Download - Stochastic optimization and risk management for an efficient planning of buildings' energy systems
Risk Manag.planning energy
systems
IFORS 2014July 17
E.L. Cano
Introduction
The problem
Background
Modeling
DeterministicModelling
Stochastic Modelling
Risk Management
Conclusions
Summary
Stochastic Optimization and Risk Managementfor an efficient planning ofbuildings’ energy systems
Emilio L. Cano, Javier M. Moguerzaand Antonio Alonso-Ayuso
Department of Computer Science and StatisticsRey Juan Carlos University
20th Conference of the International Federationof Operational Research Societies
Barcelona, July 17, 2014
20th Conference of the International Federation of Operational Research Societies 1/36
Risk Manag.planning energy
systems
IFORS 2014July 17
E.L. Cano
Introduction
The problem
Background
Modeling
DeterministicModelling
Stochastic Modelling
Risk Management
Conclusions
Summary
Outline
1 IntroductionThe problemBackground
2 ModelingDeterministic ModellingStochastic ModellingRisk Management
3 ConclusionsSummary
20th Conference of the International Federation of Operational Research Societies 2/36
Risk Manag.planning energy
systems
IFORS 2014July 17
E.L. Cano
Introduction
The problem
Background
Modeling
DeterministicModelling
Stochastic Modelling
Risk Management
Conclusions
Summary
Outline
1 IntroductionThe problemBackground
2 ModelingDeterministic ModellingStochastic ModellingRisk Management
3 ConclusionsSummary
20th Conference of the International Federation of Operational Research Societies 3/36
Risk Manag.planning energy
systems
IFORS 2014July 17
E.L. Cano
Introduction
The problem
Background
Modeling
DeterministicModelling
Stochastic Modelling
Risk Management
Conclusions
Summary
Global changes, local challenges
Global
Regulations: emissions,efficiency
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
Risk Manag.planning energy
systems
IFORS 2014July 17
E.L. Cano
Introduction
The problem
Background
Modeling
DeterministicModelling
Stochastic Modelling
Risk Management
Conclusions
Summary
Global changes, local challenges
Global
Regulations: emissions,efficiency
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
Risk Manag.planning energy
systems
IFORS 2014July 17
E.L. Cano
Introduction
The problem
Background
Modeling
DeterministicModelling
Stochastic Modelling
Risk Management
Conclusions
Summary
Global changes, local challenges
Global
Regulations: emissions,efficiency
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
Risk Manag.planning energy
systems
IFORS 2014July 17
E.L. Cano
Introduction
The problem
Background
Modeling
DeterministicModelling
Stochastic Modelling
Risk Management
Conclusions
Summary
Global changes, local challenges
Global
Regulations: emissions,efficiency
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
Risk Manag.planning energy
systems
IFORS 2014July 17
E.L. Cano
Introduction
The problem
Background
Modeling
DeterministicModelling
Stochastic Modelling
Risk Management
Conclusions
Summary
Global changes, local challenges
Global
Regulations: emissions,efficiency
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
Risk Manag.planning energy
systems
IFORS 2014July 17
E.L. Cano
Introduction
The problem
Background
Modeling
DeterministicModelling
Stochastic Modelling
Risk Management
Conclusions
Summary
Energy Systems
20th Conference of the International Federation of Operational Research Societies 5/36
Building systems energy flow: Sankey diagram
Campus Pinkafeld test site
Building systems energy flow: Sankey diagram
Demand side: requirements, uncertainty
Building systems energy flow: Sankey diagram
Supply side: Markets, renewables
Building systems energy flow: Sankey diagram
Strategic decisions are the goal
Building systems energy flow: Sankey diagram
Operational performance interdependent with strategicdecisions
Risk Manag.planning energy
systems
IFORS 2014July 17
E.L. Cano
Introduction
The problem
Background
Modeling
DeterministicModelling
Stochastic Modelling
Risk Management
Conclusions
Summary
Outline
1 IntroductionThe problemBackground
2 ModelingDeterministic ModellingStochastic ModellingRisk Management
3 ConclusionsSummary
20th Conference of the International Federation of Operational Research Societies 7/36
Risk Manag.planning energy
systems
IFORS 2014July 17
E.L. Cano
Introduction
The problem
Background
Modeling
DeterministicModelling
Stochastic Modelling
Risk Management
Conclusions
Summary
EnRiMa Project
20th Conference of the International Federation of Operational Research Societies 8/36
Risk Manag.planning energy
systems
IFORS 2014July 17
E.L. Cano
Introduction
The problem
Background
Modeling
DeterministicModelling
Stochastic Modelling
Risk Management
Conclusions
Summary
EnRiMa Models
EnRiMa DSSStrategicModule
Strategic DVs
StrategicConstraints
Upper-LevelOperational DVs
