1. Analysis, Modelling and Simulation of Energy Systems, SEE-T9 Mads Pagh Nielsen Component Modelling The interaction between conservation equations and equations describing the physical process going on internally in a component.

2. Analysis, Modelling and Simulation of Energy Systems, SEE-T9 Mads Pagh Nielsen Black box model Only offers information about the thermodynamic conditions at inlet and outlet from a given component. At stationary modelling start up phenomena and transients caused by alternating loads are not considered and thus knowledge about the internal process going on in the components is redundant.

3. Analysis, Modelling and Simulation of Energy Systems, SEE-T9 Mads Pagh Nielsen Energy- and mass conservation

4. Analysis, Modelling and Simulation of Energy Systems, SEE-T9 Mads Pagh Nielsen System boundaries Setting up conservation equations: –Two-gate approach versus multigate approach: Two-gate method: Multigate method ?? 2 components 1component One input & one output Multiple in- and outputs

5. Analysis, Modelling and Simulation of Energy Systems, SEE-T9 Mads Pagh Nielsen Example: Pump Inlet conditions: h, p, T and. T is calculated as a function of pressure and enthalpy. Besides that, either W pump or the desired exit pressure p 2 should be given. Physical property:  pump +

6. Analysis, Modelling and Simulation of Energy Systems, SEE-T9 Mads Pagh Nielsen Example: Air compressor

7. Analysis, Modelling and Simulation of Energy Systems, SEE-T9 Mads Pagh Nielsen Example: Heat exchanger

8. Analysis, Modelling and Simulation of Energy Systems, SEE-T9 Mads Pagh Nielsen LMTD-method

9. Analysis, Modelling and Simulation of Energy Systems, SEE-T9 Mads Pagh Nielsen Typical U-values: Pre-heater ~ 34 W/(m²·K) Evaporator ~ 80 W/(m²·K) Super heater ~ 72 W/(m²·K) Water-Water ~ 1500 (800-2500) W/(m²·K)

10. Analysis, Modelling and Simulation of Energy Systems, SEE-T9 Mads Pagh Nielsen Example: Gas engine Continuity: Conservation of energy:

11. Analysis, Modelling and Simulation of Energy Systems, SEE-T9 Mads Pagh Nielsen Efficiency characteristic

12. Analysis, Modelling and Simulation of Energy Systems, SEE-T9 Mads Pagh Nielsen Exhaust temperature

13. Analysis, Modelling and Simulation of Energy Systems, SEE-T9 Mads Pagh Nielsen Cooling efficiency

14. Analysis, Modelling and Simulation of Energy Systems, SEE-T9 Mads Pagh Nielsen Exhaust massflow

15. Analysis, Modelling and Simulation of Energy Systems, SEE-T9 Mads Pagh Nielsen Equations: {/////////////////////////////////////////////////////} { Gas engine } {/////////////////////////////////////////////////////} R[1]=0.6 {Relative hum. of inlet air} f[1]=humrat(AirH2o, p=p[1], h=h[1], R=R[1]) Load=100 {Full load} H_combustion[1]=49.5e6 {Lower heating value of natural gas} Eta_generator=0.95 {Efficiency of generator} Q[4]=m[2]*H_combustion {Stoichiometric combustion} Q[6]=0,04*W[5] {Heat loss from engine} W[5]=Q[4]*Eta_shaft {Shaft power} Q[7]=Q[4]*Eta_cooling {Cooling energy} W[5]=(W_el/Eta_generator) {Calculation of electricity produced} W[5]=(Load/100)*Size {Relate shaft power to load} CALL Regressions(Size;Load:T_exh[3];m_dot_exh[3];Eta_cooling;Eta_shaft)

