5(1):130–137

26.

Izadi M, Ab Kadir MZA, Gomes C, Wan Ahmad WF (2010) An analytical second-FDTD method for evaluation of electric and magnetic fields at intermediate distances from lightning channel. Prog Electromag Res 110:329–352. https://doi.org/10.2528/pier10080801

27.

Kaloudas CG, Chrysochos AI, Papagiannis GK (2014) FDTD analysis of multiphase power cable systems using distributed constant parameters. In: MedPower 2014, Athens, pp 1–8. https://doi.org/10.1049/cp.2014.1711

28.

Barakou F, De Silva HMJ, Wouters PAAF, Steennis EF (2018) Evaluation of FDTD model for transient studies with complicated cable configurations. In: 2018 power systems computation conference (PSCC), Dublin, pp 1–7. https://doi.org/10.23919/pscc.2018.8442741

29.

Tanaka H, Tanahashi D, Baba Y, Nagaoka N, Okada N, Ohki H, Takeuchi M (2016) Finite-difference time-domain simulation of partial discharges in a gas insulated switchgear. High Volt 1(1):52–56. https://doi.org/10.1049/hve.2016.0006

30.

Duzkaya H, Dincer MS, Hiziroglu HR (2009) Calculation of partial discharge inception voltages in ultradilute SF₆ + N₂ gas mixtures. In: Conference on electrical insulation and dielectric phenomena, Virginia Beach, VA, USA, pp 531–534. https://doi.org/10.1109/ceidp.2009.5377903

31.

Tezcan SS, Akcayol M, Ozerdem OC, Dincer MS (2010) Calculation of electron energy distribution functions from electron swarm parameters using artificial neural network in SF₆ and argon. IEEE Trans Plasma Sci 38(9):2332–2339. https://doi.org/10.1109/TPS.2010.2049588CrossRef

32.

Tezcan SS, Duzkaya H, Dincer MS, Hiziroglu HR (2016) Assessment of electron swarm parameters and limiting electric fields in SF₆ + CF₄ + Ar gas mixtures. IEEE Trans Dielectr Electr Insul 23(4):1996–2005. https://doi.org/10.1109/TDEI.2016.005435CrossRef

33.

Duzkaya H, Tezcan SS (2019) Boltzmann analysis of electron swarm parameters in CHF₃ + CF₄ mixtures. Turk J Electr Eng Comp Sci 27:615–622. https://doi.org/10.3906/elk-1804-187CrossRef

34.

Chen J (2018) A review of hybrid implicit explicit finite difference time domain method. J Comput Phys 363:256–267. https://doi.org/10.1016/j.jcp.2018.02.053MathSciNetCrossRefMATH

35.

Zygiridis TT (2017) A short review of FDTD-based methods for uncertainty quantification in computational electromagnetics. Mathemat Prob Eng (9247978). https://doi.org/10.1155/2017/9247978

36.

Edwards RS, Marvin AC, Porter SJ (2010) Uncertainty analyses in the finite-difference time-domain method. IEEE Trans Electromagn Compat 52(1):155–163. https://doi.org/10.1109/TEMC.2009.2034645CrossRef

37.

Gu Z, Zhang X, Sood N, Sarris CD (5) Efficient multi-parametric uncertainty quantification methods for EMC/EMI applications. In: 2015 IEEE symposium on electromagnetic compatibility and signal integrity, Santa Clara, CA, pp 361–364. https://doi.org/10.1109/emcsi.2015.7107715

38.

Ganta SS, Van Veen BD, Hagness SC (2017) On the accuracy of polynomial models in stochastic computational electromagnetics simulations involving dielectric uncertainties. IEEE Antennas Wirel Propag Lett 16:2594–2597. https://doi.org/10.1109/LAWP.2017.2733543CrossRef

39.

Shi Q, Zou B, Zhang L, Liu D (2019) Hybrid parallel FDTD calculation method based on MPI for electrically large objects. Wireless Commun Mobile Comput (7309431). https://doi.org/10.1155/2019/7309431

Title: Analysis of Partial Differential Equations in Time Dependent Problems Using Finite Difference Methods and the Applications on Electrical Engineering
Authors: Hidir Duzkaya
Suleyman Sungur Tezcan
M. Cengiz Taplamacioglu
Publisher: Springer International Publishing
Book: Numerical Methods for Energy Applications
Print ISBN: 978-3-030-62190-2

Electronic ISBN: 978-3-030-62191-9

Copyright Year: 2021
DOI: https://doi.org/10.1007/978-3-030-62191-9_2

Springer Professional

Abstract

Please log in to get access to your license.

Dont have a licence yet? Then find out more about our products and how to get one now:

Springer Professional "Wirtschaft+Technik"

Springer Professional "Technik"

Springer Professional "Wirtschaft"