Upper-LevelEnergy-BalanceConstraints
OperationalModule
Lower-LevelOperational DVs
Lower-LevelEnergy-BalanceConstraints
20th Conference of the International Federation of Operational Research Societies 9/36
Risk Manag.planning energy
systems
IFORS 2014July 17
E.L. Cano
Introduction
The problem
Background
Modeling
DeterministicModelling
Stochastic Modelling
Risk Management
Conclusions
Summary
Decision Support Systems (DSS)
Model: Symbolic Model Specification (SMS)
Data: Statistical analysis
Framework: Stakeholders dialog
20th Conference of the International Federation of Operational Research Societies 10/36
Risk Manag.planning energy
systems
IFORS 2014July 17
E.L. Cano
Introduction
The problem
Background
Modeling
DeterministicModelling
Stochastic Modelling
Risk Management
Conclusions
Summary
Decision Support Systems (DSS)
Model: Symbolic Model Specification (SMS)
Data: Statistical analysis
Framework: Stakeholders dialog
20th Conference of the International Federation of Operational Research Societies 10/36
Risk Manag.planning energy
systems
IFORS 2014July 17
E.L. Cano
Introduction
The problem
Background
Modeling
DeterministicModelling
Stochastic Modelling
Risk Management
Conclusions
Summary
Decision Support Systems (DSS)
Model: Symbolic Model Specification (SMS)
Data: Statistical analysis
Framework: Stakeholders dialog
20th Conference of the International Federation of Operational Research Societies 10/36
Risk Manag.planning energy
systems
IFORS 2014July 17
E.L. Cano
Introduction
The problem
Background
Modeling
DeterministicModelling
Stochastic Modelling
Risk Management
Conclusions
Summary
Decision Support Systems (DSS)
Model: Symbolic Model Specification (SMS)
Data: Statistical analysis
Framework: Stakeholders dialog
20th Conference of the International Federation of Operational Research Societies 10/36
Risk Manag.planning energy
systems
IFORS 2014July 17
E.L. Cano
Introduction
The problem
Background
Modeling
DeterministicModelling
Stochastic Modelling
Risk Management
Conclusions
Summary
Decision Support Systems (DSS)
Algorithms
ModelSymbolic modelVariables, relations
Underlying theoryMethodology, technique
Uncertainty modelling
DataDeterministic dataUncertain data -Stochastic processes
Data analysis
SolutionData treatmentAnalysisVisualization
DSS
Stakeholders Dialog
Interpretation
Model: Symbolic Model Specification (SMS)
Data: Statistical analysis
Framework: Stakeholders dialog
20th Conference of the International Federation of Operational Research Societies 10/36
Risk Manag.planning energy
systems
IFORS 2014July 17
E.L. Cano
Introduction
The problem
Background
Modeling
DeterministicModelling
Stochastic Modelling
Risk Management
Conclusions
Summary
Outline
1 IntroductionThe problemBackground
2 ModelingDeterministic ModellingStochastic ModellingRisk Management
3 ConclusionsSummary
20th Conference of the International Federation of Operational Research Societies 11/36
Risk Manag.planning energy
systems
IFORS 2014July 17
E.L. Cano
Introduction
The problem
Background
Modeling
DeterministicModelling
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
Risk Manag.planning energy
systems
IFORS 2014July 17
E.L. Cano
Introduction
The problem
Background
Modeling
DeterministicModelling
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
Risk Manag.planning energy
systems
IFORS 2014July 17
E.L. Cano
Introduction
The problem
Background
Modeling
DeterministicModelling
Stochastic Modelling
Risk Management
Conclusions
Summary
Time Resolution
Operational decisions (energy flows): hours
20th Conference of the International Federation of Operational Research Societies 12/36
Risk Manag.planning energy
systems
IFORS 2014July 17
E.L. Cano
Introduction
The problem
Background
Modeling
DeterministicModelling
Stochastic Modelling
Risk Management
Conclusions
Summary
Model Sets
Time resolution
p Long-term period; p ∈ Pm Mid-term representative period; m ∈Mt Short-term period; t ∈ T
The model includes the realization of short-term decisions (t)that are scaled to a long-term period (p) through a mid-termrepresentative profile (m).
Energy, technologies, markets, emissions
i Technology (generators, storage, passive); i ∈ Ik Energy type; k ∈ Kn Energy market (contract tariffs); n ∈ Nl Pollutant; l ∈ L
20th Conference of the International Federation of Operational Research Societies 13/36
Risk Manag.planning energy
systems
IFORS 2014July 17
E.L. Cano
Introduction
The problem
Background
Modeling
DeterministicModelling
Stochastic Modelling
Risk Management
Conclusions
Summary
Model Sets
Time resolution
p Long-term period; p ∈ Pm Mid-term representative period; m ∈Mt Short-term period; t ∈ T
The model includes the realization of short-term decisions (t)that are scaled to a long-term period (p) through a mid-termrepresentative profile (m).
