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RWM Control in ITER
Presented by Gerald A. Navratil
Including analysis byJim Bialek &
Oksana Katsuro-Hopkins
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OUTLINE• PASSIVE STABILIZATION OF RWM IN ITER
+ ITER PASSIVE STABILIZER PERFORMANCE: IMPORTANT ROLEOF THE BLANKET MODULES
• ACTIVE CONTROL OF RWM WITH BASELINEERROR CORRECTION COILS+ BENCHMARKING OF MARS, VALEN/DCON, AND KINX
• IMPROVED COIL DESIGN OPTIONS & ADVANCEDCONTROL ALGORITHMS+ EXTERNAL ON-VESSEL COILS
+ INTERNAL COILS
+ OPTIMAL CONTROLLER AND OBSERVER
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Passive Stabilizing Structures in ITER
• Double Wall Vacuum Vesselwith ~190 ms time constantfor each wall for 1/1 fieldpattern.
• Blanket/Shield ModulesSpecified to have 5 ms to9 ms time constant fornormal B-field soak through
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ITER Blanket/Shield Plays Important MHD Role• Blanket/Shield Modules Specified
to have 5 to 9 ms time constant• Ulrickson finds longer time
constants: 40 ms to 100 msShould be ITER Issue to Clarify
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ITER Technical Basis G A0 FDR 1 00-07-13 R1.0
Plant Description Document Chapter 4 Page 12
Table 4.3.3-1 ITER Parameters for the Non-Inductive Scenario
Parameter WNS Parameter WNS Parameter WNS
R/a (m/m) 6.35/1.85 bN 2.95 fHe (%) 4.1
BT (T) 5.18 bp 1.49 fBe (%) 2
Ip (MA) 9.0 Pfus (MW) 356 fAr (%) 0.26k95/d95 1.85/0.4 PL-H + PNB (MW) 29 + 30 Zeff 2.07
<ne> (1019m-3) 6.7 Q 6.0 P rad (MW) 37.6n/nG 0.82 Wth (MJ) 287 P loss (MW) 92.5
<Ti > (keV) 12.5 Ploss/P thr. L-H 2.59 tE (s) 3.1
<Te> (KeV) 12.3 bT % 2.77 ta*/tE 5.0
ICD/Ip (%) 51.9 li (3) 0.72 HH98 (y2) 1.57
Ibs/ Ip (%) 48.1 q95/qo/qmin 5.3/3.5/2.2IOH/Ip (%) 0
Figure 4.3.3-1 Plasma Parameter Profiles at the Current Flat-top Phase(t > 1000 s) for the Steady State WNS Operational Scenario
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ITPA Benchmark Study Shows GoodAgreement Among Codes
• RWM Dispersion Relationfor 2D axisymmetric ITERVacuum Vessel withoutports or Blanket/Modules
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ITER Ports Cause Small Reduction in Ideal Limit
5.04.03.02.02.010 - 1
10 0
10 1
10 2
10 3
10 4
10 5
10 6
beta-n(new)
grow
th r
ate
[1/s
]
no blankets & no ports
no blankets45 ports
• No wall bN limit is 2.4; Ideal Wall Limit Drops to bN ~ 3.3
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VALEN Model of ITER Double Wall Vessel and Blanket Modules
XY
Z
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ITER Blanket Opens Up Large AT Regime
• No wall βN limit is 2.4; Ideal Wall Limit With Blanket is ~ 5
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Active Control in ITER:
Baseline External Error Correction Coils
ITPA MARS/VALEN Benchmarking
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ColumbiaUniversity
ITERPASSIVE STABILIZER AND ACTIVE CONTROL COILS
Inner Vacuum Vessel Wall (6 cm-thick stainless steel)
Outer VV Wall
The ITER vessel is modeled as two walls.
. Three sets of six saddle coils, outside the vessel, but the upper and lower coils couple weakly to the RWM. .
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VALEN Model of ITER Vessel and Control Coils:Base Case Feedback Control System
• Vacuum Vessel Modeled with and without wall penetrations.
