**Energy Efficiency in Electric Devices, Machines and Drives**

Special Issue Editors **Gorazd Stumberger ˇ Boˇstjan Polajzer ˇ**

MDPI • Basel • Beijing • Wuhan • Barcelona • Belgrade • Manchester • Tokyo • Cluj • Tianjin

*Special Issue Editors* Gorazd Stumberger ˇ University of Maribor Slovenia

Bostjan Polaj ˇ zer ˇ University of Maribor Slovenia

*Editorial Office* MDPI St. Alban-Anlage 66 4052 Basel, Switzerland

This is a reprint of articles from the Special Issue published online in the open access journal *Energies* (ISSN 1996-1073) (available at: https://www.mdpi.com/journal/energies/special issues/ energy efficiency electric).

For citation purposes, cite each article independently as indicated on the article page online and as indicated below:

LastName, A.A.; LastName, B.B.; LastName, C.C. Article Title. *Journal Name* **Year**, *Article Number*, Page Range.

**ISBN 978-3-03936-356-8 (Pbk) ISBN 978-3-03936-357-5 (PDF)**

c 2020 by the authors. Articles in this book are Open Access and distributed under the Creative Commons Attribution (CC BY) license, which allows users to download, copy and build upon published articles, as long as the author and publisher are properly credited, which ensures maximum dissemination and a wider impact of our publications.

The book as a whole is distributed by MDPI under the terms and conditions of the Creative Commons license CC BY-NC-ND.

## **Contents**


## **About the Special Issue Editors**

**Gorazd Stumberger ˇ** received B.Sc., M.Sc., and Ph.D. degrees from the University of Maribor, Maribor, Slovenia, in 1989, 1992 and 1996, respectively, all in electrical engineering. Since 1989, he has been with the Faculty of Electrical Engineering and Computer Science, University of Maribor, where he is currently a Professor of electrical engineering. In 1997 and 2001, he was a Visiting Researcher with the University of Wisconsin, Madison, and with the Catholic University Leuven, Leuven, Belgium, in 1998 and 1999. His current research interests include energy management, design, modeling, analysis, optimization and control of electrical machines and drives, and power system elements. Since 2019, he has been Dean of the Faculty of Electrical Engineering and Computer Science at the University of Maribor.

**Boˇstjan Polajzer ˇ** received B.Sc. and Ph.D. degrees in electrical engineering from the Faculty of Electrical Engineering and Computer Science, University of Maribor, Maribor, Slovenia, in 1997 and 2002, respectively. Since 1998, he has been with the Faculty of Electrical Engineering and Computer Science, University of Maribor, where he has been an Associate Professor since 2010. In 2000, he was a Visiting Scholar with the Catholic University Leuven, Leuven, Belgium, and the Graz University of Technology, Graz, Austria, in 2019. His research interests include electrical machines and devices, power quality, and power-system protection and control. Bostjan Polaj ˇ zer is the head of the Power ˇ Engineering Institute at the Faculty of Electrical Engineering and Computer Science, University of Maribor.

## **Preface to "Energy Efficiency in Electric Devices, Machines and Drives"**

Energy efficiency is one of the issues that cannot be avoided when dealing with electrical devices, machines, drives, and systems. Products that do not achieve the minimum efficiency levels specified in standards cannot be sold and every increase in energy efficiency reduces energy consumption and thus the cost of energy supply. Improvements in energy efficiency on a global scale reduce the energy demand and increase the energy supply, which indirectly reduces greenhouse gas emissions.

The key element in improving the energy efficiency of electrical devices, machines, and drives is the reduction of losses, which can be achieved using various methods. The development of new materials seems to be the most challenging. New solutions in design, design improvements, and optimization can contribute significantly to improving energy efficiency. When an electrical device or machine is manufactured, further improvements in energy efficiency can be achieved by an appropriate selection and matching of power electronic components with the inherited characteristics of machines or devices. Proper control of systems consisting of electrical devices or machines, and power electronics components based on advanced system models can further improve the overall energy efficiency of systems. When electric devices, machines, and drives operate within a system, a properly implemented energy management system, based on in-depth knowledge of the technological process, can improve energy efficiency at the system level.

Some cases of the aforementioned approaches to improving energy efficiency are discussed in this Special Issue.

> **Gorazd Stumberger, Boˇ ˇ stjan Polajzer ˇ** *Special Issue Editors*

## *Article* **Impact of the Winding Arrangement on Efficiency of the Resistance Spot Welding Transformer**

#### **Gašper Habjan \* and Martin Petrun**

Faculty of Electrical Engineering and Computer Science, University of Maribor, 2000 Maribor, Slovenia; martin.petrun@um.si

**\*** Correspondence: gasper.habjan@um.si

Received: 31 July 2019; Accepted: 23 September 2019; Published: 30 September 2019

**Abstract:** In this paper, the impact of the winding arrangement on the efficiency of the resistance spot welding (RSW) transformer is presented. First, the design and operation of the transformer inside a high power RSW system are analyzed. Based on the presented analysis, the generation of imbalanced excitation of the magnetic core is presented, which leads to unfavorable leakage magnetic fluxes inside the transformer. Such fluxes are linked to the dynamic power loss components that significantly decrease the efficiency of the transformer. Based on the presented analysis, design guidelines to reduce the unwanted leakage fluxes are pointed out. The presented theoretical analysis is confirmed by measurements using a laboratory experimental system. The presented experimental results confirm that the proposed improved winding arrangement increased the efficiency of the transformer in average for 6.27%.

**Keywords:** DC-DC converter; resistance spot welding; transformer; efficiency; dynamic power loss; design

#### **1. Introduction**

Resistance spot welding (RSW) systems have a very important role in modern industry. Considering the automotive industry alone, their importance is striking, as nowadays three new cars are produced every second worldwide [1,2]. An interesting fact is that three to five thousand welding spots are required to produce a contemporary personal car. Such a high amount of welding spots requires, on the one hand, the use of fully automated welding systems that are based on robot arms and on the other hand consumes large quantities of energy. Therefore welding systems should be designed as high power density devices where the efficiency of the whole system is crucial.

RSW systems can be generally divided in two groups—systems that produce AC and systems that produce DC welding currents. Nowadays the DC RSW systems are generally replacing the older AC RSW systems due to several advantages [3,4]. A typical contemporary high power RSW system consists of a AC-DC converter that operates at a frequency around 1 kHz, which is generally classified as a medium frequency RSW system [4–7]. A medium frequency RSW system with a DC welding current is shown in Figure 1.

The first part of the discussed system is the AC-AC converter, which consists of a passive input rectifier, a DC-link and H-bridge inverter. The full-wave input rectifier produces a DC voltage *U*dc from phase voltages *u*a, *u*<sup>b</sup> and *u*c, whereas the H-bridge inverter generates a pulse-width modulated (PWM) voltage with modulation frequency of 1 kHz. The presented AC-AC converter supplies the primary side of a welding transformer and is in high power RSW system usually not mounted on a robot arm.

**Figure 1.** Schematic presentation of a typical resistance spot welding system [5].

The second part is a welding transformer, which consists of a three winding transformer with one primary and two secondary windings and an integrated center-tapped full-wave output rectifier. The main task of this transformer is to adequately increase the level of the primary current *i*p, consequently a turn ration of 55:1 is used. The high alternating currents *i*s1 and *i*s2 in both secondary windings are rectified to a DC welding current *i*<sup>l</sup> using a center-tapped output rectifier where two special high current diodes are used.

The third part of the RSW system is a welding gun that is connected to the output rectifier. The main task of a welding gun is to produce weld of prescribed quality, for what adequate electrical, mechanical and thermal conditions have to be fulfilled [2,4]. Due to very high welding currents in such systems, the welding transformer and the welding gun have to be placed together as close as possible to reduce high ohmic power losses [3]. Consequently both discussed parts are mounted on a moving robot arm, whereas the high power density of the welding transformer is one of the main goals in its design process.

