**2. Presentation of the magnetic speed multiplier**

The principle of the magnetic speed reducer or multiplier is now well known, but the use of this type of converter is uncommon and usually reserved for low power [3-6]. We will show why the transmission of substantial power with very low wind turbine operating speed is useful.

The operation of the speed multiplier is based, firstly, on the principle of a Vernier type teeth coupling [1,2,10] between a series of alternating permanent magnets and a series of magnetic teeth. The following diagram, which represents a cylindrical or discoid devel‐ oped structure, demonstrates the principle used in the calculation of the magnetic field in the air gap. In this device, a series of 2.Nr alternating permanent magnets, config‐ ured around a rotor, moves before a series of Ns magnetic teeth around a stator. The number Ns is different to Nr.

high speed (Nh) shaft

synchronous generator Turbine

gearbox

m phases

DC

DC AC

high frequency high speed rectifier

permanent magnet

Indirect drive

**Advances in Wind Power – Chapter X** 

Figure 1. Linking the wind turbine to the generator

low speed (Nl

shaft

)

**Design of a Mean Power Wind Conversion Chain with a Magnetic** 

**Speed Multiplier** 

Daniel MATT, *Institut d'Electronique du Sud - Université Montpellier 2 Place Eugène Bataillon - 34095 Montpellier Cedex 5 – France matt@univ-montp2.fr* Julien JAC, *Société ERNEO SAS Cap Alpha - Avenue de l'Europe - 34830 Clapiers – France Julien.jac@erneo.fr* Nicolas Ziegler, *Société ERNEO SAS Cap Alpha - Avenue de l'Europe - 34830 Clapiers – France Nicolas.ziegler@erneo.fr*

**Figure 2.** Cross-section of a Vernier machine with distributed windings

DC

DC AC

 s Ll = a/l e l1 l The calculation of the magnetic field at a point M, anywhere in the air gap, requires the azi‐ muthal coordinates, θs and θr, identified respectively relative to the axis Ds, linked to the sta‐ tor, and Dr, linked to the rotor. The angle, θ, between the two axes is a function of time.

dimensions of the pattern adimensional parameters

 sl1L el L a The wave of flux density in the air gap, ba(θs, θ), created by the permanent magnets, is de‐ duced from the following equation:

$$b\_a(\theta\_{s'}, \theta) \, := \mathsf{P}(\theta\_s) \cdot \varepsilon\_a(\theta\_{s'}, \theta) \tag{1}$$

where εa(θs, θ) represents the scalar magnetic potential associated with the permanent mag‐ nets and P(θs) represents the density of the air gap permeance modulated by the magnetic teeth. We retain only the initial harmonics of these waves.

$$\varepsilon\_a(\theta\_s, \theta) = \varepsilon\_1 \cdot \cos \mathcal{N}\_{\mathbf{r}}(\theta\_s - \theta) \tag{2}$$

$$\mathbf{P} = \mathbf{P}\_0 + \mathbf{P}\_{1s} \cdot \cos(\mathbf{N}\_s \theta\_s) \tag{3}$$

The multiplication leads to:

Figure 3. Elementary domain; tooth coupling

m phases

Direct drive

high frequency low speed rectifier

direct-driven permanent magnet synchronous generator

Turbine

have

A

low speed (Nl

shaft

)

The second, more recent, alternative is to link the generator directly to the turbine without a mechanical intermediary [8]. This method is known as "direct drive" and has become eco‐ nomically viable in recent years thanks to the progress made on permanent magnets. The cost of permanent magnets has dropped significantly while their performance has continued to improve. They have enabled the design of high performance, high power density, syn‐ chronous machines, well suited to the low speed operation imposed by the wind sensor, at

The direct-drive method is attractive because it eliminates the weak element of the conver‐ sion chain: the speed multiplier gearbox. This is indeed a frequent source of failure, an addi‐ tional noise source and may also require regular maintenance, resulting in high operating costs [8,9]. Finally, the multiplier can be the source of chemical pollution due to the lubricant oil. This explains why the latter option is widely preferred in the installation of small and medium size wind turbines for domestic applications, which are intended for operation over

Above a certain power level, typically 10 kW, both methods become competitive in terms of

As part of a medium-power design, there is a third method which offers an interesting alter‐ native to the mechanical speed multiplier: the use of a magnetic gear [3-7]. This chapter, then, is devoted to the description of this device and shows the utility and feasibility of such a wind conversion chain. The different magnetic multiplier structures are presented and the

