Design and Optimization Procedurefor High Voltage Pulse Power Transformers

S. Blume, M. Jaritz and J. BielaLaboratory for High Power Electronic Systems, ETH Zurich, Email: blume@hpe.ee.ethz.ch

Abstract—A design and optimization procedure for high volt-age pulse transformers is presented. The procedure is enhancedby integration of core loss measurements under pulsed excitation,by electrical peak field calculations and by checking the isolationdistances comparing them to scaled high voltage breakdown data.The procedure is applied with specifications of the CompactLinear Collider (CLIC) and the sensitivity of system parameterssuch as core material, transformer oil and high voltage cable isinvestigated by comparing their Pareto fronts. With amorphouscore material the highest efficiency is achieved. Replacing mineraloil by natural ester results in an efficiency reduction of 0.5 % andan increased cable length from 1.5 m to 5 m reduces the efficiencyby 0.6 %.

I. INTRODUCTION

In the design process of pulse transformers, optimizationprocedures not only allow an optimal design, but can also beapplied for a sensitivity analysis of system parameters. Forfast computations the procedures are either based on 2D-FEM[1], on analytical formulas [2] or a combination of both [3]. In[4] a design procedure has been presented that calculates thetransformer parasitics analytically, analyzes the pulse shape inthe time domain and determines the transformer geometry foran optimal pulse shape. In this paper several improvements tothat procedure are presented, which are highlighted in Fig. 1.At first in section II, the integration of core loss data underpulsed excitation in the procedure is described. Thereafter, insection III the integrated electrical surface field calculationas well as the post-optimization process examining the iso-lation distances are explained. Furthermore, in section IV atransformer is designed with the optimisation procedure forspecification of the compact linear collider (CLIC) and thesensitivity of the transformer design system parameters suchas the magnetic core material, transformer oil and the highvoltage cable length are investigated.

II. CORE LOSS MEASUREMENT DATA

When choosing a core material important parameters arethe core losses, the maximal flux density and the core weight.Since core loss data is usually based on sinusoidal excitation,the losses under pulsed excitation have been measured forthree different core materials using smaller sized cut C-cores.The measurement setup is depicted in Fig. 2a) and the appliedvoltage shape is displayed in Fig. 2b). The measurementmethod is described in detail in [5]. The flux density wasvaried from Bmin = 0.1 T to the respective saturation fluxdensity of the material. The relevant parameters of the mea-surements as well as a comparison of the loss energy at aflux swing of ∆B = 1 T are listed in Tab. I. The lowestlosses occur with the nanocrystalline material. Compared tothe nanocrystalline core the amorphous core shows higherlosses by a factor of 2.8, the silicon iron core even higherlosses by a factor of 13.2.By integrating the measurement data, the procedure is ex-tended by an additional free design parameter, which is themagnetic flux swing ∆B. The maximal allowed flux densitiesBmax in the optimization procedure, also listed in Tab. I, arechosen in the linear region of the BH-loop. In section IV-Athe influence of these three core materials on the transformerdesign is discussed.

Pulse Requirement eg. Rise Time,

Flat-top Stability,...

Con

stra

ints

Global Optimizer (Optimization Parameters)

Switching Losses

Optimal Design

Analytical Calculation of Lσ and Cd

Core Losses

Active Bias Losses

Winding Losses Losses

Pulse Shape Analysis Respecting Pulse Constraints

Geometric Parameter Creation

GeometricParameters

Epeak Limitation on Conductor Surface

Global External System Parameters

Core Loss MeasurementsPulsed Excitation, 3 Materials

Checked Optimal Design

Isolation Distance Examination

Em<Emax

Yes

No

New Parameter Set

Fig. 1. Optimization procedure with indication of new features. The core lossmeasurement integration, the electrical peak field calculation at the conductorsurfaces within the optimization cycle and the examination of the isolationdistances from scaled impulse breakdown data in an additional process.

