A STANDARD DAYLIGHT COEFFICIENT MODEL FOR DYNAMIC DAYLIGHTING SIMULATIONS

A STANDARD DAYLIGHT COEFFICIENT MODEL FOR DYNAMIC DAYLIGHTING SIMULATIONS

D. Bourgeois1, C.F. Reinhart 2, G. Ward3

1

École d'architecture, Université Laval

1, côte de la Fabrique, Québec (QC) CANADA G1K 7P4 [email protected]

2

National Research Council Canada

1200 Montreal Road, Ottawa (ON) CANADA K1A 0R6 [email protected]

3

Anyhere Software

1200 Dartmouth, Albany (CA) USA 94706 [email protected]

A STANDARD DAYLIGHT COEFFICIENT MODEL FOR DYNAMIC DAYLIGHTING SIMULATIONS

ABSTRACT

Daylight coefficients are normalized contributions from discretized sky or ground segments, or preset solar positions, to solar quantities calculated at various building sensor points. Once generated, daylight coefficients can be folded against luminance efficacy and distribution models to calculate for instance time series of illuminances. Over the last 25-odd years, several daylight coefficient models have been published. The objective of this paper is to propose a standard daylight coefficient model for dynamic daylighting simulations (DDS), consolidating previously-published methods. This entails the definition of a standard daylight coefficient data format and accompanying software concepts for dynamic simulation purposes; dynamic in this context meaning variable with time due to changing sky conditions and shading device settings, in contrast to static modelling concepts such as daylight factors. The DDS standard model defines daylight coefficient data that is independent of building location and scene orientation, and generated using either simulation or measurement. DDS provides functionality to take into account independently-controlled daylighting sources (e.g. windows and skylights) and to query different daylighting quantities in a simulation context (e.g. illuminance at one or more sensors, annual daylight performance metrics). A Radiance-based intermodel comparison shows that DDS-based software outperforms the original validated Daysim approach, upon which

changes in solar exposure, e.g. in an urban canyon or for sensors located far from a window.

It is the authors' intent that the proposed DDS standard daylight coefficient model, including the data format and accompanying software concepts, be adopted by daylighting and energy simulation software as a common mechanism for efficiently sharing daylight coefficient data for simulation purposes. Many concepts in this paper are presented with a wide audience in mind, yet the technical content will be more of interest to daylighting and energy simulation researchers and developers.

KEYWORDS: daylighting, daylight coefficient, simulation, energy, IFC

WORD COUNT: 8047

INTRODUCTION

Recent studies on daylight simulations have shown that daylight coefficient methods can be used to accurately calculate time series of illuminances and luminances in buildings (Tsangrassoulis and Santamouris 1997, Mardaljevic 2000, 2000, Reinhart 2001, Reinhart and Walkenhorst 2001, Reinhart and Andersen 2006). These time series can then be used to calculate annual dynamic daylight performance metrics such as daylight autonomies (DA) and useful daylight illuminances (UDI) to quantify the daylit quality of a given building design (Nabil and

Mardaljevic 2005, Reinhart et al. 2006), and annual energy savings from reduced electric lighting use, as well as the resulting impact on the building thermal regime and HVAC operation (Janak and Macdonald 1999, Ajmat et al. 2005, Bourgeois et al. 2006).

The concept of daylight coefficients, originally proposed by Tregenza and Waters (1983), is to theoretically divide the celestial hemisphere into disjoint sky segments, and to calculate the contribution of each sky segment to the total illuminance at various sensor points in a building, based on each sensor's position within a given environment (e.g. on a desk) and orientation (e.g. facing the ceiling). Figure 1 and Equation 1 show that for sensor x, a daylight coefficient DC_α (x) related to the sky segment S_α is defined as the illuminance, E, at x caused by the sky segment S_α, divided by the luminance L_α and the angular size _∆S_α  of the segment. α α α α _{L S} x E x DC ∆ = ( ) ) ( , where: (1) x sensor point α S sky segment α S ∆ angular size of S_α ) (x E_α illuminance at x due to S_α α L luminance of S_α

The total sensor illuminance, E(x), is obtained by linear superposition of each daylight coefficient, DC_α, coupled with the luminance, L_α, of its matching sky segment, S_α :

∑

The same approach is used to define diffuse ground, as well as solar contributions, as daylight coefficients. Solar daylight coefficients are calculated by assuming preset solar positions evenly distributed throughout the celestial hemisphere. Time-varying solar and sky segment luminances can be calculated using direct and diffuse irradiances from weather files, luminous efficacy models (Perez et al. 1990), and luminous distribution models (Perez et al. 1993).

Working with daylight coefficients is by definition a two-step process: first calculating daylight coefficients, then folding them against time-varying luminances. By completing the second step, one could in principal discard daylight coefficients and just continue working with the resulting annual illuminance time series. In practice, annual time series require a substantial amount of storage space: an annual one-minute time series of illuminances consists of 525 6001 real numbers for each sensor. Daylight coefficient data, however, consists only of a few hundred to a few thousand real numbers per sensor, depending on the sky division scheme. In addition, such time series would need to be recalculated from scratch if

the building scene is rotated or located elsewhere in the world. Using Equation 2, accurate annual daylight simulations can be carried out within minutes for any climate and scene orientation. It is indeed more useful to think of daylight coefficient data as an intrinsic building property that describes how a building’s form and surface properties affect available daylight, comparable to a building's overall airtightness on energy use.

A practical aspect of daylight coefficients is the opportunity of coupling advanced daylighting prediction within building energy simulation. A number of packages today provide run-time coupling of daylighting simulation (Crawley et al. 2005), yet these tools often manage daylighting and building energy data under a single building model. Geometrical parameters for daylighting are often directly inherited from low-resolution descriptions of thermal zones, which can lead to incorrect solutions. Typical model shortcomings include infinitely thin walls and the absence of window frames or mullions. Conversely, an architect or a lighting designer may come up with a novel solution using specialized daylighting software, yet is unable to share the resulting high-quality lighting predictions with building energy simulationists. Regardless of the simulation objective, a common mechanism for sharing dynamic daylighting simulation data, as schematically illustrated in Figure 2, would be beneficial. The proposed DDS model addresses this impediment.

