Michel DE LARA, CERMICS-École des Ponts ParisTech
Eligibility/Pre-requisites.
Learning outcomes. After the course the student should be able to
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/Graduate_Degree_STEEM_2017/
course webpage
Link Graduate Degree STEEM.
https://portail.polytechnique.edu/graduatedegree/steem/
Graduate Degree STEEM
map of the courses rooms
To introduce the course, we present examples of micro-grid and virtual power plant management (that can be solved using stochastic dynamic optimization):
Recalls on probability calculus: probability space, probability, random variables, law of a random variable, mathematical expectation, indicator function, independence of random variables, almost-sure convergence and law of large numbers. [Fel68,Bre93,Pit93]
Exercises on probability calculus.
Recalls and exercises on continuous optimization [Ber96].
We present, under the form of an exercise, an example of optimization problem under uncertainty: ``the newsvendor problem''. slides
Introduction to the scientific software Scicoslab. [CCN10] computer session
``Day Ahead Energy Markets'' slides
The newsvendor problem
You will send the results of the computer project
The newsvendor problem
under the form of a pdf file
TP1_STEEM_2017_MYNAME.pdf
to delara@cermics.enpc.fr before .
Two-stage stochastic programming on a scenario tree.
Non-anticipativity constraint along scenarios: tree representation.
Sizing of reserves for the balancing on an electric market
(linear and quadratic optimization on a tree)
Two-stage stochastic programming on a fan.
Non-anticipativity constraint along scenarios.
Scenario decomposition by Lagrangian relaxation. Progressive Hedging [RW91].
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_STEEM_2017_MYNAME.pdf
to delara@cermics.enpc.fr before .
Exercises on two-stage stochastic programming.
Exam on two-stage stochastic programming.
Dynamical models of storage (battery models, dam models).
Dynamical sequential systems with control.
Optimal control of dynamical sequential systems.
slides
Dynamic programming. Curse of dimensionality.
Exercises on dynamic programming.
Dynamical sequential systems with control and noise.
Optimal control of stochastic dynamical sequential systems.
slides
Stochastic dynamic programming. Curse of dimensionality.
slides
Exercises on stochastic dynamic programming.
[Bel57,Put94,Ber00,Whi82,CCCD15]
Code the dynamic programming algorithm.
A Numerical Toy Stochastic Control Problem Solved by Dynamic Programming
Dam optimal management under uncertainty
You will send the results of the computer project Dam optimal management under uncertainty
under the form of a pdf file TP3_STEEM_2017_MYNAME.pdf
to delara@cermics.enpc.fr before .
Inventory problems. Optimal storage management in the hazard-decision framework, with linear costs.
Stochastic optimal control with convex costs and linear dynamics.
Presentation of the Stochastic Dual Dynamic Programming (SDDP) algorithm. slides
Exam on stochastic dynamic programming.