Ense3 rubrique Formation 2022

Power Systems II - Grids and Components - 4EUS4PST

  • Number of hours

    • Lectures 22.0
    • Projects -
    • Tutorials 14.0
    • Internship -
    • Laboratory works 24.0


    ECTS 5.0


This module aims to acquire good knowledge of advanced technologies about transformers, their use in power grids including unbalanced operation using Fortescue transform (symmetrical components) and early notions of protection. Students will be able to characterize an unbalanced operation and calculate short-circuit currents. Tutorials, practical works and a project on a power transformer complete this course.




Electrical grid (18h CM+10h de TD):

•Basic principle of transformers
•Different types of transformers
•Operating regimes of transformers (no load, short-circuit, load, transients, inrush…)
•Operation parameters of a transformer
•Ferro resonance

Unbalanced operation of electrical grids
•Different types of unbalances
•Introduction to the analysis tools of unbalanced operations
•Symmetrical component method (Fortescue): circulant matrix, transformation matrix (transformation of currents, voltages, impedances/admittances, power)
•Case studies: short-circuits and unbalances
•Different short-circuits and unbalances
•Symmetrical model of a synchronous machine
•Symmetrical/sequence impedances of multi-generator grid
•Equivalent circuits for the three components (direct (or positive), inverse (or negative) and zero (or homopolar))
•Calculation of short-circuit currents and quantities after the fault

Disturbances and unbalances in electrical grids

Types of faults, symmetrical and unsymmetrical faults and consequences

Introduction to the protections
•Maximum current protection

Practical works on transformers (12 h):
Transformers under unbalanced operation (single phase load), direct/inverse and homopolar impedances, influence of the connections and the magnetic circuit.
No load operation of a transformer, no load magnetization current in a three phase transformer, connection and magnetic circuit influences, inrush current and its main parameters

BE/project on an industrial power transformer (20h):
Implementation and increased knowledge on an industrial transformer: verification of the manufacturer’s design and calculations from technical documents. Analysis of constraints taking into-account standards, service life, overall cost approach, capitalized cost (depreciation). Safety equipments, insulation coordination, surge arrester (atmospheric, shock wave, taking into-account of series and derivative capacities, heterogeneous insulation ...), calculation of losses, cooling, analysis of the magnetic circuit, electrodynamic forces ....


Course « Electrical energy » (S5) and power system I (S7).


Session 1: Continuous evaluation (60 %) and exam (40 %)
Continuous evaluation: practical works (25 %) + transformer project (75 %)
Session 2: new exam, no change for the continuous evaluation.

EN 60% + ER 40%


The course exists in the following branches:

see the course schedule for 2023-2024

Additional Information

Course ID : 4EUS4PST
Course language(s): FR

You can find this course among all other courses.