III. ISOLATION DISTANCE IN PULSE TRANSFORMERS

A challenge in high voltage pulse transformer design presentthe isolation distances. On the one hand small isolationdistances reduce the leakage inductance thereby maximizingefficiency and limiting the transformer size, on the other handpartial discharge must be avoided and long transformer lifetime is desired.In order to achieve an optimal balance for these contradictingrequirements, a two stage approach is presented in this paper.

+- +

-

V1 V2

A

V

CUT

a) b)

V2

V1

V1·tp= V2·(tpre+tde )

tp

tpre tde

Fig. 2. a) Schematic of core loss measurement setup [5], b) Applied voltageshape with premagnetisation time tpre, pulse duration tp and demagnetizationtime tde.

TABLE ISPECIFICATION OF CORE LOSS MEASUREMENTS UNDER PULSED

EXCITATION

Nanocrystalline Amorphous SiFe3%Parameter (VITROPERM Metglas (100µm)

500F) (2605SA1)Cross-sectional area(mm2)

795 704 748

Mean magnetic length(mm)

432 373 507

Saturation flux densityBsat(T)

1.2 1.56 2

Maximal flux densityBmax (T)

1.0 1.2 1.5

Premagnetisation timetpre (ms)

1.05 1.05 1.05

Pulse duration tp(ms)

0.14 0.14 0.14

Demagnetization timetde (ms)

1.05 1.05 1.05

Ecore(@∆B = 1 T)(J/m3)

13.97 38.87 184.29

In the first stage, the electrical peak field is limited within theoptimisation procedure to obtain a suitable transformer designwith a certain oil gap distance. In the second stage, in a post-optimization process, the design result is checked by analysisof the most critical field path.

A. Electrical Peak Field for Arbitrary Winding Geometries

In order to obtain a suitable transformer design, the pro-cedure must be equipped with an electrical field model,which is accurate and fast enough to be evaluated within anoptimization cycle. In order to achieve both goals an analyticalelectrical field model based on the 2D-charge simulationmethod (CSM) is implemented [6]. Grounded surfaces, suchas the tank wall, can be considered in the CSM by chargemirroring [4]. For the sake of speed, the electrical field isonly calculated on the conductor surfaces of the secondarywinding. In order to reach high accuracy, 16 contour pointsper secondary turn are calculated. Detailed description of theapplied method is given in [7]. The electrical peak field iscompared to 2D-FEM, reaching deviations smaller than 5 %.With the chosen approach, the procedure is able to derive themaximal electrical peak field on each conductor. In order tocheck the design result, not only the resulting peak field mustbe considered, but also the most critical electrical field path,which is described in the following section.

B. Isolation Distance Verification

In a high voltage transformer, breakdown mechanisms de-pend on many parameters and influences. Since in most casesthere only exist breakdown data for small gaps under certainexcitations, in this paper a procedure is presented which adaptsavailable breakdown data to a real size pulse transformer.The procedure is depicted in Fig. 3. At first, a method ispresented which allows a scaling from standard breakdowndata to a given pulse shape. Thereafter, the adaption of thebreakdown data to high withstand probabilities at an increasedvolume is described. Additionally, a method is presented howinhomogeneous electrical fields occurring in the design can beevaluated. Finally, a transformer design with specifications ofCLIC is compared to scaled breakdown data of mineral andester oil.

1) Pulse Shape: The most investigated pulsed voltageshapes are the switching impulse (SI) and the lightning im-pulse (LI). In [8] non-standard LI waveforms were investigatedfor pulses with different lengths. It was found that the break-down voltage does not correlate with the wavefront time, butwith the time the pulse exceeds a certain voltage. The highest

Optimal Design

No Yes

Em<Emax

2D FEM Analysis of Geometry

Obtain Most Critical Electrical Field Path

Calculate Em

Checked Optimal Design

LI and SI in Ehomd=3.8-150mm

Create New Design

Pulse ShapeV·t, t for V > 0.8∙Vmax

Emaxin Dependence of Gap Distance

Chose Withstand ProbabilityPw=99%

Consideration of Volume Effect

Fig. 3. Post-optimization process, which checks the isolation distances bycomparing the most critical electrical field path of the design with scaledbreakdown data from literature.

