- Email: [email protected]
Improved fast vertical control in KSTAR
Fusion Engineering and Design 141 (2019) 9–14
Contents lists available at ScienceDirect
Fusion Engineering and Design journal homepage: www.elsevier.com/locate/fusengdes
Improved fast vertical control in KSTAR a,⁎
b
c
b
T a
c
c
D. Mueller , S.H. Hahn , N. Eidietis , J.G. Bak , M.D. Boyer , D.A. Humphreys , A.W. Hyatt , Y.M. Jeonb, H.S. Kimb, M. Walkerc a b c
Princeton Plasma Physics Laboratory, Princeton Univ., Princeton, N.J., 08543, USA National Fusion Research Institute, Daejeon, 34133, South Korea General Atomics, San Diego, CA, 92186-5608, USA
A R T I C LE I N FO
A B S T R A C T
Keywords: Plasma control Vertical control Magnetic diagnostics Shaped plasma KSTAR
Fast vertical control of shaped plasmas is essential for the successful realization of plasma operation near the limit of vertical control to achieve maximum confinement and stable, disruption free operation. In KSTAR, the normal conducting in-vessel vertical control coil (IVC coil) is employed to respond to vertical transients much faster than the superconducting coils are capable. The power supply for the IVC coil is capable of responding in a time commensurate with the expected vertical growth rates on KSTAR. The diagnostics used for the fast vertical control since the first operation with shaped plasmas in KSTAR, however, have a low signal-to-noise ratio which limits the gains that can be used successfully in the proportional and derivative control loops and thus the speed of the control loop. The successful use of relative flux for the Z-position estimate and of the loop voltage difference from a pair of up-down symmetric loops to provide sensitive and less noisy vertical estimate will be discussed. In addition, the control loop for the IVC coil is decoupled from the slow motion controlled by the superconducting coils using a high-pass filter in the control software. Finally the noticeable improvement in plasma control for plasmas near the vertical stability limit will be discussed.
1. Introduction
of ramp-up and ramp-down that deserve their own separate discussion. During this phase of the plasma, the plasma shape is controlled by the superconducting poloidal field (PF) coils using an isoflux algorithm [7] while control of transients in the vertical position is accomplished using IVC coil feedback control based on a fast vertical position (Z) estimator consisting of two inboard magnetic probes. The vertical separation of the magnetic probes initially used successfully for control is only 0.13 m; the Zp estimator based on these probes is strictly proportional to the signal only in the range over which the approximation was designed, furthermore since the derivative with respect to Zp of B changes sign at the height of either B-probe for one of the probes, it is likely to be increasingly inaccurate outside that range. Also the small separation raises concerns about sensitivity for high triangularity plasmas due to their nearly straight vertical flux surface on the mid plane. Fig. 1 shows the cross-section of KSTAR with the location of these magnetic probes and the flux loops discussed later in this paper indicated. The plasma shape is controlled by the SC coils which can produce significantly more radial field than the IVC coil can with the result that any mismatch between the plasma vertical center as determined by the SC coils feedback loop and the fast Z target in the control loop can lead to a large offset of the IVC coil current and
Empirical scaling laws for plasma energy confinement have found that the plasma energy confinement scales positively with plasma elongation (κ), in particular the ITER98 H(y2) scaling finds τE scales as κ0.78 [1]. For the KSTAR design, the target plasma κ is 2.0 at li = 1.2 and βp = 1.9 where li is the internal inductance and βp is the average poloidal β [2]. Using the initial real-time Z diagnostics it has been impossible to achieve this target stably in KSTAR despite the adequate voltage and time response of the in-vessel vertical control (IVC) coil supply for the measured growth rates of vertical instability [3–5]. The concept of separating the frequency domains is well-known and implemented operationally for decades, see Ref. 3 for example. EAST and KSTAR each implemented separation of fast and slow Z control based upon the 2010 engineering physics memo (unpublished) by a coauthor of this paper, Michael Walker, to remove the conflict between the control of the slower superconducting (SC) coils from that of the faster internal coils. The plasma control system (PCS) on KSTAR is a version of General Atomics PCS that has been modified for KSTAR [6]. For the purposes of this paper, we will be discussing plasma control during the main experimental phase of the plasma and will be excluding discussion
⁎
Corresponding author. E-mail address: [email protected] (D. Mueller).
https://doi.org/10.1016/j.fusengdes.2019.02.046 Received 26 October 2018; Received in revised form 15 January 2019; Accepted 11 February 2019 0920-3796/ © 2019 Elsevier B.V. All rights reserved.
