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Measuring and extending vertical stabilization controllability of KSTAR Sang-hee Hahn1, D. A. Humphreys2, D. Mueller3, J.G. Bak1, N. W. Eidietis2, Y. M. Jeon1, A. Hyatt2, J.H. Kim1, M. J. Lanctot2, M. L. Walker2 1National Fusion Research Institute, Daejeon 34133, Korea 2 General Atomics, San Diego, CA, USA 3 Princeton Plasma Physics Laboratory, Princeton, NJ, USA E-mail contact of main author: hahn76 @nfri.re.kr Abstract. The first part of the paper mainly summarizes a series of multi-year experimental activities performed at KSTAR, particularly the “release-and-catch” experiments to measure the principal metrics for vertical stability as a part of the ITPA MHD stability TG from 2012 to 2015. The dynamics of the vertical movement is analyzed by magnetic reconstructions, validations against the non-magnetic diagnostics, and an axisymmetric plasma response model. The second part describes relevant experimental approaches for extending controllability of the vertical stability feedback controls. The present scheme is briefly described first, and results of a new control approach are demonstrated, which uses decoupling in the frequency domain in order to reduce competition between the “fast” feedback for vertical displacement of the plasma center and the “slow” feedback for the boundary control.

1. Introduction

Since the year 2010, KSTAR has established vertical stabilization for elongated plasmas using the Copper in-vessel coils (IVC) [1,2] with the passive plate structures [3] which reduces the natural growth rate of plasma vertical displacement event (VDE) for vertically elongated plasmas. The passive plate structures were originally designed as an up/down saddle-type loop [4], but the final installations in 2010 removed the vertical current bridges in order to reduce the uncertainty on the amount of eddy current distribution.

The vertical position control hardware was therefore redesigned in 2010 for the worst-case scenarios up to plasma current Ip ~ 2 MA double null, κ~2.0, βp~0.1 and internal inductance li~1.2. The design worked in the most cases of the experiments requiring diverted plasmas. In order to expand the operational space of KSTAR, however, it has been necessary to characterize the stability metric for detailed analysis of the controllability of the system.

The paper summarizes a series of multi-year experimental activities done as a part of activities suggested by the ITPA MHD stability TG [5] from year 2012 to year 2015, regarding year-by-year quantitative assessment of the vertical stabilization (VS) controllability and relevant experimental approaches for extending controllability of the VS feedback in the KSTAR device.

2. Dynamics of VDE

2.1. Measurement of stability metric

According to the known literature[6,7], two important metrics are found to be useful for assessing the level of performances: one is the stability margin, which is approximately the ratio of the unstable growth time to the wall penetration time, ms ≡ γz/γw. The other is known as the maximum controllable vertical displacement, ΔZMAX, which can be measured experimentally and can in addition quantify the nonlinear constraints imposed by the actuator (in this case, the IVC power supply). The ΔZMAX strongly depends on the open-loop vertical

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growth rate(γz) of the vertical displacement event, and the actuator limits, such as maximum allowable PS current/voltages (ΔImax, Vsat), the self-inductance of the coils (Lc), and the effective delay time of the power supply and signal conditioning circuits (TPS). The dependence of Ip is indirectly included to ΔZMAX as a term of vertical field at the center(Bz0).

As the first step, a series of dedicated “release-and-catch” experiments are performed at KSTAR to measure the two principal metrics for vertical stability in 2012-2015 campaigns.

The principal diagnostics for the time-dependent evolution of the vertical displacement is the magnetic reconstruction (EFIT) [8,9], both offline and online[10]. Not every VDE can be reconstructed, but it gives a reasonable estimate when the thermal quench was not the main cause of the disruption. In the case of VDE by control loss, as shown in Figure 1, the vertical displacement by the post-shot reconstruction result is compared with the maximum intensity movement obtained from the 16-channels of soft X-ray array(SXR). The direct comparison of the estimated current center (denoted as rtEFIT:Zcur) showed a good match with the

estimated center movement from the SXR. It is noted that the estimates from the control target (lmsz) or from the magnetic axis (zmaxis) generally are different from the current center.