The advantage of the magnetic speed multiplier over its mechanical counterpart is clearly the contact-free force transmission that enables operation without any maintenance. We also show that the size and efficiency of magnetic speed multiplier are not prohibitive for the in‐

The principle of the magnetic speed reducer or multiplier is now well known, but the use of this type of converter is uncommon and usually reserved for low power [3-6]. We will show why the transmission of substantial power with very low wind turbine operating speed is

The operation of the speed multiplier is based, firstly, on the principle of a Vernier type teeth coupling [1,2,10] between a series of alternating permanent magnets and a series of magnetic teeth. The following diagram, which represents a cylindrical or discoid devel‐ oped structure, demonstrates the principle used in the calculation of the magnetic field in the air gap. In this device, a series of 2.Nr alternating permanent magnets, config‐ ured around a rotor, moves before a series of Ns magnetic teeth around a stator. The

cost; only a fine techno-economic study would tip the balance one way or the other.

design of this device will allow comparison with traditional solutions.

**2. Presentation of the magnetic speed multiplier**

reasonable cost.

248 Advances in Wind Power

tended application.

number Ns is different to Nr.

useful.

a long time without maintenance.

$$\boldsymbol{b}\_{\boldsymbol{\varrho}}(\boldsymbol{\theta}\_{\boldsymbol{s}},\boldsymbol{\theta}) = \mathbb{W} \boldsymbol{\varepsilon}\_{1} \cdot \mathbf{P}\_{1\boldsymbol{s}} \cdot \cos(\left(\boldsymbol{N}\_{\boldsymbol{s}} - \boldsymbol{N}\_{\boldsymbol{r}}\right) \boldsymbol{\theta}\_{\boldsymbol{s}} + \boldsymbol{N}\_{\boldsymbol{r}} \boldsymbol{\theta}) \\ \quad + \mathbb{W} \boldsymbol{\varepsilon}\_{1} \cdot \mathbf{P}\_{1\boldsymbol{s}} \cdot \cos(\left(\boldsymbol{N}\_{\boldsymbol{s}} + \boldsymbol{N}\_{\boldsymbol{r}}\right) \boldsymbol{\theta}\_{\boldsymbol{s}} - \boldsymbol{N}\_{\boldsymbol{r}} \boldsymbol{\theta}) \\ \quad + \mathbb{\varepsilon}\_{1} \cdot \mathbf{P}\_{0} \cdot \cos N \mathbf{r} (\boldsymbol{\theta}\_{\boldsymbol{s}} - \boldsymbol{\theta}) \tag{4}$$

The second term is without practical interest, its periodicity, 2π/|Ns+Nr|, is too small for its implementation in a synchronous coupling with another magnetic field.

The third term, of a periodicity of 2π/Nr, is quite simply linked to the distribution of the per‐ manent magnets, and thus holds no interest for us in the mode of Vernier coupling as de‐ fined here.

We shall consider, then, only the first term, which is in fact the fundamental. Its periodicity, 2π/|Ns-Nr|, is characteristic of the Vernier effect:

Direct drive

direct-driven permanent magnet

Turbine

have

A

low speed (Nl

shaft

)

$$b\_a(\theta\_s, \theta) = b\_{a1} \cdot \cos(\left(N\_s - N\_r\right) \cdot \theta\_s + N\_r \theta), \text{ with } b\_{a1} = b2 \cdot \varepsilon\_1 \cdot \mathbf{P}\_{1s} \tag{5}$$

)

**Advances in Wind Power – Chapter X** 

m phases

high speed (Nh

shaft

gearbox

)

Indirect drive

DC

DC

x

AC

Taking θ = Ωr.t, the term appears as a wave rotating at a speed of Nr.Ωr/|Ns-Nr| = kv. Ωr, the coefficient kv is known as the Vernier ratio. synchronous generator synchronous generator Turbine

low speed (Nl

shaft

DC

DC

**Design of a Mean Power Wind Conversion Chain with a Magnetic** 

**Speed Multiplier** 

Daniel MATT, *Institut d'Electronique du Sud - Université Montpellier 2 Place Eugène Bataillon - 34095 Montpellier Cedex 5 – France matt@univ-montp2.fr* Julien JAC, *Société ERNEO SAS Cap Alpha - Avenue de l'Europe - 34830 Clapiers – France Julien.jac@erneo.fr* Nicolas Ziegler, *Société ERNEO SAS Cap Alpha - Avenue de l'Europe - 34830 Clapiers – France Nicolas.ziegler@erneo.fr*

