Talk at the 20th Conference of the International Federation of Operational Research Societies, Barcelona, Spain

1. Risk Manag.
planning energy
systems
IFORS 2014
July 17
E.L. Cano
Introduction
The problem
Background
Modeling
Deterministic
Modelling
Stochastic Modelling
Risk Management
Conclusions
Summary
Stochastic Optimization and Risk Management
for an ecient planning of
buildings' energy systems
Emilio L. Cano, Javier M. Moguerza
and Antonio Alonso-Ayuso
Department of Computer Science and Statistics
Rey Juan Carlos University
20th Conference of the International Federation
of Operational Research Societies
Barcelona, July 17, 2014
20th Conference of the International Federation of Operational Research Societies 1/36

2. Risk Manag.
planning energy
systems
IFORS 2014
July 17
E.L. Cano
Introduction
The problem
Background
Modeling
Deterministic
Modelling
Stochastic Modelling
Risk Management
Conclusions
Summary
Outline
1 Introduction
The problem
Background
2 Modeling
Deterministic Modelling
Stochastic Modelling
Risk Management
3 Conclusions
Summary
20th Conference of the International Federation of Operational Research Societies 2/36

3. Risk Manag.
planning energy
systems
IFORS 2014
July 17
E.L. Cano
Introduction
The problem
Background
Modeling
Deterministic
Modelling
Stochastic Modelling
Risk Management
Conclusions
Summary
Outline
1 Introduction
The problem
Background
2 Modeling
Deterministic Modelling
Stochastic Modelling
Risk Management
3 Conclusions
Summary
20th Conference of the International Federation of Operational Research Societies 3/36

4. Risk Manag.
planning energy
systems
IFORS 2014
July 17
E.L. Cano
Introduction
The problem
Background
Modeling
Deterministic
Modelling
Stochastic Modelling
Risk Management
Conclusions
Summary
Global changes, local challenges
Global
Regulations: emissions,
eciency
De-regulations: market
Global warming
Resources scarcity
Global markets
20th Conference of the International Federation of Operational Research Societies 4/36

5. Risk Manag.
planning energy
systems
IFORS 2014
July 17
E.L. Cano
Introduction
The problem
Background
Modeling
Deterministic
Modelling
Stochastic Modelling
Risk Management
Conclusions
Summary
Global changes, local challenges
Global
Regulations: emissions,
eciency
De-regulations: market
Global warming
Resources scarcity
Global markets
Local
Users' comfort
Security
Availability
Limited budget
New options
20th Conference of the International Federation of Operational Research Societies 4/36

6. Risk Manag.
planning energy
systems
IFORS 2014
July 17
E.L. Cano
Introduction
The problem
Background
Modeling
Deterministic
Modelling
Stochastic Modelling
Risk Management
Conclusions
Summary
Global changes, local challenges
Global
Regulations: emissions,
eciency
De-regulations: market
Global warming
Resources scarcity
Global markets
Local
Users' comfort
Security
Availability
Limited budget
New options
20th Conference of the International Federation of Operational Research Societies 4/36

7. Risk Manag.
planning energy
systems
IFORS 2014
July 17
E.L. Cano
Introduction
The problem
Background
Modeling
Deterministic
Modelling
Stochastic Modelling
Risk Management
Conclusions
Summary
Global changes, local challenges
Global
Regulations: emissions,
eciency
De-regulations: market
Global warming
Resources scarcity
Global markets
Local
Users' comfort
Security
Availability
Limited budget
New options
20th Conference of the International Federation of Operational Research Societies 4/36

8. Risk Manag.
planning energy
systems
IFORS 2014
July 17
E.L. Cano
Introduction
The problem
Background
Modeling
Deterministic
Modelling
Stochastic Modelling
Risk Management
Conclusions
Summary
Global changes, local challenges
Global
Regulations: emissions,
eciency
De-regulations: market
Global warming
Resources scarcity
Global markets
Local
Users' comfort
Security
Availability
Limited budget
New options
20th Conference of the International Federation of Operational Research Societies 4/36

9. Risk Manag.
planning energy
systems
IFORS 2014
July 17
E.L. Cano
Introduction
The problem
Background
Modeling
Deterministic
Modelling
Stochastic Modelling
Risk Management
Conclusions
Summary
Energy Systems
20th Conference of the International Federation of Operational Research Societies 5/36

10. Building systems energy
ow: Sankey diagram
Campus Pinkafeld test site

11. Building systems energy
ow: Sankey diagram
Demand side: requirements, uncertainty

12. Building systems energy
ow: Sankey diagram
Supply side: Markets, renewables

13. Building systems energy
ow: Sankey diagram
Strategic decisions are the goal

14. Building systems energy
ow: Sankey diagram
Operational performance interdependent with strategic
decisions

15. Risk Manag.
planning energy
systems
IFORS 2014
July 17
E.L. Cano
Introduction
The problem
Background
Modeling
Deterministic
Modelling
Stochastic Modelling
Risk Management
Conclusions
Summary
Outline
1 Introduction
The problem
Background
2 Modeling
Deterministic Modelling
Stochastic Modelling
Risk Management
3 Conclusions
Summary
20th Conference of the International Federation of Operational Research Societies 7/36

