Dynamic Congestion and Tolls with Mobile Source Emission

This paper proposes a dynamic congestion pricing model that takes into account mobile source emissions. We consider a tollable vehicular network where the users selfishly minimize their own travel costs, including travel time, early/late arrival penalties and tolls. On top of that, we assume that part of the network can be tolled by a central authority, whose objective is to minimize both total travel costs of road users and total emission on a network-wide level. The model is formulated as a mathematical program with equilibrium constraints (MPEC) problem and then reformulated as a mathematical program with complementarity constraints (MPCC). The MPCC is solved using a quadratic penalty-based gradient projection algorithm. A numerical study on a toy network illustrates the effectiveness of the tolling strategy and reveals a Braess-type paradox in the context of traffic-derived emission.Comment: 23 pages, 9 figures, 5 tables. Current version to appear in the Proceedings of the 20th International Symposium on Transportation and Traffic Theory, 2013, the Netherland

Dynamic Modelling and Optimisation of Large-Scale Cryogenic Separation Processes

In this work, the open loop dynamic optimisation of a large-scale natural gas processing plant is performed. A rigorous differential-algebraic equation (DAE) model has been formulated to represent main plant units, such as shell and tube heat exchangers, highpressure separator and demethanizing column. In the shell and tube heat exchangers, the hot stream partially condenses and equations to consider the partial condensation of the fluids have been included. A rigorous index one model for the demethanizing column has been developed. The DAE optimisation problem is solved with a simultaneous approach, in which both state and control variables are discretised and the original DAE optimisation model is transformed into a large-scale nonlinear problem (NLP), which is solved using Sequential Quadratic Programming (SQP) methods. Optimal profiles have been obtained for main operating variables to achieve an enhanced product recovery.Fil: Rodriguez, Mariela Alejandra. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Bahía Blanca. Planta Piloto de Ingeniería Química. Universidad Nacional del Sur. Planta Piloto de Ingeniería Química; ArgentinaFil: Bandoni, Jose Alberto. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Bahía Blanca. Planta Piloto de Ingeniería Química. Universidad Nacional del Sur. Planta Piloto de Ingeniería Química; ArgentinaFil: Díaz, María Soledad. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Bahía Blanca. Planta Piloto de Ingeniería Química. Universidad Nacional del Sur. Planta Piloto de Ingeniería Química; Argentin

A pressure-driven, dynamic model for distillation columns with smooth reformulations for flexible operation

Dynamic models for plants including the startup or shutdown phase are still scarce as the (dis-)appearence of phases or streams is challenging to implement. We present an approach to model a distillation column, in which these operation modes are also considered without exchanging equations. For this purpose, the well-known modeling equations for distillation columns are reformulated robustly to allow for the disappearance of the vapor phase without discontinuities. The reformulation does not depend on solving an optimization problem and could easily be applied to other column types or different unit operations. The proposed model is solved in two case studies with 10 and 40 trays, respectively. In these case studies, the influence of single phenomena on the obtained dynamic profiles is investigated, e.g., weeping, which are often neglected. The proposed modeling approach yields a dynamic model that can be solved without reinitialization for a realistically large number of trays.BMBF, 0350013A, Verbundvorhaben: ChemEFlex - Umsetzbarkeitsanalyse zur Lastflexibilisierung elektrochemischer Verfahren in der Industrie; Teilvorhaben: Modellierung der Chlor-Alkali-Elektrolyse sowie anderer Prozesse und deren Bewertung hinsichtlich Wirtschaftlichkeit und möglicher Hemmniss

Optimization for the flexibility analysis of processes: Application to the acetone-ethanol-butanol producing process

The design and operation of sustainable biorefineries is an important subject of research since the current environmental context makes urgent the development of robust methodologies able to design innovative industries. In this context, flexibility of distillation sequences plays a very important role. The design is based on nominal production data may imply operation infeasibilities, unsustainable operation and an energy overconsumption. This work proposes a new methodology for the flexibility analysis of chemical processes based on rigorous thermodynamic models and optimizations tools with special emphasis on purification processes in the biorefining field

Dynamic optimization of energy systems with thermal energy storage

textThermal energy storage (TES), the storage of heat or cooling, is a cost-effective energy storage technology that can greatly enhance the performance of the energy systems with which it interacts. TES acts as a buffer between transient supply and demand of energy. In solar thermal systems, TES enables the power output of the plant to be effectively regulated, despite fluctuating solar irradiance. In district energy systems, TES can be used to shift loads, allowing the system to avoid or take advantage of peak energy prices. The benefit of TES, however, can be significantly enhanced by dynamically optimizing the complete energy system. The ability of TES to shift loads gives the system newfound degrees of freedom which can be exploited to yield optimal performance. In the hybrid solar thermal/fossil fuel system explored in this work, the use of TES enables the system to extract nearly 50% more solar energy when the system is optimized. This requires relaxing some constraints, such as fixed temperature and power control, and dynamically optimizing the over a one-day time horizon. In a district cooling system, TES can help equipment to run more efficiently, by shifting cooling loads, not only between chillers, but temporally, allowing the system to take advantage of the most efficient times for running this equipment. This work also highlights the use of TES in a district energy system, where heat, cooling and electrical power are generated from central locations. Shifting the cooling load frees up electrical generation capacity, which is used to sell power to the grid at peak prices. The combination of optimization, TES, and participation in the electricity market yields a 16% cost savings. The problems encountered in this work require modeling a diverse range of systems including the TES, the solar power plant, boilers, gas and steam turbines, heat recovery equipment, chillers, and pumps. These problems also require novel solution methods that are efficient and effective at obtaining workable solutions. A simultaneous solution method is used for optimizing the solar power plant, while a static/dynamic decoupling method is used for the district energy system.Chemical Engineerin

