(66c) Hybrid Mechanistic Data-Driven Modelling for Real-Time Dynamic Optimization of Large-Scale Rectification Systems: Application to Air Separation Units

Schäfer, P., RWTH Aachen University
Caspari, A., RWTH Aachen University
Mhamdi, A., RWTH Aachen University
Mitsos, A., RWTH Aachen University
Today’s electricity markets are characterized by fast-changing dynamics. Flexibilization of the electricity consumption, i.e., demand side management (DSM), is thus a promising measure to increase the economics of energy-intense processes [1]. DSM measures commonly focus on optimizing the production schedule subject to time-variable electricity prices under the assumption of quasi-stationary process operation [2]. However, if the time constant of the considered process is of a similar order of magnitude as the frequency of market fluctuations, disregarding the process dynamics might lead to suboptimal or even infeasible solutions [3]. Therefore, current research addresses the consideration of dynamics in scheduling problems for processes with non-negligible response times via formulation of low-dimensional dynamic models for scheduling relevant variables [4,5]. Although consideration of process dynamics when making scheduling decisions presents a promising measure for preventing infeasible production plans, it neglects the potentials that might arise from also adapting the control structure. Integrating the economic optimization directly into a model predictive controller utilizing a detailed nonlinear model thus represents a valuable alternative [6]. This approach is commonly referred to as economic nonlinear model predictive control (eNMPC) [7]. In literature, a sound theoretical framework is provided for eNMPC [8,9]. Application of eNMPC schemes to DSM-relevant processes, such as cryogenic air separation units (ASUs), is however challenging, as large-scale nonlinear dynamic optimization problems have to be solved in real-time. Recent successful application of eNMPC schemes to ASUs using detailed mechanistic models rely mainly on suboptimal solution methods that reduce the computational burden for solving the dynamic optimization problem [10,11].

Model size is still the main bottleneck for the use of dynamic optimization methods in real-time, e.g., in distillation columns due to MESH equations for each stage. Therefore, there is a need to develop process models of substantially decreased complexity that retain accurate prediction abilities. In the context of distillation systems, model reduction approaches may be classified into three categories: (i) nonlinear wave models [12], (ii) collocation-based models [13], and (iii) compartment models [14]. All of these approaches have been applied to operational optimization of ASUs [15,16,17]. However, there is still an interest in more efficient model reduction approaches. For this purpose, we have recently proposed an advanced compartment model formulation that combines the aggregation of single stage dynamics with machine learning techniques using artificial neural networks (ANNs) [18]. More precisely, we replace the complex nonlinear input-output relations for the compartments with ANNs. We herein present the derivation of the ANN-based compartment model (ANNCM) – starting from well-known full-order stage-by-stage models (FSM) for distillation columns. We analyze and discuss thoroughly the properties of the ANNCM (compliance with integral balance relations, stationary and dynamic errors compared to an FSM, etc.). We further demonstrate that by using the ANNCM as rectification model, we achieve reductions of the computational time for state and sensitivity integration of more than one order of magnitude whilst not introducing substantial errors compared to using an FSM.

We also present the utilization of the model for a closed-loop single-layer eNMPC framework. Therein, the computational time for solving the dynamic optimization problem is controlled by restricting to a fixed number of optimizer iterations. We consider a nitrogen plant from literature as an in-silico case study and use our in-house software for sequential dynamic optimization DyOS [19]. We explicitly consider (i) model-plant mismatch, (ii) erroneous forecasts for the development of the electricity price, (iii) unmeasured disturbances influencing the process, and (iv) time delays in updating the control signals caused by the computational time for solution of the dynamic optimization problems. The computational results from this study demonstrate the real-time applicability of the suggested framework for eNMPC purposes subject to time-variable electricity prices.


The authors gratefully acknowledge the financial support of the Kopernikus project SynErgie by the Federal Ministry of Education and Research (BMBF) and the project supervision by the project management organization Projektträger Jülich. Furthermore, the authors thank Anna-Maria Ecker, Florian Schliebitz, Bernd Wunderlich, Andreas Peschel and Gerhard Zapp from Linde Engineering as well as Robert Kender from TU München for valuable discussions concerning modeling and control of cryogenic rectification columns.


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