Parameter selection in a combined cycle power plant
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The document details the analysis and optimization of the start-up process in a combined cycle power plant using parameter selection algorithms. It discusses the modeling of components, calibration methods, and the use of a subset selection algorithm to identify effective parameter sets. The results indicate improved output signals and recommend future optimizations based on the calibrated parameters.
![Parameter selection loops
2 loops are iterated for
parameter sets for 𝑛 𝑝 = [1 … 7]
Population of parameter sets:
ℙ0 - all individual parameters
ℙ 𝑐𝑜𝑚𝑏1, ℙ 𝑐𝑜𝑚𝑏2 - combination
ℙ 𝑆𝑆𝐴, ℙ 𝑄 - filtered
ℙ 𝑐𝑎𝑙1, ℙ 𝑐𝑎𝑙2 - To be calibrated
SSA loop
- Ranks all parameter sets from
their SSA score. Best sets are
calibrated.
Calibration loop
- Parameter sets with best Q
continue to next iteration
and are combined and
calibrated](https://image.slidesharecdn.com/niklasanderssonmodelica2014paramselcombcycpowerplant-140428075712-phpapp01/85/Parameter-selection-in-a-combined-cycle-power-plant-15-320.jpg)
Parameter selection in a combined cycle power plant
- 1. Parameter selection in a combined cycle power plant Niklas Andersson*, Johan Åkesson**, Kilian Link***, Stephanie Gallardo Yances***, Karin Dietl***, Bernt Nilsson* * Dept. of Chemical Engineering, Lund University **Modelon AB ***Siemens AG
- 2. Presentation outline • Background - Combined cycle power plant - Process overview • Modelling • Parameter estimation • Parameter selection • Results • Summary
- 3. Scope • The start-up of a combined cycle power plant has been analysed. • The goal has been to calibrate a model, with the purpose to optimize the start-up while maintaining long lifetime of critically stressed components. • The model contains many candidate parameters. An algorithm has been used to assist in the selection of the best parameter sets.
- 4. cooling start-up Why? • The electricity demand varies during a day • Sun and wind variations affect the available amount of electricity • Market determines when the process is profitable to run. How? • Manipulate gas turbine load and by-pass valve to steam turbine • Header and drum are sensitive to rapid temperature changes Why calibration? • Optimization of CCPPs requires a model well tuned to the real process Background
- 6. PHASE 1: • Gas turbine accelerated to full speed, no load • Gas turbine synchronized to grid PHASE 2: • Load of the gas turbine increased • Boiler starts producing steam • Generated steam bypassed to condenser PHASE 3: • Bypass valve closes • Steam drives steam turbine Included in calibration Start-up phases
- 7. Modelling approach • Models of HRSG developed in JModelica.org. • Hot gas side, statically modelled • Water side, dynamically modelled • 14 blocks modelled – Gas turbine – 3 reheaters (RH) – 3 high pressure super heaters (HPSH) – Evaporator – Drum – Header – 4 water injections • 764 eqs. (39 cont. time states) • Simulated as an FMU
- 8. Inputs to model Outputs from model
- 9. - The parameter estimation is done with a Levenberg– Marquardt algorithm. Δp = JT J + 𝜆JT J −1 JT R - The Jacobean matrix 𝐽 is estimated with finite differences (central difference). - The objective function to be minimized is formulated using weighted least squares 𝑄 𝒑 = 𝑖=1 𝑛 𝑡 𝒚𝒊 − 𝑦 𝑡𝑖, 𝒑 𝑇 𝑊( 𝒚𝒊 − 𝑦 𝑡𝑖, 𝒑 ) Calibration procedure