16. Risk Manag.
planning energy
systems
IFORS 2014
July 17
E.L. Cano
Introduction
The problem
Background
Modeling
Deterministic
Modelling
Stochastic Modelling
Risk Management
Conclusions
Summary
EnRiMa Project
20th Conference of the International Federation of Operational Research Societies 8/36

17. Risk Manag.
planning energy
systems
IFORS 2014
July 17
E.L. Cano
Introduction
The problem
Background
Modeling
Deterministic
Modelling
Stochastic Modelling
Risk Management
Conclusions
Summary
EnRiMa Models
EnRiMa DSS
Strategic
Module
Strategic DVs
Strategic
Constraints
Upper-Level
Operational DVs
Upper-Level
Energy-Balance
Constraints
Operational
Module
Lower-Level
Operational DVs
Lower-Level
Energy-Balance
Constraints
20th Conference of the International Federation of Operational Research Societies 9/36

18. Risk Manag.
planning energy
systems
IFORS 2014
July 17
E.L. Cano
Introduction
The problem
Background
Modeling
Deterministic
Modelling
Stochastic Modelling
Risk Management
Conclusions
Summary
Decision Support Systems (DSS)
20th Conference of the International Federation of Operational Research Societies 10/36

19. Risk Manag.
planning energy
systems
IFORS 2014
July 17
E.L. Cano
Introduction
The problem
Background
Modeling
Deterministic
Modelling
Stochastic Modelling
Risk Management
Conclusions
Summary
Decision Support Systems (DSS)
Model: Symbolic Model Speci

20. cation (SMS)
20th Conference of the International Federation of Operational Research Societies 10/36

21. Risk Manag.
planning energy
systems
IFORS 2014
July 17
E.L. Cano
Introduction
The problem
Background
Modeling
Deterministic
Modelling
Stochastic Modelling
Risk Management
Conclusions
Summary
Decision Support Systems (DSS)
Model: Symbolic Model Speci

22. cation (SMS)
Data: Statistical analysis
20th Conference of the International Federation of Operational Research Societies 10/36

23. Risk Manag.
planning energy
systems
IFORS 2014
July 17
E.L. Cano
Introduction
The problem
Background
Modeling
Deterministic
Modelling
Stochastic Modelling
Risk Management
Conclusions
Summary
Decision Support Systems (DSS)
Model: Symbolic Model Speci

24. cation (SMS)
Data: Statistical analysis
Framework: Stakeholders dialog
20th Conference of the International Federation of Operational Research Societies 10/36

25. Risk Manag.
planning energy
systems
IFORS 2014
July 17
E.L. Cano
Introduction
The problem
Background
Modeling
Deterministic
Modelling
Stochastic Modelling
Risk Management
Conclusions
Summary
Decision Support Systems (DSS)
Algorithms
Model
Symbolic model
Variables, relations
Underlying theory
Methodology, technique
Uncertainty modelling
Data
Deterministic data
Uncertain data -
Stochastic processes
Data analysis
Solution
Data treatment
Analysis
Visualization
DSS
Stakeholders Dialog
Interpretation
Model: Symbolic Model Speci

26. cation (SMS)
Data: Statistical analysis
Framework: Stakeholders dialog
20th Conference of the International Federation of Operational Research Societies 10/36

27. Risk Manag.
planning energy
systems
IFORS 2014
July 17
E.L. Cano
Introduction
The problem
Background
Modeling
Deterministic
Modelling
Stochastic Modelling
Risk Management
Conclusions
Summary
Outline
1 Introduction
The problem
Background
2 Modeling
Deterministic Modelling
Stochastic Modelling
Risk Management
3 Conclusions
Summary
20th Conference of the International Federation of Operational Research Societies 11/36

28. Risk Manag.
planning energy
systems
IFORS 2014
July 17
E.L. Cano
Introduction
The problem
Background
Modeling
Deterministic
Modelling
Stochastic Modelling
Risk Management
Conclusions
Summary
Time Resolution
Representative short-term periods within long-term periods
20th Conference of the International Federation of Operational Research Societies 12/36

29. Risk Manag.
planning energy
systems
IFORS 2014
July 17
E.L. Cano
Introduction
The problem
Background
Modeling
Deterministic
Modelling
Stochastic Modelling
Risk Management
Conclusions
Summary
Time Resolution
Strategic decisions: horizon 15-20 years
20th Conference of the International Federation of Operational Research Societies 12/36

