WO2019086179A1

WO2019086179A1 - Transformer winding geometry determination

Info

Publication number: WO2019086179A1
Application number: PCT/EP2018/076250
Authority: WO
Inventors: Meinhard Paffrath; Yayun Zhou; Harald Ertl; Yiqing Guo; Roland Hofmann; Markus RIEDENBAUER
Original assignee: Siemens AG; Siemens Corp
Current assignee: Siemens AG; Siemens Corp
Priority date: 2017-10-30
Filing date: 2018-09-27
Publication date: 2019-05-09
Anticipated expiration: 2020-04-30

Abstract

Present invention concerns a method (420) and a system for determining a winding (135) geometry (200) for an electrical transformer (100), the transformer (100) having a winding (135) comprising several turns of a conductor (150) and a core (120) with a core (120) window (205) for receiving the winding (135). A method (420) for determining a winding (135) geometry (200) for said transformer (100) comprises steps of determining at least one electrical requirement for the transformer (100); determining at least one physical constraint for transformer (100) dimensions; and determining a winding (135) geometry (200) based on the at least one requirements and at least one constraints. In this, the winding (135) geometry (200) comprises a winding (135) arrangement, a conductor (150) cross section and a count of turns and determination is done following an optimization algorithm with the objective to minimize a distance between a height of the winding (135) and a height of the core (120) window (205).

Description

Transformer Winding Geometry Determination Present invention concerns power transformers. More

specifically, present invention concerns the determination of a favourable winding geometry for a power transformer.

Background of the Invention

An electric transformer is used for changing the voltage of an alternating electric current (AC) . An input voltage is elevated (step-up) while the corresponding current is reduced or the voltage is lowered (step-down) , causing an increase of current. A transformer typically comprises a primary coil, a secondary coil and a magnetic core, coupling the coils. An alternating input current through the primary coil generates an alternating magnetic field that is conducted by the core to the secondary coil where it induces an alternating output current. A wide range of different constructions exist to account for parameters like a count of electrical phases, voltages levels and converted power.

Physical dimensions of a transformer rise with its power requirements. A transformer used on a ship, an urban power grid or in mining applications may be considered medium scale and handle power up to several ten MVA (apparent power in Mega volt-ampere) . A large scale transformer may be used for example in a power plant, a steelworks or a high-voltage, direct current (HVDC) electric power transmission system (also called a power super highway or electrical super highway) . An exemplary large scale transformer may conduct a power equivalent of up to 1,300 MVA, be about three storeys high and weigh more than 600 tons. Given the sheer mass and the efforts required for handling such a transformer, even a minute change in one parameter may have a significant impact on safety and costs. Despite its gross physical dimensions a transformer is a delicate unit when it comes to designing it. Occurring forces must be balanced in case of short circuits, heat dissipation must be accounted for and generally everything should be sufficiently rugged in a mechanical and electrical way, but also efficient on the employed material.

Hitherto, design of a transformer was done by an experienced electrical engineer who must find a suitable starting point considering the core and its flux density as well as the winding setup in order to find a technical solution for customer requirements and applicable standards e.g. IEC. In a second step several approaches are evaluated to achieve lowest costsThe degree of freedom for these determinations could be considerable, accounting for the shape and material of the core and a used strand or a given winding arrangement. Considerations like built-in security for a worst case scenario or sound management could also influence a

determined solution. The whole process required several iterations as changing one factor might influence one or more other factors, leading to more changes.

It is therefore an object of present invention to provide an improved way for determining dimensions for an electric transformer. The invention solves this object by the subject matter defined in enclosed independent claims. Dependent claims give preferred embodiments.

Disclosure of the Invention

Present invention concerns a method and a device for

determining a winding geometry for an electrical transformer, the transformer having a winding comprising several turns of a conductor and a core with a core window for receiving the winding. A method for determining a winding geometry for said transformer comprises steps of determining at least one electrical requirement for the transformer; determining at least one physical constraint for transformer dimensions; and determining a winding geometry based on the at least one requirements and at least one constraint. In this, the winding geometry comprises a winding arrangement, a conductor cross section and a count of turns and determination is done following an optimization algorithm with the objective to find a technical solution for given constraints with lowest costs .

