Optimization and measurements of switched reluctance motors exploiting soft magnetic composite

Abstract

In the paper, the Wind Driven Optimization WDO algorithm is applied to the optimal shape design of a class of switched reluctance motors. The goal of the optimization is to identify a class of geometries which maximize the torque and simultaneously minimize the iron losses of the motor. Because of the twofold design criterion, the multi-objective version of the wind driven algorithm M-WDO is used. Results are eventually compared with those obtained by means of a standard genetic algorithm GA. For construction of optimized model of switched reluctance (SR) motor measurements of resistance and inductances vs. rotor position of commercial motor made of steel and non-optimized model motor made of soft magnetic composite were measured. On the basis of changes in inductance, electromagnetic torques were calculated. Results of B $=$ f(H) and iron loss measurements of soft magnetic composites made of Somaloy 700 and Somaloy 700 HR powder are also shown which will be used for construction of optimized SR model motor.

Keywords

Wind-driven optimization technique optimal design finite element method analysis switched reluctance motors inductance measurements soft magnetic composites magnetization curve iron loss measurements electromagnetic torque

1. Introduction

Over the last two decades, evolutionary algorithms (EAs) have proven to be successful in solving optimization problems in the area of computational electromagnetism. In fact, EAs do not require the objective function gradient to identify the search direction, and are global-optimum oriented. Moreover, they are able to find a solution when the optimization problem is characterized by several constraints or exhibits discontinuities. Often, EAs are inspired by the models of natural phenomena: for instance, the biogeography-based optimization algorithm [1], which is inspired by the geographical distribution of species in an ecosystem, has been applied in MEMS design [2, 3]. More recently, wind-driven optimization, inspired by the wind motion, which takes place in the high atmosphere to compensate the pressure imbalance, has been proposed and applied in antenna array design [4].

In research works a commercially available Switched Reluctance Motor Drive was used. This drive mainly was used in Maytag washing machines model “Neptune”. This motor was developed by Emerson Electric Co., whereas an electronic supply and control system developed by Switched Reluctance Drives Ltd. This type of electric drive exhibits high torque, high speed, soft starts, rapid reversal and tight control. This motor have low manufacturing cost but high cost of supply and control system. However overall cost is lower than cost of similar performance drives with an another motor.

One of the main aims of work is to design and manufacture a model of Switched Reluctance (SR) motor with high efficiency using Soft Magnetic Composite (SMC) as a material for a stator and a rotor magnetic core. This material is more and more applied in commercially available motors and is widely used in research works dealing with new constructions of electric motors and actuators [11, 12]. The commercial motor have magnetic circuit made of electrical steel.

One of the main parameters of a SR motor is its inductance. Owing to different motor reluctance with changing position of a rotor in relation to a stator, inductance is variable.

For inductance measurements two motors were used. First motor was the commercial one and second was a model motor. The model motor is a motor with magnetic circuit made of SMC and it is our initial design made in previous research [9].

In last part of an article results of B $=$ f(H) and specific power loss measurements of soft magnetic composites made of Somaloy 700 and Somaloy 700 HR powder are shown.

2. Multiobjective wind-inspired algorithm

WDO is inspired by the atmospheric motion of air parcels. In fact, wind blows in a way to equalise imbalances in the air pressure; likewise, in optimization the design points are moved from high-gradient to low-gradient positions. Accordingly, a swarm of $p>$ 1 artificial air parcels is considered. The WDO algorithm is governed by the following equation:

$\displaystyle u(t_{k+1})=(1-\alpha)u_{i}(t_{k})-gx_{i}+\beta\left|{1-i^{-1}}% \right|\left({x_{opt}-x_{i}}\right)+2u^{\bot}$ (1)

where the left-hand side gives the velocity of the ith out of p air parcels at time $tk+1$ . The right-hand side is characterised by the following four terms:

The inertial term, depending on velocity at time $t_{k}$ and frictional coefficient $\alpha$ (conservative operator);

The gravitational-like term gx, which biases the current position $x_{i}$ towards the gravity centre of the design space (pull-in operator);

The pressure-gradient term (the main operator), where index i $\geqslant$ 1 is proportional to the pressure value at position $x_{i}$ while $x_{opt}$ is the position of the lowest pressure found in the previous $k-1$ iterations;

The Coriolis-like acceleration term, due to which the velocity of the $i_{\rm th}$ parcel is influenced by the orthogonal velocity of another, randomly selected parcel (information-exchange operator).