16. Analysis, Modelling and Simulation of Energy Systems, SEE-T9 Mads Pagh Nielsen Regressions for gas engine: PROCEDURE Reg(Motorstr;Last:T; m;Eta_varme;Eta_aksel) IF Motorstr<=1,5 THEN {Reg for CATERPILLAR 3500-series (k1-k3)} k1=-1,56758264751006*(Motorstr*Last) : k2=k1+8,36936811270700E-1*(Motorstr^2*Last) k3=k2+-3,42845055730651E-16*(Motorstr*Last^2) : k4=k3+ 2,99266904660311E-16*(Motorstr^2*Last^2) k5=k4+2,84051875454190E2+3,83032124894794E+2*Motorstr : k6=k5+-2,30497204202655E2*Motorstr^2+ 5,59104477611930E-1*Last T:=k6+6,85893399368642E-17*Last^2 k7=-1,14150573395760E-1*(Motorstr*Last) : k8=k7+7,96699062703951E-2*(Motorstr^2*Last) : k9=k8+ 8,36505679102166E-4*(Motorstr*Last^2) k10=k9-5,22119006981289E-4*(Motorstr^2*Last^2) : k11=k10-1,39907903460236+4,28181037738979*Motorstr : k12=k11-2,60141328430843*Motorstr^2+ 4,36490378444878E-2*Last m:=k12-2,86807025546440E-4*Last^2 k13=2,19831291406054E-2*(Motorstr*Last) : k14=k13-1,44163671822562E-2*(Motorstr^2*Last) : k15=k14+-1,60255776666399E-4*(Motorstr*Last^2) k16=k15+1,05717344183216E-4*(Motorstr^2*Last^2) : k17=k16+7,36280756330728E-1-7,62002120553441E-1*Motorstr : k18=k17+4,71623296935500E-1*Motorstr^2-9,32664939348261E-3*Last Eta_varme:=k18 +6,12378936776826E-5*Last^2 k19=-1,99946179007292E-3*(Motorstr*Last) : k20=k19+1,21549137646842E-3*(Motorstr^2*Last) : k21=k20+1,45131112263936E-5*(Motorstr*Last^2) k22=k21-9,50827088959231E-6*(Motorstr^2*Last^2) : k23=k22+1,81239004416123E-1+8,37224175248884E-2*Motorstr : k24=k23-3,05022195543315E-2*Motorstr^2+3,20380803845934E-3*Last : Eta_aksel:=k24-1,55230096707470E-5*Last^2 ELSE {Reg for CATERPILLAR 3600-series} k25=-2,53313202482839E-1*(Motorstr*Last) : k26=k25+5,08354811324176E-2*(Motorstr^2*Last) : k27=k26+2,02650561986270E-3*(Motorstr*Last^2) k28=k27-4,06683849059337E-4*(Motorstr^2*Last^2) : k29=k28+4,40706780944827E2+2,53313202482813E+1*Motorstr : k30=k29-5,08354811324126*Motorstr^2+1,42932190551758E-1*Last T:=k30-1,04234575244140E-2*Last^2 k31=-1,33788890577105E-2*(Motorstr*Last) : k32=k31+3,14987756577728E-3*(Motorstr^2*Last) : k33=k32+3,37507315437329E-4*(Motorstr*Last^2) k34=k33-4,13391073261964E-5*(Motorstr^2*Last^2) : k35=k34-1,79904317687621+9,68662711839557E-1*Motorstr : k36=k35-8,51957284061772E-2*Motorstr^2+6,21466578567492E-2*Last m:=k36-5,94451119750688E-4*Last^2 : k37=3,03270909860921E-3*(Motorstr*Last) : k38=k37-6,30752577079704E-4*(Motorstr^2*Last) k39=k38-1,82497622039065E-5*(Motorstr*Last^2) : k40=k39+3,74291908784650E-6*(Motorstr^2*Last^2) : k41=k40+3,11862476018024E-1+-1,03069392710923E-1*Motorstr : k42=k41+2,22944942660193E-2*Motorstr^2-3,98480909049131E-3*Last Eta_varme:=k42+2,81447180524241E-5*Last^2 k43=-2,33866878272789E-3*(Motorstr*Last) : k44=k43+4,26254234584089E-4*(Motorstr^2*Last) : k45=k44+1,16524914451450E-5*(Motorstr*Last^2) k46=k45-2,19352296721786E-6*(Motorstr^2*Last^2) : k47=k46+1,61524621500911E-1+9,59653427654178E-2*Motorstr :k48=k47-1,60580973780507E-2*Motorstr^2+4,66986417775120E-3*Last Eta_aksel:=k48-1,98706347417594E-5*Last^2 ENDIF END

17. Analysis, Modelling and Simulation of Energy Systems, SEE-T9 Mads Pagh Nielsen Example: Gas turbine Can be modelled almost like a gas engine. The gas turbine is modelled similarly as an air compressor. Only note that gas turbines are sensitive to pressure drop in boiler!

18. Analysis, Modelling and Simulation of Energy Systems, SEE-T9 Mads Pagh Nielsen Next time: