Recent Developments of Electrical Drives - Part 21 ppt

If the control is to be optimized for a supply voltage range [u,ur e f] in a motor speed range [0,ω max], then the equivalent optimal control parameters must be calculated for the supply

192 D’hulster et al.

determined according to an optimization criterion The current can be controlled using a hysteresis or PWM control technique With a PWM current controller the system produces less acoustic noise due to the fixed switching period, but its PI control parameters must be selected carefully In addition to this basic structure, also different torque ripple reduction principles can be implemented, of which examples in [4,5]

Voltage-speed relationship

So far, not much research is done on the control of SRMs under different supply voltage conditions Reference [6] proposes a maximum torque control strategy during short distur-bances in the dc-link voltage due to voltage sags or load transients For steady state behavior, [7] describes the similarity between supply voltage decrease and rotor speed increase on the current waveform of SR generators This reduces the number of parameter sets in the drive Equation (1) can be rewritten to:

di

d θ =

1

∂ψ(i, θ)

∂i



u − Ri

∂ψ(i, θ)

∂θ



(5)

Relation (5) states that, for a given phase current behavior, a relation exists between the phase voltage and the rotor speed:

u − Ri

For a given voltage u, speed ω(u) and reference torque, the optimal control parameters can

be obtained from the parameter set, defined for u ref, using an equivalent rotor speedω(u ref):

ω(uref) = (uref − R · iref) (u − R · iref) · ω(u) (7) with:

– i ref: reference phase current (A)

– u ref: reference phase voltage (V)

An example of this relation between supply voltage and rotor speed is given in Fig 5 with the numerical simulation results in Table 1

If the control is to be optimized for a supply voltage range [u,ur e f] in a motor speed range [0,ω max], then the equivalent optimal control parameters must be calculated for the supply voltage urefin a speed range



0, ω max·uref −R·iref u −R·iref 

Table 1 Numerical steady state simulation results

ω (rad/s) u (V) T m(Nm) P m(W) P Cu(W) P F e(W) η m

Figure 5 Comparison of current and torque behavior for voltage-speed combinations of the same

parameter set (ω1= 432 rad/s, u1= 290 V, ω2= 200 rad/s, u2= 145 V)

SRM maximum torque control

When the speed or position controller demands maximum torque performance from the motor, no freedom is left for optimization Both turn-on and dwell angle are determined

to maximize the loop-surface during energy conversion [6] In this paper only motoring operation is elaborated The turn-on angle is calculated to reach the reference current at the start of pole-overlap:

a ON = aref − ω · L u · imax

with:

– aref : start of inductance increase (pole-overlap)

– L u: inductance at unaligned rotor position [H].

For the full rotor speed range, maximum torque control parameters are obtained, using the

maximum available phase current i max Based on this maximum available torque at every rotor speed, the torque-speed plane is divided into equidistant torque-speed reference curves (Fig 6) An important feature is the equidistance between torque references This enables to design a stable speed or position controller Intersection between different reference torque-speed lines would inevitably result in unstable operating points The control angles and the

194 D’hulster et al.

Figure 6 Equidistant reference torque curves, related to the maximum torque behavior for u ref

SRM behavior for the maximum torque control are illustrated in Fig 7 Maximum torque control parameters are not obtained using the optimization algorithm because finding the parameters for the unique peak value of a surface is not an obvious task for any search tool

SRM objective functions (surfaces)

Objective functions, describing the SRM behavior as a function of the control parameters, are the input functions of the optimization platform Different functions or surfaces can

Figure 7 SRM maximum torque control angles and behavior for u and i

Figure 8 Torque, efficiency, and torque ripple for constant turn-on angle and rotor speed (a ON= 30◦

ω ref = 160.85 rad/s)

be calculated, using the nonlinear motor model, e.g., efficiency, torque ripple, acoustic noise Besides those surfaces, allowing an optimization criterion, the torque surface is also needed as a constraint function to satisfy the reference torque demand Fig 8 shows the surfaces of the torque, efficiency, and torque ripple for a fixed turn-on angle and rotor speed Different combinations of the parameters can result in the same torque production, allowing optimization of the parameters for a given reference torque constraint

Optimal control parameters determination

As pointed out, for each speed and reference torque, the appropriate input variables i ref,opt,

a ON,opt , and a DWELL,optmust be determined in such a way that the overall performance matches

an optimization criterion For SRMs, the optimality condition is in general determined by straightforward requirements with regard to the efficiency, torque ripple, or acoustic noise The efficiency should be maximized, the torque ripple and acoustic noise minimized

All objective functions are combined into a single value function, called generic cost (c).