By using an optimization algorithm it is possible to achieve a high quality for a winding geometry at substantially less human effort and considerably shorter determination time. Speed and quality of the solution may no longer be subject to experience or instinct of an engineer. Geometry optimization is preferred to be done using a Mixed Integer Optimization system. Such solvers are commercially available and well researched. The solver may run on a standard computer system and provide good results for medium to large sized optimization problems.

Geometry determination may be done using an Ant Colony

Optimization. This may help to make situations in which only a local optimum is found during optimization less probable. A search space generated by the requirements and constraints may be reduced prior to optimization. By reducing the size of the search space the time required for optimization can be reduced and quality of a found solution may be increased. For search space reduction, at least one of a strand height, a strand width, a count of axial parallel conductors and a count of radially parallel conductors may be limited in their range. Simple and reliable restrictions may be applied to restrict these variables. The more variables are restricted, the more effectively the search space may be minimized.

The winding type may comprise a disc winding wherein at least one of a count of discs and a count of turns per disc is limited in its range. Alternatively, the winding type may comprise a layer winding wherein at least one of a count of layers and a count of turns per layer is limited in its range. Disc type windings and layer windings may be mixed in the same transformer. The conductor may be of the

continuously transposed conductors type wherein a count of radially parallel conductors is limited in its range.

A method for determining a winding geometry for an electrical transformer comprises steps of: determining a range for a count of layers for each winding of layer type; determining geometry candidates, each candidate having a different combination of a winding height, a winding width and a count of layers for each of the windings; and finding an optimized winding geometry using a method described herein.

A device comprises a processing unit, wherein the processing unit is adapted to execute a method disclosed herein. The method may especially be carried out, completely or in part, on a computer system. To this end, the method may be

formulated as a computer program product with program code means. Advantages or features of the method may apply to the method and vice versa. Brief Summary of the Enclosed Figures

The above-described properties, features and advantages of present invention as well as the way they are achieved will be made clearer and better understandable in the light of the following discussion, making reference to exemplary

embodiments shown in accompanying figures, in which

Fig. 1 shows an exemplary transformer; Fig. 2 shows an exemplary winding geometry on a core of a transformer; Fig. 3 shows a graphic representation 300 of an exemplary strand dimension constraint;

Fig. 4 shows a system and a method for winding geometry

determination;

Fig. 5 shows strand layout and dimensions for a flat

strand; Fig. 6 shows conductor layout and dimensions for a

continuously transposed conductor (CTC) strand;

Fig. 7 shows a block diagram of a method for determining a winding geometry for a transformer; and

Fig. 8 shows a schematic diagram of a method for optimizing a winding geometry.

Detailed Exemplary Embodiments of the Invention

Figure 1 shows a schematic view of an exemplary transformer 100. Depicted are a side view 105, a perspective view 110 and a top view 115. The transformer 100 comprises a core 120 which in the given arrangement possesses an m-shape with three limbs 125 and a yoke 125. In other embodiments the core 105 may also have a different shape.

The iron core 105 forms the central element of the

transformer 100 and usually comprises metal sheets with thicknesses of ca. 0.35 mm or less. The individual sheets are then preferred to be assembled into the core 105 manually, for example using the "step-lap" technique. This may lead to a good flux distribution at joints, resulting in low losses and reduced no-load noise.

The transformer 100 furthermore comprises windings 135 on the limbs 125. Often, a primary winding 135 and a secondary winding 135 are disposed coaxially on the same limb 125, wherein one of the windings 135 lies radially inside the other winding 135. One winding 135 may be of disc type while another winding 135 on the same limb 125 may be of the layer type. More than two windings 135 may be disposed with radial offsets. Figure 1 shows only the items of concern in

conjunction with present invention; a real world transformer 100 would typically comprise other elements that are not shown, for example a container for the core 120 and the windings 135, oil to fill the container, an external tank for oil supply, leads and cleats as well as a bushing, measuring equipment or a tap-changer. Accessories may comprise a cooling system which may comprise a fan, a pump or a valve. More common features comprise a foundation, attachment points for lashing and the like.

Each winding 135 comprises one or more turns of a conductor 150 having one or several strands 155 and is subject to a continuously high electrical or mechanical load. The windings 135 may be implemented in one of several different

arrangements, including the layer winding and disc winding. Different arrangements of strands 155 forming a conductor 150 may be applicable. In a disc winding, the conductor 150 may be wound to a disc wherein several turns of the conductor 150 may be primarily displaced radially. Several such discs may be comprised by one winding 135. Turns of the conductor 150 may lie radially adjacent or be separated by another item like another

conductor 150. Discs may lie axially adjacent or be separated similarly .