In the RSW systems, the majority of the power loss occurs in the second and third part of the system due to very high currents. Therefore these parts are generally cooled using a cooling liquid [3,6]. By reducing the generated power loss in these parts consequently less cooling is required and the power density of the devices can be increased. In this paper the main focus was to analyze the impact of the winding arrangement on the power loss of the welding transformer. For this purpose, a laboratory experimental system was assembled that enabled comparisons of different winding arrangements. The obtained results have shown that an adequate winding layout reduced the power loss in the welding transformer significantly. The main contribution of presented research work is that presented experimental results are supported by a sound theoretical background, where also guidelines for the designing of high power transformers with center-tapped output rectifiers are discussed. The presented theoretical background and design guidelines are indispensable in the design process of the device, as they give an adequate starting point and can be applied to any contemporary design method (e.g., applying adequate winding layout in an finite element model of the device, where the dimensions of the winding can be furthermore optimized).

The paper is organized as follows. In the first section an introduction for the discussed problem is given. In the second section operation and the power loss inside a RSW system are discussed. In the third section the laboratory experimental system is presented, whereas in the fourth section the obtained results are presented and discussed. The fifth section gives a conclusion, where also the outline for future work is presented.

#### **2. Design, Operation and Power Loss Inside a RSW Transformer**

Design, operation and power loss inside a RSW transformer are inseparably interconnected. Power loss inside the transformer depends both on the operation as well as the design of the transformer, where the main focus of this paper is reduction of power loss by improving the design of the transformer.

#### *2.1. Design of the Welding Transformer*

A typical welding transformer is assembled from an iron core on which three windings are placed as shown in Figure 2.

**Figure 2.** A typical design of a welding transformer [1].

The iron core consists of a wound sheet tape of a soft magnetic material that is wound on a model to obtain adequate geometry. The iron core is usually cut in two C-like segments to simplify the assembling process of the transformer [3,6,7]. The primary winding is generally obtained from a rectangular wire that is wound to adequate coils that fit on the iron core segments [3,7]. The primary winding is assembled using 4 such coils that are connected in series and have combined 55 winding turns. Due to high currents *i*s1 and *i*s2 the secondary windings consist of massive copper conductors that represent 1 winding turn and can be also equipped with adequate cooling channels [3,6]. In the presented case the massive secondary turns were furthermore divided into two halves of individual cross sections 17 mm × 2 mm, where the total cross section of a secondary winding was 17 mm × 4 mm. In the presented case both the primary as well as the secondary windings consist of two parallel branches that are placed on the opposite parts of the core. The final assembly is furthermore mechanically reinforced as the transformer is exposed to high mechanical stress due to high currents in the windings [1]. The presented transformer is designed for operation at the frequency of 1 kHz.

#### *2.2. Operation of the Welding Transformer inside the RSW System*

The presented transformer is only a part of the RSW system. The transformer is on the primary side connected to the H-bridge and on the secondary side to the output rectifier, as shown in Figure 1. Both connected parts determine the operation of the transformer, that is, how the electromagnetic variables inside the discussed transformer change with time. These variables generate power loss inside the transformer, therefore the analysis of operation is crucial. The operation of the RSW system can be broken down into 4 characteristic states that depend on the state of the H-bridge converter. These 4 states are shown in Figure 3.

In the presented case, *T*<sup>p</sup> represents the time of one modulation period, *T*ON is the time period in which relevant transistors are set in such a way that the transformer is supplied from the DC-link and *T*OFF is the time period when all the transistors are not conducting and thus separate the transformer from the DC-link voltage. The typical 4 operation states hence correspond to conduction states of switches *S*1, *S*2, *S*<sup>3</sup> and *S*<sup>4</sup> of the H-bridge converter, which supplies the primary winding of the transformer either with voltage *u*<sup>p</sup> = *U*dc, *u*<sup>p</sup> = 0 or *u*<sup>p</sup> = −*U*dc . The primary current *i*<sup>p</sup> corresponds to the waveform of the generated voltage *u*p, where the current increases or decreases according to the individual switching state. Each conducting switching state (states 1 and 3 in Figure 3) is followed by a short additional state (states 2a and 4a), where absolute value of *i*p continuously decreases to 0 despite all transistors are already turned off. In these states the current *i*<sup>p</sup> flows through the free-wheeling diodes of the H-bridge. However, the impact on power loss of these states is in this paper neglected due to a very short duration of these two states.

**Figure 3.** Pulse-width modulation with corresponding current and voltage on the primary side of the resistance spot welding (RSW) transformer [8].

The presented states in the primary winding generate also 4 main states in the secondary winding. These states depend on the output rectifier and are shown in Figure 4.

On the secondary side of the transformer the currents *i*s1 and *i*s2 flow only when individual rectifier diodes are polarized in a conducting way. Due to the inductive nature of the load, the presented converter operates in the continuous conducting mode on the secondary side of the transformer, that is, the current *i*<sup>l</sup> flows also in states 2 and 4, where it splits equally trough the two secondary windings [4,6]. Analogous to the primary side, there are also two brief switching states 2a and 4a that are in the presented analysis omitted. The generated continuous DC welding current *i*<sup>l</sup> is finally used to generate welds of adequate quality.

**Figure 4.** Typical states of the secondary side of the RSW transformer and output rectifier [8].

#### *2.3. Power Loss Inside the Welding Transformer*

Power loss inside the welding transformer can be in general separated in the iron core and winding power loss components. Both components are heavily dependent on used materials, design as well as the operation of the transformer [3,7].

The operation of the RSW system is for the needs of the presented analysis divided into 4 characteristic states as discussed in previous subsection. These 4 states can be furthermore combined into 3 characteristic conduction states of the transformer:


These three states are determined by the direction of the currents and the activity of the windings in the transformer as shown in Figure 5.

In each of the presented state the excitation of the magnetic subsystem is substantially different; the currents in individual windings generate magneto-motive force (mmf) Θ along the iron core, which furthermore generates the magnetic flux and linkage between primary and secondary windings. The generated magnetic flux is, however, flowing not only in the magnetic core. Due to imperfections of the used materials (permeability of the iron core is not infinite, permeabilities of copper and air are not zero), magnetic flux is generated also in the areas around the core. Such areas include all the areas where mmf is generated, that is, areas where windings are located.

Due to the specific design, mmf in the iron core window acts predominantly along the *y*-direction. According to the presented conduction states, the distribution of the mmf Θ<sup>y</sup> (*x*) in the iron core

window can be easily approximated by considering that the density of current in the windings is uniform. According to the Ampere's Law, Θ<sup>y</sup> is therefore changing linearly in respect to the length of the core window (*x*-axis) as shown in Figure 6a).

**Figure 5.** Current direction and winding activity for all four characteristic switching states of the RSW system [8].

**Figure 6.** Two types of distribution of windings and a comparison of magneto-motive force for all states: (**a**) distribution of winding layout 1 and (**b**) distribution of winding layout 2 [8].

The obtained results have shown that the mmf distribution Θ<sup>y</sup> (*x*) in different conducting states changes significantly. As the magnetic flux Φ<sup>y</sup> is a direct consequence of Θ<sup>y</sup> (*x*) and in the transformer window only linear magnetic materials (copper, air, insulation) are used, the distribution of the flux Φ<sup>y</sup> (*x*) in this area corresponds to the Θ<sup>y</sup> (*x*). The significant changes in Θ<sup>y</sup> (*x*) consequently generate significant changes in Φ<sup>y</sup> (*x*). As this leakage flux is changing mostly in electrically conducting materials (windings and iron core), the corresponding induced voltage generates unwanted eddy currents that increase the power loss in the device.

