# A General Mathematical Formulation for Winding Layout Arrangement of Electrical Machines

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## Abstract

**:**

## 1. Introduction

## 2. Symmetry Conditions for Winding Design

## 3. WDT Procedure

#### 3.1. Determination of WDT

#### 3.2. WDT Post-Processing

#### 3.3. WDT for Symmetrical Non-Reduced and Normal Systems

#### 3.4. WDT for Reduced Systems

#### 3.5. WDT for Single-Phase Systems

## 4. Examples and Procedure Validation

#### 4.1. 3-Phase Windings

#### 4.2. 6-Phase Windings

#### 4.3. 2-Phase Winding

#### 4.4. 7-Phase Winding

#### 4.5. Procedures for Winding Optimization

- the WDT is developed;
- the zone widening by two slots is performed by shifting the vertical line from the middle position to the right by two cells;
- the double sided imbrication is made by shifting upwards by two cells the 2-nd, the 4-th and the 6-th negative columns.

- For normal or non-reduced system windings the columns of positive slots that are to be shifted are shifted upwards by$${s}_{pos}=\left\{\begin{array}{cc}\frac{m+1}{2}\hfill & \mathrm{if}\phantom{\rule{0.166667em}{0ex}}m\in \mathbb{U}\hfill \\ \frac{m}{2}\hfill & \mathrm{if}\phantom{\rule{0.166667em}{0ex}}m\in \mathbb{G}\hfill \end{array}\right.$$$${s}_{neg}=\left\{\begin{array}{cc}\frac{m+1}{2}\hfill & \mathrm{if}\phantom{\rule{0.166667em}{0ex}}m\in \mathbb{U}\hfill \\ \frac{m+2}{2}\hfill & \mathrm{if}\phantom{\rule{0.166667em}{0ex}}m\in \mathbb{G}\hfill \end{array}\right.$$
- For reduced system windings both the positive and the negative columns are to be shifted always upwards by 1 cell, i.e.,$${s}_{pos}=1\phantom{\rule{0.277778em}{0ex}}\phantom{\rule{0.277778em}{0ex}}\mathrm{and}\phantom{\rule{0.277778em}{0ex}}\phantom{\rule{0.277778em}{0ex}}{s}_{neg}=1$$The sign of the cells at the bottom of each shifted column must be then changed.

## 5. Conclusions

## Acknowledgments

## Author Contributions

## Conflicts of Interest

## Nomenclature

N | nr. of slots; |

m | nr. of phases; |

p | nr. of pole pairs; |

${n}_{wc}$ | nr. of wound coils per phase; |

${n}_{lay}$ | nr. of winding layers; |

${n}_{es}$ | nr. of empty slots; |

Q | nr. of slots per pole per phase; |

q | nr. of wound slots per pole per phase; |

t | greatest common divider between N and p; |

${y}_{c}$ | coil pitch (or coil span); |

$\mathbb{N}$ | the set of natural numbers; |

$\mathbb{G}$ | the set of even numbers; |

$\mathbb{U}$ | the set of odd numbers. |

## Appendix A

^{®}code for populating WDT is here reported.

M=zeros(1,N); i=1; while i<=N ind=mod(p*(i-1)+1,N); if ind==0 ind=N; end while M(ind)~=0 ind=ind+1; end M(ind)=i; i=i+1; ind=ind+1; end display(M); M1=zeros(m,2/n_lay*n_wc); for i=1:m M1(i,:)=M(2/n_lay*n_wc*(i-1)+1:2/n_lay*n_wc*i); end

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**Figure 2.**Winding schemes with different end winding layouts for a single-layer configuration with $N=24$, $m=3$, $p=2$ and $q=2$ derived from the WDT. (

**a**) Without end connections; (

**b**) for a split stator and three-plane end winding; (

**c**) with two-plane end winding and (

**d**) with three-plane end winding.

**Figure 3.**WDT for a generic normal system winding. The right side of WDT is shifted upwards by $\zeta $ steps.

**Figure 6.**(

**a**) Slot EMF star for a symmetrical single-layer coil winding and (

**b**) winding scheme. $N=27$, $m=3$, $p=3$, $Q=1+\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$2$}\right.$ and $q=2$.

