3D cross coupling effect for flux control in magnetic circuit with Permanent Magnet

Lucas Ribeiro Lopes Cardoso Julio Carlos Teixeira

Centro de Engenharia, Modelagem e Ciências Sociais Universidade Federal do ABC - UFABC

Santo André, Brazil lrlcardoso.ufabc@gmail.com

Abstract— Permanent magnet synchronous motors are used in several industrial applications. A flux control is necessary for some applications such as in wide speed range electrical vehicles. This paper presents theoretical and experimental results that show the possibility of using the 3D cross coupling effect in electrical steel to control the flux in the machine air gap. A simple experimental device was constructed and a 34 percent of flux variation has been attained.

Keywords—cross coupling effect; flux control; permanent magnet; magnetic device

I. INTRODUCTION Electric motors represent an excellent alternative to replace

the established internal combustion engine (ICE) of electric vehicles (EV). Considering efficiency and torque density, the permanent magnet synchronous motors (PMSM) stand out among other electric motors for EV. To achieve these characteristics, the PMSM are usually built with rare earth magnets.

There are mainly two types of PMSM. One is the surface permanent magnet (SPM) synchronous motor, whose magnets are mounted on the rotor surface. If the magnets are located inside the rotor, this motor is known as interior permanent magnet (IPM) synchronous motor. The main difference between these two types of electric motors is the fact that the d and q axis components of armature inductance are typically equal in SPM and different in IPM [1].

For application in EV, it is necessary to control the speed and the torque of the electric motor over a wide speed range [2]. The speed is proportional to the frequency and the torque is proportional to the current components. In the traditional synchronous motors, at speeds below the nominal speed (called constant-torque region), the field current is kept constant while the armature voltage and frequency is controlled by using an inverter. For higher speeds, the battery power limits the motor torque. Ideally, the torque is decreased as the velocity rises, so the maximum power remains constant. In this constant power region, the torque control decreases the field current of classical synchronous motor and the air gap flux density.

Different constant power control systems are proposed in the literature [1][3][4]. The physical principle of these controls can be simplified according to (1) [2]

Va ≈ K fe Bpeak (1)

where the K is a design motor constant, Va is the nominal armature voltage at the electrical frequency fe, and the peak flux density is Bpeak.

For a limited voltage Va (which occurs in the constant-power region), two different speeds need two air gap flux density as represented in (2)

B2B1

= f1f2

(2)

As (2) shows, if the B2 induction is k times smaller than B1, the frequency f2 will be k times higher than f1, showing that a reduction in the air gap flux density also increases the range of speeds at which it is possible to maintain the equality of (2), resulting in the machine power control.

However, the flux density produced by the magnet in the air gap of a PMSM is constant. To control the resultant flux density in the PMSM air gap some techniques of flux weakening based on armature current control have been proposed by several authors [1][3]-[7]. In [8] a comparison among the implementation of current controls applied to PMSM is presented. Some improvements in the PMSM design based on 2D cross coupling effect are proposed in [9] to achieve a better torque-speed behavior.

This work shows the effect of the 3D anisotropy property of ferromagnetic materials and it highlights the possibility of using this property on the flux control in PMSM.

II. CASE STUDY In the magnetic circuit represented in Fig. 1, the permanent

magnet (I) produces a magnetic flux ΦI. At the air gap, G, the flux ΦG can be controlled if the reluctance of the right side (Rp) is variable. The cross section was considered constant and the reluctance of the ferromagnetic material was neglected (except the P path).

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Fig. 1. Magnetic circuit with a permanent magnet “I” and two parallels reluctance. At the left side, the magnetic flux pass through the air gap (G). Controlling the flux at the right side, the flux in the air gap can be controlled.

A simple analysis of this circuit leads to (3)

Bg= Ri Rp

Rg Ri + Rg + Ri RpJr (3)

where the air gap flux density (Bg) produced by the magnet is a fraction of its remanent polarization (Jr). The magnitude of this fraction depends on the reluctance involved in the magnetic flux path: reluctance of the air (Rg), magnet (Ri) and Rp.

If the reluctances of the air and the magnet are constant, the air gap flux density depends only on the Rp. The variation of the reluctance Rp changes the slope of the magnetic load line setting different operating points to the permanent magnet.

III. THEORICAL CONCEPTS This paper proposes a method to change the permeability of

the P path of the magnetic circuit using the 3D anisotropy of ferromagnetic material.

The magnetization of a material is accepted as the sum of the magnetic moment domains that compose the material to generate a resulting magnetic field [10]. Thus, the exposure of a ferromagnetic material in an external (sufficiently large) magnetic field (H) is able to align the magnetic moments and produce an induced field (B) larger than the applied magnetic field (H). The B and H fields are related by the magnetic permeability (μ) of the material.

In a non-oriented electrical steel, there is an anisotropy of the magnetic properties in different directions [10]. Therefore, when two perpendicular fields are applied they interact in order to reduce the magneto-crystalline anisotropy energy.

Under the permeability perspective, an increment of the field in one direction reduces the permeability of the others directions. The result of applying crossed fields in the same plane is known as 2D cross-coupling effect. This effect in the electrical steel plane is well studied and applied in the design of electrical machines [9].

Another possible use of crossed fields takes advantage of their high anisotropy in the perpendicular direction to the electrical steel plane (3D anisotropy).

In this direction, the magnetic permeability is smaller than in the plane of the sheet. Moreover, the application of alternative field in this direction increases losses by eddy

currents in the magnetic core. For these reasons, this direction is usually avoided.

The easy direction of magnetization (ED) was considered as the direction of the sheet lamination, and the hard direction of magnetization (HD), was considered as the direction perpendicular to the sheet plane.

