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


systems

IFORS 2014July 17

E.L. Cano

Introduction

The problem

Background

Modeling



Risk Management

Conclusions

Summary

Outline

1 IntroductionThe problemBackground

2 ModelingDeterministic ModellingStochastic ModellingRisk Management

3 ConclusionsSummary



systems

IFORS 2014July 17

E.L. Cano

Introduction

The problem

Background

Modeling



Risk Management

Conclusions

Summary

Outline






systems

IFORS 2014July 17

E.L. Cano

Introduction

The problem

Background

Modeling



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



systems

IFORS 2014July 17

E.L. Cano

Introduction

The problem

Background

Modeling



Risk Management

Conclusions

Summary

Energy Systems


Building systems energy flow: Sankey diagram

Campus Pinkafeld test site


Demand side: requirements, uncertainty


Supply side: Markets, renewables


Strategic decisions are the goal


Operational performance interdependent with strategicdecisions


systems

IFORS 2014July 17

E.L. Cano

Introduction

The problem

Background

Modeling



Risk Management

Conclusions

Summary

Outline






systems

IFORS 2014July 17

E.L. Cano

Introduction

The problem

Background

Modeling



Risk Management

Conclusions

Summary

EnRiMa Project



systems

IFORS 2014July 17

E.L. Cano

Introduction

The problem

Background

Modeling



Risk Management

Conclusions

Summary

EnRiMa Models

EnRiMa DSSStrategicModule

Strategic DVs

StrategicConstraints

Upper-LevelOperational DVs

Upper-LevelEnergy-BalanceConstraints

OperationalModule

Lower-LevelOperational DVs

Lower-LevelEnergy-BalanceConstraints



systems

IFORS 2014July 17

E.L. Cano

Introduction

The problem

Background

Modeling



Risk Management

Conclusions

Summary

Decision Support Systems (DSS)

Model: Symbolic Model Specification (SMS)

Data: Statistical analysis

Framework: Stakeholders dialog



systems

IFORS 2014July 17

E.L. Cano

Introduction

The problem

Background

Modeling



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



systems

IFORS 2014July 17

E.L. Cano

Introduction

The problem

Background

Modeling



Risk Management

Conclusions

Summary

Outline






systems

IFORS 2014July 17

E.L. Cano

Introduction

The problem

Background

Modeling



Risk Management

Conclusions

Summary

Time Resolution

Representative short-term periods within long-term periods



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IFORS 2014July 17

E.L. Cano

Introduction

The problem

Background

Modeling



Risk Management

Conclusions

Summary

Time Resolution

Strategic decisions: horizon 15-20 years



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IFORS 2014July 17

E.L. Cano

Introduction

The problem

Background

Modeling



Risk Management

Conclusions

Summary

Time Resolution

Operational decisions (energy flows): hours



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IFORS 2014July 17

E.L. Cano

Introduction

The problem

Background

Modeling



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



systems

IFORS 2014July 17

E.L. Cano

Introduction

The problem

Background

Modeling



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



systems

IFORS 2014July 17

E.L. Cano

Introduction

The problem

Background

Modeling



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.


http://dx.doi.org/10.1016/j.enbuild.2014.06.030


systems

IFORS 2014July 17

E.L. Cano

Introduction

The problem

Background

Modeling



Risk Management

Conclusions

Summary

Outline






systems

IFORS 2014July 17

E.L. Cano

Introduction

The problem

Background

Modeling



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) =∞



systems

IFORS 2014July 17

E.L. Cano

Introduction

The problem

Background

Modeling



Risk Management

Conclusions

Summary




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


Infeasible 56/100Fsto(x ∗sto) = 68, 595 EUR.





systems

IFORS 2014July 17

E.L. Cano

Introduction

The problem

Background

Modeling



Risk Management

Conclusions

Summary




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


Infeasible 56/100






systems

IFORS 2014July 17

E.L. Cano

Introduction

The problem

Background

Modeling



Risk Management

Conclusions

Summary




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






systems

IFORS 2014July 17

E.L. Cano

Introduction

The problem

Background

Modeling



Risk Management

Conclusions

Summary




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




systems

IFORS 2014July 17

E.L. Cano

Introduction

The problem

Background

Modeling



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



systems

IFORS 2014July 17

E.L. Cano

Introduction

The problem

Background

Modeling



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



systems

IFORS 2014July 17

E.L. Cano

Introduction

The problem

Background

Modeling



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)



systems

IFORS 2014July 17

E.L. Cano

Introduction

The problem

Background

Modeling



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



systems

IFORS 2014July 17

E.L. Cano

Introduction

The problem

Background

Modeling



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



systems

IFORS 2014July 17

E.L. Cano

Introduction

The problem

Background

Modeling



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



systems

IFORS 2014July 17

E.L. Cano

Introduction

The problem

Background

Modeling



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



systems

IFORS 2014July 17

E.L. Cano

Introduction

The problem

Background

Modeling



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



systems

IFORS 2014July 17

E.L. Cano

Introduction

The problem

Background

Modeling



Risk Management

Conclusions

Summary

Outline






systems

IFORS 2014July 17

E.L. Cano

Introduction

The problem

Background

Modeling



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)



systems

IFORS 2014July 17

E.L. Cano

Introduction

The problem

Background

Modeling



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]



systems

IFORS 2014July 17

E.L. Cano

Introduction

The problem

Background

Modeling



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)



systems

IFORS 2014July 17

E.L. Cano

Introduction

The problem

Background

Modeling



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



systems

IFORS 2014July 17

E.L. Cano

Introduction

The problem

Background

Modeling



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



systems

IFORS 2014July 17

E.L. Cano

Introduction

The problem

Background

Modeling



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



systems

IFORS 2014July 17

E.L. Cano

Introduction

The problem

Background

Modeling



Risk Management

Conclusions

Summary

Outline






systems

IFORS 2014July 17

E.L. Cano

Introduction

The problem

Background

Modeling



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



systems

IFORS 2014July 17

E.L. Cano

Introduction

The problem

Background

Modeling



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).



systems

IFORS 2014July 17

E.L. Cano

Introduction

The problem

Background

Modeling



Risk Management

Conclusions

Summary

Discussion

Thanks for your attention !

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Stochastic optimization and risk management for an efficient planning of buildings' energy systems

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Transcript of Stochastic optimization and risk management for an efficient planning of buildings' energy systems