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Power engineering is a sub division of electrical engineering.It deals with generation,transmission and distribution of energy in electrical form.
Also design of all power equipments.
both are extremely related . just for your information some universities teach them in one major . Also mechanical engineering has a power element to it same as electrical engineering . best way to put it is the relation between the drive and the driven equipment ( one mechanical and the other electrical or vise versa )
Generally Electrical Engineering involves many specialties as Power Engineering, Electronic Engineering, Computer Analysis Engineering ---- etc. Then one of the specialty of Electrical Engineering is a Power Engineering which also includes several sections related to Power Generation, Power Transmission & Power Distribution with its applications in various fields in the Power Plants , Factories and Utilities as well as Power Utilization in the Buildings, Complex, Offices & Houses.
Power Engineering is a branch of Electrical Engineering in which we study about power systems e.g transformers, electrical machines, power transmission and distribution systems, switch gears, etc.
Power Engineering is one of the earliest fields that has developed within Electrical Engineering