Bernard Drévillon
présentation
Bernard Drévillon commence sa carrière de recherche en Physique des Hautes Energies à l’Ecole polytechnique en 1969. Il soutient sa thèse soutenue en 1973. Puis il se tourne vers la synthèse de couches minces de silicium pour applications photovoltaïques et participe à la création du Laboratoire de Physique des Interfaces et des Couches Minces (LPICM) à l’Ecole polytechnique en 1986. Il se spécialise dans une technique de caractérisation optique originale (ellipsométrie spectroscopique) qui permet le suivi en temps réel de la croissance des couches. L’instrument sera ensuite exploitée commercialement par Jobin-Yvon (devenue Horiba) à partir des années 90. Plusieurs centaines d’ellipsomètres ont été vendus depuis dans le monde entier.
B. Drévillon a dirigé le LPICM de 1999 à 2012 et participé activement à la création de l’Institut Photovoltaïque d’Ile de France (IPVF, opérationnel en 2016), en collaboration avec EDF et TOTAL. B. Drévillon est l’auteur de plus de 250 publications dans des revues à comité de lecture (facteur H : 41) et d’une trentaine de brevets d’invention. Il a dirigé plus de vingt thèses. Il est Professeur à l’École polytechnique depuis 2001, il dirige le Master Renewable Energy Science and Technology (REST) depuis 2011.  Â
CA/DER/DEP/PHYS
PHY598 - Internship for Energy Environment (2018-2019)
STEEM-1 internships will start from the end of March and shall last 16 to 20 weeks (4 to 5 months), except somewhat shorter for RENE students.
A STEEM-1 internship must be a research internship.
However, the word research can be appreciated quite widely. It is not necessarily academic research, it may be scientific, technical, industrial or economic research or development, but it is not an execution internship. Indeed, the internship must not consist of carrying out standard works, whether predefined or not, within a department; the internship must have a well-defined objective and must lead to the realization of an original deliverable: a software, an experiment, a study that can be scientific, statistical, economic .... but original!
There is also no restriction on the organization hosting you: academic lab. or company, from start-up to large industrial group, or administration or paraadministrative body.
Fundamentally what is important is to assess the managerial capacity of the host organization. In that respect, we advise against start-up internships during STEEM-1 because the management capacities are there generally insufficient for your benefit and the topic studied to narrow. It will be much more interesting for you to join a startup during the second-year internship then this company will benefit of your previous experience and your scientific background.
The ability to present the progress of your internship and your results clearly and synthetically is also very important. Therefore, the internship ends with a report and an oral defence, see on SynapseS the dedicated advices for these topics.
You will have to choose an internship at the end of December or during January, to this end you will benefit on the web of a lot of information:
- Dedicated proposals received for STEEM students will be posted.
- The list of internships done by STEEM, REST and WAPE students during the previous years.
- The Polytechnique Career Center internship proposals whatever the discipline.
- You may join the LINKEDIN group “Ecole Polytechnique Energy & Environment Master Programs” that gathers a large number of Alumni, Professors and academic or industrial partners
These links will appear in time on your Polytechnique SynapseS account.
Also, do not hesitate to contact your professors.
About the procedure:
- Once you will have found an interesting internship, first contact Alexandre STEGNER for his approval of the subject and of the hosting organisation.
- At the end of November you will receive information about internship contract procedure from Mrs Uyen-Chi NGUYEN, in charge of Master-1 internships.
- A “Convention de Stage” will be signed by you, your host organisation, a STEEM academic referent, and Ecole Polytechnique.
STEEM-1 internships will start from the end of March and shall last 16 to 20 weeks (4 to 5 months), except somewhat shorter for RENE students.
A STEEM-1 internship must be a research internship.
However, the word research can be appreciated quite widely. It is not necessarily academic research, it may be scientific, technical, industrial or economic research or development, but it is not an execution internship. Indeed, the internship must not consist of carrying out standard works, whether predefined or not, within a department; the internship must have a well-defined objective and must lead to the realization of an original deliverable: a software, an experiment, a study that can be scientific, statistical, economic .... but original!
There is also no restriction on the organization hosting you: academic lab. or company, from start-up to large industrial group, or administration or paraadministrative body.
Fundamentally what is important is to assess the managerial capacity of the host organization. In that respect, we advise against start-up internships during STEEM-1 because the management capacities are there generally insufficient for your benefit and the topic studied to narrow. It will be much more interesting for you to join a startup during the second-year internship then this company will benefit of your previous experience and your scientific background.
The ability to present the progress of your internship and your results clearly and synthetically is also very important. Therefore, the internship ends with a report and an oral defence, see on SynapseS the dedicated advices for these topics.
You will have to choose an internship at the end of December or during January, to this end you will benefit on the web of a lot of information:
- Dedicated proposals received for STEEM students will be posted.
- The list of internships done by STEEM, REST and WAPE students during the previous years.
- The Polytechnique Career Center internship proposals whatever the discipline.
