Solar thermal systems: Field design & piping network – structural analysis and derivation of fitting functions

Type: Semester project (10 credits)

Period: Autumn 2016

Assistant: Anna Sophia Wallerand

Student: –


Process integration and optimization is commonly based on Mixed Integer Linear Programming (MILP). Thereby the linearized system equations are efficiently solved by deterministic algorithms. Multi-period analysis based on typical days[1] combined with thermal energy storage (TES)[2] allows for optimal design and operation of time and weather dependent systems. Urban clusters including solar thermal collectors and photovoltaic panels are e.g. sized in such a way (see [2]).

Solar thermal collectors are mostly modeled by introducing a (radiation and temperature dependent) solar-to-thermal efficiency that may or may not be expanded by a factor accounting for the piping losses[3]. For small scale systems this approximation serves well. However with increasing field sizes e.g. for industrial applications or power plants the loss factor should be scaled. This stems from the fact that the relationship between the number of collectors and (thermal) losses is nonlinear. In fact, as the losses (at certain temperatures) are quasi proportional to the piping surface area the relationship is expected to follow power laws. These could later be linearized for use in MILP. Structural analysis of bigger scale systems was carried out[4] by many authors but without the derivation of fitting functions.

The goal of this work is to structurally analyze solar thermal field layouts and the related piping losses (thermal and pressure) for a set of collector types, temperature levels, and heat transfer fluids. Thereafter, power law fitting functions are derived for the different types of systems. The losses will be correlated to the characteristics of the pipes and the insulation material[5] which leads thermo-economic optimization problem.

Eventually the found curves may be linearized and the thermos-economic optimization problem can be solved based on MILP.


The main objective of this work is to get a general idea about the loss functions that are related to upscaling of solar collector fields.


  1. Literature review: collectors and efficiencies
  2. Data acquisition: heat transfer coefficients of piping material and insulation
  1. Modelling: piping network and losses
  1. Fitting functions: fit power laws to the output data
  1. (Derive linearized equations)
  1. Report (Hardcopy and pdf)
  1. Presentation


Desired skills are:

  • Good knowledge of thermodynamics and energy conversion systems (EPFL courses: Thermo I/II, Energy conversion, Advanced Energetics, or equivalent).
  • Programming skills: scripting (Matlab,..) optimization (Modeling and Optimization of Energy Systems course, linear programming), AMPL.
  • English and/or German language.

[1] Samira Fazlollahi, Stephane Laurent Bungener, Pierre Mandel, Gwenaelle Becker, François Maréchal, Multi-objectives, multi-period optimization of district energy systems: I. Selection of typical operating periods, Computers & Chemical Engineering, Volume 65, 4 June 2014, Pages 54-66, ISSN 0098-1354

[2] Samira Fazlollahi, Gwenaelle Becker, François Maréchal, Multi-objectives, multi-period optimization of district energy systems: II—Daily thermal storage, Computers & Chemical Engineering, Volume 71, 4 December 2014, Pages 648-662, ISSN 0098-1354

[3] Rager JMF. Urban Energy System Design from the Heat Perspective using mathematical Programming including thermal Storage: EPFL; 2015.

[4]  Wallerand AS, Albarelli JQ, Ensinas AV, Ambrosetti G, Mian A, Marechal F. Multi-objective Optimization of a Solar Assisted 1st and 2nd Generation Sugarcane Ethanol Production Plant. Proceedings of ECOS 2014. 2014.

[5] Ulrich GD. A guide to chemical engineering process design and economics: Wiley New York; 1984. p.353