Patent Publication Number: US-11651123-B2

Title: System and method for building heating and gross energy load modification modeling with the aid of a digital computer

Description:
CROSS-REFERENCE TO RELATED APPLICATION 
     This non-provisional patent application is a continuation of U.S. patent application Ser. No. 16/925,932, filed Jul. 10, 2020, pending, which is a continuation of U.S. Pat. No. 10,719,636, issued Jul. 21, 2020, which is a continuation-in-part of U.S. Pat. No. 10,719,789, issued Jul. 21, 2020, and further claims priority under 35 U.S.C. § 119(e) to U.S. Provisional Patent application, Ser. No. 61/935,285, filed Feb. 3, 2014, the disclosures of which are incorporated by reference. 
    
    
     FIELD 
     This application relates in general to energy conservation and planning and, in particular, to a system and method for building heating and gross energy load modification modeling with the aid of a digital computer. 
     BACKGROUND 
     Concern has been growing in recent days over energy consumption in the United States and abroad. The cost of energy has steadily risen as power utilities try to cope with continually growing demand, increasing fuel prices, and stricter regulatory mandates. Power utilities must also maintain existing infrastructure, while simultaneously finding ways to add more generation capacity to meet future needs, both of which add to the cost of energy. Moreover, burgeoning energy consumption continues to impact the environment and deplete natural resources. 
     Such concerns underlie industry and governmental efforts to strive for a more efficient balance between energy consumption and supply. For example, the Zero Net Energy (ZNE) initiative, backed by the U.S. Department of Energy, promotes the goal of balancing the total energy used by a building annually with the total energy generated on-site. In California, the 2013 Integrated Energy Policy Report (IEPR) builds on earlier ZNE goals by mandating that all new residential and commercial construction be ZNE-compliant, respectively, by 2020 and 2030. The IEPR defines a building as consuming zero net energy if the net amount of energy produced by renewable energy resources on-site roughly equals the value of the energy consumed by the building annually. 
     As the principal source of energy for most consumers, power utilities and energy agencies are at the forefront of energy efficiency initiatives, such as ZNE. These organizations often reach out to their customers through educational and incentive programs that are frequently pitched as ways to lower monthly energy bills. Typically, they urge energy conservation by cutting down on and avoiding wasteful energy use and by switching to energy efficient fixtures. They also often promote the on-site adoption of alternative sources of renewable energy. 
     Lowering monthly utility bills, however, is just a part of the broader problem of balancing energy consumption against supply. The average consumer continually consumes energy, whether electricity, natural gas, or other source; electricity may be purchased from the power utility or, less frequently, generated on-site. At home, energy may be used for space heating and cooling, lighting, cooking, powering appliances and electrical devices, heating water, and doing laundry. Energy may also be consumed for personal transportation needs, whether by private conveyance or public mass transit. 
     To raise energy awareness, power utilities often provide periodic energy consumption statistics that are gathered through the use of smart power meters or similar technologies. Such statistics, though, invariably reflect net power consumption based only upon the energy purchased from the power utility. Energy generated (and consumed) on-site is not included, as utilities currently lack practicable ways of gathering and aggregating on-site energy production and consumption values into their own power consumption statistics, in part, due to the vagaries in end-consumer equipment and energy consumption patterns. 
     Utility-provided net power consumption statistics can mask the overall efficiency of a building, particularly where on-site power generation and consumption significantly contributes to gross energy load. Effective energy balancing requires decreasing the amount of energy consumed and generating energy on-site. Performing both of these steps is crucial to lowering gross energy load, yet determining how efficiently energy is consumed is often skipped when a switch to an alternative energy source is made first. For instance, the installation of a photovoltaic (PV) system on a private residence frequently leads a consumer to (erroneously) conclude that further efforts at increasing energy efficiency are no longer necessary or worthwhile. The immediacy of lower monthly utility bills and favorable net power consumption statistics can reinforce this misperception. 
     Therefore, a need remains for an approach to empowering consumers, particularly residential customers, with full knowledge of actual gross energy consumption and an understanding what options and alternatives work best for their energy needs, especially in situations where renewable energy sources are already in place. 
     SUMMARY 
     The percentage of the total fuel purchased for space heating purposes can be fractionally inferred by evaluating annual fuel purchase data. An average of monthly fuel purchases during non-heating season months is first calculated. The fuel purchases for each month is then compared to the average monthly fuel purchase, where the lesser of the average and that month&#39;s fuel purchase are added to a running total of annual space heating fuel purchases. 
     In addition, the overall thermal performance of a building UA Total  can be empirically estimated through a short-duration controlled test. Preferably, the controlled test is performed at night during the winter. A heating source, such as a furnace, is turned off after the indoor temperature has stabilized. After an extended period, such as 12 hours, the heating source is turned back on for a brief period, such as one hour, then turned back off. The indoor temperature is allowed to stabilize. The energy consumed within the building during the test period is assumed to equal internal heat gains. Overall thermal performance is estimated by balancing the heat gained with the heat lost during the test period. 
     Furthermore, potential energy investment scenarios can be evaluated. Energy performance specifications and prices for both existing and proposed energy-related equipment are selected, from which an initial capital cost is determined. The equipment selections are combined with current fuel consumption data, thermal characteristics of the building, and solar resource and other weather data to create an estimate of the fuel consumption of the proposed equipment. An electricity bill is calculated for the proposed equipment, from which an annual cost is determined. The payback of the proposed energy investment is found by comparing the initial and annual costs. 
     New energy investments specifically affecting building envelope, heating source, or heating delivery can be evaluated. Data that can include the percentage of a fuel bill for fuel used for heating purposes, an existing fuel bill, existing overall thermal properties UA Total  of the building, existing furnace efficiency, new furnace efficiency, existing delivery system efficiency, new delivery system efficiency, areas of building surfaces to be replaced or upgraded, existing U-values of thermal properties of building surfaces to be replaced or upgraded, new U-values of thermal properties of building surfaces to be replaced or upgraded, and number of air changes before and after energy investment are obtained. The impact of energy investments that affect heat transfer through the building envelope due to conduction, heat losses due to infiltration, or both, are quantified by a comparative analysis of relative costs and effects on the building&#39;s thermal characteristics, both before and after the proposed changes. 