- 10. Candidate model parameters 64 parameters divided in 8 categories - Heat transfer constants 𝑘, 𝑘𝑖𝑛, 𝑘 𝑜𝑢𝑡 - Mass and volume 𝑚 𝐻2 𝑂, mFe, V - Sensor heat capacity 𝑐𝑎𝑝 - Valve dynamics parameter
- 11. Candidate model parameters Merged parameters – to reduce number of parameters parent children 𝑝9 = 𝑣 ⟹ 𝑝28 = 𝑝29 = 𝑝30 = 𝑣 A parent parameter can’t be calibrated together with its children
- 12. Parameter selection Why not choose all 64 parameters? - Large parameter confidence intervals - The sensitivity matrix gets singular (dependent parameters) Which parameters to choose? - There are 64 𝑛 𝑝 unique parameter sets with 𝑛 𝑝 number of parameters. Totally ~2 ⋅ 1018 parameter sets. A parameter selection algorithm is used to rank the parameter sets
- 13. How to choose parameters? Subset selection algorithm (SSA) - Subset Selection Algorithm ranks the parameters based on 𝛼 and 𝜅. (Cintrón et al. 2009) - Sensitivity matrix 𝜒 𝑝 = 𝜕𝑦 𝜕𝑝 calculated from nominal parameter values - Covariance matrix Σ 𝑝 = 𝜎0 2 𝜒 𝑝 𝑇 𝜒 𝑝 −1 - Parameter 𝛼 is the normalized parameter uncertainty, defined as Σ 𝑝 𝑖𝑖 𝑝 𝑖 - Parameter 𝜅 is the condition number of the sensitivity matrix. - An SSA score is introduced 𝜃 = lg 𝛼 + lg 𝜅
- 14. 𝛼 – Decreased accuracy of calibration 𝜅 - Solving difficulty. - Each point is a parameter set. - Low values of 𝛼 and 𝜅 is desirable. - When adding parameters the dot clouds get worse. SSA – ranking parameter sets
- 15. Parameter selection loops 2 loops are iterated for parameter sets for 𝑛 𝑝 = [1 … 7] Population of parameter sets: ℙ0 - all individual parameters ℙ 𝑐𝑜𝑚𝑏1, ℙ 𝑐𝑜𝑚𝑏2 - combination ℙ 𝑆𝑆𝐴, ℙ 𝑄 - filtered ℙ 𝑐𝑎𝑙1, ℙ 𝑐𝑎𝑙2 - To be calibrated SSA loop - Ranks all parameter sets from their SSA score. Best sets are calibrated. Calibration loop - Parameter sets with best Q continue to next iteration and are combined and calibrated
- 16. Combination Combination ℙ0 = {𝑝1, 𝑝2, 𝑝3, 𝑝4}ℙ𝑖𝑛 = {𝑝1,2, 𝑝2,3} All parameters (here 4 parameters) ℙ 𝑜𝑢𝑡 = 𝑝1,2,3, 𝑝1,2,4, 𝑝1,2,3, 𝑝2,3,4 ℙ 𝑜𝑢𝑡 = {𝑝1,2,3, 𝑝1,2,4, 𝑝2,3,4} Input parameter sets population
- 17. SSA Evaluation SSA Evalutation ℙ𝑖𝑛 = {𝑝1,2, 𝑝2,3, … } 𝜃 Input parameter sets population
- 18. Calibration Calibration ℙ𝑖𝑛 = {𝑝1,2, 𝑝2,3, … } 𝑄 Input parameter sets population Two populations to calibrate - ℙ 𝑐𝑎𝑙1 (from SSA loop) - ℙ 𝑐𝑎𝑙2 (from Calibration loop)
- 19. Filter Filter ℙ𝑖𝑛 = {𝑝1,2, 𝑝2,3, … } Input parameter sets population 𝑛 𝑐𝑢𝑡𝑜𝑓𝑓 ℙ 𝑜𝑢𝑡
- 20. ℙ 𝑐𝑎𝑙1 ℙ 𝑐𝑎𝑙2 Calibration results 𝒏 𝒑 = 𝟏
- 21. ℙ 𝑐𝑎𝑙1 ℙ 𝑐𝑎𝑙2 Calibration results calib Loop 𝒏 𝒑 = 𝟏 𝒏 𝒑 =2
- 22. ℙ 𝑐𝑎𝑙1 ℙ 𝑐𝑎𝑙2 Calibration results calib Loop calib Loop calib Loop calib Loop calib Loop calib Loop 𝒏 𝒑 = 𝟏 𝒏 𝒑 =2 𝒏 𝒑 = 𝟑 𝒏 𝒑 = 4 𝒏 𝒑 = 5 𝒏 𝒑 = 𝟔 𝒏 𝒑 =7
- 23. Best parameter set 24 6 6 6 13 13 13 13 13 16 16 16 1616 16 16 17 16 • The objective value is decreasing with increased number of parameters. • When 𝑛 𝑝 > 7, poor calibration convergence. (8 output signals) • Best parameter set covers the whole model. • 3 out of 6 parameters are merged. • Narrow confidence intervals for all parameters except 𝑝24
- 24. Best parameter set • The model responses follow the measurement data well. • All output signals improved • 59 calibrations were performed to reach the result Meas. data Calibrated Uncalibrated
- 25. Summary and Future Work Summary • SSA is a good method for reducing the number of parameters • All output signals were improved • Calibration loop performed better than SSA loop for this case Future Work • Perform optimizations of start-ups with the estimated parameters • Apply optimization result on real plant
- 26. Thank you!