Proceedings of the International Conference on Energy Conversion, Washington DC, August 1996.

SIMPLIFIED METHOD FOR PREDICTING

BUILDING ENERGY CONSUMPTION

USING AVERAGE MONTHLY TEMPERATURES

James A. White

Energy Management Services

Portland, Oregon 97229

Howard Reichmuth

Stellar Processes, Inc.

1033 SW Yamhill Suite 405

Portland, OR 97205

(503) 827-8336

ABSTRACT

A new method has been developed to predict monthly building energy use using average monthly temperatures. This newly discovered procedure can be applied to simple or complex buildings and is more accurate than standard calculation procedures that use heating and cooling degree days or temperature bins. The method provides useful insight into a building's energy use, without requiring complex inputs that are normally required in running sophisticated building energy programs. This new method for calculating energy consumption can be used to:

• Predict total monthly energy consumption and costs for an entire campus, large commercial building, or residential home.
• Calculate energy savings of various energy conservation measures, including control strategies.
• Size heating and cooling equipment
• Compare alternative HVAC systems,
• Compare annual weather and billings to hourly simulation results based an typical meteorological year (TMY) days, Evaluate a building's potential for beat recovery, and
• Check for gross errors of hourly simulation results.
This calculation procedure is based on the premise that a straight line results when the difference between monthly heating and cooling loads are plotted as a function of average monthly temperate. In addition, the slope of this line is equal to the building's conduction UA and infiltration heat loss coefficients of the building when normalized on a per unit of conditioned floor area basis. While this comes as no surprise for heating loads, it applies to cooling loads as well. Adding the average solar gain and internal heat gain from lights and equipment to the difference between monthly heating and cooling loads results in a UA line that intersects the average temperature axis at the mean interior setpoint temperature of the building (70 degF). This sounds somewhat complicated, but is quite straight-forward when viewed in graphical form as shown in Figures I and 2.

Once monthly heating and cooling loads am determined with this simple diagram, healing, ventilating, and air conditioning (HVAC) energy use can then he determined as a function of temperature dependent performance coefficients, for economizers, air conditioners, heat pumps, chillers, heat recovery, mechanical reheat, and various fan systems. All of this is done without sophisticated hourly computer simulations that frequently require lengthy and tedious inputs.

BACKGROUND

Existing Calculation Methods

Existing hourly simulation models, such as DOE2 or ACCESS, can estimate building heating or cooling loads, but they involve extensive zone-by-zone physical descriptions and occupancy inputs. 0thcr techniques for calculating heating or cooling energy consumption are generally not very accurate and do not characterize buildings with different internal or solar heat gain characteristics. Heating or cooling degree-day methods assume a fixed outside air temperature at which heating or cooling will begin to occur. The modified bin method developed by Knebel (1983) is an improvement but it requires a sizable database of temperature bins for each location and is hampered by the need to further interpolate for daily and weekly occupied and unoccupied periods. Another common method for calculating cooling energy requirements is the equivalent full load hours (EFLH) method. Problem with EFLH method is the EFLH must be known for the specific area in question, it is generalized for a "typical' building, and the maximum design load must he known. (ASHRAE, 1993)

The method described in this paper overcomes most of the problems described above and also presents the building's energy use characteristics in an intuitive manner. Using mean monthly temperature, as opposed to weekly, daily, or hourly temperatures, tends to filter out many of the transients and scattering of data that typically occur with similar analysis techniques.

Howdy Plot

The basis for the simplified method described in this Paper for calculating a building's heating and cooling loads was found by Howard (Howdy) Reichmuth. His discovery was made by plotting building loads as a function of average monthly temperatures. Total internal heat gains. Monthly heating loads and cooling loads were determined using DOE-2 (Lawrence Berkeley Laboratory, 1989), an hourly simulation program, These loads were normalized in terms of watts per square foot of conditioned space, and plotted as a function of average monthly temperature.

The following steps will produce a Howdy Chart from funding simulation results (such as the LS-D report from DOE2.ID). Step one, on a graph of watts per square foot versus average monthly temperature, plot the average internal gain for each month. Step two, convert each total monthly cooling load into watts per square foot and subtract this normalized cooling load from tin internal gain. Step three, convert total monthly heating load into watts per square foot and add this normalized heating to the difference between the internal gain and monthly cooling load. The result of this plot is a relatively straight line as shown in Figure 1.

The line formed by the difference between the internal gain cooling load is called the Retained Gain Line; and the heating line for reasons that will be explained later, is referred to as the UA line.

Interestingly, the final position of the UA line does not vary significantly as internal loads are varied. The UA line also does not vary significantly if the size of interior zones is enlarged and exterior zones is reduced by the same amount. The slope of the UA line does vary with changes in wall or window heat loss coefficients and window shading coefficient. If the solar heat gain from windows is removed, the UA line will intersect the temperature axis at the building's setpoint (70degF). Solar heat gains from windows will shift the line in a predictable way that is described later in this report.