     Finally, gross energy load can be determined by combining periodic net load statistics, such as provided by a power utility or energy agency, with on-site power generation, such as photovoltaic power generation, as produced over the same time period. The gross energy load provides an indication upon which other types of energy investment choices can be evaluated. These choices can include traditional energy efficiencies, such as implementing electrical efficiency measures, which includes cutting down on and avoiding wasteful energy use and switching to energy efficient fixtures, and improving the thermal efficiency and performance of a building. The choices can also include non-traditional energy efficiencies, such as replacing a gasoline-powered vehicle with an electric vehicle, fuel switching from a water heater fueled by natural gas to a heat pump water heater, and fuel switching from space heating fueled by natural gas to a heat pump space heater. 
     In one embodiment, a system and method for building heating and gross energy load modification modeling with the aid of a digital computer are provided. A gross energy load associated with a building is obtained by a computer, the computer comprising a processor and a memory within which code for execution by the processor is stored, based on electricity provided to the building by a power utility and energy provided to the building by an on-site renewable energy system. An overall thermal performance of the building is estimated by the computer by conducting an empirical test comprising remotely controlling a heating source inside the building. An effect of the one or more changes to the overall thermal performance of the building on the gross energy load is modeled by the computer, including determining a size of a further heating source needed to supply heat for the building with the changed overall thermal performance and using the size to model a change to the electricity provided to the building by the power utility. A size of a further renewable energy system needed to power the further heating source is determined by the computer. 
     Still other embodiments will become readily apparent to those skilled in the art from the following detailed description, wherein are described embodiments by way of illustrating the best mode contemplated. As will be realized, other and different embodiments are possible and the embodiments&#39; several details are capable of modifications in various obvious respects, all without departing from their spirit and the scope. Accordingly, the drawings and detailed description are to be regarded as illustrative in nature and not as restrictive. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         FIG.  1    is a Venn diagram showing, by way of example, a typical consumer&#39;s energy-related costs. 
         FIG.  2    is a flow diagram showing a function for fractionally inferring the percentage of the total fuel purchased for space heating purposes, in accordance with one embodiment. 
         FIG.  3    is a graph depicting, by way of example, annual fuel purchases, including fuel purchased for space heating purposes. 
         FIG.  4    is a flow diagram showing method for empirically estimating overall thermal performance of a building through a short-duration controlled test, in accordance with one embodiment. 
         FIG.  5    is a graph depicting, by way of example, the controlled, short-duration test of  FIG.  4   . 
         FIG.  6    is a graph depicting, by way of example, the controlled, short-duration test of  FIG.  4    for a different day. 
         FIG.  7    is a screen shot showing, by way of example, an analysis of energy investment choices. 
         FIG.  8    is a process flow diagram showing a computer-implemented method for evaluating potential energy investment scenarios from a user&#39;s perspective, in accordance with one embodiment. 
         FIG.  9    is a detail of the graphical user interface of  FIG.  7    showing, by way of example, an annotated graph of hourly electricity consumption. 
         FIG.  10    is a graph showing, by way of example, monthly net energy consumption statistics. 
         FIG.  11    is a graph showing, by way of example, average daily net energy consumption statistics, including on-site photovoltaic power generation. 
         FIG.  12    is a graph showing, by way of example, average daily gross energy consumption statistics, excluding on-site photovoltaic power generation. 
         FIG.  13    is a graph showing, by way of example, average daily gross energy consumption statistics, excluding on-site photovoltaic power generation with light emitting diode (LED) lighting fixtures and lighting usage reduction. 
         FIG.  14    is a graph showing, by way of example, average daily gross energy consumption statistics, excluding on-site photovoltaic power generation with electric vehicle usage. 
         FIG.  15    is a graph showing, by way of example, average daily gross energy consumption statistics, excluding on-site photovoltaic power generation with light emitting diode (LED) lighting fixtures, lighting usage reduction, and electric vehicle usage. 
         FIG.  16    is a graph showing, by way of example, average daily net energy consumption statistics, including on-site photovoltaic power generation with light emitting diode (LED) lighting fixtures, lighting usage reduction, and electric vehicle usage. 
         FIG.  17    is a process flow diagram showing a routine for estimating gross energy load for use in the method of  FIG.  8   . 
         FIG.  18    is a process flow diagram showing a routine for evaluating potential energy investment payback for use in the method of  FIG.  8   . 
         FIG.  19    is a graph depicting, by way of example, assumed hourly distribution factors, as used in the routine of  FIG.  8   . 
         FIG.  20    is a flow diagram showing a computer-implemented method for evaluating potential energy investment scenarios specially affecting a building&#39;s envelope, heating source, or heating delivery, in accordance with a further embodiment. 
         FIG.  21    is a process flow diagram showing a routine for selecting energy investment scenario parameters for use in the method of  FIG.  20   . 
         FIG.  22    is a block diagram depicting, by way of example, annual energy consumption by an average household in California with gasoline and natural gas consumption expressed in kilowatt hours. 
         FIG.  23    is a block diagram depicting, by way of example, the annual energy consumption of  FIG.  22    reflecting energy efficiencies implemented through traditional methodologies. 
         FIG.  24    is a block diagram depicting, by way of example, the annual energy consumption of  FIG.  22    reflecting a switch to an electric vehicle. 
         FIG.  25    is a block diagram depicting, by way of example, the annual energy consumption of  FIG.  22    reflecting a switch to a heat pump water heater. 
         FIG.  26    is a block diagram depicting, by way of example, the annual energy consumption of  FIG.  22    reflecting a switch to a heat pump space heater. 
         FIG.  27    is a block diagram depicting, by way of example, the annual energy consumption of  FIG.  22    with cumulative revised energy consumption expressed in kilowatt hours. 
         FIG.  28    is a block diagram depicting, by way of example, the cumulative revised energy consumption of  FIG.  27    overlaying a 20% efficient photovoltaic power generation system. 
         FIG.  29    is a block diagram showing a computer-implemented system  140  for empirically estimating overall thermal performance of a building through a short-duration controlled test, in accordance with one embodiment. 
     
