Recent Developments of Electrical Drives - Part 7 ppt

Frequency control of a wave energy converter The results presented in “Verfication of the Generator Models in Block B” have been generated for a known displacement measured from the test

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0 0.1 0.2 0.3 0.4 0.5

time (s) 0.6 0.7 0.8 0.9 1.0

0

predicted experimental

Figure 7 Calculated and measured no-load emf.

The correlation between experimental and simulated results is very good, giving confi-dence in the model, which can then be used to investigate the machine performance under various loading conditions

Fig 9 shows the variation in the total three-phase power at the output obtained by

subtracting the I2R loss from the product of no-load emf and generator current There will

be additional iron losses and eddy current losses in the permanent magnets, which should

be included to obtain total efficiency

Frequency control of a wave energy converter

The results presented in “Verfication of the Generator Models in Block B” have been generated for a known displacement measured from the test rig and simply fed into the model by-passing the force model This was done simply to verify the electrical parts of the model and hence served its purpose However, in any electromechanical system the interaction between the electrical and mechanical system are of interest Fig 10 shows the force data generated from the generator force model Also included in the graph are results

of force using an analytical model The force model based upon the flux-linkage map has been verified using experimental results in [10]

The wave emulator test rig is a mass-spring damper system in which the amplitude is given by equation (6) and the resonant frequency is equal to the root of the ratio of stiffness

to mass On the test rig the mass is 190 kg, the



M2

ω2− K M

2

+ B2ω2

(6)

spring stiffness is 8,000 Nm and the friction (B) is equal to 148 N/m, which was estimated by

parameter identification methods from experimental test results Fig 11 shows the frequency

characteristics of the test rig for different values of B.

46 Mueller et al.

(a)

(b)

Figure 8 (a) Calculated and measured terminal voltage (b) Calculated and measured generator phase

current

In a wave energy device active power is absorbed from the sea by its damping compo-nents These are divided into mechanical, viscous, and radiation loses in addition to the electrical damping force providing the electrical power conversion In addition some of the incident wave energy is used to supply the energy stored in the device mass and device spring stiffness The electrical analogy of this would be reactive power At resonance no reactive power is supplied to the device from the sea When the device is operating at off-resonance points a method of supplying the reactive power externally is required to optimize the energy captured Externally applied forces that modify the stiffness of the system have been proposed as a means of frequency control In order to investigate how the generator

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Force (N)

I=-15A

I=-10A

I=-5A

I=15A I=10A I=5A

I=0A force data; Red:FE Blue Simple Force model; Black: nth Force model

x (mm)

Figure 10 Generator force data for one phase.

Figure 11 Frequency characteristics of the test rig.

48 Mueller et al.

reactive force could be utilized it is represented as the sum of two forces: a damping force and an equivalent stiffness force

where B g is the equivalent electrical damping and K gis the equivalent generator stiffness The frequency response is modified to include the generator reaction force (equation (8)) and the resulting resonant frequency is given in equation (9)



M2

ω2− K w −K g M

2 +B w + B g

2

ω2

(8)

ω0 =



K w − K g

By controlling the stiffness component of force in equation (7) it is possible to modify the frequency characteristics of the device The two components of forces in equation (7) are perpendicular to one another Resolving the currents into components 90 degrees to one another will enable control of the generator damping and stiffness force Control of the latter will enable the frequency characteristics of the device to be modified and hence optimize the energy captured

Discussion

Marine energy converters, in particular wave energy devices, are highly dynamic devices Directly coupling a linear electrical generator to the device requires a dynamic model of the generator in question in order to investigate performance under realistic conditions Such a modeling tool enables the designer to compare and assess electrical generator technology before going to the next stage of production

As expected the output power from the device shown in Fig 8 is pulsating due to the reciprocating nature of the motion Energy storage is required to ensure smooth power flow from a single device which could be investigated by including an energy storage and control block in the overall model

This paper has described in detail a generator model for the VHM represented by block