**Figure 7.**(

**a**) Slot EMF star for a symmetrical single-layer bar winding and (

**b**) winding scheme. $N=27$, $m=3$, $p=3$ and $q=1+\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$2$}\right.$.

**Figure 8.**(

**a**) Coil EMF star for a symmetrical double-layer coil winding and (

**b**) winding scheme with series connected paths. $N=27$, $m=3$, $p=3$, $q=1+\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$2$}\right.$ and ${y}_{c}=4$.

**Figure 9.**(

**a**) Star of slots and (

**b**) winding configuration for a double-layer, three-phase concentrated winding with $N=9$, $p=4$ and $m=3$.

**Figure 10.**(

**a**) EMF star and (

**b**) winding scheme for a symmetrical single layer non-reduced winding with $N=36$, $m=6$, $p=5$ and $q=\raisebox{1ex}{$3$}\!\left/ \!\raisebox{-1ex}{$5$}\right.$.

**Figure 11.**(

**a**) EMF star and (

**b**) winding scheme of a double layer reduced symmetrical configuration with $N=36$, $m=6$, $p=5$ and $q=\raisebox{1ex}{$3$}\!\left/ \!\raisebox{-1ex}{$5$}\right.$.

**Figure 12.**(

**a**) Star of coils EMF and (

**b**) Winding scheme for $N=28$, $m=2$, $p=1$, $q=7$ and ${y}_{c}=12$.

**Figure 13.**Double layer seven-phase symmetrical winding with $N=42$, $p=2$, $m=7$, ${y}_{c}=9$ and $q=1+\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$2$}\right.$. (

**a**) Star of slots and (

**b**) winding scheme.

**Figure 14.**Three-phase symmetrical winding with $N=72$, $p=5$, $m=3$ and $q=2+\raisebox{1ex}{$2$}\!\left/ \!\raisebox{-1ex}{$5$}\right.$. (

**a**) Star of slots and (

**b**) winding scheme.

**Figure 15.**Double chording with a 3rd-order single-sided imbrication for $N=72$, $p=5$, $m=3$ and $q=2+\raisebox{1ex}{$2$}\!\left/ \!\raisebox{-1ex}{$5$}\right.$. (

**a**) Star of slots and (

**b**) winding scheme.

**Figure 16.**Double chording with a 3rd-order double-sided imbrication for $N=72$, $p=5$, $m=3$ and $q=2+\raisebox{1ex}{$2$}\!\left/ \!\raisebox{-1ex}{$5$}\right.$. (

**a**) Star of slots and (

**b**) winding scheme.

**Figure 17.**Single phase winding with double chording, 2nd order double-sided imbrication for $N=60$, $p=1$, $m=1$ and $q=30$. (

**a**) Star of slots and (

**b**) winding scheme.

**Figure 18.**(

**a**) Star of slots of a 6-phase reduced single-layer winding with $N=96$, $p=5$ and (

**b**) related winding scheme with 1-st order double sided imbrication.

col. 1 | col. 2 | … | col. ${\mathit{n}}_{\mathit{c}}$ | |
---|---|---|---|---|

row 1 | 1 | 2 | … | ${n}_{c}$ |

row 2 | ${n}_{c}+1$ | ${n}_{c}+2$ | … | $2{n}_{c}$ |

row 3 | $2{n}_{c}+1$ | $2{n}_{c}+2$ | … | $3{n}_{c}$ |

⋮ | ⋮ | ⋮ | ⋱ | ⋮ |

row m | $(m-1){n}_{c}+1$ | $(m-1){n}_{c}+2$ | … | $m{n}_{c}$ |

1 | 13 | 2 | 14 | 3 | 15 | 4 | 16 |

5 | 17 | 6 | 18 | 7 | 19 | 8 | 20 |

9 | 21 | 10 | 22 | 11 | 23 | 12 | 24 |

**Table 3.**Electrical angles of the star of slots ($j=1,\phantom{\rule{0.277778em}{0ex}}\dots ,\phantom{\rule{0.277778em}{0ex}}t$).