Fusion Engineering and Design 141 (2019) 9–14
D. Mueller, et al.
Fig. 1. Cross-section of KSTAR showing the location of the SC PF coils, IVC coils, magnetic probes (MP4P21R and MP4P22R), and the flux loops (FL21, etc.) that are discussed in the text.
of the noise in this initial Z estimate. The use of relative rather than absolute flux can allow for higher gains to be used in the flux measurement to reduce the significance of electronic noise. The relative flux difference made by a vertical movement of the plasma can be expressed by the following formula:
potential loss of fast control. The control of the plasma shape using isoflux control and the SC coils is a topic beyond the scope of this paper and is taken as a given, at least for already achieved plasma shapes in KSTAR. 2. Experimental procedure
Ψ1 − Ψ2 = (Mp1 − Mp2 ) Ip = ⎛ δMp1 δz − δMp2 δz ⎞ δz⋅Ip ≅ 2 ⎛ δMp1 δz ⎞ δz⋅Ip ⎝ ⎠ ⎝ ⎠
In order to determine which diagnostics to use for control, the criteria were: 1) sensor separation of over 30 cm to ensure signal linearity of plasmas up to 15 cm off the mid-plane, 2) sensors with minimum influence from the SC coil currents and 3) sensors with the fastest response to plasma motion as well as those with a good signal-to-noise ratio. Recently a major effort to reduce the noise in all the magnetic sensors using anti-aliasing filters with time constants of 2.2 kHz was successful [8], however, the initial real-time vertical position diagnostic still in use suffered from excessive noise. The reason for that is partly that absolute measurements were used, but mostly because the initial vertical diagnostic used just 2 magnetic probes and the current in the SC coils. The noise on the SC coil current sensors comprises a large fraction
Where Ψi is the flux measured at the ith flux loop, and Mpi is the mutual inductance between the plasma and the ith flux loop for up/down symmetric pairs. Note: δMp1/δz = −δMp2/δz so the sum is 2δMp1/δz. For Ip = 1 MA and the pair of up/down symmetric flux loops FL21 and FL25, the scaling used to accommodate the total absolute flux (6 Wb) results in a signal size at the PCS of only 0.3 mV which is below the noise level. By using relative flux, a higher gain can be used so that at Ip = 1 MA, a 1 mm motion corresponds to 10 mV at the PCS which is measureable. The up-down flux difference in the sensors due to imbalance of the up/down SC coils is ignored. This was done to avoid introducing the noise that would be added by attempting to correct for the SC coil 10
Fusion Engineering and Design 141 (2019) 9–14
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Fig. 2. Comparison of the response of the three selected flux loop pairs on the inner wall shown in black to that of the initial Z estimator (\lmsz) shown in red and Z0 from rtEFIT shown in blue for a plasma controlled with the initial Z estimator. The average of the 3 pairs is shown in black in the top frame. Note the obviously greater noise in \lmsz compared to even a single loop pair (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article).
filtering the signals to average over noise is not useful since it would introduce more latency into the estimate. It is essential for fast control that the measurement system introduces little or no latency into the control loop. The original plan was to use loops above and below the plasma for control, FL04 and FL42 in Fig. 1, but the passive plates in KSTAR can delay response of sensors outside the passive plates by up to 6 ms; sensors with a minimum delay must be selected. Fig. 4 shows the loop voltage difference of two loops, FL04 and FL42, above and below the passive plates overlaid on the initial Z estimate signal for a plasma oscillating with a period of ˜20 ms.
Fig. 3. Three methods to determine dZ/dt have great differences in their noise level. The time derivative of \lmsz, the initial Z estimator is shown in blue. The time derivative of new Z estimator \lmss1 from the flux loop difference FL21FL25 is shown in black. The analog difference of the loop voltage signals scaled by 1/(2*Ip*M) is shown in green. The analog difference shows 10 and 100 times less noise than the others (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article).
