Energy Systems Modelling: Energy flow-paths

Transcription

1 Energy Systes Modelling: Energy flow-paths Coputer tools for energy systes design have traditionally been constructed by reducing the coplexity of the underlying syste equations in an attept to lessen the coputational load and the corresponding input burden placed on the user. Soe aspect of the syste ay be neglected (e.g. longwave radiation exchange), soe syste paraeters ay be assued to be tie invariant (e.g. convective heat transfer coefficients) or siple boundary conditions ay be iposed (e.g. steady state or steady cyclic). Within a siulation progra such assuptions are heresy. Instead, a atheatical odel is constructed to represent each possible energy flow-path and flow-path interactions. In this sense siulation is an attept to eulate reality. 1. Siulation overview This course addresses the odelling of the energy perforance of buildings and the yriad technical systes that deliver heating, cooling and electrical power. Buildings Figure 1 depicts the energy flow-paths encountered within a building and which interact, in a dynaic anner, to dictate cofort levels and energy deands. To understand the siulation approach, it is useful to visualise such a syste as an electrical network of tie dependent resistances and capacitances subjected to tie dependent potential differences. The electrical current that flows in each branch of the network are equivalent to the heat flows between the building's parts when driven by teperature and pressure differences (analogous to voltage differences), and stochastic heat and power inputs fro sources such as occupants, cliate control equipent, photovoltaic panels and directly fro the sun. Figure 1: Typical building energy flow-paths. Continuing the analogy, constructional eleents, roo contents, glazing systes, plant coponents, renewable energy devices etc. ay be treated as a network of nodes

2 characterised by capacitance, with the inter-node connections characterised by resistance. Nodes possess 'variables of state' such as teperature and pressure (analogous to voltage) and since nodes have different capacitances, the proble is essentially dynaic; each node responding at a different rate as it copetes with its neighbours to capture, store and release energy. It is this distributed dynaic behaviour along with the non-linear nature of the network paraeters that iparts coplexity to the building odelling task. The resolution of such a odel that is, the nuber of nodes eployed is a function of the analysis objectives: an early design stage estiation of suertie teperatures will require a lower level of discretisation than a detailed study of indoor air quality. Fro a atheatical viewpoint, several coplex equation types ust be solved to accurately represent such a syste and, because these equations represent heat transfer processes that are highly inter-related, it is necessary to apply siultaneous solution techniques if the perforance prediction is to be both accurate and preserve the spatial/teporal integrity of the odelled syste. Conventional systes Figure 2 illustrates soe typical heating, ventilating and air conditioning (HVAC) coponents as eployed to control internal environental conditions. Figure 2: Typical HVAC systes. Because the building and its plant are strongly coupled, accuracy considerations dictate that they be handled siultaneously. One approach is to incorporate plant characteristics within control stateents, which are then ebedded within the solution of the building-side equations (or used to influence their forulation). Alternatively, for ore accuracy, dynaic plant syste odels can be established for solution in tande with the building odel so that the spatial and teporal interactions are respected.

3 New and renewable energy systes Future cities are likely to be characterised by a greater level of new and renewable energy systes deployent in the for of cobined heat and power plant, hydrogen fuel cells, photovoltaic coponents, ducted wind turbines and heat pups). To date, renewable energy technologies have been deployed ostly at the strategic level, with the connection of ediu-to-large scale hydro stations, bio-gas plant and wind fars to the electric grid. The further introduction of renewable energy systes at this scale will eventually give rise to network balancing and power quality issues due to the interittent nature of renewable energy sources, requiring controllable, fast responding reserve capacity to copensate for fluctuations in output, and energy storage to copensate for non-availability. The attainent of high levels of renewable energy systes penetration ay best be assisted by the introduction of active network control and the ebedding of heat and power generation at the urban level atched to the loads they serve: by utilising energy efficiency and deand anageent easures, a building's energy deand ay be reduced and the profile of this deand reshaped to accoodate the low power densities of ebedded icro-generators; any energy deficit ay then be et fro the public electricity supply. To facilitate the odelling of ebedded generators, an electrical power flow odel is required along with related odels for each generation technology. 2. Integrative odelling The ai of integrative odelling is to preserve the integrity of the entire building/plant syste by siultaneously processing all energy transport paths at a level of detail coensurate with the objectives of the proble in hand and the uncertainties inherent in the describing data. To this end, a building should be regarded as being systeic (any parts ake the whole), dynaic (the parts evolve at different rates), non-linear (paraeter values depend on the therodynaic state of the syste) and, above all, coplex (there are yriad intra- and inter-part interactions). The essential challenge is to solve a large nuber of partial differential equations that describe the conservation of ass, energy and oentu within a syste coprising any sub-parts. Once established, an integrated siulation progra can be applied throughout the design process, fro the early concept stage through detailed design. Indeed, it ay be argued that it is ore appropriate to use a single siulation progra throughout the design process than to use a progression of tools fro siplified to detailed and ignore the any theoretical discontinuities and pernicious assuptions. Siulation allows users to understand the interrelation between design and perforance paraeters, to identify potential proble areas, and so ipleent and test appropriate design odifications. The design to result is ore energy conscious, with better environental conditions aintained over tie. Underlying the flow-paths of figures 1 and 2 is the concept of energy, ass and oentu balance, governing the fundaental processes of conduction, convection, radiation and fluid flow. Any unified representation of the building and its environental control systes will therefore require odels of the heat, air, oisture, light and electricity flows as they occur within the building/plant syste when subjected to weather factors and influenced by distributed control action and occupant interactions. 3 Energy flow-paths and causal effects Before considering techniques for the developent of an integrative atheatical odel, it is