By analyzing the original winding layout shown in Figure 6a it was shown that the distribution of mmfs in individual conduction states is very imbalanced with relative high peak values. Moreover, the change of distribution Θ<sup>y</sup> (*x*) between the states is significant. The generated mmf is acting in the *y*-direction, hence also the corresponding leakage flux will flow across the transformer window in this direction. This leakage flux changes significantly with time and induces voltages in the conducting materials of the transformer. The discussed induced voltage in the windings is causing the so called proximity effect, whereas the induced voltage in the iron core is causing additional eddy currents. Both effects are qualified as so called dynamic power loss, because they are generated due to changes of electromagnetic variables. These loss components increase the total loss significantly and should therefore be minimized. The imbalanced leakage magnetic field distribution Φ<sup>y</sup> (*x*) furthermore leads to imbalanced flux in the iron core and can cause local iron core saturation in addition to increased power loss. This can again lead to increased power loss of the device, as the magnetizing current in the primary windings increases, which can be visible as characteristic current spikes in the primary current [6,9].

The key for discussed loss reduction was clear; the winding layout of the transformer should be designed in such a way that the distribution of the produced mmfs Θ<sup>y</sup> (*x*) is in all conduction states balanced, whereas the peak values of Θ<sup>y</sup> along the *x* axis should be held as low as possible. This can be achieved, for example, using the winding arrangement shown in Figure 6b. In comparison to original winding layout shown in Figure 6a, in this case the secondary windings are divided in two parallel branches that balance the mmf distribution in all states. Importantly also the peak values in Θ<sup>y</sup> (*x*) are reduced for more than 50 %, therefore the changes between the distributions in individual conducting states are significantly smaller. In this way the dynamic loss components of the transformer were significantly reduced what was confirmed with the experimental analysis presented in following subsections.

#### **3. Laboratory Experimental System**

The presented simplified theoretical analysis was applied due to the very complex nature of the problem. In a real transformer, Θ<sup>y</sup> (*x*) is due to possible skin and proximity effects not changing necessarily linearly in respect to *x*-axis. Consequently also Φ<sup>y</sup> (*x*) in the core window can be distorted (however still imbalanced in a similar fashion as in the discussed linear analysis). Furthermore, the windings outside of the transformer core produce mmf that cannot be approximated using only the component in the *y*-axis. Lastly, the connections between the transformer and output rectifier should be considered as they impact the operation of the whole system significantly. Due to these facts simulation analysis would require very complex models (e.g., a 3D finite element model) where the theoretical background of the increased additional loss components could be overlooked. Such models furthermore cannot include all the effects, especially the increased eddy currents in the iron core that occur due to leakage magnetic fields that are perpendicular to core lamination. Consequently the analysis was carried out using a laboratory experimental systems that is presented below.

The laboratory experimental system was designed in such a way that changes of various winding arrangements could be performed. For this purpose a typical industrial RSW transformer was adjusted with additional bus system on the secondary side of the transformer, as shown in Figure 7. This system consisted of three buses; upper and lower buses (marked by 1 and 3 in Figure 7) were connected to both diodes of output rectifier, whereas the middle bus (marked by 2 in Figure 7) represents the center tap of the transformer and therefore the negative potential of the full wave rectifier.

The presented buses were designed in such a way that changing of the position of secondary and primary windings was possible. In order to enable the discussed analysis, also secondary windings of the transformer were adjusted. In a typical industrial RSW transformer, both secondary windings consist of single massive copper conductors that are equipped with cooling channels. In contrast to this, the secondary windings of the laboratory transformer were split into two halves as shown in Figure 2, where the cooling channels were omitted. In this way, comparable results for the presented analysis were obtained.

**Figure 7.** Design of the laboratory experimental system [1].

The drawback of the additional bus system was, however, that the total resistances on the secondary side of the transformer were increased in comparison to a compact industrial RSW transformer [5]. The measured total resistances for both winding arrangements are shown in Table 1. Measurements of resistances were performed using an adequate bridge based DC micro ohm meter which measured a DC resistance.

**Table 1.** Total resistance of individual windings for both winding arrangements.


From the obtained measurements it was shown that the total secondary resistance (windings combined with the bus system) was lower for proposed winding arrangement in comparison to the original arrangement. This was due to slightly shorter net path of the currents trough the winding combined with the connection between the transformer and the output rectifier. Furthermore, the total resistances of both secondary branches were better balanced compared to the original arrangement. An imbalance of secondary resistance can lead to drift of magnetic flux inside the core and consequently to its saturation [6,8,9]. Furthermore, the iron core of the transformer was equipped with several measuring coils as shown in Figure 8.

These measurement coils were used to calculate the density of magnetic flux inside the core, where in each measurement coil induced voltage *u*i(*t*) was measured. The densities of magnetic flux *B*(*t*) were obtained by (1)

$$B(t) = \frac{1}{N\_{\rm m}S} \int \mu\_{\rm i}(t) \mathbf{d}t,\tag{1}$$

where *S* represents the cross-section of the core and *N*<sup>m</sup> represents the number of turns of the measurement winding. The laboratory experimental system was finally mechanically reinforced using an adequate plastic frame.

**Figure 8.** Placement of measuring coils on the core of laboratory RSW transformer [1].

#### **4. Results**

The discussed laboratory experimental system was tested for both winding arrangements using equal operation conditions. The tests were performed in such a way that the load resistance *R*<sup>l</sup> and inductance *L*<sup>l</sup> of the system were fixed, whereas the duty ratio of the H-bridge inverter was increased from 0.3 to 0.8 with a step of 0.1. The efficiency was determined by measuring the voltages and currents on the primary and secondary side of the transformer. Measurements were performed using the high performance measuring device DEWETRON DEWE-2600, where the voltages were measured directly and for the measurements of the currents special low frequency Rogowski's coils (CWT 3LFR and CWT 150LFR) were used.

Measured voltages for duty ratio of 0.6 are shown in Figure 9.

The obtained result have shown that the induced voltages in the secondary windings were slightly higher in the proposed winding arrangement in comparison to the original one. The RMS values of induced voltages in the secondary windings in the case of winding arrangement 1 were *U*s1RMS = 5.129 V and *U*s2RMS = 5.225 V. Compared to this, when winding arrangement 2 was applied, these values were *U*s1RMS = 5.249 V and *U*s2RMS = 5.268 V. This increase was attributed to lower leakage magnetic fields in the transformer window combined with lower total resistances on the secondary side of the transformer when improved winding arrangement was applied. Corresponding currents are shown in Figure 10.

The difference between all the currents in both analyzed winding arrangements was significant. The average steady state value of output welding current *i*<sup>l</sup> was in the presented operation point for 1780 A higher, what accounts for 12.7 %. This increase was attributed to higher induced voltages in both secondary windings as well as lower total resistances on the secondary side of the RSW transformer.

Based on measured voltages *u*(*t*) and currents *i*(*t*) during the welding cycles, average input as well as output powers for different duty ratios were calculated. All the average power values *P* were determined using orthogonal decomposition technique in the time domain, where measured currents were decomposed into orthogonal and co-linear components in respect to adequate voltages [10,11]. In this way, from measured primary voltage *u*<sup>p</sup> and current *i*<sup>p</sup> the average input power of the

transformer *P*in was calculated and from measured secondary voltages *u*s1 and *u*s2 as well as currents *i*s1 and *i*s2 average output powers of the transformers *P*out1 and *P*out2 were calculated, respectively. The total output average power was determined by *P*out = *P*out1 + *P*out2. Based on the obtained *P*in and *P*out, total power loss *P*tr and efficiency *η*tr of the transformer were calculated by (2) and (3), respectively.

$$P\_{\rm tr} = P\_{\rm in} - P\_{\rm out} \tag{2}$$

$$
\eta\_{\rm tr} = \frac{P\_{\rm out}}{P\_{\rm in}} \tag{3}
$$

**Figure 9.** Comparison of measured primary and secondary voltages for both winding arrangements: (**a**) voltage in the primary winding *u*p, (**b**) output voltage *u*l, (**c**) voltage in the secondary winding 1 *u*s1 and (**d**) voltage in the secondary winding 2 *u*s2.

