An Inductive 700-MW High-Voltage Pulse Generator - IEEE Xplore

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IEEE TRANSACTIONS ON PLASMA SCIENCE, VOL. 34, NO. 5, OCTOBER 2006

An Inductive 700-MW High-Voltage Pulse Generator Adam Lindblom, Hans Bernhoff, Jan Isberg, and Mats Leijon, Member, IEEE

Abstract—A repetitive inductive 700-MW high-voltage pulse generator that delivers a 150-ns square pulse with 20-ns rise time at 150 kV has been constructed. The pulse generator has a 1:10 air core transformer connected to a 25-Ω pulse forming line (PFL). The transformer and the PFL are both constructed using highvoltage cables. The closing switch of the PFL is a spark gap that is in a water tank together with the cable endings of the PFL and transformer. The electric field at the cable endings is refractively graded by the high permittivity of the surrounding water. The PFL is charged in 2.5 µs to 170 kV, and the electric field in the closing switch of the PFL reaches 33 kV/mm until the threshold voltage is exceeded. The efficiency of the pulse generator is 40%. The authors believe that this concept can be up-scaled to a 25-GW generator operating at 500 kV. An electric circuit simulation of a 25-GW pulse generator and an electrostatic simulation for a refractive cable ending are presented. Index Terms—High-voltage cable, inductive pulse generator, refractive field grading, resistive layer.

I. I NTRODUCTION

I

NDUCTIVE pulse generators using pulse forming lines (PFLs) charged by pulse transformers [1]–[3] can be used for high-power microwave (HPM) generation. The PFL is traditionally charged by either a Marx generator [4], a pulse transformer, or a combination between pulse transformers and magnetic switches [5], [6]. Spark gap switches using water as media have been used for decades as closing switches [7], [8] of PFLs. This paper describes a pulse generator using a PFL charged by an air core pulse transformer. The PFL and the transformer are designed using modern high-voltage semicon cables. The use of high-voltage cables in pulsed power enables fairly compact designs by offering an effective electrical insulation [9], [10]. The high-voltage cables have a resistive layer (semicon) on the inner conductors and on the outside of the cross-linked polyethylene (XLPE) insulation. The XLPE insulation can withstand electric fields up to 100 kV/mm [11]. The cable used in this pulse generator is designed for a continuous operation rms voltage of 24 kV. Fig. 1 shows the experimental design of the pulse generator. It has not been a priority to build a compact pulse generator in this study. The pulse generator has a 1:10 step-up transformer connected to a 25-Ω PFL. The high-voltage cables used in the transformer and PFL are terminated in a spark gap located in Manuscript received October 10, 2005; revised June 16, 2006. This work was supported by the Swedish Armed Forces, The Swedish Materiel Administration (FMV), and Swedish Defence Research Agency (FOI). The authors are with the Division for Electricity and Lightning Research, Ångströmlaboratoriet, Uppsala University, 75121 Uppsala, Sweden (e-mail: [email protected]; [email protected]; [email protected]; [email protected]). Color versions of all Figures and Tables are available online at http://ieeexplore.ieee.org. Digital Object Identifier 10.1109/TPS.2006.881279

Fig. 1. Pulse generator with 25-Ω PFL. PFL consists of one folded 40-m-long coaxial high-voltage cable wound on 1-m-high solenoids.

Fig. 2. Schematic of the pulse generator with a 1:10 step-up transformer and a 25-Ω PFL. PFL consists of a folded 40-m-long coaxial high-voltage cable. TABLE I HIGH-VOLTAGE 24-kV CABLE DIMENSION

the water tank, as illustrated in Figs. 1 and 2. The water tank has two purposes: 1) to supply refractive field grading [12] at the cable endings and 2) to reduce the gap length of the spark gap. Furthermore, the PFL relies on the air insulation between each layer in order to reduce the load voltage rise time. The high-voltage cables have previously been used in highvoltage rotating machines [13] and in dry oil-free high-voltage transformers [14]. The electric circuit of the pulse generator is illustrated in Fig. 2, where the components Cp , Rp , and Lp are the primary capacitance, resistance, and inductance, respectively. Rs and

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LINDBLOM et al.: INDUCTIVE 700-MW HIGH-VOLTAGE PULSE GENERATOR

Fig. 3.