${\mathit{\phi}}_{\mathit{k}}$ | 0° | $\mathit{\alpha}$ | $2\mathit{\alpha}$ | ⋯ | $\left(\raisebox{1ex}{$\mathit{N}$}\!\left/ \!\raisebox{-1ex}{$\mathit{t}$}\right.-1\right)\mathit{\alpha}$ |
---|---|---|---|---|---|

1-st row | 1 | 2 | 3 | ⋯ | $\raisebox{1ex}{$N$}\!\left/ \!\raisebox{-1ex}{$t$}\right.$ |

⋮ | ⋮ | ⋮ | ⋮ | ⋱ | ⋮ |

t-th row | $\left(j-1\right)\raisebox{1ex}{$N$}\!\left/ \!\raisebox{-1ex}{$t$}\right.+1$ | $\left(j-1\right)\raisebox{1ex}{$N$}\!\left/ \!\raisebox{-1ex}{$t$}\right.+2$ | $\left(j-1\right)\raisebox{1ex}{$N$}\!\left/ \!\raisebox{-1ex}{$t$}\right.+3$ | ⋯ | N |

Electr. Angles ${\mathit{\phi}}_{\mathit{k}}$ | 0° | 30° | 60° | 90° | 120° | 150° | 180° | 210° | 240° | 270° | 300° | 330° |
---|---|---|---|---|---|---|---|---|---|---|---|---|

Phasor pairs | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 |

13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 | 21 | 22 | 23 | 24 |

**Table 5.**Winding Distribution Table with ${t}^{\prime}=2$ repetitions, for a winding with $N=24$, $p=2$ and $m=3$.

1 | 2 | 3 | 4 | 13 | 14 | 15 | 16 | |

5 | 6 | 7 | 8 | + | 17 | 18 | 19 | 20 |

9 | 10 | 11 | 12 | 21 | 22 | 23 | 24 |

**Table 6.**Reordering of the rows of a WDT for an m-phase reduced system winging with $m\in \mathbb{G}$.

Phases | col. 1 | col. 1 | … | col. ${\mathit{n}}_{\mathit{c}}$ | Phases | col. 1 | col. 1 | … | col. ${\mathit{n}}_{\mathit{c}}$ | |
---|---|---|---|---|---|---|---|---|---|---|

1 | … | … | … | … | 1 | … | … | … | … | |

⋮ | ⋮ | ⋮ | ⋱ | … | $\frac{m}{2}+1$ | … | … | … | … | |

2 | … | … | … | … | ||||||

$\frac{m}{2}$ | … | … | … | … | $\phantom{\rule{0.277778em}{0ex}}\Rightarrow \phantom{\rule{0.277778em}{0ex}}$ | $\frac{m}{2}+2$ | … | … | … | … |

$\frac{m}{2}+1$ | … | … | … | … | ⋮ | ⋮ | ⋮ | ⋱ | … | |

⋮ | ⋮ | ⋮ | ⋱ | … | $\frac{m}{2}$ | … | … | … | … | |

m | … | … | … | … | m | … | … | … | … |

1 | 10 | 19 | 2 | 11 | −20 | −3 | −12 | −21 | $\phantom{\rule{0.277778em}{0ex}}\phantom{\rule{0.277778em}{0ex}}\Uparrow \phantom{\rule{0.277778em}{0ex}}\zeta =1$ |

4 | 13 | 22 | 5 | 14 | −23 | −6 | −15 | −24 | |

7 | 16 | 25 | 8 | 17 | −26 | −9 | −18 | −27 |

1 | 2 | −3 | + | 10 | 11 | −12 | + | 19 | 20 | −21 | = | 1 | 2 | 7 | 8 | 19 | 20 | −3 | −12 | −21 | $\phantom{\rule{0.277778em}{0ex}}\phantom{\rule{0.277778em}{0ex}}\Uparrow \phantom{\rule{0.277778em}{0ex}}\zeta =1$ |

4 | 5 | −6 | 13 | 14 | −15 | 22 | 23 | −24 | 4 | 5 | 13 | 14 | 22 | 23 | −6 | −15 | −24 | ||||

7 | 8 | −9 | 16 | 17 | −18 | 25 | 26 | −27 | 7 | 8 | 16 | 17 | 25 | 26 | −9 | −18 | −27 |

**Table 10.**WDT for a double-layer, three-phase winding with $N=27$, $m=3$ and $p=3$ considering all coil sides.

1 | −5 | 2 | −6 | 7 | −11 | 8 | −12 | 19 | −25 | 20 | −24 | −6 | 10 | −15 | 19 | −24 | 1 |

4 | −8 | 5 | −9 | 13 | −17 | 14 | −18 | 22 | −26 | 23 | −27 | −9 | 13 | −18 | 22 | −27 | 4 |