In addition to *P*tr, also the total power loss of the output rectifier *P*rect was determined. For this purpose furthermore the voltage *u*<sup>l</sup> and current *i*<sup>l</sup> on the output of the rectifier were measured. Based on these measurements, the average power supplied to the load *P*load was determined. The power loss in the full-wave rectifier was obtained by (4)

$$P\_{\text{rect}} = P\_{\text{out}} - P\_{\text{load}}.\tag{4}$$

whereas the efficiency of the output rectifier was calculated by (5) respectively.

$$
\eta\_{\text{rect}} = \frac{P\_{\text{load}}}{P\_{\text{out}}}.\tag{5}
$$

**Figure 10.** Comparison of measured primary and secondary currents for both winding arrangements: (**a**) current in the primary winding *i*p, (**b**) welding current *i*l, (**c**) current in the secondary winding 1 *i*s1 and (**d**) current in the secondary winding 2 *i*s2.

Due to the difference in the output currents for both winding arrangements, the obtained results were compared in respect to the output current instead of the duty ratio. The obtained results are presented in Figure 11.

The obtained results have shown that the efficiency of the transformer with improved winding arrangement was significantly higher; the efficiency improved for around 5% at low and around 6.7% at high welding currents, where the average efficiency difference between both distributions of windings was 6.27%. This increase corresponded to around 0.73 kW or 6 kW less total power loss in the transformer at low and high welding currents, respectively. In this way *P*tr was decreased for 31.7–34.7%. This decrease of power loss was a direct consequence of the decreased leakage magnetic field inside the transformer window and generates the additional dynamic power loss component. Due to improved winding arrangement the proximity effect between all the winding coils was significantly reduced. Furthermore, as the leakage magnetic flux entered the iron core perpendicular to the lamination of iron core, the dynamic loss inside the iron core was reduced also. Changes of magnetic flux that enters the iron core perpendicular to lamination generate eddy currents that are due to unfavorable direction not limited by the lamination. This effect can increase the iron core power loss significantly [12]. The decrease of *P*tr consequently enables to reduce the cooling of the transformer what furthermore increases the efficiency of the whole RSW system. In this way also weight of the transformer can be reduced, whereas the power density is improved.

**Figure 11.** Comparison of determined power loss and efficiency of the transformer (**a**,**b**) and output rectifier (**c**,**d**) for both winding arrangements.

In contrast to the transformer, the efficiency and power loss of the rectifier depended only on the output current. Therefore the results were comparable for both winding arrangements. It is worthwhile to note that the rectifier power loss was even higher than power loss of the transformer.

Using the measurement coils on the core as presented in Figure 8 distribution of magnetic flux inside the iron core was determined. The obtained results are presented in Figure 12, where the imbalance of magnetic flux in the iron core was observed.

**Figure 12.** Results of the calculated densities of magnetic flux density *B* for: (**a**) arrangement 1 and (**b**) arrangement 2.

The calculated densities of magnetic flux were substantially different in all three core parts when original winding arrangement was analyzed (Figure 12a)). In contrast to this, all three densities of magnetic flux were balanced when the improved winding arrangement was analyzed. The observed non-uniform distribution of *B* was a direct consequence of imbalanced distribution Θ<sup>y</sup> (*x*) trough all 4 characteristic states. As Θ<sup>y</sup> (*x*) was balanced in all the states if improved winding arrangement was applied, consequently also a uniform distribution of *B* inside the core was achieved. A non-uniform distribution of *B* can lead to local iron core saturation and consequently to increased power loss and decreased operation reliability of the device.

#### **5. Conclusions**

In the paper, the impact of winding arrangements on dynamic power loss inside a RSW transformer was analyzed. The layout of the windings along the transformer's core has direct impact on amplitudes and distribution of leakage magnetic fields around these windings. First a sound theoretical background for improvement of winding arrangements is discussed, where the negative consequences of discussed phenomena were pointed out. The negative consequences include increased dynamic power loss inside the windings (proximity effect) and the iron core (increased eddy currents) as well as non-uniform distribution of magnetic flux density inside the core, which can lead to local saturation. The theoretical analysis was confirmed by experimental results. The obtained experimental results have shown that the losses inside the transformer were significantly decreased when the arrangement of the windings was improved with accordance with the presented theoretical background. The efficiency of the improved transformer was in average increased for 6.27 %. With the experimental analysis it was furthermore shown that the improved winding arrangement results in a better distribution of magnetic flux density inside the core. Consequently, local saturations of the core were avoided, whereas the magnetic material inside the device was better utilized. The presented analysis therefore points out basic guidelines when designing a high power DC-DC converter that utilizes a transformer with a center tapped rectifier. Future work will be focused on analysis of the non-uniform distribution of the magnetic field on the operation and losses of the whole system for RSW.

**Author Contributions:** Supervision, M.P.; Writing—original draft, G.H. and M.P.; Writing—review & editing, M.P.

**Funding:** This research received no external funding.

**Conflicts of Interest:** The authors declare no conflict of interest.

#### **Abbreviations**

The following abbreviations are used in this manuscript:

RSW Resistance Spot Welding


#### **References**


c 2019 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

## *Article* **Modular Rotor Single Phase Field Excited Flux Switching Machine with Non-Overlapped Windings**

**Lutf Ur Rahman 1,\*, Faisal Khan 1, Muhammad Afzal Khan 1, Naseer Ahmad 1, Hamid Ali Khan 1, Mohsin Shahzad 1, Siddique Ali <sup>2</sup> and Hazrat Ali <sup>1</sup>**


Received: 15 December 2018; Accepted: 11 April 2019; Published: 25 April 2019

**Abstract:** This paper aims to propose and compare three new structures of single-phase field excited flux switching machine for pedestal fan application. Conventional six-slot/three-pole salient rotor design has better performance in terms of torque, whilst also having a higher back-EMF and unbalanced electromagnetic forces. Due to the alignment position of the rotor pole with stator teeth, the salient rotor design could not generate torque (called dead zone torque). A new structure having sub-part rotor design has the capability to eliminate dead zone torque. Both the conventional eight-slot/four-pole sub-part rotor design and six-slot/three-pole salient rotor design have an overlapped winding arrangement between armature coil and field excitation coil that depicts high copper losses as well as results in increased size of motor. Additionally, a field excited flux switching machine with a salient structure of the rotor has high flux strength in the stator-core that has considerable impact on high iron losses. Therefore, a novel topology in terms of modular rotor of single-phase field excited flux switching machine with eight-slot/six-pole configuration is proposed, which enable non-overlap arrangement between armature coil and FEC winding that facilitates reduction in the copper losses. The proposed modular rotor design acquires reduced iron losses as well as reduced active rotor mass comparatively to conventional rotor design. It is very persuasive to analyze the range of speed for these rotors to avoid cracks and deformation, the maximum tensile strength (can be measured with principal stress in research) of the rotor analysis is conducted using JMAG. A deterministic optimization technique is implemented to enhance the electromagnetic performance of eight-slot/six-pole modular rotor design. The electromagnetic performance of the conventional sub-part rotor design, doubly salient rotor design, and proposed novel-modular rotor design is analyzed by 3D-finite element analysis (3D-FEA), including flux linkage, flux distribution, flux strength, back-EMF, cogging torque, torque characteristics, iron losses, and efficiency.

