A model for calculating losses in transformer related to orders and harmonic amplitude under analysis of joule effect, eddy current and hysteresis

The electrical transformer is one of the most used equipment in electrical power systems. The non-linear electrical loads are increasing, mainly in the electrical distribution system, and the electrical power transformer is inserted in this scenario, supplying these loads. Consequently, the increasing non-linear loads affect the electrical transformers and their factors directly, like in the dependency between temperature and harmonic increase. Therefore, to study the influence of harmonics in the transformer's temperature, one should understand how it will behave with these changes in the electrical power system. For this reason, in this article, numeric simulations and tests were performed to predict the transformer temperature behavior. The proposal is a numeric technique for coupling two equations, thermal and electromagnetic, of an electrical transformer, considering heat sources regarding joule, eddy current, and hysteresis effect. To evaluate the numeric simulation and understanding the electrical transformer behavior in real-life, tests with specific harmonic orders (3rd, 5th, and 7th) and their combinations and a test with less than 10% total harmonic distortion, according to IEEE 519 standard were performed. It is verified that the electrical transformer temperature rises with the increase in harmonic amplitude and its orders. Results show that the industry must be aware of the effects of the increasing non-linear loads when designing the next generation of transformers concerning their durability and lifetime.