BIO653 - Nature-based Solutions to Substitute Fossil Resources and Address Global Warming (2020-2021)

PHY630 - Physics Refresher Course (2020-2021)

PHY698 - Internship for Energy Environment II (2020-2021)

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.

MAP661D - Stochastic Optimization and Management of Energies (2020-2021)

Master ParisTech REST
Renewable Energy Science and Technology
   
Graduate Degree STEEM
Energy Environment: Science Technology and Management

MAP661D   2019-2020

Stochastic and Decentralized Optimization
for the Management of Micro-Grids

Michel DE LARA, CERMICS-École des Ponts ParisTech

Eligibility/Pre-requisites.

• Mathematical skills (meaning the ability to manipulate abstract concepts, and to make calculus). Computer skills (meaning having already programmed).
• Mathematical background: linear algebra (vectors, matrices, symmetric matrices, positive symmetric matrices); topology on  (open and closed subsets, bounded subsets, compacity, continuity of functions); differential calculus on  (differentiation, partial derivatives, gradient, Jacobian matrix).
• Continuous optimization: linear programming, convexity, Lagrange multipliers and 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 / September 2019

Admission exam (14h30-16h00)

2 / Tuesday 7, January 2020 (Amphi Gregory)

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

3 / Tuesday 14, January 2020 (Amphi Gregory)

Lecture and exercises (14h00-16h00)

Recalls and exercises on continuous optimization [Ber96].      slides

• Recalls on mathematical background: linear algebra (vectors, matrices, symmetric matrices, positive symmetric matrices); topology on  (open and closed subsets, bounded subsets, compacity, continuity of functions); differential calculus on  (differentiation, partial derivatives, gradient, Jacobian matrix).
• 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.

Exercises (16h30-18h00)

We present, under the form of an exercise, an example of optimization problem under uncertainty: ``the newsvendor problem''.      slides

4 / Tuesday 21, January 2020 (Amphi Gregory)

Computer session

Introduction to the scientific software Scicoslab. [CCN10]      computer session

Computer session

The newsvendor problem (only the Section 1, The newsvendor problem (integer formulation))

5 / Tuesday 28, January 2020 (Amphi Gregory)

Modeling session

``Day Ahead Energy Markets''     slides

Computer session

The newsvendor problem (only the Section 1, The newsvendor problem (integer formulation))

You will send the results of the computer project The newsvendor problem (only the Section 1, The newsvendor problem (integer formulation))
under the form of a pdf file TP1_REST_2019_MYNAME.pdf or TP1_STEEM_2019_MYNAME.pdf to delara@cermics.enpc.fr before Monday 4 February 2020, 9 AM.

• 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 2019-2020or of STEEM 2019-2020.

6 / Tuesday 4, February 2020 (Amphi Gregory)

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)

Exercises

Exercises on probability, optimization and two-stage stochastic programming.

7 / Tuesday 11, February 2020 (Amphi Gregory)

Recalls and exercises on continuous optimization [Ber96].      slides

• 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.

Computer session

     Sizing of reserves for the balancing on an electric market
(linear and quadratic optimization on a tree)

8 / Tuesday 18, February 2020 (Amphi Gregory)

Lecture

Two-stage stochastic programming on a fan.      slides

Non-anticipativity constraint along scenarios.

Scenario decomposition by Lagrangian relaxation. Progressive Hedging [RW91].

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_2019_MYNAME.pdf or TP2_STEEM_2019_MYNAME.pdf to delara@cermics.enpc.fr before 20 February 2020, 18h.

9 / Tuesday 3, March 2020 (Amphi Gregory)

Correction of the computer project (14h00-14h30)

Exam (14h30-16h00)

Exam on optimization and two-stage stochastic programming.

Correction of the exam (16h30-17h00)

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.

10 / Tuesday 10, March 2020 (Amphi Gregory)

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.

[Ber00,CCCD15]

Computer session (17h00-18h00)

    Dam optimal management under uncertainty

11 / Tuesday 17, March 2020 (Amphi Gregory)

Computer session (14h00-18h00)

    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_2019_MYNAME.pdf or TP3_STEEM_2019_MYNAME.pdf to delara@cermics.enpc.fr before Wednesday 20 March 2020, 15h.