currents. Fig. 2 shows the Z determined by 3 different flux loop pairs, from real-time equilibrium analysis (rtEFIT) [9] and the initial z estimate labeled \lmsz. Note that the average of the 3 signals is shown and that reduces the apparent noise, however, each loop pair requires a different correction for unbalanced SC coils in order to be a good estimate of Z. Comparison of the dZ/dt signal from the loop voltage difference with the derivative of the initial Z estimate, \lmsz is shown in Fig. 3. The signal from the loop voltages has about 100 times lower noise than d(\lmsz)/dt and about 5–10 times lower noise than d (newZ)/dt. The frequency spectra of the noise levels suggest that the IVC power supply is the source of the noise. The noise characteristics of the IVC coil are discussed in Ref. [8]. It should be noted that further
Fig. 4. The analog difference of the pair of loops outside the passive plates (black) from the plasma exhibit a clear delay compared to what is expected from the initial Z estimator (blue). Note the vertical magnitude of the black trace was scaled arbitrarily to provide an easy visual comparison of the time response of the two signals. The derivative should lead the signal by 90°, it does not and appears to be delayed by about 5 ms (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article). 11
Fusion Engineering and Design 141 (2019) 9–14
D. Mueller, et al.
Fig. 5. Comparison of the time response of the three analog loop voltage differences to a vertical plasma oscillation. Note that the pair closest to the midplane (red) has the fastest response by 2–4 ms and was thus chosen as the pair to use for the new Z estimator (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article).
the derivative of the new Z estimator as well as dZ/dt from the loop voltage difference. This was done by setting the gains for dz/dt in the two paths shown in Fig. 6 (both the D gain in the ZFAST loop as well as in the gain in the dzdt loop) to non-zero values. That is likely responsible for the apparent noise on the IVC coil, but it does not invalidate the positive results obtained; when the D gain in the ZFAST loop was set to zero in similar discharges, not shown here, the control performed similarly but with less noise on the IVC. It is worth noting that κ of 2.16 at li of over 1.1 was achieved with the new system. Furthermore this was not limited by loss of vertical control, but by the inability of the SC coils to ramp fast enough in these high loop voltage plasmas to elongate the plasma further as can be seen in Fig. 8. This discharge had the highest elongation achieved, κ = 2.16, from 6 s until one of the shape control coils became saturated at 7.6 s. Also Fig. 8 shows the shape evolution as the plasma was elongated from 2.5 to 6.5 s. It is worth noting that none of the plasmas controlled using the new Z control system exhibited loss of fast vertical control for the high li and high loop voltage discharges used during the commissioning of the new system.
If the loop voltage difference were not delayed it would lead the Z signal by 90° or 5 ms, it does not. The inference is that passive plates delay the sensor response by about 5 ms (the initial Z estimate may have its own smaller delay) and that sensors shielded from the plasma by the passive plates are not useful for fast control [10]. Three pairs were considered, FL21-FL25, FL19-FL27 and FL17-FL29. As can be seen in Fig. 1 all 3 pairs satisfy the separation requirement. Routine test shots show that the pair FL21-FL25 has the least pickup from unbalanced SC coils; this is not unexpected since they are furthest from theSC coils. As can be seen in Fig. 5 the pair FL21-FL25 has the fastest response to plasma oscillations by about 1 to 4 ms. Therefore, the pair FL21-FL25 was chosen as the best sensors for the new control system. Inclusion of the other loops would add unwanted latency. It is important to note that the new Z estimator derived from the loops without correction for possibly unbalanced SC coils will be different than the actual plasma vertical position depending upon the SC coil currents. However, for control of fast transients with the IVC coil, it is not necessary to know the vertical position absolutely, but only the deviation from its recent mean. Correction for the SC coil currents would introduce unwanted noise in the system and should be avoided. In order to deal with this, a control algorithm called ZFAST was written for feedback control of the IVC coil [4]. This simply applies a 1 Hz high pass filter to the proportional error signal for Z in the PCS. That has proven to be effective to eliminate the slow drift in the measured Z from SC coils and provides a feedback request that depends only on faster plasma motion. A further Modification to the PCS algorithm allowed for the inclusion of the loop voltage difference as the derivative term dIpZ/dt in the IVC control loop as shown in Fig. 6.
4. Future work It remains to use the new system for vertical control in plasmas with larger vertical instability growth rates so as to determine the ultimate limit of vertical control with the new system. In particular control of plasmas with the new system during high neutral beam power and with large ELMS has yet to be tested. Further development will be required for control of KSTAR plasmas during the ramp-up phase at low Ip before the plasma is under isoflux control and the ZFAST algorithm can be used. A new algorithm will be required to add a high-pass filter to the IVC control in the ramp-up phase that is used before rtEFIT convergence. Before rtEFIT converges, plasma control use of isoflux control is not possible. The latter will require validating the new Z estimator during the ramp-up.
