paper_67 combined field and circuit theory

8/20/2019 Paper_67 Combined Field and Circuit Theory

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Combined Field and Circuit Theory for Non-Linear Material Applied on

Wind Turbine Generators

Oliver Drubel Sven Exnowski Siemens AG University of DortmundAutomation and Drives, A&D LDIOEM 2 Department of Electrical Machines Drives and Power ElectronicsPostfach 4743 Emil-Figge-Str. 70D-90025 Nürnberg, [email protected] D-44227 Dortmund, [email protected]

Abstract: In the presented paper a general machine theory isdeveloped. The theory is based on the circuit theory, butconsiders saturation effects by application of non-linear staticfield calculation. The circuit theory uses a transient timestepping method with time periods, which allow theappropriate application of power electronic voltage supply.The field calculation is applied in time periods which are

adequate for the saturation within electrical machines.Therefore only few field calculations are done during onerotor rotation. Especially the correct consideration of themachine saturation is within the focus. The theory is verified by measurements for different saturation levels therefore.

I INTRODUCTIONRecent developments in drive systems show an increasingdemand in converter fed applications. The increase is basedon three main pillars. The astonishing growth in China andIndia cause strong needs for metals and steel mills with oftenchallenging converter drive applications. Beyond this marketthe increase in the oil price motivates nearly all oil companiesto invest in equipment like compressors and pumps. Eventhough these applications have been in the past direct on linemotors, several of them are converter driven now. Converterdriven pumps and turbines often allow reducing losses withinsystems enormously. The energy market especially withabout 15GW of wind turbine applications is the third strong pillar. Most of the wind farms are of variable speed type.Either the drive consists of high torque motors, which operatedirectly at low speed or they consist of a motor which isconnected over a gearbox to the turbine. Both applicationsapply frequency converters. The high torque application is inmost of the cases a synchronous machine, which feeds afrequency converter. The frequency converter has to convert

the full nominal wind turbine power and is designed for thecomplete apparent power.Often slip ring asynchronous machines are used in case of asystem with gear box. The asynchronous motor has astandard three phase stator winding like a squirrel cageinduction machine. The rotor has instead of a copper cage athree phase winding. This winding is insulated to thelamination and connected to slip rings. Brushes transmit thecurrent to a frequency converter. The technology in power electronics is well proven andstandardized nearly independently upon the motor speedwithin power determined discrete converter modules.Research and development depend mainly upon new

semiconductor components or software modifications inorder to decrease costs. Indeed the application for the motoris often new and its limits are often challenged especially bythe speed range or electrical effects caused by the convertersupply in variable power and frequency ranges. The coupling between frequency converter and motor calculation is up tonow either handled by intensive transient numerical time

stepping algorithms [1,2], where the Finite Element problemand circuit model is solved at any time step several times, orwith a simplified machine model [3,4]. Whereas in most ofthe cases simple circuit models are sufficient, some few casesexist, where more elaborated models of the electricalmachines are needed.It is a real challenge to design the slip ring system with the brushes in a way that the system can endure voltages ofseveral kV. Additionally the system must not be damaged bythe voltage dips which are created by the converter as well.Especially these dips may cause a reduction in live time ofthe brushes as well as shaft voltages between the rotor andground. The voltage dips are in the frequency range of about

100kHz whereas the main field distribution within the motoris rotating with 50Hz.A combined field and circuit theory is developed, whichallows solving the circuit problem and the field problemwithin different time periods. The method is applied to a slipring induction machine like those, which are operated in windturbines, see fig. 1.

Fig. 1: A wind turbine type slip ring induction machine

Mainterminal

box

Slip ringmodule



The iron non-linearity is considered correctly at thenumerical calculated positions. The inductivity matrix at theactual time step of the circuit solution anywhere between position 1 and 2 is interpolated linearly.

The rotational term of equation (4) is well known by thiscalculation, as well.Only the influence of the saturation due to the current changecan not be determined in this way. Indeed the inductivitymatrix at position 1 is known from the former calculations fora current of the time step i-2. Therefore the inductancematrixes are known for two current levels at the same position. A comparison of both fluxes in each winding at thesame current level of the time step i-1 will determine theinduced voltage of the material change and is considered inequation (3). The calculated voltage is correct at position 1 but not at position 2, see fig. 3.