4 necessary to consider the various heat and ass transfer echaniss to be odelled and the factors that give rise to the. Transient conduction This lies at the heart of the energy odel and is the process by which a fluctuation of heat flux at one boundary of a solid construction (within a building or plant coponent) finds its way to another boundary, being diinished in agnitude and shifted in tie due to the construction's theral inertia. Transient conduction is a function of the teperature and heat flux excitations at exposed surfaces, the possible generation of heat within the construction, the teperature- and oisture-dependent (and therefore tie-dependent) hygro-theral properties of the individual aterials coprising the construction, and the relative position of these aterials. With the external weather excitations known tie-series data, the odelling objective is to deterine the intra-construction teperature and oisture distribution and hence the dynaic variation of heat flux at the exposed surfaces. In any situations it is iportant to consider heat flow in ore than one direction, for exaple in cases where theral bridging ight be expected to occur or where corner and edge regions are large relative to the planar area of a wall. The thero-physical properties of interest include conductivity, k (W/.K), density, ρ (kg/ 3 ), and specific heat capacity, C (J/kg.K). These properties are tie-dependent because of aterial teperature and/or oisture fluctuations, and ay be position or direction dependent if the aterial is non-hoogeneous or anisotropic respectively. In soe applications such dependencies ay be ignored and the thero-physical properties assued constant. The aterial properties coprising a construction can be cobined to provide siple indices for use at an early design stage to differentiate the perforance of different constructional approached. For exaple, the overall steady-state theral transittance, or U-value (W/ 2.K), is given by 1 U N x j R i R o R k c j 1 j where N is the nuber of layers in the construction, x j the thickness of layer j (), R the cobined radiative and convective theral resistance ( 2.K/W) and subscripts i, o, and c refer to the innerost surface, outerost surface and air gap (if any) respectively. Traditionally, designers have relied on this steady-state concept to assess the heat loss characteristics of a building s fabric. In addition to ignoring the dynaic (theral capacity) aspect of fabric response, the approach does not preserve spatial integrity since different constructional arrangeents will perfor differently even though each ay have the sae U- value. The cobined effect of these shortcoings can have significant ipact on other energy flow-paths. For exaple, if insulation is located at the innerost position of a wall then any shortwave solar radiation penetrating windows and striking that internal surface cannot be readily stored in the construction since the insulation will act as a barrier. Instead, the solar energy will cause a surface teperature rise which, in turn, will increase the rate of energy release to the adjacent air by the process of natural convection. A space experiencing high solar energy penetration is therefore likely to overheat if cooling is not introduced. Conversely, if the insulation is relocated externally, with capacity eleents exposed to the inside, then internal surface shortwave gain can access capacity to be stored. By proper design this stored energy can later be harnessed passively (rather than by echanical eans) to iniise heating requireents and avoid overheating. On the other hand, internal capacity ay give rise to increased peak plant deand due to the initial high rate of transfer of energy to capacity at plant start-up in an interittent schee. With continuous operation, capacity

