scholarly journals Equivalent Transformation of Nonlinear Constraints to Linear Constraints in Petri Nets

2015 ◽  
Vol 2015 ◽  
pp. 1-11
Author(s):  
YuFeng Chen ◽  
Abdulrahman Al-Ahmari ◽  
Chi Tin Hon ◽  
NaiQi Wu
Keyword(s):  
Linear Programming ◽  
Petri Nets ◽  
Integer Linear Programming ◽  
Programming Model ◽  
Linear Constraints ◽  
Linear Programming Model ◽  
Equivalent Transformation ◽  
Nonlinear Constraints ◽  
Nonlinear Constraint ◽  
Integer Linear Programming Model

This paper focuses on the enforcement of nonlinear constraints in Petri nets. An integer linear programming model is formulated to transform a nonlinear constraint to a minimal number of conjunctive linear constraints that have the same admissible marking space as the nonlinear one does in Petri nets. The obtained linear constraints can be easily enforced to be satisfied by a set of control places with a place invariant based method. The control places make up a supervisor that can enforce the given nonlinear constraint. For a case that the admissible marking space decided by a nonlinear constraint is nonconvex, another integer linear programming model is developed to obtain a minimal number of constraints whose disjunctions are equivalent to the nonlinear constraint with respect to the reachable markings. Finally, a number of examples are provided to demonstrate the proposed approach.

scholarly journals Optimal Operational Adjustment of a Community-Based Off-Grid Polygeneration Plant using a Fuzzy Mixed Integer Linear Programming Model

Energies ◽  
2019 ◽  
Vol 12 (4) ◽  
pp. 636 ◽  
Author(s):  
Aristotle Ubando ◽  
Isidro Marfori ◽  
Kathleen Aviso ◽  
Raymond Tan
Keyword(s):  
Linear Programming ◽  
Integer Linear Programming ◽  
Rural Areas ◽  
Mixed Integer Linear Programming ◽  
Programming Model ◽  
Clean Energy ◽  
Linear Programming Model ◽  
Mixed Integer ◽  
Community Based ◽  
Integer Linear Programming Model

Community-based off-grid polygeneration plants based on micro-hydropower are a practical solution to provide clean energy and other essential utilities for rural areas with access to suitable rivers. Such plants can deliver co-products such as purified water and ice for refrigeration, which can improve standards of living in such remote locations. Although polygeneration gives advantages with respect to system efficiency, the interdependencies of the integrated process units may come as a potential disadvantage, due to susceptibility to cascading failures when one of the system components is partially or completely inoperable. In the case of a micro-hydropower-based polygeneration plant, a drought may reduce electricity output, which can, in turn, reduce the level of utilities available for use by the community. The study proposes a fuzzy mixed-integer linear programming model for the optimal operational adjustment of an off-grid micro-hydropower-based polygeneration plant seeking to maximize the satisfaction levels of the community utility demands, which are represented as fuzzy constraints. Three case studies are considered to demonstrate the developed model. The use of a diesel generator for back-up power is considered as an option to mitigate inoperability during extreme drought conditions.

scholarly journals A Mixed Integer Linear Programming Model for the Optimization of Steel Waste Gases in Cogeneration: A Combined Coke Oven and Converter Gas Case Study

Energies ◽  
2020 ◽  
Vol 13 (15) ◽  
pp. 3781
Author(s):  
Sergio García García ◽  
Vicente Rodríguez Montequín ◽  
Henar Morán Palacios ◽  
Adriano Mones Bayo
Keyword(s):  
Linear Programming ◽  
Integer Linear Programming ◽  
Mixed Integer Linear Programming ◽  
Programming Model ◽  
Coke Oven ◽  
Linear Programming Model ◽  
Mixed Integer ◽  
Integer Linear Programming Model ◽  
Converter Gas

Off-gas is one of the by-products of the steelmaking process. Its potential energy can be transformed into heat and electricity by means of cogeneration. A case study using a coke oven and Linz–Donawitz converter gas is presented. This work addresses the gas allocation problem for a cogeneration system producing steam and electricity. In the studied facility, located in northern Spain, the annual production of the plant requires 95,000 MWh of electrical energy and 525,000 MWh of thermal energy. The installed electrical and thermal power is 20.4 MW and 81 MW, respectively. A mixed integer linear programming model is built to optimize gas allocation, thus maximizing its benefits. This model is applied to a 24-h scenario with real data from the plant, where gas allocation decision-making was performed by the plant operators. Application of the model generated profit in a scenario where there were losses, increasing benefits by 16.9%. A sensitivity analysis is also performed. The proposed model is useful not only from the perspective of daily plant operation but also as a tool to simulate different design scenarios, such as the capacity of gasholders.

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