With small sized permanent magnets (Nr large) it is possible to have a high speed ratio be‐ tween the magnetic field rotation speed and the rotor rotation speed. It is this phenomenon which is used to design the speed multiplier. The main physical limitation of the process is that the smaller the magnets, the smaller the field ba1, as a result of not being able to reduce the air gap sufficiently. Figure 1. Linking the wind turbine to the generator stator magnetic slot y Dr Ds <sup>r</sup> s s

In the Vernier structure, provided that the number of magnetic teeth or permanent magnets is large, the pitch τs, seems to be little different from pitch τrs, it is then possible to isolate a pseudo repeat pattern, characteristic of the magnetic interaction between a tooth and two magnets. This pattern is fully defined by four adimensional parameters, α, Λ, s, ε, as shown in the figure 3. low speed rotor permanent magnet rs <sup>M</sup> Ns magnetic slots 2.Nr permanent magnets

Figure 3. Elementary domain; tooth coupling **Figure 3.** Elementary domain; tooth coupling

A parametric study conducted on the elementary pattern [1,10] allows us to quantify the amplitude of the first harmonic of the flux density, ba1.

It is thus demonstrated, in [1], that ba1 that can be expressed as:

$$b\_{a1} = \frac{\alpha \cdot \Lambda}{\left(\varepsilon + \alpha\right)^2} \cdot \frac{k\_s}{\pi} \cdot B\_{ar} \tag{6}$$

where Bar represents the remanent magnetization of the permanent magnet.

A first approximation of the teeth coupling coefficient, ks, obtained through numerical calcu‐ lation of the magnetic fields, depends only on the adimensional parameters (α, Λ), and is given in the figure 4.

Figure 4. Variation of the coupling coefficient in terms of α and Λ **Figure 4.** Variation of the coupling coefficient in terms of α and Λ

( ) <sup>1</sup> 1 11 *as a s r s r a* , ) c( s(o , with ) ½ *<sup>s</sup> b b NN N b*

q

Taking θ = Ωr.t, the term appears as a wave rotating at a speed of Nr.Ωr/|Ns-Nr| = kv. Ωr, the

With small sized permanent magnets (Nr large) it is possible to have a high speed ratio be‐ tween the magnetic field rotation speed and the rotor rotation speed. It is this phenomenon which is used to design the speed multiplier. The main physical limitation of the process is that the smaller the magnets, the smaller the field ba1, as a result of not being able to reduce

Figure 1. Linking the wind turbine to the generator

In the Vernier structure, provided that the number of magnetic teeth or permanent magnets is large, the pitch τs, seems to be little different from pitch τrs, it is then possible to isolate a pseudo repeat pattern, characteristic of the magnetic interaction between a tooth and two magnets. This pattern is fully defined by four adimensional parameters, α, Λ, s, ε, as shown

A parametric study conducted on the elementary pattern [1,10] allows us to quantify the

*s*

×L × ×

A first approximation of the teeth coupling coefficient, ks, obtained through numerical calcu‐ lation of the magnetic fields, depends only on the adimensional parameters (α, Λ), and is

p

( ) *a r* <sup>1</sup> <sup>2</sup>

*<sup>a</sup> b B* a*k*

> e a

where Bar represents the remanent magnetization of the permanent magnet.

+

dimensions of the pattern adimensional parameters

a

l

<sup>M</sup> Ns magnetic slots

s

 q

low speed (Nl

shaft

)

**Design of a Mean Power Wind Conversion Chain with a Magnetic** 

**Speed Multiplier** 

Daniel MATT, *Institut d'Electronique du Sud - Université Montpellier 2 Place Eugène Bataillon - 34095 Montpellier Cedex 5 – France matt@univ-montp2.fr* Julien JAC, *Société ERNEO SAS Cap Alpha - Avenue de l'Europe - 34830 Clapiers – France Julien.jac@erneo.fr* Nicolas Ziegler, *Société ERNEO SAS Cap Alpha - Avenue de l'Europe - 34830 Clapiers – France Nicolas.ziegler@erneo.fr*

+ = ×

e×× *P* (5)

magnetic slot

permanent magnet

2.Nr permanent magnets

= (6)

Ll

= a/l

s l1L

el

high speed (Nh

shaft

synchronous generator Turbine

gearbox

m phases

DC

τ1.Lf.