3. Results The control achieved using the new Z estimator and the ZFAST algorithm is compared to that achieved using the initial Z estimator in Fig. 7. It is clear that the new algorithm using ZFAST and the new Z estimator is successful to keep the IVC coil current near zero, that the amplitude of the oscillations in the IVC coil current are smaller and most importantly that it is able to maintain vertical control during an attempt to ramp Ip to higher current, something the initial system was unable to accomplish. This inability may be the result of a delay in the x-point control and to the offset in the IVC coil current when using the initial system. The setup used for the new control included a dZ/dt from
Acknowledgments This work was supported by U.S.D.O.E. Contract No. DE-AC0209CH11466 and by the Korean Ministry of Science and ICT under the KSTAR Project contract. The authors would also like to express our appreciation to Hyeon Park, Si-woo Yoon, Yeong-Kook Oh, Raffi Nazikian and Richard Hawryluk for their support for and 12
Fusion Engineering and Design 141 (2019) 9–14
D. Mueller, et al.
Fig. 6. Block diagram of the ZFAST algorithm. The difference of the Voltage signals from the two flux loops FL21 and FL21 is taken and split into two paths, the top path in the figure indicates the integrated (flux) difference signal used in the control loop. The High-pass filter is applied to the error term in the PCS PD and the P term in the overall control loop always comes from this top path. The bottom path indicates the unintegrated analog loop voltage difference which is the time derivative of the flux signal without the integration and subsequent differentiation taken in the top path. The derivative term in the overall feedback loop can be accomplished by using non-zero D gain in the normal PD (top) path, by using non-zero gain in the analog dz/dt path (bottom) or by using non-zero gains in both paths. While the performance is similar using each of these choices, use of non-zero gain in only the analog dz/dt path resulted in the lowest noise in the control loop and is preferred.
Fig. 7. The vertical control achieved with the new system using ZFAST, the new Z estimator and the analog difference of loop voltages, shown in red is clearly superior to that achieved with the initial Z estimator and the usual PD controller in the PCS (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article). 13
Fusion Engineering and Design 141 (2019) 9–14
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Fig. 8. Experiment with highest achieved elongation (κ): #18,380 used BT = 2.4 T, Ip = 500 kA with total beam power 4.8 MW (beam energy at 100/70/95 keV) and 0.8 MW of 140 GHz ECH. The increase of elongation starts at 3.0 and last until the end of shot, in order to check the proximity. The highest value, κ = 2.16, is obtained at t˜6 s, until one of the PF coils got saturated to the operation limit (15 kA/turn per coil) and loss of shape control occurs after t = 7.6 s. In the right, the shape evolutions at t = 2.5/4.5/6.5 s are shown. All the equilibrium values/shapes are taken from the real-time EFIT (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article).
encouragement of this work over the years. The data reside on the ikstar, kstarpcs and ksim2 computers of the KSTAR project at the Korean National Fusion Research Institute.