Positive-valued constants ( $\alpha$ , $\beta$ , g) are algorithm-dependent parameters. The position of the $i_{th}$ air parcel at iteration $k+1$ is then updated as

$\displaystyle x_{i}(t_{k-1})=x_{i}(t_{k})+u_{i}(t_{k+1})$ (2)

and the boundaries are checked to prevent any air parcel from exiting the design space. The procedure continues until the maximum number of iterations is reached.

In [5], it was proposed to generalise the algorithm, and make it able to solve a multi-objective optimization problem exhibiting $m>1$ objective functions in conflict (M-WDO). The most general solution is given by the Pareto front of non-dominated solutions, i.e. the set of solutions such that no decrease of a function is possible without the simultaneous increase of at least one of the other $m-1$ function. To this end, in M-WDO a generalised pressure, which takes into account simultaneously m objective functions, is defined as follows. At the current iteration, air parcels in the swarm are sorted in sub-fronts in the objective space. All solutions within a sub-front are assigned the same generalised-pressure value, equal just to the rank index of the sub-front they belong to. This way, in the subsequent iteration the algorithm will both improve the solutions of the first sub-front and move dominated solutions towards the first sub-front, in the attempt to minimise the generalised pressure of each air parcel in the swarm. The governing equation is Eq. (1), where $x_{opt}$ is the average position of solutions in the first front.

3. Cases study: Switched reluctance motor

The motor is a 12/8 SRM [6, 9] made of Soft Magnetic Composite SMC material. Geometry and design variables are shown in Fig. 1.

Figure 1.

Case study: geometry and design variables of the SRM.

Phase configuration consists of four series-connected coils per phase, driven by unipolar current with a constant value of 1 A. In the model, it is assumed that currents in the motor windings simulate 1-phase control mode ( $i_{a}\neq 0$ , $i_{b}=$ 0, $i_{c}=$ 0).

Subregions of the magnetic circuit are characterized by different flux-density waveforms that are non-sinusoidal and exhibit different frequencies. Therefore, the loss curve of the SMC is considered at a frequency $f=$ 200 Hz in the rotor and $f=$ 2 kHz in the stator. Loss curves are shown in Fig. 2.

A finite element model of the SRM has been implemented by means of a commercial software [7].

4. Optimization problem

Geometric parameters ROR, RIR and BIT (Fig. 1) are selected as the design variables, subject to a set of constraints: overall diameter of the motor not exceeding 140 mm; Air-gap Length (AG) equal to 0.25 mm. Upper and lower bounds of design variables are reported in Table 1.

Table 1
Range of design variables

	$R_{OR}$ [mm]	$R_{IR}$ [mm]	BIT [mm]
Min	30.5	17	6
Max	41.5	26.5	13

Figure 2.

Iron losses for rotor (200 Hz) and stator (2 kHz).

Constraints are handled by means of the exterior penalty method. In terms of the design vector $x=$ [ROR, RIR, BIT], the design criteria are the static torque, to be maximised, and. the iron losses, to be minimised.

5. Optimization results

The following set of parameters tuning the M-WDO algorithm was considered: 20 parcels, 100 iterations, thermal coefficient RT $=$ 3, the gravitational coefficient $g=$ 0.2, frictional coefficient $\alpha=$ 0.4, Coriolis parameter $c=$ 0.4, and maximum velocity equal to 0.3. In order to compare results, a standard genetic algorithm GA implemented in Matlab [8] has been applied, considering 20 individuals and 100 iterations.

