1. NATIONAL TECHNICAL UNIVERSITY OF ATHENS
CHEMICAL ENGINEERING SCHOOL
COMPUTATIONAL FLUID DYNAMICS UNIT
“Optimal Decision Strategy for a Renewable Energy System consisting of Wind Generators and Fuel Cell Stacks”
P. L. Zervas*, H. Sarimveis, J. Α. Palyvos, N. C. Markatos
Fuel Cell Science & Technology 2008, 7-9 October, Copenhagen
P. L. Zervas, H. Sarimveis, J. Α. Palyvos, N. C. Markatos, Fuel Cell Science & Technology 2008, Copenhagen
NTUA, Chemical Engineering School, Computational Fluid Dynamics Unit

2. Objective of the Study
Development of an optimal-decision strategy for a Renewable Energy System with Hydrogen Storage (RESHS) based on the Model Predictive Control rolling horizon concept
Qualitative comparison between Wind and Solar energy in a RESHS
P. L. Zervas, H. Sarimveis, J. Α. Palyvos, N. C. Markatos, Fuel Cell Science & Technology 2008, Copenhagen
NTUA, Chemical Engineering School, Computational Fluid Dynamics Unit

3. Purchased Electricity
Hybrid Power Generation System
Proposed RESHS
PDir (kW)
Wind Generator
Consumer
WGOut (kW)
CS (kW)
ELIn (kW)
ELOut (m3/h)
FCIn (m3/h)
FCOut (kW)
INVIn (kW)
INVOut (kW)
Metal Hydride Tanks 1
Electrolyzer
Fuel Cells 2
Inverter 3
ETG (kW)
EFG (kW)
Inventory
Purchased Electricity
Sold Electricity
P. L. Zervas, H. Sarimveis, J. Α. Palyvos, N. C. Markatos, Fuel Cell Science & Technology 2008, Copenhagen
NTUA, Chemical Engineering School, Computational Fluid Dynamics Unit

4. Model Predictive Control rolling horizon concept
Past
Future
Future values of the Objective Function
ObjF(t)
u(t+i|t)
Future values of the Decision Variables
u(t)
t-n t
t+i
t+M
t+N
Prediction horizon
P. L. Zervas, H. Sarimveis, J. Α. Palyvos, N. C. Markatos, Fuel Cell Science & Technology 2008, Copenhagen
NTUA, Chemical Engineering School, Computational Fluid Dynamics Unit

5. Formulation of a Mixed Integer Non-Linear Programming (MINLP) optimization problem
Decision Variables
Energy consumed by the electrolyzer
Purchased/Sold Electricity from/to the grid
Amount of Hydrogen consumed by Fuel Cells Stack
Amount of Hydrogen stored in Metal Hydride Tanks
Objective Function
to minimize
Cost of electricity
Energy produced by the Wing Generator
Consumption Profile
Data
Formulation and solution of
a Mixed Integer Non-Linear Programming Problem
P. L. Zervas, H. Sarimveis, J. Α. Palyvos, N. C. Markatos, Fuel Cell Science & Technology 2008, Copenhagen
NTUA, Chemical Engineering School, Computational Fluid Dynamics Unit

6. Overall electrical energy balance
Equations-Constraints
Electrolyzer and fuel cell
performance equations
Hydrogen mass balance
Energy balance at node 1
Energy balance at node 2
Energy balance at node 3
Inverter
Overall electrical energy balance
P. L. Zervas, H. Sarimveis, J. Α. Palyvos, N. C. Markatos, Fuel Cell Science & Technology 2008, Copenhagen
NTUA, Chemical Engineering School, Computational Fluid Dynamics Unit

7. Purchased Electricity
Objective Function
PDir (kW)
Wind Generator
Consumer
WGOut (kW)
ELIn (kW)
ELOut (m3/h)
FCIn (m3/h)
FCOut (kW)
INVIn (kW)
INVOut (kW)
CS (kW)
Metal Hydride Tanks 1
Electrolyzer
Fuel Cells 2
Inverter 3
EFG (kW)
ETG (kW)
Inventory
Purchased Electricity
Sold Electricity
P. L. Zervas, H. Sarimveis, J. Α. Palyvos, N. C. Markatos, Fuel Cell Science & Technology 2008, Copenhagen
NTUA, Chemical Engineering School, Computational Fluid Dynamics Unit

8. Specifications of the installed hybrid system
Scenario
Wind Generator
1.5kWp
Electrolyzer
0.25Nm3/h
Fuel Cell Stack
1.2kW
Metal Hydride
Tanks
5m3
P. L. Zervas, H. Sarimveis, J. Α. Palyvos, N. C. Markatos, Fuel Cell Science & Technology 2008, Copenhagen
NTUA, Chemical Engineering School, Computational Fluid Dynamics Unit

