For the simulation and optimization of power plant concepts, the cycle simulation program ENBIPRO (**En**ergie **Bi**lanz** Pro**gramm) is currently being developed at the institute.

Simulation of power plant processes

The liberalization of the European energy market and the increasing usage of renewable energies such as solar plants and wind turbines lead to higher requirements concerning the power plant park. This has to be considered even while planning power plants. It is reasonable to use a simulation tool which is capable of not only handling the design calculation but also the stationary partial- and full load calculations, the dynamic simulation and the validation of measurement values. This ensures experience conclusions while operating after wards (see figure).

Usually this four methods of calculation are performed by different programs, which then again use e.g. different models and steam tables. That may lead to differences in the calculation results. For this purpose, during several dissertations ([Zindler08], [Apascaritei08], [Witkowski06], [Loehr99], [Stamatelopoulos96], [Rohse94]) ENBIPRO has been developed at the institute. ENBIPRO solves the model equations in both stationary and non-stationary cases in a closed form. It also covers the various methods of calculation.

The idea behind ENBIPRO is to construct a system of generally valid equations, including the balance equation (momentum, mass, substance and energy), the transport equations and the relations of physical characteristics. This opens the possibility to solve the system depending on the application. Depending on the application (design, full or partial load, dynamic as well as validation) a different set of parameters is needed to solve the problem.

Based on a system of generally valid equations including the laws of conservation of energy (energy, mass, momentum or the transport equations of heat and substance) as well as the relations of substance values for various applications, ENBIPRO sets up a specific system of equations and solves it.

ENBIPRO consists of the simulation program and a graphical user interface (GUI). The simulation program is based on C++. It contains the component models and the mathematical solution methods. A fluid property database is included. This database contains properties of ideal gases, real substances and mixtures as well as the water steam table IAPWS 97-IF.

While regarding the models in ENBIPRO and [Zindler06], it becomes apparent that the system of equations actually is a system of partial differential algebraic equations. With the use of a finite volume procedure, the spatial discretization takes place beforehand.

This results in an implicit ordinary system of differential algebraic equations. The vector can contain algebraic and differentiated variables. This system of equations is solved by converting the equations into a system of algebraic equations during each time step, which is then again solved via Newton's method. This way the stationary case is also covered. Compared to simple integrators modern procedures, such as the Differential Algebraic System Solver (DASSL) by instance of the of the predictor-corrector method, offer a lot of advantages: the calculation of an stimator, a step size control and an errorestimation. Because of the implicit system of equations, the variables can be chosen freely as long as the system of equations stays regularly. This way every branch of the calculations is covered.

To simplify the input of a power plant process, a graphical user interface, based on a multi-platform framework, is used. This user interface and the actual program ENBIPRO only communicate via XML-documents. The whole program is implemented in C++. This way it runs on every common operating system (Windows and Linux). The data is input through a graphical user interface.

- Design calculation
- The goal of the full load calculation is to determine the geometry of the components of a power plant. This means mass flows and performances, which are matched to each other, are set and the resulting states and geometric data (heat area size, volumes) are calculated. Based on the results e.g. the heat exchanger or the turbines can be scaled in further more detailed calculations.

For the stationary case, mass and energy balances have to be set up. When the balances are solved via a simultaneous method, a system of linear equations results. The form is AX = B, while X is the solutions vector and A is the coefficient matrix. The design of the heating surface is usually made at a 100% load. To make a thermotechnical interpretation of heat exchangers, calculations have to be carried out in order to obtain data on the form of the current and heat exchange on the side of the flue gas and water/steam. For this purpose, certain assumptions about the constructive configuration have to be made. For example the type of the heat surface: radiant heat surface inside the combustion chamber, wall- and cluster heat surfaces or supporting tubes, and the geometry: pipe diameter, thickness of the wall and the material. Using the heat transfer coefficient, which resulted from the full load calculation, the heat surface size is calculable. The temperatures at the entrance and exit are stated. This way the logarithmic temperature difference and the transmitted heat current are also given. The product of the heat transfer coefficient k and the heat surface A is the result. With the calculated heat transfer coefficient the heat surface A results.

