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A new simplified approach for the steady state analysis of self-excited induction generators employing the concepts of co-ordinate geometry

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Abstract

A methodology for the steady state analysis of self-excited induction generators (SEIGs) is proposed employing an approach using simple co-ordinate geometry. The equivalent circuit of the SEIG is taken and its three complex admittances, Y̅1, Y̅2 and Y̅3, are considered. Using the nodal analysis of the circuit and considering the nature of the parameters involved for ensuring self-excitation of the induction machine, it is shown that a triangle can be obtained by plotting Y̅1, Y̅2 and Y̅3 in the complex plane. Utilizing the well-known properties of the triangle, in a few steps, a simple equation is derived for the per unit (pu) speed, in terms of pu frequency, real part of Y̅1 and rotor resistance. This, consequently, leads to another simple expression for the calculation of the magnetizing reactance and further processing of the performance analysis of SEIG. Thus, this proposed method does not require advanced techniques or complex calculations. The analytical results arrived at are compared with those calculated using the popularly adopted genetic algorithm technique and recently evolved binary search method and also with the values obtained experimentally on a 3-phase, 3.75 kW, 230 V delta-connected induction machine run as an SEIG. A very close agreement is seen between these three sets of results.

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Availability of data and materials

No datasets were generated or analysed during the current study. However, the machine parameters used for supporting the results and analyses in the article are obtained in the laboratory.

Abbreviations

a :

Per unit (pu) frequency, fg/fr

b :

pu speed, Nr/Ns

C :

Per phase excitation capacitance, F

E̅ :

Per phase air gap voltage, V

f g :

Generated frequency, Hz

f r :

Rated frequency, Hz

N r :

Actual speed of rotor, rpm

N s :

Synchronous speed at rated frequency, rpm

R/X :

Per phase load resistance/reactance, Ω

R 1/R 2 :

Per phase stator/rotor (referred to stator) resistance, Ω

X 1/X 2 :

Per phase stator/rotor (referred to stator) reactance, Ω

X C :

Per phase excitation capacitance reactance, Ω

X m :

Per phase magnetizing reactance, Ω

X mc :

Per phase critical magnetizing reactance, Ω

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Acknowledgements

The authors gratefully acknowledge the authorities of the National Institute of Technology, Tiruchirappalli, India, for all the facilities provided for the preparation of this paper. The authors also express sincere gratitude to Dr. M. Subbiah for his unstinted support in the preparation of this paper.

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The author(s) did not receive any external funds for this research work.

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Authors and Affiliations

  1. Energy Research Institute at NTU (ERI@N), Interdisciplinary Graduate Programme, Nanyang Technological University, Singapore, 639798, Singapore

    Anusha Kumaresan

  2. Department of Electrical and Electronics Engineering, National Institute of Technology, Tiruchirappalli, India

    Hanumanthu Kesari, Kumaresan Natarajan & Nagamani Chilakapati

Authors
  1. Anusha Kumaresan
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  2. Hanumanthu Kesari
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  3. Kumaresan Natarajan
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  4. Nagamani Chilakapati
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Contributions

AK: Conceptualization, Methodology, Software, Data curation, Writing- Original draft. HK: Investigation, Software, Data curation, Writing- Original draft. KN: Supervision, formal analysis, Validation, Writing- Review and Editing. NC: Supervision, formal analysis, Validation, Writing- Review & Editing.

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Correspondence to Kumaresan Natarajan.

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Kumaresan, A., Kesari, H., Natarajan, K. et al. A new simplified approach for the steady state analysis of self-excited induction generators employing the concepts of co-ordinate geometry. Electr Eng 105, 3229–3239 (2023). https://doi.org/10.1007/s00202-023-01871-x

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