[6]
References
[7]
[1] M. Shimada, et al., Chapter 1: overview and summary. Editors of’ Progress in the ITER Physics Basis’, Nucl. Eng. 47 (6) (2019), https://doi.org/10.1088/0029-5515/ 47/6/S01.Z. [2] J.-G. Kwak, Y.K. Oh, H.L. Yang, K.R. Park, Y.S. Kim, W.C. Kim, et al., An overview of KSTAR results, Nucl. Eng. 53 (2013) 104005, https://doi.org/10.1088/0029-5515/ 53/10/104005. [3] E.A. Lazarus, et al., Control of the vertical instability in tokamaks, Nucl. Eng. 30 (1990). [4] Q.P. Yuan, B.J. Xiao, Z.P. Luo, M.L. Walker, A.S. Welander, A. Hyatt, et al., Plasma current, position and shape feedback control on EAST, Nucl. Eng. 53 (2013) 043009–043011, https://doi.org/10.1088/0029-5515/53/4/043009. [5] S.-H. Hahn, D.A. Humphreys, D. Mueller, J.G. Bak, N.W. Eidietis, Y.M. Jeon,
[8]
[9]
[10]
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M.L. Walker, “Measuring and extending vertical stabilization controllability of KSTAR”, Proceedings on the 26th IAEA Fusion Energy Conference. Kyoto, Japan (2016). S.-H. Hahn, Y.J. Kim, B.G. Penaflor, J.-G. Bak, H. Han, J.S. Hong, et al., Progress and plan of KSTAR plasma control system upgrade, Fus. Eng. Des. 112 (2016) 687–691. F. Hofmann, S.C. Jardin, Plasma shape and position control in highly elongated tokamaks, Nucl. Eng. 30 (1990) 2013–2022, https://doi.org/10.1088/0029-5515/ 30/10/003. H.-S. Kim, J.-G. Bak, S.-H. Hahn, Improvements of magnetic measurements for plasma control in KSTAR tokamak, Fus. Eng. Des. 123 (2017) 641–645, https://doi. org/10.1016/j.fusengdes.2017.02.023. J.R. Ferron, M.L. Walker, L.L. Lao, H. John, Real time equilibrium reconstruction for tokamak discharge control, Nucl. Eng. 38 (1998) 1055–1066, https://doi.org/ 10.1088/0029-5515/38/7/308. D. Mueller, N.W. Eidietis, D.A. Gates, S. Gerhardt, S.-H. Hahn, E. Kolemen, B.J. Xiao, “Improvements in the fast vertical control systems in KSTAR, EAST, NSTX and NSTX-U”, Proceedings on the 25th IAEA Fusion Energy Conference, St. Petersburg, Russia (2014).
Contents lists available at ScienceDirect
Fusion Engineering and Design journal homepage: www.elsevier.com/locate/fusengdes
Improved fast vertical control in KSTAR a,⁎
b
c
b
T a
c
c
D. Mueller , S.H. Hahn , N. Eidietis , J.G. Bak , M.D. Boyer , D.A. Humphreys , A.W. Hyatt , Y.M. Jeonb, H.S. Kimb, M. Walkerc a b c
Princeton Plasma Physics Laboratory, Princeton Univ., Princeton, N.J., 08543, USA National Fusion Research Institute, Daejeon, 34133, South Korea General Atomics, San Diego, CA, 92186-5608, USA
A R T I C LE I N FO
A B S T R A C T
Keywords: Plasma control Vertical control Magnetic diagnostics Shaped plasma KSTAR
Fast vertical control of shaped plasmas is essential for the successful realization of plasma operation near the limit of vertical control to achieve maximum confinement and stable, disruption free operation. In KSTAR, the normal conducting in-vessel vertical control coil (IVC coil) is employed to respond to vertical transients much faster than the superconducting coils are capable. The power supply for the IVC coil is capable of responding in a time commensurate with the expected vertical growth rates on KSTAR. The diagnostics used for the fast vertical control since the first operation with shaped plasmas in KSTAR, however, have a low signal-to-noise ratio which limits the gains that can be used successfully in the proportional and derivative control loops and thus the speed of the control loop. The successful use of relative flux for the Z-position estimate and of the loop voltage difference from a pair of up-down symmetric loops to provide sensitive and less noisy vertical estimate will be discussed. In addition, the control loop for the IVC coil is decoupled from the slow motion controlled by the superconducting coils using a high-pass filter in the control software. Finally the noticeable improvement in plasma control for plasmas near the vertical stability limit will be discussed.