Energy, technologies, markets, emissions
i Technology (generators, storage, passive); i ∈ Ik Energy type; k ∈ Kn Energy market (contract tariffs); n ∈ Nl Pollutant; l ∈ L
20th Conference of the International Federation of Operational Research Societies 13/36
Risk Manag.planning energy
systems
IFORS 2014July 17
E.L. Cano
Introduction
The problem
Background
Modeling
DeterministicModelling
Stochastic Modelling
Risk Management
Conclusions
Summary
Model Features
Modelling at the building level
Technologies installation and decommissioning
Energy flows (short term) along with investment (longterm)
Technologies aging through the a index
Emissions
Efficiency
Different energy types
Different technology types: generation, storage, passivemeasures
Objective: minimize total discounted cost
20th Conference of the International Federation of Operational Research Societies 14/36
Risk Manag.planning energy
systems
IFORS 2014July 17
E.L. Cano
Introduction
The problem
Background
Modeling
DeterministicModelling
Stochastic Modelling
Risk Management
Conclusions
Summary
Model Features
Modelling at the building level
Technologies installation and decommissioning
Energy flows (short term) along with investment (longterm)
Technologies aging through the a index
Emissions
Efficiency
Different energy types
Different technology types: generation, storage, passivemeasures
Objective: minimize total discounted cost
20th Conference of the International Federation of Operational Research Societies 14/36
Risk Manag.planning energy
systems
IFORS 2014July 17
E.L. Cano
Introduction
The problem
Background
Modeling
DeterministicModelling
Stochastic Modelling
Risk Management
Conclusions
Summary
Model Features
Modelling at the building level
Technologies installation and decommissioning
Energy flows (short term) along with investment (longterm)
Technologies aging through the a index
Emissions
Efficiency
Different energy types
Different technology types: generation, storage, passivemeasures
Objective: minimize total discounted cost
20th Conference of the International Federation of Operational Research Societies 14/36
Risk Manag.planning energy
systems
IFORS 2014July 17
E.L. Cano
Introduction
The problem
Background
Modeling
DeterministicModelling
Stochastic Modelling
Risk Management
Conclusions
Summary
Model Features
Modelling at the building level
Technologies installation and decommissioning
Energy flows (short term) along with investment (longterm)
Technologies aging through the a index
Emissions
Efficiency
Different energy types
Different technology types: generation, storage, passivemeasures
Objective: minimize total discounted cost
20th Conference of the International Federation of Operational Research Societies 14/36
Risk Manag.planning energy
systems
IFORS 2014July 17
E.L. Cano
Introduction
The problem
Background
Modeling
DeterministicModelling
Stochastic Modelling
Risk Management
Conclusions
Summary
Model Features
Modelling at the building level
Technologies installation and decommissioning
Energy flows (short term) along with investment (longterm)
Technologies aging through the a index
Emissions
Efficiency
Different energy types
Different technology types: generation, storage, passivemeasures
Objective: minimize total discounted cost
20th Conference of the International Federation of Operational Research Societies 14/36
Risk Manag.planning energy
systems
IFORS 2014July 17
E.L. Cano
Introduction
The problem
Background
Modeling
DeterministicModelling
Stochastic Modelling
Risk Management
Conclusions
Summary
Model Features
Modelling at the building level
Technologies installation and decommissioning
Energy flows (short term) along with investment (longterm)
Technologies aging through the a index
Emissions
Efficiency
Different energy types
Different technology types: generation, storage, passivemeasures
Objective: minimize total discounted cost
20th Conference of the International Federation of Operational Research Societies 14/36
Risk Manag.planning energy
systems
IFORS 2014July 17
E.L. Cano
Introduction
The problem
Background
Modeling
DeterministicModelling
Stochastic Modelling
Risk Management
Conclusions
Summary
Model Features
Modelling at the building level
Technologies installation and decommissioning
Energy flows (short term) along with investment (longterm)
Technologies aging through the a index
Emissions
Efficiency
Different energy types
Different technology types: generation, storage, passivemeasures
Objective: minimize total discounted cost
20th Conference of the International Federation of Operational Research Societies 14/36
Risk Manag.planning energy
systems
IFORS 2014July 17
E.L. Cano
Introduction
The problem
Background
Modeling
DeterministicModelling
Stochastic Modelling
Risk Management
Conclusions
Summary