Knowing these relationships and understanding their physical basis, one can work backward to calculate a building's monthly heating and cooling energy loads. The slope and position of the UA line is defined in terms of space temperature setpoint, exterior surface areas, heat loss characteristics, and solar gain. The internal gain is simply a characteristic of interior energy use. Retained gain is a function of the type of HVAC system selected and how the building is physically zoned.

Note that a majority of the months have both a heating and a cooling load. These are not artificial loads, such as mechanical reheat, but are physical loads such as heating required during morning warm-up, followed by a cooling load later in the day due to solar and internal gains from people and equipment. It is also caused by the mixture of warm and cool days that occur during any given month.

Internal Gain

A building's internal heat gains must first be known before a building's total energy use can be determined. Internal heat gains include lighting, office equipment, process equipment such as cooking, or negative space loads from refrigerated cases. Average internal loads would be the total energy from these sources, divided by the total time in that period. For instance, if the building has 2.0 watts of installed lighting per square foot, and these lights are on 80% 12 hours a day, five days a week, and 10% during the remaining hours, the average internal gain from lighting would be:

IG lights = 0.70 Watts/Ft2

Sensible heat gains from other internal equipment can also be calculated in terms of average watts per unit area. Heat removed by refrigerated cases would be subtracted from the total heat gains to give a total average heat gain for the building.

Another source or internal heat gains are HVAC fans. The energy from constant volume fans that run a fixed number of hours each month can be added directly to the other internal gains mentioned previously. Fan energy which varies with heating and cooling loads must be handled slightly differently. A more detailed discussion of fail energy is provided later in the discussion HVAC systems.

Heat Loss

Building heat loss is characterized in terms of conduction and air infiltration losses. Conduction losses are the total heat transmitted through the walls, windows, floors and ceilings. This heat loss is commonly referred to as the building's UA. Building UA is determined by summing up the product of individual components' U-value heat loss coefficients and corresponding surface areas.

Another factor contributing to heat loss is natural infiltration and mechanical ventilation. This value is usually presented in terms of volumetric air changes per hour and/or flow rate per unit area. Hourly computer simulations showed in general, ventilation air brought in by mechanical HVAC equipment can be directly added to the quantity of natural air infiltration. A building's total heat loss coefficient should be normalized by dividing the total beat loss per unit temperate, by the total conditioned area of the building.

Normalized UA Coefficient, in terms of Watts/SF degF =

(å UA walls + (å UA windows + (å UA Floors + (å UA Ceilings

+(Mechanical & Natural ACH) X Volume x Density Air x Specific Heat of Air)

/ (Bldg. Cond. Area x 3.413 Btu/Watt Hr)

If the window shading coefficient is set equal to zero, the normalized UA coefficient calculated above is equal to the slope of the UA line and intersects the average temperature axis at the building's setpoint temperature.

Solar Heat Gain

Solar heat gains through windows and walls are accounted for by modifying the slope of the UA line. Solar gain is closely correlated with average monthly temperature. Solar gains peak in the summer and are substantially lower in the winter. The simplified method described in this report assumes that solar gains vary linearly with average monthly temperature (Vadon et al., 1991; and Knebel, 1983). At a low enough average monthly temperature, the building's solar gain is effectively zero. For simplicity, zero degrees Fahrenheit was selected as the average monthly temperature at which solar gains are considered negligible. Most areas do not have an average winter temperature of zero degrees in the winter and consequently there is some solar gain that occurs in these areas, even during the coldest months. The UA line without any solar gain adjustment passes through the average temperature line at 70° F. It has a slope equal to the Normalized UA Line. Knowing these two factors establishes the Y-intercept. The UA line is then rotated about the Y-intercept. The amount of rotation is equal to the average solar gain on the design day. Graphically this is shown in Figure 3.

Peak solar gains occur in June, but peak average monthly temperature normally occurs in July. This one-month offset causes a small amount of hysteresis scatter in the UA line. This method assumes that a majority of the solar heat gain comes from windows. Solar gain from other surfaces can be included based on wall mass, color, and orientation. The approach used in this paper uses an average solar gain that occurs on the peak cooling day (assumed to be July 21st). Total solar gains for all windows during the peak cooling day are divided by 24 hours and the building's conditioned area. The units of the normalized solar gain in terms of Watts/Ft2 is shown as follows:

Solar Gain, Watts/Ft2 =

Shading Coefficient x å (Window Area x Solar Heat Gain Factor)

Conditioned Area x 3.413 Btu/Watt Hr x 24 Hr/Day

While this method sounds rather crude, it has been surprisingly accurate for predicting heating and cooling loads for a variety of buildings modeled in Houston, Texas, Salt Lake City, Utah and Portland, Oregon. Based on the computer simulation comparisons made so far, this method of using average monthly temperatures seems to reasonably predict monthly cooling loads, even though there are substantial differences in local humidity levels.