- Partial load calculations
- The procedure of the partial load calculations is inverse. The complete geometry of the power plant components or the summarizing data, like areas, volumes, heat transfer coefficient etc. and the condition of the entering substance flow are given in beforehand. Based on this data the condition of the exiting substance flow is calculated. Different from the design case, in which the outlet temperature at the heat exchangers are stated and the product out of the heat transfer coefficient k and the heat surface A is calculated, in the partial load case the calculations of the outlet temperatures and the transferred heat streams and the kA-value are calculated iteratively. Should there be a phase change inside of the heat exchangers, a fictive split for each phase is done. This way for every split's kA-value can be calculated.

- Validation
- The validation of measured values is a procedure to calculate from a set of measured values a set of correct measured values. These meet the requirements of the balance equations, the transfer equation and the material properties. However it is assumed, that an accurate mathematical model and inaccurate measured values are present. As many properties of a plant as possible are measured. By way of minimizing the sum of square of errors (see VDI-guideline 2048 [VDI2048]), it is possible to calculate the most likely state variables, which satisfy the system of equations, especially the balance equation. With the help of this method it is possible to detect measurement errors or malfunction of measuring devices respectively, if the measurement error is outside of the confidence interval.

To set the state of a system definitely, the amount of measurements have to meet the amount of equations. Oftentimes, the measured values contain errors. This causes them to not satisfy the system of equations and specially the balance equitation. For this reason more measurement points than necessary are used. This way the system would be overdetermined without measurement errors. The purpose of the measurement value validation is to find adjustments for the measurements inside specific tolerances, which then again solve the system and adjust the measurements as little as possible. The measurement values can be validated using the L1- or L2-norm. By way of the L2-norm the sum of square of errors is minimized (via Gauß), as opposed to the L1-norm where the sum of the absolute value is minimized (via LaPlace). - Dynamics
- Whereas the initial three tasks are calculated stationary, the control-engineering and analysis of the non-stationary behavior of an energy-relevant plant need to be calculated dynamically. A system of algebraic equations is usually transformed to a system of differential algebraic equations. In a dynamic calculation, similar to the partial load calculation, the complete plant geometry needs to be known. The non-stationary simulation is based on a finite volume-method. To achive this, components of the steam generator are discretized in control volumes and the conservation law for mass, momentum and energy is solved. The flue gas- and the working substance side is connected via the tube wall. The solution is made using a semi-implicit method. The internal code structure of the non-stationary calculation is made similar to the stationary parts. This way the same code can be used for similar calculations, for example the constituent equations.

Examples for simulated circulations and circuits.

These listed examples are a variety of calculated cycles. In case you need more information to the simulated examples, please make a request via email.

- Conventional thermal power plants
- Gas- and steam turbine plants
- High-temperature-fuel cells
- Combined circulations with gasification/ reformation of hydrocarbon
- Storage of mass and energy
- Geothermal organic – rankine – circulations
- Circulations with CO2 – deposition
- Solar-thermal power plants
- Control-engineering / simulation using generalized transfer functions

Currently, there are over 80 different components provided in ENBIPRO. Among the standard components like heat exchangers, bifurcations, pumps and turbines, there are even specific component groups like storage-modules, fuel cells and components of control-engineering.

Software system

The processing core is a C++ based code. The data is secured with XML-databases, as seen in the following image. This way, the processing core is plattform independent. We are supporting Windows and Linux natively.