In the first part of this paper, a standard sky and solar division scheme for daylight coefficients is proposed. These daylight coefficients can be used to calculate illuminances/irradiances or luminances/radiances under arbitrary sky conditions and for different building locations and scene orientations. Annual illuminance simulations using this new sky division scheme are then compared to simulation results using the validated Daysim daylight coefficient method (Reinhart 2001), as well Radiance (Ward Larson and Shakespeare 1998). In the second part, a file format is proposed to organize DDS daylight coefficient and sensor data, and to provide standard functionality to associate sensors to different building areas, from thermal zones to individual workstations, to dynamically consider independently-controlled daylighting sources (e.g. windows and skylights) and to query different daylighting quantities in a simulation context (e.g. current illuminance at one or more sensors, annual daylight performance metrics).

DEFINITION OF A STANDARD DAYLIGHT COEFFICIENT SCHEME

The proposed dynamic daylight simulation (DDS) sky and solar division scheme distinguishes between contributions from various luminous sources, as follows:

145 diffuse sky segments 1 diffuse ground segment 145 indirect solar positions 2305 direct solar positions

Daylight coefficients corresponding to each segment or position can be coupled with a sky model, e.g. the All Weather Perez model (1993), as described in Equation 3:

∑

∑

∑

Diffuse sky contributions

The first part of Equation 3 represents the diffuse contribution from the sky, necessitating a one-to-one mapping of 145 diffuse sky daylight coefficients to 145 diffuse sky segments. While the original Tregenza (1987) division scheme divided the hemispheres into circular sky segments with a cone opening angle of 10.15°, as shown in Figure 3(a), the DDS scheme adopts the Daysim approach, illustrated in Figure 3(b), of rectangular sky segments that completely cover the celestial hemisphere without any overlap, i.e. no rays hitting the hemisphere are ever discarded or double counted. The centres of the rectangular segments correspond to the centres of the original Tregenza circular segments.

Diffuse ground contributions

The second daylight coefficient in Equation 3 represents the total diffuse contribution from the ground, modeled as a single daylight coefficient matching the entire ground hemisphere surrounding a building scene. If no surrounding landscape is modeled, the actual diffuse ground contribution

recommended to explicitly model the surrounding landscape as part of the building scene (Reinhart and Walkenhorst 2001, Mardaljevic 2004), the ground daylight coefficient has been added to avoid bookkeeping errors caused by downward rays that may miss the modeled ground plane, notably near the horizon. Such rays can lead to substantial simulation errors especially for ceiling mounted photocell controls (Reinhart and Herkel 2000).

Solar contributions

In the past, daylight coefficient methods mostly differed in how they treated contributions from direct sunlight. Daysim defines a set of around 65 representative, latitude-dependent solar positions that form a grid amongst all possible solar positions throughout the year. The positions nearest to the horizon are set by default at a minimum altitude of 2°; below which sky conditions cannot be adequately captured by the All Weather Perez sky model (1993), given the significance of local effects of the atmosphere and surrounding landscape. Figure 4 provides an example of hourly mean solar positions as dotted lines for Freiburg, Germany (47.98°N, 7.83°E), along with the 65 representative Daysim solar positions for that latitude as crosses. While the assignment of diffuse sky and ground luminances to corresponding daylight coefficients is rather unambiguous, the assignment of the solar luminance to the 65 latitude-dependent Daysim solar daylight coefficients can be optionally carried out in various ways (Reinhart 2001). Overall, however, it has been found that

an interpolation algorithm, illustrated in Figure 5, tends to yield reliable results for the most common cases (Reinhart and Walkenhorst 2001, Reinhart and Andersen 2006). This interpolation algorithm is based on the concept that 4 of the 65 representative solar positions effectively circumscribe the actual sun at any given time of the year. The calculated luminance from the sun, Lsun, is then distributed among these 4 solar positions based on interpolation weights; a function of time and altitude differences between each of the 4 positions and the actual sun, with contributions from the remaining 61 solar positions set to zero. Figure 5 illustrates an example of the distribution of the four weights at 13:25 solar time on May 7th for Freiburg. In this example, the weights attributed to the 2 representative solar positions at 13:00, versus those at 14:00, are estimated based on the fraction 25:352. Subsequently, the 2 solar position pairs on June and April/August 21st are weighed based on the relative altitude difference of each position with that of the actual sun on those dates for that time. For Freiburg, the solar altitude is 60° at 13:25 on June 21st and 49° on April/August 21st, while on May 7th the solar altitude is 54°. Thus the weight attributed to the solar position at 13:00 solar time on June 21st is 27%3. The weights of the other 3 positions are shown in Figure 5.

Indirect solar contributions

Similarly to daylight coefficient methods presented by Mardaljevic (2000), DDS considers indirect and direct solar contributions separately, as

rays that are reflected off surfaces, while the direct contribution consists only of the direct beam of sunlight that hits a sensor, excluding all reflected contributions. Rather than setting around 65 representative solar positions that lie along the sun path on certain days of the year for a given latitude, as with Daysim, DDS evenly distributes 145 indirect solar positions across the hemisphere; more precisely at the centre of each of the 145 diffuse sky segments. As with Daysim, the altitudes of the lowest row of indirect solar positions lying along the horizon are reset at 2°. And as with Daysim, the 4 nearest indirect solar positions that circumscribe the sun are chosen to determine the indirect solar contribution at any given moment. Interpolation weights, wisun, are attributed to each of the 4 positions based on their respective angular distances from the sun; contributions from the remaining 141 indirect solar positions are set to zero. Figure 6 compares the celestial distribution of the proposed DDS indirect solar positions versus the original Daysim 65 altitude-dependent positions for Freiburg (47.98 °N).

