Modeling of components aging increases system simulation accuracy in long term operation and the optimum decision variables would be more reliable and realistic. Moreover, the developed aging based optimal scheduling framework considers aging cost in the objective function as well as components aging in the optimization procedure. Aging cost is defined as the hourly preventive and corrective maintenance costs. As a result, optimal hourly schedule is affected by not only the income of selling electricity and operation cost but also the maintenance cost. Therefore, plant hourly profit is more realistic and the optimal schedule has a higher utility in comparison with other scheduling methodologies such as day-ahead method. The framework outputs determine the plant startup time, production level and maintenance intervals. This framework can be used in the sensitivity analysis of energy price and ambient conditions as well.

1. Degradation Based Framework for Long-Term Analysis
and Optimization of Energy Conversion Systems
By:
Tarannom Parhizkar
1
December 2020

2. 2Introduction
Introduction

3. 3
Performance
Time
Degradation mechanisms
Introduction Literature review Framework Application & results Conclusion
Diagnosing degradation mechanisms, helps to define energy conversion system
performance more accurately.
Degradation effects

4. Type of degradation Typical causes
Recoverable deg Clogging, scaling and build up of deposits on the working
surface
Non-recoverable deg Tear, loss of working surface, corrosion/oxidation, erosion.
A gradual and irreversible accumulation of damage that
occurs during a system’s life cycle. This process is
known as degradation
4Degradation definition
Introduction Literature review Framework Application & results Conclusion

5. 5
Investment cost
Operation cost
Maintenance cost
Income
Income
timet1 t2 t3 t4 t5 t6 t7 t8 t9 t10 t11 t12
timet1 t2 t3 t4 t5 t6 t7 t8 t9 t10 t11 t12
Cost
Introduction Literature review Framework Application & results Conclusion
Degradation long term economic effects

6. 6
Operating conditions have effect on energy conversion
components degradation rate.Performance
Time
Introduction Literature review Framework Application & results Conclusion
Research necessity
Different environ
and operational co

7. 7Research objective
Life time cost
DAMAGE
Life time income
$ $
Introduction Literature review Framework Application & results Conclusion
Developing the framework of “degradation based optimization (DBO)” model by
optimizing system operating conditions

8. 8Framework
Framework

9. 9
Developing the methodology of degradation based optimization (DBO) model to:
Maximizing plant lifetime profit
Minimizing cost of electricity
Maximizing power plant energy production
Framework objective
S.t
Technical/economical constraints
Introduction Literature review Framework Application & results Conclusion

10. 10
Operation cost
Income
Income
timet1 t2 t3 t4 t5 t6 t7 t8 t9 t10 t11 t12
timet1 t2 t3 t4 t5 t6 t7 t8 t9 t10 t11 t12
Cost
Framework advantages
Introduction Literature review Framework Application & results Conclusion
1

11. 11
Investment cost
Operation cost
Maintenance cost
Income
timet1 t2 t3 t4 t5 t6 t7 t8 t9 t10 t11 t12
Cost
$
operating hour
Maintenance cost
in a time interval
Introduction Literature review Framework Application & results Conclusion
Framework advantages
2

12. 12Framework models
Introduction Literature review Framework Application & results Conclusion
Optimization
Model
Optimum Operating Conditions Objective Function

13. 13
Optimization framework
Objective function
S.t.
Process models
Degradation mechanisms models
Operation and economical constraints
Optimization model
Introduction Literature review Framework Application & results Conclusion
( )
( )
0
0
y(t),u(t), x(t)
[ ( ), ( )]
y(t),u(t), x(t) .
f
f
t
t
Investment cost C
Min J u t x t
p dt
+
=
ò
ò
( )
0
y(t),u(t), x(t) .
ft
Max J p dt= ò
Productivity maximization
Cost of electricity minimization

14. 14
, , , )(Operating mode Fuel characteristic Ambient conditions Degf
Optimization framework
Objective function
S.t.
Process models
Degradation mechanisms models
Operation and economical constraints
Optimization model
Income
Fuel cost Maintenance cost
Introduction Literature review Framework Application & results Conclusion
Profit maximization
( ) ( ) ( ) ( )
( ) ( ) ( )
10
y(t),u(t), x(t) y(t) y(t),u(t), x(t) y(t)
y(t),u(t), x(t) y(t) y(t),u(t), x(t)
f
p h
t m
f a
m m
m
Max Z p C h C
hr C C dr
=
= ´ + ´
æ ö
- ´ + ´ç ÷
è ø
åò

15. 15
$
MC dr
dr
= ´å
Optimization framework
Objective function
S.t.
Process models
Degradation mechanisms models
Operation and economical constraints
Optimization model
Maintenance cost
Introduction Literature review Framework Application & results Conclusion
Operating condition
$
.
.
MC kW hr
kW hr
= ´å
$
MC hr
hr
= ´å
Time
MC
$
MC EOH
EOH
= ´å