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10-1
100
101
102
103
2.5 3 3.5
tarragona.2005
passive growth rate (bench)g Gp/Gd=e8/e8g+ Gp/Gd=e8/e8g Gp/Gd=e9/e9g+ Gp/gd=e9/e9
grow
th ra
te [
1/s]
βn
tarragona.2005
idea
l wal
l lim
it
passive
Gp [v/w] = 108
Gd [v/v] = 108
Gp [v/w] = 109
Gd [v/v] = 109
3.18
100
101
102
108 109 1010
tarragona.2005
g Gd scan Gp=e+9 s=0.1
grow
th ra
te [
1/s]
Gd [v/v] scan @ fixed βn = 3.22 & Gp [v/w] = 109
tarragona.2005
ITER Baseline Six External Coils with 10 s time ConstantsInvestigate combined Gp [v/w] & Gd [v/v] gain
Vcc = Gp x(sensor flux ) + Gd x( sensor voltage)
Stabilized to βn = 3.18When both Gp & Gd used
Could not reachβn = 3.22 with different Gd
Selectedgains
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6/12
RWM stabilization with PD controller: Results obtained in 2005
All codes have shown that proportional control algorithm for the current in feedback coils can stabilize RWM up to Cβ = 0.6-0.7. However effect of the feedback derivative gain (k2) on RWM stabilization was different. It is significant in MARS-F and KINX and very minor in VALEN. A proper choice of k1 and k2 in MARS-F and KINX allows stabilization of RWMs with Cβ ≈ 0.85. To clarify the reason of differences, comparison of the RWM response to the coil current was proposed (Y.Liu).
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Benchmarking model used in this analysis . below we show a cut away view of axisymmetric vacuum vessel (2 walls ) and VALEN approximation of continuous RWM coil
60 picture frame coilswith no overlap. Thetotal gap between allCoils = 1 toroidal degree
Each coil has adifferent current,this results in a n=1 distributionof current
No blanketModules
Coil top+3.9 m
Coil bottom-3.0 m
Br & Bz sensors atr,z = 8.85,0.45 m
This models theIdealized n=1 RWM coil
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7/12
RWM response to coil current (transfer function)
The RWM response to the coil current can be expressed via transfer function:
)()()(
0 sjbsbsP ϑ=
, bϑ(s), j(s) – Laplace transformations of the amplitudes of poloidal magnetic field, Bϑ(t), and current in 2D coils, J0(t). b0 - amplitude of radial component of magnetic field produced by unit DC current of the sinusoidal coil mode on the magnetic sensors.
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-0.6
-0.4
-0.2
0
0.2
0.4
0.6
-0.2 0 0.2 0.4 0.6 0.8 1 1.2ITERpolar.wrtI.01.2006
IM+IM-Im 3,3,48DB
Im [
P(jω
)]
Re[ P(jω)]
MARS(previous talk)
VALEN
withoutplasma
VALEN3 pole fit
VALEN / MARS quantitative comparison of ‘Msf ‘
MARSbr = 3.63e-8 [T/A] gaussian distributionbr = 8.02e-8 [T/A] cylindrical approximation
VALENbr = 9.369e-8 [T/A]
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Nyquist plots are consistent with previous VALENclosed loop (feedback) calculations. Nyquist diagramspredict stability up to Cβ > 58%. All Nyquist plots areup/down symmetric ( as expected from model ).
Cβ = 23.6%
Cβ = 46%
All curves shown have asingle counter clockwiseclosed path as jω is mappedfrom -infinity to +infinity.
Simple scaling by a positiveconstant (Kp) will make allthese curves enclose thepoint ( -1,0 ).
More scaling (gain) is neededfor higher Cβ
Curves shown are VALENtransfer functions, notcurve fits
Cβ = 58%
-1
-0.5
0
0.5
1
-1.5 -1 -0.5 0 0.5ITER.nyquist.02.2006
all 23% Imall 46% Imall 58% Im
Im P
(jω)
Re P(jω)
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VALEN Nyquist analysis as a function of Cβ isvery similar to published MARS results.
[Nucl. Fusion 44 (2004) 232-242 by Liu, Bondeson, Gribov & Polevoi]
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-0.3
-0.2
-0.1
0
0.1
0.2
0.3
-0.6 -0.5 -0.4 -0.3 -0.2 -0.1 0ITER.nyquist.02.2006
58% + Im58% - Im72% + Im72% - Im89.48% + Im89.48% - Im
Im P
(jω)
Re P(jω)
Nyquist plots derived fromVALEN are consistent withprevious VALEN closed loopfeedback calculations and MARSNyquist analysis at lower Cβ.