30. Risk Manag.
planning energy
systems
IFORS 2014
July 17
E.L. Cano
Introduction
The problem
Background
Modeling
Deterministic
Modelling
Stochastic Modelling
Risk Management
Conclusions
Summary
Time Resolution
Operational decisions (energy
ows): hours
20th Conference of the International Federation of Operational Research Societies 12/36

31. Risk Manag.
planning energy
systems
IFORS 2014
July 17
E.L. Cano
Introduction
The problem
Background
Modeling
Deterministic
Modelling
Stochastic Modelling
Risk Management
Conclusions
Summary
Model Sets
Time resolution
p Long-term period; p 2 P
m Mid-term representative period; m 2M
t Short-term period; t 2 T
The model includes the realization of short-term decisions (t)
that are scaled to a long-term period (p) through a mid-term
representative pro

32. le (m).
20th Conference of the International Federation of Operational Research Societies 13/36

33. Risk Manag.
planning energy
systems
IFORS 2014
July 17
E.L. Cano
Introduction
The problem
Background
Modeling
Deterministic
Modelling
Stochastic Modelling
Risk Management
Conclusions
Summary
Model Sets
Time resolution
p Long-term period; p 2 P
m Mid-term representative period; m 2M
t Short-term period; t 2 T
The model includes the realization of short-term decisions (t)
that are scaled to a long-term period (p) through a mid-term
representative pro

34. le (m).
Energy, technologies, markets, emissions
i Technology (generators, storage, passive); i 2 I
k Energy type; k 2 K
n Energy market (contract taris); n 2 N
l Pollutant; l 2 L
20th Conference of the International Federation of Operational Research Societies 13/36

35. Risk Manag.
planning energy
systems
IFORS 2014
July 17
E.L. Cano
Introduction
The problem
Background
Modeling
Deterministic
Modelling
Stochastic Modelling
Risk Management
Conclusions
Summary
Model Features
Modelling at the building level
20th Conference of the International Federation of Operational Research Societies 14/36

36. Risk Manag.
planning energy
systems
IFORS 2014
July 17
E.L. Cano
Introduction
The problem
Background
Modeling
Deterministic
Modelling
Stochastic Modelling
Risk Management
Conclusions
Summary
Model Features
Modelling at the building level
Technologies installation and decommissioning
20th Conference of the International Federation of Operational Research Societies 14/36

37. Risk Manag.
planning energy
systems
IFORS 2014
July 17
E.L. Cano
Introduction
The problem
Background
Modeling
Deterministic
Modelling
Stochastic Modelling
Risk Management
Conclusions
Summary
Model Features
Modelling at the building level
Technologies installation and decommissioning
Energy
ows (short term) along with investment (long
term)
20th Conference of the International Federation of Operational Research Societies 14/36

38. Risk Manag.
planning energy
systems
IFORS 2014
July 17
E.L. Cano
Introduction
The problem
Background
Modeling
Deterministic
Modelling
Stochastic Modelling
Risk Management
Conclusions
Summary
Model Features
Modelling at the building level
Technologies installation and decommissioning
Energy
ows (short term) along with investment (long
term)
Technologies aging through the a index
20th Conference of the International Federation of Operational Research Societies 14/36

39. Risk Manag.
planning energy
systems
IFORS 2014
July 17
E.L. Cano
Introduction
The problem
Background
Modeling
Deterministic
Modelling
Stochastic Modelling
Risk Management
Conclusions
Summary
Model Features
Modelling at the building level
Technologies installation and decommissioning
Energy
ows (short term) along with investment (long
term)
Technologies aging through the a index
Emissions
20th Conference of the International Federation of Operational Research Societies 14/36

40. Risk Manag.
planning energy
systems
IFORS 2014
July 17
E.L. Cano
Introduction
The problem
Background
Modeling
Deterministic
Modelling
Stochastic Modelling
Risk Management
Conclusions
Summary
Model Features
Modelling at the building level
Technologies installation and decommissioning
Energy
ows (short term) along with investment (long
term)
Technologies aging through the a index
Emissions
Eciency
20th Conference of the International Federation of Operational Research Societies 14/36

41. Risk Manag.
planning energy
systems
IFORS 2014
July 17
E.L. Cano
Introduction
The problem
Background
Modeling
Deterministic
Modelling
Stochastic Modelling
Risk Management
Conclusions
Summary
Model Features
Modelling at the building level
Technologies installation and decommissioning
Energy
ows (short term) along with investment (long
term)
Technologies aging through the a index
Emissions
Eciency
Dierent energy types
20th Conference of the International Federation of Operational Research Societies 14/36

42. Risk Manag.
planning energy
systems
IFORS 2014
July 17
E.L. Cano
Introduction
The problem
Background
Modeling
Deterministic
Modelling
Stochastic Modelling
Risk Management
Conclusions
Summary
Model Features
Modelling at the building level
Technologies installation and decommissioning
Energy
ows (short term) along with investment (long
term)
Technologies aging through the a index
Emissions
Eciency
Dierent energy types
Dierent technology types: generation, storage, passive
measures
20th Conference of the International Federation of Operational Research Societies 14/36