Model Features
Modelling at the building level
Technologies installation and decommissioning
Energy flows (short term) along with investment (longterm)
Technologies aging through the a index
Emissions
Efficiency
Different energy types
Different technology types: generation, storage, passivemeasures
Objective: minimize total discounted cost
20th Conference of the International Federation of Operational Research Societies 14/36
Risk Manag.planning energy
systems
IFORS 2014July 17
E.L. Cano
Introduction
The problem
Background
Modeling
DeterministicModelling
Stochastic Modelling
Risk Management
Conclusions
Summary
Model Features
Modelling at the building level
Technologies installation and decommissioning
Energy flows (short term) along with investment (longterm)
Technologies aging through the a index
Emissions
Efficiency
Different energy types
Different technology types: generation, storage, passivemeasures
Objective: minimize total discounted cost
20th Conference of the International Federation of Operational Research Societies 14/36
Risk Manag.planning energy
systems
IFORS 2014July 17
E.L. Cano
Introduction
The problem
Background
Modeling
DeterministicModelling
Stochastic Modelling
Risk Management
Conclusions
Summary
Energy-dispatching Decision Flow
Market
Demand
Purchases
Renewables
Generation
Storage
N
K
I
ISales
K y
u
u
u
w
uw
z
riro
ri
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
Risk Manag.planning energy
systems
IFORS 2014July 17
E.L. Cano
Introduction
The problem
Background
Modeling
DeterministicModelling
Stochastic Modelling
Risk Management
Conclusions
Summary
Energy-dispatching Decision Flow
Market
Demand
Purchases
Renewables
Generation
Storage
N
K
I
ISales
K y
u
u
u
w
uw
z
riro
ri
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
Risk Manag.planning energy
systems
IFORS 2014July 17
E.L. Cano
Introduction
The problem
Background
Modeling
DeterministicModelling
Stochastic Modelling
Risk Management
Conclusions
Summary
Outline
1 IntroductionThe problemBackground
2 ModelingDeterministic ModellingStochastic ModellingRisk Management
3 ConclusionsSummary
20th Conference of the International Federation of Operational Research Societies 16/36
Risk Manag.planning energy
systems
IFORS 2014July 17
E.L. Cano
Introduction
The problem
Background
Modeling
DeterministicModelling
Stochastic Modelling
Risk Management
Conclusions
Summary
Deterministic vs. Stochastic
Five periods, two technologies (CHP, PV), only electricity.
100 scenarios simulation
20
40
60
80
2013 2014 2015 2016
Dem
and
leve
l (kW
)
Energy demand
0
500
1000
1500
2000
2500
0
500
1000
1500
2000
2500
0
500
1000
1500
2000
2500
CH
PP
VR
TE
2013 2014 2015 2016 2017
EU
R/k
W
Investment cost
0.1
0.2
0.3
0.1
0.2
0.3
CH
PR
TE
2013 2014 2015 2016
EU
R/k
Wh
25
50
75
100Scenario
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) =∞
20th Conference of the International Federation of Operational Research Societies 17/36
Risk Manag.planning energy
systems
IFORS 2014July 17
E.L. Cano
Introduction
The problem
Background
Modeling
DeterministicModelling
Stochastic Modelling
Risk Management
Conclusions
Summary
Deterministic vs. Stochastic
Five periods, two technologies (CHP, PV), only electricity.
100 scenarios simulation
20
40
60
80
2013 2014 2015 2016
Dem
and
leve
l (kW
)
Energy demand
0
500
1000
1500
2000
2500
0
500
1000
1500
2000
2500
0
500
1000
1500
2000
2500
CH
PP
VR
TE
2013 2014 2015 2016 2017
EU
R/k
W
Investment cost
0.1
0.2
0.3
0.1
0.2
0.3
CH
PR
TE
2013 2014 2015 2016
EU
R/k
Wh
25
50
75
100Scenario
Energy price
Fdet(x∗det) = 66, 920 EUR.
Infeasible 56/100Fsto(x ∗sto) = 68, 595 EUR.
Robust, optimal against all
VSS = Fsto(x ∗det)− Fsto(x ∗sto) =∞
20th Conference of the International Federation of Operational Research Societies 17/36
Risk Manag.planning energy
systems
IFORS 2014July 17
E.L. Cano
Introduction
The problem
Background
Modeling
DeterministicModelling
Stochastic Modelling
Risk Management
Conclusions
Summary
Deterministic vs. Stochastic
Five periods, two technologies (CHP, PV), only electricity.
100 scenarios simulation
20
40
60
80
2013 2014 2015 2016
Dem
and
leve
l (kW
)
Energy demand
0
500
1000
1500
2000
2500
0
500
1000
1500
2000
2500
0
500
1000
1500
2000
2500
CH
PP
VR
TE
2013 2014 2015 2016 2017
EU
R/k
W
Investment cost
0.1
0.2
0.3
0.1
0.2
0.3
CH
PR
TE
2013 2014 2015 2016
EU
R/k
Wh
25
50
75
100Scenario
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) =∞
20th Conference of the International Federation of Operational Research Societies 17/36
Risk Manag.planning energy
systems
IFORS 2014July 17
E.L. Cano
Introduction
The problem
Background
Modeling
DeterministicModelling
Stochastic Modelling
Risk Management
Conclusions
Summary
Deterministic vs. Stochastic
Five periods, two technologies (CHP, PV), only electricity.
