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A model for electrical fast transient analyses of the ITER NBI power supplies and the MAMuG accelerator
Fusion Engineering and Design 84 (2009) 446–450
Contents lists available at ScienceDirect
Fusion Engineering and Design journal homepage: www.elsevier.com/locate/fusengdes
A model for electrical fast transient analyses of the ITER NBI power supplies and the MAMuG accelerator M. Bigi a,∗ , A. De Lorenzi a , L. Grando a , K. Watanabe b , M. Yamamoto b a b
Consorzio RFX, EURATOM-ENEA Association, Corso Stati Uniti 4, 35127 Padova, Italy Japan Atomic Energy Agency, 801-1 Mukoyama, Naka, Ibaraki-ken 311-0193, Japan
a r t i c l e
i n f o
Article history: Available online 4 March 2009 Keywords: Neutral Beam Injector (NBI) Breakdown Circuit model
a b s t r a c t The design of ITER Neutral Beam Injector (NBI) is based on a five-stage electrostatic accelerator, known as Multi-Aperture Multi-Grid (MAMuG) and characterised by an overall acceleration voltage of −1 MV. The MAMuG accelerator requires a five-stage power supply system under strict load protection requirements, being subjected in operation to breakdowns. In this paper a circuit model of ITER Neutral Beam Injector power supplies and MAMuG accelerator is illustrated, for the simulation of fast transients related to accelerator breakdowns in particular. Consideration of the high voltage involved and of the complex inductive and capacitive couplings implied careful assessment of stray parameters by calculations with finite element techniques. The circuit model, developed to address a number of design issues requiring simulations at system level, is now ready for use—the optimisation of passive protections being the most significant application. © 2009 M. Bigi. Published by Elsevier B.V. All rights reserved.
1. Introduction In the present ITER design, each Neutral Beam Injector must be capable of delivering a power of 16.6 MW. This is obtained neutralising a deuterium negative ion beam having 1 MeV energy and 40 A current [1]. Production and electrostatic acceleration of an ion beam with the ITER parameters involves three main electrical systems: (a) Ion Source and Extractor Power Supplies (ISEPS), necessary to operate the ion source [2] and to extract an ion beam with minimum fraction of electrons. (b) Acceleration Grid Power Supply (AGPS), transferring energy to the ion beam through a five-stage electrostatic accelerator known as Multi-Aperture Multi-Grid (MAMuG) [1]. (c) Transmission Line (TL), connecting ISEPS and AGPS to the ion source and the accelerator. AGPS and Transmission Line in particular pose several technological challenges, related to the rated voltage of −1 MV dc and to grid breakdowns during beam extraction. The breakdown events are crucial to the design of the electric system. Strict limits apply to arc energy (50 J [3]) and peak break-
∗ Corresponding author. Tel.: +39 0498295045; fax: +39 0498700718. E-mail address: [email protected] (M. Bigi).
down current, to ensure that the accelerator is not damaged or voltage holding degraded [4]. A first implication is that the AGPS must be able to block within 150 s from a trip request. Secondly passive components must be added to the circuit, to control the fast discharge of capacitive stored energy: these components traditionally consist in a combination of resistors, air core inductors and magnetic core “snubbers” [5–7]. Integration of the different items of plant and design of the passive protections have been the prime reasons for developing the circuit model of ITER Neutral Beam Injector presented in this paper. More specifically, the model aims at simulating the fast transients following a breakdown of the accelerator or a failure of the insulation at a different point. For this reason it is purely passive, looking at the free evolution of the system after the breakdown. Other areas of study that may benefit from the availability of a breakdown simulation at system level include: • Scheme for the connections among power supplies, Transmission Line conductors and accelerator grids. • Voltage rise to local ground at a distance from the injector grounding point. • Transient waveforms experienced by dc insulation. • Integration of breakdown detectors/diagnostics. • Emission of ElectroMagnetic Interference. The model as it stands cannot simulate beam extraction and is limited to the high voltage side of the circuit.
0920-3796/$ – see front matter © 2009 M. Bigi. Published by Elsevier B.V. All rights reserved. doi:10.1016/j.fusengdes.2009.02.003
M. Bigi et al. / Fusion Engineering and Design 84 (2009) 446–450
447
Fig. 1. Reference electrical scheme of ITER NBI on which the circuit model is based.