Location and orientation independence

As the spatial resolution between both schemes is very similar, the accuracy of both solutions should be comparable for indirect solar contributions. An obvious disadvantage of the DDS solution is an increase in simulation time to produce the increased number of indirect daylight coefficients. For instance, if Radiance was used to calculate these coefficients, calculation times would roughly double when going from 65 to

145 light sources. The main advantage of the 145 evenly-distributed indirect daylight coefficient set is its independence of site location (i.e. latitude) and scene orientation, as previously stated. Location-independence may seem irrelevant for a designer concentrating on an individual building design, as site location is usually set in stone. This advantage is more of relevance for researchers investigating the performance of prototypical solutions set in different world locations. The ability to assess the impact of room orientation on annual daylight availability is however highly relevant for initial form-giving explorations during the early design stage. If a typical room design, e.g. an office space or a classroom, is expected to be distributed along north, east, south and west facing building façades, then a single daylight coefficient set can be used to produce the 3 other orientation-specific sets through simple matrix rotations. Here, what originally seems to be a calculation time penalty of two turns into an overall time gain of two. An obvious limitation of this orientation independence is the potential influence of nearby buildings and other solar obstructions on daylight distribution, particularly in urban settings. In cases where neighbouring structures are part of the building scene, orientation-specific daylight coefficient sets would need to be calculated.

Direct solar contributions

greater spatial resolution than for indirect contributions. This higher resolution stems from a desire to increase the accuracy of direct solar daylight coefficient methods, notably for sensors often subjected to sudden changes in solar exposure, e.g. in an urban canyon or if located far from a window, as a result of the ever-changing shadow patterns cast from the sun. To increase the estimation accuracy of daylight coefficient methods in this regards, Mardaljevic (2000) suggested a distribution of 5010 evenly-distributed direct solar positions across the hemisphere and that the calculation of the direct solar contribution be based on the daylight coefficient associated to the nearest position to that of the actual sun. DDS comprises a default number of 2305 evenly-distributed direct solar positions, as indicated in Equation 3, yet as with indirect contributions, the altitudes of the lowest row of positions are set at 2°. Again, the 4 nearest direct solar positions to the actual sun are also identified at each time step and used to calculate the direct solar contribution through weighed interpolation, based on their respective angular distances from the sun. As with indirect contributions, the resulting direct solar daylight coefficients are latitude and orientation independent. The 2305 positions are obtained by quadrupling the original number of Tregenza horizontal rows of sky segments, then quadrupling the original number of Tregenza segments per row, while keeping a single zenith position4. Altogether, the proposed standard defines 2596 daylight coefficients per sensor for a given setting, 89% of which describe direct solar contributions. Details on the distribution and on how to increase the default resolution are provided in Appendix A.

Intermodel comparison

As both DDS and Daysim sky division schemes differ only in direct solar position resolution, one would expect to find prediction discrepancies only in cases where sensors are often subjected to sudden changes in solar exposure. This hypothesis is validated in the following example.

Simulation experiment

Figure 7 illustrates an example office space with a depth of 4.7m, a width of 3.0m and a height of 2.8m. Floor, wall and ceiling reflectances are 20%, 50% and 80%, respectively. The west-facing façade is glazed above work plane height and has a glazing visual transmittance of 80%. The chosen site location is Vancouver, Canada (49.2°N, 123.2°W) (Energy Plus Weather Data, 2006). The Daysim program gen_dc generated daylight coefficients for 14 upward-facing indoor sensors located along the room centreline, as well as an unobstructed upward-facing outdoor sensor, using both DDS and the original Daysim sky division schemes. Indoor sensors are spaced apart by 0.3m at a height of 0.85m from the floor, as shown in Figure 7. Two virtual floating cubes, upon which sensors #1 and #10 are centred, are provided only for visual reference (i.e. they have not been modelled as part of the Radiance scene and do not influence results). Figure 8 illustrates the shifting solar patterns within the space between 16:03 and 17:03 on September 12th, at 15 minute intervals.

Illuminance time series using DDS and Daysim schemes, as well as conventional Radiance, during sunlit hours on September 12th are plotted in Figure 9 for sensors #1 (nearest to the window) and #10, as well as the unobstructed outdoor sensor. "Daysim" time series were produced with the Daysim program ds_illum, while "DDS" values were produced using a new program, dds. Only the direct solar distribution scheme differs between methods with regards to simulation accuracy5. The Radiance program gendaylit was used to produce the "Radiance" time series, i.e. without the use of daylight coefficients, which serve as a benchmark against which "Daysim" and "DDS" results are compared.

Analysis

Generally, results are nearly identical for all sensors. Figure 8 shows that sensor #10 is only sunlit slightly after 16:00. Both the DDS scheme and Radiance predict a spike in illuminance when the sun hits the sensor a few minutes past 16:00, peaking at around 30 000 lux, as shown in Figure 9. The original Daysim scheme fails to predict this spike, going up to around 10 000 lux. In addition, it also systematically predicts a steady increase in illuminances until around 17:00 when all three time series converge, while relying on the DDS scheme yields the same results as Radiance and correctly predicts decreasing illuminances as the sun is setting.

These discrepancies are attributable to each approach's prediction of cast shadows from architectural features, such as the window frame in the

example application. To yield reliable results with either DDS or Daysim schemes, the four nearest direct solar positions to the sun should ideally all see a sensor if that sensor is actually directly sunlit at a given time. If a sensor is sunlit yet one or more of the four neighbouring positions is not in direct line of sight with the sensor, than the interpolation algorithm will systematically introduce errors, as positions that do not see a sensor have direct solar contributions of 0. Solar positions at 16:00 and 17:00 on August and September 21st comprise the four nearest Daysim positions on September 12th during that hour, yet two of these do not actually see sensor #10 at 16:00 (on September and August), as shown in Figure 10(a) and Figure 10(b). As a result, the original Daysim solution yields lower results than the DDS scheme and Radiance during this time interval. After 17:00, all four newly-appointed neighbouring positions in Daysim are in direct line of sight with sensor #10, yielding almost identical results to the DDS approach and Radiance.

