Climate Calculations[LINK]

The location of the facility under analysis is critical for the determination of energy consumption, heating/cooling loads, daylighting potential, and a host of other calculations. In EnergyPlus, both external (i.e, weather files supplied from others) and internal (i.e., solar position, design day temperature/humidity/solar profiles) data is used during simulations.

The “Site:Location” input object includes parameters (Latitude, Longitude, Elevation, Timezone) that allow EnergyPlus to calculate the solar position (using Latitude, Longitude and Timezone) for any day of the year as well as supply the standard barometric pressure (using elevation). Solar position modeling is discussed in more detail in both the Sky Radiance and Shading Calculation sections that directly follow this section.

Weather files have hourly or sub-hourly data for each of the critical elements needed during the calculations (i.e., Dry-Bulb Temperature, Dew-Point Temperature, Relative Humidity, Barometric Pressure, Direct Normal Radiation, Diffuse Horizontal Radiation, Total & Opaque Sky Cover, Wind Direction, Wind Speed) as well as some auxiliary data such as Rain or Snow that assist in certain calculational aspects. Weather file excerpts such as might be used in sizing calculations also have this breadth of data. The input object “SizingPeriod:DesignDay” describes design days (meant to mimic ASHRAE design conditions but in a whole day profile) using certain characteristics for the day and then EnergyPlus supplies the remaining portions to complete outdoor conditions needed for program execution. SizingPeriod:DesignDay are perhaps the best objects for sizing equipment as the ASHRAE specified design conditions can be input AND weather files may or may not have the conditions necessary to size equipment properly.

Two other objects, however, can be used at times: SizingPeriod:WeatherFileDays and SizingPeriod:WeatherFileConditionType. With the first of these, one specifies a set of weather file days similar to a RunPeriod (but will be used for the Sizing calculations). In the second, the extreme or typical conditions that are calculated for the weather file during processing can be used by name. Of course, either of these can be used as a measure of usage over small periods.

The ASHRAE Handbook of Fundamentals describes their criteria in creating design condition synopses. “Design data based on dry-bulb temperature represent peak occurrences of the sensible component of ambient outdoor conditions. Design values based on wet-bulb temperature are related to the enthalpy of the outdoor air. Conditions based on dewpoint relate to the peaks of the humidity ratio. The designer, engineer, or other user must decide which set(s) of conditions and probability of occurrence apply to the design situation under consideration.”

EnergyPlus Design Day Temperature Calculations[LINK]

In EnergyPlus, the typical design day input includes a “high” and a “low” dry-bulb temperature for the day. As these two temperatures are insufficient to represent a full 24 hour period, the program uses a “range multiplier” profile to represent the full day’s temperatures:

Default Daily Temperature Range Profile

The multipliers are taken from the ASHRAE 2009 HOF, Table # 6, p. 14.11.. More explicitly, EnergyPlus creates an air temperature for each timestep by using the entered maximum dry-bulb temperature in conjunction with the entered daily range and the above multiplier values. The actual equation used is shown below:

$T_{c u r r e n t} = T_{M a x} - T_{r a n g e} \cdot T_{M u l t i p l i e r}$

where

T $_{c u r r e n t}$ = Air temperature of current Hour of Day

T $_{M a x}$ = User supplied Max Dry-bulb Temperature

T $_{r a n g e}$ = User supplied Daily Temperature Range

T $_{M u l t i p l i e r}$ = Range multiplier as shown on the above graph

The range multiplier values represent typical conditions of diurnal temperatures (i.e. the low temperature for the day occurring about 5:00 AM and the maximum temperature for the day occurring about 3:00 PM. Note that EnergyPlus does not shift the profile based on the time of solar noon as is optionally allowed by ASHRAE procedures.

ASHRAE research indicates that dry-bulb and wet-bulb temperatures typically follow the same profile, so EnergyPlus can use the default daily temperature profile to generate humidity conditions based on maximum and range of wet-bulb temperature.

