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# Open Physics

### formerly Central European Journal of Physics

Editor-in-Chief: Seidel, Sally

Managing Editor: Lesna-Szreter, Paulina

IMPACT FACTOR 2018: 1.005

CiteScore 2018: 1.01

SCImago Journal Rank (SJR) 2018: 0.237
Source Normalized Impact per Paper (SNIP) 2018: 0.541

ICV 2017: 162.45

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ISSN
2391-5471
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Volume 15, Issue 1

# Field-circuit analysis and measurements of a single-phase self-excited induction generator

Krzysztof Makowski
• Corresponding author
• Wrocław University of Science and Technology, Faculty of Electrical Engineering, Wrocław, Poland
• Email
• Other articles by this author:
/ Aleksander Leicht
Published Online: 2017-12-29 | DOI: https://doi.org/10.1515/phys-2017-0110

## Abstract

The paper deals with a single-phase induction machine operating as a stand-alone self-excited single-phase induction generator for generation of electrical energy from renewable energy sources. By changing number of turns and size of wires in the auxiliary stator winding, an improvement of performance characteristics of the generator were obtained as regards no-load and load voltage of the stator windings as well as stator winding currents of the generator. Field-circuit simulation models of the generator were developed using Flux2D software package for the generator with shunt capacitor in the main stator winding. The obtained results have been validated experimentally at the laboratory setup using the single-phase capacitor induction motor of 1.1 kW rated power and 230 V voltage as a base model of the generator.

PACS: 84.50.+d; 41.20.-q

## 1 Introduction

Performance characteristics of single-phase induction generators usually have been improved by introducing power electronics to vary capacitance of an excitation capacitor without changing design of the generator itself. To investigate steady-state performance characteristics of the single-phase induction generators, circuit models based on field revolving theory are commonly used with taking saturation into account [1, 2, 3]. To study transients phenomena in the generators, two axis dq model with saturation included may be used [4]. A comprehensive simulation model valid both for steady-state and transients may be obtained only by field-circuit modeling of the induction generators. Such field-circuit models can be found in recent papers [5, 6, 7, 8, 9]. They allow to analyze all relevant electromagnetic phenomena in induction machines and usually yield more accurate results but are more expensive in terms of computing time. A study of the phenomena occurring in the single-phase induction generators by field-circuit models have cognitive importance since not enough space is devoted so far to voltage self-regulation and self-excitation requirements from design point of view of the single-phase induction generators.

## 2 A field-circuit model of the generator

The single-phase capacitor induction motor of 1.1 kW, 230 V, employed for stand-alone generating operation has 4 poles and 30 skewed rotor bars. The ratings of the induction machine are listed in Table 1.

Table 1

Ratings of the single phase induction machine

Taking into consideration geometrical symmetry and electromagnetic periodicity of the machine, two-dimensional magnetic field computation of the generator was reduced to two pole pitches of the cross-section. The FE model of the generator accounts for nonlinear magnetizing characteristic of the magnetic core (Figure 1) and skin-effect in the rotor bars. The finite element mesh of the generator (Figure 2) was built of 11244 second-order triangular and quadrangular elements

Figure 1

Magnetization characteristic of magnetic core of tested induction machine

Figure 2

FE mesh of 2D field-circuit model of the SPSEIG

The 2D magnetic field in the induction generator is determined by the equations:

$curlν⋅curlA=JSin stator windingsJb−σ⋅∂A/∂tin rotor bars0in air, iron core and shaft$(1)

where A[0, 0, A(x, y, t)] is the magnetic vector potential, Js[0, 0, Js(x, y, t)] – the current density in the stator slots, Jb[0, 0, Jb(x, y, t)] – the current density in the rotor bars, ν – reluctivity of magnetic material, σ – electric conductivity. Two-dimensional field equations coupled with voltage equations of stator and rotor windings [5] were solved simultaneously to obtain voltages and currents induced in the stator and rotor. Having the variables A and J computed, the other quantities of electromagnetic field as magnetic flux, magnetic induction, etc. may be determined taking into account the magnetization characteristic of iron magnetic core of the generator. Furthermore it was also assumed, that iron core losses in the field-circuit simulation model of the generator were neglected.

## 3 Self-excitation transients of the generator

The single-phase four poles induction machine operating as a single-phase self-excited induction generator (SPSEIG) was modeled applying 2D vector potential formulations of magnetic field in cross-section of the induction generator. The field-circuit model of the generator was described in detail in [5]. Self-excitation transients of voltages and currents of stator windings obtained by measurements at no-load and speed n = 1620 rpm for NA = 444 and 424 turns, and excitation capacitor Cex = 40 μF with capacitor Csh = 20 μF connected in parallel to terminals, are presented in Figures 3-6.