Integration of design and NMPC-based control of processes under uncertainty

The implementation of a Nonlinear Model Predictive Control (NMPC) scheme for the integration of design and control demands the solution of a complex optimization formulation, in which the solution of the design problem depends on the decisions from a lower tier problem for the NMPC. This formulation with two decision levels is known as a bilevel optimization problem. The solution of a bilevel problem using traditional Linear Problem (LP), Nonlinear Problem (NLP) or Mixed-Integer Nonlinear Problem (MINLP) solvers is very difficult. Moreover, the bilevel problem becomes particularly complex if uncertainties or discrete decisions are considered. Therefore, the implementation of alternative methodologies is necessary for the solution of the bilevel problem for the integration of design and NMPC-based control. The lack of studies and practical methodologies regarding the integration of design and NMPC-based control motivates the development of novel methodologies to address the solution of the complex formulation. A systematic methodology has been proposed in this research to address the integration of design and control involving NMPC. This method is based on the determination of the amount of back-off necessary to move the design and control variables from an optimal steady-state design to a new dynamically feasible and economic operating point. This method features the reduction of complexity of the bilevel formulation by approximating the problem in terms of power series expansion (PSE) functions, which leads to a single-level problem formulation. These functions are obtained around the point that shows the worst-case variability in the process dynamics. This approximated PSE-based optimization model is easily solved with traditional NLP solvers. The method moves the decision variables for design and control in a systematic fashion that allows to accommodate the worst-case scenario in a dynamically feasible operating point. Since approximation techniques are implemented in this methodology, the feasible solutions potentially may have deviations from a local optimum solution. A transformation methodology has been implemented to restate the bilevel problem in terms of a single-level mathematical program with complementarity constraints (MPCC). This single-level MPCC is obtained by restating the optimization problem for the NMPC in terms of its conditions for optimality. The single-level problem is still difficult to solve; however, the use of conventional NLP or MINLP solvers for the search of a solution to the MPCC problem is possible. Hence, the implementation of conventional solvers provides guarantees for optimality for the MPCC’s solution. Nevertheless, an optimal solution for the MPCC-based problem may not be an optimal solution for the original bilevel problem. The introduction of structural decisions such as the arrangement of equipment or the selection of the number of process units requires the solution of formulations involving discrete decisions. This PhD thesis proposes the implementation of a discrete-steepest descent algorithm for the integration of design and NMPC-based control under uncertainty and structural decisions following a naturally ordered sequence, i.e., structural decisions that follow the order of the natural numbers. In this approach, the corresponding mixed-integer bilevel problem (MIBLP) is transformed first into a single-level mixed-integer nonlinear program (MINLP). Then, the MINLP is decomposed into an integer master problem and a set of continuous sub-problems. The set of problems is solved systematically, enabling exploration of the neighborhoods defined by subsets of integer variables. The search direction is determined by the neighbor that produces the largest improvement in the objective function. As this method does not require the relaxation of integer variables, it can determine local solutions that may not be efficiently identified using conventional MINLP solvers. To compare the performance of the proposed discrete-steepest descent approach, an alternative methodology based on the distributed stream-tray optimization (DSTO) method is presented. In that methodology, the integer variables are allowed to be continuous variables in a differentiable distribution function (DDF). The DDFs are derived from the discretization of Gaussian distributions. This allows the solution of a continuous formulation (i.e., a NLP) for the integration of design and NMPC-based control under uncertainty and structural decisions naturally ordered set. Most of the applications for the integration of design and control implement direct transcription approaches for the solution of the optimization formulation, i.e., the full discretization of the optimization problem is implemented. In chemical engineering, the most widely used discretization strategy is orthogonal collocation on finite elements (OCFE). OCFE offers adequate accuracy and numerical stability if the number of collocation points and the number of finite elements are properly selected. For the discretization of integrated design and control formulations, the selection of the number of finite elements is commonly decided based on a priori simulations or process heuristics. In this PhD study, a novel methodology for the selection and refinement of the number of finite elements in the integration of design and control framework is presented. The corresponding methodology implements two criteria for the selection of finite elements, i.e., the estimation of the collocation error and the Hamiltonian function profile. The Hamiltonian function features to be continuous and constant over time for autonomous systems; nevertheless, the Hamiltonian function shows a nonconstant profile for underestimated discretization meshes. The methodology systematically adds or removes finite elements depending on the magnitude of the estimated collocation error and the fluctuations in the profile for the Hamiltonian function. The proposed methodologies have been tested on different case studies involving different features. An existent wastewater treatment plan is considered to illustrate the implementation of back-off strategy. On the other hand, a reaction system with two continuous stirred reaction tanks (CSTRs) are considered to illustrate the implementation of the MPCC-based formulation for design and control. The D-SDA approach is tested for the integration of design, NMPC-based control, and superstructure of a binary distillation column. Lastly, a reaction system illustrates the effect of the selection and refinement of the discretization mesh in the integrated design and control framework. The results show that the implementation of NMPC controllers leads to more economically attractive process designs with improved control performance compared to applications with classical descentralized PID or Linear MPC controllers. The discrete-steepest descent approach allowed to skip sub-optimal solution regions and led to more economic designs with better control performance than the solutions obtained with the benchmark methodology using DDFs. Meanwhile, the refinement strategy for the discretization of integrated design and control formulations demonstrated that attractive solutions with improved control performance can be obtained with a reduced number of finite elements