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   2019-2020

Stochastic and Decentralized Optimization
for the Management of Micro-Grids

Michel DE LARA, CERMICS-École des Ponts ParisTech

Eligibility/Pre-requisites.

• Mathematical skills (meaning the ability to manipulate abstract concepts, and to make calculus). Computer skills (meaning having already programmed).
• Mathematical background: linear algebra (vectors, matrices, symmetric matrices, positive symmetric matrices); topology on  (open and closed subsets, bounded subsets, compacity, continuity of functions); differential calculus on  (differentiation, partial derivatives, gradient, Jacobian matrix).
• Continuous optimization: linear programming, convexity, Lagrange multipliers and 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 / September 2019

Admission exam (14h30-16h00)

2 / Tuesday 7, January 2020 (Amphi Gregory)

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

3 / Tuesday 14, January 2020 (Amphi Gregory)

Lecture and exercises (14h00-16h00)

Recalls and exercises on continuous optimization [Ber96].      slides

• Recalls on mathematical background: linear algebra (vectors, matrices, symmetric matrices, positive symmetric matrices); topology on  (open and closed subsets, bounded subsets, compacity, continuity of functions); differential calculus on  (differentiation, partial derivatives, gradient, Jacobian matrix).
• 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.

Exercises (16h30-18h00)

We present, under the form of an exercise, an example of optimization problem under uncertainty: ``the newsvendor problem''.      slides

4 / Tuesday 21, January 2020 (Amphi Gregory)

Computer session

Introduction to the scientific software Scicoslab. [CCN10]      computer session

Computer session

The newsvendor problem (only the Section 1, The newsvendor problem (integer formulation))

5 / Tuesday 28, January 2020 (Amphi Gregory)

Modeling session

``Day Ahead Energy Markets''     slides

Computer session

The newsvendor problem (only the Section 1, The newsvendor problem (integer formulation))

You will send the results of the computer project The newsvendor problem (only the Section 1, The newsvendor problem (integer formulation))
under the form of a pdf file TP1_REST_2019_MYNAME.pdf or TP1_STEEM_2019_MYNAME.pdf to delara@cermics.enpc.fr before Monday 4 February 2020, 9 AM.

• 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 2019-2020or of STEEM 2019-2020.

6 / Tuesday 4, February 2020 (Amphi Gregory)

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)

Exercises

Exercises on probability, optimization and two-stage stochastic programming.

7 / Tuesday 11, February 2020 (Amphi Gregory)

Recalls and exercises on continuous optimization [Ber96].      slides

• 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.

Computer session

     Sizing of reserves for the balancing on an electric market
(linear and quadratic optimization on a tree)

8 / Tuesday 18, February 2020 (Amphi Gregory)

Lecture

Two-stage stochastic programming on a fan.      slides

Non-anticipativity constraint along scenarios.

Scenario decomposition by Lagrangian relaxation. Progressive Hedging [RW91].

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_2019_MYNAME.pdf or TP2_STEEM_2019_MYNAME.pdf to delara@cermics.enpc.fr before 20 February 2020, 18h.

9 / Tuesday 3, March 2020 (Amphi Gregory)

Correction of the computer project (14h00-14h30)

Exam (14h30-16h00)

Exam on optimization and two-stage stochastic programming.

Correction of the exam (16h30-17h00)

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.

10 / Tuesday 10, March 2020 (Amphi Gregory)

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.

[Ber00,CCCD15]

Computer session (17h00-18h00)

    Dam optimal management under uncertainty

11 / Tuesday 17, March 2020 (Amphi Gregory)

Computer session (14h00-18h00)

    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_2019_MYNAME.pdf or TP3_STEEM_2019_MYNAME.pdf to delara@cermics.enpc.fr before Wednesday 20 March 2020, 15h.

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.

PHY652A - Physics of Solar Cell Devices (Intro to PV) (2020-2021)

PHY652E - Introduction to Power Systems (Intro to PS) (2020-2021)

PHY652I - Topical Seminars (2020-2021)

PHY652J - Solar Resource Seminar (2020-2021)

PHY652K - Lecture (2020-2021)

PHY661E - Fluvial and Maritime Resources for Renewable Energy (Fluv) (2020-2021)