The direction of the curves haschanged at Cβ = 72%, where weobserve two clockwise rotations(unstable) as we map the line jω -not seen in MARS analysismaybe 3D eddy effect.
‘Simple’ feedback nolonger works!
Cβ = 58%
Cβ = 72%
Cβ = 89%
VALEN Shows More Complex Unstable Transfer Function at High Cβ
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Nyquist plots derived fromVALEN are consistent withprevious VALEN closed loopfeedback calculations and MARSNyquist analysis at lower Cβ.
The direction of the curves haschanged at Cβ = 72%, where weobserve two clockwise rotations(unstable) as we map the line jω -not seen in MARS analysismaybe 3D eddy effect.
Lead/Lag Compensation infeedback does not work!
VALEN Shows More Complex Unstable Transfer Function at High Cβ
[Y. Liu, 22 March 2006 Report]
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Improved Active Control in ITER:
Improved Coil Geometry
Improved Control Algorithms Beyond PID
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Proposed Alternative ITER RWM Control Coil Set:Nine Coils Located on Outer VV Wall
• Compare Performance with ITER Baseline Designboth with and without Blanket/Shield Modules
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VALEN Model of Alternative Control Coils With Gp
Performance Comparable to Baseline ITER Coil Set where
Best Stabilized βn with Proportional Gain ~ 3.18
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Internal vs External RWM Coils on ITER
• The study analyses the effect of a single turn coil in the 10 cm gap between theblanket shield module (BSM) and the port extension of a mid-plane port plug.
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RWM Coil Concept for ITER
• Baseline RWM coils located outside TF coils
Applying Internal RWM Feedback Coils to the Port Plugs in ITER Increases β−limit for n = 1 from βN = 2.5 to ~ 4
VALEN Analysis with Blanket Module
No-wall limit
• 7 RWM Coils mounted behind Port Plug Blanket Module with simple proportional gain Gp feedback control loop• Ulrickson “split” Blanket/Shield analysis Suggests βn > 4 possible
• Internal RWM coils would be located insidethe vacuum vessel behind shield modulebut inside the vacuum vessel on theremovable port plugs.
10-1
100
101
102
103
104
2.5 3 3.5 4 4.5 5 5.5
tarragona.2005
passive g ABMintc g #5 ABM e+7intc g #5 ABM e+8intc g+ #5 ABm e+8intc g #5 ABM e+9intc g+ #5 ABM e+9
grow
th ra
te [
1/s]
βn
tarragona.2005
best resultsβ
n = 3.94
Cβ = 53% ( 2.52 / 5.21 )
idea
l wal
l lim
it
Gp=107
Gp=108
Gp=109
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Proposed Approach to Combined RWM/ELM Control Coil• ITER Engineering VERY OPPOSED to any in-vessel coils behind the
blanket and shield modules.• Explore RWM and ELM Control performance of a hybrid internal port
plug set combined with an on-vessel (but external) set similar toDIII-D I-Coil set.
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Next Step: Go Beyond PID and Lead-Lag Compensation
• At 2005 ITPA MHD Group Meeting in Tarragona Joe Listeradvocated use of modern ‘state-space’ feedback controlmethods to better understand and optimize our modeling ofITER RWM active stabilization.
• Formulation of RWM Control Model in ‘State Space’ form isentry point to modern control theory that offers:+ Improved performance control loop using pure proportional gain+ Reduced noise using Optimal Observer and Kalman Filter+ Reduced dimension model for real-time application.
• This approach has been used in fusion modeling of n=0 stability, e.g.:D. J. N. Limebeer and J. P. Wainwright, IEEE Symposium on Industrial Electronics, p21-27 (1998).Al-Husari, Hendel, Jaimouka, Kasenally, Limebeer, Portone, 30th Conf. On Decision andControl, p 1165-1170 (1991)
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State Variables: A Dynamical Systems Approach
•Basic “state variable” or phase space representation using 1st order ODEs ratherthan transfer functions to describe system
€
r ˙ x =t A ⋅ r x unforced system dynamics (open loop γ)
€
r y =t C ⋅ r x output equations (what you what controlled)
•Can be nonlinear,
€
r ˙ x = f r x ( ), also
•Add feedback input control vector
€
r u (but do not close the loop yet)
€
r ˙ x =t A ⋅ r x +
t B ⋅ r u
€
t B gives coupling of
€
r u to system states
€
r y =t C ⋅ r x +
t D ⋅ r u
€
t D represents direct coupling of control
€
r u
What can we say about the open loop system dynamics without specifying afeedback law?