In a layer winding, the conductor 150 may be wound such that several of its turns lie primarily displaced in an axial direction so that the turns form a hollow cylinder. Several coaxial hollow cylinders may be comprised by a winding 135. The conductor 150 may have a continuous slope over one turn or extend chiefly in a plane perpendicular to the winding axis and change its axial position only once or a few times per turn.

Other arrangements than disc and layer type may also be available. The conductor 150 may comprise one or more strands 155 which are preferred to be nominally of oblong cross section .

A flat conductor 150 may comprise one or more strands that follow a fixed arrangement as the conductor 150 is wound around the limb 125 and its winding axis. Several strands 155 that are entwined in a predetermined way to form a conductor 150 are called Continuously Transposed Conductors (CTC) . Such conductors 150 are generally more complex to wind but may offer superior electrical properties.

Between turns of the windings 135, cooling channels may be provided for a coolant to flow and remove excess heat during transformer operation. The windings 135 are preferred to be manufactured with high precision, in one piece and from a material with narrow tolerance dimensions. Multi-layer windings 135, especially for low voltages, often consist of concentrically superimposed cylindrical coils separated by axial oil ducts. The finished windings 135 may be pressed, dried under constant pressure, impregnated with oil, measured exactly, and geometrically adjusted if required.

Figure 2 shows a winding geometry 200 on a core 120 of a transformer 100. For better understanding, only one winding 135 one the middle limb 125 is shown. It is understood that the shown winding 135 may be disposed radially on the outside of another winding 135 on the same limb 125. The core 120 forms one or more windows 205 of height 210 into which at least one winding 135 may be installed. A windings' 135 height 215 should be smaller than the window height 210.

An advantageous winding geometry 200 may make good use of an available space. It is proposed to determine an optimized winding geometry 200 on the basis of available electrical and/or mechanical specifications or constraints. Further constraints may be determined on the basis of cost and manufacturing relevant requirements. The specifications and constraints, as well as possible additional variables, form a search space in which an optimal combination is determined. It is proposed to conduct an automated search with an

objective function that permits a winding geometry 200 to fill an available space as best it can, that is, a winding geometry 200 is sought that optimizes the winding's 135 height 215 into the window height 210. A predetermined yoke distance 220 between the winding 135 and the yoke must be kept . Since the optimization variables contain integer variables, a black-box MINLP (mixed-integer-non-linear-programming) solver is suggested for solving the optimization problem. According to test results, this can lead to automatically generated valid winding geometry within seconds, while a corresponding manual process might take hours even by an experienced design engineer. A generated winding geometry may fulfil given cost and manufacturing requirements and even have a higher quality than a geometry initially proposed by a design engineer. Possible variables include:

- strand height: d_a

- strand width: d_r

- number of radial parallel strands (for CTC conductor) : n_s,_r (integer)

- number of axial parallel strands: n_Sia (integer)

- number of axial parallel conductors: n_c,_a (integer)

- number of radial parallel conductors: n_Ci∑ (integer)

- number of discs and number of turns per disc (for disc winding) : n_Disc, n_TurriPerDisc (integer)

- number of layers and number of turns per layer (for

layer winding) : n_Layer, n_{TurriPerLayer} (integer) Possible winding constraints include:

- strand dimension constraints

- window height: h_windows-h_wiri(lirig-d_yOke^≥0

- conductor area (current density -> (minArea, maxArea)

^conductor ~ d_r * d_a * 2 * s,a * ^ca * ^ ,r

- number of total turns:

- disc: n_Total = η- Di·sc ^ilTurnPerDisc

layer: nT-otal ^— l^Layer * ^TurnPerLayer Dimensions of the strand 155 may cover certain combinations of width (w) vs. height (h) . Figure 3 shows a graphic

representation 300 of an exemplary constraint. A horizontal direction shows a strand width and a vertical direction a strand height. A polygon 305 outlines combinations of height and width of a strand 155 that are considered sensible or feasible. An optimal combination 310 is as yet to be

determined .

An object of the optimization could then be:

with h_wiridows: window height

hiding: winding height

dyoke: yoke distance. The conductor may generally come flat or as CTC. A flat conductor may comprise more than one strand but an

arrangement of the conductors is constant over the turns of a winding 135. A CTC conductor always comprises more than one strand and an arrangement of the strands is varied over the turns of a winding 135. In this, different variation schemes may apply. The following two figures give definitions for characteristically geometric measurements.