    
    
     DETAILED DESCRIPTION 
     Private individuals enjoy an immediacy to decision-making on matters of energy consumption and supply. As a result, individuals are ideally positioned to make the kinds of changes necessary to decrease their personal energy consumption and avoid energy waste, and to choose appropriate sources of renewable energy, among other actions. However, merely having a motivation to better balance energy consumption and supply, including adopting a ZNE goal, is not enough, as the possible ways that personal energy consumption can be improved are myriad, and navigating through the option space can be time-consuming and frustrating. Individual consumers need, but often lack, the information necessary to guide the energy consumption and supply decisions that are required to accomplish their conservational goals, particularly when a switch to an alternative on-site energy source has already been made without first determining how efficiently energy is being consumed in a building. 
     The problem of providing consumers with the kinds of information needed to wisely make energy-related decisions can be approached by first developing a cost model that depicts the energy consumption landscape of the average consumer.  FIG.  1    is a Venn diagram showing, by way of example, a typical consumer&#39;s energy-related costs  10 . The costs  10  include both fuel costs and operational costs, where appropriate, which provide the basis of the cost model. For purposes of illustration, the cost model assumes that the hypothetical consumer has a private residence, as opposed to an apartment or condominium, and uses a personal vehicle as a primary mode of transportation, rather than public mass transit or a physical mode of travel. The cost model can be adapted mutatis mutandis to other modeling scenarios for apartment dwellers or urban city commuters, for instance, who may have other energy consumption and supply types of expenses. 
     The cost model reflects the choices made by consumers that affect their energy consumption. For example, residential consumers must choose between various energy options or alternatives concerning weather stripping or caulking to seal a house; increased ceiling, floor, and wall insulation; high-efficiency windows; window treatments; programmable thermostats; cool roofs, that is, roofs that have a high solar reflectance; radiant barriers; roof venting; electric and natural gas furnaces for space heating; air source and geothermal heat pumps for space heating and cooling; compressive and evaporative air conditioners; natural gas or electric and tank-based or tank-less water heaters; air source heat pump water heaters; incandescent, fluorescent, and LED lights; high efficiency appliances, including clothes washers, clothes dryers, refrigerators, dishwashers, and microwave ovens; electric (conductive and inductive) and natural gas stoves; electric and natural gas ovens; and electronic equipment that consume electricity, such as Wi-Fi routers, televisions, stereos, and so on. Consumers must also choose between standard gasoline- or diesel-fueled vehicles; hybrid gasoline- or diesel-fueled vehicles; natural gas vehicles; plug-in hybrid electric vehicles; and pure electric vehicles. 
     The cost model also reflects the choices made by consumers that affect their energy supply. A consumer can be faced purchasing energy, that is, electricity and natural gas, from their local utility; purchasing gasoline, diesel or other automobile fuel from a gasoline station; generating hot water using solar hot water heating; and generating electricity, either for home or transportation purposes, using photovoltaic power generation systems or, less commonly, small wind, small hydroelectric, or other distributed power generation technologies. 
     In the cost model, the energy-related costs  10  can be divided into two categories, home energy costs  11  and personal transportation costs  12 . Home energy costs  11  may include energy consumed for space heating and cooling  13 , lighting  14 , cooking  15 , powering appliances and electrical devices  16 , heating water  17 , and doing laundry  18 , although fewer or more home energy costs may also be possible, such as where a consumer lacks in-home laundry facilities. Personal transportation costs  12  may include the actual cost of the vehicle  19 , fuel costs  20 , and maintenance expenses  21 , although fewer or more transportation costs may also be possible, such as where a company car is provided to the consumer free of charge. 
     Home energy costs  11  can be sub-grouped into those costs that are always in the form of electricity consumption  22 . These costs include lighting  14  and (most) appliances and electrical devices  16 . For these types of costs, the only practicable options to lower energy consumption are replacing lighting fixtures, appliances, or electrical devices with higher efficiency units or modifying or eliminating their usage. The remaining home energy costs  11  could either be due to electricity consumption or consumption of energy from other sources, depending upon the type of fixtures or appliances used. A gas range, for instance, consumes a minimal amount of electricity, as heat for cooking and baking are generated from natural gas, whereas an electric range can consume a significant amount of electricity, when used heavily. This dichotomy of electricity-dependent energy costs and energy costs that could be based on some other form of energy further complicates the energy consumption landscape of the average consumer. 
     Power utilities and energy agencies often promote energy conservation by providing periodic net energy consumption statistics to their customers. Such statistics are helpful in determining fuel costs for electricity and emphasize energy costs that are always in the form of electricity consumption  22 . On the other hand, these statistics can hide underlying inefficiencies in overall energy consumption, particularly where a consumer has already made a switch to an alternative energy source, by only showing a partial picture of gross energy consumption, as further described infra beginning with  FIG.  10    et seq. 
     For purposes of the cost model, fuel costs include electricity (F); fuel for heating (F), which could be natural gas, propane, or fuel oil; and fuel for transportation (G), which could be gasoline, diesel, propane, LPG, or other automobile fuel. In addition, maintenance costs will be included in the cost model. A consumer&#39;s total energy-related costs (C Total ) equals the sum of the electricity cost (C E ), fuel for heating cost (C E ), gasoline (or other automobile fuel) cost (C G ), and maintenance cost (C M ), which can be expressed as:
 
