technical university of munich non-linear state estimator ...martin (2010), (only heat) subcooler...

Institute for Energy SystemsDepartment of Mechanical EngineeringTechnical University of Munich

Roberto Pili, M.Sc.

Eyerer Sebastian, M.Sc.

Fabian Dawo, M.Sc.

Christoph Wieland, Dr.-Ing.

Hartmut Spliethoff, Prof. Dr.-Ing.

Technical University of Munich

Department of Mechanical Engineering

Chair of Energy Systems

Athens, 11th September 2019

Non-Linear State Estimator for Advanced Control of an ORC Test Rig for Geothermal Application

1. ORC Units for Geothermal Application and Flexibility

2. Advanced Control and Non-Linear State Estimation

3. Test Rig at TUM

4. Procedure

5. Development of Dynamic Model in Dymola and Validation

6. Development in MATLAB®/Simulink

7. UKF Observer Performance

8. Summary and Future Outlook

2Chair of Energy Systems | 5th International Seminar on ORC Power Systems | Pili Roberto

Outline


1. ORC Units for Geothermal Application and Flexibility

Figure 1: Geothermal plant with heat

and ORC power production

Low enthalpy geothermal plants

often supply:

- low temp. heat for district heating

- electricity with ORC technology

ORC plant has to be flexible and

guarantee safe operation, maximing

the net power production

EVA

T

REC

P

CO

PM

G

Heat source

Cold sink

PH

District heating

Figure 2: District

heating annual duration

curve for a location in

Germany (Wieland,

2016)


2. Advanced Control of ORC Units



To achieve high efficiency and

flexible operation, it is important to:

- set the optimal expander inlet

pressure and temperature

- (set the optimal condensation

pressure)

Degrees of freedom:

- Pump rotational speed

- Expander rotational speed

- (Cooling medium flow rate)

EVA

T

REC

P

CO

PM

G

Heat source

Cold sink

PH

District heating


2. Advanced Control of ORC Units



The pump and expander rotational

speeds both affect pressure and degree

of superheating at expander inlet.

Multivariable control to ensure:

- Safe operation

- Tracking of pressure and superheating

setpoints

- Optimal performance

Linear Quadratic Control

Model Predictive Control

A state estimation is required for

state-space control, since internal

variables in the evaporator are not

measurable

EVA

T

REC

P

CO

PM

G

Heat source

Cold sink

PH

District heating

Estimator Linear/Non-

linear

Stochastic CPU effort

Luenberger Linear No Low

Kalman Filter Linear Yes Low

Extended

Kalman Filter

Linearization Yes Medium

Unscented

Kalman Filter

Non-linear Yes Medium/High

Particle Filter Non-linear Yes High

Moving State

Horizon

Non-linear Yes High


2. Non-Linear State Estimation


3. Test rig at TUM

Figure 2: Simplified P&I diagram of the ORC test rig

p1PIR

T1TIRC

T2TIR

p4PIRC

T4TIR

p5PIR

T5TIR

p9PIR

T8TIR

T7TIRC

p7PIR

p3PIR

T3TIR

FR2FIRC

N1NIR

E1EIR

FR1FIRC

p6PIR

T6TIR

Liquid

Vapor (containing oil)

Measurement and control line

3-phase power line T9TIR

Working fluid R1233zd(E)

Heat source Electric heater,

200 kW (135 °C)

Expander Twin-screw

compressor

(inverse), Bitzer

OSN5361-K,

swept volume

0.678 l, built-in

volume ratio 3.1

Heat exchangers Brazed-plate,

Alfa Laval


4. Procedure for Observer Development

Start

Experiments on test rig at different operating points/

load changes

Develop Observer

Test observer capability vs

measurements/dynamic model

End

Development dynamic model in Dymola and

validation

Export as FMU to MATLAB® /Simulink or

develop simplified Simulink model +

Validation

• TIL-Library 3.5.0 (TLK-Thermo GmbH)

• Fluid properties REFPROP 9.1

• Heat exchangers: Finite volume, 15 cells

• Heat transfer and pressure drop correlations

• Expander model: Lemort, 2009


5. Validation of dynamic model in Dymola

ComponentFluid Heat transfer and pressure drop correlation

Hot side Cold side Hot side Cold side

Evaporator Hot water Working fluid Martin (2010), (only heat)Single phase: Martin (2010);

Two-phase: Amalfi et al. (2016)

Condenser Working fluid Cooling waterSingle phase: Martin (2010);

Two-phase: Yan et al. (1999)Martin (2010), (only heat)

Subcooler Working fluid Cooling water 2 x Martin (2010) Martin (2010), (only heat)

volume p, h

volume p, h

leakage

Isentropic expansion

frictionOver/

underexpansion

Mechanical power

High pressure

Low pressure

Heat rate at suction

Heat rate at

discharge

Suction cross-sectional area:

0.509 m2

Discharge cross-sectional area:

0.502 m2

Leakage cross-sectional area: 3.2335e-5 m2

Qamb = UA (T – Tamb)UA = 66.08 W/K

Tamb = 25°C

.

50% friction losses50% friction losses + +

Figure 3: Expander model and fitting results.


Relative

mean

square

error < 1 %


Figure 4: Experimental results from test rig.



Figure 5: Validation of expander/generator/inverter model.

