DYNAMIC OPTIMIZATION OF DISTRICT HEATING SYSTEMS
The optimization of district heating networks (normal l y refer red to as production planning) can be formulated as an optimization problem, involving both discrete („Is my unit on or off?“) and continuous decision variables („How much heat should be produced? At what temperature level? “), transport delays, nonlinear and dynamical behavior. The resulting optimization problem is known as a mixed-integer-optimal control problem for which no general, robust and scalable method exists. We propose a novel method that enables a precise solution, while the solution time is sufficiently low for
Causal model (Simulink)
Figure 2: A simple mechanic model; the Modelica model is much more simple to interpret compared to the Matlab Simulink model.
real-time applications. Generally, sophisticated optimization methods are written in low level languages and they are difficult to use for engineers. The Modelica language extension Optimica was introduced to allow the formulation of optimization problems based on Modelica models. This extension enables a flexible and easily understandable formulation of the optimization problem including an objective (“What is the goal of the optimization (€, CO2, etc.)?”) and constraints (min/max temperatures, pressures, mass flows, etc.). The major advantages of including model coherences based on physical laws into the optimization formulation are high accuracy and the possibility to impose constraints on physically and operational relevant variables such as temperature, pressure or mass flow, based on limitations of the real system. A NEW MODELING PARADIGM FOR ENERGY SYSTEM MODELLING: ADVANTAGES AND POSSIBILITIES Modelica is an open, equation-based modeling language for multi-physic systems. Modelica has clear advantages over other languages mainly for the following reasons: (i) It can represent the physical structure of systems. Compared to causal languages, it is simple to interpret the graphical representation of models (see Figure 1). Models representing physical entities can be easily connected together using a graphical editor. This makes Modelica particularly suitable for application engineers. (ii) It is simple to code and to read the code. Model knowledge is stored in books (and human minds) in the form of equations. This knowledge usually cannot be transferred directly to computers, since conventional modelling languages do not allow equations. Modelica enables the modeler to model a system directly by the means of equations. This significantly increases the reusability, extensibility and adoptability of models and it enables faster developments compared to conventional modelling languages. (iii) Models described by equation- based languages can be integrated easily into optimization problems. Previous work has shown that the use of computer algebra in combination with equation based languages can speed up the solution significantly compared to conventional optimization methods. (iv) Modelica is particularly suitable for cross disciplinary developments.
Modelica has a lot of validated and well documented libraries in many physical domains including libraries for different subsystems of energy systems. A large variety of free and commercial libraries and modelling environments are available for modeling, simulation, optimization, model-based design and product life cycle management. These libraries consist of so-called “out of the box” models, which can be used via drag and drop. Modelica is a well-established modelling language in industry (7% of German power production is based on Modelica models. Furthermore, Modelica supports Functional Mock-up Interface (FMI). FMI is a tool independent, industrial standard for co- simulation of dynamic models and it is supported by more than 90 tools. Complex models are usually decomposed into subsystems (power – heat – buildings). Classically, such systems are modelled in a single tool, but very often there are more suitable tools available for different subsystems. In the context of energy systems, this offers novel possibilities. The model of an entire urban energy system could be decomposed into different subsystems, and these subsystems can be linked together via FMI. WHO BENEFITS FROM THE PROPOSED FRAMEWORK? Precise, physics-based models and a framework that is easy to use for engineers allow energy suppliers to increase the efficiency of existing systems as well as to design novel systems that may differ fundamentally from those of today. Furthermore, this framework can be used by the scientific community to work on concepts for future urban energy systems; the framework can be extended to other domains.
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