 C   Total   =C   E   +C   F   +C   G   +C   M   (1)
 
     In Equation (1), each cost component can be represented as the product of average price and annual quantity consumed, assuming that the price is zero when the quantity consumed is zero. As a result, the total energy-related costs C Total  can be expressed as:
 
 C   Total   =P   E   Q   E   +P   F   Q   F   +P   G   Q   G   +P   M   Q   M    (2)
 
     Price and quantity in Equation (2) need to be consistent with each other, but price and quantity do not need to be the same across all cost components. Fuel units depend upon the type of fuel. Electricity price (P E ) is expressed in dollars per kilowatt hour ($/kWh) and electricity quantity (Q E ) is expressed in kilowatt hours (kWh). For natural gas, fuel for heating price (P F ) is expressed in dollars per thermal unit ($/therm) and fuel quantity (Q F ) is expressed in thermal units (therms). Gasoline (or other automobile fuel) price (P G ) is expressed in dollars per gallon ($/gallon) and gasoline quantity (Q G ) is expressed in gallons. If only automobile maintenance costs are included and not the vehicle cost, maintenance price (P M ) can be in dollars per mile driven ($/mile) and maintenance quantity (Q M ) can be expressed in miles. 
     Pricing of fuel for heating (P F ) may be a function of the amount of fuel consumed or could be a non-linear value, that is, a value determined independent of amount used, or a combination of amount and separate charges. In the cost model, for clarity, the fuel for heating cost (C F ) assumes that the quantity of fuel actually used for space heating is separable from other loads in a home that consume the same type of fuel, as further explained infra. 
     For fuels for heating sold by bulk quantity, such as propane or fuel oil, fuel pricing is typically on a per-unit quantity basis. For other fuels for heating, such as natural gas, a number of utilities have tiered natural pricing that depend upon the quantity consumed. In particular, electricity pricing can be complicated and may depend upon a variety of factors, including the amount of electricity purchased over a set time period, such as monthly, for instance, tiered electricity prices; the timing of the electricity purchases, for instance, time-of-use electricity prices; fixed system charges; and so forth. As a result, accurately calculating average electricity pricing often requires detailed time series electricity consumption data combined with electricity rate structures. Conventional programs and online services are available to perform electricity pricing calculations. A slightly different formulation of electricity pricing may be used where the quantity of electricity purchased nets out to zero consumption, but the total cost does not, such as can occur due to a flat service surcharge. 
     In the cost model, the quantity of electricity (Q E ), fuel for heating (Q F ), and gasoline (or other automobile fuel) (Q G ) purchased is assumed to equal the quantity consumed for meeting the consumer&#39;s energy consumption requirements. Gasoline (or other automobile fuel) fuel quantity (Q G ) can be fairly estimated based on miles driven annually over observed or stated vehicle fuel efficiency, such as available from http://www.fueleconomy gov. Electricity quantity (Q E ) can generally be obtained from power utility bills. 
     The quantity of fuel for heating (Q F ) grossly represents the amount of fuel that needs to be purchased to provide the desired amount of heat in the consumer&#39;s home. The amount of fuel used for heating may actually be smaller than the total amount of fuel delivered to the home; depending upon the types of components installed in a home, the fuel used for heating may also be the same fuel used for other purposes, which may include fuel used, for example, for heating water, cooking, or drying clothes. Notwithstanding, utilities that provide fuel to their customers for heating and other purposes, in particular, natural gas, via piped-in public utility service generally meter net fuel purchases at the point of delivery. Individual loads are not metered. Thus, the total quantity of fuel (Q F ) consumed may need to be divided into the amount of fuel used strictly for space heating (Q F-Heating ) and the amount of fuel used for other non-space heating purposes (Q F-Non-Heating ). For instance, in many residential situations, much of the non-space heating fuel will be used for water heating. The load-corrected quantity of fuel (Q F ) can be expressed as:
 
 Q   F   =Q   F-Heating   +Q   F-Non-Heating   (3)
 
