Swayam Central

Electrical Equipment and Machines: Finite Element Analysis

By Prof. Shrikrishna V. Kulkarni   |   IIT Bombay
The course consists of theory and applications of Finite Element Method (FEM). This numerical technique, applied for solving partial differential equations, is popularly used by researchers and practicing engineers for design, development and optimization of electrical equipment and machines. A course of FEM is being included in many universities in India at UG and PG level. This module will be helpful for students and working professionals to understand and apply FEM effectively for analysis of devices. Freeware based FEM simulations and coding procedures will be a part of this course. Students can develop their own codes for practical two- dimensional problems using freeware software.
There are two existing NPTEL courses on computational electromagnetics covering various numerical techniques especially for high-frequency electromagnetics. This course is exclusively for FE Analysis of low-frequency machines and equipment. Four unique features of this proposed course are:
1. Explanation of EM concepts relevant for low frequency electromagnetic computations
2. Use of field distributions and interactive Java based examples hosted in a virtual lab (
3. Application of the Finite Element theory for different low frequency electromagnetic problems related to electrical machines and equipment
4. Solving the developed Finite Element formulations using freeware platforms like Scilab and Gmsh
Prof. S. V. Kulkarni has conducted many Continuing Education Programs for industry and academia on electromagnetic fields and numerical techniques
For more details of his educational outreach and other credentials, please visit: "https://www.ee.iitb.ac.in/wiki/faculty/svk"

Electrical and Electronics Engineering Students, Electrical Industry Professionals
PREREQUISITES Basics of Electromagnetic Fields and Electrical Machines
INDUSTRIES  SUPPORT     : Companies manufacturing electrical and electronic products consisting of magnetic and insulating components

Course TAs: B. Sai Ram and Greeshma Mohan U.

Learners enrolled: 596


Course Status : Upcoming
Course Type : Elective
Duration : 8 weeks
Start Date : 20 Jul 2020
End Date : 11 Sep 2020
Exam Date : 27 Sep 2020
Enrollment Ends : 27 Jul 2020
Category :
  • Electrical, Electronics and Communications Engineering
  • Level : Undergraduate/Postgraduate
    This is an AICTE approved FDP course


    Week 1:Lecture 1: Course Outline and Introduction
                  Lecture 2: Analytical and Numerical Methods
                  Lecture 3: Revisiting EM Concepts: Vector Algebra & Coordinate Systems
          Lecture 4: Revisiting EM Concepts: Vector Calculus and Electrostatics
                Lecture 5: Revisiting EM Concepts: Current Densities and Electric Fields in Materials
    Week 2:Lecture 6: Revisiting EM Concepts: Electrostatic Boundary Conditions and Shielding
                  Lecture 7: Revisiting EM Concepts: Magnetostatics
                  Lecture 8: Revisiting EM Concepts: Magnetic Forces and Materials
                  Lecture 9: Revisiting EM Concepts: Time Varying Fields
                  Lecture 10: Revisiting EM Concepts: Theory of Eddy Currents
    Week 3:Lecture 11: FEM: Variational Approach
                  Lecture 12: Finding Functional for PDEs
                  Lecture 13: Whole Domain Approximation
                  Lecture 14: 1D FEM: Problem Definition and Shape Function
                  Lecture 15: 1D FEM: Procedure
    Week 4:Lecture 16: 1D FEM: Scilab Code
                  Lecture 17: 2D FEM: Problem Definition and Shape Functions
                  Lecture 18: 2D FEM: Procedure
                  Lecture 19: 2D FEM Scilab Code: Manual Meshing
                  Lecture 20: 2D FEM Code: Gmsh and Scilab
    Week 5:Lecture 21: Computation of B and H Field and Method of Weighted Residuals 
                  Lecture 22: Galerkin Method
                  Lecture 23: Calculation of Leakage Inductance of a Transformer
                  Lecture 24: Calculation of Inductance of an Induction Motor and a Gapped-Core Shunt Reactor
                  Lecture 25: Insulation Design Using FE Analysis
    Week 6:Lecture 26: Quadratic Finite Elements
                 Lecture 27: Time Harmonic FE Analysis
                 Lecture 28: Calculation of Eddy Current Losses
                 Lecture 29: Eddy Losses in Transformer Windings
                 Lecture 30: Torque Speed Characteristics of an Induction Motor and FE Analysis of Axisymmetric Problem
    Week 7:Lecture 31: Permanent Magnets: Theory 
                  Lecture 32: Permanent Magnets: FEM Implementation
                  Lecture 33: Periodic and Antiperiodic Boundary Conditions in Rotating Machines
                  Lecture 34: FE Analysis of Rotating Machines
                  Lecture 35: Voltage Fed Coupled Circuit Field Analysis
    Week 8:Lecture 36: Current Fed Coupled Circuit Field Analysis 
                  Lecture 37: Transient FE Analysis
                  Lecture 38: Nonlinear FE Analysis
                  Lecture 39: Computation of Forces using Maxwell Stress Tensor
                  Lecture 40: Computation of Forces using Virtual Work Method