Literature

(extract)

- [Apascaritei08]
- Apascaritei, B.: Error Analysis for Energy Process Simulation; Dissertation, Institut für Wärme- und Brennstofftechnik, TU Braunschweig, 2008
- [Brenan95]
- Brenan, K. E.; Campbell, S. L.; Petzold, L. R.: Numerical Solution of Initial-Value Pro blems in Differential-Algebraic Equations; siam; 1995
- [Depta08]
- Depta, D.: Überblick über ORC-Prozesse für die Stromerzeugung aus Geothermie; 20. Kasseler Abfall- und Bioenergieforum Kassel 08/10.04.2008
- [EOLSS02]
- Leithner, R.: Encyclopedia of Life Support Systems, Kapitel 6.43.32, Automation and Control of thermal processes; 2002
- [Hauschke07]
- Hauschke, A.: Dynamische Simulation und Optimierung eines Abhitzedampferzeugers;Diplomarbeit, Institut für Wärme- und Brennstofftechnik, TU Braunschweig, 2007
- [Ladwig08]
- Ladwig, M.; Lindvall, K.; Conzelmann, R.: Gasturbinenprozess mit sequentieller Verbrennung; BWK Bd. 60 Nr. 3 S. 52-58, 2008
- [Leithner07]
- Leithner, R.; Schlitzberger, C.: Isobaric Adiabatic Compressed Air Energy Storage Combined Cycle with High Levels of Storage Efficiency; 2. International Renewable Energy Storage Conference (IRES 2), Bonn 19/21.11.2007
- [Leithner08]
- Leithner, R.; Mönnigmann, M.; Schlitzberger, C.; Chen, S.; Dietrich, R.-U.; Oelze, J.; Lindermeier, A.; Carlowitz, O.; Spitta, C.; Steffen, M.; SchÂ¨onbrod, B.; Beck, A.; Heinzel, H.; Stagge, H.-P.: SOFC-Brennstoffzelle mit partieller Anodenabgas-Rückführung zur Reformierung; 6. VDI Fachtagung Brennstoffzelle VDI-Berichte Nr. 2036 Brennstoffzelle, S. 217-230 Braunschweig 27/28.08.2008
- [Loehr99]
- Löhr, T.: Simulation stationärer und instationärer Betriebszustände kombinierter Gasund Dampfturbinenanlagen; VDI-Fortschritt-Berichte Reihe 6 Nr.: 432; 1999
- [Rohse94]
- Rohse, H.: Untersuchung der Vorgänge beim Ubergang vom Umwälz- zum Zwangsdurchlaufbetrieb mit einer dynamischen Dampferzeugersimulation; VDIFortschrittsberichte, Reihe 6: Energietechnik, Nr. 327, ISBN 3-18-332706-6, 1994
- [Stamatelopoulos96]
- Stamatelopoulos, G.: Berechnung und Optimierung von Kraftwerkskreisläufen; VDI-Fortschrittsberichte, Reihe 6: Energietechnik, Nr. 340, ISBN 3-18- 334006-2, 1996
- [Strelow07]
- Strelow, M.: Optimierung von Kraftwerksprozessen für solarthermische Kraftwerke Einsatz intelligenter Optimierungsverfahren zur Wirkungsgradmaximierung des Dampfkraftwerksprozesses; Diplomarbeit am Institut für Wärme- und Brennstofftechnik, TU Braunschweig, 2007
- [VDI2048]
- VDI-Richtlinie 2048: Messunsicherheiten bei Abnahmemessungen an energie- und kraftwerkstechnischen Anlagen;Beuth Verlag, Blatt 1, 2000, Berlin
- [Witkowski06]
- Witkowski, A.: Simulation und Validierung von Kraftwerksprozessen; Dissertation, Institut für Wärme- und Brennstofftechnik, TU Braunschweig, Der Andere Verlag, 2006
- [Zindler06]
- Zindler H.; Leithner R.: Combining FVM and PECE Algorithms with Adjoint Methodsfor the dynamical Simulation of Power Plants; WSEAS Int. Conf. on Heat Transfer, Thermal Engineering and Environment, Agios Nikolaos, Kreta, Griechenland, 2006
- [Zindler08]
- Zindler H.: Dynamische Kraftwerkssimulation - Kopplung von Finiten Volumenverfahren und Prädiktor-Korrektor-Verfahren mit Adjungiertenverfahren; Dissertation, Institut für Wärme- und Brennstofftechnik, TU Braunschweig, VDI-Fortschrittberichte, 2008

Further information

For additional information and the initial contact please approach us at any time!

**Reference person**: Prof. Dr. techn. Reinhard Leithner