B in Fig 3 It forms the basis of a system model including any prime mover model or control models to optimize performance of the whole systems An indication of how the model might be used to control the frequency characteristics has been given in “Frequency Control of a Wave Energy Converter.” Since the generator model is the basic building block in the system, the designer must have confidence in it The model has been verified using experimental results obtained from the prototype in Fig 2 A sample of experimental and calculated results is shown in Fig 8(a,b), which shows very good correlation giving confidence in the electrical generator model

Conclusion

A dynamic model of the VHM has been presented and verified in this paper using near sinusoidal displacement data The model forms the basic building block to investigate the performance and control of direct drive wave energy converters

The authors would like to thank Durham University for providing facilities to do this work and the Engineering and Physical Sciences Research Council for funding (Grant no 38299)

References

[1] H Weh, H Hoffman, J Landrath, “New Permanent Magnet Excited Synchronous Machine with High Efficiency at Low Speeds”, Proceedings of the International Electrical Machines Conference, Pisa, Italy, September 1988, pp 35–40

[2] B.C Mecrow, A.G Jack, “A New High Torque Density Permanent Magnet Machine Config-uration”, Proceedings of the International Electrical Machines Conference, Cambridge, MA, USA, September 1990

[3] E Spooner, L Haydock, Vernier hybrid machines, IEE Proc Part B Electr Power Appl., Vol

150, No 6, pp 655–662

[4] M.A Mueller, N.J Baker, P.R.M Brooking, J Xiang, “Low Speed Linear Electrical Gen-erators for Renewable Energy Applications”, Proceedings of the Linear Drives in Industrial Applications Conference, Birmingham, UK, September 2003

[5] M.A Mueller, N.J Baker, “A Low Speed Reciprocating Electrical Generator”, IEE Power Electronics, Machines and Drives Conference, Bath, April 2002

[6] H Polinder, B.C Mecrow, A.G Jack, P Dickinson, M.A Mueller, “Linear Generators for Direct Drive Wave Energy Converters”, Proceedings of the International Electrical Machines and Drives Conference, Madison, WI, 2003

[7] M.J Tucker, Waves in Ocean Engineering: Measurement, Analysis, Interpretation, Ellis Hor-wood Series in Marine Science, 1991, ISBN 0-13-932955-2

[8] N.J Baker, M.A Mueller, P.J Tavner, “Development of Reciprocating Test-Rig for Wave and Tidal Power at the New and Renewable Energy Centre”, Proceedings of Marine Renewable Energy Conference, Newcastle, July 2004

[9] M.A Mueller, N.J Baker, Modelling the performance of the vernier hybrid machine, IEE Proc Part B Electr Power Appl., Vol 150, No 6, pp 649–654, 2003

[10] J Falnes, Ocean Wave and Oscillating Systems: Linear Interactions Including Wave-Energy Extraction, Cambridge University Press, London, 2002, ISBN 0521782112

I-5 FINITE ELEMENT ANALYSIS OF TWO

PM MOTORS WITH BURIED MAGNETS

J Kolehmainen

ABB Oy, Electrical Machines, FI-65101 Vaasa, Finland

jere.kolehmainen@fi.abb.com

Abstract In this paper, a permanent magnet synchronous motor (PMSM) with buried V-shape

magnets is compared to a motor with unusual design with buried U-shape magnets in every second pole It is shown that the motor design with U-shape magnets has same electrical properties than the design with V-shape magnets

Introduction

Permanent magnet synchronous motors (PMSM) with buried magnets have been considered

in a wide range of variable speed drives A buried magnet design has many advantages compared to designs with surface mounted and inset magnets Flux concentration can be achieved which induces higher air gap flux density Higher air gap flux density give a possibility to raise torque of a machine The buried magnets construction also gives a possibility to form air gap and get smoother torque [1] The rotor can also be produced easier Some of the different rotor with buried magnets types are presented in Fig 1 Buried magnet designs give the possibility to reduce reluctance by narrowing and length-ening the magnets but keeping the amount of the magnets the same By using buried magnets

in V-shape or radial magnets, there are limits to reducing reluctance Designs with U-shape magnets in every pole have good properties of both designs with V-shape and radial magnets [2] However, with a design with U-shape magnets in every second pole it is possible to reduce reluctance further