43. Risk Manag.
planning energy
systems
IFORS 2014
July 17
E.L. Cano
Introduction
The problem
Background
Modeling
Deterministic
Modelling
Stochastic Modelling
Risk Management
Conclusions
Summary
Model Features
Modelling at the building level
Technologies installation and decommissioning
Energy
ows (short term) along with investment (long
term)
Technologies aging through the a index
Emissions
Eciency
Dierent energy types
Dierent technology types: generation, storage, passive
measures
Objective: minimize total discounted cost
20th Conference of the International Federation of Operational Research Societies 14/36

44. Risk Manag.
planning energy
systems
IFORS 2014
July 17
E.L. Cano
Introduction
The problem
Background
Modeling
Deterministic
Modelling
Stochastic Modelling
Risk Management
Conclusions
Summary
Energy-dispatching Decision Flow
Renewables
Market
Demand
Purchases
Generation
Storage
N
K
I
I
Sales
K y
u
u
u
w
u
w
z
ri
ri
ro
Technologies
Technologies
r
20th Conference of the International Federation of Operational Research Societies 15/36

45. Risk Manag.
planning energy
systems
IFORS 2014
July 17
E.L. Cano
Introduction
The problem
Background
Modeling
Deterministic
Modelling
Stochastic Modelling
Risk Management
Conclusions
Summary
Energy-dispatching Decision Flow
Renewables
Market
Demand
Purchases
Generation
Storage
N
K
I
I
Sales
K y
u
u
u
w
u
w
z
ri
ri
ro
Technologies
Technologies
r
Cano EL, Groissbock M, Moguerza JM and Stadler M (2014).
A Strategic Optimization Model for Energy Systems Planning.
Energy and Buildings.
http://dx.doi.org/10.1016/j.enbuild.2014.06.030.
20th Conference of the International Federation of Operational Research Societies 15/36

46. Risk Manag.
planning energy
systems
IFORS 2014
July 17
E.L. Cano
Introduction
The problem
Background
Modeling
Deterministic
Modelling
Stochastic Modelling
Risk Management
Conclusions
Summary
Outline
1 Introduction
The problem
Background
2 Modeling
Deterministic Modelling
Stochastic Modelling
Risk Management
3 Conclusions
Summary
20th Conference of the International Federation of Operational Research Societies 16/36

47. Risk Manag.
planning energy
systems
IFORS 2014
July 17
E.L. Cano
Introduction
The problem
Background
Modeling
Deterministic
Modelling
Stochastic Modelling
Risk Management
Conclusions
Summary
Deterministic vs. Stochastic
Five periods, two technologies (CHP, PV), only electricity.
100 scenarios simulation
80
60
40
20
2013 2014 2015 2016
Demand level (kW)
Energy demand
2500
2000
1500
1000
500
0
2500
2000
1500
1000
500
0
2500
2000
1500
1000
500
0
CHP PV RTE
2013 2014 2015 2016 2017
EUR/kW
Investment cost
0.3
0.2
0.1
0.3
0.2
0.1
CHP RTE
2013 2014 2015 2016
EUR/kWh
Scenario
100
75
50
25
Energy price
20th Conference of the International Federation of Operational Research Societies 17/36

48. Risk Manag.
planning energy
systems
IFORS 2014
July 17
E.L. Cano
Introduction
The problem
Background
Modeling
Deterministic
Modelling
Stochastic Modelling
Risk Management
Conclusions
Summary
Deterministic vs. Stochastic
Five periods, two technologies (CHP, PV), only electricity.
100 scenarios simulation
80
60
40
20
2013 2014 2015 2016
Demand level (kW)
Energy demand
2500
2000
1500
1000
500
0
2500
2000
1500
1000
500
0
2500
2000
1500
1000
500
0
CHP PV RTE
2013 2014 2015 2016 2017
EUR/kW
Investment cost
0.3
0.2
0.1
0.3
0.2
0.1
CHP RTE
2013 2014 2015 2016
EUR/kWh
Scenario
100
75
50
25
Energy price
Fdet (x det ) = 66; 920 EUR.
20th Conference of the International Federation of Operational Research Societies 17/36

49. Risk Manag.
planning energy
systems
IFORS 2014
July 17
E.L. Cano
Introduction
The problem
Background
Modeling
Deterministic
Modelling
Stochastic Modelling
Risk Management
Conclusions
Summary
Deterministic vs. Stochastic
Five periods, two technologies (CHP, PV), only electricity.
100 scenarios simulation
80
60
40
20
2013 2014 2015 2016
Demand level (kW)
Energy demand
2500
2000
1500
1000
500
0
2500
2000
1500
1000
500
0
2500
2000
1500
1000
500
0
CHP PV RTE
2013 2014 2015 2016 2017
EUR/kW
Investment cost
0.3
0.2
0.1
0.3
0.2
0.1
CHP RTE
2013 2014 2015 2016
EUR/kWh
Scenario
100
75
50
25
Energy price
Fdet (x det ) = 66; 920 EUR.
Fsto(x sto) = 68; 595 EUR.
20th Conference of the International Federation of Operational Research Societies 17/36