1. Introduction
of ramp-up and ramp-down that deserve their own separate discussion. During this phase of the plasma, the plasma shape is controlled by the superconducting poloidal field (PF) coils using an isoflux algorithm [7] while control of transients in the vertical position is accomplished using IVC coil feedback control based on a fast vertical position (Z) estimator consisting of two inboard magnetic probes. The vertical separation of the magnetic probes initially used successfully for control is only 0.13 m; the Zp estimator based on these probes is strictly proportional to the signal only in the range over which the approximation was designed, furthermore since the derivative with respect to Zp of B changes sign at the height of either B-probe for one of the probes, it is likely to be increasingly inaccurate outside that range. Also the small separation raises concerns about sensitivity for high triangularity plasmas due to their nearly straight vertical flux surface on the mid plane. Fig. 1 shows the cross-section of KSTAR with the location of these magnetic probes and the flux loops discussed later in this paper indicated. The plasma shape is controlled by the SC coils which can produce significantly more radial field than the IVC coil can with the result that any mismatch between the plasma vertical center as determined by the SC coils feedback loop and the fast Z target in the control loop can lead to a large offset of the IVC coil current and
Empirical scaling laws for plasma energy confinement have found that the plasma energy confinement scales positively with plasma elongation (κ), in particular the ITER98 H(y2) scaling finds τE scales as κ0.78 [1]. For the KSTAR design, the target plasma κ is 2.0 at li = 1.2 and βp = 1.9 where li is the internal inductance and βp is the average poloidal β [2]. Using the initial real-time Z diagnostics it has been impossible to achieve this target stably in KSTAR despite the adequate voltage and time response of the in-vessel vertical control (IVC) coil supply for the measured growth rates of vertical instability [3–5]. The concept of separating the frequency domains is well-known and implemented operationally for decades, see Ref. 3 for example. EAST and KSTAR each implemented separation of fast and slow Z control based upon the 2010 engineering physics memo (unpublished) by a coauthor of this paper, Michael Walker, to remove the conflict between the control of the slower superconducting (SC) coils from that of the faster internal coils. The plasma control system (PCS) on KSTAR is a version of General Atomics PCS that has been modified for KSTAR [6]. For the purposes of this paper, we will be discussing plasma control during the main experimental phase of the plasma and will be excluding discussion
⁎
Corresponding author. E-mail address: [email protected] (D. Mueller).
https://doi.org/10.1016/j.fusengdes.2019.02.046 Received 26 October 2018; Received in revised form 15 January 2019; Accepted 11 February 2019 0920-3796/ © 2019 Elsevier B.V. All rights reserved.
Fusion Engineering and Design 141 (2019) 9–14
D. Mueller, et al.
Fig. 1. Cross-section of KSTAR showing the location of the SC PF coils, IVC coils, magnetic probes (MP4P21R and MP4P22R), and the flux loops (FL21, etc.) that are discussed in the text.
of the noise in this initial Z estimate. The use of relative rather than absolute flux can allow for higher gains to be used in the flux measurement to reduce the significance of electronic noise. The relative flux difference made by a vertical movement of the plasma can be expressed by the following formula:
potential loss of fast control. The control of the plasma shape using isoflux control and the SC coils is a topic beyond the scope of this paper and is taken as a given, at least for already achieved plasma shapes in KSTAR. 2. Experimental procedure
Ψ1 − Ψ2 = (Mp1 − Mp2 ) Ip = ⎛ δMp1 δz − δMp2 δz ⎞ δz⋅Ip ≅ 2 ⎛ δMp1 δz ⎞ δz⋅Ip ⎝ ⎠ ⎝ ⎠
In order to determine which diagnostics to use for control, the criteria were: 1) sensor separation of over 30 cm to ensure signal linearity of plasmas up to 15 cm off the mid-plane, 2) sensors with minimum influence from the SC coil currents and 3) sensors with the fastest response to plasma motion as well as those with a good signal-to-noise ratio. Recently a major effort to reduce the noise in all the magnetic sensors using anti-aliasing filters with time constants of 2.2 kHz was successful [8], however, the initial real-time vertical position diagnostic still in use suffered from excessive noise. The reason for that is partly that absolute measurements were used, but mostly because the initial vertical diagnostic used just 2 magnetic probes and the current in the SC coils. The noise on the SC coil current sensors comprises a large fraction
Where Ψi is the flux measured at the ith flux loop, and Mpi is the mutual inductance between the plasma and the ith flux loop for up/down symmetric pairs. Note: δMp1/δz = −δMp2/δz so the sum is 2δMp1/δz. For Ip = 1 MA and the pair of up/down symmetric flux loops FL21 and FL25, the scaling used to accommodate the total absolute flux (6 Wb) results in a signal size at the PCS of only 0.3 mV which is below the noise level. By using relative flux, a higher gain can be used so that at Ip = 1 MA, a 1 mm motion corresponds to 10 mV at the PCS which is measureable. The up-down flux difference in the sensors due to imbalance of the up/down SC coils is ignored. This was done to avoid introducing the noise that would be added by attempting to correct for the SC coil 10
Fusion Engineering and Design 141 (2019) 9–14
D. Mueller, et al.
Fig. 2. Comparison of the response of the three selected flux loop pairs on the inner wall shown in black to that of the initial Z estimator (\lmsz) shown in red and Z0 from rtEFIT shown in blue for a plasma controlled with the initial Z estimator. The average of the 3 pairs is shown in black in the top frame. Note the obviously greater noise in \lmsz compared to even a single loop pair (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article).