For more insight, DDS and Daysim daylight coefficients for all 15 sensors were calculated for south, east and north facing variants of the initial example office space6. Annual illuminance time series for all sensors were subsequently calculated using the resulting DDS and Daysim daylight coefficient data. Relative mean bias errors (MBEs) and relative root mean squared errors (RMSEs), calculated for DDS-predicted illuminances in reference to Daysim values when outdoor illuminances were above 1000

lux, are provided in Table 1. Values in brackets refer to MBEs and RMSEs when illuminances for sensor #1 exceed 10 000 lux.

For times when indoor illuminances are below 10 000 lux (i.e. the sensitive range of conditions for daylighting performance metric calculations), RMSEs for all sensors fall under 13%, indicating that both Daysim and DDS schemes are very similar in terms of accuracy. MBEs are under 5% on average for all sensors, showing very good agreement between DDS and Daysim time series under 10 000 lux, although results do show that DDS yields on average slightly higher illuminances than Daysim near the window and lower values near the back of the room. Compared to the findings in Figure 9 where DDS instead yields higher illuminances when sensor #10 (i.e. at the back of the room) is directly sunlit, it can be hypothesized that DDS allows better prediction of sudden shifts in solar exposure, and thus yields more accurate results.

For times when indoor illuminances exceed 10 000 lux (values in brackets), MBEs for all sensors remain under 5%, showing good agreement between time series on average. On the other hand, RMSEs suggest much larger discrepancies, as high as 28%, which signifies that the DDS scheme tends to yield more accurate results in simulation cases where high illuminances – or corresponding irradiances – are likely to occur.

Discussion

Just how significant these discrepancies are depends on the simulation objective. Several daylighting performance metrics track the percentage of the year a given sensor receives sufficient amounts of daylight, e.g. above 2000 lux, such as useful daylight illuminance (UDI) (Nabil and Mardaljevic 2005) and maximum daylight autonomy (DAmax) (Reinhart et al. 2006). Yet, as all three approaches in the above example are capable of predicting illuminances in excess of 10 000 lux, well above the usual maximum daylighting thresholds, and at relatively the same time for approximately the same duration, it is unlikely that either approaches would yield significantly different performances. In fact, DDS and Daysim schemes yield equal annual UDI values for sensor #10. In applications where maximum thresholds do not apply however, e.g. when daylight coefficients are used to calculate impinging irradiances on surfaces (Ajmat et al. 2005), such prediction discrepancies appear to be much more significant.

As stated earlier, the gain in accuracy going from the original Daysim scheme to DDS is due only to the direct solar discretisation resolution, i.e. 2305 versus ~65 direct solar positions for DDS and Daysim, respectively. Under what conditions is the default DDS resolution sufficient? Results of the intermodel comparison suggest that for spatial geometries similar to the example office space, 2305 direct solar positions are enough. Greater

complex sunlight patterns generated from detailed geometrical features, e.g. sharp spatial and temporal differences in irradiances on a grid of sensors due to detailed external shading (Janak 2003, Ajmat et al. 2005). As previously stated, to yield reliable results using a weighed interpolation approach, sensors in the sun at a given time should consistently see the four neighbouring solar positions. The likelihood of such inconsistencies increases with the degree of geometrical detail. An increase in the default direct solar discretisation resolution, as described in Appendix A, decreases this likelihood of prediction inconsistencies. To be consistent with the mentioned objective however, the grid of sensors should be sufficiently dense and the simulation time steps sufficiently short to capture the sudden changes in solar exposure. Any increase in direct solar discretisation resolution, the number of sensors or time step frequency increases calculation time, in some cases quite substantially, and so should be consistent with respect to the simulation objective.

A STANDARD DDS FILE SYSTEM

In this section, a data format is proposed to organize DDS daylight coefficient and sensor data, and to provide standard functionality to assign sensors to different building areas (e.g. from thermal zones to individual workstations), to dynamically consider independently-controlled daylighting sources (e.g. windows and skylights) and to query different daylighting quantities in a simulation context (e.g. current illuminance at

one or more sensors, annual daylight performance metrics). The file format is based on the eXtensible Markup Language (XML), a self-descriptive format based on HTML (Hypertext Markup Language) and SGML (Standard Generalised Markup Language) which is commonly used in the web services industry.

Sensor data

A valid DDS file requires at least two critical XML <elements>: sensor data and a reference daylight coefficient set, as described in Figure 11. The <sensor_data> provides basic information for all sensors in a building. For brevity, only sensors #1, #2, #10 and #14, illustrated in Figure 7, are described in Figure 11. The <type> specifies whether the sensor relates to illuminance, luminance, radiance or irradiance. Each sensor's XYZ position and vector orientation, in relation to the scene origin and orientation convention, are also defined. Finally, one or more optional <association> tags can be provided to isolate individual or clustered sensors. This can be used to distinguish, from a dense grid of desk plane illuminance sensors in a large room, those that are effectively seen by a single ceiling-mounted photocell - an important distinction when considering daylighting controls for electric lighting systems. Association tags can also be used to differentiate sensors that are located in distinct zones in a building (e.g. do south- rather than east-facing classrooms provide more suitable daylight?). This differentiation is particularly useful in

process loads in a zone-per-zone sequence. In Figure 11, all sensors are associated to office 101 located in the west wing of an example office building. The sensors placed atop the floating cubes in Figure 7 are provided with the additional association tag cubicle, which for instance could be used to track the daylight availability for two distinct workstation cubicles.

Reference daylight coefficient data

A minimal valid DDS file also requires reference daylight coefficient data for all sensors. The number of daylight coefficients for each sensor depends on the selected DDS direct solar resolution. If the default DDS resolution is chosen, e.g. 2305 direct solar positions, then each reference daylight coefficient set would comprise 2596 daylight coefficients as space-separated real numbers. Each sensor's reference set is provided in a DDS file in the same order as the sensors themselves, e.g. the first reference <set> refers to the first <sensor>. One, and only one, reference daylight coefficient set per sensor is required, but additional sets can be integrated to account for changes in shading settings, as described further on.

