Mathematical Analysis of Power Quality Disturbances in Electrical Distribution Systems: Detection, Classification, and Mitigation Strategies

Abstract

Maintaining a high-quality power source is an important part of modern electricity distribution systems for making sure that many industrial, business, and domestic uses work reliably and efficiently. Power quality disruptions, on the other hand, make this goal much harder to reach. This essay gives a thorough statistical study of power quality problems, focused on how to find them, classify them, and find ways to fix them. The first part of the study talks about how to find power quality problems, which means finding changes in voltage, current, or frequency that don't make sense. Different signal processing methods, like Fourier analysis, wavelet transform, and advanced machine learning algorithms, are tested to see how well they can find and describe different kinds of problems. Second, the paper talks about how to classify power quality problems, which is important for figuring out what causes them and choosing the best ways to fix them. There are different kinds of disturbances, such as voltage sags, swells, interruptions, harmonics, and transients. Each type needs a different way of being analyzed and dealt with. Researchers are looking into whether statistical methods, pattern recognition tools, and artificial intelligence can correctly group events based on their unique features. Lastly, the paper talks about ways to lessen the bad effects of power quality problems on electrical distribution systems and loads that are related to them. These methods include both preventative steps, like making equipment better designed and rearranging networks, and defensive ones, like using active power filters, voltage controls, and energy storage systems. Coordinating spread energy resources with smart grid technologies is also being looked into as a way to make the system more resistant to disruption. In general, the mathematical analysis in this paper gives us useful information about how complicated power quality problems are and gives us a way to find them, sort them into groups, and fix them. Electrical companies, equipment makers, and system workers can come up with better ways to make sure that modern distribution systems have a stable and high-quality power source by using advanced mathematical methods and new technologies.