     Modeling the quantity of fuel consumed for space heating (Q F ) requires consideration of the type of space heating employed in a home. A separate quantity of fuel for space heating is only required if the type of heating system used does not use electricity for active heat generation. Active heating sources, such as central heating systems, include a heating element that heats the air or water, for instance, a furnace or boiler, and a heating delivery or distribution component, such as ductwork through which the heated air is forced by an electric fan or pipes through which the heated water is circulated via an electric pump. Thus, where the heating element requires, for instance, natural gas, propane, or fuel oil to generate heat, the quantity of fuel for space heating consumed will be equal to the consumer&#39;s energy consumption for space heating requirements. In contrast, where the heating element relies on electricity for active heat generation, such as passive radiant heating or an electric-powered air source heat pump, the quantity of fuel for space heating will be zero, although the total quantity of electricity (Q E ) consumed will be significantly higher due to the electricity used for heat generation. The fuel for space heating quantity (Q F ) can be normalized to the quantity of electricity (Q E ) for purposes of comparison. Estimating the amount of fuel consumed for space heating requirements will now be discussed. 
     The overall rate of heat transfer of a building equals the rate of the heat transfer or conduction through each unique building surface plus the rate of heat transfer through infiltration, that is, air leakage into a building. Conduction rate and infiltration rate are based on the thermal characteristics of the material in each surface of the building and upon the indoor and outdoor temperatures and airtightness of the building. 
     Heat transfer can be individually calculated for each building surface, then summed to yield overall heat transfer. Alternatively, a building&#39;s overall thermal performance (UA Total ) can first be calculated, expressed in units of Btu per ° F.-hour. Overall thermal performance can then be combined with the difference between the indoor and outdoor temperature. When the latter approach is used, the heat loss over a one-hour period Q Heat Loss  equals UA Total  times the difference between the average indoor and outdoor temperature times one hour, which can be expressed as:
 
 Q   Heat Loss =( UA   Total )( T   Indoor   −T   Outdoor )(1 hour)  (4)
 
Equation (4) can be rearranged to yield UA Total :
 
     
       
         
           
             
               
                 
                   
                     UA 
                     Total 
                   
                   = 
                   
                     
                       Q 
                       
                         Heat 
                         ⁢ 
                             
                         Loss 
                       
                     
                     
                       
                         ( 
                         
                           
                             T 
                             Indoor 
                           
                           - 
                           
                             T 
                             Outdoor 
                           
                         
                         ) 
                       
                       ⁢ 
                       
                         ( 
                         
                           1 
                           ⁢ 
                               
                           hour 
                         
                         ) 
                       
                     
                   
                 
               
               
                 
                   ( 
                   5 
                   ) 
                 
               
             
           
         
       
     
     Total heat loss Q Heat Loss  can be analytically estimated based on furnace sizing for the building, such as described in H. Rutkowski,  Manual J Residential Load Calculation , (8 th  ed. 2011) (“Manual J”), and also as provided via the Air Conditioning Contractors of America&#39;s Web-fillable Form RPER 1.01, available at http://ww.acca.org. Per the Manual J approach, winter and summer design conditions are specified, including indoor and outdoor temperatures. In addition, surface measurements and materials, estimated infiltration, heating and cooling equipment capacities, and duct distribution system design are specified. 
     These values are used in the Manual J approach to estimate total heat loss per hour, from which a recommended heating output capacity is determined. For example, a heating system having a 64,000 Btu/hour heating output capacity would be appropriate in a building with an estimated total heat loss of 59,326 Btu/hour. Assuming an outdoor temperature of −6° F. and an indoor temperature of 70° F., Equation (5) can be used to estimate UA Total  based on the estimated total heat loss of 59,326 Btu/hour, such that: 
                     UA   Total     =         59   ,   326   ⁢         Btu         [     70   ⁢   °   ⁢           F   .     -     (       -   6     ⁢   °   ⁢           F   .       )           ]     ⁢     (     1   ⁢         hour     )         =       781   ⁢         Btu       °   ⁢           F   .   -     ⁢   hour                 (   6   )               
The result is that this building&#39;s overall thermal performance is 781 Btu/hr−° F. Other ways of estimating total heat loss Q Heat Loss  are possible.
 
     Equation (4) provides an estimate of the heat loss over a one-hour period Q Heat Loss  for a building. Equation (4) can also be used to derive the amount of heat that needs to be delivered to a building Q Heat Delivered  by multiplying the building&#39;s overall thermal performance UA Total  times 24 hours per day, times the number of Heating Degree Days, such as described in J. Randolf et al., Energy for  Sustainability: Technology, Planning, Policy , p. 248 (2008), which can be expressed as:
 
 Q   Heat Delivered =( UA   Total )(24)(HDD Location   Set Point Temp )   (7)
 
     The number of Heating Degree Days, expressed as HDD Location   Set Point Temp  in ° F.-day per year, is determined by the desired indoor temperature and geographic location and can be provided by lookup tables. 
     In turn, the annual amount of heat delivered by a furnace to a building for end-use Q Heat Delivered-Furnace , expressed in Btu per hour, equals the product of furnace fuel requirements R Furnace , also expressed in Btu per hour, percentage of furnace efficiency η Furnace , percentage of delivery system efficiency η Delivery  and hours of operation Running-Time, such that:
 
 Q   Heat Delivered-Furnace =( R   Furnace )(η Furnace η Delivery )(Running-Time)   (8)
 
     The annual amount of heat delivered Q Heat Delivered-Furnace  can be discounted by the amount of energy passively obtained on-site. For instance, if the solar savings fraction (SSF) represents the fraction of energy by a building due to solar gains, the heat that needs to be delivered by the furnace can be expressed by:
 
 Q   Heat Delivered-Furnace   =Q   Heat Delivered (1−SFF)   (9)
 
For the time being, ignore any gains in indoor temperature due to internal sources of heat.
 