For example, the generic cost function of efficiency and torque ripple is:

c = w1(1− ηm) + w2



T ripple max(T ripple)



(9) The optimal solution is a combination of input variables for which the cost function is minimized, for a given speed and reference torque

Although the surfaces of Fig 8 seem relatively smooth, this is not the general behavior

In practice, noise on the surface results in many combinations of input variables with the

196 D’hulster et al.

0 100 200 300 400 500

0 0.2 0.4 0.6 0.8

1

2

3

4

5

6

7

8

rotor speed [rad/s]

Tref/ Tmax

iref, opt

Figure 9 Optimal reference i ref,opt for u ref (w1= 0.5; w2= 0.5)

same value for the cost function As a direct consequence, only numerical algorithms able

to find a global solution can be used, avoiding local minima As a general constraint with regard to the final implementation, the chosen algorithm should always find the solution within a reasonable time Moreover, the solution should be found from any initial starting point

There are several algorithms to determine the desired minimum, but only two were implemented The first attempt uses a genetic algorithm (GA) as it is characterized by a high probability to find a global minimum However, for a few operating points, no useful solution is found A second algorithm (“search for all”) takes all possible combinations

of input variables with a constant step and determines the constrained minimum This method is straightforward to implement and a solution is found for every operating point The calculation time is function of the number of parameters and the step size A GA search method has the disadvantage that a solution is not guaranteed and that one particular solution is searched, without taking into account that this combination could be useful for other torque reference values The direct “search for all” method calculates the objective and constraint function values for a parameter combination and tests the cost for all torque reference values This strongly reduces the computation time

With a weight of 0.5 for efficiency and 0.5 for torque ripple, the optimal control param-eters are presented in Figs 9–11, using the “search for all” algorithm

Measurement results

The optimal control parameters, are programmed into a SRM drive and its behavior is measured on a test setup with load machine Validating if the control is really optimal is

0 100 200 300 400

500

0

0.2

0.4 0.6 0.8 1

20

25

30

35

40

45

rotor speed [rad/s]

aON, opt

Figure 10 Optimal turn-on angle a ON,opt for u ref (w1= 0.5; w2= 0.5)

not easy The model accuracy is verified by means of torque and efficiency measurements Fig 12 represents the measured torque-speed performance, according to the reference torque values for every rotor speed No intersection between the lines occurs, resulting in a stable position or speed controller Efficiency is determined by measuring the electrical power,

0 100 200 300 400 500

0 0.2 0.4 0.6 0.8

1

5

10

15

20

25

30

rotor speed [rad/s]

aDWELL, opt

Figure 11 Optimal dwell angle a for u (w = 0.5; w = 0.5)

198 D’hulster et al.

0

1

2

3

4

5

6

rotor speed [rad/s]

Figure 12 Measured torque-speed performance with optimal control parameters for u ref (w1= 0.5;

w2= 0.5)

supplied to the motor, and the mechanical shaft torque Efficiency measurements as function

of reference torque and rotor speed are compared with simulations in Figs 13 and 14

Conclusions

Different torque control strategies can be implemented in SRM drives, operating at varying supply voltage conditions A technique is presented to obtain optimal SRM torque control parameters, according to a weighted optimization criterion The dc-link voltage is not con-sidered as a fundamental parameter due to its analogy with rotor speed Using a nonlinear

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

ηm

measurement simulation

Figure 13 Measured and simulated motor efficiency as function of reference torque (u ref;ω = 214

rad/s)

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

rotor speed [rad/s]

ηm

Figure 14 Measured and simulated motor efficiency as function of rotor speed (u ref ; T ref = 0.5T max)

SRM drive model, the behavior is stored in N -dimensional surfaces, serving as objective

and constraint functions for the optimization platform The objective functions in this paper are limited to motor efficiency and torque ripple but can easily be extended with acoustic noise or temperature The surfaces are calculated only once for each motor geometry and different control parameter sets can be obtained for different application demands