- You may join the LINKEDIN group “Ecole Polytechnique Energy & Environment Master Programs” that gathers a large number of Alumni, Professors and academic or industrial partners
These links will appear in time on your Polytechnique SynapseS account.
Also, do not hesitate to contact your professors.
About the procedure:
- Once you will have found an interesting internship, first contact Alexandre STEGNER for his approval of the subject and of the hosting organisation.
- At the end of November you will receive information about internship contract procedure from Mrs Uyen-Chi NGUYEN, in charge of Master-1 internships.
- A “Convention de Stage” will be signed by you, your host organisation, a STEEM academic referent, and Ecole Polytechnique.
PHY652A - Physics of Solar Cell Devices (Intro to PV) (2018-2019)
PHY652E - Introduction to Power Systems (Intro to PS) (2018-2019)
PHY652I - Topical seminars (2018-2019)
PHY652J - Solar Resource Seminar (2018-2019)
PHY652K - Lecture (2018-2019)
PHY661E - Fluvial and Maritime Resources for Renewable Energy (Fluv) (2018-2019)
PHY698 - Internship for Energy Environment II (2018-2019)
STEEM-2 internships will start from the end of March and shall last 20 to 24 weeks (5 to 6 months).
A STEEM-2 internship must be a research internship.
However, the word research can be appreciated quite widely. It is not necessarily academic research, it may be scientific, technical, industrial or economic research or development, but it is not an execution internship. Indeed, the internship must not consist of carrying out standard works, whether predefined or not, within a department; the internship must have a well-defined objective and must lead to the realization of an original deliverable: a software, an experiment, a study that can be scientific, statistical, economic .... but original!
There is also no restriction on the organization hosting you: academic lab. or company, from start-up to large industrial group, or administration or paraadministrative body, in France or abroad (but this may cause visa problems).
Fundamentally what is important is to assess the managerial capacity of the host organization, how it can guide you in your research and what you can learn there.
When choosing your internship, think about what you plan to do the year after. Do you plan to begin a PhD, to find a job in a company, to launch a start-up or anything else? There will be many opportunities for you, but some of them require a specific internship.
For an academic PhD prefer an internship in an academic lab, it may give you good references and even propose PhD opportunities. A thesis in a company is also conceivable, in this case favour rather important companies, small ones rarely have the means to support a PhD student.
For a future career in a company remember to become the real specialist they will need, the internship is there to train you in a specialty but also to give you the opportunity to prove your scientific and technical competences, often big or small companies use internships to test their future employers, it will be your last student exam so don’t miss it!
Whatever the type of internship you will choose, your ability to present the progress of your work and your results clearly and synthetically is also very important and may influence strongly your future. Therefore, the internship ends with a report and an oral defence, see on SynapseS the dedicated advices for these topics.
You will have to choose an internship at the end of December or during January, to this end you will benefit on the web of a lot of information:
- Dedicated proposals received for STEEM students will be posted.
- The list of internships done by STEEM, REST and WAPE students during the previous years.
- The Polytechnique Career Center internship proposals whatever the discipline.
- You may join the LINKEDIN group “Ecole Polytechnique Energy & Environment Master Programs” that gathers a large number of Alumni, Professors and academic or industrial partners
These links will appear in time on your Polytechnique SynapseS account
Also do not hesitate to contact your professors.
About the procedure:
- Once you will have found an interesting internship, first contact Alexandre STEGNER for his approval of the subject and of the hosting organisation.
- At the end of November you will receive information about internship contract procedure from Mrs Michèle Gesbert, in charge of Master-2 internships.
- A “Convention de Stage” will be signed by you, your host organisation, a STEEM academic referent, and Ecole Polytechnique.
STEEM-2 internships will start from the end of March and shall last 20 to 24 weeks (5 to 6 months).
A STEEM-2 internship must be a research internship.
However, the word research can be appreciated quite widely. It is not necessarily academic research, it may be scientific, technical, industrial or economic research or development, but it is not an execution internship. Indeed, the internship must not consist of carrying out standard works, whether predefined or not, within a department; the internship must have a well-defined objective and must lead to the realization of an original deliverable: a software, an experiment, a study that can be scientific, statistical, economic .... but original!
There is also no restriction on the organization hosting you: academic lab. or company, from start-up to large industrial group, or administration or paraadministrative body, in France or abroad (but this may cause visa problems).
Fundamentally what is important is to assess the managerial capacity of the host organization, how it can guide you in your research and what you can learn there.
When choosing your internship, think about what you plan to do the year after. Do you plan to begin a PhD, to find a job in a company, to launch a start-up or anything else? There will be many opportunities for you, but some of them require a specific internship.
For an academic PhD prefer an internship in an academic lab, it may give you good references and even propose PhD opportunities. A thesis in a company is also conceivable, in this case favour rather important companies, small ones rarely have the means to support a PhD student.
For a future career in a company remember to become the real specialist they will need, the internship is there to train you in a specialty but also to give you the opportunity to prove your scientific and technical competences, often big or small companies use internships to test their future employers, it will be your last student exam so don’t miss it!