2. Reference electrical scheme of the Neutral Beam Injector A reference scheme exists for the power supply system of ITER Neutral Beam Injector [8]. A simplified version is shown in Fig. 1, where the Ground Related Power Supplies have been omitted, being almost unaffected by accelerator breakdowns. The circuit model is based on the diagram of Fig. 1. The structure of the AGPS [9,10] is based on five high voltage DC Generators (DCGs), dc insulated to ground and having a rated output voltage of −200 kV dc with maximum ripple ±5% (for other ratings see Table 1). The DC Generators are series connected at the output, for a total output voltage of −1 MV dc to ground. The number of output terminals of the AGPS is six, corresponding to the number of grids of the MAMuG accelerator having the following nominal voltages to ground: 1. Extraction Grid (EG): −1000 kV. 2. Acceleration Grid 1 (AG1): −800 kV. 3. Acceleration Grid 2 (AG2): −600 kV. Table 1 Main parameters of DCG, ISEPS and passive protections. −200 kV DCG rated current −400 kV DCG rated current −600 kV DCG rated current −800 kV DCG rated current −1000 kV DCG rated current AGPS output filter Max ripple of AGPS output voltage Isolation transformer ISGT RF generator Extraction Grid PS AGPS series resistor Core snubbers (CS1 CS2) Intermediate voltage resistors: AG1, AG2, AG3, and AG4
66 A 64 A 59 A 56 A 54 A R = 68 ; C = 300 nF (per stage) ±5% 3ph 50 Hz; 22/6.6 kV Output 200 kW, 50 Output 12 kV, 140 A dc 50 750 H, 175 ; 250 H, 130 400, 300, 200, and 100
4. Acceleration Grid 3 (AG3): −400 kV. 5. Acceleration Grid 4 (AG4): −200 kV. 6. Post acceleration or Grounded Grid (GG): 0 V. The 0 V output terminal of the AGPS is connected to ground at the accelerator, following the principle of single grounding point. Each DC Generator is composed of a step-up transformer with dc insulation of the secondary windings, a high voltage diode rectifier and an RC smoothing filter. Regulation of the AGPS output voltage and fast switch off in response to a load breakdown are performed by an inverter, feeding the primary windings of the DC Generator step-up transformer. The main ratings of the DC Generator are listed in Table 1. The ISEPS include several distinct pieces of equipment, the largest ones in terms of power being: • The 1 MHz radio-frequency generators (see ratings in Table 1) used to produce, by inductive coupling, the ion source plasma. • The Extraction Grid Power Supply (EGPS, see ratings in Table 1), feeding at a rated output voltage of −12 kV dc the extraction gap between Plasma Grid (PG) and Extraction Grid. Since the design of the MAMuG accelerator is such that the grid at the exit is at ground potential, the ion source is polarised at the full AGPS output voltage of −1 MV dc. The present solution to ensure insulated supply to the ISEPS loads inside the ion source foresees a 50 Hz isolation transformer, with secondary windings insulated to ground for −1 MV dc [8]. From the isolation transformer supply is brought to an air insulated platform, known as “High Voltage Deck 1” (HVD1) [10], where the ISEPS are located. The main ratings of isolation transformer and EGPS are listed in Table 1. The Transmission Line, connecting AGPS and ISEPS to the Neutral beam Injector, is insulated with pressurised SF6 gas and consists of three distinct sections (Fig. 1):
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Fig. 3. Simulated breakdown current of the Plasma Grid conductor.
Fig. 2. Equipotential lines [volt] for Transmission Line 2. The white circles correspond to the intermediate voltage conductors.