filtering the signals to average over noise is not useful since it would introduce more latency into the estimate. It is essential for fast control that the measurement system introduces little or no latency into the control loop. The original plan was to use loops above and below the plasma for control, FL04 and FL42 in Fig. 1, but the passive plates in KSTAR can delay response of sensors outside the passive plates by up to 6 ms; sensors with a minimum delay must be selected. Fig. 4 shows the loop voltage difference of two loops, FL04 and FL42, above and below the passive plates overlaid on the initial Z estimate signal for a plasma oscillating with a period of ˜20 ms.
Fig. 3. Three methods to determine dZ/dt have great differences in their noise level. The time derivative of \lmsz, the initial Z estimator is shown in blue. The time derivative of new Z estimator \lmss1 from the flux loop difference FL21FL25 is shown in black. The analog difference of the loop voltage signals scaled by 1/(2*Ip*M) is shown in green. The analog difference shows 10 and 100 times less noise than the others (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article).
currents. Fig. 2 shows the Z determined by 3 different flux loop pairs, from real-time equilibrium analysis (rtEFIT) [9] and the initial z estimate labeled \lmsz. Note that the average of the 3 signals is shown and that reduces the apparent noise, however, each loop pair requires a different correction for unbalanced SC coils in order to be a good estimate of Z. Comparison of the dZ/dt signal from the loop voltage difference with the derivative of the initial Z estimate, \lmsz is shown in Fig. 3. The signal from the loop voltages has about 100 times lower noise than d(\lmsz)/dt and about 5–10 times lower noise than d (newZ)/dt. The frequency spectra of the noise levels suggest that the IVC power supply is the source of the noise. The noise characteristics of the IVC coil are discussed in Ref. [8]. It should be noted that further
Fig. 4. The analog difference of the pair of loops outside the passive plates (black) from the plasma exhibit a clear delay compared to what is expected from the initial Z estimator (blue). Note the vertical magnitude of the black trace was scaled arbitrarily to provide an easy visual comparison of the time response of the two signals. The derivative should lead the signal by 90°, it does not and appears to be delayed by about 5 ms (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article). 11
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Fig. 5. Comparison of the time response of the three analog loop voltage differences to a vertical plasma oscillation. Note that the pair closest to the midplane (red) has the fastest response by 2–4 ms and was thus chosen as the pair to use for the new Z estimator (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article).
the derivative of the new Z estimator as well as dZ/dt from the loop voltage difference. This was done by setting the gains for dz/dt in the two paths shown in Fig. 6 (both the D gain in the ZFAST loop as well as in the gain in the dzdt loop) to non-zero values. That is likely responsible for the apparent noise on the IVC coil, but it does not invalidate the positive results obtained; when the D gain in the ZFAST loop was set to zero in similar discharges, not shown here, the control performed similarly but with less noise on the IVC. It is worth noting that κ of 2.16 at li of over 1.1 was achieved with the new system. Furthermore this was not limited by loss of vertical control, but by the inability of the SC coils to ramp fast enough in these high loop voltage plasmas to elongate the plasma further as can be seen in Fig. 8. This discharge had the highest elongation achieved, κ = 2.16, from 6 s until one of the shape control coils became saturated at 7.6 s. Also Fig. 8 shows the shape evolution as the plasma was elongated from 2.5 to 6.5 s. It is worth noting that none of the plasmas controlled using the new Z control system exhibited loss of fast vertical control for the high li and high loop voltage discharges used during the commissioning of the new system.