50. Risk Manag.
planning energy
systems
IFORS 2014
July 17
E.L. Cano
Introduction
The problem
Background
Modeling
Deterministic
Modelling
Stochastic Modelling
Risk Management
Conclusions
Summary
Deterministic vs. Stochastic
Five periods, two technologies (CHP, PV), only electricity.
100 scenarios simulation
80
60
40
20
2013 2014 2015 2016
Demand level (kW)
Energy demand
2500
2000
1500
1000
500
0
2500
2000
1500
1000
500
0
2500
2000
1500
1000
500
0
CHP PV RTE
2013 2014 2015 2016 2017
EUR/kW
Investment cost
0.3
0.2
0.1
0.3
0.2
0.1
CHP RTE
2013 2014 2015 2016
EUR/kWh
Scenario
100
75
50
25
Energy price
Fdet (x det ) = 66; 920 EUR.
Fsto(x sto) = 68; 595 EUR.
VSS = Fsto(x det ) Fsto(x sto) = 1
20th Conference of the International Federation of Operational Research Societies 17/36

51. Risk Manag.
planning energy
systems
IFORS 2014
July 17
E.L. Cano
Introduction
The problem
Background
Modeling
Deterministic
Modelling
Stochastic Modelling
Risk Management
Conclusions
Summary
Deterministic vs. Stochastic
Five periods, two technologies (CHP, PV), only electricity.
100 scenarios simulation
80
60
40
20
2013 2014 2015 2016
Demand level (kW)
Energy demand
2500
2000
1500
1000
500
0
2500
2000
1500
1000
500
0
2500
2000
1500
1000
500
0
CHP PV RTE
2013 2014 2015 2016 2017
EUR/kW
Investment cost
0.3
0.2
0.1
0.3
0.2
0.1
CHP RTE
2013 2014 2015 2016
EUR/kWh
Scenario
100
75
50
25
Energy price
Fdet (x det ) = 66; 920 EUR. Infeasible 56/100
Fsto(x sto) = 68; 595 EUR.
VSS = Fsto(x det ) Fsto(x sto) = 1
20th Conference of the International Federation of Operational Research Societies 17/36

52. Risk Manag.
planning energy
systems
IFORS 2014
July 17
E.L. Cano
Introduction
The problem
Background
Modeling
Deterministic
Modelling
Stochastic Modelling
Risk Management
Conclusions
Summary
Deterministic vs. Stochastic
Five periods, two technologies (CHP, PV), only electricity.
100 scenarios simulation
80
60
40
20
2013 2014 2015 2016
Demand level (kW)
Energy demand
2500
2000
1500
1000
500
0
2500
2000
1500
1000
500
0
2500
2000
1500
1000
500
0
CHP PV RTE
2013 2014 2015 2016 2017
EUR/kW
Investment cost
0.3
0.2
0.1
0.3
0.2
0.1
CHP RTE
2013 2014 2015 2016
EUR/kWh
Scenario
100
75
50
25
Energy price
Fdet (x det ) = 66; 920 EUR. Infeasible 56/100
Fsto(x sto) = 68; 595 EUR. Robust, optimal against all
VSS = Fsto(x det ) Fsto(x sto) = 1
20th Conference of the International Federation of Operational Research Societies 17/36

53. Risk Manag.
planning energy
systems
IFORS 2014
July 17
E.L. Cano
Introduction
The problem
Background
Modeling
Deterministic
Modelling
Stochastic Modelling
Risk Management
Conclusions
Summary
Scenario Trees
20th Conference of the International Federation of Operational Research Societies 18/36

54. Risk Manag.
planning energy
systems
IFORS 2014
July 17
E.L. Cano
Introduction
The problem
Background
Modeling
Deterministic
Modelling
Stochastic Modelling
Risk Management
Conclusions
Summary
Scenario Trees
Time
v Tree node
m Representative pro

55. le
t Short-term period
Tree structure
PRv Probability of the node
Pa(v) Parent of the node
PTv Period of the node
20th Conference of the International Federation of Operational Research Societies 18/36

56. Risk Manag.
planning energy
systems
IFORS 2014
July 17
E.L. Cano
Introduction
The problem
Background
Modeling
Deterministic
Modelling
Stochastic Modelling
Risk Management
Conclusions
Summary
Strategic Decisions
Decision Variables
hv
k;n Tari choice;
xivi
Technologies to install;
xdv;a
i Technologies to decommission;
x v;a
i Technologies installed;
xcvi
Available capacity of technologies.
20th Conference of the International Federation of Operational Research Societies 19/36

