Alternative equilibrium reconstruction code for the plasma control
Alternative equilibrium reconstruction code for the plasma control of FTU G. Artaserse 1 R. Albanese 2, L. Boncagni 1, D. Carnevale 3 1 Associazione Euratom-ENEA sulla Fusione, Via Enrico Fermi 45, I-00044 Frascati (RM), Italy 2 Associazione Euratom-ENEA-CREATE sulla Fusione, Via Claudio 21, I-80125 Napoli, Italy 3 Dipartimento di Informatica, Sistemi e Produzione, Università di Roma, Tor Vergata, Via del Politecnico, 00133 Roma, Italy Contribution to the EPS 2013/02/08 WIP, Frascati G Artaserse 1
Outline q Aims q XCTools description q XSCTools main assumptions q Input treatment q Benchmark cases q Breakdown/Plasmaless q Plasma run q Open loop simulations q Conclusions q Future work 2013/02/08 WIP, Frascati G Artaserse 2
Aims : - to give to the FTU session leader a tool to easily design desired magnetic configurations with a user friendly interface - to help to identify in a reliable way the location of field null formation during the plasma current breakdown phase - to detect probes faulty, misalignment of probe orientation in the poloidal plane or wrong calibration factors - to have a linearized model of the equilibrium to simulate the plasma quantities of interest - to have a robust plasma control of plasma current, plasma shape and position - to design new control strategies for PF coils currents - to study the plasma-wall interaction due his coupling with EDGE 2 D tool (the equilibrium is given even in EQDSK format) - beware! @ the moment is an off-line (post-pulse) tool 2013/02/08 WIP, Frascati G Artaserse 3
![XSCTools: (e. Xtreme Shape Controller Tools) [1/4] q Set of procedures written in Mat.](http://slidetodoc.com/presentation_image_h2/7c6db0831433b417a8eb7f7ccbcba326/image-4.jpg "XSCTools: (e. Xtreme Shape Controller Tools) [1/4] q Set of procedures written in Mat.")
XSCTools: (e. Xtreme Shape Controller Tools) [1/4] q Set of procedures written in Mat. Lab with Graphical User Interface (GUI) q CREATE NL (CNL), CREATE L (CL), CREATE_EGENE (CE) q Linearized model describing the electromagnetic behaviour of plasma surrounded by conducting structures and in presence of ferromagnetic materials q valid in the neighbourhood of an equilibrium point q Used for 2 D axysimmetric modelling q Used for electromagnetic control q current, position, shape q Used with success for operation of JET and design in ITER q Designed to be FLEXIBLE and MACHINE INDEPENDANT 2013/02/08 WIP, Frascati G Artaserse 4
![XSCTools: (e. Xtreme Shape Controller Tools) [2/4] … Settings GRID 2 D EQDSK MCF](http://slidetodoc.com/presentation_image_h2/7c6db0831433b417a8eb7f7ccbcba326/image-5.jpg "XSCTools: (e. Xtreme Shape Controller Tools) [2/4] … Settings GRID 2 D EQDSK MCF")
XSCTools: (e. Xtreme Shape Controller Tools) [2/4] … Settings GRID 2 D EQDSK MCF XSCTools CREATE NL CREATE_EGENE PCF linearized form (assuming I=I 0+i, U=U 0+u, W=W 0+w, Y=Y 0+y) L* di/dt + R i = u – LE* dw/dt (L* = ∂ /∂I, LE* = ∂ /∂W) y=Ci+Fw ( C = ∂Y/∂I, F = ∂Y/∂W ) state-space form (assuming x=i, A= (L*)-1 R, B= (L*)-1 , E= (L*)-1 LE*) dx/dt = A x + B u + E dw/dt Model (space state form) y = C Linearized i+Fw ü … EXP DATA EDGE 2 D ü Used for 2 D axysimmetric modelling ü Used for electromagnetic control § current, position, shape ü Used with success for the design&operation of ITER, JET ü MACHINE INDEPENDENT ü Set of procedures written in Mat. Lab with Graphical User Interface (GUI) § CREATE NL (CNL), CREATE L (CL), CREATE_EGENE (CE) Linearized model describing the electromagnetic behaviour of plasma surrounded by conducting structures § valid in the neighbourhood of an equilibrium point Machine Configuration File (MCF): • geometric and electric data of the PF system (region accessible to the plasma, PF coil system geometry, connections and current limits, magnetic diagnostics etc. . ). Program Configuration File (PCF): • users chooses what inputs to drive the system, whether plasma is present, what passive structures to consider, what model of a circuit to use, what results he is interested in (geometrical descriptors, magnetic measurements, currents, voltages, etc. . ). 2013/02/08 WIP, Frascati G Artaserse 5
