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\fB\s+9Section Five\s0\fR
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\fB\s+5Theoretical basis and validity\s0\fR
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\fB\s+5ESP-r system\s0\fR
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.SH
Contents
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5.0 Introduction
5.1 Theoretical basis
5.2 Validity
5.3 Model value
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.SH
5.0 Introduction
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A comprehensive description of ESP-r's mathematical
model, and the verification tests applied to it, would
occupy much space, and so is not undertaken here. Instead, ESP-r's
theory is stated conceptually and the various publications
covering theory and validity are referenced.
.SH
5.1 Theoretical basis
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ESP-r uses an advanced numerical method to integrate the
various equation types (algebraic, ordinary differential
and partial differential) which can be used to represent heat and
mass balances within buildings.
The system is non-building type specific and can handle
any plant system as
long as the necessary component models are installed in the
plant components' database. Components, if missing, can be added
by a user so that they become available for
selection to participate in any multi-component plant
configuration.
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But since component models must conform to
state-space formulations, new component derivation and insertion
is often a non-trivial task - the price of plant modelling in the
transient domain.
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In addition to the usual energy analysis features (comfort assessment,
condensation checks, and the like), ESP-r
can handle the spectral analysis of glazing systems which include thin films,
time varying shading caused by site obstructions, solar ray tracing, pressure
and buoyancy induced air movement and complex, distributed control
systems.
.LP
A conceptual explanation of ESP-r's calculation technique
would go something like:
.IP
The system offers a way to rigorously analyse the
energy performance of a building and its environmental
control systems. For each observable energy flow-path in
the real world, ESP-r has a corresponding mathematical structure.
Within a simulation, a special numerical technique
ensures that all flow-paths evolve simultaneously to fully
preserve the important spatial and temporal relationships.
Stated briefly, ESP-r will accept some building/plant description
in terms of 3-D geometry, construction, usage and control.
This continuous system is then made discrete
by division into many small, but finite, volumes of space -
perhaps as many as 10,000 for a medium sized building.
These finite volumes will represent the various regions of
the building and plant within and between which energy and mass can
flow. Throughout any subsequent simulation, ESP-r will track
the energy and mass balance for all finite volumes as they
evolve under the influence of the system boundary conditions
(climate & control) and the constraints imposed by the inter-volume links.
This technique ensures that all regions
of the building are correctly connected across space and time
and so any excitation at some point in space or time will
have the correct causal effect.
.LP
The following publication details
the theory and structure of ESP-r:
.RS
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Clarke J A, \fIEnergy Simulation in Building Design\fR,
2nd Edition, Butterworth-Heinemann, Oxford, 2001.
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ESP-r's mathematical approach is derived
and the numerical method used to
achieve the repetitive and simultaneous integration of each
flow-path over time is explained.
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As described in Section One, ESRU maintains a list of
bibliographic references, describing much of ESP-r's
technical detail and philosophy. This list is available
from ESRU on request.
.SH
5.2 Validity
.LP
Many model users do not yet appreciate the complexities
of large scale energy model validation. Indeed it is
probably true that absolute declarations of validity  will
never be possible. This is because the data used to
describe the problem is itself subject to great uncertainty,
and because the combinatorial links between
input assumptions, logic representations,
mathematical techniques and output interpretations
is very large. It is now widely recognised that
confidence levels can only be improved by developing
verification
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methodologies
and by repeatedly undertaking
studies which aim to verify discrete aspects of a model
under different operating conditions. In this respect ESP-r
has a good track record. It was/is a participant
model in the International Energy Agency's Annex 1, 4 and
10 projects concerned with inter-model and empirical
model verification in both building and systems simulation
modes. ESP-r has also been tested by several organisations
external to ESRU and found to agree well with known
analytical solutions and monitored data sets. On the basis
of these findings the program has been declared the European
Reference Model for Passive Solar Architectural Design and
has been examined extensively in a SERC (now EPSRC) funded
research project to develop a model verification
methodology. ESP-r has also been well tested within
the EC's PASSYS project. Several validation reports have been generated
at ESRU and elsewhere. iA summary can be obtained by file transfer
from: <ftp://ftp.strath.ac.uk/Esru_public/documents/validation.pdf>.
.SH
5.3 Model value
.LP
ESP-r is a state-of-the-art model which allows the rapid
performance assessment of proposed building designs
incorporating traditional and/or advanced energy features.
For the first time, a user is able to conduct a high
integrity, first principle appraisal whilst modelling all
aspects of the energy subsystem simultaneously and in the
transient domain. Indeed many design problems (for example
fabric design, comfort or condensation assessment, control
system appraisal, etc.) can only be meaningfully assessed
when considered in this manner, as one portion of some
complex set of interactions.
That is, a piecemeal approach, in which a particular region
is considered in isolation, is totally inappropriate and
often misleading. At an early design stage a model such as
ESP-r is particularly powerful since it can be used to
quantify the performance impact of the site, the building geometry
and construction; all factors which have considerable impact
on operational performance and costs. Then, at the more detailed design
stage, the model allows the designer to focus on issues of
control and comfort. 