100 scenarios simulation
20
40
60
80
2013 2014 2015 2016
Dem
and
leve
l (kW
)
Energy demand
0
500
1000
1500
2000
2500
0
500
1000
1500
2000
2500
0
500
1000
1500
2000
2500
CH
PP
VR
TE
2013 2014 2015 2016 2017
EU
R/k
W
Investment cost
0.1
0.2
0.3
0.1
0.2
0.3
CH
PR
TE
2013 2014 2015 2016
EU
R/k
Wh
25
50
75
100Scenario
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) =∞
20th Conference of the International Federation of Operational Research Societies 17/36
Risk Manag.planning energy
systems
IFORS 2014July 17
E.L. Cano
Introduction
The problem
Background
Modeling
DeterministicModelling
Stochastic Modelling
Risk Management
Conclusions
Summary
Deterministic vs. Stochastic
Five periods, two technologies (CHP, PV), only electricity.
100 scenarios simulation
20
40
60
80
2013 2014 2015 2016
Dem
and
leve
l (kW
)
Energy demand
0
500
1000
1500
2000
2500
0
500
1000
1500
2000
2500
0
500
1000
1500
2000
2500
CH
PP
VR
TE
2013 2014 2015 2016 2017
EU
R/k
W
Investment cost
0.1
0.2
0.3
0.1
0.2
0.3
CH
PR
TE
2013 2014 2015 2016
EU
R/k
Wh
25
50
75
100Scenario
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) =∞
20th Conference of the International Federation of Operational Research Societies 17/36
Risk Manag.planning energy
systems
IFORS 2014July 17
E.L. Cano
Introduction
The problem
Background
Modeling
DeterministicModelling
Stochastic Modelling
Risk Management
Conclusions
Summary
Deterministic vs. Stochastic
Five periods, two technologies (CHP, PV), only electricity.
100 scenarios simulation
20
40
60
80
2013 2014 2015 2016
Dem
and
leve
l (kW
)
Energy demand
0
500
1000
1500
2000
2500
0
500
1000
1500
2000
2500
0
500
1000
1500
2000
2500
CH
PP
VR
TE
2013 2014 2015 2016 2017
EU
R/k
W
Investment cost
0.1
0.2
0.3
0.1
0.2
0.3
CH
PR
TE
2013 2014 2015 2016
EU
R/k
Wh
25
50
75
100Scenario
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) =∞
20th Conference of the International Federation of Operational Research Societies 17/36
Risk Manag.planning energy
systems
IFORS 2014July 17
E.L. Cano
Introduction
The problem
Background
Modeling
DeterministicModelling
Stochastic Modelling
Risk Management
Conclusions
Summary
Scenario Trees
Time
v Tree nodem Representative profilet Short-term period
Tree structure
PRv Probability of the nodePa(v) Parent of the nodePT v Period of the node
20th Conference of the International Federation of Operational Research Societies 18/36
Risk Manag.planning energy
systems
IFORS 2014July 17
E.L. Cano
Introduction
The problem
Background
Modeling
DeterministicModelling
Stochastic Modelling
Risk Management
Conclusions
Summary
Scenario Trees
Time
v Tree nodem Representative profilet Short-term period
Tree structure
PRv Probability of the nodePa(v) Parent of the nodePT v Period of the node
20th Conference of the International Federation of Operational Research Societies 18/36
Risk Manag.planning energy
systems
IFORS 2014July 17
E.L. Cano
Introduction
The problem
Background
Modeling
DeterministicModelling
Stochastic Modelling
Risk Management
Conclusions
Summary
Strategic Decisions
Decision Variables
hvk ,n Tariff choice;
xivi Technologies to install;
xdv ,ai Technologies to decommission;
x v ,ai Technologies installed;
xcvi Available capacity of technologies.
Relations
x v ,0i = xivi
x v ,ai = x v ′,a−1
i − xdv ,ai
xcvi = Gi ·∑a
AGai · x
v ,ai
∑n
hvk ,n = 1
20th Conference of the International Federation of Operational Research Societies 19/36
Risk Manag.planning energy
systems
IFORS 2014July 17
E.L. Cano
Introduction
The problem
Background
Modeling
DeterministicModelling
Stochastic Modelling
Risk Management
Conclusions
Summary
Strategic Decisions
Decision Variables
hvk ,n Tariff choice;
xivi Technologies to install;
xdv ,ai Technologies to decommission;
x v ,ai Technologies installed;
xcvi Available capacity of technologies.