7 | −11 | 8 | −12 | 16 | −20 | 17 | −21 | 25 | −2 | 26 | −3 | −3 | 7 | −12 | 16 | −21 | 25 |

1 | 8 | −6 | ⟹ | 1 | 8 | −9 | ⟹ | 8 | −9 | 1 | ⟹ | 8 | −9 | −9 | 1 | 1 | −2 |

4 | 2 | −9 | 4 | 2 | −3 | 2 | −3 | 4 | 2 | −3 | −3 | 4 | 4 | −5 | |||

7 | 5 | −3 | 7 | 5 | −6 | 5 | −6 | 7 | 5 | −6 | −6 | 7 | 7 | −8 |

**Table 12.**Winding Distribution Table for a symmetrical non-reduced winding with $N=36$, $m=6$, $p=5$ and $q=\raisebox{1ex}{$3$}\!\left/ \!\raisebox{-1ex}{$5$}\right.$.

1 | 30 | 23 | −16 | −9 | −2 | $\phantom{\rule{0.277778em}{0ex}}\phantom{\rule{0.277778em}{0ex}}\Uparrow \phantom{\rule{0.277778em}{0ex}}\zeta =2$ |

31 | 24 | 17 | −10 | −3 | −32 | |

25 | 18 | 11 | −4 | −33 | −26 | |

19 | 12 | 5 | −34 | −27 | −20 | |

13 | 6 | 35 | −28 | −21 | −14 | |

7 | 36 | 29 | −22 | −15 | −8 |

**Table 13.**Winding Distribution Table for a symmetrical reduced winding with $N=36$, $m=6$, $p=5$ and $q=\raisebox{1ex}{$3$}\!\left/ \!\raisebox{-1ex}{$5$}\right.$.

1 | 2 | 3 | 4 | 5 | 6 | 7 | −15 | −16 | −17 | −18 | −19 | −20 | −21 |

8 | 9 | 10 | 11 | 12 | 13 | 14 | −22 | −23 | −24 | −25 | −26 | −27 | −28 |

1 | 2 | −3 | + | 22 | 23 | −24 | = | 1 | 22 | 2 | 23 | −3 | −24 | $\phantom{\rule{0.277778em}{0ex}}\phantom{\rule{0.277778em}{0ex}}\Uparrow \phantom{\rule{0.277778em}{0ex}}\zeta =3$ |

4 | 5 | −6 | 25 | 26 | −27 | 4 | 25 | 5 | 26 | −6 | −27 | |||

7 | 8 | −9 | 28 | 29 | −30 | 7 | 28 | 8 | 29 | −9 | −30 | |||

10 | 11 | −12 | 31 | 32 | −33 | 10 | 31 | 11 | 32 | −12 | −33 | |||

13 | 14 | −15 | 34 | 35 | −36 | 13 | 34 | 14 | 35 | −15 | −36 | |||

16 | 17 | −18 | 37 | 38 | −39 | 16 | 37 | 17 | 38 | −18 | −39 | |||

19 | 20 | −21 | 40 | 41 | −42 | 19 | 40 | 20 | 41 | −21 | −42 |

**Table 16.**Winding Distribution Table for a winding with $N=72$, $p=5$, $m=3$ and $q=2+\raisebox{1ex}{$2$}\!\left/ \!\raisebox{-1ex}{$5$}\right.$.

1 | 30 | 59 | 16 | 45 | 2 | 31 | 60 | 17 | 46 | 3 | 32 | −37 | −66 | −23 | −52 | −9 | −38 | −67 | −24 | −53 | −10 | −39 | −68 |

49 | 6 | 35 | 64 | 21 | 50 | 7 | 36 | 65 | 22 | 51 | 8 | −13 | −42 | −71 | −28 | −57 | −14 | −43 | −72 | −29 | −58 | −15 | −44 |

25 | 54 | 11 | 40 | 69 | 26 | 55 | 12 | 41 | 70 | 27 | 56 | −61 | −18 | −47 | −4 | −33 | −62 | −19 | −48 | −5 | −34 | −63 | −20 |

**Table 17.**Double chording with a 3-rd order single-sided imbrication for $N=72$, $p=5$, $m=3$ and $q=2+\raisebox{1ex}{$2$}\!\left/ \!\raisebox{-1ex}{$5$}\right.$.