![XSCTools: (e. Xtreme Shape Controller Tools) [3/4] How modify an equilibria • linearized backward](http://slidetodoc.com/presentation_image_h2/7c6db0831433b417a8eb7f7ccbcba326/image-6.jpg "XSCTools: (e. Xtreme Shape Controller Tools) [3/4] How modify an equilibria • linearized backward")
XSCTools: (e. Xtreme Shape Controller Tools) [3/4] How modify an equilibria • linearized backward equilibrium code • change an equilibrium generated by Create-NL • change the plasma shape and current parameters generating a linearized new model corresponding to the new equilibrium in terms of currents to be applied to the reference equilibria • Keeping as constrains the flux linked to the plasma and the chosen geometrical desriptors XSCTools: CREATE EGENE (CE) 2013/02/08 WIP, Frascati G Artaserse 6
![XSCTools: (e. Xtreme Shape Controller Tools) [4/4] Ø Due the machine independant philosophy the](http://slidetodoc.com/presentation_image_h2/7c6db0831433b417a8eb7f7ccbcba326/image-7.jpg "XSCTools: (e. Xtreme Shape Controller Tools) [4/4] Ø Due the machine independant philosophy the")
XSCTools: (e. Xtreme Shape Controller Tools) [4/4] Ø Due the machine independant philosophy the XSCTools have been ported to the following machines: Existing ones: JET, FTU, RFX, AUG, MAST, EAST(on-going). Designed: ITER, IGNITOR, DEMO, MAST U (ongoing). Satellite tokamak: FAST. Ø Provide reliable linearized model for the plasma control for each of the below tokamaks FAST FTU JET ITER IGNITOR MAST AUG RFX 2013/02/08 WIP, Frascati G Artaserse 7
![XSCTools main assumptions : Mesh [1/7] For the FEM (Finite Element Method) it has](http://slidetodoc.com/presentation_image_h2/7c6db0831433b417a8eb7f7ccbcba326/image-8.jpg "XSCTools main assumptions : Mesh [1/7] For the FEM (Finite Element Method) it has")
XSCTools main assumptions : Mesh [1/7] For the FEM (Finite Element Method) it has been built a 2 D mesh using the Mat. Lab PDE toolbox with about 30000 first order elements and 15000 nodes 2013/02/08 WIP, Frascati G Artaserse 8
![XSCTools main assumptions : Poloidal Field Circuits [2/7] - 4 active PFCs (T, V,](http://slidetodoc.com/presentation_image_h2/7c6db0831433b417a8eb7f7ccbcba326/image-9.jpg "XSCTools main assumptions : Poloidal Field Circuits [2/7] - 4 active PFCs (T, V,")
XSCTools main assumptions : Poloidal Field Circuits [2/7] - 4 active PFCs (T, V, H, F) 2013/02/08 WIP, Frascati G Artaserse 9
![XSCTools main assumptions : Poloidal Field Circuits [3/7] XSCTools circuit schematization Transformer circuit (T):](http://slidetodoc.com/presentation_image_h2/7c6db0831433b417a8eb7f7ccbcba326/image-10.jpg "XSCTools main assumptions : Poloidal Field Circuits [3/7] XSCTools circuit schematization Transformer circuit (T):")
XSCTools main assumptions : Poloidal Field Circuits [3/7] XSCTools circuit schematization Transformer circuit (T): Ohmic heating coils used to start the discharge, plasma breakdown voltage up to 40 V and providing most of the flux variation, 5. 1 Vs. This circuit is used in feedback to control the plasma Ip current intensity. 2013/02/08 WIP, Frascati CNL reconstructed flux map of IT current G Artaserse 10
![XSCTools main assumptions : Poloidal Field Circuits [4/7] XSCTools circuit schematization Vertical circuit (V):](http://slidetodoc.com/presentation_image_h2/7c6db0831433b417a8eb7f7ccbcba326/image-11.jpg "XSCTools main assumptions : Poloidal Field Circuits [4/7] XSCTools circuit schematization Vertical circuit (V):")
XSCTools main assumptions : Poloidal Field Circuits [4/7] XSCTools circuit schematization Vertical circuit (V): Vertical field windings providing the pre-programmed equilibrium field (up to 0. 65 T) and contributing to the flux variation during the rise of the plasma current with 1. 3 Vs. This circuit is not used in feedback, but is used to control the plasma equilibrium, jx. B= p. 2013/02/08 WIP, Frascati CNL reconstructed flux map of IV current G Artaserse 11