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Measured impedance and phase for the 24-kV high-voltage cable versus frequency. (Right) Cole–Cole plot for the same frequency range.

Ls are the secondary resistance and inductance, respectively. The switches S1 and S2 are both self-closing spark gaps with threshold voltages of 18 and 170 kV, respectively. The spark gaps are of the uniform field type having Rogowski-type [15] electrodes. Spark gap S1 is air insulated, while S2 is water insulated. The pulse generator is operated as follows: The primary capacitive energy storage Cp is discharged through the primary winding Lp by closing spark gap S1 . The magnetically stored energy in the transformer is converted to electric energy in PFLs T1 and T2 . The spark gap S2 closes at maximum charge energy, and a square load voltage is formed. II. P ULSE G ENERATOR A. High-Voltage Cable The transformer and the PFL are constructed using highvoltage semicon cables. The cable type is WINDONE 24 kV and was manufactured in 1999 by ABB. The PFL is made coaxial by the addition of a 35-mm2 braided copper screen. Table I shows the dimensions for the cable without the copper screen. The cable has an inner conductor with radius r1 consisting of 20 aluminum strands. The first resistive layer (semicon) surrounding the inner conductor has radius r2 followed by an XLPE insulation layer with radius r3 . A second resistive layer completes the cable at r4 . The capacitance has been measured for the cable in order to determine if the resistive layers contribute to create an effective relative permittivity or if they can be accounted for as conductors. The effective relative permittivity is the combination between resistive layers and XLPE. The authors in [16]–[18] report values between 102 and 104 for the relative permittivity εr in the outer resistive layer for semicon cables. The calculated capacitance using the relative permittivity εr = 2.3 for XLPE gives 185 pF/m using 2πε0 εr / ln(r4 /r1 ). Here, r1 and r4 are the inner and outer conductor radii, as presented in Table I. However, assuming that the resistive layers act like conductors, the capacitance can be calculated through 2πε0 εr / ln(r3 /r2 ). Capacitance calculation using the radii r2 and r3 gives 250 pF/m, and the measurements in Section II-B agree. The resistive layers have a dc conductivity

of 7 S/m, which is apparently enough to be considered as a conductor in this context. The dc conductivity of the resistive layer is determined by measuring the resistance on the outer resistive layer and using σ = l(RA)−1 . Here, l is the length, and R and A are the resistance and cross-sectional area of the sample, respectively. The measured conductivity (7 S/m) for the resistive layer is similar to the values obtained by other authors [18]. B. Measuring the Relative Permittivity The capacitance per meter was determined for a 2.18-m-long sample of the cable presented in Section II-A. The measurement system uses a lock-in amplifier (EG&G 7265, preamp. EG&G 5182) controlled by a PC. The left part of Fig. 3 shows the impedance and phase in the frequency range from 1 Hz to 100 kHz. The right part shows a Cole–Cole plot [19] of the real and imaginary parts of the impedance. The Cole–Cole plot suggests that the measured cable acts as a capacitor and resistor connected in parallel. The measurement set-up uses a screened box, and the lock-in amplifier was connected with coaxial cables between the amplifier and the box. The measured capacitance per meter for the semicon cable (1) was calculated using the imaginary part of the Cole–Cole plot in the frequency range where the modulus of the phase angle is close to 90◦ . The capacitance per meter for the cable is C0 = (ω Im(Z))−1 = 250 pF/m

(1)

where ω is the angular frequency, and Z is the impedance calculated using the measured current and voltage. The presented measurement data shown in Fig. 3 are for the cable length of 2.18 m. C. Transformer The transformer used in this pulse generator has a stepup ratio of 10 and is wound in Archimedean spirals. Fig. 4 shows the transformer and its primary terminals, where the outer terminal is connected to the ground, and the inner to the capacitor bank. Each layer on the primary winding has an adjacent secondary layer. The first layer shown in Fig. 4 is

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Fig. 6. Uniform field spark gap S2 has brass electrodes with gap distance ∼5 mm. The spark discharge is in deionized water. Fig. 4. Step-up transformer with air core and winding ratio 1:10. Table shows the transformer data.

