Improved Big-M reformulation for generalized disjunctive programs

Trespalacios, Francisco; Grossmann, Ignacio E.

doi:10.1016/j.compchemeng.2015.02.013

Cited by 57 publications

(28 citation statements)

References 23 publications

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“…Disjunctive constraints can be linearized using a set of disjunctive parameters. This type of reformulation (also known as big-M technique) was well studied in (Lee and Grossmann 2000) and (Trespalacios and Grossmann 2015). The choice of disjunctive parameters is critical for linear reformulation of disjunctive constraints.…”

Section: The Linearization Of Disjunctive Constraints (6d)mentioning

confidence: 99%

“…The literature provides several methodologies for tuning the disjunctive parameter. The methodologies for tuning the disjunctive parameter can be found in (Trespalacios and Grossmann 2015) and (Hooker 2011). These methodologies are proved to provide good approximations of the disjunctive parameters under certain conditions but additional large scale optimization problems need to be solved for each case and optimality of the outcome still cannot be guaranteed.…”

Section: Introductionmentioning

confidence: 99%

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Transmission Network Investment Using Incentive Regulation: A Disjunctive Programming Approach

et al. 2020

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A well-planned electric transmission infrastructure is the foundation of a reliable and efficient power system, especially in the presence of large scale renewable generation. However, the current electricity market designs lack incentive mechanisms which can guarantee optimal transmission investments and ensure reliable integration of renewable generation such as wind. This paper first proposes a stochastic bilevel disjunctive program for optimal transmission investment based on the newly proposed theoretical H-R-G-V incentive mechanism. The upper level is a profit-maximization problem of an independent transmission company (Transco), while the lower level is a welfare maximization problem. The revenue of the Transco is bounded by a regulatory constraint set by the regulator in order to induce socially optimal investments. The application of the H-R-G-V mechanism allows the regulator to ensure social maximum transmission investments and helps to reduce transmission congestion and wind power spillage. The transmission investment under the H-R-G-V mechanism is modeled as a stochastic bilevel disjunctive program. To solve the developed mathematical model we first propose a series of linearization and reformulation techniques to recast the original model as a stochastic mixed integer linear problem (MILP). We exploit the disjunctive nature of the reformulated stochastic MILP model and further propose a Bean decomposition algorithm to efficiently solve the stochastic MILP model. The proposed decomposition algorithm is also modified and accelerated to improve the computational performance. The computational performance of our MILP modeling approach and modified and accelerated Bean decomposition algorithm is studied through several examples in detail. The simulation results confirm a promising performance of both the modeling approach and its solution algorithm. Keywords Transmission network investments • Incentive regulation • Bean decomposition algorithm • Disjunctive programming.

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Section: The Linearization Of Disjunctive Constraints (6d)mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Transmission Network Investment Using Incentive Regulation: A Disjunctive Programming Approach

et al. 2020

View full text Add to dashboard Cite

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“…Note that the relaxation may be improved by selecting unique values of M for each constraint [48]. For a tighter continuous relaxation, the HR formulation found in Appendix B may be used.…”

Section: Solution Strategiesmentioning

confidence: 99%

“…More recently, Pyomo.GDP [46] has emerged as an open-source ecosystem for GDP modeling and development, built on top of the Pyomo algebraic modeling language [47] in Python. As an open-source platform, it has been able to incorporate recent innovations in reformulation strategies [48] and logic-based solution algorithms [22]. Powerful options now exist for formulating and solving GDP models.…”

Section: Introductionmentioning

confidence: 99%

Modern Modeling Paradigms Using Generalized Disjunctive Programming

Chen

Grossmann

2019

Processes

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Models involving decision variables in both discrete and continuous domain spaces are prevalent in process design. Generalized Disjunctive Programming (GDP) has emerged as a modeling framework to explicitly represent the relationship between algebraic descriptions and the logical structure of a design problem. However, fewer formulation examples exist for GDP compared to the traditional Mixed-Integer Nonlinear Programming (MINLP) modeling approach. In this paper, we propose the use of GDP as a modeling tool to organize model variants that arise due to characterization of different sections of an end-to-end process at different detail levels. We present an illustrative case study to demonstrate GDP usage for the generation of model variants catered to process synthesis integrated with purchasing and sales decisions in a techno-economic analysis. We also show how this GDP model can be used as part of a hierarchical decomposition scheme. These examples demonstrate how GDP can serve as a useful model abstraction layer for simplifying model development and upkeep, in addition to its traditional usage as a platform for advanced solution strategies.

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“…The literature provides several methods to tune the big-M parameter. The methodologies for tuning big-M can be found in [35,36]. The methods are proved to provide good approximations of the big-M parameters under certain conditions but additional large scale optimization problems should be solved for each case and the optimality still cannot be guaranteed.…”

Section: Strong Duality Conditionmentioning

confidence: 99%

Optimal Investment Planning of Bulk Energy Storage Systems

2018

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Many countries have the ambition to increase the share of renewable sources in electricity generation. However, continuously varying renewable sources, such as wind power or solar energy, require that the power system can manage the variability and uncertainty of the power generation. One solution to increase flexibility of the system is to use various forms of energy storage, which can provide flexibility to the system at different time ranges and smooth the effect of variability of the renewable generation. In this paper, we investigate three questions connected to investment planning of energy storage systems. First, how the existing flexibility in the system will affect the need for energy storage investments. Second, how presence of energy storage will affect renewable generation expansion and affect electricity prices. Third, who should be responsible for energy storage investments planning. This paper proposes to assess these questions through two different mathematical models. The first model is designed for centralized investment planning and the second model deals with a decentralized investment approach where a single independent profit maximizing utility is responsible for energy storage investments. The models have been applied in various case studies with different generation mixes and flexibility levels. The results show that energy storage system is beneficial for power system operation. However, additional regulation should be considered to achieve optimal investment and allocation of energy storage.

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Improved Big-M reformulation for generalized disjunctive programs

Cited by 57 publications

References 23 publications

Transmission Network Investment Using Incentive Regulation: A Disjunctive Programming Approach

Transmission Network Investment Using Incentive Regulation: A Disjunctive Programming Approach

Modern Modeling Paradigms Using Generalized Disjunctive Programming

Optimal Investment Planning of Bulk Energy Storage Systems

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