correlation resulted when voltages up to 80 % of the crest valuewere considered. Therefore, in order to obtain a comparativemeasure, the voltage time product (V T ) is applied describedby

V T =

∫ t2

t1

V (t)dt, t1 = (V = 0.8 · Vmax ∧dV

dt> 0),

t2 = (V = 0.8 · Vmax ∧dV

dt< 0) (1)

where V (t) is the time-dependent pulse voltage and Vmax thecrest value of the pulse. SI and LI of ester and mineral oil havebeen compared for a 3.8mm-gap with standard sphere-sphereelectrodes applying the standard ASTM D 3300 method, listedin Tab. II [9]. V T values of SI and LI are interpolated to obtainthe mean breakdown voltage of the desired pulse shape as wellas a scaling factor SF . Since the V T of the pulse shape isclose to the V T of the lightning impulse, the breakdown datafrom [10] and [9] is applied with the corresponding SF in thefollowing sections for the negative lightning impulse since aklystron is connected as load.

2) Volume Effect and Withstand Probability: To derive abreakdown probability for a given voltage, breakdown data isapproximated with a Weilbull distribution, which is dependenton the scale parameter α, the shape parameter β and theapplied voltage V [11]. Since the geometry dimension inbreakdown tests is much smaller than in the real transformer,the volume effect has to be considered. The breakdown prob-ability of a volume, which is n-times the tested one, can be

TABLE IICOMPARISON OF SI, LI AND INVESTIGATED PULSE SHAPE.

Parameter LI SI pulseVmax (kV/mm) 160 160 160Rise time (µs) 1.2 250 5Time to half value of wave tail (µs) 50 2500 -Voltage time product (V T ) (Vs) 5.78 293 24V50% (ester) (kV/mm) 205.0 169.2 207V50% (mineral) (kV/mm) 251.9 184.3 249SF (LI, SI to pulse) (ester) - 0.965 1.22 -SF (LI, SI to pulse) (mineral) - 0.952 1.35 -

0 5 10 15 20 25 30 35 40 45 50 550

2

4

6

8

10

12

14

16

18

Gap distance (mm)

Ele

ctric

al fi

eld

(kV

/mm

)

a) b)

Em (12kV/mm)

Ecrit (10kV/mm)

Emax(ester)

Emax(mineral)

Em (10kV/mm)

Fig. 4. a) Transformer geometry with specifications listed in Tab. III. b) Emobtained from the most critical electrical field shape line Ecrit for Epeak =10 kV/mm and Epeak = 12 kV/mm in comparison to Emax of naturalester and mineral oil for transformer with CLIC specifications.

described by [12]

Pn(V ) = 1− exp[−n ·

(V

α

)]β(2)

In [9] a 1 % breakdown probability is proposed as a designcriteria, which is also applied in this paper.In pulse transformer design, the electrical field is in many casesinhomogeneous. Therefore, in the next section an adaption forinhomogeneous electrical fields is presented.

C. Inhomogeneous Electrical FieldsIn order to achieve a compromise between an excessive peak

electrical field and a too conservative design it was proposed in[11], to calculate the mean electrical field for different intervalsalong the oil gap length. The resulting electrical field Em canbe described by

Em(z) =1

z

∫ z

x1

E(z′)dz′, (3)

where x1 is the beginning of the oil gap, E(z′) is theelectrical field at point z′ and z is the the interval length ofthe investigated path. This resulting Em must remain belowthe desired maximal value Emax for homogeneous electricalfields for the entire path length. In the following section atransformer design is examined with the proposed methoddepicted in Fig. 3