The information contained in Figure 11 is enough to calculate annual time series of daylighting quantities (e.g. illuminances) at arbitrary frequencies (e.g. at 5 minute intervals), as long as site characteristics (e.g. latitude) and dynamic inputs such as solar time and meteorological data (e.g. direct

normal and diffuse horizontal irradiances) are provided. There can be additional <elements> in a minimal valid DDS file that are not explicitly described here, such as standard XML version number and encoding protocol. Optional elements can also be added for documentation purposes, such as how the reference daylight coefficient data was generated, listed under DDS <scene> elements. For instance, if Radiance was used to calculate daylight coefficients, the path to the Radiance scene file (.rad) and Radiance simulation parameters could be listed under the reference <scene> element.

Probes

Rather than post-processing annual time series data for subsequent daylighting performance analysis, applications should ideally report at the end of an annual simulation various daylighting performance metrics, such as standard, continuous or maximum daylight autonomies (DA, DAcon, DAmax) as well as useful daylight illuminances (UDI), for one or more sensor points (Reinhart et al. 2006). The DDS mechanism used to instruct applications to dynamically calculate these indices, as well as for additional queries, is a probe. Figure 12 illustrates how the DDS file described in Figure 11 is extended to include two example probes. Each probe comprises a unique user-defined <name>, a chosen <metric> and optionally, one or more related <sensors>. Inputs written in capital letters, such as DAYLIGHT_AUTONOMY and MIN_ILLUMINANCE, are

enable relevant features. For example, the first example DDS probe instructs applications to dynamically compute and store in memory daylight autonomies for all sensor points on file, eventually to be written out or passed as arguments to some parent application. The second example DDS probe instructs applications to dynamically compute the minimum illuminance amongst sensors associated to tags west wing, office 101 and cubicle. This information can be passed on directly to building energy simulation programs at run-time, for instance, as input to determine whether electric lighting for cubicles in the west wing's office 101 is indeed required at a given time step. This constitutes an example of how association tags can be used to effectively discriminate between sensors.

Controls

Functionality to dynamically alter daylight coefficient data is required to account for changes in shading settings, e.g. venetian blinds. In both Daysim and ESP-r daylight coefficient approaches (Janak and Macdonald 1999, Reinhart 2001), illuminances are dynamically calculated using either one of two alternate daylight coefficient sets (e.g. one when blinds are retracted, the other when blinds are deployed), requiring 2 independent daylight coefficient calculation runs. If the glazing unit in the previous example office space (Figure 7) was instead subdivided into 4 equal sections, each with independently-controlled venetian blinds, than relying on alternate daylight coefficient sets, as described above, would entail a

total of 16 independent daylight coefficient calculation runs to account for all possible blind combinations7 in a simulation. To avoid this exponential growth in calculation runs, DDS provides a simple solution based on differential daylight coefficients, reducing the total number of calculation runs to 5 in this case.

The procedure requires that the reference daylight coefficient data be calculated with the maximum daylight penetration, e.g. when all 4 blinds are retracted. Subsequently, additional daylight coefficient calculations are carried out, 4 runs in this case, with blinds deployed in front of each individual window section, one at a time, as illustrated in Figure 13. For instance, deploying blinds in front of section W1 would result in alternate

daylight coefficient data W1,dc, W2 as W2,dc, and so on. As a last step, each

alternate daylight coefficient data set is subtracted one at a time from the reference data to produce individual differential daylight coefficient data sets that isolate the impact of each section's blinds. For example, subtracting W1,dc from the reference data produces dW1,dc. In the end, only

the resulting differential daylight coefficient data sets, in addition to the reference data, are specified under <control> elements in a DDS file, as shown in Figure 14; a further extension of the example DDS files in Figure 11 and Figure 12. For brevity, only controls relating to W1 and W4 are

Each control definition requires a unique <name>, a chosen <method> of altering the reference daylight coefficient data, as well as a differential daylight coefficient set formatted similarly to the reference data. Binary switching (ON/OFF) mechanisms based the control <name> can be used to instruct applications to deploy each independent venetian blinds dynamically within a simulation. The controls in Figure 14 rely on the DDS SUBTRACTION keyword, instructing applications to effectively subtract any of the alternate daylight coefficients from the reference data, if either control names are flagged by some parent application at a given time.

There are cases where controls could rely on predicted daylighting quantities associated to one or more sensors as driving variables. If required, each control could be provided with one or more sensor association tags as with probes. For instance, switchable variable-tint glazing technology is being developed to instantaneously alter glazing visual transmittance to match a design setpoint illuminance (Lee 2006). In DDS, this can be based on one or more specific sensors. Rather than subtracting differential daylight coefficient data from the reference data, as illustrated in the preceding example, the DDS <method> LINEAR_INTERPOLATION would instruct applications to instantaneously reset the resulting daylight coefficient data as to float between the reference values (e.g. maximum transmittance) and some alternate set (e.g. minimum transmittance), based on a design <setpoint>. Similar

approaches have been developed for other daylight coefficient models (Janak and Macdonald 1999).

The aforementioned differential daylight coefficient approach becomes a significant time-saver in cases where many window sections, each with their own independently-controlled shading system, are considered. For instance, if the glazing in the above example office space is instead divided into 8 independently-controlled sections, 256 independent daylight coefficient calculation runs are required to account for all possible blind arrangements. On the other hand, the differential daylight coefficient approach would only require 9 runs in this case, taking less than 4% of the initial estimated computational time. In addition, the approach can also be used to efficiently consider more than one blind slat angle setting. An important caveat is that it applies only in cases where light through one shading system does not significantly affect light interaction with another. In the example above, all 4 window sections are essentially independent, parallel daylighting sources. In cases where shading systems are mounted in series in front of a single window section, e.g. switchable glazing in addition to an indoor venetian blind, the differential daylight coefficient approach no longer becomes a viable time-saving solution. Such complex arrangements are nonetheless possible to model, yet the development of robust methods of doing so in various simulation contexts are part of continuing efforts, and will likely only be made available within the next

SUMMARY

A new standard model is introduced for using daylight coefficients in dynamic daylighting simulations (DDS), largely based on – and consolidating - previously-published methods. The model includes the definition of a standard XML file format to structure daylight coefficient data for different sensors and shading device settings in a building, as well as the development of accompanying software concepts for dynamic simulation purposes. The model offers independence from site location and orientation, estimation techniques and simulation applications. It is the authors' intent that the proposed standard daylight coefficient model, including the file data format and accompanying software concepts, be eventually adopted by daylighting software as a mechanism for sharing daylight coefficient data for dynamic simulation purposes. The new file format could potentially lead to a new property block for building information models (BIMs), such as Industry Foundation Classes (IFCs).