57. Risk Manag.
planning energy
systems
IFORS 2014
July 17
E.L. Cano
Introduction
The problem
Background
Modeling
Deterministic
Modelling
Stochastic Modelling
Risk Management
Conclusions
Summary
Strategic Decisions
Decision Variables
hv
k;n Tari choice;
xivi
Technologies to install;
xdv;a
i Technologies to decommission;
x v;a
i Technologies installed;
xcvi
Available capacity of technologies.
Relations
x v;0
i = xivi
x v;a
i = x v0;a1
i xdv;a
i
xcvi
= Gi
X
a
AGai
x v;a
i
X
n
hv
k;n = 1
20th Conference of the International Federation of Operational Research Societies 19/36

58. Risk Manag.
planning energy
systems
IFORS 2014
July 17
E.L. Cano
Introduction
The problem
Background
Modeling
Deterministic
Modelling
Stochastic Modelling
Risk Management
Conclusions
Summary
Embedded Operational Decisions
Basic variables
uv;m;t
k;n Purchase of energy (kWh)
wv;m;t
k;n Sale of energy (kWh)
yv;m;t
i ;k Input of energy k to technology i (kWh)
qi v;m;t
i ;k Energy type k added to storage technology i
(kWh)
qov;m;t
i ;k Energy type k released from storage technology i
(kWh)
20th Conference of the International Federation of Operational Research Societies 20/36

59. Risk Manag.
planning energy
systems
IFORS 2014
July 17
E.L. Cano
Introduction
The problem
Background
Modeling
Deterministic
Modelling
Stochastic Modelling
Risk Management
Conclusions
Summary
Embedded Operational Decisions
Basic variables
uv;m;t
k;n Purchase of energy (kWh)
wv;m;t
k;n Sale of energy (kWh)
yv;m;t
i ;k Input of energy k to technology i (kWh)
qi v;m;t
i ;k Energy type k added to storage technology i
(kWh)
qov;m;t
i ;k Energy type k released from storage technology i
(kWh)
Calculated variables
z v;m;t
i ;k Output of energy type k from technology i (kWh)
r v;m;t
i ;k Energy type k to be stored in technology j (kWh)
ev;m;t Energy consumption (kWh)
20th Conference of the International Federation of Operational Research Societies 20/36

60. Risk Manag.
planning energy
systems
IFORS 2014
July 17
E.L. Cano
Introduction
The problem
Background
Modeling
Deterministic
Modelling
Stochastic Modelling
Risk Management
Conclusions
Summary
Energy Balance and Links
Energy Balance
X
i2IGen
z v;m;t
i;k
X
i2IGen
yv;m;t
i;k +
X
n2NPur(k)
uv;m;t
k;n
X
n2NS(k)
wv;m;t
k;n
+
X
i2ISto
rov;m;t
i;k ri v;m;t
i;k
= Dv;m;t
k
1
X
i2IPU
ODvi
;k xcvi
!
20th Conference of the International Federation of Operational Research Societies 21/36

61. Risk Manag.
planning energy
systems
IFORS 2014
July 17
E.L. Cano
Introduction
The problem
Background
Modeling
Deterministic
Modelling
Stochastic Modelling
Risk Management
Conclusions
Summary
Energy Balance and Links
Energy Balance
X
i2IGen
z v;m;t
i;k
X
i2IGen
yv;m;t
i;k +
X
n2NPur(k)
uv;m;t
k;n
X
n2NS(k)
wv;m;t
k;n
+
X
i2ISto
rov;m;t
i;k ri v;m;t
i;k
= Dv;m;t
k
1
X
i2IPU
ODvi
;k xcvi
!
Strategic Operational links
z v;m;t
i;k DTm AFv;m;t
i xcvi
OAvi
;k xcvi
r v;m;t
i;k OBvi
;k xcvi
uv;m;t
k;n hv
k;n MEk;n DTm
20th Conference of the International Federation of Operational Research Societies 21/36

62. Risk Manag.
planning energy
systems
IFORS 2014
July 17
E.L. Cano
Introduction
The problem
Background
Modeling
Deterministic
Modelling
Stochastic Modelling
Risk Management
Conclusions
Summary
Objectives
Minimize total discounted expected cost
c =
X
v2V
(1 + DR)PTv
PRv cnv
Minimize total expected emissions
p =
X
v2V
PRv
X
l2L
pnvl
Minimize total expected primary energy consumption
et =
X
v2V
PRv env
20th Conference of the International Federation of Operational Research Societies 22/36