As shown in Figure 2, both the ms and the ΔZMAX are experimentally measured by disabling coil feedback for an amount of time (10~20 ms) in a stable KSTAR plasma discharge. A dedicated control setup, called as “VDE current freeze”, was installed to the KSTAR plasma control system so that we invoke the algorithm whenever we want during the discharge. When the algorithm is triggered, it tries to maintain present level of control coil current, disregarding all the preprogrammed shape/VS controls. After that,

Figure 1. Verification of VDE movement. (a) At the shot #8181, movements of the plasma reconstructed at 10.42s ~ 10.46s, 10ms interval. (b) The Line of sight map for the soft X-ray (SXR) array. (c) Movement of the current center of plasma (denoted as rtEFIT:Zcur, red line with cross symbol) is compared with the maximum intensity of the SXR array measurement.

Figure 2. ΔZMAX measurement in the shot 12805. When the shape feedbacks were off by up to 16ms, the system was able to catch the plasma again, but 20ms-off lost the plasma.

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the PCS gets the feedback gains back and tries to catch the plasma from the VDE. The typical experimental setup is to programme a few occasions of the current freeze

algorithm during the discharge with different durations of the control-off time. In the Figure 2, the current freeze algorithm turned the coil controls off by 8/16/20ms. The discharge survived when the control of vertical stability by the IVC was off until 16 ms, but 20ms off blew the discharge off. The estimate of ΔZMAX from the initial position can be obtained by measuring maximum vertical displacement that the control system was not able to catch the plasma again. In the Figure 2, the measured ΔZMAX in 2015 was 2.47 ± 0.94 cm. The experiment used discharges with elongation=1.7~1.9, depending on the discharges available in each campaign, and a range of (βp, li) which can be obtained by adding/removing the neutral beam power. It was found that the change of the gain at the VS controller PID loop did not change the growth rate (γz).

., Table 1. Measurements of open-loop vertical growth rate γZ for selected shots in 2012-2015. All plasma parameters are taken from the real-time EFIT. The toroidal 1-turn resistance of passive stabilizer is denoted as Rpp. year Rpp

[mOhm] γZ [rad/s]

βp li elongation Ip

2015 2.4 198 0.2 1.2 1.9 500 2015 2.4 111 1.33 0.96 1.73 600 2014 7.1 140.2 1.6 0.95 1.9 600 2013 7.1 91.32 1.3 0.93 1.9 600 2012 2.1 68.2 1.2 0.8 1.9 600

2.2. Effect of passive conductor structure

These particular experiments were proven to be extremely useful to track down changes of the vacuum conductor structure installations, in particular, the outboard passive stabilizer structure. The passive stabilizer mainly regulates the open-loop vertical growth by 4 sets of

the toroidal gap resistors installed between the quadrants. By performing the experiments and measuring the γz, incidental changes to the electric property of the gap resistors, which accompanied mechanical fortifications, were validated and adjusted.

The annual scan of ΔZMAX revealed that the VDE growth varies whenever the vessel conducting structure electronically changes. For example, the 2015 estimate ΔZMAX=2.47 ± 0.94 cm, with γZ=111 rad/s, which apparently is an increase than the similar discharge in 2013, ΔZMAX=1.8 ± 0.8 cm, with γZ=91 rad/s. Table I shows obtained

Figure 3. Annual changes of the passive plate structures occurred in years 2013-2015.

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sets of parameters and corresponding measurements of γZ in the annual base. It was discovered that the growth rate of the year 2013-2014 increases for the same shape and same βp, which is consistent with the the mechanical change on the toroidally connected conductors surrounding the plasmas: the vacuum vessel, limiters, divertors and first wall structures. Especially, the mechanical modifications on passive stabilizer (PS) configuration in 2013-2014 modified the amount and profile of the toroidal eddy currents in the in-vessel conducting structure.

It has been turned out that in 2013, the value of the toroidal 1-turn gap resistor per upper/lower passive plate has been modified to one 3 times bigger than the one in year 2012. This occurred when the gap resistor (Rpp), which regulates the amount the toroidal eddy current when the plasma moves, is replaced to a new mechanical design [switch a rod type to a plate type]. The change on the Rpp increased the growth rate approximately by 30%. Comparison with an axisymmetric plasma response model, which can directly simulate the experimental settings/results in the appropriate time scale (~1 ms) [11], also confirmed the increase of the gap resistance.

From 2014 June, as shown in Figure 3, each up/down toroidal PS plate is fastened by additional 12 vertical supporters so that the additional movement by mechanical vibrations is minimized, which is caused by collision of the plasma current column at VDE. The insulation plates between the PS and the supporter are removed so that additional toroidal current path through the new supporters can be made between the PS and the inner Vacuum vessel. In consequence, all the mechanical bridges between the upper/lower passive plates are removed, but the gap resistance value remained the same until the end of year 2014. As shown in Figure 4, the removal of the mechanical bridges did not resolve the disruption/VDE force issues, since the VDE growth rate rather increased unless the gap resistance changes.