Whatever the type of internship you will choose, your ability to present the progress of your work and your results clearly and synthetically is also very important and may influence strongly your future. Therefore, the internship ends with a report and an oral defence, see on SynapseS the dedicated advices for these topics.
You will have to choose an internship at the end of December or during January, to this end you will benefit on the web of a lot of information:
- Dedicated proposals received for STEEM students will be posted.
- The list of internships done by STEEM, REST and WAPE students during the previous years.
- The Polytechnique Career Center internship proposals whatever the discipline.
- You may join the LINKEDIN group “Ecole Polytechnique Energy & Environment Master Programs” that gathers a large number of Alumni, Professors and academic or industrial partners
These links will appear in time on your Polytechnique SynapseS account
Also do not hesitate to contact your professors.
About the procedure:
- Once you will have found an interesting internship, first contact Alexandre STEGNER for his approval of the subject and of the hosting organisation.
- At the end of November you will receive information about internship contract procedure from Mrs Michèle Gesbert, in charge of Master-2 internships.
- A “Convention de Stage” will be signed by you, your host organisation, a STEEM academic referent, and Ecole Polytechnique.
BIO652 - Nature-based solutions to substitute fossile resources and address global change (2018-2019)
Nature-based solutions to substitute fossile resources and address global change
Lecturer: Benoît Gabrielle - Agro-ParisTech
Natural ecosystems and the services they provide are a key to address current environmental challenges, such as climate change, the preservation of air and water quality, and the transition toward a low-carbon economy. Engineering these services via the management of ecosystems, land-use planning or the integration of plants in urban environments can « pave the way towards a more resource efficient, competitive and greener economy » (EU Research Agenda, 2015). Nature-based solutions include for example the production of bio-based alternatives to fossile-based products, the mitigation of heat waves in cities via the presence of vegetation, the enhacement of carbon storage in ecosystems or the management of watersheds to reduce flood risks.
The aim of the course is to raise the awareness of these solutions, with a particular focus on biomass production and transformation into fuels, materials and chemicals to substitute fossile resources, and to equip them with key concepts and know-hows on the design and assessment of such solutions. The course will provide students with a detailed understanding of the issues associated with the development of nature-based solutions to meet our needs for food and energy, mitigate climate change or air pollution, and methods to their sustainability along the environmental and economic dimensions.
Langue du cours : Anglais
Credits ECTS : 4
Nature-based solutions to substitute fossile resources and address global change
Lecturer: Benoît Gabrielle - Agro-ParisTech
Natural ecosystems and the services they provide are a key to address current environmental challenges, such as climate change, the preservation of air and water quality, and the transition toward a low-carbon economy. Engineering these services via the management of ecosystems, land-use planning or the integration of plants in urban environments can « pave the way towards a more resource efficient, competitive and greener economy » (EU Research Agenda, 2015). Nature-based solutions include for example the production of bio-based alternatives to fossile-based products, the mitigation of heat waves in cities via the presence of vegetation, the enhacement of carbon storage in ecosystems or the management of watersheds to reduce flood risks.
The aim of the course is to raise the awareness of these solutions, with a particular focus on biomass production and transformation into fuels, materials and chemicals to substitute fossile resources, and to equip them with key concepts and know-hows on the design and assessment of such solutions. The course will provide students with a detailed understanding of the issues associated with the development of nature-based solutions to meet our needs for food and energy, mitigate climate change or air pollution, and methods to their sustainability along the environmental and economic dimensions.
Langue du cours : Anglais
Credits ECTS : 4
MEC652F - Wind Power (2018-2019)
Lecturer: Fawad Massouh
Eligibility/Pre- requisites
Due to use of experimental facilities, the number of students is limited to 24
This course needs basic knowledge in fluid mechanics and in electricity
Learning outcomes
-
Global vision of wind power and the evolution of wind turbines
-
Ability to analyze wind data on a site and calculate the potential of wind energy
-
Understanding the operation and control of the chain of energy transfer formed by the wind turbine.
-
Understanding the technical problems related to the connection of wind turbines to power grids
-
Understanding of basic aerodynamic models for the rotor of wind turbines
-
Experience in numerical simulation of flow around wind turbines
-
Experience in wind tunnel experimentation undertaken to obtain wind turbine performances
-
Experience in writing a scientific paper and its oral public presentation
Course main content
-
General presentation of wind energy and wind turbines
Evolution and classification of wind turbines, Wind turbine components. Overview of the wind power industry in European Union and worldwide. Considerations in wind farm siting and operation
-
Wind characteristics and wind energy potential
Characteristics of wind. Meteorological aspects. Weibull distribution. Calculation of theoretical wind energy potential. Calculation of produced energy by a given wind turbine. General presentation of atmospheric boundary layer. Wind velocity measurements.
-
Aerodynamics of wind turbines
Aerodynamics of an airfoil, forces and coefficients. Operation in normal and stall mode. Rotor aerodynamics. Momentum theory, Betz’ law, Blade element momentum theory, vortex theories.