(i) Transmission Line 1 (TL1, reference length 30 m), connecting the AGPS output to High Voltage Deck 1. From High Voltage Deck 1, ISEPS conductors and services join the Transmission Line through a dedicated bushing [11]. (ii) Transmission Line 2 (TL2, reference length 65 m), running from High Voltage Deck 1 bushing to “High Voltage Deck 2” (HVD2), where cooling supplies for the ion source and the acceleration grids at intermediate voltages (Acceleration Grid 1 to Acceleration Grid 4) connect to the Transmission Line. (iii) Transmission Line 3 (TL3, reference length 15 m), running from High Voltage Deck 2 to the beam source vessel bushing, hereinafter referred to as “High Voltage Bushing”—HVB [12]. The Transmission Line is multipolar and has a complex design. There exists an inner hollow cylindrical conductor, at a dc potential to ground of −1000 kV (TL1) or −1012 kV (TL2 and TL3). The inner conductor is coaxial to the outer hollow cylindrical conductor, connected to the Grounded Grid. The intermediate voltage conductors do not follow the coaxial geometry and are placed in the region between inner and outer conductor (visible as white circles in Fig. 2). A typical cross-section of MAMuG Transmission Line can be found in [9]. The ISEPS conductors in Transmission Line 2 and Transmission Line 3 are housed inside the inner conductor. In Transmission Line 1 and Transmission Line 2 four conductors are present for the AGPS intermediate voltages from −800 to −200 kV. In Transmission Line Table 2 Symmetric matrix of couplings for Transmission Line 2. The elements above the diagonal are the capacitance values [10−12 F/m] while the ones below are the inductance values [10−9 H/m].
3 the number of intermediate voltage conductors doubles because of cooling requirements: each pair of intermediate voltage conductors acts as inlet and outlet cooling pipes. A number of passive protection components are included in the ITER neutral beam circuit: 1. A resistor in series to the AGPS return conductor [7], as shown in Fig. 1 between diode rectifiers and RC filters. 2. A first core snubber (CS1) at the end of Transmission Line 2. 3. A second core snubber (CS2) at the start of Transmission Line 3. 4. Resistors in series to the intermediate voltage conductors (immediately upstream of Transmission Line 3). As additional element of optimisation of the passive protections, a resistor known as “damper” [13] has been proposed, in series to the ground connection of the post acceleration grid. Having given an overview of the main items of plant that play a role in the breakdown simulation, the specifics of fast transient modelling will be discussed next. 3. Modelling issues The goal of the circuit model presented here is the simulation of the first few tens of microseconds following a breakdown in the ITER Neutral Beam Injector. Because of the high voltage involved, stray capacitance plays a crucial role in the dynamics of the transient and a calculation is required of the capacitance associated to significant component of the circuit. The anticipated harmonic content of the breakdown transient voltages and currents is up to the range of several megahertz [6] and for the Transmission Line, having non negligible dimension as compared to the associated wavelength, has lead to a model with multiple cells (see Section 4). 3.1. Capacitive and magnetic coupling The components of the Neutral Beam Injector have complex geometry characterised by capacitive and magnetic coupling that affect significantly current and voltage transient distributions. Consequently, as a pre-requisite to the implementation of a circuit model, the electric and magnetic coupling matrices have been evaluated for Transmission Line 1, Transmission Line 2, Transmission Line 3 and High Voltage Bushing. The calculation of capacitive and inductive parameters has been carried out by a bi-dimensional finite element model in static regime using the ANSYS® code, under the following assumptions:
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The outer conductor of each section of Transmission Line has been assumed as reference for the potential in the calculation of the capacitance and as return conductor for the total injected current in the calculation of the inductance. The vessel has been assumed as reference for the potential in the calculation of the capacitance of High Voltage Bushing and beam source. The post-insulators supporting Transmission Line conductors and the accelerator mounting flanges have been neglected. The computation of magnetic coupling for the accelerator considers, as current path across the grids, only the arc present during a breakdown. The arc has been modelled as a concentrated column with a value of inductance of 1 H/m and negligible resistivity. Table 2 lists, as an example, the symmetric matrix of capacitance and inductance for Transmission Line 2 and Fig. 2 shows the corresponding distribution of equipotential lines. Fig. 4. Simulated voltage to ground at the start of Transmission Line 1, following a grid breakdown.
3.2. Voltage distribution along the ground Due to stray capacitance, a path through the ground exists for the current flowing out of the AGPS, in parallel to the Transmission Line outer conductor. In normal operation, due to the low frequency involved and to the corresponding high impedance, the fraction of current diverted through the ground is negligible. On the contrary, during fast transients the current flowing in the ground must be taken into account. The effect of the ground has been modelled under the following assumptions: • The impedance of the ground is included only along the Transmission Line span. • The ground has no resistivity, i.e. ground resistance and internal inductance are both zero [14]. • Inductive coupling among intermediate voltage conductors and ground is neglected (an approximation of perfectly coaxial conductors). Under these assumptions, the circuit model of the ground reduces to a series inductance and a transverse capacitance to the Transmission Line outer conductor. Labelling h the height of the Transmission Line axis over the ground and R the radius of the Transmission Line outer conductor, the expression for the ground series inductance Lg and for the ground transverse capacitance, as computed with the principle of images, are given by
2h − R
Lg =
0 ln 2
Cg =
2ε0 ln((2h − R)/R)
R
(1) (2)
The circuit model has been developed in Simulink® , making use of the SimPowerSystems toolbox and selecting an integration technique with variable time step. Below a description is given of the circuit model adopted for two main items of the plant. 4. A fast transient circuit model for the Neutral Beam Injector 4.1. Acceleration Grid Power Supply In the model of the AGPS, single phase equivalent representations are used for step-up transformers and diode rectifiers. The most significant circuit parameter is the large 10−9 F capacitance between high voltage windings and electrostatic screen of the stepup transformer. The electrostatic screen is connected to the outer conductor of the Transmission Line.