5 can help to iniise the peaks and axiise the troughs of plant deand and so proote good load levelling. This, in turn, will give a stable environent and encourage efficient operation by allowing plant to operate consistently at or near full load. The risk of interstitial condensation is greater in the case of internally located insulation since a portion of the construction ay fall below the dew point teperature of oist air pereating through the construction in the absence of an effective vapour barrier. The use of a odel based on a U- value approach cannot readily differentiate between such cases. In suary, transient conduction will affect energy requireents, load diversity, peak plant deand, load levelling, plant operating efficiency and condensation potential. Unfortunately, there is no siple design paradig that can be used to select an optiu construction. Theral diffusivity, α = k/ρ.c ( 2 /s), and effusivity, ε = (k.ρ.c) ½ (J/ 2.K.s ½ ), are useful dynaic perforance indicators. Materials with high α values transit boundary heat flux fluctuations ore rapidly than do aterials with correspondingly low values, while aterials with high ε values will ore readily absorb a surface heat flux. These paraeters can be usefully applied to real constructions by reducing the ultiple layers to an equivalent hoogeneous layer: k C 1. 1 R k C 1. 1 R i i k C o k C e R o 0. 1 R i 0. 1 R R e R e where subscripts e, i, and o refer to the equivalent, innerost, interediate and outerost layers respectively (=0 for a 2 layer construction and kρc=0 for an air gap). If the second ter on the right-hand side of this equation becoes negative (i.e. R o 0) then it should be neglected. The equivalent resistance is given by R e x k o o where, for the case of an air gap, x /k is the cobined convective/radiative resistance. The equivalent (ρc) value is obtained fro k C e R e C e x o x x i so that the theral diffusivity/effusivity of the equivalent layer ay be deterined fro the equivalent k and ρc values. x k x k i i The tie constant, τ, of a ulti-layered construction ay be evaluated fro M k C R 0. 1 R 0. 1 R 1. 1 Cx Cx o o i j i j 1 j 1 U M j. Within a siulation, the start-up period (required to eliinate the effects of the arbitrarily assigned initial conditions) can be epirically related to the axiu tie constant occurring within a given design. These above derived properties ay be use to differentiate the behaviour of different constructional aterials, For exaple, consider two hypothetical aterials, A and B, as listed in the following Table. Table 1.1: Two hypothetical aterials. Material Diffusivity ( 2 /s) Effusivity (J/ 2.K.s ½ ) A 7.7 x x 10 3 B 8.3 x

6 Material B will transit a boundary heat flux fluctuation the fastest because its theral diffusivity is largest but will absorb a surface heat flux less readily because its theral effusivity is lowest. Surface convection This is the process by which heat flux is exchanged between a surface (opaque or transparent) and the adjacent air layer. In building odelling it is usual to differentiate between external and internal exposures. In the forer case, convection is usually wind induced and considered as forced whereas, at internal surfaces, natural and/or forced air oveent can occur depending on the location of echanical equipent and the flow field to result. It is noral practice to ake use of tie-varying, but surface-averaged, convection coefficients, h c (W/ 2.K), corresponding to walls, floors and ceilings subjected to different flow regies. Forced convection is a function of the prevailing fluid flow vector. Typically, for external building surfaces, wind speed and direction data are available for soe reference height and techniques exist to estiate non-reference height values in ters of characteristic vertical velocity profiles. Forced convection estiation for internal surfaces is ore probleatic, requiring knowledge of the distribution and operation of air handling equipent. Natural convection is a ore tractable proble to study and any forulations have eerged which give convection coefficients as a function of the surface-to-air teperature difference, surface roughness, direction of heat flow and characteristic diensions. Internal surface long-wave radiation exchange In ost siplified ethods, surface heat transfer coefficients are treated as cobinations of convection and long-wave radiation although the values used are often dubious. In reality, the two processes are related by the fact that they both can raise or lower surface teperatures and so influence each other. Inter-surface long-wave radiation is a function of the prevailing surface teperatures, surface eissivities, the extent to which the surfaces are in visual contact (represented by a view factor), and the nature of the surface reflection (diffuse, specular or ixed). The flow-path will tend to establish surface teperature equilibriu by cooling hot surfaces and heating cold ones. It is an iportant flow-path where teperature asyetry prevails, as in passive solar buildings where an attept is ade to capture solar energy at soe selected surface. A standard energy efficiency easure is to upgrade windows with glazings incorporating a low eissivity coating. This increases the reflection of long-wave radiation flux and so acts to break inter-surface heat exchange. The atheatical representation of the flow-path is nonlinear in the teperature ter and this introduces odelling coplications. External surface long-wave radiation exchange The exchange of energy by long-wave radiation between external (opaque and transparent) surfaces and the sky vault, surrounding buildings and ground can result in a substantial lowering of surface teperatures, especially under clear sky conditions and at night. This can lead to sub-zero surface teperatures, especially with exposed roofs, and can give rise to high heat loss in cases of low insulation level. Conversely, the flow-path can result in a net gain of energy, although under ost conditions this will be negligible. The adequate treatent of this flow-path will require an ability to estiate several contributing factors: the effective sky teperature as a function of the prevailing cloud cover and type; the teperature of surrounding buildings; the teperature of the ground as a