D. Application in High Voltage Pulse Transformer DesignIn order to check a transformer design, the optimization

procedure is applied with specifications of CLIC, listed inTab. IV, with a maximal electrical peak field at the conductorsurface of Epeak = 10 kV/mm. The resulting geometry isanalyzed with 2D-FEM and depicted in Fig. 4a), which showsan equal electrical peak field. The enlarged view of the pictureshows that the peak electrical field occurs on top of the fieldshape ring, which is in this case the secondary turn with thehighest potential. Most of the transformer volume is onlysubjected to electrical fields smaller than E = 5 kV/mmand therefore is not considered as critical volume. For safetyreasons the entire area indicated in Fig. 4a) is taken intoaccount, assuming that all field paths in this area are equalto the most critical one Ecrit. In Fig. 4b) Ecrit and Em (3)are depicted for Epeak = 10 kV/mm. They are compared tothe scaled Emax of mineral and ester oil for gap lengths 3.8-150 mm (2). Scaled Emax values of 3.8 mm-gap are used aslimit to avoid data extrapolation. In both cases the calculatedEm remains below the maximal electrical field. Additionally,a design was investigated with Epeak = 12 kV/mm, whichintersects with Emax-curve of natural ester, but not with the

TABLE IIIPULSE TRANSFORMER DATA

ParameterVolume tank (m3) 0.91

Critical affected Volume (m3) 0.033Peak electrical field calc (kV/mm) 10

Peak electrical field 2D-FEM (kV/mm) 10Field shape ring diameter (mm) 12

Oil gap (mm) 52

mineral oil curve. Therefore, higher electrical peak fields andthereby smaller isolation distances can be applied if mineraloil is selected in the design.

IV. SENSITIVITY ANALYSIS

Optimization procedures allow the designer to evaluatethe sensitivity of system parameters. The reference pulsetransformer fulfills the CLIC specifications listed in Tab. IV.The isolation distances are adapted to the specified maximalvoltage Vmax = 180 kV, even though the pulse shape isoptimized for Vkn = 160 kV. Due to the primary current ofIprim ≤ 10 kA at least four switching units are required andsince the system complexity should be minimized, the numberof magnetic cores is chosen to Nc = 2. To limit core weight,the minimal number of primary turns is set to nprim,min = 4.In order to reach highest pulse efficiency, i.e. the ratio betweenthe entire pulse and the part of the pulse which complieswith the flat-top criteria, a critical damped pulse is required.Therefore, the procedure matches the distributed capacitanceCd and the leakage inductance Lσ for a given set of externalconstraints.In the following sections, three different system parametersare analysed and compared.

A. Core Material Selection

In order to compare the three investigated core materials ina design, the optimisation procedure was set to maximize theefficiency without any volume constraints.The optimization results are listed in Tab.V. For the nanocrys-talline and the amorphous material, the algorithm selects ahigh flux density, whereas with silicon iron only 75 % ofthe possible flux density is selected. This effect is due tothe significantly higher core losses of silicon iron. Therefore,the total efficiency of the transformer is reduced by almost1 %. Even though the nanocrystalline material shows by factor2.5 lower core losses, its transformer efficiency does notexceed the one of the amorphous material. This is due tothe fact that for both materials the share of the core lossesis smaller than 10 %. Since the maximal flux density ofthe nanocrystalline material is smaller than the amorphousmaterial one, the resulting transformer volume is increased.The increased volume results in higher Lσ , thereby increasingthe rise time. This effect lowers the pulse efficiency, whichovercompensates the lower core losses. Therefore, for CLIC

TABLE IVSELECTED SPECIFICATIONS OF CLIC AFTER THE REBASELINING

Pulse voltage Vkn 160 kVMaximal voltage Vmax 180 kV

Pulse current Ikn 173.6 APrimary voltage Vprim 2667 kVPrimary current Iprim 10416 A

Rise + settling time tsettle 8 µsFlat-top length tflat 140 µs

Flat-top stability FTS 0.85 %Overshoot os 1 %

Perveance klystron k 2.54e-06

TABLE VCOMPARISON OF CORE MATERIALS WITH SPECIFICATIONS OF CLIC

Nanocrystalline Amorphous SiFe3%Parameter (VITROPERM Metglas (100µm)