Based on simplified geometries, the stray capacitance of diode and output filter tanks have also been included in the model. 4.2. Transmission Line The Transmission Line parameters have been computed as illustrated in Section 3: The inductive couplings, with as many as ten coupled conductors in Transmission Line 3, has been implemented in Simulink® using voltage controlled current sources as reported in [15]. Each Transmission Line section has been split in several cells, in order to take into account propagation effects. The chosen length is 2.5 m per cell, following an iterative process where further reduction of length would not change the results. 5. Results of breakdown simulations In Figs. 3 and 4 two examples are shown of simulated waveforms obtained with the Neutral Beam Injector circuit model. In the hypothesis of a breakdown short-circuiting all the acceleration grids at the same time and in absence of damper, Fig. 3 shows the predicted fault current flowing through the Plasma Grid conductor of the High Voltage Bushing. Fig. 4 shows the simulated voltage of Transmission Line 1 outer conductor near the 50 series resistor. The waveform has a delay of about 300 ns with respect to the instant of the breakdown (t = 1 ns in the simulation), corresponding to the Transmission Line length divided by the speed of light. This is evidence that, having modelled the Transmission Line with multiple cells, propagation effects are reproduced. The peak voltage of Fig. 4, around 200 kV, is noticeable and might be used as a basis for sizing the overvoltage protections of the Transmission Line. The results of Figs. 3 and 4 are examples, among the many possible, of conditions one would want to consider as part of a comprehensive design study, requiring a circuit simulator like the one described in this paper. 6. Conclusions Some salient features have been presented of a circuit model for fast transient analyses of the ITER Neutral Beam Injector. It has been shown that the model works and is ready to be used as a design tool, for the optimisation of the passive protection system. The resulting waveforms might be useful to other and more specific circuit models, studying the effects of the breakdown on AGPS conversion system and ISEPS. A further task is represented by the study of ElectroMagnetic Interference and its mitigation.
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Updates will be necessary, as design of the individual components and layout at the ITER site progress. Acknowledgments This work, supported by the European Communities under the contract of Association between EURATOM/ENEA, was carried out within the framework of the European Fusion Development Agreement. The views and opinions expressed herein do not necessarily reflect those of the European Commission. References [1] R.S. Hemsworth, A. Tanga, V. Antoni, Status of the ITER neutral beam injection system, Review of Scientific Instruments 79 (2008), 02C109. [2] P. Franzen, H.D. Falter, U. Fants, W. Kraus, M. Berger, S. Christ-Koch, et al., Progress of the development of the IPP RF negative ion source for the ITER neutral beam system, Nuclear Fusion 47 (2007) 264–270. [3] ITER Design Description Document 4.1, Pulsed power supplies, N 41 DDD 16 01-07-06 R 0.3. [4] H.M. Owren, W.R. Baker, K.H. Berkner, D.B. Hopkins, D.J. Massoletti, The effect of capacitive stored energy on neutral beam accelerator performance, in: Pro˝ ceedings of the 12th Symposium on Fusion Technology, Julich, Germany, 13–17 September, 1982. [5] J.H. Fink, W.R. Baker, H.M. Owren, Analysis and application of a transformer core that acts as an arc snubber, IEEE Transactions on Plasma Science PS-8 (1980) 33–38.