**Keywords:** flux switching machine; modular rotor; non-overlap winding; magnetic flux analysis; iron losses; copper loss; stress analysis; finite element method

#### **1. Introduction**

In everyday applications, universal motors are mostly used in such devices as power tools, blenders, and fans. They are operated at high speed and deliver high starting torque as getting direct power from the ac-grid. At high speeds, universal motors cause noise due to their mechanical commutators, and they have a comparatively short maintenance period. To cope with these snags, research of a high-performance and low-cost brushless machine is greatly in demand [1,2]

Switched-flux brushless machines, a new class of electric machine were first presented in the 1950s [3]. Flux switching machines (FSMs), an unconventional machine, originated from the combination of principles among induction alternator and switched reluctance motor [4]. Distinct features of FSMs are their high torque density and robust rotor structure resulting from putting all excitation on the stator. In the past decade, various novel FSMs have been developed for several applications, confines from domestic appliances [5], automotive application [6,7], electric vehicles [8,9], wind power, and aerospace [10]. FSMs are categorized into permanent magnet flux switching machines (PMFSM), field excited flux switching machines (FEFSM), and hybrid excited flux switching machines (HEFSM). Permanent magnet FSMs and field excited FSMs have a permanent magnet (PM) and field excitation coil (FEC) for generation of flux source respectively, whilst both PM and FEC are generation sources of flux in HEFSM. The major advantage of FSMs is their simple/robust structure of rotor and easy management of temperature rise as all the excitation housed on stator. Recently, use of a permanent magnet as a primary source of excitation has dominated in flux switching research, due to their high torque/ high power density and optimum efficiency [11]. However, the maximum working temperature of PM is limited due to potential irreversible demagnetization. The use of PM in not always desirable due to high cost of rare earth material. For low cost applications, it is desirable to reduce the use of permanent magnets and hence they are replaced by DC-FEC. FEFSMs are capable of strengthening and weakening the generated flux as it is controlled by dc-current. FEFSMs have the disadvantage of less starting torque, fixed rotational direction, and high copper losses. The cumulative advantages of both FEC and PM are embedded in HEFSM having high torque capability/high torque density, HEFSMs also have high efficiency and flux weakening capability. However, the demerits of HEFSMs include a more complex structure, saturation of stator-core due to use of PM on stator, greater axial length, and high cost due to use of rare earth material. Therefore, FEFSMs could be considered a better alternative for requirements of low cost, wide speed controllability, high torque density, simple construction, less need of permanent magnet, and flux weakening operations as compared to other FSMs [12].

Numerous single-phase novel FS machines topologies has been developed for household appliances and different electric means. Single phase FSMs were first presented in [13] and further investigated in [14,15] by C. Pollock, they analyzed an 8S-4P doubly salient machine that offers high power density and low cost as shown in Figure 1. The FEC and armature has an overlapped winding arrangement resulting in longer end winding. To overcome the drawback of long end winding, the 12S-6P FSM has been developed that has same coil pitch as eight stator slots and four rotor poles but shorter end winding [16]. Figure 2 depicts how a 12-slot/6-pole machine has fully pitched winding arrangement as with C. Pollock's design. The end windings effect is even shorter by re-arranging the armature winding and FEC to different pitch of one and three slot pitches as shown in Figure 3. Both machines with F2-A2-six-pole and F1-A3-six-pole coil pitches have better copper consumption than a conventional machine (F2-A2-four-pole) for short axial length but has a disadvantage of higher iron loss due to more rotor poles [17]. The stator slots and rotor poles could be halved into F1-A3-3P machine as shown in Figure 4, that is more appropriate for high speeds due to a significant reduction in iron loss [16]. When the axial length is short, that is up to 25 mm, the average torque of both F2-A2/4P and six-pole machine is similar. However, F1-A3/3P exhibit higher average torque than F1-A3/6P machine at longer axial length of 60 mm. At the point when end winding is disregarded, a machine with fewer stator teeth and rotor poles has less average torque as compared to a machine with fewer rotor poles and stator slots for the same type of machine.

**Figure 1.** 8S/4P FEFS machine (F2-A2-4P). (**a**) Cross-sectional model; (**b**) 3D model [16].

**Figure 2.** 12S/6P FEFS machine (F2-A2-6P). (**a**) Cross-sectional model; (**b**) 3D model [16].

**Figure 3.** 12S/6P FEFS machine with rearranged winding (F1-A3-6P). (**a**) Cross-sectional model; (**b**) 3D model [16].

**Figure 4.** 6S/3P FEFS machine (F1-A3-3P). (**a**) Cross-sectional model; (**b**) 3D model [16].

In single phase FS machines, torque is generated with doubly salient structure due to the tendency of rotor to align itself into a minimum reluctance position as shown in Figure 5. When the stator slot and rotor pole are aligned at a minimum reluctance position, the motor cannot generate torque (called 'dead zone of torque') at aligned positions unless armature current direction is reversed. The dead zone of torque is eliminated in [18] with sub-part rotor structure having different pole arc lengths. The eight-slot/four-pole sub-part rotors are merged on the same face and pole axes are not parallel. However, sub-rotor poles cannot be allied with stator slots at a same-time, thus reluctance torque is generated at any rotor position. The single phase 8S/4P sub-part rotor FSM only applicable for a situation that requires a continuous unidirectional rotation. The conventional sub-part rotor design has demerit of overlapped winding arrangements between FEC and armature winding that results in higher copper consumption and higher iron losses due to salient rotor structure. A single phase sub-rotor FS machine minimizes the advantage of high speed, as it cannot operate at speed higher than normal level.

**Figure 5.** Sub-part rotor structure. (**a**) Manifestation of sub-part rotor; (**b**) pole arc of sub rotor-1; (**c**) pole arc of sub rotor-2.

This paper presents a novel-modular rotor structure for single phase FS machines as shown in Figure 6. The proposed design comprises of non-overlapped winding arrangements between armature winding and FEC, and modular rotor structure. The consumption of copper is much reduced due to non-overlapped winding arrangements. The modular rotor single phase FSM exhibit a significant reduction in iron losses, also reduces the rotor mass and lower the use of stator back-iron without diminishing output torque.

**Figure 6.** Modular rotor structure.

#### **2. Design Methodology**

The proposed novel modular rotor single phase eight-slot/six-pole FEFSM with non-overlapping winding arrangements is presented, as shown in Figure 7. To design the modular structure, JMAG designer ver.14.1 is used and the results obtained are validated by the 3D finite element analysis (3D-FEA). First, every section of motor such as stator, rotor, field excitation coil (FEC), and armature coil of modular design with eight stator slots and six rotor poles is designed in Geometry Editor. Then, the material, mesh properties, circuit, various properties, and conditions of the machine is selected and is simulated in the JMAG designer. The complete flow of the proposed design starts in Geometry Editor up to coil test analysis is shown in Figure 8. An electromagnetic steel sheet is used for the stator and rotor core. The design parameters and specifications of the modular design is illustrated in Table 1.

**Figure 7.** 8S-6P FEFSM with modular rotor.



**Figure 8.** Design procedure.

#### **3. Deterministic Optimization**

The average torque analyses of eight-stator slots/six-rotor poles are examined. The maximum output torque obtained by the initial design is 0.88 Nm at speed of 400 rpm, which is much lower from the other designs. In order to improve the average torque characteristics, deterministic optimization is used. First optimization cycle consists of five steps, that is *RIR*, θ, *SR*, *TWA*, *TRA*, *TWD*, and *TRD*, as shown in Figure 9. Design free parameters *RIR*, θ, *SR*, *TWA*, *TRA*, *TWD*, and *TRD* are defined in rotor and stator part, as depicts in Figure 10 are optimized, while the outer radius of stator, air gap, and shaft of the motor are kept constant.

**Figure 9.** Optimization procedure.

**Figure 10.** Design parameters of modular rotor design.

Initially, the design free parameters of rotor are updated, first of all, the inner rotor radius, *RIR*, changes while the other parameters of stator and rotor remain constant. Then, rotor pole angle, θ, and split ratio, *SR*, are varied and adjusted. The rotor pole angle, θ, is a dominant parameter in modular design to increase torque characteristics. Once the combination of promising values of rotor part for highest average output torque is determined, the next step is to refine the *TWD* and *TRD* of FEC, while rotor and armature slot parameter are kept constant. Finally, the essential armature slot is optimized by changing *TWA* and *TRA* while all other design parameters are preserved. To attain the highest average output torque, the above design optimization process is repeated. Figure 11 illustrates the highest average torque result after two cycles of optimization by updating several parameters that are already mentioned above. From Figure 11, it is also clear that during the first cycle the torque increases to a certain level by varying the above parameters of the machine and it becomes constant.

**Figure 11.** Effect of design parameters on average torque

During the first cycle, 32 percent of increase in the average output torque is achieved by refining the dominant parameter of rotor pole angle, θ, whilst other free design parameter adjustment shows less improvement in torque. In comparison with the initial design, the average output torque is improved by 40 percent after completion of second optimization cycle. The initial and optimized structure of 8S/6P modular design is illustrated in Figure 12. Additionally, the comparison of parameters of initial and final design is presented in Table 2.