Acknowledgments

The authors wish to thank the Flemish Government (IWT) for granting the research project

“Bepaling van de optimale stuur- en regelparameters voor systemen met SR-motor aandri-jving Ontwerp van een ontwikkelingsplatform.” (IWT 020343) The general optimization work is part of the IUAP/PAI P4/20 project “Coupled problems” sponsored by the Belgian Federal Government

References

[1] E Lomonova, A Matveev, “Application of genetic algorithm for design of switched reluctance drives,” Proceedings of the European Conference on Power Electronics and Applications (EPE 2003), Toulouse, France, p 12, 2003

[2] F D’hulster, K Stockman, J Desmet, R Belmans, “Advanced nonlinear modelling techniques for switched reluctance machines,” IASTED International Conference on Modelling, Simulation and Optimization (MSO 2003), Banff, Alberta, Canada, pp 44–51, July 2–4, 2003

[3] J Reinert, R Inderka, R W De Doncker, “A novel method for the prediction of losses in switched reluctance machines,” Proceedings of the European Conference on Power Electronics and Applications (EPE 1997), Trondheim, Norway, pp 3608–3612, 1997

[4] I Husain, M Ehsani, “Torque ripple minimization in switched reluctance motor drives by PWM current control,” IEEE Transactions on Power Electronics, Vol 11, No 1, pp 83–88, 1996

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[5] R.B Inderka, R.W De Doncker, “DITC – Direct instantaneous torque control of switched reluctance drives,” Proceedings of the IEEE-IAS Annual Meeting, Pittsburgh, Pennsylvania, USA, pp 1605–1609, October 13–18, 2002

[6] F D’hulster, K Stockman, R Belmans, “Maximum torque control strategy for switched reluc-tance motors during dc-link disturbances,” Proceedings of the European Conference on Power Electronics and Applications (EPE 2003), Toulouse, France, p 6, 2003

[7] R.B Inderka, M Menne, R.W De Doncker, “Generator operation of a switched reluctance machine drive for electric vehicles”, EPE journal, Vol 11, No 3, August 2001

OF AN INDUCTION MOTOR

A Belahcen

Laboratory of Electromechanics, Helsinki University of Technology, P.O Box 3000,

FIN-02015 HUT, Finland

anouar.belahcen@hut.fi

Abstract A model for the magnetoelastic coupling in electrical machines is presented It couples

transient electromagnetic field equations with dynamic elastic ones Computations are made to show the effect of stress-dependent magnetostriction on the vibrations of the stator core of an induction machine It is shown that the magnetostriction changes the amplitude of vibrations velocity up to 800% A relative difference of more than 6,000% is found between calculation with stress-dependent and stress-independent magnetostriction Measurements are made for validation

Introduction

The effect of magnetostriction and inverse magnetostriction (Villary effect) on the vibrations and acoustic noise of rotating electrical machines is still a subject of controversy Indeed, different authors [1–3] presented different models for the magnetostriction and came up with different results Some authors believe that the magnetostriction affects the vibrations

of rotating electrical machines [1,2]; others claim that the magnetostriction can be ignored [3] We investigate the problems of magnetoelasticity and magnetostriction by means of coupled transient and dynamic FE analysis

Models for static analysis with current-supplied systems have been presented by Ren

et al [4] and further developed by Mohammed et al [5] Uncoupled dynamic models for the vibrations of rotating electrical machines also have been presented [6–8] The model

we purpose is developed from both the static coupled and dynamic uncoupled models It is

a model that handle transient dynamic systems with voltage-supply

The goal of this study is to establish the effect of magnetostriction and magnetoelastic coupling on the vibrations and noise of rotating electrical machines Results about the effect

of coupling on the vibrations have already been presented in [9] The data about the magnetic properties of the materials used in this work and its measurements have been presented

in [10]

This paper presents the effect of magnetostriction and stress-dependent magnetostriction

on the vibrations of an induction motor

S Wiak, M Dems, K Kom˛eza (eds.), Recent Developments of Electrical Drives, 201–210.

2006 Springer.