Burn Stabilization of a Tokamak Power Plant with On-Line Estimations of Energy and Particle Confinement Times

Transcription

1 Burn Stabilization of a Tokamak Power Plant with On-Line Estimations of Energy and Particle Confinement Times Javier E. Vitela vitela@nucleares.unam.mx Instituto de Ciencias Nucleares Universidad Nacional Autónoma de México México, D.F. Burn Stabilization... p.1/29

2 Deuterium - Tritium Fueled Reactor D + T He + n (3.5 MeV) (14.1MeV) Energy Balance heating losses heating aux ohm losses rad transp Burning Regime: Gain G fusion aux ohm Burn Stabilization... p.2/29

3 Some Relevant Phenomena in a Burning Regime Impact of profiles. -heating on particle density and current equilibria Hot electron mode. Energy transport (confinement). New MHD instabilities due to energetic particles. Change in -heating profile. Thermal instabilities Energy extraction at the plasma boundary. New materials highly resistant to heat and neutron activation. Burn Stabilization... p.3/29

4 Energy and Particles Transport Losses Dominated by Turbulent Processes THEORETICAL & NUMERICAL CALCULATIONS (still) EXPERIMENTAL RESULTS Design studies : Transport modeled by extrapolating global confinement times. TOKAMAK EXPERIMENTAL DATABASIS SCALING LAW (UNCERTAINTIES) Burn Stabilization... p.4/29

5 Active Control To allow long pulse operation at nominal operating condition. Mechanism to supress transients due to: thermal instabilities. turbulence and changes in the scaling laws due to different confinement regimes. sudden increments in MHD activity. Supress transients independently of their particle and energy scaling laws. Burn Stabilization... p.5/29

6 Neural Network Controller Radial basis NN with Gaussian units in the hidden layer and sigmoidal in the output layer, Tokamak Power Plant Model Simple particle and energy transport model for the electrons and ions assuming they have different temperatures. Thermalization time delay of the particles produced by fusion are included in the balance equations. Burn Stabilization... p.6/29

7 Two-Temperatures Dynamical Equations (1) DT DT DT th frac Burn Stabilization... p.7/29

8 + * ',, 8, = Two-Temperatures Dynamical Equations (2) # "! frac aux 465 ) ( E 132 ei.0/ -, eff $&% and 45 E 1 2 ei. /, 7 aux, Ar Be # "!, frac > = 9 9 < 9;: Quasi-neutrality condition: Burn Stabilization... p.8/29

9 TokamaK 0-D Dynamical Model Volume-averaged 0-D model of the evolution of the particle densities, electron and ion temperatures. Electron and ion temperatures radial profiles: Particle density assumed homogeneous throughout the plasma volume. Include alpha particles thermalization delay. Transport of energy and particles taken into account by global confinement times, and. Large uncertainties! Burn Stabilization... p.9/29

10 Nominal Steady State (Tokamak Model: ITER-FEAT Design Parameters) Densidad de electrones: Central electron temperature : Central ion temperature : Kev m KeV Helium ash fraction He : Fraction of high-z impurities (Be and Ar) : Be, Ar Burn Stabilization... p.10/29

11 Steady State Solution : of the 0-D Eqs. for the control variables at the nominal operating point as function of, and sec total sec MW total aux,e MW total aux,i Burn Stabilization... p.11/29

12 Actuator s values as function of two sets of ratios and. in steady state for DT refueling rate He-4 inj. rate ( x sec -1 ) Aux. electron heating (MW) Aux. ion heating (MW) ( x sec -1 ) DT refueling rate ( x sec -1 ) He-4 inj. rate ( x sec -1 ) Aux. electron heating (MW) Aux. ion heating (MW) t a / t e = 4.0 t p / t a = t a / t e = 5.0 t p / t a = Energy confinement time (sec) Energy confinement time (sec) Burn Stabilization... p.12/29

13 Margin threshold Gain factor Gain Factor and L-H Transition Margin as Function of Energy Confinement Time Energy confinement time (sec) 0 Burn Stabilization... p.13/29