![XSCTools main assumptions : Poloidal Field Circuits [5/7] XSCTools circuit schematization Feedback circuit (F):](http://slidetodoc.com/presentation_image_h2/7c6db0831433b417a8eb7f7ccbcba326/image-12.jpg "XSCTools main assumptions : Poloidal Field Circuits [5/7] XSCTools circuit schematization Feedback circuit (F):")
XSCTools main assumptions : Poloidal Field Circuits [5/7] XSCTools circuit schematization Feedback circuit (F): This circuit is used in feedback to control the horizontal plasma current position Rp. 2013/02/08 WIP, Frascati CNL reconstructed flux map of IF current G Artaserse 12
![XSCTools main assumptions : Poloidal Field Circuits [6/7] XSCTools circuit schematization Horizontal circuit (H):](http://slidetodoc.com/presentation_image_h2/7c6db0831433b417a8eb7f7ccbcba326/image-13.jpg "XSCTools main assumptions : Poloidal Field Circuits [6/7] XSCTools circuit schematization Horizontal circuit (H):")
XSCTools main assumptions : Poloidal Field Circuits [6/7] XSCTools circuit schematization Horizontal circuit (H): This circuit is used in feedback to control the vertical plasma current position Zp. 2013/02/08 WIP, Frascati CNL reconstructed flux map of IH current G Artaserse 13
![XSCTools main assumptions: Probes location, Geometrical descriptors [7/7] Saddle Loops Pick. Up coils (poloidal](http://slidetodoc.com/presentation_image_h2/7c6db0831433b417a8eb7f7ccbcba326/image-14.jpg "XSCTools main assumptions: Probes location, Geometrical descriptors [7/7] Saddle Loops Pick. Up coils (poloidal")
XSCTools main assumptions: Probes location, Geometrical descriptors [7/7] Saddle Loops Pick. Up coils (poloidal view) 2013/02/08 WIP, Frascati G Artaserse 14
![CNL input treatment [1/2] The CNL code inputs must be treated to remove electronic](http://slidetodoc.com/presentation_image_h2/7c6db0831433b417a8eb7f7ccbcba326/image-15.jpg "CNL input treatment [1/2] The CNL code inputs must be treated to remove electronic")
CNL input treatment [1/2] The CNL code inputs must be treated to remove electronic offset and toroidal field effects 2013/02/08 WIP, Frascati G Artaserse 15
![CNL input treatment [2/2] The CNL code running need as input the following quantities:](http://slidetodoc.com/presentation_image_h2/7c6db0831433b417a8eb7f7ccbcba326/image-16.jpg "CNL input treatment [2/2] The CNL code running need as input the following quantities:")
CNL input treatment [2/2] The CNL code running need as input the following quantities: q Poloidal Field Coils currents (amplifier currents) IPF, “ 0_SHOT. Zx. M=I’’ from FTU database with electronic offset removed, where x = {T, V, H, F} q Trusted magnetic measurements (used only for plasma run as best fit) 16 measurements from Oct. #4 Pick up coils (MARTEFE or ODIN channels) ZZZZED. IPL MARTEFE: “MARTEFE. VBww”, where ww = {01: 16} I 20 k. A ODIN: “EQLB 04. Bpyy”, where yy = {01: 16} 16 measurements from Oct. #4 Saddle loops (MARTEFE or ODIN channels) MARTEFE. IPL MARTEFE: “MARTEFE. VSww”, where ww = {01: 16} ODIN: “EQLB 04. SAyy”, where yy = {01: 16} q Other Data Plasma Current , Ipl: “MARTEFE. IPL”, computed from compensated magnetic measurements Plasma centroid coordinates, Rp: “$EQERAX”, Zp: “$EQZAX” forced @0!!, both from equilibria Poloidal beta , βp: “$EQEBETA”, from equilibria Internal inuctance , Li: “$EQELI 2”, multiplied by 2 (CNL code need Li instead of Li/2) , from equilibria Toroidal field @ vaccum chamber centre , Btor: “%E. BTOR” 2013/02/08 WIP, Frascati G Artaserse 16
![Benchmark case: Breakdown (‘’plasmaless’’) [1/3] q FTU case #36527@-0. 100 s %e. eqlplotx 0_SHOT.](http://slidetodoc.com/presentation_image_h2/7c6db0831433b417a8eb7f7ccbcba326/image-17.jpg "Benchmark case: Breakdown (‘’plasmaless’’) [1/3] q FTU case #36527@-0. 100 s %e. eqlplotx 0_SHOT.")