1 | −54 | 59 | −40 | 45 | −26 | 31 | 60 | 17 | 46 | 3 | 32 | 61 | 18 | 47 | −52 | −9 | −38 | −67 | −24 | −53 | −10 | −39 | −68 |

49 | −30 | 35 | −16 | 21 | −2 | 7 | 36 | 65 | 22 | 51 | 8 | 37 | 66 | 23 | −28 | −57 | −14 | −43 | −72 | −29 | −58 | −15 | −44 |

25 | −6 | 11 | −64 | 69 | −50 | 55 | 12 | 41 | 71 | 27 | 56 | 13 | 42 | 71 | −4 | −33 | −62 | −19 | −48 | −5 | −34 | −63 | −20 |

↑ | ↑ | ↑ | ↑ | ↑ | ↑ |

**Table 18.**Double chording with a 3-rd order double-sided imbrication for $N=72$, $p=5$, $m=3$ and $q=2+\raisebox{1ex}{$2$}\!\left/ \!\raisebox{-1ex}{$5$}\right.$.

1 | −54 | 59 | −40 | 45 | −26 | 31 | 60 | 17 | 46 | 3 | 32 | −37 | 18 | −23 | 4 | −9 | 62 | −67 | −24 | −53 | −10 | −39 | −68 |

49 | −30 | 35 | −16 | 21 | −2 | 7 | 36 | 65 | 22 | 51 | 8 | −13 | 66 | −71 | 52 | −57 | 38 | −43 | −72 | −29 | −58 | −15 | −44 |

25 | −6 | 11 | −64 | 69 | −50 | 55 | 12 | 41 | 71 | 27 | 56 | −61 | 42 | −47 | 28 | −33 | 14 | −19 | −48 | −5 | −34 | −63 | −20 |

↑ | ↑ | ↑ | ↑ | ↑ | ↑ |

**Table 19.**Triple chording with a 3-rd order double-sided imbrication and zone widening by 2 coils for $N=72$, $p=5$, $m=3$ and $q=2+\raisebox{1ex}{$2$}\!\left/ \!\raisebox{-1ex}{$5$}\right.$.

1 | −54 | 59 | −40 | 45 | −26 | 31 | 60 | 17 | 46 | 3 | 32 | 61 | 18 | −23 | 4 | −9 | 62 | −67 | 48 | −53 | −10 | −39 | −68 |

49 | −30 | 35 | −16 | 21 | −2 | 7 | 36 | 65 | 22 | 51 | 8 | 37 | 66 | −71 | 52 | −57 | 38 | −43 | 24 | −29 | −58 | −15 | −44 |

25 | −6 | 11 | −64 | 69 | −50 | 55 | 12 | 41 | 71 | 27 | 56 | 13 | 42 | −47 | 28 | −33 | 14 | −19 | 72 | −5 | −34 | −63 | −20 |

↑ | ↑ | ↑ | ↑ | ↑ | ↑ |

**Table 20.**Winding factor harmonics with different optimization techniques for $N=72$, $p=5$, $m=3$ and $q=2+\raisebox{1ex}{$2$}\!\left/ \!\raisebox{-1ex}{$5$}\right.$.

Normal Chording | Double Chording | Triple Chording | |||
---|---|---|---|---|---|

Harm. Order | WDT (${\mathit{y}}_{\mathit{c}}=\mathbf{7}$) | Chording (${\mathit{y}}_{\mathit{c}}=\mathbf{6}$) | 1-Sided Imbric. | 2-Sided Imbric. | 2-Sided Imbric. + Zone Widen. |

1-st | 0.955 | 0.923 | 0.902 | 0.881 | 0.878 |

3-rd | 0.633 | 0.451 | 0.365 | 0.277 | 0.268 |

5-th | 0.201 | 0.154 | 0.026 | 0.002 | 0.002 |

7-th | 0.132 | 0.036 | 0.008 | 0.020 | 0.017 |

9-th | 0.201 | 0.154 | 0.013 | 0.154 | 0.109 |

11-th | 0.080 | 0.087 | 0.078 | 0.072 | 0.055 |

**Table 21.**WDT with a double chording and a 3-rd order double-sided imbrication for $N=60$, $p=1$, $m=1$ and $q=30$.

1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | −11 | −12 | −13 | −14 | −15 | −16 | −17 | −18 | −19 | −20 |

21 | 22 | 23 | 24 | 25 | 26 | 27 | 28 | 29 | 30 | −31 | −32 | −33 | −34 | −35 | −36 | −37 | −38 | −39 | −40 |