In this paper two buried magnet machines are compared, one with V-shape magnets and another with U-shape magnets in every second pole The analysis is done by using time stepping and static calculations with Finite Element Method (FEM) [3] Also these machines with different magnetic width and length are considered

Motor designs

Both designs with buried magnets inside the rotor make the assembly of the rotor easier compared to the other designs Rotor disks keep the magnets in place and no extra reinforcing bandage is needed The magnets are inserted into punched slots in the laminated rotor iron The example of design with buried magnets in V-shape is shown in Fig 2 and with buried U-shape magnets in every second pole in Fig 3

S Wiak, M Dems, K Kom˛eza (eds.), Recent Developments of Electrical Drives, 51–58.

2006 Springer.

a) b) c)

Figure 1 Rotor constructions of buried permanent magnet motors with (a) tangential magnets, (b)

radial magnets, and (c) V-shape magnets

Figure 2 12-pole PM motor design with magnets in V-shape.

Figure 3 12-pole PM motor design with magnets in U-shape in every second pole.

I-5 Finite Element Analysis of PMSM with Buried Magnets 53 The only difference of these two motors is in their internal rotor structure Areas of the magnets are same and in the structure of Fig 3 magnets per one pole are thinner and longer Also, a structure where magnets per one pole have same width and length is considered In addition, all sizes of the iron bridges between the magnets and air gap are the same The number of magnet pieces in U-shape design is also reduced to 3/4 of number in V-shape design This saves time for inserting magnets to rotor

Calculation results

The electrical properties of the motors with V-shape and the U-shape designs are studied Studied motor data is shown in Table 1 Calculations are done with the time stepping method with FEM [3] Properties are studied with different loads

In calculations voltage source and delta connection is used Because of the different structure of rotors, two poles of each construction are modeled Circuit of calculations

is shown in Fig 4 In the circuit there are three voltage sources, six winding connection and three end winding resistances and three end winding inductances In all time stepping calculations, voltage angle of the stator and amplitude are same Calculations are started with different rotor angles and stopped when transient phenomena is over Constant rotor speed is used

The flux lines of three example designs with nominal load are shown in Figs 5–7 The packing of the flux can also be seen Every second pole in the U-shape designs is different which means that the structure between two poles is not symmetric In Figs 5 and 6, total length, width, and area of magnets per one rotor pole are same

Fig 8 shows flux densities in the stator teeth as a function of time with nominal load calculations of V-shape and U-shapeA designs The effect of difference of designs can be

Table 1 Motor data

Figure 4 Circuit used in calculations.

Figure 5 Packing of flux with nominal load and original design (V-shape).

seen It is relatively small It can also be seen that absolute value of flux is periodically symmetric between two poles in our shapeA design Flux is also symmetric with U-shapeB design No deviation of symmetry can be seen

Fig 9 shows flux densities of V-shape and U-shapeA designs produced only by magnets

in the stator teeth with different rotor angles Length and width of magnets per one rotor pole are same Maximum and average flux densities of V-shape and U-shapeA designs are 1.463 T, 1.420 T and 0.932 T, 0.926 T Flux densities with U-shapeA design is slightly smaller because of small effect of gaps between the magnets

Nominal and maximum loads of our three example designs are calculated with time stepping calculations In Table 2, the calculation results are compared to experimental results of V-shape design It can be seen that calculation of V-shape design gives a correct

Figure 6 Packing of flux with nominal load and new design A (U-shapeA).

I-5 Finite Element Analysis of PMSM with Buried Magnets 55

Figure 7 Packing of flux with nominal load and new design B (U-shapeB).

Figure 8 Flux densities of V-shape and U-shapeA designs in the stator teeth on one period with

nominal loads

Figure 9 Flux densities of V-shape and U-shapeA designs produced only by magnets in the stator

teeth with different rotor angles