16. 16
11 12 1
21 22 2
1 2
...
...
. . . .
. . . .
. . . .
...
1,2,..,24; 1,2,..,12; 1
n
n
k
ij
mnm m
I I I
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I
I I I
n m k
é ù
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ê ú
ê ú
ê ú
ê ú
ê ú
ê úë û
=
= = =
Operating mode
Fuel characteristic
Ambient conditions
Process
model
Output power
Useful generated heat
Heat rate
11 12 1
21 22 2
1 2
...
...
. . . .
. . . .
. . . .
...
1,2,..,24; 1,2,..,12; 1
n
n
k
ij
mnm m
O O O
O O O
O
O O O
n m k
é ù
ê ú
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ê ú
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ê ú
ê ú
ê úë û
=
= = =
Optimization framework
Objective function
S.t.
Process models
Degradation mechanisms models
Operation and economical constraints
Introduction Literature review Framework Application & results Conclusion
Process models

17. 17
Optimization framework
Objective function
S.t.
Process models
Degradation mechanisms models
Operation and economical constraints
Degradation models
Introduction Literature review Framework Application & results Conclusion
11 12 1
21 22 2
1 2
...
...
. . . .
. . . .
. . . .
...
1,2,..,24; 1,2,..,12; 1
n
n
k
ij
mnm m
I I I
I I I
I
I I I
n m k
é ù
ê ú
ê ú
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ê ú
ê ú
ê ú
ê ú
ê ú
ê úë û
=
= = =
Operating mode
Fuel characteristic
Ambient conditions
Operation time
Process
model
11 12 1
21 22 2
1 2
...
...
. . . .
. . . .
. . . .
...
1,2,..,24; 1,2,..,12; 1
n
n
k
ij
mnm m
O O O
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O
O O O
n m k
é ù
ê ú
ê ú
ê ú
ê ú
ê ú
ê ú
ê ú
ê ú
ê úë û
=
= = =
Degradation
mechanism
model
Output power, Output power deterioration
Useful generated heat, Useful generated heat deterioration
Heat rate, Heat rate increase

18. 18
Optimization framework
Objective function
S.t.
Process models
Degradation mechanisms models
Operation and economical constraints
Operation and economical constraints
Introduction Literature review Framework Application & results Conclusion
11 12 1
21 22 2
1 2
...
...
. . . .
. . . .
. . . .
...
1,2,..,24; 1,2,..,12; 1
n
n
k
ij
mnm m
I I I
I I I
I
I I I
n m k
é ù
ê ú
ê ú
ê ú
ê ú
ê ú
ê ú
ê ú
ê ú
ê úë û
=
= = =
Operating mode
Fuel characteristic
Ambient conditions
Operation time
Process
model
11 12 1
21 22 2
1 2
...
...
. . . .
. . . .
. . . .
...
1,2,..,24; 1,2,..,12; 1
n
n
k
ij
mnm m
O O O
O O O
O
O O O
n m k
é ù
ê ú
ê ú
ê ú
ê ú
ê ú
ê ú
ê ú
ê ú
ê úë û
=
= = =
Degradation
mechanism
model
Output power, Output power deterioration
Useful generated heat, Useful generated heat deterioration
Heat rate, Heat rate increase

19. 19
Objective function
0
[ ( ), ( ), ]fmin J u t x t t
( , , , ) 0g x x u t =!
( , , , ) 0h x x u t ³!
Initial operating points
0 0( )x t x=
min max( )x x t x£ £
min max( )u u t u£ £
Model equations
Model restrictions
Optimization
model
Process
model
Degradation
model
Introduction Literature review Framework Application & results Conclusion
Degradation based optimization framework

20. 20
Optimum operation parameter through system life time
System performance (efficiency, output power)
Operating and design parameters
Degradation
model
Optimization
model
Process model
Introduction Literature review Framework Application & results Conclusion
Framework data flow
Degradation based process model

21. 21
References:
[1] Parhizkar, T., & Roshandel, R. (2017). Long term performance degradation analysis
and
optimization of anode supported solid oxide fuel cell stacks. Energy Conversion and
Management, 133, 20-30.
[2] Roshandel, R., & Parhizkar, T. (2016). Degradation based optimization framework for
long term applications of energy systems, case study: Solid oxide fuel cell stacks.
Energy, 107, 172-181.
[3] Parhizkar, T., Mosleh, A., & Roshandel, R. (2017). Aging based optimal scheduling
framework for power plants using equivalent operating hour approach. Applied Energy,
205, 1345-1363.
[4] Roshandel, R., & Parhizgar, T. (2013). A new approach to optimize the operating
conditions of a polymer electrolyte membrane fuel cell based on degradation
mechanisms. Energy Systems, 4(3), 219-237. Chicago
[5] Sotoodeh, A. F., Parhizkar, T., Mehrgoo, M., Ghazi, M., & Amidpour, M. (2019). Aging
based design and operation optimization of organic rankine cycle systems. Energy
Conversion and Management, 199, 111892. Chicago

22. 22
The key is not to prioritize what's on your
schedule, but to schedule your priorities.
Stephen Covey