Benchmark case: Breakdown (‘’plasmaless’’) [1/3] q FTU case #36527@-0. 100 s %e. eqlplotx 0_SHOT. ZTM=I CNL reconstructed flux map (input 0_Shot cleaned from el. offset ) 0_SHOT. ZVM=I 0_SHOT. ZFM=I 0_SHOT. ZHM=I L Discovered discrepancies beetween CNL and ODIN regarding the location of poloidal field null during breakdown phase 2013/02/08 WIP, Frascati G Artaserse 17
![Benchmark case: reconstruction polidal field null evolution [2/3] q FTU case #30226@-0. 100 s](http://slidetodoc.com/presentation_image_h2/7c6db0831433b417a8eb7f7ccbcba326/image-18.jpg "Benchmark case: reconstruction polidal field null evolution [2/3] q FTU case #30226@-0. 100 s")
Benchmark case: reconstruction polidal field null evolution [2/3] q FTU case #30226@-0. 100 s CNL reconstructed flux map Using 0_Shot as input Using pre-programmed currents as input %e. eqlplotx MAXFEA Using pre-programmed currents as input Which polidal fields currents use ODIN (%e. eqlplotx ) as input Good agreement with MAXFEA 2013/02/08 WIP, Frascati G Artaserse 18
![Benchmark case: Breakdown phase comparison with MAXFEA [3/3] q FTU case #36527@[-0. 100, -0.](http://slidetodoc.com/presentation_image_h2/7c6db0831433b417a8eb7f7ccbcba326/image-19.jpg "Benchmark case: Breakdown phase comparison with MAXFEA [3/3] q FTU case #36527@[-0. 100, -0.")
Benchmark case: Breakdown phase comparison with MAXFEA [3/3] q FTU case #36527@[-0. 100, -0. 060, -0. 040, -0. 020, 0, +0. 002, +0. 004]s 2013/02/08 WIP, Frascati G Artaserse 19
![Benchmark case: Plasma run [1/5] q FTU case #36527@0. 5 s, Poloidal limiter @0](http://slidetodoc.com/presentation_image_h2/7c6db0831433b417a8eb7f7ccbcba326/image-20.jpg "Benchmark case: Plasma run [1/5] q FTU case #36527@0. 5 s, Poloidal limiter @0")
Benchmark case: Plasma run [1/5] q FTU case #36527@0. 5 s, Poloidal limiter @0 cm (quiet position), assuming no eddy currents CNL rt. ODIN Snapshot of CNL outcome Equilibria reconstruction time ODIN 2013/02/08 WIP, Frascati q Max reconstruction error on plasma boundary less than 1 cm!! q Same contact point of rt. ODIN and ODIN G Artaserse 20
![Benchmark case: Plasma run [2/5] q FTU case #36527@0. 5 s, Poloidal limiter @0](http://slidetodoc.com/presentation_image_h2/7c6db0831433b417a8eb7f7ccbcba326/image-21.jpg "Benchmark case: Plasma run [2/5] q FTU case #36527@0. 5 s, Poloidal limiter @0")
Benchmark case: Plasma run [2/5] q FTU case #36527@0. 5 s, Poloidal limiter @0 cm (quiet position), assuming no eddy currents q using MARTEFE mag. meas and MARTEFE. IPL as CNL input Faulty probe 2013/02/08 WIP, Frascati q Absolute relative error on pick up coils signals less than 5% q Pick. Up coils: measurements from oct. #4 more reliable than oct. #10? ? q Detect faulty probes q Absolute relative error on saddle loop signals around 30%!!!!! q Revise saddle loop role and treatment in the CNL G Artaserse 21
![Benchmark case: Plasma run [3/5] q FTU case #36527@0. 5 s, Poloidal limiter @0](http://slidetodoc.com/presentation_image_h2/7c6db0831433b417a8eb7f7ccbcba326/image-22.jpg "Benchmark case: Plasma run [3/5] q FTU case #36527@0. 5 s, Poloidal limiter @0")
Benchmark case: Plasma run [3/5] q FTU case #36527@0. 5 s, Poloidal limiter @0 cm (quiet position) CNL vs ODIN Comparison not reliable near the internal vessel q Fair agreement with the ODIN flux map q Bad identification of magnetic axes q Comparison not reliable near internal vessel: due the not wise choice of region of interest to compute ODIN flux map with ftupsi routine CNL contact point 2013/02/08 WIP, Frascati G Artaserse 22