An intermodel comparison shows that the DDS sky division scheme yields more accurate results than the original Daysim solution, upon which DDS is based, notably in cases where sensors are often subjected to sudden changes in solar exposure, e.g. in an urban canyon or for sensors located far from a window. The new approach has since been implemented into the Daysim software.

DDS also provides useful mechanisms to calculate and query daylighting quantities at various frequencies and dynamically change shading settings. Preliminary descriptions are provided on how these mechanisms can be used in a simulation context, whether for standalone daylighting performance analysis or integrated building energy/daylighting simulations. Additional DDS resources, including an XML Schema, are provided on the DDS web site (2006).

The DDS model presented in this paper has already been implemented and tested within the current version of the Lightswitch Wizard (Reinhart 2001), a non-expert design tool to assess the influence of key architectural and system variables on the quality of daylighting distribution in offices and classrooms, and the total annual energy impact of daylighting under realistic conditions. The wizard couples pre-calculated DDS daylight coefficient data to the ESP-r building energy simulation engine (ESRU 2002).

ACKNOWLEDGEMENT

This paper is the result of several lengthy email exchanges between the authors and other experts in the field. We would like to thank particularly John Mardaljevic for his insight with us. Finally, we acknowledge the financial support for the writing of this paper provided by National Research Council Canada, Natural Resources Canada, and the Panel for Energy Research and Development (PERD, contract 082).

ENDNOTES

1 _{8760 hours/year x 60 minutes/hour x 1 real number/minute} 2 _{[minutes : minutes]}

3 _{100% * [ 35min / 60min ] * [ ( 54° - 49° ) / ( 60° - 49° ) ]} 4 _{( 144 x 4 x 4 ) + 1 = 2305}

5 _{Both approaches are available within the Daysim software package}

6 _{DDS daylight coefficient data for south, east and north facing variants} were produced in a few seconds by matrix rotations

REFERENCES

Energy Plus Weather Data, Energy Efficiency and Renewable Energy,

U.S. Department of Energy,

www.eere.energy.gov/buildings/energyplus/cfm/weather_data.cfm (2006,

latest update: February 2006, accessed: August 2006).

Ecotect, Square One Research, www.squ1.com (2006, latest update: July

2006, accessed: August 2006).

DDS, irc.nrc-cnrc.gc.ca/ie/lighting/daylight/dds.html (2006, latest update:

August 2006, accessed: August 2006).

Ajmat, R., Mardaljevic, J. and Hanby, V.I. (2005) Evaluation of shading

devices using a hybrid dynamic lighting thermal model. Proceedings of

BS2005, the 9th IBPSA Conference, Montreal.

Bourgeois, D., Reinhart, C.F. and Macdonald, I. (2006) Adding advanced

total energy impact of manual and automated lighting control. Energy and

Buildings 38(7), 814-823.

Crawley, D.B., Hand, J.W., Kummert, M. and Griffith, B.T. (2005)

Contrasting the capabilities of building energy performance simulation

programs, US Department of Energy, U. of Strathclyde (ESRU) & U. of

Wisconsin-Madison (SEL).

ESRU (2002) The ESP-r system for building energy simulation, user guide

version 10 series. ESRU Manual U02/1, University of Strathclyde.

Janak, M. and Macdonald, I. (1999) Current state-of-the-art of integrated

thermal and lighting simulation and future issues. Proceedings of Building

Simulation '99, an IBPSA Conference, Kyoto, 1173-1180.

Janak, M. (2003) Whole building energy simulation with complex external

Lee, E. (2006) A design guide for early-market electrochromic windows,

Lawrence Berkeley National Laboratory for the California Energy

Commission, CEC-500-2006-052-AT16.

Mardaljevic, J. (2000) Daylight simulations: validation, sky models and

daylight coefficients, Ph.D., De Monfort University.

Mardaljevic, J. (2000) Simulation of annual daylighting profiles for internal

illuminance. Lighting Research & Technology 32(2), 111-118.

Mardaljevic, J. (2004) Verification of program accuracy for illuminance

modelling: assumptions, methodology and an examination of conflicting

findings. Lighting Research & Technology 36(3), 218-238.

Nabil, A. and Mardaljevic, J. (2005) Useful daylight illuminance: a new

paradigm to access daylight in buildings. Lighting Research & Technology

Perez, R., Ineichen, P., Seals, R., Michalsky, J. and Stewart, R. (1990)

Modeling daylight availability and irradiance components from direct and

global irradiance. Solar Energy 44(5), 271-289.

Perez, R., Seals, R. and Michalsky, J. (1993) All-weather model for sky

luminance distribution - preliminary configuration and validation. Solar

Energy 50(3), 235-245.

Reinhart, C.F. and Herkel, S. (2000) The simulation of annual daylight

illuminance distributions - a state-of-the-art comparison of six

RADIANCE-based methods. Energy and Buildings 32(2), 167-187.

Reinhart, C.F. (2001) Daylight availability and manual lighting control in

office buildings: simulation studies and analysis of measurement, Ph.D.,

Lightswitch Wizard, Reinhart, C.F., Institute for Research in Construction,

National Research Council of Canada, www.buildwiz.com (2001, latest

update: March 2004, accessed: August 2006).

DAYSIM, Reinhart, C.F., Institute for Research in Construction, National

Research in Construction, www.daysim.com (2001, latest update: July

2006, accessed: August 2006).

Reinhart, C.F. and Walkenhorst, O. (2001) Dynamic RADIANCE-based

daylight simulations for a full-scale test office with outer venetian blinds.

