Authors: - Niklas Andersson, Dept. of Chemical Engineering, Lund University - Johan Åkesson, Modelon AB - KilianLink, Siemens AG - Stephanie Gallardo Yances, Siemens AG - Karin Dietl, Siemens AG - Bernt Nilsson, Dept. of Chemical Engineering, Lund University A combined cycle power plant is modeled and considered for calibration. The dynamic model, aimed for start-up optimization, contains 64 candidate parameters for calibration. The number of parameter sets that can be created are huge and an algorithm called subset selection algorithm is used to reduce the number of parameter sets. The algorithm investigates the numerical properties of a calibration from a parameter Jacobean estimated from a simulation of the model with reasonably chosen parameter values. The calibrations were performed with a Levenberg-Marquardt algorithm considering the least squares of eight output signals. The parameter value with the best objective function value resulted in simulations in good compliance to the process dynamics. The subset selection algorithm effectively shows which parameters that are important and which parameters that can be left out. Full text at: https://www.modelica.org/events/modelica2014/proceedings/html/submissions/ECP14096809_AnderssonAkessonLinkGallardoyancesDietlNilsson.pdf http://www.modelon.com/news/news-display/artikel/modelica-conference/

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

5. Process overview

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!