Table 3 depicts comparison of cogging torque, flux linkage, back-EMF, average torque, and power of 3D-modular un-optimized and optimized design. The cogging torque and flux linkage of optimized designs is 0.3374 Nm and 0.2114 Wb respectively, which is 50% lower than the un-optimized cogging torque and flux linkage. Whilst, back-EMF of optimized modular 8S/4P is improved by 15%, that is still much lower than the applied input voltage of 220V. Furthermore, before optimization of modular design the maximum average output torque and power obtained is 9.77 Nm and 162.9 Watts respectively, at maximum FEC current density, *Je*, is set to 10 A/mm<sup>2</sup> and 25 A/mm<sup>2</sup> is assigned to the armature coil, which is improved to 1.66 Nm and 288 Watts, respectively. Comparatively, average output torque and power is improved by 58.85% and 56.40%, respectively.

**Figure 12.** Structure of eight-slot/six-pole modular design.


**Table 2.** Initial and refined design parameters of Novel-modular rotor design

**Table 3.** Results comparison of optimized and un-optimized design


#### **4. Result and Performance Based on 3D-FEA Finite Element Analysis (3D-FEA)**

#### *4.1. Flux Linkage*

Comparison of flux linkages of three field excited FSM at no-load is examined by 3D-FEA [16,18]. To analyze the sinusoidal behavior of flux, the input current density of FEC, and armature coil is fixed to 10 A/mm2 and 0 A/mm2 respectively. Figure 13 shows that proposed modular design has peak flux of 0.021 Wb which is approximately equal to the peak flux of 15% of F1-A3-3P design. Similarly, sub-part rotor design has a 66% higher peak flux linkage than 8S/6P modular structure due to different pole arc length. The conventional F1-A3-3P design has the highest peak flux as compared to modular design, as well as sub-part rotor design due to the doubly salient structure.

**Figure 13.** Comparison of U-flux linkages.

#### *4.2. Flux Distribution*

Flux density distribution generated by the DC coil in three FEFSM is shown in Figure 14. The red spot mention in Figure 14a–d show saturation of stator teeth and back-iron respectively of both conventional designs. F1-A3-3P design and sub-part rotor design has vector plot value of magnetic flux density distribution of 1.9953 and 1.9760 maximum, respectively. Whilst, the flux density distribution of modular design from the vector plot is 2.2528 maximum at 0◦ rotor position. Additionally, in comparison with 8S/4P sub-part rotor design and 6S/3P design, the proposed 8S/6P modular rotor design exhibits higher flux distribution. For completely utilizing flux in the proposed design, various parameters of the machine are optimized to enhance the flux distribution from the stator to the rotor and vice versa. The peak flux in the modular rotor pole at its lowest magnetic loading is 0.0453 Wb, which increases with increasing magnetic loading. Figure 15 illustrates flux density distribution at maximum armature current density of 25 A/mm2.

**Figure 14.** Flux distribution at no-load. (**a**,**b**) Flux distribution in conventional F1-A3-3P design; (**c**,**d**) Flux distribution in sub-part rotor design; (**e**,**f**) Flux distribution in proposed modular rotor design.

**Figure 15.** Flux distribution at maximum load. (**a**,**b**) Flux distribution in conventional F1-A3-3P design; (**c**,**d**) Flux distribution in sub-part rotor design; (**e**,**f**) Flux distribution in proposed modular rotor design.

#### *4.3. Flux Strengthening*

The effect of flux strength is analyzed by increasing current density; *Je* of field excitation coil (FEC) is varied from 0 A/mm2 to 20 A/mm2, whilst armature current density; *Ja* is set 0 A/mm2. The FEC input current is calculated from (1)

$$I\_{\varepsilon} = \frac{J\_{\varepsilon} \alpha S\_{\varepsilon}}{N\_{\varepsilon}} \tag{1}$$

where, *Ie*, *Je*, α, *Se*, and *Ne* are the input current of FEC, field current density, filling factor, slot area of FEC, and number of turns of field coil respectively. The analysis of coil test can be verified from the flux strengthening. Increasing the current densities of FEC, the pattern plot clearly shows a linear increase in flux until 0.027 Wb at *Je* of 20 A/mm<sup>2</sup> as shown in Figure 16.

**Figure 16.** Peak flux strengthening with Modular rotor at various *Je*.

#### *4.4. Back-EMF Versus Speed*

"Back-EMF is the induce voltages in the armature winding which opposes the change in current through which it is induced". The back-EMF (*ea*) in the armature can be determined from the rate of change in armature flux or applying the co-energy concept [19]. For motor with *Nr* rotor poles

$$\mathfrak{e}\_a = a\psi\_f \frac{2K\mathcal{N}\_d\mathcal{N}\_r}{\pi} \tag{2}$$

where *Na*, *Nr*, ω, φ*<sup>f</sup>* and *K* is number of armature turns, number of rotor poles, rotational speed, field flux, and constant of field flux that are linked with the armature winding respectively. Substituting the φ*<sup>f</sup>* (field flux) with

$$
\phi\_f = \frac{N\_f I\_f}{\mathcal{R}} \tag{3}
$$

$$e\_d = \frac{2K\mathcal{N}\_r}{\pi\mathcal{R}}\mathcal{N}\_d N\_f I\_f \omega \tag{4}$$

where *Nf* , *If* , and R is the number of field turns, the field current and reluctance of magnetic circuit. For the maximum conversion of electro-mechanical energy, armature current must flow in the opposite direction of the induced-EMF in the armature.

Figure 17 shows the 3D-FEA predicted induced-EMF of eight-slot/six-pole modular rotor structure at a fixed field current density (*Je*; 10 A/mm2) and various speeds. The induced-EMF increases linearly with increasing speed. The maximum induced voltage is 22 V at a maximum speed of 1600 rpm which is quite lower than the applied input voltage (220 V) which confirms the motor actioning of the machine.

#### *4.5. Intantaneous Torque and Torque Ripple Calculation*

Figure 18, investigates the instantaneous torque versus rotor mechanical revolution in electrical degrees of eight-slot/four-pole, six-slot/three-pole, and eight-slot/six-pole FESF machines. Six-slot/three-pole (F1-A3-3P) rotor design has high peak to peak torque as compared to eight-slot/six-pole (modular design) and eight-slot/four-pole (sub-part rotor) FESF machines. Figure 18 illustrates that characteristics of instantaneous torque at 10 A/mm<sup>2</sup> of six-slot/three-pole are better as compared to eight-slot/six-pole and eight-slot/four-pole FESF machines.

**Figure 17.** Maximum back-EMF at various speed.

**Figure 18.** Comparison of instantaneous torque.

Whilst F1-A3-3P design exhibits the highest torque ripples comparatively to sub-part rotor design and modular rotor design. The proposed modular design has lower torque ripples than both the conventional designs, that is 29% and 60% lower than sub-part rotor design and F1-A3-3P design, respectively. Torque ripples are calculated from expression (5)

$$\left(\frac{\tau\_{\text{max}} - \tau\_{\text{min}}}{\tau\_{\text{avg}}}\right) \times 100\tag{5}$$

#### *4.6. Total Harmonics Distortion (THD)*

Total harmonics distortion is the ratio of the summation of all harmonic components to the fundamental frequency harmonics of the power or harmonics distortion that exists in flux. In electric machines, THD occurs due to harmonics present in flux. THD determines the electromagnetic performance of the machine as it is the representation of the harmonics in the machine. Mathematically, the THD of an electric machine can derived from equation (6)

$$THD = \frac{\sqrt{\Sigma\_{n=1,2\dots}^{k=2n+1} \Phi\_k^2}}{\Phi\_1} \tag{6}$$

where *k* is odd number and Φ*<sup>k</sup>* is the odd harmonics of flux. THD of proposed design is higher as compared to conventional design due to the modular structure of rotor. Figure 19 shows the THD of three FEFS machines. The graph shows that the THD of sub-part rotor design and F1-A3-3P design is 7% and 4% respectively, while THD of the proposed modular rotor design is 16.4%.