6. Inductance measurements of switched reluctance motors

Inductance can be measured with different methods e.g. such as using LCR meters or using ammeter and voltmeter. Measurements done by LCR meters can be made for different frequencies, but LCR meters can produce only a low value of a measuring current. For ironless inductors value of inductance is constant with changes of current. For magnetic circuits with ferromagnetic materials inductance is variable with changes of current in inductor’s wires.

For measurements of inductance of SR motor was used frequency generator, power amplifier, ammeter and voltmeter. By supplying a motor with sinusoidal voltage with defined frequency of 50 Hz, inductance is calculated from impedance and resistance of a motor’s phase. Measurement were carried for different values of current supplying a motor’s phase. For different values of current with the same angle of rotation, inductance has maximum 10% difference, because motor’s magnetic circuit is unsaturated. Inductance for each angle is an average value of inductances for different currents.

Phase resistances of SR motors were measured using ammeter and voltmeter for supplying each phase with DC current.

Rotation of motor’s rotor was conducted by a stepper motor with a resolution of 3 ${}^{\circ}$ . Inductances of motors are shown in Figs 4 and 5.

Table 2
Parameters of switched reluctance motors

	Type of motor and type of magnetic circuit
	Commercial – electrical steel	Model – soft magnetic composite
Phase resistance	2.2 ohms	6.1 ohms
Phase inductance – aligned	53 mH	141 mH
Phase inductance – unaligned	10 mH	24 mH

Figure 3.

Optimization results: circle – M-WDO, star – GA, dot – random sampling.

Figure 4.

Inductance of commercial SRM at different angles.

Figure 5.

Inductance of SRM model made of soft magnetic composite at different angles.

Changes of inductance resemble triangle waveform vs. angle of rotation.

Figure 6 shows a test bench with SRM with magnetic circuit made of soft magnetic composite (left) and stepper motor with supply and control unit (right).

Figure 6.

Photo of the test-bench with a switched reluctance motor.

Figure 7.

Electromagnetic torque as a function of angle of rotation for the commercial motor for $I=$ 2.5 A.

Table 2 shows main parameters of two SRMs.

Figure 8.

Electromagnetic torque as a function of angle of rotation for the model motor for $I=$ 1.3 A.

Figure 9.

Measurement samples made of Somaloy 700 and Somaloy 700 HR.

As it can be seen from Table 2, the two types of motor have different resistances and inductances. Commercial motor is supplied by a 120 V AC line, whereas the model motor is supplied by a 230 V AC line. In these two motors the configuration of coils in phases is different.

For comparison, the calculation of the electromagnetic torque $T$ of the two motors were done on the basis of differences in inductance measurements [10]. This equation is valid for a non-saturated motor, which is true for this motor.

$\displaystyle T=0.5i^{2}\frac{dL}{d\theta}$ (3)

where: $i$ is a current in a coil, whereas $dL/d\Theta$ is the inductance change versus the rotation of the rotor.

Inductance measurements for each motor were done with the same current and 50 Hz frequency, at $I=$ 2.5 A for the commercial one, and $I=$ 1.3 A for the model one. This ensures the same apparent power consumed by motors.

The first motor was a commercial switched reluctance motor, whereas the second was a model with soft magnetic composite core. The results are presented in Figs 7 and 8.

The curves on Figs 7 and 8 show that maximum electromagnetic torque of soft magnetic composite core motor is lower than commercial motor for about 14%.

Figure 10.

Amplitude magnetization curves $B_{m}=f(H_{m})$ for Somaloy 700 and Somaloy 700 HR composites.

Figure 11.

Specific total loss for Somaloy 700 composite.

7. Magnetization and losses characteristics measurements of soft magnetic composites used in the model switched reluctance motor

Soft Magnetic Composites that were used in model of switched reluctance motor were measured. Stator and rotor of the motor was made in Tele and Radio Research Institute. In rotor magnetic flux density has lower frequencies than in a stator A stator was made of Somaloy 700 powder whereas a rotor was made of Somaloy 700 HR powder. Measuring samples were prepared according the same technological parameters as parts of the motor. Magnetization curves B $=$ f(H) at 50 Hz frequency and specific total loss curves for frequencies $f=$ (50–2000 Hz) at different amplitude magnetic flux densities were measured. Measurements were conducted according to IEC 60404-6 standard on ring samples. During measurements magnetic flux density was kept sinusoidal with form factor 1.11.