If two crossed fields with the same magnitude – one in the ED and the other in the HD – are applied in the electrical steel, then the alignment of the magnetic domains occurs mainly in the ED. Therefore, the low magneto-crystalline anisotropy energy in ED can be used to avoid the alignment of the domains in the HD, thus reducing the magnetic permeability relative to this direction.

This paper proposes the reluctance variation (Rp) using sheets that compose the path P, perpendicular to the plane of the drawing (Fig. 2), and applying an external field (BEXT) in the ED. The permeability of the path P will vary depending on the BEXT’s magnitude.

Fig. 2. Disposing the sheets that composes the P path such a way that its plane is perpendicular to the flux produced by the magnet, one can apply an external magnetic field (BEXT), producing a magnetic flux perpendicular (ΦEXT) to the magnetic flux (ΦI).

The knowledge of the external field H effect in the permeability variation allows the use of (3) to obtain the air gap flux density variation.

IV. METODOLOGY Two different devices have been constructed. The first one

is similar to that presented in Fig. 2. Non-oriented steel and a Neodymium (NdFeB) magnet (about 32 MGOe) were used. Fig. 3 shows different views of the constructed device.

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Fig. 3. Different views of the device constructed toestablished in (3). (a) Front view. On the left, the exterfor producing the flux towards ED of the P path. On there is the main circuit whose flux is produced by the Top view of the experimental device; (c) Top view of th

Fig. 3c shows the permanent magnet, theP and the air gap. Over the air gap, some shegap length.

The second device coil (Fig. 4) producesperpendicular direction of the electrical steeexternal electromagnet, a continuous maapplied in the ED of the sheets. The BH obtained for different ED applied magnetic fi

Fig. 4. Transformer built for the magnetic HD chenlarged detail of the image (below) one can see that tup the transformer are arranged in such a way that its plto the flux produced by the windings.

verify the relationship

rnal circuit, responsible the right, horizontally, permanent magnet; (b)

he main circuit.

e flux control path eets regulate the air

s the H field in the el (HD). Using an agnetic field was curve of HD was

ields.

haracterization. In the the sheets which make lanes are perpendicular

V. EXPERIM

Fig. 5 shows the result obtai

Fig. 5. The curve relates the magncoil (360 turns) of the external circuit i

Fig. 5 points out the 3D device. The increase in theconsequence of the P path permcurrent applied in the external cwith a large air gap (approvariation was achieved.

Using (3) and the experimeis possible to identify the permthe HD as a function of the elethe ED. However, (3) has so meffects, no flux dispersion, onlaccount) that these results welements method (FEM) to calcircuit, it was possible to identicircuit.

The P path of the magnetiusing the experimental results are presented in Fig. 6 (“Experi

To generalize these partiamagnetic field on the permeabusing the Fig. 4 device. The re(“Experiment 2”).

Fig. 6. The dotted line is the permcoupling effect obtained by using the the same conditions obtained from identification using FEM model.

Fig. 6 shows the 3D cpermeability in the perpendic

MENTAL RESULTS ined by the first device.

nitude of the direct current applied to the in Fig. 3 with the air gap flux density.

cross coupling effect in Fig. 3 e air gap flux density is a

meability reduction caused by the circuit coil. In this simple circuit oximately 4mm), a 34% field

ntal results presented in Fig. 5 it meability of the circuit P part in ectric current producing field in

many simplifications (no fringing ly linear effects were taken into

were not useful. Using a finite lculate the magnetic field in the fy the P path permeability of the

ic circuit permeability obtained of Fig. 5 and FEM simulation

iment 1 + Simulation”).

al results, the effect of a ED bility in the HD was measured esults are presented in the Fig. 6

meability change caused by the 3D cross

device of Fig. 4. The red dots indicate the device of Fig. 3 and the field

cross coupling effect on the cular direction of the electrical

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steel plane (HD). For BEXT equal to zero the HD relative permeability was approximately 100.

Fig. 6 points out that the permeability on the HD when low fields were applied in the ED can be reduced almost 4 times. It shows that the effect of cross coupling is not verified for fields smaller than 0.4T. Over this value, there was a marked and almost constant decrease in permeability with the external field application in the ED.

The 3D cross coupling effect can be used to reduce the field in the air gap using low current in the ED. The effect of the P path permeability was studied in the Fig. 3 device. Fig. 7 relates the percentage of change in the P path permeability with the corresponding percentage of variation in the air gap induction.

Fig. 7. Relation between the percentage of change in the air gap flux density caused by a percentage of change in the P path permeability of the Fig. 3 device.

As expected, the variation in the P path permeability changed the induction in the air gap G. The greatest percentage of change in the permeability was 74% and was achieved by applying a direct current of approximately 6.4 A in the external circuit coil (360 turns). This change caused a magnetic induction increment of about 34% in the air gap.

VI. CONCLUSIONS Theoretical and experimental results show that it is possible

to control the flux in a magnetic device using a permanent magnetic material and 3D cross coupling effect.

Once this 3D cross coupling effect depends strongly on the characteristics of the electrical steel used and on the geometry of the designed circuit, the results obtained here should be further explored in order to achieve greater efficiency of the current required to control the air gap flux in PMSM.

ACKNOWLEDGMENT To the Instituto de Pesquisas Tecnológicas do Estado de

São Paulo, Brazil (IPT) for the use of their experimental facilities.

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[6] N. Mutoh, S. Kaneko, T. Miyazaki, R. Masaki and S. Obara, “A torque controller suitable for electric vehicles”, IEEE Transactions on Industrial Electronics, vol. 44 nº 1, Feb 1997.

[7] T. M. Jahns, G. B. Kliman and T. W. Neumann, “Interior permanent-magnet synchronous motors for adjustable-speed drives”, IEEE Transactions on lndustriy Applications, vol. 1A-22 nº 4, July/August 1986.

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