Relations
x v ,0i = xivi
x v ,ai = x v ′,a−1
i − xdv ,ai
xcvi = Gi ·∑a
AGai · x
v ,ai
∑n
hvk ,n = 1
20th Conference of the International Federation of Operational Research Societies 19/36
Risk Manag.planning energy
systems
IFORS 2014July 17
E.L. Cano
Introduction
The problem
Background
Modeling
DeterministicModelling
Stochastic Modelling
Risk Management
Conclusions
Summary
Embedded Operational Decisions
Basic variables
uv ,m,tk ,n Purchase of energy (kWh)
wv ,m,tk ,n Sale of energy (kWh)
yv ,m,ti ,k Input of energy k to technology i (kWh)
qiv ,m,ti ,k Energy type k added to storage technology i
(kWh)
qov ,m,ti ,k Energy type k released from storage technology i
(kWh)
Calculated variables
z v ,m,ti ,k Output of energy type k from technology i (kWh)
rv ,m,ti ,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
Risk Manag.planning energy
systems
IFORS 2014July 17
E.L. Cano
Introduction
The problem
Background
Modeling
DeterministicModelling
Stochastic Modelling
Risk Management
Conclusions
Summary
Embedded Operational Decisions
Basic variables
uv ,m,tk ,n Purchase of energy (kWh)
wv ,m,tk ,n Sale of energy (kWh)
yv ,m,ti ,k Input of energy k to technology i (kWh)
qiv ,m,ti ,k Energy type k added to storage technology i
(kWh)
qov ,m,ti ,k Energy type k released from storage technology i
(kWh)
Calculated variables
z v ,m,ti ,k Output of energy type k from technology i (kWh)
rv ,m,ti ,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
Risk Manag.planning energy
systems
IFORS 2014July 17
E.L. Cano
Introduction
The problem
Background
Modeling
DeterministicModelling
Stochastic Modelling
Risk Management
Conclusions
Summary
Energy Balance and Links
Energy Balance
∑i∈IGen
z v ,m,ti,k −
∑i∈IGen
yv ,m,ti,k +
∑n∈NPur(k)
uv ,m,tk ,n −
∑n∈NS(k)
wv ,m,tk ,n
+∑
i∈ISto
(rov ,m,t
i,k − riv ,m,ti,k
)= Dv ,m,t
k ·
(1−
∑i∈IPU
ODvi,k · xcvi
)
Strategic & Operational links
z v ,m,ti,k ≤ DTm ·AF v ,m,t
i · xcvi
OAvi,k · xcvi ≤ rv ,m,t
i,k ≤ OBvi,k · xcvi
uv ,m,tk ,n ≤ hv
k ,n ·ME k ,n ·DTm
20th Conference of the International Federation of Operational Research Societies 21/36
Risk Manag.planning energy
systems
IFORS 2014July 17
E.L. Cano
Introduction
The problem
Background
Modeling
DeterministicModelling
Stochastic Modelling
Risk Management
Conclusions
Summary
Energy Balance and Links
Energy Balance
∑i∈IGen
z v ,m,ti,k −
∑i∈IGen
yv ,m,ti,k +
∑n∈NPur(k)
uv ,m,tk ,n −
∑n∈NS(k)
wv ,m,tk ,n
+∑
i∈ISto
(rov ,m,t
i,k − riv ,m,ti,k
)= Dv ,m,t
k ·
(1−
∑i∈IPU
ODvi,k · xcvi
)
Strategic & Operational links
z v ,m,ti,k ≤ DTm ·AF v ,m,t
i · xcvi
OAvi,k · xcvi ≤ rv ,m,t
i,k ≤ OBvi,k · xcvi
uv ,m,tk ,n ≤ hv
k ,n ·ME k ,n ·DTm
20th Conference of the International Federation of Operational Research Societies 21/36
Risk Manag.planning energy
systems
IFORS 2014July 17
E.L. Cano
Introduction
The problem
Background
Modeling
DeterministicModelling
Stochastic Modelling
Risk Management
Conclusions
Summary
Objectives
Minimize total discounted expected cost
c =∑v∈V
(1 + DR)−PTv
· PRv · cnv
Minimize total expected emissions
p =∑v∈V
PRv ·∑l∈L
pnvl
Minimize total expected primary energy consumption
et =∑v∈V
PRv · env
20th Conference of the International Federation of Operational Research Societies 22/36
Risk Manag.planning energy
systems
IFORS 2014July 17
E.L. Cano
Introduction
The problem
Background
Modeling
DeterministicModelling
Stochastic Modelling
Risk Management
Conclusions
Summary
Objectives (cont.)
