Modeling of Energy Conversion Systems

Rationale/Begrundelse:

Control of energy conversion systems is increasingly important due to focus on efficient use of resources. This demands models which describe the dynamics sufficiently well and yet simple enough to be useful in controller design.

Objectives/Mål:

The purpose is to be able to apply methods for finding models with distributed as well as lumped parameters using balance equations completed with descriptions of flows of mass or energy which are included in the balance. Furthermore students should be able to apply methods to simplify the models to a complexity where they are tractable for control design and simulation. Application of methods to handle models described by differential algebraic equations.

Course notes

Kursusnote (dansk) (pdf) These notes from 1996 cover part of the course. Part of the notes are also included in a course note used in the 6th semester course 'Modeldannelse og simulering'. We will refer to the pages we use in the notes. Since the notes are in danish we will also refer to pages of litteratur in english.

Minimodulplan:

Minimodul 1

Subjects: Derivation of models for thermohydaulic systems with concentrated or distributed parameters
Litteratur: Course notes, chapters 2 and 4
or English notes (pdf)
Opgave (pdf)
løsning til opgaven (pdf)

Minimodul 2

Emne: Simulering af systemer med fordelte parametre
Litteratur: Kursusnote kapitel 5
Opgave (pdf)

Minimodul 3

Emne: To-fase systemer og 'Moving boundary models'
Litteratur: Afsnit 2.1, 2.3 (pp 9-15) og 3.1 og 3.2 (pp 19-32) og 3.4 se også evt. 3.3 og App B (B1-B4) i vedhæftede rapport
Dynamic Modeling of Thermo-Fluid Systems
Opgave (pdf)

Minimodul 4

Emne: Moving boundary model, implementation af simuleringsmodel, modelreduktion
Litteratur: 3.2, 3.4 og Appendiks B.1, B.5 i Jacob Munch Jensen
Dynamic Modeling of Thermo-Fluid Systems
Opgave:
Filen subcooled_simulering.m indeholder funktioner for masse-matrix og tidsafledte for en subcooled region. Tilstandsvektoren består af L_0, p, og T_w0.
Antag at masseflowet ud af 2-fase-regionen er proportionalt med trykket (pga. en turbine) og at masseflowet mellem regionerne er det samme.

Find udtryk for stationære arbejdspunkter
Find realistiske parametre og udfyld filen, så man kan simulere systemet med Ta, mdotin, hin, dhin/dt som input. Brug en ode-løser med masse-matrix.
Lav en numerisk linearisering i et arbejdspunkt og sammenlign responsen med den ulineære simulering. Er springresponsen for hin realistisk?

Minimodul 5

Emne: Modelreduktion, balanced truncation for lineære modeller, anvendelse på den ulineære model
Litteratur:Zhou, Doyle, Glover: Robust and Optimal Control, 3.8-3.9
Opgave:
Hvis I har lyst, kan I prøve at opdele modellen (udleveres ved forespørgsel) i flere sektioner. Lineariser modellen numerisk og undersøg vha. balancering, hvordan man bedst reducerer modelordenen. Gør det en forskel, om inputtet er gas-temperatur eller indløbstemperatur?