-
Mechanical Design
Normal and extreme loads as defined by the standards, Blade design, presentation of employed materials. Mechanical behavior and test. Aeroelasticity of blades. Rotor in operation.
-
Electrical Power conversion in wind turbines
Fixed speed wind turbine. Variable speed wind turbine. Full power electronic converter. Double feed induction machine. Integration of wind turbines in electrical networks of transport and of distribution.
-
Control and Regulation of wind turbines
Power electronic converter control
Wind turbine control strategy: stall, pitch control.
-
Introduction to CFD and simulations of flow and wake of a wind turbine. Practice
of CAO and preparation of the numerical model. Analysis and synthesis of results.
Submission of a report.
-
Experimental investigation in ENSAM wind tunnel.
Tests of a wind turbine and determination of its characteristic curves: thrust, torque
and power. Analysis of results and submission of a testing report.
-
Initiation to scientific communication.
The student is asked to do a personal work within a small group about a research subject in the field of wind enegy. A specific bibliographic revue must be prepared. This work must be finalized as a written paper respecting a given template and also as an oral presentation.
Examination and requirements for final grade
Students are graded through :
- Written final exam (open book) 60%
- Numerical simulation session and report 10%
- Wind tunnel experiments and report 10%
- Written bibliographic revue and oral presentation 20%
Coordinator Instructors
Fawaz MASSOUH, ENSAM ParisTech
Marc RAPIN, Xavier GUILLAUD, Ivan DOBREV, Sofiane KHELLADI
Langue du cours : Anglais
Credits ECTS : 4
Lecturer: Fawad Massouh
Eligibility/Pre- requisites
Due to use of experimental facilities, the number of students is limited to 24
This course needs basic knowledge in fluid mechanics and in electricity
Learning outcomes
-
Global vision of wind power and the evolution of wind turbines
-
Ability to analyze wind data on a site and calculate the potential of wind energy
-
Understanding the operation and control of the chain of energy transfer formed by the wind turbine.
-
Understanding the technical problems related to the connection of wind turbines to power grids
-
Understanding of basic aerodynamic models for the rotor of wind turbines
-
Experience in numerical simulation of flow around wind turbines
-
Experience in wind tunnel experimentation undertaken to obtain wind turbine performances
-
Experience in writing a scientific paper and its oral public presentation
Course main content
-
General presentation of wind energy and wind turbines
Evolution and classification of wind turbines, Wind turbine components. Overview of the wind power industry in European Union and worldwide. Considerations in wind farm siting and operation
-
Wind characteristics and wind energy potential
Characteristics of wind. Meteorological aspects. Weibull distribution. Calculation of theoretical wind energy potential. Calculation of produced energy by a given wind turbine. General presentation of atmospheric boundary layer. Wind velocity measurements.
-
Aerodynamics of wind turbines
Aerodynamics of an airfoil, forces and coefficients. Operation in normal and stall mode. Rotor aerodynamics. Momentum theory, Betz’ law, Blade element momentum theory, vortex theories.
-
Mechanical Design
Normal and extreme loads as defined by the standards, Blade design, presentation of employed materials. Mechanical behavior and test. Aeroelasticity of blades. Rotor in operation.
-
Electrical Power conversion in wind turbines
Fixed speed wind turbine. Variable speed wind turbine. Full power electronic converter. Double feed induction machine. Integration of wind turbines in electrical networks of transport and of distribution.
-
Control and Regulation of wind turbines
Power electronic converter control
Wind turbine control strategy: stall, pitch control.
-
Introduction to CFD and simulations of flow and wake of a wind turbine. Practice
of CAO and preparation of the numerical model. Analysis and synthesis of results.
Submission of a report.
-
Experimental investigation in ENSAM wind tunnel.
Tests of a wind turbine and determination of its characteristic curves: thrust, torque
and power. Analysis of results and submission of a testing report.
-
Initiation to scientific communication.
The student is asked to do a personal work within a small group about a research subject in the field of wind enegy. A specific bibliographic revue must be prepared. This work must be finalized as a written paper respecting a given template and also as an oral presentation.
Examination and requirements for final grade
Students are graded through :
- Written final exam (open book) 60%
- Numerical simulation session and report 10%
- Wind tunnel experiments and report 10%
- Written bibliographic revue and oral presentation 20%
Coordinator Instructors
Fawaz MASSOUH, ENSAM ParisTech
Marc RAPIN, Xavier GUILLAUD, Ivan DOBREV, Sofiane KHELLADI
Langue du cours : Anglais
Credits ECTS : 4
MAP661D - Stochastic Optimization and Management of Energies (2018-2019)
Master ParisTech REST
Renewable Energy Science and Technology
Graduate Degree STEEM
Energy Environment: Science Technology and Management
MAP661D 2018-2019
Stochastic and Decentralized Optimization
for the Management of Micro-Grids
Michel DE LARA, CERMICS-École des Ponts ParisTech
Eligibility/Pre-requisites.
- Mathematical skills. Computer skills.