[6] K. Watanabe, M. Mizuno, S. Nakajima, T. Iimura, Development of a high performance core snubber for high power neutral beam injectors, Review of Scientific Instruments 69 (1998) 4136. [7] M. Bigi, V. Toigo, L. Zanotto, Protections against grid breakdowns in the ITER neutral beam injector power supplies, Fusion Engineering and Design 82 (2007) 905–911. [8] E. Gaio, V. Toigo, A. De Lorenzi, R. Piovan, L. Zanotto, The alternative design concept for the ion source power supply of the ITER neutral beam injector, Fusion Engineering and Design 83 (2008) 21–29. [9] K. Watanabe, M. Kashiwagi, S. Kawashima, Y. Ono, Y. Yamashita, C. Yamazaki, et al., Development of a dc 1 MV power supply technology for NB injectors, Nuclear Fusion 46 (2006) S332–S339. [10] A. Ferro, V. Toigo, L. Zanotto, Supporting analyses for the design of the acceleration grid power supply of the neutral beam injector of ITER, this conference. [11] M. Boldrin, M. Dalla Palma, F. Milani, The high voltage platform and feedthrough for the NBI ion source & extraction power supplies, this conference. [12] T. Inoue, M. Hanada, M. Kashiwagi, M. Taniguchi, H. Tobari, M. Dairaku, et al., Development of beam source and bushing for ITER NB system, Fusion Engineering and Design 82 (2007) 813–818. [13] A. Pesce, A. De Lorenzi, L. Grando, A new approach to passive protection design against high energy and high current breakdowns in the ITER NBI accelerator, this conference. [14] M. D’Amore, M.S. Sarto, Simulation models of a dissipative transmission line above a lossy ground for a wide-frequency range—Part I: single conductor configuration, IEEE Transactions on Electromagnetic Compatibility 38 (1996) 127–138. [15] P. Bettini, M. Cavinato, A. De Lorenzi, Model of the RFX-mod poloidal field circuit, Fusion Engineering and Design 82 (2007) 966–973.
Contents lists available at ScienceDirect
Fusion Engineering and Design journal homepage: www.elsevier.com/locate/fusengdes
A model for electrical fast transient analyses of the ITER NBI power supplies and the MAMuG accelerator M. Bigi a,∗ , A. De Lorenzi a , L. Grando a , K. Watanabe b , M. Yamamoto b a b
Consorzio RFX, EURATOM-ENEA Association, Corso Stati Uniti 4, 35127 Padova, Italy Japan Atomic Energy Agency, 801-1 Mukoyama, Naka, Ibaraki-ken 311-0193, Japan
a r t i c l e
i n f o
Article history: Available online 4 March 2009 Keywords: Neutral Beam Injector (NBI) Breakdown Circuit model
a b s t r a c t The design of ITER Neutral Beam Injector (NBI) is based on a five-stage electrostatic accelerator, known as Multi-Aperture Multi-Grid (MAMuG) and characterised by an overall acceleration voltage of −1 MV. The MAMuG accelerator requires a five-stage power supply system under strict load protection requirements, being subjected in operation to breakdowns. In this paper a circuit model of ITER Neutral Beam Injector power supplies and MAMuG accelerator is illustrated, for the simulation of fast transients related to accelerator breakdowns in particular. Consideration of the high voltage involved and of the complex inductive and capacitive couplings implied careful assessment of stray parameters by calculations with finite element techniques. The circuit model, developed to address a number of design issues requiring simulations at system level, is now ready for use—the optimisation of passive protections being the most significant application. © 2009 M. Bigi. Published by Elsevier B.V. All rights reserved.
1. Introduction In the present ITER design, each Neutral Beam Injector must be capable of delivering a power of 16.6 MW. This is obtained neutralising a deuterium negative ion beam having 1 MeV energy and 40 A current [1]. Production and electrostatic acceleration of an ion beam with the ITER parameters involves three main electrical systems: (a) Ion Source and Extractor Power Supplies (ISEPS), necessary to operate the ion source [2] and to extract an ion beam with minimum fraction of electrons. (b) Acceleration Grid Power Supply (AGPS), transferring energy to the ion beam through a five-stage electrostatic accelerator known as Multi-Aperture Multi-Grid (MAMuG) [1]. (c) Transmission Line (TL), connecting ISEPS and AGPS to the ion source and the accelerator. AGPS and Transmission Line in particular pose several technological challenges, related to the rated voltage of −1 MV dc and to grid breakdowns during beam extraction. The breakdown events are crucial to the design of the electric system. Strict limits apply to arc energy (50 J [3]) and peak break-
∗ Corresponding author. Tel.: +39 0498295045; fax: +39 0498700718. E-mail address: [email protected] (M. Bigi).
