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Courses/Engineering/Electrical Transformers

Power Transformers and Per-Units

Master the principles of transformer modeling and leverage the per-unit system to simplify the analysis of complex power networks.

Created byFoad Alvandi
BeginnerUpdated Feb 21, 2026
Power Transformers and Per-Units

What You'll Learn

check_circleDevelop and draw the electrical model of ideal and real single-phase two-winding transformers.
check_circleUnderstand and work with the different configurations of three-phase transformers.
check_circleApply the per-unit system to analyzing three-phase transformers.
check_circleRead and correctly interpret equipment specs that are often given in terms of per-unit values.
check_circleConvert the nameplate per-unit quantities to a common base in the particular given power network.
check_circlePerform base changes based on the rated voltage of the particular section of the power network.

About This Course

This webinar, through slides, discussions, and numerical examples, starts with the different aspects, construction, and operation of ideal and practical two-winding single-phase transformers. The discussions start with an introduction to the characteristics and construction of ideal transformers and develop equations that relate primary and secondary voltages and currents for these transformers. Reflection of load from one side of the transformer to the other side is covered, as well as the dot notation of polarity.

Coverage continues with the introduction of real (practical) transformers along with their electrical model. Copper and core losses for these transformers are calculated, and the relation between core dimension, core permeability, and number of turns with different electrical parameters of the transformer are discussed. Two important test protocols, namely the short-circuit test and open-circuit test, which allow calculation of the most important electrical parameters of transformers, are explained.

The per-unit system, which is an important tool in the analysis of power systems, is explained in detail. The rationale for working with per-unit values and the advantages of their use are emphasized. Change of base, which is an important aspect of introducing equipment into a power network, is explained. Finally, the application of the per-unit system to three-phase balanced systems is covered.

Coverage moves on to the topic of three-phase transformers, their configurations, primary/secondary voltage and phase relations, and the application of per-unit values to circuits containing such transformers. Next, autotransformers are covered, as well as the advantages and disadvantages of their use in power networks. Coverage of three-winding transformers and their equivalent circuit and primary/secondary/tertiary current/voltage relations form the final subject of this webinar.

Each topic is immediately followed by well-chosen numerical examples and detailed steps leading to the solution of each to further enhance the learning experience of the participants. This webinar is intended for electrical engineers, as well as design personnel who are interested in learning the fundamentals of the operations of power transformers.

Your Instructor

Foad Alvandi
Foad Alvandi

Professional Engineer with over 40 years of experience

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Mr. Foad Alvandi is an online PDH course provider of continuing education for LearnFormula Mr. Alvandi holds a Bachelor of Science degree in Electrical Engineering and a Master of Science degree in Electrical and Computer Engineering from George Mason University. He is a registered Professional Engineer in the State of Maryland. Mr. Alvandi is a seasoned engineer with over 40 years of experience in the electrical and solar power industries, as well as a number of years of teaching experience. He is an adjunct professor with Johns Hopkins University and presently teaches the graduate-level “Introduction to Electrical Power Systems” course in their online EP (Engineering for Professionals) program. He has retired in recent years from full-time work in the industry, but continues to teach and keeps updated on the latest developments in the solar and electrical power industries in general.

Credit Information

Do these courses count toward my professional development requirements?

This portal is provided as a training and development resource for City of Markham employees. Every course is delivered by a qualified subject matter expert or learning organization, is quantifiable in hours, and is verifiable — you receive a documented certificate of completion for every course you finish, stored on LearnFormula indefinitely.

If you hold a professional designation (for example in engineering, accounting, human resources, or law), courses may be counted as professionally relevant, verifiable learning activities toward your continuing professional development. Individual practitioners are responsible for confirming that an activity meets the requirements of their professional body. For questions about the City of Markham's training and development policies, please speak with your people leader or Human Resources.

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We are a registered provider with 327+ associations and regulatory bodies worldwide. We operate across 29 global markets including Canada, the US, Australia, and the UK. Every course page clearly displays its specific accreditations. Upon completion, you receive a professional certificate that can be validated online. Our certificates include all necessary accreditation details, credit hours, and completion dates, and are formatted specifically to meet the submission requirements of most global regulatory bodies.