     The amount of fuel used strictly for space heating Q F-Heating  can be found by substituting Equation (7) into Equation (9), setting the result equal to Equation (8), and solving for Q F-Heating . The amount of fuel that needs to be purchased for space heating uses Q F-Heating  equals the product of furnace fuel requirements R Furnace  and hours of operation hours Running-Time. Thus, solving for Q F-Heating . 
     
       
         
           
             
               
                 
                   
                     Q 
                     
                       F 
                       - 
                       Heating 
                     
                   
                   = 
                   
                     
                       
                         ( 
                         
                           UA 
                           Total 
                         
                         ) 
                       
                       ⁢ 
                       
                         ( 
                         24 
                         ) 
                       
                       ⁢ 
                       
                         ( 
                         
                           HDD 
                           Location 
                           
                             Set 
                             ⁢ 
                                 
                             Point 
                             ⁢ 
                                 
                             Temp 
                           
                         
                         ) 
                       
                       ⁢ 
                       
                         ( 
                         
                           1 
                           - 
                           SSF 
                         
                         ) 
                       
                     
                     
                       
                         η 
                         Furnace 
                       
                       ⁢ 
                       
                         η 
                         Delivery 
                       
                     
                   
                 
               
               
                 
                   ( 
                   10 
                   ) 
                 
               
             
           
         
       
     
     Calculating the solar savings fraction SSF typically requires extensive computer modeling. However, for an existing building, the SSF can be determined by setting Equation (10) equal to the amount of fuel required for space heating and solving for the solar savings fraction. 
     In general, utilities that provide fuel to their customers via piped-in public utility services meter fuel purchases at the point of delivery and not by individual component load. In situations where the fuel is used for purposes other than solely space heating, the total fuel purchased for space heating Q F-Heating  may only represent a fraction of the total fuel purchased Q F . Q F-Heating  can be expressed as:
 
 Q   F-Heating =( H )( Q   F )   (11)
 
where H fractionally represents the percentage of the total fuel purchased for space heating purposes.
 
     The fraction H can be empirically inferred from fuel purchase data. Fuel purchased in the months occurring outside of the heating season are assumed to represent the fuel purchased for non-space heating needs and can be considered to represent a constant baseline fuel expense.  FIG.  2    is a flow diagram showing a function  30  for fractionally inferring the percentage of the total fuel purchased for space heating purposes, in accordance with one embodiment. The function  30  can be implemented in software and execution of the software can be performed on a computer system, such as further described infra with reference to  FIG.  29   , as a series of process or method modules or steps. 
     Initially, fuel purchase data is obtained (step  31 ), such as can be provided by the fuel utility. Preferably, the data reflects fuel purchases made on at least a monthly basis from the utility. An average of the fuel purchased monthly during non-heating season months is calculated (step  32 ). In some regions, the heating season will only include traditional winter months, beginning around mid-December and ending around mid-March; however, in most other regions, space heating may be required increasingly in the months preceding winter and decreasingly in the months following winter, which will result in an extended heating season. 
     Each month (or time increment represented by each fuel purchase) is then iteratively processed (steps  33 - 40 ), as follows. For each month (step  33 ), the fuel purchase for that month is chosen (step  34 ) and added to a running total of annual fuel purchases (step  35 ). If the monthly fuel purchase is greater than the average of the fuel purchased monthly during non-heating season months (step  36 ), the average of the fuel purchased monthly is subtracted from that monthly fuel purchase (step  37 ) and the remainder represents the fuel purchased for space heating in that month. Otherwise, the monthly fuel purchase is subtracted from itself (step  38 ), effectively indicating that the fuel purchased for space heating in that month is zero. The difference of the subtraction, that is, the fuel purchased for space heating in that month, is added to a running total of annual space heating fuel purchases (step  39 ), and the process repeats for each subsequent month (step  40 ). Finally, the ratio of the running total of annual space heating fuel purchases to the running total of annual fuel purchases is returned (step  41 ) as the fraction H. 
     The relationship between total annual fuel purchases and total annual space heating fuel purchases can be visualized.  FIG.  3    is a graph  50  depicting, by way of example, annual fuel purchases, including fuel purchased for space heating purposes. The x-axis  51  represents months. The y-axis  52  represents natural gas consumption, expressed in therms per day. May through September are considered non-winter (non-heating season) months. The natural gas (fuel) purchases  53  for each month are depicted as circles. Total annual fuel purchases  54  can be interpolated by connecting each monthly natural gas purchase  53 . The fraction H for the percentage of the total fuel purchased for space heating purposes each month is determined, from which a baseline annual fuel expense  55  can be drawn. The region between the baseline annual fuel expense  55  and the interpolated total annual fuel purchases  54  represents the total annual space heating (fuel) purchases  56 . 
     The relationship between the total annual fuel purchases, baseline fuel expenses, and total space heating purchases can be formalized. First, the average monthly fuel purchased for non-winter months  Q F-Non-Winter over    a set number of months is calculated, as follows: 
                       Q     F   -   Non   -   Winter       _     =         ∑     i   =     Non   -   Winter   ⁢         Start   ⁢         Month         Non   -   Winter   ⁢         End   ⁢         Month             Fuel   ⁢           Purchased   i           Number   ⁢         of   ⁢         Months               (   12   )               
where i represents the range of non-winter months within the set number of months; and Fuel Purchased i  represents the fuel purchased in the non-winter month i.
 