Energy and Buildings 33(7), 683-697.

Reinhart, C.F. and Andersen, M. (2006) Development and validation of a

Radiance model for a translucent panel. Energy and Buildings 38(7),

Reinhart, C.F., Mardaljevic, J. and Rogers, Z. (2006) Dynamic daylight

performance metrics for sustainable building design. Leukos, (submitted

April 2006).

Tregenza, P.R. and Waters, I.M. (1983) Daylight coefficients. Lighting

Research & Technology 15(2), 65-71.

Tregenza, P.R. (1987) Subdivision of the sky hemisphere for luminance

measurements. Lighting Research & Technology 19, 13-14.

Tsangrassoulis, A. and Santamouris, M.J. (1997) Daylighting modelling

with Passport-Light. Proceedings of the 5th IBPSA Conference, Prague,

73-78.

Ward Larson, G. and Shakespeare, R. (1998) Rendering with RADIANCE.

The Art and Science of Lighting Visualization, Morgan Kaufmann, San

APPENDIX A: DDS SKY DIVISION AND SOLAR POSITION SCHEME

The Tregenza-based (1987) DDS sky division scheme divides the hemisphere vertically into 7 superimposed horizontal rows, each representing a differential altitude of 12°, with the hemisphere topped at its zenith by a circular segment having a half-cone angle of 6°. Each horizontal row is then divided into rectangular segments based on the Tregenza convention, defined in Table 2 , for a total of 144 rectangular and 1 circular segments. The ordering scheme is based on the Daysim convention, shown in Figure 3(b), where the first segment starts at the lowest row along the horizon with a centre azimuth of 6° north of east, with subsequent segments following counter clockwise, moving up a row once a 360° span of the horizon is completed. The 145 DDS indirect solar positions are centred on the 145 sky segments except for the first row above the horizon, taking on an altitude of 2° rather than 6°. The ordering scheme is the same as with diffuse sky segments.

A scaling factor, F, is introduced to increase the number of DDS direct solar positions. Consider the following expressions of the static differential altitude of the original 7 Tregenza rows, _{α, the number of solar positions} per row, Npositions/row, and the total number of solar positions in the sky,

Ntotal, as a function of F:

( )

F row Tregenza rows positions N N _{/ = / ⋅}2 ₍₅₎ 1 ) 144 4 ( ⋅ + = F total N ₍₆₎

If F is set to 0, then _α becomes 12°, Npositions/row 1 becomes 30 and Ntotal

becomes 145, i.e. the original Tregenza variables. Values of F greater than 0 trigger a decrease in differential altitude, a corresponding increase in the number of rows, and an increase in the number of positions per row1:

For F = 1, _α = 6°, Ntotal = 577, and Npositions / row 1 = 60

For F = 2, _α = ~3.2°, Ntotal = 2305, and Npositions / row 1 = 120

For F = 3, _α = ~1.6°, Ntotal = 9217, and Npositions / row 1 = 240

1

Table 1: Relative mean bias errors (MBEs) and relative root mean squared errors (RMSEs) of annual DDS and Daysim illuminance time series for all

sensors, when outdoor values exceed 1000 lux. MBEs and RMSEs in brackets consider time series when indoor illuminances exceed 10 000 lux

south west north east

# MBE (%) RMSE (%) MBE (%) RMSE (%) MBE (%) RMSE (%) MBE (%) RMSE (%)

1 0 [ 1 ] 7 [12] 1 [ 3 ] 13 [17] 1 [ 1 ] 4 [ 4 ] 1 [ 2 ] 9 [14] 2 1 [ 5 ] 5 [25] 0 [ 0 ] 3 [12] 0 [ 0 ] 2 [ 2 ] 0 [-1 ] 3 [10] 3 2 [-4 ] 5 [18] 0 [ 0 ] 4 [13] 0 [ 0 ] 2 [ 2 ] 0 [-1 ] 4 [10] 4 0 [ 1 ] 4 [14] -1 [-1 ] 4 [10] -1 [-1 ] 2 [ 2 ] -1 [-2 ] 3 [ 9 ] 5 1 [-2 ] 4 [15] -1 [-1 ] 4 [12] -1 [-1 ] 3 [ 3 ] -2 [-2 ] 4 [11] 6 1 [ 2 ] 5 [20] 0 [ 1 ] 5 [19] -1 [-1 ] 3 [ 3 ] -1 [-1 ] 4 [14] 7 0 [ 1 ] 5 [15] 0 [ 1 ] 5 [13] 0 [ 0 ] 3 [ 3 ] 0 [ 0 ] 4 [11] 8 -1 [-1 ] 5 [14] -3 [-3 ] 6 [11] -3 [-3 ] 4 [ 4 ] -2 [-3 ] 5 [ 9 ] 9 -1 [-2 ] 5 [13] 0 [-1 ] 6 [12] 0 [ 0 ] 3 [ 3 ] 0 [-2 ] 4 [11] 10 -1 [ 2 ] 6 [24] -3 [ 0 ] 7 [28] -4 [-4 ] 5 [ 5 ] -4 [-3 ] 6 [20] 11 -2 [-1 ] 6 [13] -3 [ 0 ] 7 [23] -5 [-5 ] 6 [ 6 ] -3 [-1 ] 6 [17] 12 -3 [-2 ] 7 [ 9 ] -3 [-1 ] 7 [18] -1 [-1 ] 4 [ 4 ] -1 [ 0 ] 5 [13] 13 -3 [-3 ] 7 [10] -4 [-3 ] 8 [13] -4 [-4 ] 6 [ 6 ] -3 [-4 ] 7 [10] 14 -2 [-2 ] 7 [ 9 ] -5 [-5 ] 9 [12] -5 [-5 ] 6 [ 6 ] -5 [-5 ] 8 [10] out 0 [ 0 ] 3 [ 3 ] 0 [ 0 ] 3 [ 3 ] 0 [ 0 ] 3 [ 3 ] 0 [ 0 ] 3 [ 3 ]