Since this default temperature profile may not be applicable to all locations, the user can give a different profile as part of the design day definition.

Sky Radiation Modeling[LINK]

EnergyPlus calculates the Horizontal Infrared Radiation Intensity in Wh/m $^{2,}$ if it is missing on the weather file or for design days, from the Opaque Sky Cover field as shown in the following explanation.

$H o r i z o n t a l_{I} R = S k y_{e m i s s i v i t y} \cdot S i g m a \cdot T e m p e r a t u r e_{d r y b u l b}^{4}$

where

Horizontal_IR = horizontal IR intensity {W/m $^{2}$ }

Sky $_{e m i s s i v i t y}$ = sky emissivity

Sigma = Stefan-Boltzmann constant = 5.6697e-8 {W/m $^{2}$ -K $^{4}$ }

Temperature $_{d r y b u l b}$ = drybulb temperature {K}

The sky emissivity is given by

$S k y_{e m i s s i v i t y} = (.787 + .764 \cdot ln (\frac{T e m p e r a t u r e_{d e w p o i n t}}{273.})) \cdot (1. + .0224 N - .0035 N^{2} + .00028 N^{3})$

where

Temperature $_{d e w p o i n t}$ = dewpoint temperature {K}

N = opaque sky cover {tenths}

Example: Clear sky (N = 0), Temperature $_{d r y b u l b}$ = 273+20 = 293 K, Temperature $_{d e w p o i n t}$ = 273+10 = 283 K:

Sky $_{e m i s s i v i t y}$ = 0.787 + 0.764*0.036 = 0.815

Horizontal_IR = 0.815*5.6697e-8*(293**4) = 340.6 W/m $^{2}$

References for these calculations are contained in the references section at the end of this list of fields. (Walton, 1983) (Clark and Allen, 1978).

EnergyPlus Sky Temperature Calculation[LINK]

The default calculation for sky temperature is:

$S k y_{T e m p e r a t u r e} = {(\frac{H o r i z o n t a l_{I} R}{S i g m a})}^{.25} - T e m p e r a t u r e_{K e l v i n}$

Where

Sky $_{T e m p e r a t u r e}$ = Sky radiative temperature {C}

Horiizontal_IR = Horizontal Infrared Radiation Intensity as described in the previous section {Wh/m $^{2}$ }

Temperature $_{K e l v i n}$ = Temperature conversion from Kelvin to C, i.e. 273.15

The Sky Temperature can also be set by the user from several options using the WeatherProperty:SkyTemperature object.

EnergyPlus Design Day Solar Radiation Calculations[LINK]

Similarly, calculating solar irradiance (solar modeling) is one of the important effects to be accomplished. Several solar models exist with varying complexity.

ASHRAE Clear Sky Solar Model[LINK]

The default model used is the ASHRAE Clear Sky model. The ASHRAE clear sky model described in ASHRAE HOF 2005 Chapter 31 can be used to estimate hourly clear-day solar radiation for any month of the year in U.S. or similar temperate climates in the northern hemisphere. EnergyPlus calculations extend the clear sky application to both northern and southern hemispheres. Note that the Clear Sky model has been updated in the ASHRAE HOF 2009 (see ASHRAE Revised Clear Sky Model below).

At the earth’s surface on a clear day, direct normal irradiation is represented by

$D i r e c t N o r m a l I r r a d i a t i o n = \frac{A}{e x p (\frac{B}{sin β})}$

where

A = apparent solar irradiation at air mass m = 0 (Table)

B = atmospheric extinction coefficient Table)

Values of A and B vary during the year because of seasonal changes in the dust and water vapor content of the atmosphere and because of the changing earth-sun distance. Equation does not give the maximum value of direct normal irradiation that can occur in each month but yields values that are representative of conditions on cloudless days for a relatively dry and clear atmosphere. For very clear atmospheres, direct normal irradiation can be 15% higher than indicated by Equation , using values of A and B in Table below.