**Figure 19.** THD values of the conventional and proposed designs.

#### *4.7. Cogging Torque*

The interaction between the Stator excitation source (PM, excitation coil) and rotor pole of machine at no-load is called cogging torque. The magnetic circuit consists of an existing PM and coil having co-energy, the total co-energy is formulated as [20,21].

$$\mathcal{W}\_{\mathbb{C}} = Niq\rho\_{m} + \frac{1}{2} \Big( \mathrm{Li}^{2} + (\mathcal{R} + \mathcal{R}\_{m})\varphi\_{m}{}^{2} \Big) \tag{7}$$

where, *N*, *i*, R*m*, *L*, R and ϕ*<sup>m</sup>* are the number of turns, current, magnetic flux, inductance of coil, magneto-motive force, and magnetic flux linkage respectively. The change in total co-energy with respect to the mechanical angle of the rotor determines the average torque of the machine.

$$T\_{\mathcal{E}} = \frac{\partial \mathcal{W}\_{\mathcal{E}}}{\partial \theta} \text{ with } \mathbf{i} = \text{constant} \tag{8}$$

where, *Wc* and θ are total co-energy and mechanical rotor angle, respectively.

$$T\_{\varepsilon} = \frac{\partial \Big(\mathrm{N}i\rho\_{m} + \frac{1}{2} \Big(\mathrm{L}i^{2} + (\mathsf{R} + \mathcal{R}\_{m})\rho\_{m}{}^{2}\Big)\Big)}{\partial \theta} \quad T\_{\varepsilon} = \mathrm{N}i\frac{d\rho\_{m}}{d\theta} + \frac{1}{2}i^{2}\frac{dL}{d\theta} - \frac{1}{2}\rho\_{m}{}^{2}\frac{d\mathsf{R}}{d\theta} \tag{9}$$

The third term in Equation (9) changes in mmf with respect to the mechanical position of rotor causes cogging torque. The cogging torque produces unwanted noise and vibration. As Equation (9) shows that the cogging torque lead to a significant reduction in the average torque.

The cogging torque of F1-A3-3P, sub-part rotor and modular designs is comparing in Figure 16. The cogging of modular design is less than F1-A3-3P and sub-part rotor designs as depicts in Figure 16. Figure 20 illustrates that the cogging torque of modular design is 12% of F1-A3-3P and 53% of sub-part rotor. As a result, the modular design has less vibration and more average torque as to compare to F1-A3-3P and sub-part rotor design.

**Figure 20.** Comparison of cogging torque.

#### *4.8. Copper Loss versus Torque*

In field excited FSM, the copper consumption is the main constituent affecting the overall cost of the machine. As compared to other materials for FEFSM, copper is more expensive. The copper-loss of single phase FEFSM can be calculated from the formula as

$$P\_{\mathbb{C}u} = I\_a^2 R\_a + I\_f^2 R\_f$$

where *Ia*, *Ra*, *If*, and *Rf* is the armature current, armature winding resistance, field current, field winding resistance, respectively. The comparison of copper loss-torque curve of three field excited FSM is shown in Figure 21. The average output torque modular design is almost similar to the sub-part rotor design but is much higher than the F1-A3-3P design. At fixed copper loss of 60 watts, the average torque of conventional sub-part rotor design, F1-A3-3P design, and proposed modular design is 1.6 Nm, 0.98 Nm, and 1.58 Nm, respectively. However, the plot clearly shows that modular design achieves a higher average torque under the constraint of maximum copper loss of 120 watts due to the short pitch coils.

**Figure 21.** Comparison of average torque at fixed copper losses.

#### *4.9. Torque versus Current Density*

Torque versus current density of three FEFS machines is calculated at various current density and maximum current set to 25 A/mm2. Figure 22 illustrates torque versus the current density of sub-part rotor design, F1-A3-3P design, and modular rotor design. Both conventional machines are saturated beyond 10 A/mm2, while proposed machine has increasing torque profile, by increasing current density. At maximum 25 A/mm2 current density F1-A3-3P design has higher average torque than modular rotor and sub-part rotor 65.6% and 63.05%, respectively. F1-A3-3P demonstrates high torque due to high flux linkage.

**Figure 22.** Comparison of average torque versus current densities.

#### *4.10. Torque Density and Power Density*

Torque density and power density of three FEFS machines is calculated at a fixed current density of 10 A/mm2. Figure 23 illustrates torque densities of sub-part rotor design, F1-A3-3P design, and modular rotor design. Comparatively, the torque density of the F1-A3-3P design is 1.89 times higher than modular rotor design and 1.71 times higher than sub-part rotor design as shown in Figure 23. The proposed modular design has a reduced total mass of 23% and 44.8% as compared to sub-part rotor design and F1-A3-3P design, respectively, as shown in Table 4.

**Figure 23.** Torque density of three FEFS machines.


**Table 4.** Comparison of active mass

The power density of conventional and proposed design is expressed in Figure 24. Power density attains by modular rotor design is 0.0783 Watt/kg at current density of FEC, *Je*, and armature current density, *Ja*, of 10 A/mm2 as shown in Figure 24. High power density exhibits high efficiency and better electromagnetic performance. The proposed 8S/4P modular rotor design achieves 1.3 times and 1.9 times higher power densities as compared to F1-A3-3P design and sub-part rotor design respectively.

#### *4.11. Torque and Power Versus Speed Characteristics*

The comparison of torque and power versus speed curve of three single phase FEFSM are illustrated in Figure 25. At a rated speed of 1664 rpm, the maximum average torque of the modular rotor design is 1.64 Nm which corresponds to the power generated by the proposed design at 286 W. Additionally, the average torque obtained by conventional 8S-4P sub part rotor design and 6S-3P salient rotor is 1.4 Nm and 3.77 Nm, at a base speed of 1389 rpm and 1053 rpm, respectively. The average torque of proposed design is higher as compared to the sub part rotor design. At a speed of 1600 rpm, the average torque of the proposed design is similar to 6S-3P design while being 19 percent higher than the 8S-4P design. Although the generated power of 8S-6P modular design is 28.4 percent higher than 8S-4P design, it is 31 percent lower than F1-A3-3P design. The pattern plot shows that, beyond rated speed, the average torque of the machine starts to decrease and power is decreased as well. The power of 6S-3P FEFSM decreases more rapidly due to an increase in iron loss above the rated speed.

**Figure 25.** (**a**) Comparison of torque versus speed; (**b**) Comparison of power versus speed of three FEFSM.

#### *4.12. Rotor Stress versus Speed*

Rotor stress analysis is a technique to identify the principal stress, nodal force, and displacement occurred in the rotor structure in an ideal state after load is applied. Generally, the condition for mechanical stress of the rotor structure is accomplished by centrifugal force due to the longitudinal rotation of the rotor. Additionally, centrifugal force of the rotor is greatly affected by the speed. The rotor could highly withstand stress, if the principal stress of the rotor is higher. Principal stress is a crucial result in the analysis of stress. By increasing the angular velocity of the rotor, principal stress is increased exponentially. Thus, the rotor principal stress versus the speed of the three-field excited flux switching machines (rotor structure) is analyzed using 3D-FEA. The angular velocity varies from 0 rpm to 20,000 rpm for conventional three-pole salient rotor structure, four-pole sub-part rotor structure, and the proposed six-pole modular structure to analyze the maximum capability of

mechanical stress. The constraints that coincide with the force acting on the rotor is faces, edges, and vertices. The maximum principal stress on each rotor at various speed is shown in Table 5.