It is

It is

DC

x

y

AC

high frequency high speed rectifier

permanent magnet

low speed rotor

stator

)

Indirect drive

**Advances in Wind Power – Chapter X** 

q q

m phases

250 Advances in Wind Power

Direct drive

high frequency low speed rectifier

direct-driven permanent magnet synchronous generator

Turbine

have

A

low speed (Nl

shaft

)

the air gap sufficiently.

s

rs

e

given in the figure 4.

l1

**Figure 3.** Elementary domain; tooth coupling

in the figure 3.

Figure 3. Elementary domain; tooth coupling

coefficient kv is known as the Vernier ratio.

DC

AC

= × -

s

L

amplitude of the first harmonic of the flux density, ba1.

It is thus demonstrated, in [1], that ba1 that can be expressed as:

DC

Dr Ds <sup>r</sup>

high speed rotor magnetic slot Nrh permanent magnets Lf : length of the rotor Taking the following typical values: Λ = 1, α = 0.2, ε = 0.05, Bar = 1 T, we obtain k<sup>s</sup> ≈ 0.12, i.e. ba1 ≈ 0.12 T. It would appear that the magnetic field, ba, is always weak, but in fact the field varies with time to a high frequency, becoming higher as Nr becomes greater. It is precisely this phenomenon which will be advantageously exploited in the transmission of mechanical force within the converter that we will describe. 0,1 0,15 

low speed rotor stator permanent magnet Nrs permanent magnets The second principle used in the design of a magnetic speed multiplier is that of the magnet‐ ic coupler. This device combines two rotors through the magnetic field produced by perma‐ nent magnets. 0,05 **ks**

 Figure 5. Magnetic gear: operating principle In a magnetic speed multiplier, as shown in the figure below, an intermediate stator allows the decoupling of the velocity of the two rotors using the principle of teeth coupling as seen in the Vernier structure. 0 0,5 1 1,5 2 2,5 3 Figure 4. Variation of the coupling coefficient in terms of α and Λ

Figure 5. Magnetic gear: operating principle **Figure 5.** Magnetic gear: operating principle

0

Figure 8. Tangential force density for different values of kv (Bar = 1.2 T)

10000

Figure 6. Position at maximum force

Figure 8. Tangential force density for different values of kv (Bar = 1.2 T)

**Fst (N/m²)**

20000

Figure 6. Position at maximum force

τ1.Lf.

30000 40000 50000 60000 **Fst (N/m²)** kv = 5 kv = 10 high speed rotor stator Lf : length of the rotor la l The number of pairs of magnetic poles, p, of this structure, is defined by the number of pairs of permanent magnets linked to the high speed rotor, Nrh. This must correspond to the number of poles created by the coupling between the Nrs number of permanent mag‐ net pairs on the low speed rotor, and the Ns stator teeth. The following formula must then be verified:

> 0 0,2 0,4 0,6 0,8 1 **beta**

> > kv = 5 kv = 10

0 0,2 0,4 0,6 0,8 1 **beta**

kv =20

kv =20

low speed rotor

$$\left| \mathcal{N}\_s - \mathcal{N}\_{rs} \right| = \left| \mathcal{P} \right| = \mathcal{N}\_{rh} \tag{7}$$

Operation is possible with Ns > Nr: the high speed rotor will then move in the opposite di‐ rection to the low speed rotor; or Nr > Ns: the two rotors will rotate in the same direction. Previous studies of Vernier structures [2] show however that the first configuration, Ns > Nr, is far better, giving higher force in relation to the air gap surface.

When the low speed rotor is displaced to the value of one small magnet pitch, τ2, the high speed rotor will displace to the value of one large permanent magnet pitch, τ1. The gear ratio is simply obtained by calculating the ratio of τ1 and τ2:

$$\left|k\_{m} = \left|\mathbf{N}\_{high} \;/\; \mathbf{N}\_{low}\right| = \tau\_{1} \;/\; \tau\_{2} = \; \mathbf{N}\_{rs} \;/\; \mathbf{N}\_{rh} = k\_{v} \tag{8}$$

Operation in synchronous mode, characterized by the above equation, is possible only if the torque on the output shaft does not exceed a maximum value. We also show the consequen‐ ces of a possible stall.