63. Risk Manag.
planning energy
systems
IFORS 2014
July 17
E.L. Cano
Introduction
The problem
Background
Modeling
Deterministic
Modelling
Stochastic Modelling
Risk Management
Conclusions
Summary
Objectives (cont.)
Minimize total discounted expected cost
c =
X
v2V
(1 + DR)PTv
PRv cnv
cnv =
X
i2I
snvi
+
X
i2I
mnvi
+
X
k2K;n2Nk
Pur
ucvk
;n
X
k2K;n2Nk
Sal
wcvk
;n
+
X
i2IGen
zcvi
+
X
i2ISto
rcvi
8 v 2 V
20th Conference of the International Federation of Operational Research Societies 23/36

64. Risk Manag.
planning energy
systems
IFORS 2014
July 17
E.L. Cano
Introduction
The problem
Background
Modeling
Deterministic
Modelling
Stochastic Modelling
Risk Management
Conclusions
Summary
Objectives (cont.)
Minimize total expected emissions
p =
X
v2V
PRv
X
l2L
pnvl
pnvl
=
X
m2M
DMm
X
t2T m
Tm
0
@
X
k2Ki In
LHvk
;l yv;m;t
i ;k
+
X
k2K;n2Nk
Pur
LCvk
;l ;n uv;m;t
k;n
1
A8 l 2 L; v 2 V
20th Conference of the International Federation of Operational Research Societies 24/36

65. Risk Manag.
planning energy
systems
IFORS 2014
July 17
E.L. Cano
Introduction
The problem
Background
Modeling
Deterministic
Modelling
Stochastic Modelling
Risk Management
Conclusions
Summary
Objectives (cont.)
Minimize total expected energy consumption
et =
X
v2V
PRv env
env =
X
m2M
DMm
X
t2T m
Tm
ev;m;t 8 v 2 V
ev;m;t =
X
k2K;n2Nk
Pur
Bk;n uv;m;t
k;n
8 v 2 V; m 2M; t 2 T m
Tm
20th Conference of the International Federation of Operational Research Societies 25/36

66. Risk Manag.
planning energy
systems
IFORS 2014
July 17
E.L. Cano
Introduction
The problem
Background
Modeling
Deterministic
Modelling
Stochastic Modelling
Risk Management
Conclusions
Summary
Outline
1 Introduction
The problem
Background
2 Modeling
Deterministic Modelling
Stochastic Modelling
Risk Management
3 Conclusions
Summary
20th Conference of the International Federation of Operational Research Societies 26/36

67. Risk Manag.
planning energy
systems
IFORS 2014
July 17
E.L. Cano
Introduction
The problem
Background
Modeling
Deterministic
Modelling
Stochastic Modelling
Risk Management
Conclusions
Summary
Risk Measures
So far: risk neutral models
Optimal average outcome
Likely very bad for extreme scenarios
Solution: de

68. ne and optimize risk measures
20th Conference of the International Federation of Operational Research Societies 27/36

69. Risk Manag.
planning energy
systems
IFORS 2014
July 17
E.L. Cano
Introduction
The problem
Background
Modeling
Deterministic
Modelling
Stochastic Modelling
Risk Management
Conclusions
Summary
Risk Measures
So far: risk neutral models
Optimal average outcome
Likely very bad for extreme scenarios
Solution: de

70. ne and optimize risk measures
Conditional Value at Risk (CVaR)
Cost (uncertain)
Probability Density
Average 100 VaR = 100 Max 150
0.4
0.3
0.2
0.1
0.0
5%
CVaR = 150
(average)
20th Conference of the International Federation of Operational Research Societies 27/36

71. Risk Manag.
planning energy
systems
IFORS 2014
July 17
E.L. Cano
Introduction
The problem
Background
Modeling
Deterministic
Modelling
Stochastic Modelling
Risk Management
Conclusions
Summary
VaR and CVaR
Value at Risk
Given a con

72. dence level , 0 1, the VaR is the
lowest cost that ensures a probability lower than
1 of getting a cost higher than such value.
VaR(; x ) = min f : P [!jf (!; x ) ] 1 g
20th Conference of the International Federation of Operational Research Societies 28/36

73. Risk Manag.
planning energy
systems
IFORS 2014
July 17
E.L. Cano
Introduction
The problem
Background
Modeling
Deterministic
Modelling
Stochastic Modelling
Risk Management
Conclusions
Summary
VaR and CVaR
Value at Risk
Given a con

74. dence level , 0 1, the VaR is the
lowest cost that ensures a probability lower than
1 of getting a cost higher than such value.
VaR(; x ) = min f : P [!jf (!; x ) ] 1 g
Conditional Value at Risk
CVaR is the conditional expectation of losses that
exceed the VaR level .
CVaR = min fE[f (!; x )jf (!; x ) ]g
20th Conference of the International Federation of Operational Research Societies 28/36

75. Risk Manag.
planning energy
systems
IFORS 2014
July 17
E.L. Cano
Introduction
The problem
Background
Modeling
Deterministic
Modelling
Stochastic Modelling
Risk Management
Conclusions
Summary
Example
If VaR = 100, the probability of getting a cost greater
than 100 is 0.05;
If CVaR = 150 for = 0:95, the average cost in the 5%
worst scenarios is equal to 150.
Cost (uncertain)
Probability Density
Average 100 VaR = 100 Max 150
0.4
0.3
0.2
0.1
0.0
5%
CVaR = 150
(average)
20th Conference of the International Federation of Operational Research Societies 29/36