7 function of terrain conditions; the local air teperature; the surface waring effect of any incident short-wave solar flux; and view factor inforation to geoetrically couple the surface with the three possible portions of its scene ssky, ground and surroundings. The atheatical representation of the flow-path requires that the describing data odel be extended to include a building s surroundings. Short-wave radiation In ost buildings, the gain of energy fro the sun constitutes a significant portion of the total cooling load (or overheating potential if cooling is not available). The ethod of treatent of the shortwave flow-paths will therefore significantly dictate the accuracy of the overall predictions. Soe portion of the short-wave energy ipinging on an external surface arriving directly fro the sun or diffusely after atospheric scatter and terrain reflections ay, depending on subsequent teperature variations affecting transient conduction, find its way through the fabric where it will contribute to the inside surface heat flux at soe later tie. It is not uncoon for exposed surfaces to be as uch as C above abient teperature. In the case of copletely transparent structures, the shortwave energy ipinging on the outerost surface is partially reflected and partially transitted. Within the glazing layers and substrates of the syste any further reflections take place and soe portion of the energy is absorbed within the aterial to raise its teperature. This teperature rise will augent the noral transient conduction process and, thereby, help to establish inner side and outer side surface teperatures which, in turn, will drive the surface convection and long-wave radiation flow-paths. Thus, in effect, absorbed shortwave radiation penetrates the building envalope via convection and longwave radiation. The coponent of the incident bea which is transitted will strike (with no perceptible tie lag) one or ore internal surface where it behaves as did the external surface ipingeent: opaque surface absorption/reflection, transparent surface absorption/reflection and transission (back to outside or onward to another zone), and giving rise to behind-thesurface transient conduction where the flux is stored and lagged. Accurate solar irradiation odelling therefore requires ethods for the prediction of surface position relative to the solar bea, and the assessent of the oving pattern of insolation of internal and external surfaces. The forer ethod is a function of site latitude and longitude, tie of day/year and surface geoetry, while the latter ethod requires the existence of ray tracing techniques. The thero-physical properties of interest include shortwave absorptivity and reflectivity for opaque eleents and absorptivity, transissivity and reflectivity for transparent eleents. The agnitude of these properties is dependent on the angle of incidence of the short-wave flux and on its spectral coposition. With regard to the latter, it is coon practice to accept properties that are averaged over the entire solar power spectru. Shading and insolation These factors control the agnitude and point of application of solar energy within the building zone or solar device. Both tie-series require point projection or hidden line/surface techniques for their estiation, as well as access to a data structure that contains the geoetry of obstruction features. It is usual to assue that façade shading caused by reote obstructions (such as surrounding buildings and trees) will reduce the agnitude of direct insolation, leaving the diffuse bea