Figure 4 shows a system 400 for determining a winding

geometry 200 for a transformer 100. The system 400 comprises a data interface 405, a processing system 410 and an optional reference database 415. Using the data interface 405, definitions and constraints for a transformer 100 may be entered or selected. The processing system 410 is adapted to determine a winding geometry 200 for the transformer 100 according to the teachings herein. The reference database 415 is adapted to hold reference data of known transformers 100 and/or winding geometries 200. The processing system 410 may especially comprise a programmable microcomputer or

microcontroller that is adapted to execute a computer program product that processes a method that is described herein. Advantages or features of the processing system 410 may apply for the method and vice versa.

The processing system 410 is preferred to be adapted to carry out a method 420 for determining the winding geometry 200. The method 420 is also shown in figure 4 in schematic form.

The method 420 may come as a computer program product and may be stored on a computer readable medium.

In a step 425, definition data for a transformer 100 for which a winding geometry 200 is to be determined may be entered or selected. In a step 430 the processing system 410 may be initialized. Data on a known transformer 100 or a known winding geometry may be retrieved from the database 415. In a step 432, geometry 200 of a transformer 100 is evaluated. An objective function and constraints are

evaluated. In a step 435, a penalty function is calculated to evaluate a winding design 200.

In a transformer simulation / evaluation step 435, the value of the defined objective function and constraints is

determined. In a step 435, a penalty function value is calculated to evaluate the generated winding design. The penalty function value of step 430 will guide the solver 440 in generating a new winding design. These steps are iterated until the generated winding design fulfils all requirements and a minimum of the objective function is reached. An optimized transformer geometry may be output in a step 445. It is preferred that optimization in step 440 is done using a MINLP solver. Such solvers are commercially available and may run on standard computer systems. A MINLP solver is generally adapted to find an optimal solution in a given search space. The search space is determined by a number of design

parameters and corresponding parameter characteristics

(range, min, max, step size) . As the number of parameters gets larger, the dimension of the search space may grow excessively. Constraints and relationships between parameters may also be given. A solution is generally a valid

combination of design parameters. Quality of a solution may be determined using a penalty function that combines the value of an objective function and corresponding constraints. In present case, quality may be indicative of how well a winding geometry fills an available winding space. An MINLP solver generally starts at a solution and tries to improve it in the search space. If the solution cannot be improved any further, it may be output. Several such runs may be required to find a globally optimized solution. Depending on the application, in a MINLP solver it is generally known how far a determined solution is away from a theoretically achievable optimal solution ("gap") . In present embodiment it may more specifically be known that in a perfect solution the winding 135 fills the available window 205 completely so that a remaining gap between winding 135 and the boundary of window 205 has size zero. Optimization may terminate (a) if an optimal solution is found, (b) a predetermined search time has been used up or (c) the search space has been

exhaustively traversed.

The output may comprise one or more geometric designs from which a user may then chose. Given the computation power of a modern computer, the method 420 may evaluate thousands proposed designs within a matter of seconds. The method 420 may reduce the design time for a transformer 100 and enable a user to concentrate on his main engineering tasks (electrical design / costs) and not to take care of geometrical details. Besides, the method may also explore solutions which are sometimes neglected by design engineers, leading to novel and better transformer designs.

Besides, present method 420 may also provide to a user the option to work interactively with the system 400: when the processing system 410 delivers a geometry design, the user may change a parameter search area, remove or add a new constraint, and run the optimization method 420 again. The processing system 420 may then determine a new geometry design according to the modification very fast. In this way, the user can continuously improve the design of the

transformer 100.

The next two figures 5 and 6 show geometric dimensions of a conductor 150 in a winding 135 of a transformer 100.

Symbols used in these figures comprise: number of axial parallel strands NAPS

number of radial parallel strands NRPS

axial height of a single strand DHS

radial width of a single strand Dws

thickness of enamel DTEN

inner insulation thickness D_IIT

middle insulation thickness DMIT

outer insulation thickness DOIT

pressing factor for paper Cppp

pressing factor for pressboard Cppp

tolerance of the height for strand DTHS

tolerance of the width for strand DTWS

epoxy thickness D_ET

corner radius of strand DCRS

Figure 5 shows dimensions of a flat conductor 150. In a first option 505 (FLAT) , a conductor 150 with generally rectangular cross section may be used. In a second option 510 (TWIN) , the conductor 150 may comprise two strands 155 that are stacked in a radial direction with respect to a winding axis for windings 135. In a third option 515 (TWUP) , the conductor 150 may comprise two strands 155 that are stacked in an axial direction with respect to a winding axis for windings 135. Finally, in a fourth option 520 (QUAD) , four strands 155 are combined in both radial and axial direction.

