Introduction to stochastic programming

The paper reviews different approaches, technologies, and strategies to manage large-scale schemes of variable renewable electricity such as solar and wind power. We consider both supply and demand side measures. In addition to presenting energy system flexibility measures, their importance to renewable electricity is discussed. The flexibility measures available range from traditional ones such as grid extension or pumped hydro storage to more advanced strategies such as demand side management and demand side linked approaches, e.g. the use of electric vehicles for storing excess electricity, but also providing grid support services. Advanced batteries may offer new solutions in the future, though the high costs associated with batteries may restrict their use to smaller scale applications. Different “P2Y”-type of strategies, where P stands for surplus renewable power and Y for the energy form or energy service to which this excess in converted to, e.g. thermal energy, hydrogen, gas or mobility are receiving much attention as potential flexibility solutions, making use of the energy system as a whole. To “functionalize” or to assess the value of the various energy system flexibility measures, these need often be put into an electricity/energy market or utility service context. Summarizing, the outlook for managing large amounts of RE power in terms of options available seems to be promising.

https://research.aalto.fi/files/6557604/lund_et_al_review.pdf

Review of energy system flexibility measures to enable high levels of variable renewable electricity

The Benders decomposition algorithm: A literature review

Optimizing the production scheduling of a single machine to minimize total energy consumption costs

Energy-efficient scheduling in manufacturing companies: A review and research framework

Optimal production planning under time-sensitive electricity prices for continuous power-intensive processes

http://egon.cheme.cmu.edu/Papers/MitraSunGrossmann_CHP_Energy_revised.pdf

Optimal scheduling of industrial combined heat and power plants under time-sensitive electricity prices

Optimal multi-scale capacity planning for power-intensive continuous processes under time-sensitive electricity prices and demand uncertainty. Part I: Modeling

http://egon.cheme.cmu.edu/Papers/Mitra_Multiscale_Capacity_part2_v8.pdf

Optimal multi-scale capacity planning for power-intensive continuous processes under time-sensitive electricity prices and demand uncertainty. Part II: Enhanced hybrid bi-level decomposition

We describe a cross-decomposition algorithm that combines Benders and scenario-based Lagrangean decomposition for two-stage stochastic programming investment planning problems with complete recourse, where the first-stage variables are mixed-integer and the second-stage variables are continuous. The algorithm is a novel cross-decomposition scheme and fully integrates primal and dual information in terms of primal---dual multi-cuts added to the Benders and the Lagrangean master problems for each scenario. The potential benefits of the cross-decomposition scheme are demonstrated with numerical experiments on a number of instances of a facility location problem under disruptions. In the original formulation, where the underlying LP relaxation is weak, the cross-decomposition method outperforms multi-cut Benders decomposition. If the formulation is improved with the addition of tightening constraints, the performance of both decomposition methods improves but cross-decomposition clearly remains the best method for large-scale problems.

/pdf/a-cross-decomposition-scheme-with-integrated-primal-dual-ew4ojvfejy.pdf

Sumit Mitra

Papers

Optimal production planning under time-sensitive electricity prices for continuous power-intensive processes

Optimal scheduling of industrial combined heat and power plants under time-sensitive electricity prices

Optimal multi-scale capacity planning for power-intensive continuous processes under time-sensitive electricity prices and demand uncertainty. Part I: Modeling

Optimal multi-scale capacity planning for power-intensive continuous processes under time-sensitive electricity prices and demand uncertainty. Part II: Enhanced hybrid bi-level decomposition

A cross-decomposition scheme with integrated primal---dual multi-cuts for two-stage stochastic programming investment planning problems