Introduction - Energy modelling techniques

Key concepts

Lecture structure

Here we will address:

Summary

This section discusses simplified energy modelling methods, the most commonly encountered energy modelling techniques, and indicates the technique on which the remainder of this course will concentrate.

 

Course material (initial):

Simplified Energy Modelling Methods

In principle each building energy flow-path can be modelled and calculated by a simplified method. Simplified means in this context that certain features or phenomena are not taken into consideration. Examples of simplified approaches are:

Conduction
Fourier's heat conduction equation is often simplified by assuming that steady-state conditions prevail, that heat flow takes place in one direction only and that the material has zero heat capacity.
Overall fabric heat transfer
A common simplification in modelling fabric heat transfer is to assuming (constant) surface resistances (Rsi and Rso), which are then combined with the above conduction simplifications to give an overall thermal transmittance or U-value.
Convection
Convective heat transfer coefficients are often assumed to be time invariant and valid over an entire surface.
Radiation (long-wave)
Long-wave radiation is often simplified by the use of a linearised `radiative' heat transfer coefficient, which is assumed to be time invariant and valid for an entire surface. At external, exposed surfaces the radiative effects are often combined with the convective effects through the use of an overall heat transfer coefficient. In this case the influence of sky temperature is ignored.
Radiation (short-wave)
This process is often treated as a long-term average on the basis of design values listed in technical handbooks. In this case the short-term temporal and spatial variations are not considered. Since not all solar gains are usable in terms of decreasing the heating demand of a building, it is usual practice in simplified methods to introduce a utilisation factor.
Airflow
A common simplified method is to base calculations on design air change rates taken from some handbook. These are usually assumed to be fixed in time and imply perfectly mixed zones - i.e. air flows within the zone itself are not taken into account.
Casual gains
Often assumed to equal design values as found in handbooks with temporal and spatial variations ignored. As with fortuitous solar gain, it is normal practice to introduce a utilisation factor in an attempt to quantify the portion which can usefully offset the heating load or will contribute to overheating.
Climate
A building's boundary condition, at its most simple, is reduced to standard design temperatures (in case of load calculations) or to degree days plus average solar radiation levels (in case of heat requirement calculations). This means that high frequency phenomena and micro-climatic effects are ignored.
Plant
The influence of plant operation on final fuel consumption is often represented by the use of a single efficiency factor. Some simplified methods attempt to improve this by introducing separate efficiencies for emission, transport, generation and control.
Building dynamics
In simplified methods the indoor temperature is often considered to be constant over time. In practice this is almost never the case, some methods will introduce correction factors in an attempt to account for factors such as intermittent heating. 


Energy Modelling Techniques



From a thermal point of view, a building is a complex network of thermal
resistances and capcitances linking different regions and representing
conductive, convective, advective, radiative and heat storage processes.
The manner in which this network is treated mathematically - some portion
may be neglected, fixed values may be assigned or simplifying boundary
condition assumptions might be made - will determine the flexibility of
the modelling technique to emerge. In broad terms most building energy
models will fall into one of five `catch-all' categories: steady-state;
simple dynamic; response function; numerical; elecrical analogue.



Each method is concerned, at its own level, to satisfy the first and
second laws of thermodynamics but, as the level of sophistication of the
method falls, so many of the active flowpaths are ignored and the method
becomes indicative rather than deterministic and subject to the inaccuracies
touched on before.





Steady State



These methods have no mechanism for the accurate inclusion of the effects
of solar gains, casual gains, longwave radiation exchanges, plant operational
strategies etc, and so many models typically address only fabric heat flow
(under very special boundary conditions) and not building energy. Typical
inadequacies include the omission of any consideration of the dynamic response
of buildings, an inability to deal realistically with many of the energy
flows occurring within buildings, and an inability to effect the correct
relationship between building fabric and installed plant operation. In
consequence these methods are being subsumed by the dynamic theories and
will play a diminishing role even at an early design stage where, as well
as accuracy problems, their ability to provide even indicative results
can be seriously questioned. 



Simple Dynamic



In recent years a number of simplified methods of energy assessment
have been produced which address dynamic performance. These methods are
mostly based on regression techniques applied to the results of multiple
parametric runs of more powerful modelling systems. The results to emerge
can often be reduced to simple relationships or presented in tabular or
graphical form. 



Response Function


  
It is possible, by so specifying system boundary conditions, to solve the 
    partial differential heat equation, which governs the flow of heat within 
    the building fabric, to provide a means of modelling the dynamic response 
    of a building. Two main branches of this method exist, time-domain response 
    function and frequency-domain response function methods. An example is the 
    so-called admittance 
    - or means and swings - method as advocated by the UK Chartered 
    Institute of Building Services Engineers. Some workers are still pursuing 
    technique refinement.



Numerical



With the advent of powerful computing systems many problems of varying
complexity can be solved by numerical means. Two main numerical techniques
exist: finite difference and finite element. The former is the technique
most commonly applied to the problem of building energy modelling. 


  
Electrical 
    Analogue


  
The analogy that exists between electrical flow and heat flow has led to the 
    construction of electrical 
    analogue devices useful in the study of complex heat flow phenomena. The 
    technique is useful as a research tool, allowing long-term simulations to 
    be completed in a short elapsed time, but has little application in a design 
    context. 





The extant systems for building energy simulation are based either on
response function method but mostly on numerical techniques in finite difference
form and, for this reason, we will concentrate on the latter in this course.