500F) (2605SA1)tflattop (µs) 4.77 4.36 4.53Transformer volume (m3) 1.57 1.05 1.04Bex/Bmax (%) 95 100 75Core losses Pcore (kW) 0.184 0.482 2.28Total losses Ptot (kW) 5.92 5.37 8.45Bex (T) 0.95 1.2 1.1250Core volume (m3) 0.35 0.2391 0.2545Total core weight (T) 2.57 1.71 1.952System efficiency (%) 96.82 96.93 96.0

specifications, the amorphous core material is identified as themost suitable and will be selected in all further analyzes.

B. Transformer Oil and HV Cable Length SelectionIn modulator systems there is an increasing demand to

replace mineral oil with more environmentally friendly oilssuch as natural esters. Therefore, the influence of such an oilreplacement is investigated.In the previous section the optimization procedure was appliedfor maximizing the efficiency. In the design process, however,a compromise between highest efficiency and smallest volumehas to be achieved. Therefore, the procedure was adaptedto minimize the volume for a given efficiency limit. Theefficiency limit is then varied, resulting in a Pareto front.The high voltage cable length connecting the transformer tothe klystron load was set to its minimum lHV = 1.5 m,resulting in an additional capacitance of Cd,cable = 153 pF.Also an additional capacitance of Cadd = 100 pF due toklystron tank and high voltage divider was assumed.In a first comparison, equal isolation distances are applied forboth oils. The oils still differ in their relative permittivity(εr,mineraloil = 2.2 , εr,ester = 3.2 ). The results aredisplayed in Fig.5, which show that for mineral oil a highervolume is needed at lower efficiencies. The mineral oil curveonly slightly surpasses the one of ester oil for volumes higherthan V = 0.88 m3. The lower εr and therefore the lower Cdof mineral oil is not beneficial, since it would also requirea reduced Lσ for an efficient rise time. Since the windingdistance cannot be reduced due to the required isolation, Lσcan only be decreased by increasing the height of the winding,which leads to a higher volume.In a second step, the maximal electrical peak field is set formineral oil to Emax = 12 kV/mm (c.f. section III-A). In thiscase, the isolation distances can be decreased, which leads to abetter match between Lσ and Cd and therefore to an efficiencyincrease of 0.5 %.Additionally, the effect of a 5 m instead of a 1.5 m connectioncable is investigated. For both oils the additional cable lengthleads to an efficiency decrease of 0.6 %. In case of the mineraloil the lower Cd due to the lower εr can almost compensatethe additional cable capacitance and results in a similar curveto ester oil with a short cable length.

V. CONCLUSION

In this paper, an enhanced pulse transformer optimisationprocedure is presented. The procedure controls the electricalpeak field in the entire geometry. It is explained how theisolation distances in pulse transformers can be checked byscaling breakdown data from standard LI or SI tests. With theprocedure, the influence of the core material, the transformeroil and high voltage cable on the transformer design areinvestigated by identifying the Pareto limits. It is demonstratedthat amorphous core material is most suitable for CLIC

0.650.70.750.80.850.90.9511.05

0.955

0.96

0.965

0.97

0.975

0.98

0.985

Transformer volume (m3)

Effic

ienc

y (%

)

Mineral oil, 5m cable

Natural ester

Natural ester, 5m cable

Mineral oil, Epeak=12kV/mmMineral oil

Fig. 5. Pareto limit of pulse transformer with 1) ester oil and lHV = 1.5 m,2) ester oil and lHV = 5 m, 3) mineral oil and with lHV = 1.5 m and 4)mineral oil and lHV = 5 m.

specifications. Additionally, is it shown that replacing mineraloil with natural ester decreases the efficiency by 0.5 % and a3.5 m longer high voltage cable length results in an efficiencyreduction of 0.6 %.

ACKNOWLEDGMENT

The authors would like to thank project the partners SNF(project number 144324) and CERN very much for theirstrong financial support of the research project.

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