- Continuous optimization: linear programming, convexity, duality, first-order optimality conditions. [Ber96]
- Probability calculus: probability space, probability, random variables, independence, law of large numbers. [Fel68]
- Software Scicoslab to be installed Scicoslab (else, install software Scilab)
Learning outcomes. After the course the student should be able to
- design mathematical models for energy storage and delivery of renewable energies, especially in micro-grids, and formulate cost-minimization problems,
- use the scientific software Scicoslab and numerically solve small scale problems.
Course main content. The course mixes theoretical sessions, modeling exercises and computer sessions.
In introduction, we present examples of micro-grid and virtual power plant management -- where the question of electrical storage is put, due to the need to answer a varying demand and to incorporate intermittent and highly variable renewable energies. During the course, we will present concepts and tools to formulate such problems as stochastic dynamic optimization problems. For this purpose, the first sessions are dedicated to mathematical recalls in probability and optimization, followed by an introduction to the scientific software Scicoslab.
Then, we turn to stochastic optimization. In a deterministic optimization problem, the values of all parameters are supposed known. What happens when this is no longer the case? And when some values are revealed during the stages of decision? We present stochastic optimization, at the same time as a frame to formulate problems under uncertainty, and as methods to solve them according to the formulation. More precisely, we present two-stage stochastic programming (and the resolution on scenario tree or by scenarios) and multi-stage stochastic control (and the resolution by stochastic dynamic programming). We finish with the Stochastic Dual Dynamic Programming (SDDP) algorithm (used in commercial software in the world of the energy), which mixes dynamic programming and cutting plane algorithm. Depending on time availability, we will try to shed light on decomposition methods that lead to decentralized optimization (especially adapted to micro-grid management).
Modeling exercises and computer sessions tackle issues like optimal economic dispatch of energy production units, storage/delivery optimization problem to buffer an intermittent and variable source of energy, dam optimal management with stochastic water inflows, battery optimal management with renewable energy inputs.
Examination and requirements for final grade. At the end of each computer session, the student produces a report, which receives a mark after evaluation. Mini-exams, presence and participation also contribute to the final grade.
Contact person. Michel De Lara (Cermics--École des Ponts ParisTech) professional webpage
Link course. http://cermics.enpc.fr/~delara/TEACHING/STEEM2-REST/ course webpage
Link master REST. http://www.master-renewable-energy.com/ master REST webpage
Link Graduate Degree STEEM. https://portail.polytechnique.edu/graduatedegree/steem/ Graduate Degree STEEM map of the courses rooms
Program
1 / Tuesday 8, January 2019 (Amphi XXX)
Scanning the course schedule (14h00-14h30)
Introductory talk (14h30-15h30)
To introduce the course, we present an example of micro-grid management that can be solved using stochastic dynamic optimization.
Work done by François Pacaud (Efficacity and Cermics--École des Ponts ParisTech)
``Optimal Energy Management of a Urban District'' slides
Lecture and exercises (16h00-18h00)
Recalls on probability calculus: probability space, probability, random variables, law of a random variable, mathematical expectation (linearity), indicator function (law, expectation), independence of random variables, almost-sure convergence and law of large numbers. [Fel68]
Exercises on probability calculus. The blood testing problem. slides
2 / Tuesday 15, January 2019 (Amphi XXX)
Lecture and exercises (14h00-16h00)
Recalls and exercises on continuous optimization [Ber96]. slides
- Recalls on convexity: convex sets, convex functions, strict and strong convexity (characterization by the Hessian in the smooth case), operations preserving convexity.
- Abstract formulation of a minimization problem: criterion, constraints. Sufficient conditions for the existence of a minimum (continuity and compacity/coercivity).
Sufficient condition for the uniqueness of a minimum (strict convexity). Exercises with a quadratic objective function on an interval. - Definition of a local minimizer; necessary condition in the differentiable case. Formulation of a minimization problem under explicit equality constraints.
Necessary first-order optimality conditions in the regular/affine equality constraints case; Lagrangian, duality, multipliers.
Sufficient first-order optimality conditions in the convex-affine case. Exercises.
Exercises (16h30-18h00)
We present, under the form of an exercise, an example of optimization problem under uncertainty: ``the newsvendor problem''. slides
3 / Tuesday 22, January 2019 (Amphi XXX)
Computer session
Introduction to the scientific software Scicoslab. [CCN10] computer session
Computer session
4 / Tuesday 29, January 2019 (Amphi XXX)
Modeling session
``Day Ahead Energy Markets'' slides
Computer session
The newsvendor problem
You will send the results of the computer project The newsvendor problem
under the form of a pdf file TP1_REST_2018_MYNAME.pdf or TP1_STEEM_2018_MYNAME.pdf to delara@cermics.enpc.fr before 2 February 2019, 12h.
- You can choose any software for the computation (but Scicoslab is recommended).
- You can choose any text editor for the report.
- You can insert computer code, but in limited amount.
- The report will display on the first page: title, given name followed by family name, date, mention of REST 2018-2019or of STEEM 2018-2019.
5 / Tuesday 5, February 2019 (Amphi XXX)
Lecture
Two-stage stochastic programming on a scenario tree.