Controllability and Observability (solvability conditions)
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VALEN Circuit Equations Have A Built-in State Space
After including plasma stability effects the fluxes at the wall, plasma, andfeedback coils are given by (J. Bialek, et al., PoP 2001)
€
r Φ w =
t L ww ⋅
r I w +
t L wf ⋅
r I f +
t L wp ⋅ Id
€
r Φ f =
t L fw ⋅
r I w +
t L ff ⋅
r I f +
t L fp ⋅ Id
€
Φ =t
L pp ⋅ Id +t
L pw ⋅r I w +
t L pf ⋅
r I f
Using Faraday and Ohms law yields equations for system evolution
€
t L ww
t L wf
t L pwt
L fwt
L fft
L fpt L pw
t L pf
t L pp
⋅
ddt
r I wr I fId
=
t R w
t 0
r 0
t 0
t R f
r 0
r 0
r 0 Rd
r I wr I fId
+
r 0 r
V fr 0
This can easily be put in state space form…
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VALEN Mesh Current State Feedback
•The VALEN code, interestingly enough, has a “natural” intrinsic set of state variables. Theyare the circuit mesh currents used in the finite element model of the plasma,conductingwall, and feedback coil structures.
VALEN equations can be naturally written as,
€
r ˙ x =t A ⋅ r x +
t B ⋅ r u =
t A +
t B ⋅
t K ( ) ⋅ r x
The state vector of the system is given by:
€
r x =r I w ,
r I f , Id{ }
The control vector is the feedback coil voltages:
€
r u =r 0 ,
r V f ,0{ }
And with,
€
t A =
t L −1 ⋅
t R and
€
t B =
t L −1
Sensor flux as output
€
r y =r Φ s
with
€
r V f =
t G p
Φ ⋅r Φ s ≡
t K ⋅ r x and
€
r V f =
t G p
Φ ⋅t
L sw
t L sf
t L sp[ ]
r I wr I fId
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Apply DIII-D Noise Spectrum to ITER Baseline
Broadband white noise with amplitude of 10 Gauss[about 7 times level in DIII-D – ratio of IITER/IDIII-D]
No ELMs in applied noise spectrum
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Large Gd Leads to Very High Voltage Applied to Coils
Voltage Levels Reach ~ 1 MV: Need to Reduce
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Improved Stabilization of ITER RWM with NewOptimal Controller and Observer
• Optimal controller and observer were designed based on reduced to 20 modes ITERVALEN model for Cβ = 85%. In the presence of 10 Gauss sensor noise RWM wasstabilzed up to Cβ = 86%, as compared to Cβ = 68% reached by classical controller withderivative and proportional gains.• No derivative Gain is needed with Optimal Controller.• Significantly reduction in power requirements for Optimal Controller.
1.E-01
1.E+00
1.E+01
1.E+02
1.E+03
1.E+04
1.E+05
1.E+06
2.0 2.5 3.0 3.5 4.0 4.5 5.0
βn
γ, 1
/sec
PassiveGp/Gd=e9/e9OC_50%OC_85%Ideal Wall Limit
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ITER Optimal Controller Transient AnalysisControl Coil Voltage Measured Sensor Flux
• Modest Overshoot at Cβ ~ 80%
• Substantial Noise Reduction!
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Summary & Next Steps
• Baseline ITER External Coil Set can stabilize at βn ~ 3 level requiredfor basic Scenario 4 steady-state plasmas with RWM growth ratesγ~10/sec. Optimal Controller/Observer needed to reduce powerrequirements to acceptable levels and provide margin for RWMControl
• Blanket Modules in ITER extend the RWM reduced growth ratebranch up to βn ~ 5 and create an extended AT regime with importantDEMO implications.
• Accessibility of DEMO AT relevant βn ≥ 4 requires installation ofinternal control coils to stabilize RWM growth rates γ > 100/sec.
• USBPO & ITPA exploring possible combination RMP ELM Controland RWM Control normal conductor set trading off against BaselineSuperconducting Error Correction Coil Set & HV Power Supplies.