Fig. 5. PFL with two parallel 25-Ω coaxial cables wound into solenoids with air insulation between each turn. Semicon cables used in the PFL are designed for 34-kV continuous voltages, and the high-voltage tests are made at 170 kV in Section II-E.

the primary winding. The next layer is the secondary winding, which is grounded at the outer terminal (not shown in Fig. 4). As the secondary winding (Archimedean spiral) reaches the inner radius of the transformer, another primary layer is applied on top. The secondary cable is elevated above the primary layer and wound from the inner radius and out. This procedure is repeated to form the necessary winding ratio. The size of the transformer is close to 200% larger than the coaxial transformer presented in [9] and [20]. The advantage with this type of transformer is that it allows for a simple primary terminal insulation. A lumped electric circuit model [21] was developed for a coaxial transformer based on high-voltage cables. The simulation model was presented in [9] and is accurate for this type of transformer as well. Each primary layer consists of a 5-m cable, and the total length of the secondary winding is 50 m. It is possible to decrease the weight and dimensions of the transformer by using a cable with less insulation in the primary winding. The dimensions of the cable used in the primary winding are determined by the primary current and voltage. The primary current determines the conductor cross-sectional area, and the primary voltage determines the insulation thickness.

Fig. 7. (Left) Partial cross section for an XLPE high-voltage cable with resistive layers, while the outer resistive layer is removed from the insulation. (Right) An axisymmetric electrostatic simulation set-up of the cable.

Fig. 8. Refractive field grading at the cable ending for two different types of surrounding media. (Left) Equipotential lines using air, and (right) using water. Gray shade shows the norm of the electric field where the darkest shade represents the highest field.

D. PFL and Closing Switch The PFL consists of two separate coaxial lines T1 and T2 having an impedance of 12.5 Ω. Each line T1 and T2 consists of two coaxial 25-Ω cables in parallel, as illustrated in Figs. 2 and 5. The lines T1 and T2 are wound on plastic cylinders with a diameter of 200 mm and a height of 1000 mm. The air insulation reduces the capacitance between the coaxial screen and ground, which must be kept low in order to effectively deliver the power into the load. The cable is designed for a continuous peak voltage of 34 kV at an electric field of 12 kV/mm next to the inner conductor. The high-voltage test reaches 170 kV, and the electric stress is more than five times the designed electric field. The recommended bending radius of the cable is 15D in the field and 10D in installations according to the manufacturer. The bending radius for this PFL is 100 mm, and the cable diameter is 16 mm, which gives a ratio of 6.

The cables from the transformer and PFL enter the water tank and terminate in the spark gap, as illustrated in Fig. 2. The outer resistive layer of the cables has been removed for 300 mm at the ends; removing the resistive layer reveals the XLPE insulation inside (cf. Fig. 7). The surface of the XLPE is grinded smooth in order to remove cracks and voids that can produce excessive electric field stress. The outer resistive layer of the simulation illustrated in Fig. 7 is grounded. Moreover, the water exerts refractive field grading [12] at the cable endings due to its high dielectric constant (cf. Fig. 8). The plastic tank utilizing the water, spark gap, and cable endings is grounded on the outside using copper sheets, as illustrated in Fig. 1. The spark gap S2 has two uniform brass electrodes with dimensions and shape as shown in Fig. 6. The load consists of CuSO4 in water and has a resistance of 30 Ω.


Fig. 9.

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(Left) Primary current peaks at 15 kA, and the secondary transformer voltage reaches 130 kV. (Right) Spark gap and secondary current of the transformer.

Fig. 10. PFL charged to 170 kV as the spark gap S2 (Fig. 2) closes. 150-kV load voltage is calculated from the measured current times the 30-Ω load. (Right) Measured load current having a 10%–90% rise time of 20 ns.