**Table 5.** Stress analysis at various speed

Figure 26 shows that comparison of principal stress of three different rotor structures versus speed. At a maximum speed of 20,000 rpm, the principal stress of salient rotor structure, sub-part rotor structure and modular rotor structure is 6.73 MPa, 11.61 MPa, and 2.11 MPa respectively. The pattern plot clearly shows that principal stress of proposed modular rotor structure is much lower as compared to the conventional rotor design. The maximum allowable principal stress of 35H210 electromagnetic steel is 300 MPa. All the three rotor structures are capable of high-speed applications, but the only salient rotor structure can be operated at high speeds due to the single piece rotor structure. Whilst the sub-part rotor and modular structure are only applicable for low-speed applications.

**Figure 26.** Principal stress against speed.

#### *4.13. Copper Losses versus Je at Various Ja*

Copper losses of three FEFSM at various armature current densities is shown in Figure 27. To analyze the total copper losses, FEC current density, *Je*, is set to 10 A/mm2, and armature current density is varied from 0 A/mm2 to 25 A/mm2. Figures 28–30, illustrate copper losses of both armature coil and FEC, in isolation at fixed *Je*, whilst *Ja* changes to maximum. The pattern plot clearly showed that the copper losses are increased with increasing current densities. Comparatively, the proposed modular rotor design shows approximately 56% and 88% lower copper losses to sub-part rotor design and F1-A3-3P design respectively, at a maximum armature current density of 25 A/mm2 as depicted in Figure 27. However, the proposed structure has reduced copper losses, indicating improved efficiency compared with the conventional designs.

**Figure 27.** Copper losses versus various *Ja*.

**Figure 28.** Copper losses of modular rotor design.

**Figure 29.** Copper losses of sub-part rotor design.

**Figure 30.** Copper losses of F1-A3-3P design.

#### *4.14. Iron Loss versus Speed*

Iron loss is a significant portion in the total losses of machine. Machine performance is greatly affected by iron losses due to flux emphasis of novel-modular topology in the stator, which generates a variation of flux densities in the rotor and stator core [17,22]. The flux density variation is expected to be reduced by implementing the novel-modular topology due to the reduction in utilization of the stator. Iron losses are increased with increasing electrical loading due to higher armature reaction [23]. The iron losses of the switched flux machine also vary greatly with speed at every part as shown in Figures 31–33. At low-speed, the machine dominates electromagnetic losses. The method of iron loss calculation can be found in [17,24].

**Figure 31.** Iron loss at various parts of sub-part rotor design.

**Figure 32.** Iron loss at stator and rotor part of F1-A3-3P design.

The iron loss of each component of three-field excited FSM is calculated by 3D-FEA. In Figure 34, the plot clearly shows that the proposed modular rotor structure has lowest iron loss then the conventional sub-part rotor design and F1-A3-3P design. At a maximum speed of 4000 rpm, modular design reduces the iron losses of 29.44% and 7.22% compared with the conventional F1-A3-3P design and sub-part rotor design respectively. The reason for iron loss reduction in the stator is due to the modular rotor, variation of flux densities in the stator-core is investigated in [25].

**Figure 33.** Iron loss at stator and rotor part of modular rotor design.

**Figure 34.** Comparison of iron losses at various speeds.

#### *4.15. Motor Losses and E*ffi*ciency Analysis*

The efficiencies of three FEFSMs are computed by 3D-FEA, considering all motor losses (iron losses in core laminations and copper losses in FEC and armature coil). Copper losses (*Pcu*) are calculated at fixed current densities of 10 A/mm2, for both *FEC*, *Je*, and armature coil, *Ja*, for all designs. Whilst, the iron losses are calculated at varying speed of 1000–4000 rpm. In single phase FEFS machines, copper losses can be illustrated as

$$P\_{\mathbb{C}u} = I\_a^2 R\_u + I\_f^2 R\_f \tag{10}$$

where *Pcu*, *If*, *Rf*, *Ia*, and *Ra* are copper losses, field current, total field coil resistance, armature current, and total armature coil resistance, respectively. Figure 35a–c shows iron losses (*Pi*), copper losses (*Pcu*), output power (*Po*), and efficiency at different speeds (range: 1000–4000 rpm) of sub-part rotor design, F1-A3-3P design, and modular rotor design, respectively. However, with increasing speed the iron losses increase in addition to further degrading efficiency. Furthermore, at every operating speed from 1000 rpm to 4000 rpm, the proposed design achieves comparatively higher efficiencies. At a max speed of 4000 rpm, the iron losses of the proposed modular rotor design are 9% and 30% lower than the conventional sub-part rotor design and F1-A3-3P design, respectively. However, reduction in iron losses shows a significant reduction in total machine losses, approximately 49% of F1-A3-3P design and 15% of sub-part rotor design. Furthermore, by adopting the modular structure, the proposed 8S/6P design achieves a higher average efficiency of approximately 12.8% and 11.4% higher than the

conventional F1-A3-3P and sub-part rotor designs, respectively. Finally, it can be seen from Figure 36 that the efficiency of a single phase modular 8S/4P FEFS machine exhibit higher efficiency than other conventional FEFS machines.

**Figure 35.** (**a**) Losses and efficiency of sub-part rotor design at various speeds. (**b**) Losses and efficiency of F1-A3-3P design at various speeds. (**c**) Losses and efficiency of modular rotor design at various speeds.

**Figure 36.** Comparison of efficiency at various rotor speeds.

#### **5. Conclusions**

A novel single-phase field excited topology of modular rotor flux switching machine is presented and the result is investigated by 3D-FEA.

In this paper, a comparison of single-phase eight-slot/four-pole sub rotor design and six-slot/three-pole salient rotor design with a novel modular rotor eight-slot/six-pole FSM is demonstrated. For comparison of flux linkage, cogging torque, average torque, and other different analyses of proposed FEFSMs, an optimal split ratio is set identical to the conventional designs.

The performance comparison of the three different types of single-phase eight-slot/four-pole sub rotor design and six-slot/three-pole salient rotor designs with a novel modular rotor eight-slot/six-pole FSM is demonstrated. he optimal split ratio is kept the same as the conventional designs for comparison of flux linkage, cogging torque, average torque, and other analyses of the proposed FSM. The initial design achieved inadequate power and torque production. Therefore, a deterministic optimization technique was adopted to improve the characteristics. The optimized design enhanced power, torque, and efficiency compared to existing eight-slot/four-pole and six-slot/three-pole FESF machines.

Novel modular 8S/6P single phase FSM with non-overlapped winding arrangement is designed. Copper consumption of modular rotor design is much lower than conventional designs that is 90% lower than F1-A3-3P and 56% than sub-part rotor design, at *Ja* = 25 A/mm2, due to non-overlap winding between FEC and armature coil. The proposed design shows a higher average output torque when compared under constraints of fixed copper losses. Modular rotor structure also exhibits a significant reduction in iron losses, 30% as compared to F1-A3-3P and 9% reduced when compared with sub-part rotor design. Due to the modular structure of the rotor, the active rotor mass of the proposed design is reduced and the use of stator back-iron is lowered without diminishing torque output. This research also examines the principal rotor stress of the conventional rotor designs (sub-part rotor design and three-pole salient rotor design) and proposed (modular) rotor design with a different direction of constraints. Additionally, average efficiency of proposed modular design is increased by 12.8% compared with F1-A3-3P design and 11.4% compared with sub-part rotor design. Hence, the proposed motor is suitable for pedestal fan application by replacing induction machine. The proposed design has not yet been comprehensively analyzed and will be examined in our future work.

**Author Contributions:** Conceptualization, L.U.R. and F.K.; methodology, M.S.; software, H.A.K.; validation, N.A., L.U.R.; investigation, L.U.R.; resources, F.K.; data curation, H.A.K.; writing—original draft preparation, L.U.R.; writing—review and editing, L.U.R.; visualization, S.A.; supervision, F.K.; project administration, M.A.K.; funding acquisition, L.U.R., F.K., and H.A.

**Funding:** There is no external funding.

**Acknowledgments:** This work was supported by COMSATS University Islamabad, Abbottabad Campus and Higher Education Commission of Pakistan (No 8114/KPK/NRPU/R&D/HEC/2017).

**Conflicts of Interest:** The authors declare no conflict of interest.

#### **References**


© 2019 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

#### *Article*