     Next, the fuel consumed each month for heating, which is the difference between the monthly fuel purchase and the minimum of either the monthly fuel purchase or the average monthly fuel purchased for non-winter months, is added to a summation to yield the total annual fuel consumed for heating Q F-Heating  as follows: 
     
       
         
           
             
               
                 
                   
                     Q 
                     
                       F 
                       - 
                       Heating 
                     
                   
                   = 
                   
                     
                       ∑ 
                       
                         i 
                         = 
                         1 
                       
                       12 
                     
                       
                     
                       ( 
                       
                         
                           Fuel 
                           ⁢ 
                               
                           
                             Purchased 
                             i 
                           
                         
                         - 
                         
                           min 
                           ⁡ 
                           ( 
                           
                             
                               Fuel 
                               ⁢ 
                                   
                               
                                 Purchased 
                                 i 
                               
                             
                             , 
                             
                               
                                 Q 
                                 
                                   F 
                                   - 
                                   Non 
                                   - 
                                   Winter 
                                 
                               
                               _ 
                             
                           
                           ) 
                         
                       
                       ) 
                     
                   
                 
               
               
                 
                   ( 
                   13 
                   ) 
                 
               
             
           
         
       
     
     Assuming that the total annual fuel purchases Q F  are non-zero, the ratio of the total annual fuel consumed for heating Q F-Heating  and the total fuel purchases Q F  is taken to yield the fraction H, as follows: 
     
       
         
           
             
               
                 
                   H 
                   = 
                   
                     
                       Q 
                       
                         F 
                         - 
                         Heating 
                       
                     
                     
                       Q 
                       F 
                     
                   
                 
               
               
                 
                   ( 
                   14 
                   ) 
                 
               
             
           
         
       
     
     Finally, the percent of heat supplied by the solar savings fraction can be determined by setting Equation (10) equal to Equation (11) and solving for SSF, in accordance with: 
     
       
         
           
             
               
                 
                   SSF 
                   = 
                   
                     1 
                     - 
                     
                       
                         
                           ( 
                           H 
                           ) 
                         
                         ⁢ 
                         
                           ( 
                           
                             Q 
                             F 
                           
                           ) 
                         
                         ⁢ 
                         
                           ( 
                           
                             η 
                             Furnace 
                           
                           ) 
                         
                         ⁢ 
                         
                           ( 
                           
                             η 
                             Delivery 
                           
                           ) 
                         
                       
                       
                         
                           ( 
                           
                             UA 
                             Total 
                           
                           ) 
                         
                         ⁢ 
                         
                           ( 
                           24 
                           ) 
                         
                         ⁢ 
                         
                           ( 
                           
                             HDD 
                             Location 
                             
                               Set 
                               ⁢ 
                                   
                               Point 
                               ⁢ 
                                   
                               Temp 
                             
                           
                           ) 
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   15 
                   ) 
                 
               
             
           
         
       
     
     A building&#39;s overall thermal performance UA Total  is key to estimating the amount of fuel consumed for space heating requirements. Equation (5), discussed supra, presents one approach to estimating UA Total , provided that the total heat loss Q Heat Loss  can be estimated. An analytical approach to determining UA Total  requires a detailed energy audit, from which UA Total  is then calculated using a set of industry-standard engineering equations. With both approaches, the building&#39;s actual thermal performance is not directly measured. A third approach through UA Total  can be empirically quantified will now be presented. 
     The total heat transfer of a building at any instant in time (q Total ) equals the sum of the heat transferred through the building envelope by conduction (q envelope ) plus the heat transferred through infiltration (q Infiltration ), which can be expressed as:
 
 q   Total   =q   Envelope   +q   Infiltration    (16)
 
     An energy audit does not directly measure the heat transferred through the building envelope by conduction q Envelope . Rather, q Envelope  is calculated using a series of steps. First, the surface areas of all non-homogeneous exterior-facing surfaces are either physically measured or verified, such as by consulting plans for the building. Non-homogeneous surfaces are those areas that have different insulating materials or thicknesses. The surface areas of all floors, walls, ceilings, and windows are included. 
     Second, the insulating properties of the materials used, quantified as “R-values,” or the capacity of an insulating material to resist heat flow for all surfaces area determined. R-values are generally determined by visual inspection, if the insulation is exposed, such as insulation batts used in an attic. When the insulation cannot be visually inspected, as with wall insulation, R-values are estimated based on surface thickness and the age of the building. 
     These first two steps are difficult, time-consuming, and carry the risk of mistakes. Accurately measuring all of the exterior-facing surfaces can be tedious, and the manual nature of the visual inspection admits of error. For instance, some wall surfaces may appear to be only interior-facing, yet parts of a wall may actually be both interior- and exterior-facing, as can happen in a split-level home along the wall dividing the “split” sections of the house (also referred to as a knee wall). When viewed from inside, the wall along the split, on both sides, appears to be an interior-facing wall, yet the upper section of that wall is often partially exposed to the exterior along the outer wall surface extending beyond the ceiling height of the lower section of the split. In addition, issues, such as improperly installed insulation and insulation falling away from a wall, can be missed by a visual inspection. 
     Third, the R-values are inverted to yield U-values, which are then multiplied by their corresponding surface areas. The results are summed across all N surfaces of the building. Total heat transfer through the building envelope by conduction q Envelope  equals the product of this summation times the difference between the indoor and outdoor temperatures, expressed as: 
                     q   Envelope     =       (       ∑     i   =   1     N             U   i     ⁢     A   i         )     ⁢     (       T   Indoor     -     T   Outdoor       )               (   17   )               
where U i  represents the U-value of surface i, A i  represents the surface area of surface i; and T Indoor  and T Outdoor  are respectively the indoor and outdoor temperatures relative to the building.
 
