Section Five
Theoretical
basis and validity
of the
ESP-r system
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.
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. 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.
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.
A conceptual explanation of ESP-r’s calculation technique would go something like:
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.
The following publication details the theory and structure of ESP-r:
Clarke J A, Energy Simulation in Building Design, 2nd Edition, Butterworth-Heinemann, Oxford, 2001.
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.
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.
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 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>.
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.
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