A Mathematical Review Study on Dynamical Models of Symmetrical Three-Phase Induction Machine in Various Reference Frames

Year 2024, Volume: 14 Issue: 3, 1401 - 1430, 15.09.2024

Mehmet Ali Usta

https://doi.org/10.31466/kfbd.1472193

Abstract

This paper presents dynamic models of a three-phase induction machine in various reference frames widely employed in alternating-current (ac) machine analysis. The main objective is to derive and explain the machine model in relatively basic terms by using the idea of rotating reference frame theory. Many matrix manipulations and complex frame-to-frame transformations performed to obtain an advanced model from primitive dynamical equations are presented in a more compact and easy-to-understand way. Therefore, this paper reviews a detailed, yet simple and understandable mathematical background on the dynamic models of the induction machine. Furthermore, a unified and broadly applicable simulation model is proposed for simulating the dynamic behavior of the machine in any desired reference frame. The simulation model has also a modular and user-friendly structure. For the simulation studies, Matlab/Simulink environment is preferred due to its popularity. A Simulink machine model with several subsystems is explicitly given. The simulation study is realized for a small power induction machine operating under both load and no-load conditions. The variations of three-phase currents, electromagnetic torque, and rotor mechanical speed as well as the rotor flux-linkage components are shown. The key features of each reference frame are discussed, especially through the measured rotor flux-linkage components.

Keywords

Induction machine, Reference frame theory, Dynamic model, Simulation model

Simetrik Üç Fazlı Asenkron Makinanın Çeşitli Referans Çerçevelerinde Dinamik Modelleri Üzerine Matematiksel Bir İnceleme Çalışması

Abstract

Bu makale, alternatif akım (aa) makine analizinde yaygın olarak kullanılan çeşitli referans çerçevelerinde üç fazlı asenkron makinanın dinamik modellerini sunmaktadır. Temel amaç, dönen referans çerçeve teorisi fikrini kullanarak makina modelini nispeten basit terimlerle türetmek ve açıklamaktır. İlkel dinamik denklemlerden gelişmiş bir model elde etmek için gerçekleştirilen birçok matris manipülasyonu ve karmaşık çerçeveden çerçeveye dönüşümler, daha kompakt ve anlaşılması kolay bir şekilde sunulmaktadır. Bu nedenle, bu makale asenkron makinanın dinamik modellerine ilişkin ayrıntılı, ancak basit ve anlaşılır bir matematiksel arka planı gözden geçirmektedir. Bundan başka, makinanın dinamik davranışını istenen herhangi bir referans çerçevesinde simüle etmek için birleşik ve geniş çapta uygulanabilir bir simülasyon modeli önerilmektedir. Simülasyon modeli aynı zamanda modüler ve kullanıcı dostu bir yapıya sahiptir. Simülasyon çalışmalarında popülerliği nedeniyle Matlab/Simulink ortamı tercih edilmektedir. Birkaç alt sisteme sahip bir Simulink makina modeli açıkça verilmiştir. Simülasyon çalışması hem yük hem de yüksüz koşullar altında çalışan küçük güçlü bir asenkron makina için gerçekleştirilmiştir. Üç fazlı akımların, elektromanyetik torkun ve rotor mekanik hızının yanı sıra rotor akı bileşenlerinin değişimleri gösterilmektedir. Her bir referans çerçevesinin temel özellikleri, özellikle ölçülen rotor akı bileşenleri aracılığıyla tartışılmaktadır.

Keywords

Asenkron makina, Referans çerçeve teorisi, Dinamik model, Benzetim modeli

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