9. WG Power Generation-Load Profile (Deterministic)
time (h)
P. L. Zervas, H. Sarimveis, J. Α. Palyvos, N. C. Markatos, Fuel Cell Science & Technology 2008, Copenhagen
NTUA, Chemical Engineering School, Computational Fluid Dynamics Unit

10. WG Power Generation-Load Profile (Updated)
P. L. Zervas, H. Sarimveis, J. Α. Palyvos, N. C. Markatos, Fuel Cell Science & Technology 2008, Copenhagen
NTUA, Chemical Engineering School, Computational Fluid Dynamics Unit

11. Deterministic and Updated decision strategies with true WG Power Output and Consumption profiles
P. L. Zervas, H. Sarimveis, J. Α. Palyvos, N. C. Markatos, Fuel Cell Science & Technology 2008, Copenhagen
NTUA, Chemical Engineering School, Computational Fluid Dynamics Unit

12. Summary of Deterministic and Updated decision strategies (RESHS based on Wind Energy)
Total Purchased Energy
(kWh)
Total Discarded Energy
Objective function (€)
Deterministic schedule using predicted WGOut & CS temporal profiles
2.0305
0.0
0.18
Deterministic schedule using true WGOut & CS temporal profiles
23.619
3.36
Updated schedule using true
WGOut & CS temporal profiles
1.11
P. L. Zervas, H. Sarimveis, J. Α. Palyvos, N. C. Markatos, Fuel Cell Science & Technology 2008, Copenhagen
NTUA, Chemical Engineering School, Computational Fluid Dynamics Unit

13. PV array Power Generation-Load Profile (Updated)
P. L. Zervas, H. Sarimveis, J. Α. Palyvos, N. C. Markatos, Fuel Cell Science & Technology 2008, Copenhagen
NTUA, Chemical Engineering School, Computational Fluid Dynamics Unit

14. Deterministic and Updated decision strategies with true PV Power Output and Consumption profiles
P. L. Zervas, H. Sarimveis, J. Α. Palyvos, N. C. Markatos, Fuel Cell Science & Technology 2008, Copenhagen
NTUA, Chemical Engineering School, Computational Fluid Dynamics Unit

15. Deterministic and Updated decision strategies with true WG Power Output and Consumption profiles
P. L. Zervas, H. Sarimveis, J. Α. Palyvos, N. C. Markatos, Fuel Cell Science & Technology 2008, Copenhagen
NTUA, Chemical Engineering School, Computational Fluid Dynamics Unit

16. Conclusions
Development of a model that realistically describes the operation and the constraints of any hybrid system consisting of RES and hydrogen technologies
Formulation and solution of an optimization problem that minimizes the cost for purchasing electrical energy. The formulation takes into account the estimated RES power generation over a future prediction horizon and a profile of the energy demand over the same time horizon
The developed optimal making decision framework ensures the minimum electricity to be purchased from the grid making the system to operate in an autonomous way
P. L. Zervas, H. Sarimveis, J. Α. Palyvos, N. C. Markatos, Fuel Cell Science & Technology 2008, Copenhagen
NTUA, Chemical Engineering School, Computational Fluid Dynamics Unit

17. Finally the proposed model..
..may prove to be a very useful tool
for optimal decision making in
hybrid power generation systems which
combine RES and hydrogen technologies
P. L. Zervas, H. Sarimveis, J. Α. Palyvos, N. C. Markatos, Fuel Cell Science & Technology 2008, Copenhagen
NTUA, Chemical Engineering School, Computational Fluid Dynamics Unit

18. THANK YOU!!! pzervas@chemeng.ntua.gr
P. L. Zervas, H. Sarimveis, J. Α. Palyvos, N. C. Markatos, Fuel Cell Science & Technology 2008, Copenhagen
NTUA, Chemical Engineering School, Computational Fluid Dynamics Unit

19. NATIONAL TECHNICAL UNIVERSITY OF ATHENS
CHEMICAL ENGINEERING SCHOOL
COMPUTATIONAL FLUID DYNAMICS UNIT
“Optimal Decision Strategy for a Renewable Energy System consisting of Wind Generators and Fuel Cell Stacks”
P. L. Zervas*, H. Sarimveis, J. Α. Palyvos, N. C. Markatos
Fuel Cell Science & Technology 2008, 7-9 October, Copenhagen
P. L. Zervas, H. Sarimveis, J. Α. Palyvos, N. C. Markatos, Fuel Cell Science & Technology 2008, Copenhagen
NTUA, Chemical Engineering School, Computational Fluid Dynamics Unit

20. APPENDIX
P. L. Zervas, H. Sarimveis, J. Α. Palyvos, N. C. Markatos, Fuel Cell Science & Technology 2008, Copenhagen
NTUA, Chemical Engineering School, Computational Fluid Dynamics Unit