14 NN Controller and Tokamak Plant Array τ τ on line E on line α U k On line estimation τ E τ α Fusion Reactor Z k+1 Z k n Z k Time steps delays Burn Stabilization... p.14/29

15 Regulatory Actions: Concurrent modulation of: D-T refueling rate Injection of neutral He-4 Auxiliary heating power to electrons Auxiliary heating power ions Constraints: Actuator values lies between zero and a maximum value. Control variables are update periodically keeping their values constant between update times. Burn Stabilization... p.15/29

16 Input to the RBNN: Electron density Relative helium ash particles fraction Ions temperature Electrons temperature Estimated values of : and Burn Stabilization... p.16/29

17 @ Actuators range: Injection DT fuel rate: total sec He injection rate: total sec Auxiliary heating power to electrons: total : MW Auxiliary heating power to ions: total MW Burn Stabilization... p.17/29

18 : : Two Transient Examples with: IPB98(y,2) scaling for the energy confinement IPB98 Arbitrary scaling for the helium ash particle confinement (illustration purposes only) : Burn Stabilization... p.18/29

19 Simulation of On-Line Estimations of E and Input values feed into the RBNN are estimated simulating measurements "On-Line" by obtaining and through the use of pseudo Gaussian white processes: : mean value from IPB98 and standard deviation IPB98 : mean value from and standard deviation Burn Stabilization... p.19/29

20 @ : First Transient Example: : enhancement confinement factor Fraction of energetic particles lost before thermalization: 10% :, operating point. Second Transient Example:, and : enhancement confinement factor Fraction of energetic particles lost before thermalization: 10% and 50%.,, and : Burn Stabilization... p.20/29

21 First Example: Behaviour as Function of Time into the Transient of the Normalized State and Control Variables Electron density Electrons Temperature helium ash fraction Ions Temperature DT refueling rate He-4 injection rate Aux. heating to electrons Aux. heating to ions Time (sec) Time (sec) Burn Stabilization... p.21/29

22 First Example (Cont.): Time Behaviour into the Transient of IPB98 and the Noisy Estimation of. 6 t E (sec) Estimatedt E (sec) Time (sec) Time (sec) Burn Stabilization... p.22/29

23 First Example (Cont.): Time behaviour into the transient of. and the ratio t a (sec) Estimation t a / t E Time (sec) time (sec) Burn Stabilization... p.23/29

24 Second Example : Transient comparison between 10% and 50% of Anomalous Lost of Energetic Particles (1) Electron density (continuos lines) Ions Temperature ( dotted lines) frac = 0.5 frac = 0.1 frac = 0.5 frac = time (sec) frac = 0.5 frac = 0.1 frac = 0.5 frac = 0.1 He ash fraction (continuous lines) Electrons temperature (dotted lines) time (sec) Burn Stabilization... p.24/29

25 Second Example (Cont.): Comparison between 10% and 50% of Anomalous Lost of Energetic Particles (2) DT refueling rate (continuos lines) Aux. heating ions (dotted lines) frac = 0.5 frac = 0.1 frac = 0.5 frac = He-4 inj. rate (continuos lines) Aux. heating electrons (dotted lines) frac = 0.5 frac = 0.1 frac = 0.5 frac = time (sec) time (sec) Burn Stabilization... p.25/29

26 Conclusions Robust burn control with RBNN is promising Independent energy and He ash scalings Noisy "on-line" estimations of and Satisfactory response to changes in anomalously loss of energetic particles due to sudden increases in MHD activity. Burn Stabilization... p.26/29

27 : Experimental observations: H mode confinement hold when the L-H transition margin power threshold exceeds one net threshold with threshold eff and net aux,e aux,i ohm rad core Burn Stabilization... p.27/29

28 MW L-H Transition Power Threshold and Net Heating Power as Function of Time into the Transient ( Example # 1) L-H transition power threshold Net heating power Time (sec) Burn Stabilization... p.28/29

29 Total training error E Number of cells converging Total Training Error as Function of the Iteration No. of the NN Training Algorithm (725 transients at each iteration) Left axis Right axis Iteration number 0 Burn Stabilization... p.29/29