Figure 9 shows prepared samples for measurements and Fig. 10 shows amplitude magnetization curves $B_{m}=f(H_{m})$ for Somaloy 700 and Somaloy 700 HR composites.

Figures 11 and 12 show specific total loss for Somaloy 700 and Somaloy 700 HR composites

Figure 12.

Specific total loss for Somaloy 700 HR composite.

Composites made of Somaloy 700 exhibit better magnetization curve however at higher frequencies they have higher specific total loss than composites made of Somaloy 700 HR.

8. Conclusion

The generalization of wind-driven optimization algorithm to the multi-objective case makes it possible to approximate the Pareto front of design problems characterized by conflict criteria. Accordingly, the family of optimal shapes trading off torque and power loss of a SRM was successfully identified.

Inductance and resistance measurements conducted for two motors are essential for the next step of work. They will help in the construction of the SR motor optimized in this paper, made of soft magnetic composite core and in the comparison with existing motors that have the same dimensions of the optimized one, as the commercial motor made by Emerson Electric Co.

Measurements of magnetic parameters of magnetic composites made of Somaloy 700 and Somaloy 700 HR powder were also helpful for optimization of a switched reluctance motor.

References

Simon

, Biogeography-based optimization, IEEE Trans. Evol. Comput.12(6) (2008), 702–713.

Di Barba

Dughiero

Mognaschi

M.E.

Savini

and Wiak

, Biogeography-inspired multiobjective optimization and mems design, IEEE Transactions on Magnetics52(3) (2016).

Di Barba

Mognaschi

M.E.

Savini

and Wiak

, Island biogeography as a paradigm for MEMS optimal design, IJAEM51(s1) (2016), 97–105.

Bayraktar

Komurcu

Bossard

J.A.

and Werner

D.H.

, The wind driven optimization technique and its application in electromagnetics, IEEE Trans. on Antennas and Propagation61(5) (2013), 2745–2757.

Di Barba

, Multi-objective wind-driven optimisation and magnet design, Electronics Letters52(14) (2016), 1216–1218.

Di Barba

Mognaschi

M.E.

Przybylski

Rezaei

Slusarek

and Wiak

, Geometry optimization for a class of switched-reluctance motors: A bi-objective approach, IJOAEM56(S1) (2018), 107–122. approac, in press on IJAEM, DOI: 10.3233/JAE-172282,2017.

www.infolytica.com.

www.mathworks.com.

Jankowski

Kapelski

Karbowiak

Przybylsk

and Ślusarek

, Analysis of static characteristics of a switched reluctance motor, Lecture Notes in Electrical Engineering vol.324, Springer 2014, pp. 289–294.

10.

Miller

T.J.E.

, Brushless Permanent – Magnet and Reluctance Motor Drives, Oxford Science Publications, 1989.

11.

Guo

Y.G.

Zhu

J.G.

Zhong

J.J.

Watterson

P.A.

and Wu

, An improved method for predicting magnetic power losses in SMC electrical machines, International Journal of Applied Electromagnetics and Mechanics19(1–4) (2004), 75–78.

12.

Yuan

Ishikawa

and Oono

, Steady state analysis of a new linear actuator with soft magnetic composite material, International Journal of Applied Electromagnetics and Mechanics33(1,2) (2010), 629–637.

Optimization and measurements of switched reluctance motors exploiting soft magnetic composite

Abstract

Keywords

1. Introduction

2. Multiobjective wind-inspired algorithm

Table 1 Range of design variables

6. Inductance measurements of switched reluctance motors

Table 2 Parameters of switched reluctance motors

References

Table 1
Range of design variables

Table 2
Parameters of switched reluctance motors