down current, to ensure that the accelerator is not damaged or voltage holding degraded [4]. A first implication is that the AGPS must be able to block within 150 s from a trip request. Secondly passive components must be added to the circuit, to control the fast discharge of capacitive stored energy: these components traditionally consist in a combination of resistors, air core inductors and magnetic core “snubbers” [5–7]. Integration of the different items of plant and design of the passive protections have been the prime reasons for developing the circuit model of ITER Neutral Beam Injector presented in this paper. More specifically, the model aims at simulating the fast transients following a breakdown of the accelerator or a failure of the insulation at a different point. For this reason it is purely passive, looking at the free evolution of the system after the breakdown. Other areas of study that may benefit from the availability of a breakdown simulation at system level include: • Scheme for the connections among power supplies, Transmission Line conductors and accelerator grids. • Voltage rise to local ground at a distance from the injector grounding point. • Transient waveforms experienced by dc insulation. • Integration of breakdown detectors/diagnostics. • Emission of ElectroMagnetic Interference. The model as it stands cannot simulate beam extraction and is limited to the high voltage side of the circuit.
0920-3796/$ – see front matter © 2009 M. Bigi. Published by Elsevier B.V. All rights reserved. doi:10.1016/j.fusengdes.2009.02.003
M. Bigi et al. / Fusion Engineering and Design 84 (2009) 446–450
447
Fig. 1. Reference electrical scheme of ITER NBI on which the circuit model is based.
2. Reference electrical scheme of the Neutral Beam Injector A reference scheme exists for the power supply system of ITER Neutral Beam Injector [8]. A simplified version is shown in Fig. 1, where the Ground Related Power Supplies have been omitted, being almost unaffected by accelerator breakdowns. The circuit model is based on the diagram of Fig. 1. The structure of the AGPS [9,10] is based on five high voltage DC Generators (DCGs), dc insulated to ground and having a rated output voltage of −200 kV dc with maximum ripple ±5% (for other ratings see Table 1). The DC Generators are series connected at the output, for a total output voltage of −1 MV dc to ground. The number of output terminals of the AGPS is six, corresponding to the number of grids of the MAMuG accelerator having the following nominal voltages to ground: 1. Extraction Grid (EG): −1000 kV. 2. Acceleration Grid 1 (AG1): −800 kV. 3. Acceleration Grid 2 (AG2): −600 kV. Table 1 Main parameters of DCG, ISEPS and passive protections. −200 kV DCG rated current −400 kV DCG rated current −600 kV DCG rated current −800 kV DCG rated current −1000 kV DCG rated current AGPS output filter Max ripple of AGPS output voltage Isolation transformer ISGT RF generator Extraction Grid PS AGPS series resistor Core snubbers (CS1 CS2) Intermediate voltage resistors: AG1, AG2, AG3, and AG4
66 A 64 A 59 A 56 A 54 A R = 68 ; C = 300 nF (per stage) ±5% 3ph 50 Hz; 22/6.6 kV Output 200 kW, 50 Output 12 kV, 140 A dc 50 750 H, 175 ; 250 H, 130 400, 300, 200, and 100
4. Acceleration Grid 3 (AG3): −400 kV. 5. Acceleration Grid 4 (AG4): −200 kV. 6. Post acceleration or Grounded Grid (GG): 0 V. The 0 V output terminal of the AGPS is connected to ground at the accelerator, following the principle of single grounding point. Each DC Generator is composed of a step-up transformer with dc insulation of the secondary windings, a high voltage diode rectifier and an RC smoothing filter. Regulation of the AGPS output voltage and fast switch off in response to a load breakdown are performed by an inverter, feeding the primary windings of the DC Generator step-up transformer. The main ratings of the DC Generator are listed in Table 1. The ISEPS include several distinct pieces of equipment, the largest ones in terms of power being: • The 1 MHz radio-frequency generators (see ratings in Table 1) used to produce, by inductive coupling, the ion source plasma. • The Extraction Grid Power Supply (EGPS, see ratings in Table 1), feeding at a rated output voltage of −12 kV dc the extraction gap between Plasma Grid (PG) and Extraction Grid. Since the design of the MAMuG accelerator is such that the grid at the exit is at ground potential, the ion source is polarised at the full AGPS output voltage of −1 MV dc. The present solution to ensure insulated supply to the ISEPS loads inside the ion source foresees a 50 Hz isolation transformer, with secondary windings insulated to ground for −1 MV dc [8]. From the isolation transformer supply is brought to an air insulated platform, known as “High Voltage Deck 1” (HVD1) [10], where the ISEPS are located. The main ratings of isolation transformer and EGPS are listed in Table 1. The Transmission Line, connecting AGPS and ISEPS to the Neutral beam Injector, is insulated with pressurised SF6 gas and consists of three distinct sections (Fig. 1):
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Fig. 3. Simulated breakdown current of the Plasma Grid conductor.