Fig.3: Consideration of material-changes due to current

Here it is an approximation only. Otherwise iteration isnecessary. The matrix has to be recalculated at the position 2with the new calculated currents of the actual time step.Again a flux difference can be determined with the newcurrents, which allows for an improved voltage value due tomaterial changes.

III COMPARISON BETWEEN MEASURED ANDCALCULATED SLIP RING INDUCTION MACHINES

Any new theory has to be proven by appropriatemeasurements. The linear circuit theory has been applied ondifferent phenomena since decades. Therefore a measurementhas been chosen which reveals the theories applicability to

non-linear phenomena. Especially the no load characteristicof an induction machine shows the influence of saturation. A355kW high voltage 6kV slip ring asynchronous machine has been chosen as measurement base. The machine is a 6-polemachine with a double layer winding in the stator and asingle layer winding in the rotor. The stator winding is starconnected. Several machines of the type have been built andtested.During the no load test different voltages are applied to thestator winding. No load is applied to the shaft. The statorcurrents are measured during the test. Based on the measuredstator current it is possible to calculate the individualinductivity of one phase according to equation 5:

δ ω

1

0

011 3

1

33

2 L

I

U L +

⋅⋅⋅= (5)

The influence of the leakage inductance on the determinationof the self induction is in the range of 3%. This leakageinductance is not measured directly and therefore neglectedin the following. The ohmic resistance influences theinductivity by about 1% in the other direction and isneglected as well.The calculation model considers the exact design dimensionsof the machine’s active part. The end winding region is notconsidered. The non-linearity of the rotor and stator core istaken into account as well as the non-linearity of themagnetic slot wedges. The correct material parameters of thewedges have a strong influence on the machine inductance. A

comparison between calculated and measured inductances isgiven in fig. 4.

300

350

400

450

500

550

600

3500 4000 4500 5000 5500 6000 6500 7000

No load voltage (V)

S t a t o r i n d u c t i v i t y ( m H )

20% corridor around the

measurement

measurement for one motor

calculated inductivities

measurement for five

more motors of same type

Fig. 4: Comparison between measured and calculated statorinductivities

Indeed the difference between measurement and calculationis for the nearly linear case at low terminal voltages of 0.6p.u.about 18%. Even though this result is not too bad forasynchronous machines with small air gaps it is worth toevaluate some potential sources of the difference. In [5] adeviation of 10% is considered to be a good result. Differentreasons are given for a possible deviation here. Indeed most

of them would case a larger magnetization current in themeasurement than expected.Calculation errors for self inductances due to finite elementdiscretisation are in the range of 3%.Measurements on the same motor type but for differentmotors show a stable manufacturing process. The variation between motors of the same type is lower than 4%.Beside errors in the methods of the numerical calculation andmeasurement deviations may occur due to the assumptionswhich have been applied to the calculation model.The end winding flux has been neglected in the calculationmodel. The influence is especially for a six pole machinerelative small. It is assumed to be in the range of 2-3%. A

stronger influence can be expected by variations in the air

Pos. 1 Pos. 2

i-2

i-1

i

Time step i

of fieldcalculation

Rotor position

Current ii-2

Current ii-1 Current ii-1

Current ii

Induced voltage asused in equation (3)for time step k

Induced voltageas used inequation (3) fortime ste k+4

δψ i / δ t |ϕ k , ik =const.

δψ i+1 / δ t |ϕ k+4 , ik+4=const.

Time step k ofcircuit calculation k-2 k-1 k k+1 k+2



V INFLUENCE OF THE FIELD AND CIRCUIT TIME-PERIODE ON MACHINE CURRENTS

The motor is calculated for on load operation at different time periods. Indeed the grid calculation is relatively fast in

comparison to the numerical determination of the magneticfield. The time period of 25µs of the grid calculation is keptconstant. The distance between two field calculations has been modified between the different calculations. In fig. 8 atime period between two numerical field calculations of 1msis considered, in fig. 9 a time period of 2ms is taken intoaccount and in fig. 10 of 8ms.The time period of the Finite Element calculation determinesmainly the amplitude and period of the higher harmonics inthe rotor current. An extremely wide period of 8 ms modifiesthe fundamental currents as well. The fundamental currentsin stator and rotor hardly change any more between 2ms and1ms.

The inductivities are linearly interpolated between two rotor positions. This interpolation causes inherently higherharmonics. In order to investigate higher harmonics due to physical effects, the Finite Element time period has to beadjusted to the targeted harmonic.

-100

-80

-60

-40

-20

0

20

40

60

80

100

10 20 30 40 50 60 70 80 90 100

Time (ms)

C u r r e n t ( A )

Rotorcurrents

Statorcurrents

Influence of FE-time periode

Fig. 8: Stator and rotor currents for a stator voltage of 3235Vat a slip of 0.1 and a rotor voltage of 250V with a grid periodof 25µs and a finite element period of 1ms

-100

-80

-60

-40

-20

0

20

40

60

80

100

10 20 30 40 50 60 70 80 90 100

Time (ms)

C u r r e

n t ( A )

Rotorcurrents

Statorcurrents

Fig. 9: Stator and rotor currents for a stator voltage of 3235Vat a slip of 0.1 and a rotor voltage of 250V with a grid periodof 25µs and a finite element period of 2ms

-100

-80

-60

-40

-20

0

20

40

60

80

100

10 20 30 40 50 60 70 80 90 100

Time (ms)

C u r r e n t ( A )

Statorcurrents

Rotorcurrents

Fig. 10: Stator and rotor currents for a stator voltage of3235V at a slip of 0.1 and a rotor voltage of 250V with a grid period of 25µs and a finite element period of 8ms

Fig. 11 shows the currents in case of a converter fed rotor.The non-sinusoidal rotor-voltage causes block wise rotor-currents. Again a numerical imposed harmonic is found in therotor-currents, which is in line with the time period of thefield calculation.

-100

-80

-60

-40

-20

0

20

40

60

80

100

10 20 30 40 50 60 70 80 90 100

Time (ms)

C u r r e n t ( A )

Statorcurrents

Rotorcurrents

Fig. 11: Currents for a stator voltage of 3235V at a slip of 0.1and a converter fed rotor voltage of 250V with a grid periodof 25µs and a numerical period of 2ms

VI CONCLUSIONThe developed machine calculation theory allows for a strongseparation between high frequency converter effects and low

frequency machine behaviour within one mathematicalmodel. The number of necessary circuit or field calculationcan be adjusted to the focus of the individual investigation.The theory has been verified by measurements in case of noload operation. Indeed the difference between measurementand calculation of 18% is not only due to the normalmeasurement variation, but also due to the basic finiteelement model which does not include effects like air gapeccentricities.The influence of material saturation is in the range of 10%for no load operation and of 30% in case of on load operationwith an increase of the effects from magnetic wedges.The time period of the numerical field calculation has to be

adjusted to the highest harmonic, which should be



investigated in the machine current. Reasonable values have been reached if the minimum numerical time period is chosento be 10% of the highest harmonic time period

IV REFERENCES[1] Darabi A., Tindall C. Ferguson S., “Finite Element Time

–Step Coupled Generator, Load, AVR, andBrushless Exciter Modelling “, IEEE Trans. Energy

Conversion, vol. 19, no. 2, pp.258-264, June 2004. [2] Darabi A., Tindall C., “Damper Cages in Genset Alternators: FE Simulation and Measurement “, IEEE Trans. Energy

Conversion, vol. 19, no. 1, pp.73-80, March 2004. [3] Basic D., Zhu J. G., Boardman G., “Transient Performance

Study of a Brushless Doubly Fed Twin Stator InductionGenerator”, IEEE Trans. Energy Conversion, vol. 18, no. 3,

pp.400-408, Sept. 2003.

[4] Welchko B. A., Jahns T. M., Hiti S., “IPM SynchronousMachine Drive Response to a Single-Phase Open Circuit

Fault“, IEEE Trans. Power Electronics, vol. 17, no.5, pp.764-771, Sept. 2002. [5] Oberretl K.: “Die genaue Berechnung des

Magnetisierungsstromes von dreiphasigenAsynchronmaschinen”, Bulletin Oerlikon, no. 335, pp.66-84, Aug. 1959.

[6] Reichert K.: “Über ein numerisches Verfahren zurBerechnung von Magnetfeldern und Wirbelströmen inelektrischen Maschinen“, Habilitation UniversitätStuttgart, 1968

paper_67 combined field and circuit theory

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