![Benchmark case: Plasma run [4/5] q FTU case #36527@0. 5 s, Poloidal limiter @0](http://slidetodoc.com/presentation_image_h2/7c6db0831433b417a8eb7f7ccbcba326/image-23.jpg "Benchmark case: Plasma run [4/5] q FTU case #36527@0. 5 s, Poloidal limiter @0")
Benchmark case: Plasma run [4/5] q FTU case #36527@0. 5 s, Poloidal limiter @0 cm (quiet position) CNL vs rt. ODIN (MARTEFE) q Fair agreement with the rt. ODIN flux map ONLY in the LFS region q Bad identification of magnetic axes q Bad agreement q Raw discretization of rt. ODIN flux map in future refinement of angle (omega) for a better comparison q rt. ODIN flux map affected by mesh generation (eye) CNL contact point 2013/02/08 WIP, Frascati G Artaserse 23
![Benchmark case: Plasma run [5/5] q FTU case #36437@0. 5 s, Poloidal limiter inserted](http://slidetodoc.com/presentation_image_h2/7c6db0831433b417a8eb7f7ccbcba326/image-24.jpg "Benchmark case: Plasma run [5/5] q FTU case #36437@0. 5 s, Poloidal limiter inserted")
Benchmark case: Plasma run [5/5] q FTU case #36437@0. 5 s, Poloidal limiter inserted of -1 cm CNL rt. ODIN Without knowing poloidal limiter position Knowing poloidal limiter position Beware to the poloidal limiter position!!!! 2013/02/08 WIP, Frascati G Artaserse 24
![Benchmark case: Open loop simulation [1/2] FTU CREATE-NL 2013/02/08 WIP, Frascati G Artaserse 25](http://slidetodoc.com/presentation_image_h2/7c6db0831433b417a8eb7f7ccbcba326/image-25.jpg "Benchmark case: Open loop simulation [1/2] FTU CREATE-NL 2013/02/08 WIP, Frascati G Artaserse 25")
Benchmark case: Open loop simulation [1/2] FTU CREATE-NL 2013/02/08 WIP, Frascati G Artaserse 25
![Benchmark case: Open loop simulation [2/2] FTU case #36527@0. 5 s Using the space](http://slidetodoc.com/presentation_image_h2/7c6db0831433b417a8eb7f7ccbcba326/image-26.jpg "Benchmark case: Open loop simulation [2/2] FTU case #36527@0. 5 s Using the space")
Benchmark case: Open loop simulation [2/2] FTU case #36527@0. 5 s Using the space state model matrices ABCD given by a single CNL linearized model Input: Ipl, IT, IV, IH, IF Disturbances: Betapol, Li Simulated Outputs: Mag. Meas, Rp, Zp, Elongation, Gaps… Time window simulation [0. 1, 0. 7]s SA 03_04 BP 01_04 BP 10_04 IPL Rp SA 15_04 2013/02/08 WIP, Frascati G Artaserse 26
Conclusions: q Create NL code ported to FTU case to reconstruct magnetic equilibria and provide ‘’reliable’’ linearized model (neglected eddy currents effect if any) q Comparison of CNL and MAXFEA flux map of dry run shows good agreement q Comparison of CNL and ODIN (or rt. ODIN) flux map of plasma run shows a fair agreement q Comparison of CNL and rt. ODIN boundary shows a reconstruction error less than 1 cm q Reconstructed signals of pick-up coils shows a good agreemnt with the experimental ones q Preliminary open loop symulation of experimental magnetic measurements shows a good agreement, (using the CNL linearized model in the space state form ABCD drived by PF coils an plasma current) q CNL model capable to reproduce plasma current overshoot in the plasma current ramp-up Future work: q Understand discrepancies beetween CNL and ODIN regarding the location of poloidal field null during breakdown phase q Improve boundary reconstruction (understanding role/modelling in the MCF of saddle loops) q Comaprison of plasma flux map computed by MAXFEA code q Integrate CNL linearized model in the FTU plasma current, position and shape control q Study eddy currents effect (if any) to improve dynamic simulations q … 2013/02/08 WIP, Frascati G Artaserse 27
Draft Abstract EPS 2013: 2013/02/08 WIP, Frascati G Artaserse 28
- Slides: 28