Non-anticipativity constraint along scenarios: tree representation. slides
[SDR09]
Computer session
Sizing of reserves for the balancing on an electric market
(linear and quadratic optimization on a tree)
6 / Tuesday 12, February 2019 (Amphi XXX)
Exercises
Exercises on probability, optimization and two-stage stochastic programming.
Computer session
Sizing of reserves for the balancing on an electric market
(linear and quadratic optimization on a tree)
Lecture
Two-stage stochastic programming on a fan. slides
Non-anticipativity constraint along scenarios.
Scenario decomposition by Lagrangian relaxation. Progressive Hedging [RW91].
7 / Tuesday 19, February 2019 (Amphi XXX)
Exam (14h00-15h30)
Exam on optimization and two-stage stochastic programming.
Computer session (16h00-18h00)
Sizing of reserves for the balancing on an electric market
(linear and quadratic optimization on a fan)
You will send the results of the computer project Sizing of reserves for the balancing on an electric market
under the form of a pdf file TP2_REST_2018_MYNAME.pdf or TP2_STEEM_2018_MYNAME.pdf to delara@cermics.enpc.fr before 20 February 2019, 18h.
8 / Tuesday 5, March 2019 (Amphi XXX)
Correction of the exam (14h00-16h00)
Lecture and exercises
Obtaining the value of a mine by dynamic programming.
Dynamical models of storage (battery models, dam models).
Dynamical sequential systems with control.
9 / Tuesday 12, March 2019 (Amphi XXX)
Lecture and exercises (14h00-17h00)
Dynamical sequential systems with control and noise.
Optimal control of stochastic dynamical sequential systems. slides
Stochastic dynamic programming. Curse of dimensionality. slides
Exercise on stochastic dynamic programming.
Computer session (17h00-18h00)
Dam optimal management under uncertainty
10 / Tuesday 19, March 2019 (Amphi XXX)
Exam (14h00-15h30)
Exam on stochastic dynamic programming.
Computer session (16h00-18h00)
Dam optimal management under uncertainty
You will send a report of the computer project Dam optimal management under uncertainty
(up to Question 8 included) under the form of a pdf file TP3_REST_2018_MYNAME.pdf or TP3_STEEM_2018_MYNAME.pdf to delara@cermics.enpc.fr before 20 March 2019, 18h.
Bibliography
- Ber96
- D. P. Bertsekas.
Constrained Optimization and Lagrange Multiplier Methods.
Athena Scientific, Belmont, Massachusetts, 1996. - Ber00
- D. P. Bertsekas.
Dynamic Programming and Optimal Control.
Athena Scientific, Belmont, Massachusetts, second edition, 2000.
Volumes 1 and 2. - CCCD15
- P. Carpentier, J.-P. Chancelier, G. Cohen, and M. De Lara.
Stochastic Multi-Stage Optimization. At the Crossroads between Discrete Time Stochastic Control and Stochastic Programming.
Springer-Verlag, Berlin, 2015. - CCN10
- Stephen Campbell, Jean-Philippe Chancelier, and Ramine Nikoukhah.
Modeling and Simulation in Scilab/Scicos with ScicosLab 4.4.
Springer-Verlag, New York, 2 edition, 2010. - Fel68
- W. Feller.
An Introduction to Probability Theory and its Applications, volume 1.
Wiley, New York, third edition, 1968. - RW91
- R.T. Rockafellar and R. J-B. Wets.
Scenarios and policy aggregation in optimization under uncertainty.
Mathematics of operations research, 16(1):119-147, 1991. - SDR09
- A. Shapiro, D. Dentcheva, and A. Ruszczynski.
Lectures on stochastic programming: modeling and theory.
The society for industrial and applied mathematics and the mathematical programming society, Philadelphia, USA, 2009.
Master ParisTech REST
Renewable Energy Science and Technology
Graduate Degree STEEM
Energy Environment: Science Technology and Management
MAP661D 2018-2019
Stochastic and Decentralized Optimization
for the Management of Micro-Grids
Michel DE LARA, CERMICS-École des Ponts ParisTech
Eligibility/Pre-requisites.
- Mathematical skills. Computer skills.
- Continuous optimization: linear programming, convexity, duality, first-order optimality conditions. [Ber96]
- Probability calculus: probability space, probability, random variables, independence, law of large numbers. [Fel68]
- Software Scicoslab to be installed Scicoslab (else, install software Scilab)
Learning outcomes. After the course the student should be able to
- design mathematical models for energy storage and delivery of renewable energies, especially in micro-grids, and formulate cost-minimization problems,
- use the scientific software Scicoslab and numerically solve small scale problems.
Course main content. The course mixes theoretical sessions, modeling exercises and computer sessions.
In introduction, we present examples of micro-grid and virtual power plant management -- where the question of electrical storage is put, due to the need to answer a varying demand and to incorporate intermittent and highly variable renewable energies. During the course, we will present concepts and tools to formulate such problems as stochastic dynamic optimization problems. For this purpose, the first sessions are dedicated to mathematical recalls in probability and optimization, followed by an introduction to the scientific software Scicoslab.