The dimension polygon 305 of a flat conductor is generally drawn based on empiric values. Conductor 150 height, width and cross section can be determined thus:

Height of conductor:

PFP + (N4PS - 1) * D_ET

Width of conductor:

D_WC — N_RPS * + (N_RPS - 1) * D_ET

Cross section of a conductor: cc = N_APS * N_RPS * [D_HS * D_WS - (D_CRS) ² * (4

Cross section of a cable:

A cable may comprise several isolated conductors 150 running in parallel. A cross section of the cable comprises the cross sections of all its conductors 150.

Figure 6 shows exemplary dimensions of a CTC conductor 150 in a first option 605 and a second option 610. The number of axial parallel strands is preferred to be fixed, while the number of radial parallel strands may be an optimization variable. The strand dimension polygon 305 of a CTC conductor 150 is generally drawn based on empiric values. Strand height, width and cross section can be determined thus:

Height of a CTC conductor:

DHC— NAPS * D_HS + D_THS + D_TEN + I D_IIT +

*C P,FB + D HCC

Width of conductor:

Dwc = (N_RPS + 0.5) * (D_ws + D_TWS + D_TEN + D_UT) + (D_MIT + D_0IT)(N_RPS + 0.5 - 1)

*D_ET

Cross section of a conductor:

Acc = N_APS * N_RPS * [D_HS * D_ws - (D_CRC)² * (4 - π)]

Cross section of a conductor 150:

A_CCA = NA_PS * N_RPS * [D_HC * D_wc - (D_CRC)² * (4 - π)\

The height of a winding 135 may be calculated differently for layer and disc windings 135. For a layer winding 135 the height may be determined thus:

N_S

DEH, (N_R + 1) * N_Apc * D_HC + ^ D_HS * C_PFS + (N_APC wherein

N_S = (N_T + 1) * N_APC - 1;

and

^NAPC

D_RT — N_Apc * D_HC + ^ D_HS * C_PFS

k=l

Symbols comprise (cf . Fig. 6) : nominal height of the winding D WH width of the winding DRW

cross section of strand A_CC

number of axially parallel conductors N_APC

number of radially parallel conductors N_RPC

number of axial turns per layer N_T

number of layers N_L

conductor corner radius DCRC

For a disc winding 135 the height may be determined

Symbols comprise: axial height of conductor 150 after pressing D_HC

height of spacer D_HS

count of disc type used in a winding 135 N_D

number of discs used in the winding NDSC

pressing factor for each spacer C_PFS With the given parameters, variables and constraints, an optimized winding geometry 200 may be determined by an optimization method as described above or performing an exhaustive search. However, a search space may be very large so that processing may take a very long time even on a high performance computer system. In order to reduce the time required for search or optimization it is proposed to reduce the search space beforehand.

For a layer winding 135 it is proposed to reduce search ranges for at least one of the following variables:

Step 0: reduce upper limit for the height of the strand:

Max_StrandHeight =

Max_ConductorHeightNoPress/NoAxialParallelStrand Step 1 : reduce range for number of layers Max_NoLayer =

Ceil (Max_StrandHeight*NoAxialParallelStrands *NoAxialParallelC onductor (assumption = 1) *TotalTurns) /WindingHeight )

Min_NoLayer =

Ceil (Min_StrandHeight*NoAxialParallelStrands *NoAxialParallelC onductor (assumption = 1 ) *TotalTurns/WindingHeight )

Step 2: reduce range for number of axially parallel

conductors Min_NoAxialParallelConductor =

Ceil (Min_NoLayer*WindingHeight/ (Max_StrandHeight*NoAxialParal lelStrand*TotalTurns) )

Max_NoAxialParallelConductor =

Ceil (Max_NoLayer*WindingHeight/ (Min_StrandHeight*NoAxialParal lelStrand*TotalTurns) )

Step 3: reduce upper limit for number of radially parallel conductors (only for CTC)