E. Refractive Field Grading It is imperative to design the cable ending or termination of a high-voltage cable with resistive layers properly. The ending must use a stress cone or a geometrical field grading in order to control the electric field, which by far is the most common [12] method. However, it is possible to use refractive field grading as electrical breakdown prevention using a material with high relative permittivity. This type of electric field control uses the properties of the media that surround the cable termination. The pulse generator described above has the cable endings from the PFL and transformer terminated in the spark gap. The spark gap and the cable endings are located in the water tank. An electrostatics simulation with conductive media is shown in Fig. 7, where the inner conductor is set at a potential U0 , and the outer resistive layer is grounded. The boundary box is set to the axial symmetry on one side and zero charge on the other sides. Furthermore, the subdomains representing the cable materials such as the resistive layers are set to a relative permittivity of εr = 103 , and the XLPE has εr = 2.3. The conductivity of the resistive layers is set to 7 S/m, and the conductivity of the copper is set to 5.998 × 107 S/m. The conductivity of the XLPE insulation and the surrounding media is set to 10−15 S/m. Fig. 8 shows a simulation where the surrounding media have been changed from air to water. The conclusion from the results in

TABLE II CAPACITIVE ENERGY IN THE PRIMARY CAPACITOR, TRANSFORMER, AND PFL; L OAD E NERGY I S C ALCULATED U SING THE MEASURED POWER SHOWN IN FIG. 11

Fig. 8 is that refractive field grading keeps the electric field inside the XLPE insulation. High electric fields are preferably kept inside the XLPE insulation since it can withstand higher electrical fields than the surrounding media. III. H IGH -V OLTAGE R ESULTS A Tektronix TDS 3034 (300 MHz, 2.5 Gs/s) oscilloscope was used in the measurements. Each measurement was made with the oscilloscope running on grid power. Tests were made with the oscilloscope running on battery power in order to investigate if the ground potential was affected. However, no difference was found. The current monitors were grounded

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Fig. 11. Input and output power for PFL. (Right) Measured and simulated energy.

at the oscilloscope by the coaxial cable, and the capacitive coupling to the local ground next to the probes is believed to have less effect on the measurements. The primary and secondary currents of the transformer were measured using Pearson probes (mod. 101, rise time 100 ns). The load current and the spark gap current were measured using Pearson (mod. 5046, rise time 20 ns) and (101, rise time 100 ns), respectively. The secondary charge voltage was measured with a capacitive probe (ratio 73:1). The capacitive probe was calibrated using a high-voltage probe (Ross Eng. Corporation, Model VMP120, 120 kVDC). A. Charging and Switching PFL The PFL was charged to 130 and 170 kV by using two different charge voltages in the primary capacitor bank. Fig. 9 shows the 130-kV measurement data: the primary current and the secondary transformer voltage are shown to the left, while the right figure shows the spark gap S2 current and the secondary transformer current. The spark gap S2 closes at ∼ 2.9 µs, and the peak shown in the secondary current Is comes from a capacitive discharge from the secondary winding of the transformer. Fig. 10 shows the 170-kV measurement data: the secondary voltage and the load voltage are shown to the left, while the right figure shows the load current with a 10%–90% rise time of 20 ns. The load voltage is calculated from the measured load current times the load resistance, and the pulse length is 150 ns. The mean electric field between the electrodes in the spark gap is ∼33 kV/mm at a charging voltage of 170 kV. The electric field is calculated using the gap distance 5.2 mm and voltage 170 kV; moreover, the breakdown field strength shows similar results as that in [8]. The conductivity of the water in the tank was 60 nS/cm. B. Efﬁciency A typical test with 18 kV in the primary capacitor Cp charges the Blumlein to 170 kV. Table II shows the capacitive energy stored in the pulse generator at different times. The secondary winding of the transformer consists of a 50-m cable, and the

voltage is linearly distributed. The capacitive energy stored in the secondary winding of the transformer is WT =

C0 lU 2 8

(2)

where C0 is the capacitance per meter of the cable, and U and l are the charge voltage and winding length, respectively. The left part of Fig. 11 shows the input and output power for the PFL, and the right figure shows the energy. The charge energy WCHARGE (Fig. 11, right) consists of the capacitive energy WT stored in the transformer, and the capacitive energy WPFL in the PFL. The charge energy WCHARGE is calculated from the cumulative sum [22] of the charge power, which is shown to the left in Fig. 11. The charge power is the product between the measured secondary current and voltage. The load energy WLOAD is calculated from the cumulative sum of RI 2 , where R is the load resistance, and I is the measured current shown in Fig. 10. The energy in the primary capacitor WP is calculated using Cp Up2 /2, where Cp is the primary capacitance, and Up is the charge voltage. The energy in the PFL for two cables in parallel is WPFL = C0 (lT 1 + lT 2 )U 2