Retained Gain

Retained gain is a term that was coined by Howard Reichmuth to refer to monthly cooling loads that are less than or equal to that month's heating load. Graphically it is shown by the shaded area in the figure below.

Constructing the retained gain line is important in determining the overall beating and cooling loads within a building. The retained gain line blends into the UA line on the higher temperature side, and approaches the internal gain less the constant cooling load on the low temperature side of the average monthly temperature chart This can be done graphically or by assigning a function to the line. Algebraically, the retained gain line can be defined in terms of a cubic equation. The cubic equation is constrained to pass through two points on the UA line above the building setpoint temperature and two points on the constant cooling portion of the internal gain line.

Retained gain illustrates many characteristics or a building's energy loads. It is the monthly amount of cooling load that could be used to offset the building's heating load. Retained gain is dependent upon the relative size of interior loads and the type of HVAC system selected. For example, a building with an interior space with large internal loads, such as a mainframe computer, requires constant cooling regardless or the outside air temperature. The retained gain illustrates the maximum amount of this waste beat that could he used to satisfy a portion of the building's heating requirements. Normally, the amount of recoverable heat will be less than the maximum due to the inability of the HVAC system to stores excess heat or inability of the HVAC system to put this excess heat into areas where it is needed.

An interesting thing about the Howdy plot is that the same plot can be used to determine design loads. Peak design loads are read directly off the graph using healing and cooling design temperatures instead or average monthly temperature.

HVAC SYSTEMS & CONTROLS

Changes to Retained Gain

Retained gain is the portion of cooling load that is less than or equal to that month's heating load. It occurs cool days requiring heating are combined with warm days in the same month that require cooling. On a daily basis, it can occur if a building requires heat during the morning warm-up and cooling later in the day as a result of solar gains, lights, and equipment. The type of HVAC system can also influence the amount of retained gain. HVAC systems that mix return air from warm interior zones with cool air from perimeter zones have a small amount of retained gain.

HVAC systems, such as the four-pipe system, that heat and cool rooms independently of one another cannot take advantage of the excess heat in one room to heat another. A modification to the four-pipe system would be to install a double bundled heat recovery chiller. In this way, heat could be moved mechanically from one space and added to a space in another part of the building. A plot of Retained Gain graphically illustrates the maximum potential savings that could occur by installing a heat recovery chiller.

The proportion of a building's total internal gain that must be constantly cooled will depend on the characteristics of each particular building. A large complex office building may have 10% or the floor space that requires dedicated cooling equipment. A small office building with a packaged rooftop unit will not have any.

Reheat

Reheat occurs whenever heat must he added to previously cooled air that was created by an HVAC system. Reheat can significantly add to the energy consumption of a building's heating and cooling system. Reheat normally occurs in buildings with multiple zones and constant volume air handlers. Variable air volume systems can also have a significant amount of reheat if their minimum airflows are relatively high. The amount of reheat in variable air volume systems is dependent upon the minimum amount of constant airflow. The reheat effect on exterior zones diminishes during the summer as artificial hearing is replaced by natural heat from solar gain, conduction and warm air infiltration. As shown in Figure 6, perimeter reheat on the Howdy Chart is represented by shifting the left side of the retained gain line down.

The reheat line can also be shifted down on the right side to represent interior zone reheat that can occur during the months. This is generally not necessary because warm return air can he used as the heat source during hot periods of the year.

A similar method for characterizing and rating the effect of simultaneous heating and cooling was previously developed by Roddy, et al (1993).

The amplitude in terms of watts per square foot of the reheat shift, as a function of minimum constant air flow to exterior zones and constant supply air temperature, is given by:

Reheat Shift W/Ft2 = 0.3165 x Min. Air Flow, CFM/Ft2

x % Exterior Zones X (Setpoint, ° F - Supply Air Temp) Fan Energy

There arc two types of fan energy, fan energy that operates a fixed number of hours per day, regardless of load, and fan energy that varies as a function of load. Constant volume fans that run for a fixed number of hours per month can be treated as an internal load and are simply added to the building's internal light and equipment loads. Other fan loads, such as constant volume fans that cycle on and off as a function of heating or cooling loads, and variable air volume fans will have different fan loads for each month. Both the constant and varying fan loads can be expressed in terms of watts per square foot by knowing monthly heating and cooling loads, fan static pressure, fan efficiency, motor efficiency, and supply air temperature. The relationship that combines all these factors is given by the

Total Fan Energy =

Pressure Drop. Inch H2O x 3.612 x (Heat Load W/Ft2 or Cool Load W/Ft2)

8.5 x Fan Eff. x Motor Eff. D T Heat, ° F D T Cool, ° F

Constant volume fans that run continuously during occupied hours would use the peak system loads to determine the monthly fan loads. Peak loads can be estimated from the Howdy chart using peak design temperatures instead or monthly average temperature as mentioned previously in this paper. Variable air volume or fan systems that cycle ON and OFF have loads that vary as a function of load, The above function should be used to calculate monthly varying fan loads using each month's heating and cooling loads.