Minimize total discounted expected cost
c =∑v∈V
(1 + DR)−PTv
· PRv · cnv
cnv =∑i∈I
snvi +
∑i∈I
mnvi
+∑
k∈K,n∈N kPur
ucvk ,n −∑
k∈K,n∈N kSal
wcvk ,n
+∑
i∈IGen
zcvi +∑
i∈ISto
rcvi ∀ v ∈ V
20th Conference of the International Federation of Operational Research Societies 23/36
Risk Manag.planning energy
systems
IFORS 2014July 17
E.L. Cano
Introduction
The problem
Background
Modeling
DeterministicModelling
Stochastic Modelling
Risk Management
Conclusions
Summary
Objectives (cont.)
Minimize total expected emissions
p =∑v∈V
PRv ·∑l∈L
pnvl
pnvl =
∑m∈M
DMm ·∑
t∈T mTm
∑k∈Ki
In
LH vk ,l · y
v ,m,ti ,k
+∑
k∈K,n∈N kPur
LC vk ,l ,n · u
v ,m,tk ,n
∀ l ∈ L, v ∈ V
20th Conference of the International Federation of Operational Research Societies 24/36
Risk Manag.planning energy
systems
IFORS 2014July 17
E.L. Cano
Introduction
The problem
Background
Modeling
DeterministicModelling
Stochastic Modelling
Risk Management
Conclusions
Summary
Objectives (cont.)
Minimize total expected energy consumption
et =∑v∈V
PRv · env
env =∑m∈M
DMm ·∑
t∈T mTm
ev ,m,t ∀ v ∈ V
ev ,m,t =∑
k∈K,n∈N kPur
Bk ,n · uv ,m,tk ,n
∀ v ∈ V, m ∈M, t ∈ T mTm
20th Conference of the International Federation of Operational Research Societies 25/36
Risk Manag.planning energy
systems
IFORS 2014July 17
E.L. Cano
Introduction
The problem
Background
Modeling
DeterministicModelling
Stochastic Modelling
Risk Management
Conclusions
Summary
Outline
1 IntroductionThe problemBackground
2 ModelingDeterministic ModellingStochastic ModellingRisk Management
3 ConclusionsSummary
20th Conference of the International Federation of Operational Research Societies 26/36
Risk Manag.planning energy
systems
IFORS 2014July 17
E.L. Cano
Introduction
The problem
Background
Modeling
DeterministicModelling
Stochastic Modelling
Risk Management
Conclusions
Summary
Risk Measures
So far: risk neutral models
Optimal average outcome
Likely very bad for extreme scenarios
Solution: define and optimize risk measures
Conditional Value at Risk (CVaR)
Cost (uncertain)
Pro
babi
lity
Den
sity
Average < 100 VaR = 100 Max > 150
0.0
0.1
0.2
0.3
0.4
5%
CVaR = 150
(average)
20th Conference of the International Federation of Operational Research Societies 27/36
Risk Manag.planning energy
systems
IFORS 2014July 17
E.L. Cano
Introduction
The problem
Background
Modeling
DeterministicModelling
Stochastic Modelling
Risk Management
Conclusions
Summary
Risk Measures
So far: risk neutral models
Optimal average outcome
Likely very bad for extreme scenarios
Solution: define and optimize risk measures
Conditional Value at Risk (CVaR)
Cost (uncertain)
Pro
babi
lity
Den
sity
Average < 100 VaR = 100 Max > 150
0.0
0.1
0.2
0.3
0.4
5%
CVaR = 150
(average)
20th Conference of the International Federation of Operational Research Societies 27/36
Risk Manag.planning energy
systems
IFORS 2014July 17
E.L. Cano
Introduction
The problem
Background
Modeling
DeterministicModelling
Stochastic Modelling
Risk Management
Conclusions
Summary
VaR and CVaR
Value at Risk
Given a confidence level α, 0 < α < 1, the VaR is thelowest cost λ that ensures a probability lower than1− α of getting a cost higher than such value.
VaR(α,xxx ) = min λ : P [ω|f (ω,xxx ) > λ] ≤ 1− α
Conditional Value at Risk
CVaR is the conditional expectation of losses thatexceed the VaR level λ.
CVaR = min E [f (ω,xxx )|f (ω,xxx ) > λ]
20th Conference of the International Federation of Operational Research Societies 28/36
Risk Manag.planning energy
systems
IFORS 2014July 17
E.L. Cano
Introduction
The problem
Background
Modeling
DeterministicModelling
Stochastic Modelling
Risk Management
Conclusions
Summary
VaR and CVaR
Value at Risk
Given a confidence level α, 0 < α < 1, the VaR is thelowest cost λ that ensures a probability lower than1− α of getting a cost higher than such value.
VaR(α,xxx ) = min λ : P [ω|f (ω,xxx ) > λ] ≤ 1− α
Conditional Value at Risk
CVaR is the conditional expectation of losses thatexceed the VaR level λ.