76. Risk Manag.
planning energy
systems
IFORS 2014
July 17
E.L. Cano
Introduction
The problem
Background
Modeling
Deterministic
Modelling
Stochastic Modelling
Risk Management
Conclusions
Summary
CVaR Implementation
Rockafellar and Uryasev (2000)
Risk Term
R = +
1
1
X
!2
P[!]s(!)
= VaR
s(!) is the solution of max f0; f (!; x ) g
The following constraints are also needed for all ! 2
:
f (!; x ) s(!); s(!) 0
20th Conference of the International Federation of Operational Research Societies 30/36

77. Risk Manag.
planning energy
systems
IFORS 2014
July 17
E.L. Cano
Introduction
The problem
Background
Modeling
Deterministic
Modelling
Stochastic Modelling
Risk Management
Conclusions
Summary
CVaR Implementation
Rockafellar and Uryasev (2000)
Risk Term
R = +
1
1
X
!2
P[!]s(!)
= VaR
s(!) is the solution of max f0; f (!; x ) g
The following constraints are also needed for all ! 2
:
f (!; x ) s(!); s(!) 0
Adding this term to the objective function allows managing risk
20th Conference of the International Federation of Operational Research Societies 30/36

78. Risk Manag.
planning energy
systems
IFORS 2014
July 17
E.L. Cano
Introduction
The problem
Background
Modeling
Deterministic
Modelling
Stochastic Modelling
Risk Management
Conclusions
Summary
Adding Risk Management to the Model
Risk Term
rt = vr + (1 AL)1
X
s2S
PRLeaf (s) sr s
CVaR computation
X
v2Vs
Path
(1 + DR)PTv
cnv vr sr s 8 s 2 S
Weighted objective function
oc = (1 BE) c + BE rt
20th Conference of the International Federation of Operational Research Societies 31/36

79. Risk Manag.
planning energy
systems
IFORS 2014
July 17
E.L. Cano
Introduction
The problem
Background
Modeling
Deterministic
Modelling
Stochastic Modelling
Risk Management
Conclusions
Summary
Environmental and Social Risk
Risk of high emissions
op = (1 BE) p + BE rt
Risk of high energy consumption
oe = (1 BE) et + BE et
20th Conference of the International Federation of Operational Research Societies 32/36

80. Risk Manag.
planning energy
systems
IFORS 2014
July 17
E.L. Cano
Introduction
The problem
Background
Modeling
Deterministic
Modelling
Stochastic Modelling
Risk Management
Conclusions
Summary
Outline
1 Introduction
The problem
Background
2 Modeling
Deterministic Modelling
Stochastic Modelling
Risk Management
3 Conclusions
Summary
20th Conference of the International Federation of Operational Research Societies 33/36

81. Risk Manag.
planning energy
systems
IFORS 2014
July 17
E.L. Cano
Introduction
The problem
Background
Modeling
Deterministic
Modelling
Stochastic Modelling
Risk Management
Conclusions
Summary
Summary
Innovative energy systems modeling
Models tested and validated at real sites
Demonstrated the usefulness of SP in energy systems
optimization
Risk Management at the building level
A new application of risk management
20th Conference of the International Federation of Operational Research Societies 34/36

82. Risk Manag.
planning energy
systems
IFORS 2014
July 17
E.L. Cano
Introduction
The problem
Background
Modeling
Deterministic
Modelling
Stochastic Modelling
Risk Management
Conclusions
Summary
Acknowledgements
This work has been partially funded by the project Energy
Eciency and Risk Management in Public Buildings (EnRiMa)
EC's FP7 project (number 260041)
We also acknowledge the projects:
OPTIMOS3 (MTM2012-36163-C06-06)
Project RIESGOS-CM: code S2009/ESP-1685
HAUS: IPT-2011-1049-430000
EDUCALAB: IPT-2011-1071-430000
DEMOCRACY4ALL: IPT-2011-0869-430000
CORPORATE COMMUNITY: IPT-2011-0871-430000
CONTENT INTELIGENCE: IPT-2012-0912-430000
and the Young Scientists Summer Program (YSSP) at the International Institute
of Applied Systems Analysis (IIASA).
20th Conference of the International Federation of Operational Research Societies 35/36

83. Risk Manag.
planning energy
systems
IFORS 2014
July 17
E.L. Cano
Introduction
The problem
Background
Modeling
Deterministic
Modelling
Stochastic Modelling
Risk Management
Conclusions
Summary
Discussion
Thanks for your attention !
emilio.lopez@urjc.es
20th Conference of the International Federation of Operational Research Societies 36/36