Extraterrestrial Solar Irradiance and Related Data Note: Data are for 21st day of each month during the base year of 1964.
	I $_{o}$ {W/m $^{2}$ }	Equation of Time {minutes}	Declination {degrees}	A {W/m $^{2}$ }	B {}	C {}
Jan	1416	-11.2	-20.0	1202	0.141	0.103
Feb	1401	-13.9	-10.8	1187	0.142	0.104
Mar	1381	-7.5	0.0	1164	0.149	0.109
Apr	1356	1.1	11.6	1130	0.164	0.120
May	1336	3.3	20.0	1106	0.177	0.130
Jun	1336	-1.4	23.45	1092	0.185	0.137
Jul	1336	-6.2	20.6	1093	0.186	0.138
Aug	1338	-2.4	12.3	1107	0.182	0.134
Sep	1359	7.5	0.0	1136	0.165	0.121
Oct	1380	15.4	-10.5	1166	0.152	0.111
Nov	1405	13.8	-19.8	1190	0.144	0.106
Dec	1417	1.6	-23.45	1204	0.141	0.103

For locations where clear, dry skies predominate (e.g., at high elevations) or, conversely, where hazy and humid conditions are frequent, values found by using Equation and Table should be multiplied by the clearness numbers in Threlkeld and Jordan (1958), reproduced as Figure # 5 in Chapter 33 of the 2007 ASHRAE Handbook—HVAC Applications.

The Clear Sky model usually over estimates the amount of solar radiation available to the building.

ASHRAE Revised Clear Sky Model (“Tau Model”)[LINK]

The ASHRAE 2009 HOF introduced a revised clear sky model based on location-specific optical depths for direct and diffuse radiation. These values are tabulated by month for all 5564 locations in the ASHRAE design data that accompanies the 2009 HOF.

The model requires air mass, m, calculated as follows –

$m = 1 / [sin β + 0.50572 \cdot {(6.07995 + β)}^{- 1.6364}]$

where $β$ = solar altitude, degrees.

Direct and diffuse irradiance are determined with the following relationships,

$E_{b} = E_{o} \cdot exp [- τ_{b} \cdot m^{a b}]$

$E_{d} = E_{o} \cdot exp [- τ_{d} \cdot m^{a d}]$

where:

$E_{b}$ = beam normal irradiance, W/m $^{2}$

$E_{d}$ = diffuse horizontal irradiance,

$E_{o}$ = extraterrestrial normal irradiance,

$m$ = air mass

$τ$ $_{b}$ and $τ$ $_{d}$ = beam and diffuse optical depths (from ASHRAE climatic design data)

$a b$ and $a d$ = beam and diffuse air mass exponents (see below)

Values of $τ$ $_{b}$ and $τ$ $_{d}$ are location-specific and vary during the year. They embody the dependence of clear sky solar radiation upon local conditions, such as elevation, precipitable water content, and aerosols.

The air mass exponents $a b$ and $a d$ were correlated to $τ$ $_{b}$ and $τ$ $_{d}$ through the following empirical relationships:

$a b = 1.219 - 0.043 \cdot τ_{b} - 0.151 \cdot τ_{d} - 0.204 \cdot τ_{b} \cdot τ_{d}$

$a d = 0.202 + 0.852 \cdot τ_{b} - 0.007 \cdot τ_{d} - 0.357 \cdot τ_{b} \cdot τ_{d}$

Studies done as part of ASHRAE research projects show that the revised tau model produces more physically plausible irradiance values than does the traditional clear sky model. In particular, diffuse irradiance values are more realistic.