CVaR = min E [f (ω,xxx )|f (ω,xxx ) > λ]
20th Conference of the International Federation of Operational Research Societies 28/36
Risk Manag.planning energy
systems
IFORS 2014July 17
E.L. Cano
Introduction
The problem
Background
Modeling
DeterministicModelling
Stochastic Modelling
Risk Management
Conclusions
Summary
Example
If VaR = 100, the probability of getting a cost greaterthan 100 is 0.05;
If CVaR = 150 for α = 0.95, the average cost in the 5%worst scenarios is equal to 150.
Cost (uncertain)
Pro
babi
lity
Den
sity
Average < 100 VaR = 100 Max > 150
0.0
0.1
0.2
0.3
0.4
5%
CVaR = 150
(average)
20th Conference of the International Federation of Operational Research Societies 29/36
Risk Manag.planning energy
systems
IFORS 2014July 17
E.L. Cano
Introduction
The problem
Background
Modeling
DeterministicModelling
Stochastic Modelling
Risk Management
Conclusions
Summary
CVaR ImplementationRockafellar and Uryasev (2000)
Risk Term
R = λ+1
1− α∑ω∈Ω
P[ω]s(ω)
λ = VaR
s(ω) is the solution of max 0, f (ω,xxx )− λThe following constraints are also needed for all ω ∈ Ω:
f (ω,xxx )− λ ≤ s(ω); s(ω) ≥ 0
Adding this term to the objective function allows managing risk
20th Conference of the International Federation of Operational Research Societies 30/36
Risk Manag.planning energy
systems
IFORS 2014July 17
E.L. Cano
Introduction
The problem
Background
Modeling
DeterministicModelling
Stochastic Modelling
Risk Management
Conclusions
Summary
CVaR ImplementationRockafellar and Uryasev (2000)
Risk Term
R = λ+1
1− α∑ω∈Ω
P[ω]s(ω)
λ = VaR
s(ω) is the solution of max 0, f (ω,xxx )− λThe following constraints are also needed for all ω ∈ Ω:
f (ω,xxx )− λ ≤ s(ω); s(ω) ≥ 0
Adding this term to the objective function allows managing risk
20th Conference of the International Federation of Operational Research Societies 30/36
Risk Manag.planning energy
systems
IFORS 2014July 17
E.L. Cano
Introduction
The problem
Background
Modeling
DeterministicModelling
Stochastic Modelling
Risk Management
Conclusions
Summary
Adding Risk Management to the Model
Risk Term
rt = vr + (1−AL)−1 ·∑s∈S
PRLeaf (s) · sr s
CVaR computation
∑v∈Vs
Path
(1 + DR)−PTv
· cnv − vr ≤ sr s ∀ s ∈ S
Weighted objective function
oc = (1− BE ) · c + BE · rt
20th Conference of the International Federation of Operational Research Societies 31/36
Risk Manag.planning energy
systems
IFORS 2014July 17
E.L. Cano
Introduction
The problem
Background
Modeling
DeterministicModelling
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
Risk Manag.planning energy
systems
IFORS 2014July 17
E.L. Cano
Introduction
The problem
Background
Modeling
DeterministicModelling
Stochastic Modelling
Risk Management
Conclusions
Summary
Outline
1 IntroductionThe problemBackground
2 ModelingDeterministic ModellingStochastic ModellingRisk Management
3 ConclusionsSummary
20th Conference of the International Federation of Operational Research Societies 33/36
Risk Manag.planning energy
systems
IFORS 2014July 17
E.L. Cano
Introduction
The problem
Background
Modeling
DeterministicModelling
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 systemsoptimization
Risk Management at the building level
A new application of risk management
20th Conference of the International Federation of Operational Research Societies 34/36
Risk Manag.planning energy
systems
IFORS 2014July 17
E.L. Cano
Introduction
The problem
Background
Modeling
DeterministicModelling
Stochastic Modelling
Risk Management
Conclusions
Summary
Acknowledgements
This work has been partially funded by the project EnergyEfficiency 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-1685HAUS: IPT-2011-1049-430000EDUCALAB: IPT-2011-1071-430000DEMOCRACY4ALL: IPT-2011-0869-430000CORPORATE COMMUNITY: IPT-2011-0871-430000CONTENT & INTELIGENCE: IPT-2012-0912-430000
and the Young Scientists Summer Program (YSSP) at the International Instituteof Applied Systems Analysis (IIASA).
20th Conference of the International Federation of Operational Research Societies 35/36
Risk Manag.planning energy
systems
IFORS 2014July 17
E.L. Cano
Introduction
The problem
Background
Modeling
DeterministicModelling
Stochastic Modelling
Risk Management
Conclusions
Summary
Discussion
Thanks for your attention !
20th Conference of the International Federation of Operational Research Societies 36/36