    [1] S. V. Kulkarni and S. A. Khaparde, Transformer engineering: design, technology, and diagnostics, Second Edition, Boca Raton: CRC Press (Taylor & Francis Group), 2012
    [2] S. J. Salon, Finite element analysis of electrical machines, Springer International Edition (1995), Indian Reprint (2007)
    [3] J. P. A. Bastos and N. Sadowski, Electromagnetic modeling by finite element methods, CRC Press, 2003
    [4] N. Bianchi, Electrical machine analysis using finite elements, CRC Press, 2005
    [5] M. N. O. Sadiku, Numerical techniques in electromagnetics, CRC Press, 2000
    [6] M.N.O. Sadiku and S.V. Kulkarni, Principles of electromagnetics, Sixth Edition, Oxford University Press, India, 2015 (Asian adaptation of 'M.N.O. Sadiku, Elements of electromagnetics, Sixth International Edition, Oxford University Press')


    Prof. Shrikrishna V. Kulkarni

    IIT Bombay
    Dr. S. V. Kulkarni is Professor in the Department of Electrical Engineering, Indian Institute of Technology Bombay. He was INAE (Indian National Academy of Engineering) Chair Professor in the Department for two years (April 2018 - March 2020). He is a Fellow of IEEE and INAE. He was Editor of IEEE Transactions on Power Delivery and IEEE Power Engineering Letters (2012-2019). He worked at Crompton Greaves Limited (1990-2001) and specialized in the design and development of transformers up to 400 kV class. He was a recipient of the Young Engineer Award conferred by INAE in 2000 for his contributions to Electromagnetic Field Computations and High Voltage Insulation Design in transformers. He was also honoured with the Career Award for Young Teachers from All India Council for Technical Education in 2001. He received Best Paper Awards in international conferences on transformers held in 2002 and 2006.

    He has authored a book Transformer Engineering: Design, Technology, and Diagnostics, Second Edition, published by CRC Press in September 2012 and he received IIT Bombay Research Dissemination Award 2016 for the book. He has also written a chapter Challenges and Strategies in Transformer Design in the book Transformers: Analysis, Design, and Measurement published by CRC Press in June 2012. He has adapted an undergraduate text book on electromagnetics for Asia, Principles of Electromagnetics, Oxford University Press, published in October 2015.

    His extensive interactions with transformer and power industries are reflected in his numerous consultancy projects for them. He has organized several training programs on transformers and computational electromagnetics for engineers from industries and academia in India. He has also set up the Field Computation Laboratory and the Insulation Diagnostics Laboratory in the Electrical Engineering Department at IIT Bombay.

    He has more than 190 publications to his credit in reputed journals and conferences, and has two US patents. His current areas of research include Analysis and Diagnostics of Power Transformers, Advanced Electromagnetic and Coupled Field Computations, and Distributed Generation and Smart Grids


    •The course is free to enroll and learn from. But if you want a certificate, you have to register and write the proctored exam conducted by us in person at any of the designated exam centres.
    •The exam is optional for a fee of Rs 1000/- (Rupees one thousand only).
    Date and Time of Exams: 27 September 2020, Morning session 9am to 12 noon; Afternoon Session 2pm to 5pm. 
    •Registration url: Announcements will be made when the registration form is open for registrations.
    • The online registration form has to be filled and the certification exam fee needs to be paid. More details will be made available when the exam registration form is published. If there are any changes, it will be mentioned then.
    •Please check the form for more details on the cities where the exams will be held, the conditions you agree to when you fill the form etc.

    • Average assignment score = 25% of average of best 6 assignments out of the total 8 assignments given in the course. 
    • Exam score = 75% of the proctored certification exam score out of 100
    •Final score = Average assignment score + Exam score

    •If one of the 2 criteria is not met, you will not get the certificate even if the Final score >= 40/100.
    • Certificate will have your name, photograph and the score in the final exam with the breakup.It will have the logos of NPTEL and IIT Bombay. It will be e-verifiable at nptel.ac.in/noc.
    •Only the e-certificate will be made available. Hard copies will not be dispatched.