If the loop voltage difference were not delayed it would lead the Z signal by 90° or 5 ms, it does not. The inference is that passive plates delay the sensor response by about 5 ms (the initial Z estimate may have its own smaller delay) and that sensors shielded from the plasma by the passive plates are not useful for fast control [10]. Three pairs were considered, FL21-FL25, FL19-FL27 and FL17-FL29. As can be seen in Fig. 1 all 3 pairs satisfy the separation requirement. Routine test shots show that the pair FL21-FL25 has the least pickup from unbalanced SC coils; this is not unexpected since they are furthest from theSC coils. As can be seen in Fig. 5 the pair FL21-FL25 has the fastest response to plasma oscillations by about 1 to 4 ms. Therefore, the pair FL21-FL25 was chosen as the best sensors for the new control system. Inclusion of the other loops would add unwanted latency. It is important to note that the new Z estimator derived from the loops without correction for possibly unbalanced SC coils will be different than the actual plasma vertical position depending upon the SC coil currents. However, for control of fast transients with the IVC coil, it is not necessary to know the vertical position absolutely, but only the deviation from its recent mean. Correction for the SC coil currents would introduce unwanted noise in the system and should be avoided. In order to deal with this, a control algorithm called ZFAST was written for feedback control of the IVC coil [4]. This simply applies a 1 Hz high pass filter to the proportional error signal for Z in the PCS. That has proven to be effective to eliminate the slow drift in the measured Z from SC coils and provides a feedback request that depends only on faster plasma motion. A further Modification to the PCS algorithm allowed for the inclusion of the loop voltage difference as the derivative term dIpZ/dt in the IVC control loop as shown in Fig. 6.
4. Future work It remains to use the new system for vertical control in plasmas with larger vertical instability growth rates so as to determine the ultimate limit of vertical control with the new system. In particular control of plasmas with the new system during high neutral beam power and with large ELMS has yet to be tested. Further development will be required for control of KSTAR plasmas during the ramp-up phase at low Ip before the plasma is under isoflux control and the ZFAST algorithm can be used. A new algorithm will be required to add a high-pass filter to the IVC control in the ramp-up phase that is used before rtEFIT convergence. Before rtEFIT converges, plasma control use of isoflux control is not possible. The latter will require validating the new Z estimator during the ramp-up.
3. Results The control achieved using the new Z estimator and the ZFAST algorithm is compared to that achieved using the initial Z estimator in Fig. 7. It is clear that the new algorithm using ZFAST and the new Z estimator is successful to keep the IVC coil current near zero, that the amplitude of the oscillations in the IVC coil current are smaller and most importantly that it is able to maintain vertical control during an attempt to ramp Ip to higher current, something the initial system was unable to accomplish. This inability may be the result of a delay in the x-point control and to the offset in the IVC coil current when using the initial system. The setup used for the new control included a dZ/dt from
Acknowledgments This work was supported by U.S.D.O.E. Contract No. DE-AC0209CH11466 and by the Korean Ministry of Science and ICT under the KSTAR Project contract. The authors would also like to express our appreciation to Hyeon Park, Si-woo Yoon, Yeong-Kook Oh, Raffi Nazikian and Richard Hawryluk for their support for and 12
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Fig. 6. Block diagram of the ZFAST algorithm. The difference of the Voltage signals from the two flux loops FL21 and FL21 is taken and split into two paths, the top path in the figure indicates the integrated (flux) difference signal used in the control loop. The High-pass filter is applied to the error term in the PCS PD and the P term in the overall control loop always comes from this top path. The bottom path indicates the unintegrated analog loop voltage difference which is the time derivative of the flux signal without the integration and subsequent differentiation taken in the top path. The derivative term in the overall feedback loop can be accomplished by using non-zero D gain in the normal PD (top) path, by using non-zero gain in the analog dz/dt path (bottom) or by using non-zero gains in both paths. While the performance is similar using each of these choices, use of non-zero gain in only the analog dz/dt path resulted in the lowest noise in the control loop and is preferred.
Fig. 7. The vertical control achieved with the new system using ZFAST, the new Z estimator and the analog difference of loop voltages, shown in red is clearly superior to that achieved with the initial Z estimator and the usual PD controller in the PCS (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article). 13
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Fig. 8. Experiment with highest achieved elongation (κ): #18,380 used BT = 2.4 T, Ip = 500 kA with total beam power 4.8 MW (beam energy at 100/70/95 keV) and 0.8 MW of 140 GHz ECH. The increase of elongation starts at 3.0 and last until the end of shot, in order to check the proximity. The highest value, κ = 2.16, is obtained at t˜6 s, until one of the PF coils got saturated to the operation limit (15 kA/turn per coil) and loss of shape control occurs after t = 7.6 s. In the right, the shape evolutions at t = 2.5/4.5/6.5 s are shown. All the equilibrium values/shapes are taken from the real-time EFIT (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article).
encouragement of this work over the years. The data reside on the ikstar, kstarpcs and ksim2 computers of the KSTAR project at the Korean National Fusion Research Institute.
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