Max_NoRadialParallelStrand =

Ceil (Max_ConductorWidth/Min_StrandWidth -1)

Step 4: reduce range for number of radially parallel

conductors

Min_NoRadialParallelConductor =

ceil (Min_ConductorArea/ (Max_StrandArea*NoAxialParallelStrand* Max_NoRadialParallelStrand*Max_NoAxialParallelCondcutor) )

Max_NoRadialParallelConductor =

floor (Max_ConductorArea/ (Min_StrandArea*NoAxialParallelStrand *Min NoRadialParallelStrand*Min NoAxialParallelCondcutor) ) For a disc winding 135 it is proposed to reduce search ranges for at least one of the following variables:

Step 0: reduce upper limit for the height of the strand 150

Max_StrandHeight =

Max_ConductorHeightNoPress/NoAxialParallelStrand

Step 1: reduce range for number of axially parallel

conductors Min_NoAxialParallelConductor =

Ceil (Min_NoTurnsPerDisc*WindingHeight/ (Max_StrandHeight*NoAxi alParallelStrand*TotalTurns) )

Max_NoAxialParallelConductor =

Ceil (Max_NoTurnsPerDisc*WindingHeight/ (Min_StrandHeight*NoAxi alParallelStrand*TotalTurns) )

Step 2: reduce upper limit for number of radially parallel strands (only for CTC)

Max_NoRadialParallelStrand =

Ceil (Max_CodunctorWidth/Min_StrandWidth - 1)

Step 3: reduce range for number of radially parallel

conductors

Min_NoRadialParallelConductor =

Max_NoRadialParallelConductor =

floor (Max_ConductorArea/ (Min_StrandArea*NoAxialParallelStrand *Min NoRadialParallelStrand*Min NoAxialParallelCondcutor) ) In order to further improve search / optimization performance, an extra constraint for the number of radially parallel strands 150 may be introduced.

Should the number of radially parallel strands be lower than a predetermined number, say 10, then the number of radially parallel conductors may be set to a predetermined number, say 1. An example in pseudo notation: IF NoRadialParallelStrand < 10 THEN NoRadialParallelConductor = 1 END

Should the number of radially parallel strands be within a predetermined range, say within 10 and 30, then the number or radially parallel conductors may be limited to another predetermined number, say 2. Example: IF 10 <=

NoRadialParallelStrand <= 30 THEN NoRadialParallelConductor <= 2 END

Should the number or radially parallel strands exceed yet another predetermined number, say 30, then the number of radially parallel conductors may be limited to the maximum number of radially parallel conductors. Example: IF

NoRadialParallelStrand > 30 THEN NoRadialParallelConductor <= MaxNoRadialParallelConductor END

The optimization process may follow a deterministic or white box approach that guarantees global optimality and quick convergence and requires the given formulation of the

mathematical MINLP in an explicit way. Alternatively a stochastic or black box approach may be used that does not require the mathematical formulation of the optimization problem but requires a high amount of function evaluation.

Figure 7 shows a block diagram of a method 700 for

determining a winding geometry 200 for a transformer, wherein short circuit impedance is taken into account. Short circuit impedance of a transformer 100 determines the regulation (voltage drop across the transformer 100) under load conditions. By ensuring predetermined impedance, a short circuit current and a resulting force on the core 120 or a strand 150 may be limited. The short circuit impedance of a transformer 100 is generally a design goal and may be

specified by a customer or determined by a predetermined standard like IEEE. The short circuit impedance may be expressed in percent of rated impedance, which is equal to a percent value of a short circuit value, or in Watts related to primary or secondary side of the transformer 100. In general, the impedance is Z=R+jX, but resistance (R) may be negligible. In this, jX depends on geometry, amp-turns, base power and frequency of the transformer 100.

Short circuit reactance of a transformer 100 may be

calculated using a magnetic field program (based for instance on a finite element or Rabins approach) or can be estimated using simple formulas.

A high value of stray reactance in design may result in one or more of the following:

• high leakage flux, leading to high additional (eddy) losses in windings and constructional parts,

· increase in the highest (hot-spot) temperature

• higher manufacturing cost;

• the value of voltage regulation is high

• short circuit currents are limited, forces are low. A low value of impedance may result in larger short circuit currents, leading to higher forces. Designing is difficult, more copper must be added, epoxy bonded CTC strands 150 have to be used, more spacers between turns of the strand 150 may have to be added.