Fig. 2. Equipotential lines [volt] for Transmission Line 2. The white circles correspond to the intermediate voltage conductors.
(i) Transmission Line 1 (TL1, reference length 30 m), connecting the AGPS output to High Voltage Deck 1. From High Voltage Deck 1, ISEPS conductors and services join the Transmission Line through a dedicated bushing [11]. (ii) Transmission Line 2 (TL2, reference length 65 m), running from High Voltage Deck 1 bushing to “High Voltage Deck 2” (HVD2), where cooling supplies for the ion source and the acceleration grids at intermediate voltages (Acceleration Grid 1 to Acceleration Grid 4) connect to the Transmission Line. (iii) Transmission Line 3 (TL3, reference length 15 m), running from High Voltage Deck 2 to the beam source vessel bushing, hereinafter referred to as “High Voltage Bushing”—HVB [12]. The Transmission Line is multipolar and has a complex design. There exists an inner hollow cylindrical conductor, at a dc potential to ground of −1000 kV (TL1) or −1012 kV (TL2 and TL3). The inner conductor is coaxial to the outer hollow cylindrical conductor, connected to the Grounded Grid. The intermediate voltage conductors do not follow the coaxial geometry and are placed in the region between inner and outer conductor (visible as white circles in Fig. 2). A typical cross-section of MAMuG Transmission Line can be found in [9]. The ISEPS conductors in Transmission Line 2 and Transmission Line 3 are housed inside the inner conductor. In Transmission Line 1 and Transmission Line 2 four conductors are present for the AGPS intermediate voltages from −800 to −200 kV. In Transmission Line Table 2 Symmetric matrix of couplings for Transmission Line 2. The elements above the diagonal are the capacitance values [10−12 F/m] while the ones below are the inductance values [10−9 H/m].
3 the number of intermediate voltage conductors doubles because of cooling requirements: each pair of intermediate voltage conductors acts as inlet and outlet cooling pipes. A number of passive protection components are included in the ITER neutral beam circuit: 1. A resistor in series to the AGPS return conductor [7], as shown in Fig. 1 between diode rectifiers and RC filters. 2. A first core snubber (CS1) at the end of Transmission Line 2. 3. A second core snubber (CS2) at the start of Transmission Line 3. 4. Resistors in series to the intermediate voltage conductors (immediately upstream of Transmission Line 3). As additional element of optimisation of the passive protections, a resistor known as “damper” [13] has been proposed, in series to the ground connection of the post acceleration grid. Having given an overview of the main items of plant that play a role in the breakdown simulation, the specifics of fast transient modelling will be discussed next. 3. Modelling issues The goal of the circuit model presented here is the simulation of the first few tens of microseconds following a breakdown in the ITER Neutral Beam Injector. Because of the high voltage involved, stray capacitance plays a crucial role in the dynamics of the transient and a calculation is required of the capacitance associated to significant component of the circuit. The anticipated harmonic content of the breakdown transient voltages and currents is up to the range of several megahertz [6] and for the Transmission Line, having non negligible dimension as compared to the associated wavelength, has lead to a model with multiple cells (see Section 4). 3.1. Capacitive and magnetic coupling The components of the Neutral Beam Injector have complex geometry characterised by capacitive and magnetic coupling that affect significantly current and voltage transient distributions. Consequently, as a pre-requisite to the implementation of a circuit model, the electric and magnetic coupling matrices have been evaluated for Transmission Line 1, Transmission Line 2, Transmission Line 3 and High Voltage Bushing. The calculation of capacitive and inductive parameters has been carried out by a bi-dimensional finite element model in static regime using the ANSYS® code, under the following assumptions:
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The outer conductor of each section of Transmission Line has been assumed as reference for the potential in the calculation of the capacitance and as return conductor for the total injected current in the calculation of the inductance. The vessel has been assumed as reference for the potential in the calculation of the capacitance of High Voltage Bushing and beam source. The post-insulators supporting Transmission Line conductors and the accelerator mounting flanges have been neglected. The computation of magnetic coupling for the accelerator considers, as current path across the grids, only the arc present during a breakdown. The arc has been modelled as a concentrated column with a value of inductance of 1 H/m and negligible resistivity. Table 2 lists, as an example, the symmetric matrix of capacitance and inductance for Transmission Line 2 and Fig. 2 shows the corresponding distribution of equipotential lines. Fig. 4. Simulated voltage to ground at the start of Transmission Line 1, following a grid breakdown.