8 undiinished. Conversely, shading caused by façade obstructions (such as overhangs and window recesses) ight also be applied to the diffuse bea since the effective solid angle of the external scene, as subtended at the surface in question, is arkedly reduced. At any point in tie the short-wave radiation directly penetrating an exposed window will be associated with one or ore internal surface, depending on the prevailing solar angle and the internal building geoetry. The receiving surface(s) ay be opaque, a window in another wall (connecting the zone to another zone or back to abient conditions), ites of furniture, or special surfaces included in the odel to represent occupants or control syste sensors. Air flow Within buildings, three air flow paths predoinate: infiltration, zone-coupled flow and echanical ventilation. These flow-paths give rise to advective (fluid-to-fluid) heat exchanges and each are vector quantities in that only air flowing to a region is considered to cause the theral loading of that region, any loss being the driving force for a corresponding replaceent to aintain a ass balance. Infiltration is the nae given to the leakage of air fro outside and coprises two coponents: the unavoidable oveent of air through distributed leakage paths such as the sall cracks around windows and doors and through the fabric itself; and the ingress of air through intentional openings (windows, vents, etc.) often referred to as natural ventilation. Zone-coupled air flow, as with infiltration, is caused by pressure variations and by buoyancy forces resulting fro the gravitational and density differences associated with the coupled air volues. Mechanical ventilation is the deliberate supply of air to satisfy a fresh air requireent and, perhaps, heat or cool a space. Rando occurrences, such as occupant induced window/door opening, changes in the prevailing wind conditions, and the interittent use of echanical ventilation, will influence the levels of infiltration and zone-coupled air flow. Notwithstanding the stochastic nature of these occurrences, air flow odels of varying coplexity can be constructed. At a level appropriate to building energy odelling, air oveent is often represented by a nodal network in which nodes represent fluid volues and inter-nodal connections represent the distributed leakage paths connecting these volues and through which flow can occur. Nuerical techniques are applied to this network to establish the ass balance corresponding to a given nodal teperature field and boundary pressure condition. The ethod is well suited to the deterination of the contribution of air oveent to energy requireents. A ore coprehensive approach involves the solution of the energy, ass and oentu equations when applied to a discretised flow doain. In addition to supporting energy analysis, such a ethod will also provide inforation on the spatial variation of indoor air quality and theral cofort levels. Casual gains In ost non-doestic buildings, the effects of the heat gains fro lighting installations, occupants, sall power equipent, counication devices and the like can be considerable. It is iportant therefore to process these heat sources in as realistic a anner as possible. Typically, this will necessitate the separate processing of the heat (radiant and convective) and oisture eissions, and the provision of a echanis to allow each casual source to change its agnitude over tie. It is usual to assue that the convective heat eission is experienced instantaneously as an air load whereas the radiant portion is apportioned between the internal opaque and transparent surfaces according to soe distribution strategy. Because

9 of the inherent relationship with the construction capacity, the radiant coponent will experience a tie lag before it can contribute to the cooling load or elevate the internal air teperature. Soe casual gain sources, such as luinaires and counication equipent, will require the elaboration of a odel of their electrical behaviour in order to odulate heat eission as a function of the electrical power usage. For exaple, this would be required in the case of daylight responsive luinaire diing. Control To direct the path of a siulation, the cobined building and supply systes odel ust be subjected to control action. This involves the establishent of several control loops, each one coprising a sensor (to easure soe siulation paraeter or aggregate of paraeters), an actuator (to receive and act upon the controller output signal) and a regulation law (to relate the sensed condition to the actuated state). These control loops are used to regulate HVAC coponents and anage building-side entities, such as solar control devices, in response to departures fro desired environental conditions. Control loops can also be used to effect changes to the active odel at run-tie, e.g. to ipose alternative heat transfer coefficients or activate a ore rigorous treatent of air oveent at soe critical point in tie. Control loops ay also be used to eulate plant behaviour in ters of the location of flux addition/extraction, the prevailing radiant/convective split, and any physical constraints iposed on the installed capacity. This is a useful feature where there is insufficient inforation to allow a detailed plant odel to be established. Moisture Dapness and ould growth are recognised as ajor probles affecting a significant proportion of houses throughout the world. Approxiately 2.5 illion UK residences are affected, with well docuented cases for the rest of Europe and North Aerica. It has been estiated that the cost of repairing the daage caused by tiber decay in the UK housing stock is approxiately 400M per annu. Apart fro aesthetic considerations, there is now considerable epideiological evidence to support the view that ouldy housing has a detriental effect on the physical and ental health of occupants. High levels of airborne spores ay occur due to the growth of fungi on walls and furnishings. Data fro previous Scottish housing condition survey indicate that around 12% of Scottish houses are affected, with inadequate heating, insulation and ventilation cited as the principal causal factors. Fluctuations in oisture levels within the building's fabric can also be probleatic, leading to interstitial condensation or causing variations in a aterial's thero-physical properties and, thereby, adversely affecting its therodynaic perforance. Approaches to the odelling of airborne oisture transport and the flow of oisture within porous edia will therefore be required if the siulation progra is to anticipate the conditions required for the proliferation of ould growth. Passive solar eleents Many designers have coe to favour the use of design features that act to capture and process solar radiation passively and without recourse to echanical systes. Figure 3 suarises the range of possible passive solar eleents. In each case, factors can be identified which, in particular, will ipose technical coplexity on any odelling exercise: a) non-diffusing direct gain systes will require adequate treatent of the apping of the

