Webinar/Video. Generalized Stochastic Dual Dynamic Programming (G-SDDP) & Real-Time Distributed Optimization Electric Sector Applications

September 2, 2020 - 16:00 Greenwich - 11:00 Bogotá?

Video: https://www.facebook.com/100014972564724/videos/945360099306400

PDF Version: https://www.doanalytics.net/Documents/DOA-Webinar-GDDP-MP4.0.pdf?

Documents

• Chapter II-5 - GDDP/G-SDDP – Implementation and Electric Sector Applications of the book Mathematical Programing 4.0 for Industry 4.0 Cyber-Physical Systems

https://www.doanalytics.net/Documents/Chapter-II-5-G-SDDP–Implementation-Electric-Sector-Applications.pdf?

Diplomado Virtual:

• Analítica Avanzada & Optimización Aplicadas al Sector?Eléctrico (Aplicaciones en GAMS)

https://www.dhirubhai.net/pulse/analítica-avanzada-optimización-aplicadas-al-sector-gams-velasquez/??

STOCHASTIC & DYNAMIC BENDERS THEORY

Abstract. This chapter presents a review of the use of the theories of partition and decomposition of Benders (BT, Benders 1962), and its variations, emphasizing its use in complex dynamic stochastic systems. Three topics are studied: i) stochastic optimization (from a general point of view), ii) modeling of dynamic systems and iii) the union of the two previous topics. Two methodologies are presented to solve the problem: Nested Benders Decomposition (NBD, (Donohue and Birge, 2000) and Generalized Dual Dynamic Programming (GDDP, Velasquez 2002), including the extensions to Stochastic Programing (SP). At the end, several cases of implementation of GDDP in the electricity sector are presented.

INDEX

?1.?????Modeling Dynamic Systems

?2.?????Nested Benders Decomposition (NBD)

2.1.?Determinist Nested Benders

2.2.?Stochastic Nested Benders

2.3.?NBD Versions & Sampling

2.3.1.???????Dual Dynamic Programming (DDP)

2.3.2.???????Abridged Nested Benders (ANB)

2.3.3.???????Cutting-Plane and Partial-Sampling (CUPPS)

2.3.4.???????Recombining Scenario Trees

2.3.5.???????EVPI-S Algorithms

2.3.6.???????Nested Benders Extensions

3.?????Generalized Stochastic Dual-Dynamic Programming (G-SDDP)

3.1.?GDDP Basic Theory

3.2.?G-SDDP Basic Theory

4.?????Electric Sector GDDP/G-SDDP Modeling?

4.1.?Economic Dispatch

4.2.?Electric Sector Stochastic Supply Chain Design

4.3.?Conclusions

5.?????Acknowledgments

1.?????Modeling Dynamic Systems

We call Benders Dynamic Theory the application of the concepts Benders to dynamic problems modeled based on discrete periods/stages, the case of continuous time-based applications is not classified within this group, while thus they cease to be dynamic applications but with a very important combinatorial component.

To presents the Benders Dynamic Theory we defined a conceptual framework for discrete-time models of dynamic systems. The selected framework is common for three fundamental methodologies: i) Optimal Control; ii) Dynamic Programming, and iii) State Estimation. The two first methods are oriented to optimization and them are the results of the works of Lev Pontryagin (Pontryagin’s Maximum Principle, Pontryagin et al. 1962) and Richard Bellman (Dynamic Programming) during the 1950s, after the contributions to Calculus of Variations by Edward J. McShane (1974) .?State estimation are methodologies oriented to reconstruction (smoothing and filtering) and to forecasting the state variables of the system, considering the uncertainty and partial observation of the system in the time-space domain, the most famous application in state estimation if the Kalman Filter methodology (Kalman,

?This common framework is based on:

1. Two types of variables:

• State variables: are the set of variables that are used to describe the mathematical "state" of a dynamical system, that describes, enough about, the system to determine its future behavior in the absence of any external forces that affect the system.
• Control variables: are the set of variables associated to external forces that can change the “natural” behavior of the dynamical system

2. A set of constraints that describes:

• The dynamic relation between state variables on two consecutive periods (t and t+1)
• The relations between control during each period t
• The relation between state variables and control variables during each period t

If you want to real the full draft chapter Version: https://www.doanalytics.net/Documents/DOA-Benders-Theory-Dynamic-&-Stochastic-Optimization.pdf????

Other working paper about Benders Theory:

• The Future: Mathematical Programming 4.0

https://www.dhirubhai.net/pulse/future-mathematical-programming-jesus-velasquez/

• OPTEX – Optimization Expert System??

https://www.dhirubhai.net/pulse/optex-optimization-expert-system-new-approah-make-models-velasquez/