• Unscented Kalman Filter needs state-space representation of system:

ሶ𝑥 = 𝑓 𝑥, 𝑢

𝑦 = 𝑔 𝑥, 𝑢

• Model in MATLAB®/Simulink – simplified from Dymola model

• Reduction to 10 cells

• Heat transfer coefficient: 𝛼 = 𝛼𝑛𝑜𝑚ሶ𝑚

ሶ𝑚𝑛𝑜𝑚

𝛾

• Look-up tables for fluid properties

• Filter for heat transfer coefficient and pressure: 𝑑𝛼𝑠𝑡

𝑑𝑡=

𝛼− 𝛼𝑠𝑡

𝑇𝛼

• UKF parameters:

• 𝛼 = 0.1, 𝜅 = 0, 𝛽 = 2

• Sample time = 0.5 s


6. Model in MATLAB®/Simulink


7. UKF Observer Performance

Figure 6: Observer performance.

Summary:

A validated dynamic model of the ORC test rig for geothermal application has been

developed in Dymola, based on experimental data.

Based on this, a validated (simplified) model has been developed in MATLAB®/Simulink to

develop a non-linear state-based observer (Unscented Kalman Filter).

The UKF observer has shown promising state estimation capabilities.

Future work:

Simulation with combined UKF and LQI controller.

Implementation of the control architecture and experimental tests on the ORC facility at

TUM and comparison with current PI control.


8. Conclusions

Amalfi, R. L., Vakili-Farahani, F., Thome, J. R., 2016, Flow boiling and frictional pressure

gradients in plate heat exchangers. Part 2. Comparison of literature methods to database and

new prediction methods, Int. J. Refrig., vol. 61: p. 185–203.

Lemort, V., Quoilin, S., Cuevas, C., Lebrun, J., 2009, Testing and modeling a scroll expander

integrated into an Organic Rankine Cycle, Appl. Therm. Eng., vol. 29, no. 14-15: p. 3094–

3102.

Martin, H., 2010, Pressure Drop and Heat Transfer in Plate Heat Exchangers, Section N6 in

VDI Heat Atlas, 2. ed. Heidelberg: Springer, 1608.

Wieland, C., Meinel. D., Eyerer, S., Spliethoff, H. Innovative CHP concept for ORC and its

benefit compared to conventional concepts. App. Energ., vol. 183, p. 478-490.

Yan, Y.-Y., Lio, H.-C., Lin, T. F., 1999: Condensation heat transfer and pressure drop of

refrigerant R-134a in a plate heat exchanger, Int. J. Heat Mass Tran., vol. 42, no. 6: p. 993–

1006.


References


Thank you very much for the attention.

Roberto Pili, M.Sc.

Chair of Energy Systems

Department of Mechanical Engineering

Technical University of Munich

[email protected]

Quantity Unit Noise

Specific enthalpy, wf kJ/kg 0.1

Heat transfer coeff, wf W/m2K 10

Wall temperature K 1

Specific enthalpy, hs kJ/kg 0.1

Derivative of pressure, wf bar/s 10-3

Pressure, wf bar 10-2


Noise on measurements

States

Output

Quantity Unit Noise

Pressure, wf bar 0.08

Temperatures, wf/hs K 0.1

Augmented state vector (dim. 𝑁): 𝑥k−1𝑎 = 𝑥k−1|k−1

𝑎 =

𝑥𝑘−1𝑤𝑘−1𝑣𝑘−1

Covariance matrix of augmented state

vector (dim. 𝑁 𝑥 𝑁):

Sigma-points (2𝑁 + 1): 𝑋𝑖,k−1|k−1𝑎 =

ො𝑥𝑘−1|𝑘−1𝑎 ,

ො𝑥𝑘−1|𝑘−1𝑎 + 𝛾𝑆𝑖 ,

ො𝑥𝑘−1|𝑘−1𝑎 + 𝛾𝑆𝑖−𝑁 ,

With: 𝑆 = 𝑃k−1|k−1𝑎 ; 𝛾 = 𝑁 + 𝜆 ; 𝜆 = 𝛼2 𝑁 + 𝜅 − 𝑁


Unscented Kalman Filter

𝑥 state (dim. 𝑛)𝑤 process noise (dim. 𝑞);𝑣 measurement noise (dim. 𝑟)

𝑃k−1|k−1𝑎 =

𝑃𝑘−1|𝑘−1 0𝑛𝑥𝑞 0𝑛𝑥𝑟

0𝑞𝑥𝑛 𝑄𝑘−1 𝑃𝑘−1𝑤𝑣

0𝑟𝑥𝑛 𝑃𝑘−1𝑤𝑣 𝑅𝑘−1

𝑖 = 0

𝑖 = 1,… ,𝑁

𝑖 = 𝑁 + 1,… , 2𝑁

p1PIR

T1TIRC

T2TIR

p4PIRC

T4TIR

p5PIR

T5TIR

p9PIR

T8TIR

T7TIRC

p7PIR

p3PIR

T3TIR

FR2FIRC

N1NIR

E1EIR

FR1FIRC

p6PIR

T6TIR

Liquid

Vapor (containing oil)

Measurement and control line

3-phase power line T9TIR



UKF

𝑝4′

𝑇4𝑇2

𝑇𝑤,𝑖ℎℎ𝑠,𝑖ℎ𝑤𝑓,𝑖

𝛼𝑤𝑓,𝑖𝑝4

𝑑𝑝

𝑑𝑡4

technical university of munich non-linear state estimator ...martin (2010), (only heat) subcooler...

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