(3)

where lT 1 and lT 2 are the lengths of the lines. The capacitance per meter C0 for the semicon cable is possible to calculate from the energy stored in the PFL and the secondary winding of the transformer. The charge energy illustrated in Fig. 11 is simply WCHARGE = WPFL + WT . Combining (2) and (3) and solving for the capacitance of the cable gives C0 =

U2

W l CHARGE . 8 + lT 1 + lT 2

(4)

Further, calculating the capacitance using (4) gives 245 pF/m. The relative permittivity is 2.25 using the relation C0 ln(r3 /r2 )(2πε0 )−1 , which deviates only 2% from the other measured value in Section II-B. Table II shows the energy and charge relation for the pulse generator. The efficiency is calculated at different stages in the pulse generator, and the least loss is found between the PFL and the load. The loss in the PFL


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Fig. 12. Electric circuit for the 25-GW pulse generator. Low-impedance PFL has several folded parallel-connected high-voltage cables.

Fig. 13. (Left) Simulated current and voltage from the primary capacitor. (Right) Secondary voltage and the voltage over the 10-Ω load. Load voltage has a rise time of 20 ns and pulse length of 200 ns.

is ∼7%, while the largest loss ∼40% is located in the primary winding of the transformer. The values of the energies presented in Table II are calculated using the measured data. An electric circuit simulation [21] is included in Fig. 11 to support the measurement data, and the electric circuit model is explained further in Section IV. IV. S PICE S IMULATIONS A 25-GW pulse generator with the same set-up as the experimental 0.7-GW pulse generator has been simulated. The transformer model used in this simulation has the same lumped circuit structure as the one used in [9]. The transformer model is extended so that it has a winding ratio of 1:10. The full simulation model is not presented here due to its complexity. The electric circuit for this pulse generator is illustrated to the left in Fig. 12, where S1 and S2 are the closing switches, and C is the primary capacitor bank. The primary capacitor bank C is charged to 50 kV, and the secondary voltage reaches 500 kV as the capacitor bank is discharged. The PFL consists of several folded high-voltage cables in parallel. The cables are folded in order to reduce the number of cable endings. The right part of Fig. 12 shows a table presenting the components used in the simulation. The primary current and voltage are presented in the left part of Fig. 13. The primary voltage starts out at 50 kV and ends up at −15 kV, which is a maximum reversal of 30%. The secondary voltage Us (or PFL charge voltage) is presented to the right in

Fig. 13 together with the load voltage UL . The switch S2 is activated when the PFL contains maximal energy at 3.5 µs. The impedance of a space charge HPM radiator such as a Vircator [23] varies during the pulse. It normally starts high and ends up low. The reflections are minimized at 10 Ω because this resistance value is matched to the PFL. The load voltage and the amplitude of the reflections increase as the load resistance is changed from 10 to 50 Ω. The 3.5 µs required to charge the PFL is relatively long, which gives a little more stress on the cable and cable endings. However, if the cable endings are designed properly, the long charge time should not pose a problem at 500 kV. By comparing Figs. 9 and 10 with Fig. 13, the similarities between the 0.7- and 25-GW pulse generator is clear. The 25-GW pulse generator is designed to operate on a similar time basis (∼ 3 µs) as the 0.7-GW model. V. C OMMENTS The transformer model used in the simulation of the 25-GW pulse generator has primary and secondary inductances of 2 µH and 0.2 mH, respectively. The high inductance of the primary winding was chosen in order to reduce the cost of the primary capacitors and closing switch. A transformer having a single turn low inductance primary winding is possible to use if low inductance capacitors are installed as the primary energy storage. The choice of a transformer using a higher primary inductance reduces the demands on the primary circuitry, but other challenges are introduced. The high primary inductance

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puts extra stress on the insulation such as cable and cable endings due to the longer charge time of the PFL. Moreover, the electrostatic simulation with conductive media explains why we use the value εr = 103 for the relative permittivity on the resistive layer. The copper conductor uses the conductivity σ = 5.998 × 107 S/m and relative permittivity of εr = 1. The resistive layers has conductivity σ = 7 S/m, and if we use εr = 1, the electric field totally occupies the resistive layers, which is not the case. Therefore, the relative permittivity is set to εr = 103 , which is supported by measurements made in [16]–[18].