21. P. L. Zervas, H. Sarimveis, J. Α. Palyvos, N. C
P. L. Zervas, H. Sarimveis, J. Α. Palyvos, N. C. Markatos, Fuel Cell Science & Technology 2008, Copenhagen
NTUA, Chemical Engineering School, Computational Fluid Dynamics Unit

22. Electrolyzer – Fuel Cell performance equations
P. L. Zervas, H. Sarimveis, J. Α. Palyvos, N. C. Markatos, Fuel Cell Science & Technology 2008, Copenhagen
NTUA, Chemical Engineering School, Computational Fluid Dynamics Unit

23. Wind Generator performance equations
P. L. Zervas, H. Sarimveis, J. Α. Palyvos, N. C. Markatos, Fuel Cell Science & Technology 2008, Copenhagen
NTUA, Chemical Engineering School, Computational Fluid Dynamics Unit

24. Global Solar Irradiance Model based on NNM techniques
P. L. Zervas, H. Sarimveis, J. Α. Palyvos, N. C. Markatos, Fuel Cell Science & Technology 2008, Copenhagen
NTUA, Chemical Engineering School, Computational Fluid Dynamics Unit

25. Part I: Prediction of the PV Power Generation
Global Solar Irradiance on tilted surface
Location data, astronomical data, slope of the PV Array
Global Solar Irradiance on horizontal surface
Neural Network Model
Sun
Ambient Temperature
PVOut=f(GSIT,Tamb) V I
Photovoltaic Αrray
P. L. Zervas, H. Sarimveis, J. Α. Palyvos, N. C. Markatos, Fuel Cell Science & Technology 2008, Copenhagen
NTUA, Chemical Engineering School, Computational Fluid Dynamics Unit

26. August
P. L. Zervas, H. Sarimveis, J. Α. Palyvos, N. C. Markatos, Fuel Cell Science & Technology 2008, Copenhagen
NTUA, Chemical Engineering School, Computational Fluid Dynamics Unit

27. Summary of Deterministic and Updated decision strategies (RESHS based on Solar Energy)
Total Purchased Energy
(kWh)
Total Discarded Energy
Objective function (€)
Deterministic schedule using predicted PVOut & CS temporal profiles
9.7808
4.9563
0.63
Deterministic schedule using true PVOut & CS temporal profiles
1.64
Updated schedule using true
PVOut & CS temporal profiles
7.9778
0.79
P. L. Zervas, H. Sarimveis, J. Α. Palyvos, N. C. Markatos, Fuel Cell Science & Technology 2008, Copenhagen
NTUA, Chemical Engineering School, Computational Fluid Dynamics Unit

28. Decision strategies for November reference day

29. P. L. Zervas, H. Sarimveis, J. Α. Palyvos, N. C
P. L. Zervas, H. Sarimveis, J. Α. Palyvos, N. C. Markatos, Fuel Cell Science & Technology 2008, Copenhagen
NTUA, Chemical Engineering School, Computational Fluid Dynamics Unit

30. Decision strategies for March reference day
P. L. Zervas, H. Sarimveis, J. Α. Palyvos, N. C. Markatos, Fuel Cell Science & Technology 2008, Copenhagen
NTUA, Chemical Engineering School, Computational Fluid Dynamics Unit

31. Part II: PV Power Generation-Load Profile (Deterministic)
P. L. Zervas, H. Sarimveis, J. Α. Palyvos, N. C. Markatos, Fuel Cell Science & Technology 2008, Copenhagen
NTUA, Chemical Engineering School, Computational Fluid Dynamics Unit

32. Formulation of the LP optimization problem
minfTx A*x<=b
x Aeq*x=beq
lb<=x<=ub
x = linprog(f, [], [],Aeq,beq)
7 variables*72 time periods
4*72 time periods (equalities)
1*72 time periods (inequatlities)
P. L. Zervas, H. Sarimveis, J. Α. Palyvos, N. C. Markatos, Fuel Cell Science & Technology 2008, Copenhagen
NTUA, Chemical Engineering School, Computational Fluid Dynamics Unit

33. Objective Function Constraints: Part I
P. L. Zervas, H. Sarimveis, J. Α. Palyvos, N. C. Markatos, Fuel Cell Science & Technology 2008, Copenhagen
NTUA, Chemical Engineering School, Computational Fluid Dynamics Unit

34. Alternative Equations to previous “IF statements”
Constraints: Part II
Alternative Equations to previous “IF statements”
P. L. Zervas, H. Sarimveis, J. Α. Palyvos, N. C. Markatos, Fuel Cell Science & Technology 2008, Copenhagen
NTUA, Chemical Engineering School, Computational Fluid Dynamics Unit