The proposed method 700 uses a first block 705 in which a winding geometry 200 for the transformer 100 is determined and a second block 710 in which the transformer 100 itself is designed. The second block 710 may use one or several known approaches to determine transformer characteristics excluding the winding geometry 200. Based on design variables from a step 712, the first block 705 determines the number of layers used on the transformer 100 in a step 715. The count of layers corresponds to how many strands 155 may lie in parallel in a radial direction as part of one conductor 150.

The determination is based on a planned target window height 210 (cf . Figure 2) . As the number of layers may be dependent on other parameters, several different window heights 210 may be determined that may be treated as candidates.

In a step 720, the second block 710 determines at least some characteristic values of the transformer's 100 geometry on the basis of the candidate window heights 210 and a

predetermined current density. This results in a number of datasets wherein each dataset has a winding height 215, a winding width and a count of layers.

In a step 725, the above described optimization process for the winding geometry 200 using mixed integer nonlinear programming is performed once for each of the datasets. As will be shown below, optimization may be done iteratively over the windings 135, effectively reducing the number of required optimization runs. For each winding 135 not only one but several optimizations may be run. Optimization yields one optimized winding geometry which may then be used.

In a step 730 the second block 710 may perform a fine concept optimization, that is, other parameters of the transformer 100 may be adapted to the chosen winding geometry 200.

Method 700 is special over other methods in that it firstly decouples the problem of determining a transformer 100 design into a winding geometry optimization 705 and a design generation 710, and secondly in the novel approach to reduce the number of optimizations required in step 720.

By decoupling the winding geometry optimization 705 from the design generation 710, optimization in step 725 may work iteratively. The iterative approach may be further

accelerated by processing only promising datasets and

discarding redundant or inferior ones. It has been found that a brute force approach where all possible parameters of a transformer 100 are thrown into one big optimization run, an average computer system may easily be unable to cope with the size of the resulting search space. While an optimization run for one of the datasets may be complete within a few seconds, exhaustive optimization of all parameters may take time in the order of weeks. The probability that such an optimization may get stuck at a local minimum is high. An interactive design process with exhaustive optimization would therefore be practically unfeasible. Figure 8 shows a schematic diagram of a method 800 for winding geometry optimization. Method 800 may be an

implementation of step 725 of method 700. The method 800 will be explained with reference to sample datasets that may have been provided by step 720. Each dataset is represented as one line in a table 1:

Table 1 In a first step 805, table 1 is sorted according to the number of layers in each of the windings 135 in descending direction. After sorting, the winding 135 with the biggest change range of number of layers comes first. In present case, three windings Wl, W2 and W3 are used. However, the second winding W2 will be a disc type so that the

corresponding number of layers is meaningless. All entries in this column are therefore set to -1. Wl has the smallest change range (1-2 layers) . The sorting results in table 2:

Table 2

The winding 135—145 with the highest change range (here: W3) defines groups where its number (or count) of layers is unique. In present example a first group comprises variants 1, 3 and 5 and a second group comprises variants 2, 4 and 6. In each group, number of layers for winding W3 will be 1, 2 or 3. For each group one optimization will be run. If the difference between target heights is small, the second optimization is expected to take much less time than the first one, since the solution achieve of the first

optimization is used as the initial achieve of the second optimization. In present example, the optimized number of layers for W3 in the first group is 1 (variant 1) and the optimized number of layers in the second group is 2 (variant 4) . Then, the next winding (here: Wl) is optimized, using the results from the previous optimization. In present example, optimization is run on variants 1 and 4. The process repeats until all layer type windings 135 are optimized. In present example only four optimization runs are required for

optimization of six variants. In a following step, the disc windings (here: W2) and possible regulation windings may be optimized. The overview of this sequential winding geometry optimization method is described in Figure 8.

In a step 805, layer winding indices are sorted in descending order according to the change range of variable ("NoLayer" (number of layers) . In a successive step 810, target value groups are built as described above. For each group, an optimization is run in a step 815. In a step 820 it can be determined if an optimum has been found. Should this not be the case, the target windings of the next optimized winding may be set to -1, effectively excluding this winding from optimization.

In the alternative, when at least one optimum has been found, the variant index of the found optimum may be taken as target values of next optimized winding. In other words, another group may be built from the found optima and another

optimization may be run on that group.

In a step 835 it may be determined if the target value groups have all been processed. If this is not the case, method 800 may proceed with step 815. Otherwise, in a step 840 the optimized winding index is deleted from the sorted indices. In a step 845 it may be determined if the sorted indices have reached an end. In this case optimizations for disc type and regulation windings may be performed in a step 850.

Otherwise, method 800 may proceed with step 810.

The proposed methods 700, 800 may be used to generate a winding geometry 200 design that fulfils a predetermined short-circuit impedance requirement. The methods 700, 800 take all the winding geometry of a transformer system into consideration. Comparing with another method that optimizes the winding geometry separately and checks the impedance later for further adaption, the proposed methods 700, 800 are straightforward and may deliver a global optimum.

Present invention optimizes the winding geometries 200 sequentially. Each optimization contains only the design parameters of one winding 135, therefore the dimension of optimization is reduced, making it require less resource and reducing the risk of the optimization getting stuck on a local minimum. By using the solution archive from a previous optimization as initial value, optimization for successive runs may be sped up considerably. If a difference between target heights of a winding 135 is small, the second

optimization is expected to take much less time than the first one. In this invention, we propose a novel method to run the optimization 725 sequentially. Compared to a brute force method that runs optimization using each row of the input table as constraint, the proposed method has obvious

advantage. For a transformer system with N layer windings and M disc and regulation windings, with change ranges of NoLayer being k_n, k_n_i,... ki respectively, the total number of

optimizations needed by the proposed method is

1+M. The number of optimizations required by a brute force method is \[\_=n k_x * (N + M) .

Taking the case of table 1 as an example, the proposed method 700, 800 needs to run 4 optimizations to complete the task, while the brute force method will need 18 optimizations, plus additional post-processing. When the number of windings 135 and the change ranges of the variables "number of layers" increase, the advantage becomes more and more drastic. Even though present invention has been illustrated and explained in detail above with reference to the preferred embodiments, the invention is not to be construed as limited to the given examples. Variants or alternate combinations of features given in different embodiments may be derived by a subject matter expert without exceeding the scope of present invention .

Claims

Patent Claims

1. Method (420) for determining a winding (135) geometry

(200) for an electrical transformer (100), the transformer (100) having a winding (135) comprising several turns of a conductor (150) and a core (120) with a core (120) window (205) for receiving the winding (135), wherein the method (420) comprises steps of:

- determining at least one electrical requirement for the transformer (100);

- determining at least one physical constraint for

transformer (100) dimensions; and

- determining a winding (135) geometry (200) based on the at least one requirements and at least one constraints, - wherein the winding (135) geometry (200) comprises a winding (135) arrangement, a strand cross section and a count of turns;

- wherein determination is done following an optimization algorithm with the objective to minimize a distance between a height of the winding (135) and a height of the core (120) window (205) .

2. Method (420) according to claim 1, wherein geometry

optimization is done using a Mixed Integer Optimization system.

3. Method (420) according to claim 1 or 2, wherein Method

(420) a search space generated by the requirements and constraints is reduced prior to optimization.

4. Method (420) according to claim 3, wherein at least one of a strand height, a strand width, a count of axial parallel conductor (150) s and a count of radially parallel

conductor (150) s is limited in its range.

5. Method (420) according to one of claims 3 or 4, wherein the winding (135) type comprises a disc winding (135) and at least one of a count of discs and a count of turns per disc is limited in its range.

Method (420) according to one of claims 3 or 4, wherein the winding (135) type comprises a layer winding (135) and at least one of a count of layers and a count of turns per layer is limited in its range.

Method (420) according to one of the preceding claims, wherein the strand comprises continuously transposed conductor (150) s and a count of radially parallel strands is limited in its range.

Method (420) for determining a winding (135) geometry (200) for an electrical transformer (100), the method (420) comprising steps of:

- determining a range for a count of layers for each

winding (135) of layer type;

- determining geometry candidates, each candidate having a different combination of a winding (135) height, a winding (135) width and a count of layers for each of the winding (135) s; and

- finding an optimized winding (135) geometry (200) using a method (420) according to one of the above claims.

Computer program product with program code means, wherein the computer program product is adapted to implement a method (420) according to one of the above claims when the program code means is running on a processing unit (410) .

Device (400), comprising a processing unit (410), wherein the processing unit (410) is adapted to execute a method (420) according to one of claims 1 through 8.