Definition of an object oriented library for the dynamic simulation of advanced energy systems: methodologies, tools and application to combined ICE-ORC power plants

Abstract

The present Thesis covers part of the work that has been carried out during the three year Ph.D. course in Industrial Engineering at the University of Parma. Scope of the work is developing theoretical methodologies and a full library of dynamic models that can represent the components that usually appear in energy conversion systems. The proposed library should endorse the possibility to create any desire arrangement of the studied systems, to overcome the lack of testing facilities in order to create full virtual machines capable of representing the main phenomena that occur in the real systems to get a full and deep understanding on the way they operate and respond to transients and off design operating condition.

In Chapter Two an overview and classification of modeling techniques, suitable for energy systems analysis, is presented. Among the different classification criteria introduced, it is crucial to define whether state variables can be used for the considered component. This option leads to very different ways of developing the model: if the component modeled displays some “storage” capabilities (i.e. it is assumed to be able to store mass, energy, momentum, or moment of momentum) it is intended as a “state determined” system and state variables are defined through the introduction of cardinal physical laws in differential form. From a mathematical viewpoint this implies integrating in time (time is the only domain considered within this work) ordinary differential equations (ODE) expressed in term of the state variables, whose evolution hence will not depend only on the system inputs but on its complete “history”, that starts with the initialization at simulation time t=0. If the storage capabilities of the model are neglected it will be defined as “not state determined” and only algebraic equations (AE) will be introduced. Often the equations used in this case are derived from steady state performance data, gathered either from experimental investigations or by more complex model tools, thus simplifying the description of their transient behaviour as a continuous progression of steady state operating conditions. This modelling approach is known as “quasi-steady”. The models that will be created should be proper (i.e. models that achieve the accuracy required by the application with minimal complexity) scalable and flexible. The approach is followed is typical of object-oriented modeling and each realized component refers to a physical part (or a physical phenomena) of the system. Particular attention is also paid to causality, i.e. every model should be created in such a way to properly represent the cause-effect correlation between inputs and outputs. Another issue faced is the modeling environment to be chosen. After assessing some of the most widely known softwares that looked suitable for the scope, the choice has fallen on the Matlab®/Simulink® package. Simulink® is appreciated for modelling, simulation and analysis of dynamic systems by use of standard or customized blocks that allow great flexibility in model designing and are suitable for control purposes. Matlab® is exploited for its graphical and result analysis capabilities and the possibility to write specific functions which can be called during simulation. The potentialities in matrix calculation of the Matlab® language are also often exploited.

In Chapter Three the complete library of components is presented. According to what seen previously the components created have been split in the two main sub-libraries depending if dealing with “state determined” or “not state determined” components. A full complete system model should comprise a proper alternation of components coming from the two libraries to guarantee a better numerical solvability of the system of equations generated and to avoid algebraic loops. The two realized libraries have been enclosed in the Simulink® library root from where the realized custom blocks can be choosen, analogously to the way the standard blocks are employed. This option not only allows easy access to the developed block in creating any new lay-out, but turns useful since the models picked up from the library, if improved or modified, extend the changes to any Simulink® lay-out where they are employed. For each component a detailed description of the inputs, outputs and state variables (if present) is provided. The realized Simulink® models are also shown along with the specific dialog windows realized to introduce model parameters. Nearly all the models are based on s-functions, which allows executing the compiled Matlab® code while Simulink® is performing the simulation of a system. The sub-library ‘state determined components’ will contain the following components:

 thermal solar collectors;  single phase heat exchangers;  heat exchangers with phase change;  drums;  constant pressure combustion chambers;  rotating shafts dynamics;  General fluid Receivers;  ICE intercoolers.

Among these particular emphasis is given on the models of heat exchangers. This component has been characterized through the adoption of finite volume approach where a set of differential equations, expressing the energy balances in the axial nodes, is introduced and solved numerically adopting a forward finite difference method. Peculiarity of the proposed procedure is the degree of accuracy that may be tuned by the user defining the precision of the component discretization. The approach has also been applied to model an heat exchanger with phase change (evaporator or condenser) where also mass balances are considered in the component control volumes. The ‘not state determined’ library contains the following models:

 compressors;  turbines;  pumps;  valves;  heat exchangers with no thermal dynamics;  in cylinder combustion processes (in ICE).

As seen the library features all the “flow control devices’ that may appear in a fluid system, such as turbines, compressors, pumps and valves. Among the elements introduced, a special one in the “ICE in-cylinder processes”. The component is based on characteristic maps that allow to know the state of gases trapped inside an ICE cylinder at the end of expansion stroke. This model will turn useful in realizing a full dynamic model of an ICE. The maps are not based on experimental data, as common practice, but are obtained by means of a specifically developed computer code that resolves the chemical equations that refer to species dissociation at chemical equilibrium. Even though it is just an approximation of the real combustion process, the procedure has been believed to be a useful way to gather information of the engine combustion processes when no (or limited) experimental data are available.

In Chapter Four examples of applications of the realized models for fluid components are provided, with reference to power systems widely diffused and of known and proven design. The scope is to display the ease of creating new full models from the base component blocks, and the way to properly couple and link them together. Besides a simple example of a cogenerative micro gas turbine system, deeper insight is provided to the models of an organic Rankine power cycle and an alternative stationary internal combustion engine used for cogeneration purposes. These models will be employed for further analysis in Chapter Five. Results of simulations are presented for all the full models described under transient operating conditions inducted by some changes in the main model inputs. All the presented models have been introduced in a further Simulink® sub-library (‘complete power systems’). To be noted that the example presented are not exhaustive of the capabilities of the presented set of computer models discussed in Chapter Three, but new systems can be easily created depending on the research needs.

Chapter Five show the way the developed models are intended for system design purposes. It is author’s belief that a full validated computer model for the dynamic simulation of energy systems can constitute a proper tool aimed at developing, assessing and optimizing new system design configurations, developed to increase energy conversion efficiency and reducing primary energy consumption. In this case a combined ICE-ORC system (intended for stationary applications) is proposed as solution to improve the second principle efficiency of the engine generating unit. Many configurations are proposed and discussed through a comprehensive energy and exergy analysis of the system, in order to highlight the theoretical benefits in terms of energy conversion efficiency that can be achieved in some cases. To prove the feasibility of the design and to deeply assess the mutual interactions that exist between the two prime engines, a complete dynamic model of the system has been proposed and some results, under transient operational conditions are reported. The dynamic model of the full system therefore constitute a virtual test bench for development and enhancement of the new proposed energy conversion unit, relieving the energy system researcher from the costly and demanding real testing that, at least in the first stages of development, can thus be substituted by the simulation model.