Then, we turn to stochastic optimization. In a deterministic optimization problem, the values of all parameters are supposed known. What happens when this is no longer the case? And when some values are revealed during the stages of decision? We present stochastic optimization, at the same time as a frame to formulate problems under uncertainty, and as methods to solve them according to the formulation. More precisely, we present two-stage stochastic programming (and the resolution on scenario tree or by scenarios) and multi-stage stochastic control (and the resolution by stochastic dynamic programming). We finish with the Stochastic Dual Dynamic Programming (SDDP) algorithm (used in commercial software in the world of the energy), which mixes dynamic programming and cutting plane algorithm. Depending on time availability, we will try to shed light on decomposition methods that lead to decentralized optimization (especially adapted to micro-grid management).
Modeling exercises and computer sessions tackle issues like optimal economic dispatch of energy production units, storage/delivery optimization problem to buffer an intermittent and variable source of energy, dam optimal management with stochastic water inflows, battery optimal management with renewable energy inputs.
Examination and requirements for final grade. At the end of each computer session, the student produces a report, which receives a mark after evaluation. Mini-exams, presence and participation also contribute to the final grade.
Contact person. Michel De Lara (Cermics--École des Ponts ParisTech) professional webpage
Link course. http://cermics.enpc.fr/~delara/TEACHING/STEEM2-REST/ course webpage
Link master REST. http://www.master-renewable-energy.com/ master REST webpage
Link Graduate Degree STEEM. https://portail.polytechnique.edu/graduatedegree/steem/ Graduate Degree STEEM map of the courses rooms
Program
1 / Tuesday 8, January 2019 (Amphi XXX)
Scanning the course schedule (14h00-14h30)
Introductory talk (14h30-15h30)
To introduce the course, we present an example of micro-grid management that can be solved using stochastic dynamic optimization.
Work done by François Pacaud (Efficacity and Cermics--École des Ponts ParisTech)
``Optimal Energy Management of a Urban District'' slides
Lecture and exercises (16h00-18h00)
Recalls on probability calculus: probability space, probability, random variables, law of a random variable, mathematical expectation (linearity), indicator function (law, expectation), independence of random variables, almost-sure convergence and law of large numbers. [Fel68]
Exercises on probability calculus. The blood testing problem. slides
2 / Tuesday 15, January 2019 (Amphi XXX)
Lecture and exercises (14h00-16h00)
Recalls and exercises on continuous optimization [Ber96]. slides
- Recalls on convexity: convex sets, convex functions, strict and strong convexity (characterization by the Hessian in the smooth case), operations preserving convexity.
- Abstract formulation of a minimization problem: criterion, constraints. Sufficient conditions for the existence of a minimum (continuity and compacity/coercivity).
Sufficient condition for the uniqueness of a minimum (strict convexity). Exercises with a quadratic objective function on an interval. - Definition of a local minimizer; necessary condition in the differentiable case. Formulation of a minimization problem under explicit equality constraints.
Necessary first-order optimality conditions in the regular/affine equality constraints case; Lagrangian, duality, multipliers.
Sufficient first-order optimality conditions in the convex-affine case. Exercises.
Exercises (16h30-18h00)
We present, under the form of an exercise, an example of optimization problem under uncertainty: ``the newsvendor problem''. slides
3 / Tuesday 22, January 2019 (Amphi XXX)
Computer session
Introduction to the scientific software Scicoslab. [CCN10] computer session
Computer session
4 / Tuesday 29, January 2019 (Amphi XXX)
Modeling session
``Day Ahead Energy Markets'' slides
Computer session
The newsvendor problem
You will send the results of the computer project The newsvendor problem
under the form of a pdf file TP1_REST_2018_MYNAME.pdf or TP1_STEEM_2018_MYNAME.pdf to delara@cermics.enpc.fr before 2 February 2019, 12h.
- You can choose any software for the computation (but Scicoslab is recommended).
- You can choose any text editor for the report.
- You can insert computer code, but in limited amount.
- The report will display on the first page: title, given name followed by family name, date, mention of REST 2018-2019or of STEEM 2018-2019.
5 / Tuesday 5, February 2019 (Amphi XXX)
Lecture
Two-stage stochastic programming on a scenario tree.
Non-anticipativity constraint along scenarios: tree representation. slides
[SDR09]
Computer session
Sizing of reserves for the balancing on an electric market
(linear and quadratic optimization on a tree)
6 / Tuesday 12, February 2019 (Amphi XXX)
Exercises
Exercises on probability, optimization and two-stage stochastic programming.
Computer session
Sizing of reserves for the balancing on an electric market
(linear and quadratic optimization on a tree)
Lecture
Two-stage stochastic programming on a fan. slides
Non-anticipativity constraint along scenarios.
Scenario decomposition by Lagrangian relaxation. Progressive Hedging [RW91].
7 / Tuesday 19, February 2019 (Amphi XXX)
Exam (14h00-15h30)
Exam on optimization and two-stage stochastic programming.