3.2. Voltage distribution along the ground Due to stray capacitance, a path through the ground exists for the current flowing out of the AGPS, in parallel to the Transmission Line outer conductor. In normal operation, due to the low frequency involved and to the corresponding high impedance, the fraction of current diverted through the ground is negligible. On the contrary, during fast transients the current flowing in the ground must be taken into account. The effect of the ground has been modelled under the following assumptions: • The impedance of the ground is included only along the Transmission Line span. • The ground has no resistivity, i.e. ground resistance and internal inductance are both zero [14]. • Inductive coupling among intermediate voltage conductors and ground is neglected (an approximation of perfectly coaxial conductors). Under these assumptions, the circuit model of the ground reduces to a series inductance and a transverse capacitance to the Transmission Line outer conductor. Labelling h the height of the Transmission Line axis over the ground and R the radius of the Transmission Line outer conductor, the expression for the ground series inductance Lg and for the ground transverse capacitance, as computed with the principle of images, are given by
2h − R
Lg =
0 ln 2
Cg =
2ε0 ln((2h − R)/R)
R
(1) (2)
The circuit model has been developed in Simulink® , making use of the SimPowerSystems toolbox and selecting an integration technique with variable time step. Below a description is given of the circuit model adopted for two main items of the plant. 4. A fast transient circuit model for the Neutral Beam Injector 4.1. Acceleration Grid Power Supply In the model of the AGPS, single phase equivalent representations are used for step-up transformers and diode rectifiers. The most significant circuit parameter is the large 10−9 F capacitance between high voltage windings and electrostatic screen of the stepup transformer. The electrostatic screen is connected to the outer conductor of the Transmission Line.
Based on simplified geometries, the stray capacitance of diode and output filter tanks have also been included in the model. 4.2. Transmission Line The Transmission Line parameters have been computed as illustrated in Section 3: The inductive couplings, with as many as ten coupled conductors in Transmission Line 3, has been implemented in Simulink® using voltage controlled current sources as reported in [15]. Each Transmission Line section has been split in several cells, in order to take into account propagation effects. The chosen length is 2.5 m per cell, following an iterative process where further reduction of length would not change the results. 5. Results of breakdown simulations In Figs. 3 and 4 two examples are shown of simulated waveforms obtained with the Neutral Beam Injector circuit model. In the hypothesis of a breakdown short-circuiting all the acceleration grids at the same time and in absence of damper, Fig. 3 shows the predicted fault current flowing through the Plasma Grid conductor of the High Voltage Bushing. Fig. 4 shows the simulated voltage of Transmission Line 1 outer conductor near the 50 series resistor. The waveform has a delay of about 300 ns with respect to the instant of the breakdown (t = 1 ns in the simulation), corresponding to the Transmission Line length divided by the speed of light. This is evidence that, having modelled the Transmission Line with multiple cells, propagation effects are reproduced. The peak voltage of Fig. 4, around 200 kV, is noticeable and might be used as a basis for sizing the overvoltage protections of the Transmission Line. The results of Figs. 3 and 4 are examples, among the many possible, of conditions one would want to consider as part of a comprehensive design study, requiring a circuit simulator like the one described in this paper. 6. Conclusions Some salient features have been presented of a circuit model for fast transient analyses of the ITER Neutral Beam Injector. It has been shown that the model works and is ready to be used as a design tool, for the optimisation of the passive protection system. The resulting waveforms might be useful to other and more specific circuit models, studying the effects of the breakdown on AGPS conversion system and ISEPS. A further task is represented by the study of ElectroMagnetic Interference and its mitigation.
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