10 solar bea onto the internal receiving surfaces or obstruction objects such as furniture; b) diffusing direct gain systes will require solar energy apportioning to the various internal surfaces; c) earth banking will introduce coplexity in the odelling of ground heat exchange; d) attached sunspaces will require that the odel be able to establish the level of penetration of solar radiation to interior contained zones; Figure 3: Passive solar eleents in architectural design. e) thero-siphon systes will require buoyancy driven air flow odelling; f) double envelopes will require sophistication on the part of solar algoriths since radiation ay penetrate the external skin to cause `deep' construction heating; g) ass Trobe-Michel walls will require a ulti-diensional conduction odel; h) water Trobe-Michel Walls will require a detailed treatent of convective heat transfer; i) induced ventilation schees will require accurate odelling of buoyancy and pressure induced air flows; j) phase change aterials will necessitate the switching fro sensible heating behaviour to constant teperature behaviour in the transient conduction schees; k) transwalls will ipose deands on the solar and conduction algoriths since direct shortwave transission and fluid otion will occur;

11 l) roof ponds will require accurate external longwave radiation assessent; ) evaporative cooling systes will require cobined heat and ass flow odelling; n) desiccant aterials will exhibit a change of dehuidification potential with tie and require odels for regeneration; o) ovable shading will require device operation odelling and sophistication on the part of the shading/insolation prediction algoriths; p) ovable insulation iplies a tie-dependent syste definition; and q) selective thin fils will require detailed spectral response odelling. Advanced odelling systes seek to include these and all other energy flow-paths while respecting the inevitable interactions and underlying coplexities. Environental ipact Buildings will typically account for around 50% of the total energy consuption in a developed country and a siilar portion of the carbon dioxide eissions. Significant additional energy consuption is associated with the production and transportation of construction aterials. In the UK, for exaple, this aounts to around 25% of the doestic sector energy consuption. Associated with these consuptions are gaseous eissions that can give rise to atospheric pollution (SO x and NO x ) and, it is claied, global waring (CO 2 ). The integrated perforance odelling approach is able to address all aspects of a building's life cycle and thereby help designers to strike a balance between energy use, indoor cofort and local/global ipact. Uncertainty Since all design paraeters are subject to uncertainty, progras need to be able to apply uncertainty bands to their input data and use these bands to deterine the ipact of uncertainty on likely perforance. Progras so endowed will be able to assess risk, rather than erely presenting perforance data to their users. Surely it is better to give the probability of overheating than to output an operative teperature profile and trust to the user's interpretive skill. 4. The need for accuracy and flexibility It is ipossible to establish, in advance, the optiu level of odel accuracy and flexibility in the field of energy siulation. Nevertheless, it is iportant to differentiate between siplified odels and coprehensive odels which are capable of siplified odel eulation. In the forer case a nuber of siplifying assuptions are applied to the underlying theral network and/or solution schee. Invariably, soe flow-paths are crudely approxiated or oitted entirely. The odel to result is then valid only when applied to probles that ebody the sae siplifications. In the latter case, a coprehensive odel is designed to operate on input data ranging fro siplified to detailed. This is achieved by incorporating context specific defaults to allow the inclusion of any flow-path not explicitly addressed in the input data set. This approach is substantially ore flexible, with the accuracy level changing as a function of the quality of the design inforation supplied. As a general strategy, it would see reasonable to ai for a high level of accuracy cobined with a odel structure that is capable of adapting to the inforation available at any design stage. It is likely that a truly siple odel, as perceived by a user, will be internally coprehensive in its treatent of the energy flow-paths, relying on the proper design of the interface for its operational flexibility. The contention underlying such an approach is that accurate and flexible appraisal tools can only be achieved by an approach that achieves conservation of energy whilst including all flow-paths, ensures integrity of the atheatical odel vis-à-vis the reality, and wins acceptability through proper interface design in

12 conjunction with rigorous validity and applicability testing. 5. Energy odelling techniques Conteporary siulation progras are based either on response function or nuerical ethods. The forer ethod is appropriate for the solution of systes of linear differential equations possessing tie invariant paraeters. In use, it is usual to assue a high degree of equation decoupling. Nuerical ethods, on the other hand, can be used to solve tie varying, non-linear equation systes without need to assue equation decoupling as a coputational convenience. Nuerical ethods are favoured for a nuber of reasons. First, to ensure accuracy it is essential to preserve the spatial and teporal integrity of real energy systes by arranging that whole syste partial differential equation-sets be solved siultaneously at each coputational tie step. Second, nuerical ethods, unlike their response function counterpart, can handle coplex flow-path interactions. Third, tie varying syste paraeters can be accoodated. Fourth, processing frequencies can be adapted to handle so-called stiff systes in which tie constants vary significantly between the different parts of the proble (building fabric, HVAC coponents, fluid flow doains, control syste eleents, renewable energy coponents, radiation distribution, light flow, etc.).