Computer session (16h00-18h00)
Sizing of reserves for the balancing on an electric market
(linear and quadratic optimization on a fan)
You will send the results of the computer project Sizing of reserves for the balancing on an electric market
under the form of a pdf file TP2_REST_2018_MYNAME.pdf or TP2_STEEM_2018_MYNAME.pdf to delara@cermics.enpc.fr before 20 February 2019, 18h.
8 / Tuesday 5, March 2019 (Amphi XXX)
Correction of the exam (14h00-16h00)
Lecture and exercises
Obtaining the value of a mine by dynamic programming.
Dynamical models of storage (battery models, dam models).
Dynamical sequential systems with control.
9 / Tuesday 12, March 2019 (Amphi XXX)
Lecture and exercises (14h00-17h00)
Dynamical sequential systems with control and noise.
Optimal control of stochastic dynamical sequential systems. slides
Stochastic dynamic programming. Curse of dimensionality. slides
Exercise on stochastic dynamic programming.
Computer session (17h00-18h00)
Dam optimal management under uncertainty
10 / Tuesday 19, March 2019 (Amphi XXX)
Exam (14h00-15h30)
Exam on stochastic dynamic programming.
Computer session (16h00-18h00)
Dam optimal management under uncertainty
You will send a report of the computer project Dam optimal management under uncertainty
(up to Question 8 included) under the form of a pdf file TP3_REST_2018_MYNAME.pdf or TP3_STEEM_2018_MYNAME.pdf to delara@cermics.enpc.fr before 20 March 2019, 18h.
Bibliography
- Ber96
- D. P. Bertsekas.
Constrained Optimization and Lagrange Multiplier Methods.
Athena Scientific, Belmont, Massachusetts, 1996. - Ber00
- D. P. Bertsekas.
Dynamic Programming and Optimal Control.
Athena Scientific, Belmont, Massachusetts, second edition, 2000.
Volumes 1 and 2. - CCCD15
- P. Carpentier, J.-P. Chancelier, G. Cohen, and M. De Lara.
Stochastic Multi-Stage Optimization. At the Crossroads between Discrete Time Stochastic Control and Stochastic Programming.
Springer-Verlag, Berlin, 2015. - CCN10
- Stephen Campbell, Jean-Philippe Chancelier, and Ramine Nikoukhah.
Modeling and Simulation in Scilab/Scicos with ScicosLab 4.4.
Springer-Verlag, New York, 2 edition, 2010. - Fel68
- W. Feller.
An Introduction to Probability Theory and its Applications, volume 1.
Wiley, New York, third edition, 1968. - RW91
- R.T. Rockafellar and R. J-B. Wets.
Scenarios and policy aggregation in optimization under uncertainty.
Mathematics of operations research, 16(1):119-147, 1991. - SDR09
- A. Shapiro, D. Dentcheva, and A. Ruszczynski.
Lectures on stochastic programming: modeling and theory.
The society for industrial and applied mathematics and the mathematical programming society, Philadelphia, USA, 2009.
PHY630 - Refresher Course in Physics (2018-2019)
PHY558B - Photovoltaïcs Solar Energy (2018-2019)
Course outline :
- General introduction : Photovoltaic energy (PV) in the worldwide energetic context. Evolution of the PV market.
- Introduction to the physics of crystalline semiconductors : band structure, optical absorption, recombination, intrinsic and extrinsic semiconductors.
- Transport phenomena in semiconductors. The p-n junction. Photovoltaic effect.
- Asymetrical devices. Metal/semiconductor contacts. Heterojunctions
- Solar cell operation. Solar cells and modules.
- Crystalline silicon (c-Si) solar cells and III-V compounds
- Amorphous and nanocrystalline semiconducors (structure, doping)
- Silicon thin film solar cells. Comparison with c-Si. Silicon heterojunctions
- Cost of PV electricity. Environmental and social impact. Grid-integration challenges.
Niveau requis :
Recommended courses for Ecole polytechnique's students :
PHY430 - Advanced Quantum Physics and PHY433 - Statistical Physics
Langue du cours : English
Credits ECTS : 5
Course outline :
- General introduction : Photovoltaic energy (PV) in the worldwide energetic context. Evolution of the PV market.
- Introduction to the physics of crystalline semiconductors : band structure, optical absorption, recombination, intrinsic and extrinsic semiconductors.
- Transport phenomena in semiconductors. The p-n junction. Photovoltaic effect.
- Asymetrical devices. Metal/semiconductor contacts. Heterojunctions
- Solar cell operation. Solar cells and modules.
- Crystalline silicon (c-Si) solar cells and III-V compounds
- Amorphous and nanocrystalline semiconducors (structure, doping)
- Silicon thin film solar cells. Comparison with c-Si. Silicon heterojunctions
- Cost of PV electricity. Environmental and social impact. Grid-integration challenges.
Niveau requis :
Recommended courses for Ecole polytechnique's students :
PHY430 - Advanced Quantum Physics and PHY433 - Statistical Physics
Langue du cours : English
Credits ECTS : 5