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Electrical & power both are two side of one coin. Power generation is division of electrical system. If we talk about the power whihc will generate after electrical energy only.
Power engineering is a part of Electrical engineering
Basically Power Engineering is the one who generates and distributes of electricity like hydroelectric Power Energy, Steam Power Energy, Solar Power or any Power Plant, but it is almost one division in terms of Electrical, Electrical Engineering generally they are more on execution and applications.
electrical and sepclized in power engineering
Power engineering is a sub division of electrical engineering. It deals with generation, transmission and distribution of energy in electrical form. Design of all power equipments also comes under power engineering. Power engineers may work on the design and maintenance of the power grid i.e. called on grid systems and they might work on off grid systems that are not connected to the system.
If you study the first chapter of Electricity in most of the text books , you will find the Principles of Electricity Generation or Power Generation by rotating magnetic field placed in between the two coils.
We can say Power Engineering and Electrical Engineering are Interrelated or there is a difference that we canot spot on.
Power Engineering can be considered as a sub-field of the Electrical Engineering field. It deals with electric power generation,transmission and distribution.
Power engineers also work on a variety of power electronic components (like thyristors; ...) and on power conversion (the process of transforming power from one form into another,one)
Everything start with the law Ohm-law U=RxI