Modifications on electrical topology of passive plate structures will surely modify the open-loop growth rate of the non-circular plasma, and hence will affect the performance of the vertical stabilization. The problem here is that it becomes very difficult to exactly estimate total toroidal eddy current on the passive stabilizer due to additional current paths through the additional supporters. Uncertainty on the effective 1-turn toroidal resistance at the passive plates, depending on the installation method and the mechanical design, has been always an issue. In the year 2015, the 1-turn gap resistance value returned to the value of year 2010-2012.

After returning to the smaller gap resistance in 2015, the release-and-catch experiment was conducted for the worst-case scenario (βp~0.1, li~1.2, elongation ~1.9 at #14319, using the best ITER-similar shape ohmic setup), and the VDE growth rate measured for this shot is 198 rad/s which is consistent with the worst-case calculation at the design. The result indirectly indicates that the surrounding conducting structure now becomes comparable to that of year 2012.

Figure 4. Comparison of vertical displacement increase for different passive plate structure configurations tried in years 2012-2014. The slope of each line is the growth rate γZ.

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3. Extending the vertical controllability

3.1. Limitation of the present VS feedback

In order to extend the operational range of the available shape, especially for the available elongation κ, there have been many attempts to improve the vertical stability controls.

The present control scheme for the VS is based on a ~20kHz SISO feedback using a position estimator which consists of 2 inboard normal field probes, with are located ~6 cm away from each other, behind the inboard limiter. The actuator, the in-vessel control coil (IVC) with max 1000V, 6000A*6 turns switching power supply, is anti-series connected to a Cu load. Since the vertical stabilization is the fastest feedback loop, the 4 kHz isoflux control [10] responsible for the shape feedback does not directly control the current center, hence does not include the IVC as actuator. The location of the PF and IVC coils is shown in Figure 5. Since the estimate of the vertical position at could be different from the other, the two controllers tend to fight one another, since the isoflux/DNULL algorithm basically does not care about the Z location by definition. This became more serious when the 1-turn gap resistor value increased in years 2013-2014. Typical signature of fighting algorithms was seen as very-low frequency oscillations on Z [around several Hz at the Z position]. Even the optimal setup was found, but changes in the isoflux setup design may cause the problem again, which may result in limitations on the controllable vertical ranges. For example, for 2012-2014 runs, the maximum “drSep” (defined as the distance between the flux of the upper separatrix and the lower one at the double null shape) practically allowed was +- 2 cm unless we adjusted the Z location target at the VS algorithm target. For +4 cm of drSep, we had to adjust the Zp target as +2 cm also. The problem here is that no one (even the operator who made it work) knows why we need to set it as +2 cm, not 4 cm. This discrepancy between the VS algorithm and the isoflux seems to be the cause of high DC offset at the IVC coil current, which reduces the IVC coil current margin available and hence the ΔZMAX. There are also issues of the coils aligned at the same line of influence in geometry: If we draw a line between the plasma center and the PF6U/L circuits, the IVC coil is on the way, hence the magnetic field by the IVC is constantly interfered by a large load PF6. Moreover, the IVC coil circuit is too fast compared to the speed of the PF6U/L circuits. During the applications of the dZ/dt signals into the VS algorithm done in 2014[12], it was pointed out that we need to let the isoflux control the slowest part of vertical position in order to reduce the DC current at IVC, but the responsible coils (PF6 for example) are too slow to get along with the Z offset signals produced in the present Zp feedback. The interference of the PF & IVC produced unpredictable DC offset on the IVC coil current, resulted in the higher value of the proportional gain that is to be required. In order to find solutions to reduce dependency on the absolute value of the Zp estimator, two ways are suggested historically: One is to use another estimator signal that measures the speed of Z (=dZ/dt), not the absolute position of Z. The method has been demonstrated to be feasible in 2013-2014, as described in [12]. The other way is at first suggested in 2014, which makes separation of related feedback loops in the frequency domain, moving the slow part ( < 2 Hz) to the isoflux and let the IVC care only the fast movement.

3.2. Decoupling of control in the frequency domain

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The separation of control in the frequency domain has been demonstrated in 2015 for the first time as a prerequisite of the ITER similar shape (ISS) development research. The idea is to create a “fast Z” signal by extracting high-frequency responses from the original Zp estimator (or any other proxies we can represent the disturbance of the current center). A realtime software highpass filter was introduced for the calculation of the signals. The corner frequency of the highpass is determined by analyzing the frequency responses of each main actuator circuit, shown in Figure 6(a).

