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Dealing with the unknown: distributionally robust optimization for energy systems and markets - with industrial partner
In this project, we aim to construct data-driven
discrepancy-based ambiguity sets and use them to provide novel reformulations for static and two-stage stochastic programs in the area of energy systems and markets. We will then validate the formulations with real-world data from industrial partners.
Keywords: Distributionally robust optimization; Optimization under uncertainty; Energy systems and markets; Industrial partners.
The energy system is undergoing a sharp transition
in the run to meet the global emission
targets. Traditional and controllable generation
sources, such as power plants, are progressively
being replaced by renewable generation
sources such as solar and wind. However, the
integration of these uncontrollable and intermittent
generation sources in the main grid has
brought new technical and economical challenges,
that are calling for novel algorithmic solutions
and market design structures. The main
challenge is due to the stochastic nature of both
the generation and the demand (for example,
consider the high penetration of electric vehicles),
which highly complicates the design (i.e.,
sizing) of new energy hubs, the real-time operations
of energy hubs, as well as the strategic
bidding process into day-ahead spot and/or reserve
markets.
Many of the aforementioned problems can be cast as stochastic optimization programs, where
one (or many) of the problem parameters are unknown, but follow specific (yet possibly unknown
to the practitioner) probability distributions. Roughly speaking, we can broadly classify the above
problems into two problem classes: (i) static problems and (ii) two-stage (or multi-stage) problems.
In static problems, we do not wait for the occurrence of any event or realization of some random
variable(s) before taking our decisions (hence, our only concern is risk); an example is offered by
the day-ahead power nomination of the owner of a portfolio of renewable assets. In two-stage
problems, decisions should be based on data available at the time the decisions are made and
cannot depend on future observations (hence, our concerns are both risk and time): the first-stage
decision, also called “here-and-now", are taken before any realizations of the random event, while
the second-stage decision, also called “wait-and-see", are taken after the observation of the random
outcome. An example is designing an energy hub at the minimum cost: here, the sizing variables
are the first-stage ones, while the operations variables are the second-stage ones.
When the knowledge of the underlying generating probability distribution is vague, standard
stochastic methods fail to offer the robustness we are looking for. Recently, the paradigm of distributionally
robust optimization (DRO) has gained momentum owning it to the ability to robustify
against uncertainty in the distribution of the stochastic parameter by considering the worst-case distribution
in a so-called ambiguity set. Several types of ambiguity sets may be constructed based on
the prior information availables and can be broadly classified into (i) moment-based ambiguity sets,
and (ii) discrepancy-based ambiguity sets. In this project, we aim to construct data-driven
discrepancy-based ambiguity sets and use them to provide novel reformulations for static and twostage
stochastic programs that are able to provide the sought probabilistic guarantees even in the
presence of training-testing distribution shift. We aim to validate the proposed method on one of the
mentioned problems in the energy and power domain using real-world data from Swiss utility companies
(industrial partners) and compare it with standard approaches from stochastic and robust
optimization to showcase the benefits of our formulations.
The energy system is undergoing a sharp transition in the run to meet the global emission targets. Traditional and controllable generation sources, such as power plants, are progressively being replaced by renewable generation sources such as solar and wind. However, the integration of these uncontrollable and intermittent generation sources in the main grid has brought new technical and economical challenges, that are calling for novel algorithmic solutions and market design structures. The main challenge is due to the stochastic nature of both the generation and the demand (for example, consider the high penetration of electric vehicles), which highly complicates the design (i.e., sizing) of new energy hubs, the real-time operations of energy hubs, as well as the strategic bidding process into day-ahead spot and/or reserve markets.
Many of the aforementioned problems can be cast as stochastic optimization programs, where one (or many) of the problem parameters are unknown, but follow specific (yet possibly unknown to the practitioner) probability distributions. Roughly speaking, we can broadly classify the above problems into two problem classes: (i) static problems and (ii) two-stage (or multi-stage) problems. In static problems, we do not wait for the occurrence of any event or realization of some random variable(s) before taking our decisions (hence, our only concern is risk); an example is offered by the day-ahead power nomination of the owner of a portfolio of renewable assets. In two-stage problems, decisions should be based on data available at the time the decisions are made and cannot depend on future observations (hence, our concerns are both risk and time): the first-stage decision, also called “here-and-now", are taken before any realizations of the random event, while the second-stage decision, also called “wait-and-see", are taken after the observation of the random outcome. An example is designing an energy hub at the minimum cost: here, the sizing variables are the first-stage ones, while the operations variables are the second-stage ones.
When the knowledge of the underlying generating probability distribution is vague, standard stochastic methods fail to offer the robustness we are looking for. Recently, the paradigm of distributionally robust optimization (DRO) has gained momentum owning it to the ability to robustify against uncertainty in the distribution of the stochastic parameter by considering the worst-case distribution in a so-called ambiguity set. Several types of ambiguity sets may be constructed based on the prior information availables and can be broadly classified into (i) moment-based ambiguity sets, and (ii) discrepancy-based ambiguity sets. In this project, we aim to construct data-driven discrepancy-based ambiguity sets and use them to provide novel reformulations for static and twostage stochastic programs that are able to provide the sought probabilistic guarantees even in the presence of training-testing distribution shift. We aim to validate the proposed method on one of the mentioned problems in the energy and power domain using real-world data from Swiss utility companies (industrial partners) and compare it with standard approaches from stochastic and robust optimization to showcase the benefits of our formulations.
The goals of the project are as follows:
1. Learn about Two-stage Stochastic Optimization, Distributionally Robust Optimization, Energy
systems and markets;
2. Familiarize with the available data and model the problem of interest as distributionally robust
optimization program (static or two-stage) with data-driven ambiguity sets;
3. Provide tractable reformulations for the problem with statistical guarantees;
4. Validate the designed algorithm via numerical simulations using real-world data from industrial
partners and compare it with the state-of-art.
The goals of the project are as follows:
1. Learn about Two-stage Stochastic Optimization, Distributionally Robust Optimization, Energy systems and markets;
2. Familiarize with the available data and model the problem of interest as distributionally robust optimization program (static or two-stage) with data-driven ambiguity sets;
3. Provide tractable reformulations for the problem with statistical guarantees;
4. Validate the designed algorithm via numerical simulations using real-world data from industrial partners and compare it with the state-of-art.
To apply please send your resume/CV (including lists of relevant publications/projects) and transcript of
records in PDF format via email to {mfochesato,aliviu}@ethz.ch.
We are looking for an outstanding and highly motivated student with interest in Optimization under
Uncertainty and a strong background in Mathematics.
• Some familiarity with distributionally robust optimization and stochastic gradient descent will
be helpful;
• Good programming skills (Python is preferred) are mandatory;
• Enrollment in a master program;
• Proficiency in English.
To apply please send your resume/CV (including lists of relevant publications/projects) and transcript of records in PDF format via email to {mfochesato,aliviu}@ethz.ch.
We are looking for an outstanding and highly motivated student with interest in Optimization under Uncertainty and a strong background in Mathematics.
• Some familiarity with distributionally robust optimization and stochastic gradient descent will be helpful;
• Good programming skills (Python is preferred) are mandatory;