41 | 42 | 43 | 44 | 45 | 46 | 47 | 48 | 49 | 50 | −51 | −52 | −53 | −54 | −55 | −56 | −57 | −58 | −59 | −60 |

**Table 22.**WDT with a double chording and a 3-rd order double-sided imbrication for $N=60$, $p=1$, $m=1$ and $q=30$.

**Table 23.**Winding factor harmonics with different optimization techniques for $N=60$, $p=1$ and $m=1$.

Harmonic Order | WDT (${\mathit{y}}_{\mathit{c}}=30$) | Chording (${\mathit{y}}_{\mathit{c}}=24$) | Single-Sided Imbrication | Double-Sided Imbrication |
---|---|---|---|---|

1-st | 0.827 | 0.787 | 0.778 | 0.761 |

3-rd | 0 | 0 | 0 | 0 |

5-th | 0.167 | 0 | 0 | 0 |

7-th | 0.121 | 0.071 | 0.035 | 0.20 |

9-th | 0 | 0 | 0 | 0 |

11-th | 0.080 | 0.076 | 0.014 | 0.087 |

**Table 24.**WDT of a 6-phase reduced winding with $N=96$, $p=5$, $q=1+\raisebox{1ex}{$2$}\!\left/ \!\raisebox{-1ex}{$10$}\right.$.

1 | 30 | 59 | 16 | 45 | 2 | 31 | 60 | 17 | 46 | 3 | 32 |

61 | 18 | 47 | 4 | 33 | 62 | 19 | 48 | 5 | 34 | 63 | 20 |

49 | 6 | 35 | 64 | 21 | 50 | 7 | 36 | 65 | 22 | 51 | 8 |

37 | 66 | 23 | 52 | 9 | 38 | 67 | 24 | 53 | 10 | 39 | 68 |

25 | 54 | 11 | 40 | 69 | 26 | 55 | 12 | 41 | 70 | 27 | 56 |

13 | 42 | 71 | 28 | 57 | 14 | 43 | 72 | 29 | 58 | 15 | 44 |

**Table 25.**WDT of a 6-phase reduced winding with $N=96$, $p=5$, $q=1+\raisebox{1ex}{$2$}\!\left/ \!\raisebox{-1ex}{$10$}\right.$, after swapping.

1 | 30 | 59 | 16 | 45 | 2 | −37 | −66 | −23 | −52 | −9 | −38 |

31 | 60 | 17 | 46 | 3 | 32 | −67 | −24 | −53 | −10 | −39 | −68 |

61 | 18 | 47 | 4 | 33 | 62 | −25 | −54 | −11 | −40 | −69 | −26 |

19 | 48 | 5 | 34 | 63 | 20 | −55 | −12 | −41 | −70 | −27 | −56 |

49 | 6 | 35 | 64 | 21 | 50 | −13 | −42 | −71 | −28 | −57 | −14 |

7 | 36 | 65 | 22 | 51 | 8 | −43 | −72 | −29 | −58 | −15 | −44 |

↑ | ↑ |

**Table 26.**WDT of a 6-phase reduced winding with $N=96$, $p=5$, $q=1+\raisebox{1ex}{$2$}\!\left/ \!\raisebox{-1ex}{$10$}\right.$, and double sided imbrication of the 1-st order.

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**MDPI and ACS Style**

Caruso, M.; Di Tommaso, A.O.; Marignetti, F.; Miceli, R.; Ricco Galluzzo, G. A General Mathematical Formulation for Winding Layout Arrangement of Electrical Machines. *Energies* **2018**, *11*, 446.
https://doi.org/10.3390/en11020446

**AMA Style**

Caruso M, Di Tommaso AO, Marignetti F, Miceli R, Ricco Galluzzo G. A General Mathematical Formulation for Winding Layout Arrangement of Electrical Machines. *Energies*. 2018; 11(2):446.
https://doi.org/10.3390/en11020446

**Chicago/Turabian Style**

Caruso, Massimo, Antonino Oscar Di Tommaso, Fabrizio Marignetti, Rosario Miceli, and Giuseppe Ricco Galluzzo. 2018. "A General Mathematical Formulation for Winding Layout Arrangement of Electrical Machines" *Energies* 11, no. 2: 446.
https://doi.org/10.3390/en11020446