Since the PF6 shows a very slow response (1.5 Hz corner), the corner frequency of the HP filter was selected as 2Hz, later changed to 1Hz for the ISS development. In the scheme feedback of the slow part, i.e. the center movement less than 1Hz, is essential. Since the isoflux does not calculate the center of the current profile in the realtime manner, a “slow Z proxy” was defined as a difference of two up/down segment errors to represent the corresponding movement of the center. Figure 6(b) shows an example of the definition of the slow Z proxy for a lower single null (LSN) discharge. In the reality, the proxy was determined by a few trial and error and was tested by a simulation that gets the equilibrium information of an old shot for the construction of the response model [11].

Figure 6. (a) Frequency responses of the vertical position controllers. The unfiltered response for the IVC+fast Z (green) is altered by 2Hz highpass Z filters (blue) so that the “slow Z” proxy control by the PF6U&L can only respond to the slow movement relevant to the shape control. (b) The location of the control segments, denoted by thick red bars, for calculating the slow Z proxy.

Figure 7. Application of the Relay Feedback algorithm to VS. An automated IVC control coil current request (left bottom) generates a stable oscillation at the control target “lmezfast” (left top). By measuring 2A, Pu for known 2h, the ultimate gain can be determined: Application of the ultimate gain, the ~37 Hz oscillation present in the original PID disappears from the spectrum.

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Once the decoupling technique was applied, it is now possible to tune the vertical stabilization loop as an independent PID. If the PID is not yet optimized, the unoptimized responses often make a 20-40Hz oscillation on the vertical position, depending on the VDE growth rate. In order to optimize the gains within the minimal try, the application of the relay feedback technique [11,13] to the IVC and the fast Z signal was attempted and got positive result: As shown in Figure 7, it was proven that the application of the ultimate gain immediately removed the ~37Hz oscillation in the FFT spectrum of the fast Z signal.

Figure 8 shows a dedicated demonstration of the algorithm for a set of highly elongated shots: #12481 is a reference using the present Z feedback and the isoflux scheme that was very common through the 2015 campaign. Increasing the bottom Zx target, hence increasing the elongation, the discharge becomes oscillatory when it reaches to -92 cm, corresponding to the elongation=1.8. Without frequency decoupling, oscillations get bigger and bigger to disrupt finally in the shot 12481. The #12493 uses a decoupled Z estimator (recorded as LMSZFAST) by applying a software highpass filter with corners 2 Hz in the VS algorithm, and switched the feedback measurement from the old-school (LMSZ) to the decoupled Z (LMSZFAST) at 3.0-3.2s.

As shown in Figure 8, the slower motion, a sub-Hz Z position drift, was defined at the Isoflux algorithm in a form of subtraction from SEG05 to SEG11, that is by definition a difference between the upper/lower reference flux errors. The application of frequency separation immediately removed the IVC current offset by ~2kA/turn, and the Zx oscillation is not triggered even at a high-elongation target Zx = -96cm, which made the discharge last

until the Ip rampdown occurred at 5.7s. During the ISS control development, the decoupling algorithm was tested to be able to create a discharge that the current center positioned up to -10 cm from the machine geometry center.

4. Summary

Through a series of

experimental measurements on the VS controllability in 2012-2015, it was found that the maximum controllable vertical displacement ΔZMAX is 2.47 ± 0.94 cm for the plasmas with elongation=1.75, γZ ~ 110 rad/s. Since this is a small value for ~180 cm height plasmas, it is important to maximize the available control coil current margin, which is often reduced when an up/down asymmetric shape target is attempted. In

Figure 8. Experimental demonstration of feasibility on the control separation in the frequency domain: Without any frequency decoupling, the bottom Zx starts oscillating as it reaches to -92 cm (#12481, black). In the shot #12493 (red), after applying the frequency separation using high-pass filtered Z estimator (Zfast) at t=3.0-3.2s, the IVC DC current offset disappears and the bottom Zx went to -96 cm (kappa~1.88) earlier, without any significant oscillations.

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2013-2014 campaigns, introduction of a dedicated speed estimator enabled to reduce the PD gains with same controllability. A new approach using decoupling in the frequency domain was introduced in 2015, in order to aim a reduction of fast/slow control competitions. The application of the decoupling, combined with a relay-feedback tuning technique, demonstrated extension of the available vertical position up to -10 cm without manual compensations of the Z target and the shape target.

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