Zhang-Huang Solar Model[LINK]

The Zhang-Huang solar model was developed for initial use in modeling typical meteorological years for China weather sites. This model seems to be good for other locations as well. Using total cloud cover, dry-bulb temperature, relative humidity, and wind speed as the independent variables, the total (global horizontal) solar radiation is estimated by:

$I = \frac{[I_{0} \cdot sin (h) \cdot (c_{0} + c_{1} \cdot C C + c_{2} \cdot C C^{2} + c_{3} (T_{n} - T_{n - 3}) + c_{4} \cdot φ + c_{5} \cdot V_{w}) + d]}{k}$

Where

I = estimated hourly solar radiation, W/m $^{2}$

I $_{0}$ = global solar constant, 1355 W/m $^{2}$

h = solar altitude angle, i.e, the angle between the horizontal and the line to the sun

CC = cloud cover

$φ$ = relative humidity, %

$T_{n}, T_{n - 3}$ = dry-bulb temperature at hours n (current) and n-3, respectively

$V_{w}$ = Wind speed, m/s

$c_{0}, c_{1}, c_{2}, c_{3}, c_{4}, c_{5}, d, k$ = regression coefficients

The constants were determined by analysis from measured data and are as follows:

c $_{0}$ = .5598, c $_{1}$ = .4982, c $_{2}$ = -.6762, c $_{3}$ = .02842, c $_{4}$ = -.00317, c $_{5}$ = .014, d = -17.853, k = .843.

This is the same model used to estimate the global solar radiation value (when it is absent from the source data) in the Weather Converter. References given in the reference section (Watanabe, Urano, Hayashi, 1983) (Zhang, Huang, 2002).

Perez Direct/Diffuse Splitting Model[LINK]

Splitting from global calculated (EnergyPlus) or entered values (WeatherConverter) into direct normal and diffuse horizontal components are done using the Perez direct/diffuse split. References shown in the reference section (Perez et al, 1992) (Perez et al, 1990)

Weather File Solar Interpolation[LINK]

The solar values on the weather file are average values over the hour. For interpolation of hourly weather data (i.e., when the specified timestep is greater than 1), the average value is assumed to be the value at the midpoint of the hour. The reported values in the output are totals for each reporting period. So, hourly reported values will not match the original values in the weather file, but the total solar for a day should agree. Reference (Ellis, Liesen, Pedersen, 2003)

References[LINK]

Walton, G. N. 1983. Thermal Analysis Research Program Reference Manual. NBSSIR 83-2655. National Bureau of Standards, p. 21.

Clark, G. and C. Allen, “The Estimation of Atmospheric Radiation for Clear and Cloudy Skies,” Proceedings 2nd National Passive Solar Conference (AS/ISES), 1978, pp. 675-678.

Watanabe, T., Urano, Y., and Hayashi, T. 1983. “Procedures for Separating Direct and Diffuse Insolation on a Horizontal Surface and Prediction of Insolation on Tilted Surfaces” (in Japanese), Transactions, No. 330, Architectural Institute of Japan, Tokyo, Japan.

Zhang, Q.Y. and Huang, Y.J. 2002. Development of typical year weather files for Chinese locations, LBNL-51436, ASHRAE Transactions, Vol. 108, Part 2.

Perez R., Ineichen P., Maxwell E., Seals, R. and Zelenka, A. 1992. Dynamic Global-to-Direct Irradiance Conversion Models. ASHRAE Transactions-Research Series,354-369.

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, 271-289.

Ellis, P.G., Liesen, R.J. and Pedersen, C.O. 2003. “Energyplus Experimental Data Validation Work: Development and Validation of the Unvented Trombe Wall Model and Other Heat Balance Components”, CERL Final Report DACA42-01-D-0004, Task 3.

Engineering Reference — EnergyPlus 8.7

Engineering Reference

Climate Calculations[LINK]

EnergyPlus Design Day Temperature Calculations[LINK]

Sky Radiation Modeling[LINK]

EnergyPlus Sky Temperature Calculation[LINK]

EnergyPlus Design Day Solar Radiation Calculations[LINK]

ASHRAE Clear Sky Solar Model[LINK]

ASHRAE Revised Clear Sky Model (“Tau Model”)[LINK]

Zhang-Huang Solar Model[LINK]

Perez Direct/Diffuse Splitting Model[LINK]

Weather File Solar Interpolation[LINK]

References[LINK]