Table 2: Tregenza convention on the row-specific number of sky segments

row no. segments altitude (°) _{∆∆∆∆azimuth (°)}

1 30 6 12 2 30 18 12 3 24 30 15 4 24 42 15 5 18 54 20 6 12 66 30 7 6 78 60

E(x)αααα ∆∆∆∆Sαααα

energy data building data (e.g. BIM) daylight data DDS DC data daylighting analysis integrated building energy simulation DDS DC calculation daylighting performance metrics energy performance metrics energy data building data (e.g. BIM) daylight data DDS DC data daylighting analysis integrated building energy simulation DDS DC calculation daylighting performance metrics energy performance metrics

Figure 2: Daylight coefficient (DC) data exchange for dynamic daylight simulation (DDS); either for standalone daylighting analysis or integrated

(a) Tregenza division

(b) continuous division

Figure 3: Sky division schemes: (a) according to Tregenza: 145 sky segments with a cone opening angle of 10.15°, with 68% of the celestial hemisphere covered by sky segments; (b) continuous division, as used by

Figure 4: The dotted lines mark all possible hourly mean solar positions for Freiburg, Germany (47.98°N); the crosses mark the 65 representative Daysim solar positions for which direct daylight coefficients are calculated

for that site. The box in the figure surrounds four representative solar positions which correspond to the actual solar positions at 13:00 and

31 % solar time 13:00 altitude 63° solar time 14:00 solar time 13:00 altitude 51° solar time 14:00 altitude 46° solar time 13:25 27 % 19 % 23 % altitude 56° solar time 13:25 altitude 54° 31 % solar time 13:00 altitude 63° solar time 14:00 solar time 13:00 altitude 51° solar time 14:00 altitude 46° solar time 13:25 27 % 19 % 23 % altitude 56° solar time 13:25 altitude 54°

Figure 5: Visualization of the interpolation algorithm to assign direct solar luminances to the four representative solar positions for Freiburg, Germany (47.98°N). The four crosses correspond to those within the box

Figure 6: Comparison of the distribution of DDS indirect solar positions versus the 65 Daysim altitude-dependent solar positions for Freiburg

0 1m

10 1

Figure 7: Example office space: 3D view from Ecotect (2006) facing west; cross section illustrates sensor placement along room centreline. Two floating cubes, upon which sensors #1 and #10 are centred, are illustrated

16:03 16:18 16:33 16:48 17:03

Figure 8: Shifting solar patterns in the west facing variant example office space between 16:03 and 17:03 on September 12, at 15 minute intervals

0 20000 40000 60000 80000 5 7 9 11 13 15 17 19 time of day [ h ] illum ina nce [ lux ] DDS DAYSIM RADIANCE outdoor sensor sensor #1 sensor #10

Figure 9: Predicted illuminances on September 12 for sensor #1 and #10 and an unobstructed outdoor sensor, for example office space

Figure 10: Architectural features blocking direct line of sight between sensor #10 and sun at 16:00 on (a) September 21st and (b) August 21st

<sensor_data> <sensor>

<type>illuminance</type>

<x>1.525</x> <y>0.305</y> <z>0.850</z> <ux>0.000</ux> <uy>0.000</uy> <uz>1.000</uz>

<association>west wing</association> <association>office 101</association> <association>cubicle</association> </sensor> <sensor> <type>illuminance</type>

<x>1.525</x> <y>0.610</y> <z>0.850</z> <ux>0.000</ux> <uy>0.000</uy> <uz>1.000</uz>

<association>west wing</association> <association>office 101</association> </sensor> […] <sensor> <type>illuminance</type>

<x>1.525</x> <y>3.050</y> <z>0.850</z> <ux>0.000</ux> <uy>0.000</uy> <uz>1.000</uz>

<association>west wing</association> <association>office 101</association> <association>cubicle</association> </sensor> […] <sensor> <type>illuminance</type>

<x>1.525</x> <y>4.270</y> <z>0.850</z> <ux>0.000</ux> <uy>0.000</uy> <uz>1.000</uz>

<association>west wing</association> <association>office 101</association> <association>cubicle</association> </sensor> </sensor_data> <reference_data> <set> (DC1,1) (DC1,2) […] (DC1,2596)</set> <set> (DC2,1) (DC2,2) […] (DC2, 2596)</set> […] <set> (DC10,1) (DC10,2) […] (DC10, 2596)</set> […] <set> (DC14,1) (DC14,2) […] (DC14, 2596)</set> </reference_data>

Figure 11: Example of a minimal DDS file, comprising sensor data and reference daylight coefficients

<probe> <name>project_daylight_autonomies</name> <metric>DAYLIGHT_AUTONOMY</metric> </probe> <probe> <name> minimum_cubicle_illuminances</name> <metric> MIN_ILLUMINANCE</metric> <sensors> <association>west wing</association> <association>office 101</association> <association>cubicle</association> </sensors> </probe>

W1 W2 W3 W4

Figure 13: Example office space with glazing divided into 4 equal sections, with venetian blinds in front of each individual window section to produce

<control> <name> W1</name> <method> SUBTRACTION</method> <differential_data> <set> (dDCW1,1,1) (dDCW1,1,2) […] (dDCW1,1,2305)</set> <set> (dDCW1,2,1) (dDCW1,2,2) […] (dDCW1,2,2305)</set> […] <set> (dDCW1,10,1) (dDCW1,10,2) […] (dDCW1,10,2305)</set> […] <set> (dDCW1,4,1) (dDCW1,14,2) […] (dDCW1,14,2305)</set> </differential_data> </control> […] <control> <name> W4</name> <method> SUBTRACTION</method> <differential_data> <set> (dDCW4,1,1) (dDCW4,1,2) […] (dDCW4,1,2305)</set> <set> (dDCW4,2,1) (dDCW4,2,2) […] (dDCW4,2,2305)</set> […] <set> (dDCW4,10,1) (dDCW4,10,2) […] (dDCW4,10,2305)</set> […] <set> (dDCW4,4,1) (dDCW4,14,2) […] (dDCW4,14,2305)</set> </differential_data> </control>