[8] [9]

[10]

[11] [12]

VI. C ONCLUSION

[13]

The pulse generator delivers a 150-kV 150-ns square pulse with 20-ns rise time. The overall efficiency of the pulse generator is 40%, which is calculated from the primary energy storage to the load. The refractive electric field grading exerted by the water at the cable endings have worked well, and no electrical breakdowns have been discovered. The electric field in the cables peaks at 60 kV/mm, and the cables have been able to withstand more than 50 repetitions at 170 kV while maximum longevity remains unexplored. The electric circuit simulation of the 25-GW pulse generator indicates that the PFL can be charged intermediate by an air core pulse transformer. The simulation of the 25-GW pulse generator behaves similar to the 0.7-GW generator.

[14]

ACKNOWLEDGMENT

[15] [16]

[17]

[18] [19] [20]

The authors would like to thank Draka Kabel for their highvoltage cable support.

[21]

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Adam Lindblom was born in Kalix, Sweden, in 1973. He received the B.Sc. degree in mechanical engineering from Umeå University, Umeå, Sweden, in 1998, the M.Sc. degree in engineering physics from Luleå University of Technology, Luleå, Sweden, in 2003, and the Ph.D. degree in electricity from Uppsala University, Uppsala, Sweden, in 2006. His research is mainly within electromagnetic fields and pulsed power.

Hans Bernhoff received the Ph.D. degree in the characterization and synthesis of high-temperature superconductors from the Royal Institute of Technology, Sweden, in 1992. In 1992, he held a postdoctoral position with the IBM Research Laboratory, Rueschlikon, Switzerland. In 1993, he joined ABB Corporate Research, Västerås, Sweden, where he worked as a Project Leader for several innovative projects in the area of electrotechnology, in particular research on singlecrystal diamond as a wide bandgap semiconductor. In 2001, he was appointed Associate Professor at Uppsala University, Uppsala, Sweden, in the area of high-performance systems.


Jan Isberg was born in Stockholm, Sweden, in 1964. He received the M.Sc. degree in physics and the Ph.D. degree in theoretical particle physics and quantum field theory with emphasis mainly on string theory and supersymmetry from Stockholm University, Stockholm, in 1987 and 1992, respectively. From 1993 to 1994, he held a postdoctoral position with the Department of Mathematics, King’s College, London, U.K. In 1995, he joined ABB Corporate Research, Västerås, Sweden, where he worked in the area of electrotechnology, in particular research on single-crystal diamond as a wide bandgap semiconductor. In 2004, he was appointed Associate Professor with Uppsala University, Uppsala, Sweden. His current research interests include pulsed power and diamond semiconductor physics.

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Mats Leijon (M’88) received the Ph.D. degree from Chalmers University of Technology, Gothenburg, Sweden, in 1987. From 1993 to 2000, he was the Head of the Department for High Voltage Electromagnetic Systems, ABB Corporate Research, Västerås, Sweden. In 2000, he became a Professor of electricity with Uppsala University, Uppsala, Sweden. Prof. Leijon is a member of IEE, WEC, and Cigre as well as the Swedish Royal Academy of Engineering Science. He received the Chalmers award “John Ericsson medal” in 1984, the “Porjus International Hydro Power Prize” in 1998, the Royal University of Technology “Grand Price” in 1998, the Finnish academy of science “Walter Alstrom prize” in 1999, and the 2000 Chalmers “Gustav Dahlen medal.” He both received the Grand Energy Prize in Sweden and the Polhem Prize in 2001 as well as the Thureus Prize 2003.