Figure 3

Self-excitation: a) no-load voltage and b) current, of main stator winding, for NA = 444, Cex= 40 μF, Csh = 20 μF

Figure 4

Self-excitation: a) no-load voltage and b) current of excitation stator winding, for NA = 444, Cex = 40 μF, Csh = 20 μF

Figure 5

Self-excitation: a) no-load voltage and b) current of main stator winding, for NA = 424, Cex = 40 μF, Csh = 25μF

Figure 6

Self-excitation: a) no-load voltage, and b) current of excitation stator winding, for NA = 424, Cex = 40 μF, Csh = 25 μF

From the above magnified transients it is clear seen distortion of the stator winding currents due to saturation of magnetic core of the generator at no-load conditions, especially in the main stator winding.

In order to ensure nominal voltage at terminals of the main stator winding for NA = 424 turns, it is necessary to apply larger excitation capacitor, e.g. Cex = 40 μF and shunt capacitor (Csh = 25 μF) in the main stator winding, as presented in Figures 5 and 6.

## 4 Steady-state performance characteristics of the generator

For validation of the simulation field-circuit model of the generator, computed load characteristics of the tested single-phase self-excited induction generator for reduced number of turns in the excitation stator winding (NA) and suitable capacitor connected to the load stator winding, are compared with experimental results in Figures 7-10. Operating characteristics of the base model of the generator (NA = 528, Cex = 30 μF, Csh = 15 μF) and the models with reduced number of turns in the excitation winding were measured using the test setup shown in Figure 11.

Figure 7

Voltages versus output power of generator with shunt capacitor in load stator winding: NA = 444, Cex = 40 μF, Csh = 20 μF

Figure 8

Currents versus output power of generator with shunt capacitor in load stator winding: NA = 444, Cex = 40 μF, Csh = 20 μF

Figure 9

Voltages versus output power of generator with shunt capacitor in load stator winding: NA = 424, Cex = 40 μF, Csh = 25 μF

Figure 10

Currents versus output power of generator with shunt capacitor in load stator winding: NA= 424, Cex = 40 μF, Csh = 25 μF

Figure 11

Block diagram of laboratory setup for the SPSEIG

Load characteristics of base model of the generator with shunt capacitor in the main stator winding, obtained by simulations and measurements were presented in Figures 12 and 13.

Figure 12

Voltages versus output power of base model of the SPSEIG with shunt capacitor in load stator winding

Figure 13

Currents versus output power of base model of the SPSEIG with shunt capacitor in load stator winding

## 5 Conclusions

For the sake of inconvenience caused by necessity of applying two different circuit models, separate for transients and steady-states performance of the generator, and owing to comprehensiveness of field-circuit analysis, the two-dimensional field-circuit model of the single-phase induction generator was implemented for computation of performance characteristics for transients and steady-state operation. The reduction of number of turns of the excitation winding of the base model causes profitable reduction of voltage magnitude to about 300 V, which for the original excitation stator winding reaches above 400 V. Limitation in reduction of induced voltage in the auxiliary stator winding results from restriction of increase of current in the stator winding. Some discrepancy between the simulation and experimental characteristics, noticeable outside the range of stable operation of the generator, are caused mainly by difference between real and calculated magnetization characteristic of the magnetic core and also due to omitting iron losses in magnetic core of the generator in calculation of performance characteristics.

## References

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Leicht A., Makowski K., Dynamic analysis of single-phase induction motor operating as a self-excited induction generator, International Symposium on EPNC 2012, Pula, Croatia, June 24-29, 2012. Google Scholar

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Makowski K., Leicht A., Field-circuit evaluation of performance characteristics of a single-phase self-excited induction generator, 2017 18th International Symposium on Electromagnetic Fields in Mechatronics, Electrical and Electronic Engineering (ISEF) Book of Abstracts,2017, .

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Kumbhar G.B., Kulkarni S.V., Escarela-Perez R., Campero-Littlewood E., Applications of coupled field formulations to electrical machinery, COMPEL, 2007, 26, 2, 489-523, .

Accepted: 2017-11-12

Published Online: 2017-12-29

Citation Information: Open Physics, Volume 15, Issue 1, Pages 913–917, ISSN (Online) 2391-5471,

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