Temperature Setback

The Howdy chart can be used to calculate energy savings from temperature setback during unoccupied hours. Temperature setback during unoccupied hours is equivalent to shifting the position of the UA and retained gain lines. The effect of heating setback is a shift of the UA line to the left, while cooling setback is equivalent to shift of the retained gain line to the right. A simple way to apply this shift is to calculate equivalent heating and cooling setback D Ts. These equivalent hearing or cooling setback can then be added or subtracted respectively to the average monthly temperature to determine that month's heating and cooling load.

Economizers

Airside economizer savings can be determined by multiplying the cooling loads times an economizer adjustment. Economizer adjustment can be approximated a zero cooling below a certain temperature, animating to 100% or the monthly temperature above an average monthly temperature of 70 degF.

Efficiency & COP Improvements

HVAC equipment efficiency can be applied in several ways. For simple equipment, such as gas furnaces and electric resistance heaters, the hearing energy is found by dividing the heating load by the appropriate equipment efficiency. Heat pumps and air conditioners can be represented by dividing each monthly load by the equipment efficiency or COP that occurs for a given average monthly temperature.

THEORETICAL BASIS

Monthly degree-hours calculated using either individual bin hours or average monthly temperature are mathematically equivalent for months where temperatures do not exceed the building's balance point temperature. The following mathematical proof shows that, in specific instances, the monthly heat loss and heat gain method descried in this paper using average monthly temperature is mathematically equivalent to conventional temperature bin or degree-hour methods. This proof helps explain the fundamental approach of using a single straight line based on the building's UA for both heating and cooling. Conduction and infiltration heat losses and gains are linear for the temperatures above and below the building's instantaneous balance point temperature.

Given

Tsp = Fixed Setpoint Temperature

TbinN = Average temperature in Bin N

HrN = Number of Hours/Month that Temperature is in Bin N

Tavg = Average Monthly Temperature

Proof

Degree Hour - (Setpoint Temp. - Outdoor Temp.) x No. Hours at Temp.

1. Degree Hour Using Bin Hours = å 1,Ni [(Tsp - TbinN) x HrN]
2. Degree Hour Using Avg. Monthly T = (Tsp - Tavg) x å 1,N HrN

3.

Set equation 1 and 2 equal to one another:

Degree Hour Using Bin Hours = degree Hours Using Avg. Monthly T

4. å 1,Ni [(Tsp - TbinN) x HrN] = (Tsp - Tavg) x å 1,N HrN

5. Weighted average temperature is equal to the sum individual bin temperature multiplied by the number of hours at that temperature divided by the total hours in that month.

6. Tavg = å 1,Ni (TbinN x HrN) / å 1,N HrN

Substituting equation 4 into 3 results in:

å 1,Ni [(Tsp - TbinN) x HrN]

= (Tsp - å 1,N (TbinN x HrN) + å 1,N HrN / å 1,N HrN

å 1,N [(Tsp - TbinN) x HrN]

= Tsp x å 1,N HrN - å 1,N (TbinN x HrN)

å 1,N [(Tsp - TbinN)X HrN]

= å 1,N [(Tsp - TbinN) x HrN] (Confirmed)

ACKNOWLEDGMENTS

The authors of this report would like to thank PacifiCorp, Inc. in Portland, Oregon for their financial assistance in performing much of the technical work described in this report.

REFERENCES

ASHRAE, 1993, ASHRAE Handbook 1993 Fundamentals, American Society of Heating, Refrigeration, and Air Conditioning Engineers, Inc., Atlanta, GA.

DOE-2.1D, 1989, Building Energy Analysis Program, developed By Lawrence Berkeley Laboratory, University of California with major support of the United States Department of Energy.

Knebel, D. E., 1983, 'Simplified Energy Analysis Using the Modified Bin Method,' American Society of Heating, Refrigeration and Air Conditioning Engineers, Inc., Atlanta, GA.

Reddy, T. A., Kissock. J. K., Katiparnula, S., Claridge, D.E., 'An Energy Delivery Efficiency lndex to Evaluate Simultaneous Heating and Cooling Effects in Large Commercial Buildings," ASME Journal of Solar Energy Engineering, ESL-PA-93/10-01.

Vadon, M., Kreider, J. F., and Norford, I. K., 1991, 'Improvement of the Solar Calculations in the Modified Bin Method,' ASHRAE Transactions, Vol. 97. Part 2. pp, 204-211.