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Increasingly volatile electricity prices make simultaneous scheduling optimization desirable for production processes and their energy systems. Simultaneous scheduling needs to account for both process dynamics and binary on/off-decisions in the energy system leading to challenging mixed-integer dynamic optimization problems. We propose an efficient scheduling formulation consisting of three parts: a linear scale-bridging model for the closed-loop process output dynamics, a data-driven model for the process energy demand, and a mixed-integer linear model for the energy system. Process dynamics is discretized by collocation yielding a mixed-integer linear programming (MILP) formulation. We apply the scheduling method to three case studies: a multiproduct reactor, a single-product reactor, and a single-product distillation column, demonstrating the applicability to multiple input multiple output processes. For the first two case studies, we can compare our approach to nonlinear optimization and capture 82% and 95% of the improvement. The MILP formulation achieves optimization runtimes sufficiently fast for real-time scheduling., AIChE Journal, 68 (8), ISSN:1547-5905, ISSN:0001-1541

Volatile electricity prices make demand response attractive for processes that can modulate their production rate. However, if nonlinear dynamic processes must be scheduled simultaneously with their local multi-energy system, the resulting scheduling optimization problems often cannot be solved in real time. For single-input single-output processes, the problem can be simplified without sacrificing feasibility by dynamic ramping constraints that define a derivative of the production rate as the ramping degree of freedom. In this work, we extend dynamic ramping constraints to flat multi-input multi-output processes by a coordinate transformation that gives the true nonlinear ramping limits. Approximating these ramping limits by piecewise affine functions gives a mixed-integer linear formulation that guarantees feasible operation. As a case study, dynamic ramping constraints are derived for a heated reactor-separator process that is subsequently scheduled simultaneously with its multi-energy system. The dynamic ramping formulation bridges the gap between rigorous process models and simplified process representations for real-time scheduling., Computers & Chemical Engineering, 172, ISSN:0098-1354, ISSN:1873-4375

Existing open-source modeling frameworks dedicated to energy systems optimization typically utilize (mixed-integer) linear programming ((MI)LP) formulations, which lack modeling freedom for technical system design and operation. We present COMANDO, an open-source Python package for component-oriented modeling and optimization for nonlinear design and operation of integrated energy systems. COMANDO allows to assemble system models from component models including nonlinear, dynamic and discrete characteristics. Based on a single system model, different deterministic and stochastic problem formulations can be obtained by varying objective function and underlying data, and by applying automatic or manual reformulations. The flexible open-source implementation allows for the integration of customized routines required to solve challenging problems, e.g., initialization, problem decomposition, or sequential solution strategies. We demonstrate features of COMANDO via case studies, including automated linearization, dynamic optimization, stochastic programming, and the use of nonlinear artificial neural networks as surrogate models in a reduced-space formulation for deterministic global optimization., Comment: 24 pages, 1 graphical abstract, 13 figures, 4 tables

With fluctuating electricity prices, demand side management (DSM) promises to reduce energy costs. DSM of processes and energy supply systems requires scheduling optimization to consider transient behavior and binary on/off-decisions resulting in challenging mixed-integer dynamic programs. In this work, we present an efficient scheduling optimization approach that captures scheduling-relevant dynamics in a linear scale-bridging model and relies on collocation for time discretization. The resulting mixed-integer linear program (MILP) can be solved with state-of-the-art solvers. We apply the approach to a case study on building DSM. A detailed simulation model represents an office building, which allows load shifting through dynamic concrete core activation and is heated by a heat pump with minimum part-load. The DSM scheduling optimization approach reduces energy cost significantly compared to a rule-based scheduler without DSM if electricity price volatility is high. At the same time, the optimization is sufficiently fast to perform online scheduling.

This paper presents an application-oriented comparison of optimization approaches for Model-based Control of a stationary hybrid energy system. The energy system consists of a hybrid storage system with a battery and a hydrogen storage including an electrolyzer and a fuel cell system. The hybrid storage aims at improving the supply security of the intermittent renewable energy sources wind and photovoltaic in a grid-connected context. We show the potential of Mixed Integer Linear Programming (MILP) with a linear cost function in the optimization of a supervisory Model-based Control. The optimization takes into account minimum power for electrolyzer and fuel cell. Furthermore, the non-linear partial load behavior of the components is extracted from experimental data and in good fit modeled via piecewise affine functions. By utilizing this MILP in the optimization we increase the hybrid discharging efficiency by 7 % compared to Linear Programming.