     Heat transfer also occurs due to infiltration. “A major load for your furnace is heating up cold air leaking into your house, while warm indoor air leaks out. These infiltration losses are driven in part by the difference in the indoor-to-outdoor temperature (stack-driven infiltration) and in part by the pressure differences caused by the wind blowing against the side of the house (wind-driven insolation).” J. Randolf et al. at p. 238, cited supra. Formally, the rate of heat transfer due to infiltration q Infiltration  can be expressed as:
 
 q   Infiltration   =ρcnV ( T   Indoor   −T   Outdoor )   (18)
 
where ρ represents the density of air, expressed in pounds per cubic foot; c represents the specific heat of air, expressed in Btu per pound ° F.; n is the number of air changes per hour, expressed in number per hour; and V represents the volume of air per air change, expressed in cubic feet per air change.
 
     In Equation (18), ρ and c are constants and are the same for all buildings; ρ equals 0.075 lbs/ft 3  and c equals 0.24 Btu/lb-° F. n and V are building-specific values. V can be measured directly or can be approximated by multiplying building square footage times the average room height. Measuring n, the number of air changes per hour, requires significant effort and can be directly measured using a blower door test. 
     Total heat transfer q Total  can now be determined. To review, q Total  equals the sum of the heat transfer through the building envelope by conduction q Envelope  plus the heat transfer through infiltration q Infiltration . Substitute Equation (17) and Equation (18) into Equation (16) to express the rate of heat loss q Total  for both components:
 
 q   Total   =UA   Total ( T   Indoor   −T   Outdoor )   (19)
 
where:
 
     
       
         
           
             
               
                 
                   
                     UA 
                     Total 
                   
                   = 
                   
                     
                       ( 
                       
                         
                           ∑ 
                           
                             i 
                             = 
                             1 
                           
                           N 
                         
                           
                         
                           
                             U 
                             i 
                           
                           ⁢ 
                           
                             A 
                             i 
                           
                         
                       
                       ) 
                     
                     + 
                     
                       ρ 
                       ⁢ 
                           
                       c 
                       ⁢ 
                           
                       n 
                       ⁢ 
                           
                       V 
                     
                   
                 
               
               
                 
                   ( 
                   20 
                   ) 
                 
               
             
           
         
       
     
     Equation (19) presents the rate of heat transfer q Total  at a given instant in time. Instantaneous heat transfer can be converted to total heat transfer over time Q Δt   Total  by adding a time subscript to the temperature variables and integrating over time. UA Total  is constant over time. Integrating Equation (19), with UA Total  factored out, results in:
 
 Q   Δt   Total   =UA   Total ∫ t     0     t     0     +Δt ( T   t   Indoor   −T   t   Outdoor ) dt    (21)
 
     Equation (21) can be used in several ways. One common application of the equation is to calculate annual fuel requirements for space heating. Building occupants typically desire to maintain a fixed indoor temperature during the summer and a different fixed indoor temperature during the winter. By the same token, building operators typically want to determine the costs of maintaining these desired indoor temperatures. 
     For example, take the case of maintaining a fixed indoor temperature during the winter. Let the temperature be represented by T Indoor-Set Point Temp  and let Δt equal one year. Equation (21) can be modified to calculate the annual heat loss Q Annual   Heat Loss  by adding a maximum term, such that:
 
 Q   Annual   Heat Loss   =UA   Total ∫ t     0     t     0     +Δt  max( T   t   Indoor-Set Point Temp   −T   t   Outdoor ,0) dt    (22)
 
Solving Equation (22) yields:
 
 Q   Annual   Heat Loss   =UA   Total (24*HDD Indoor-Set Point Temp )   (23)
 
where HDD represents the number of degree days when the outdoor temperature exceeds the desired indoor temperature. A typical indoor temperature used to calculate HDD is 65° F.
 
     Equation (23) is a widely-used equation to calculate annual heat loss. UA Total  is the core, building-specific parameter required to perform the calculation. UA Total  represents the building&#39;s overall thermal performance, including heat loss through both the building envelope through conduction and heat loss through infiltration. 
     Conventional practice requires an energy audit to determine UA Total , which requires recording physical dimension, visually inspecting or inferring R-values, and performing a blower door test. A formal energy audit can require many hours and can be quite expensive to perform. However, UA Total  can be empirically derived. 
     In slightly modified form, Equation (21) can be used to calculate Heating (or Cooling) Degree Days for estimating fuel costs for a one-year period by assuming that the indoor temperature is constant. The equation can also be used to calculate short-term heat loss, as part of an input to an empirical approach to deriving a building&#39;s overall thermal performance UA Total    FIG.  4    is a flow diagram showing method for empirically estimating overall thermal performance of a building  60  through a short-duration controlled test, in accordance with one embodiment. The method  60  requires the use of a controllable heating (or cooling) source, and the measurement and analysis aspects of the method  60  can be implemented in software. Execution of the software can be performed with the assistance a computer system, such as further described infra with reference to  FIG.  29   , as a series of process or method modules or steps. 
     Briefly, the empirical approach is to perform a controlled test over a short duration, for instance, 12 hours. During the controlled test, heat loss from a building occurs and a controllable heat source, such as a furnace, is subsequently used to compensate for the heat loss. Preferably, the controlled test is performed during the winter months. The same controlled test approach can be used during the summer months, where heat gain occurs and a controllable cooling source, such as an air conditioner, is subsequently used to compensate for the heat gain. 
     As a preliminary step, an appropriate testing period is chosen, during which heat gain is controllable, such as during the night, when solar gain will not be experienced.  FIG.  5    is a graph depicting, by way of example, the controlled, short-duration test of  FIG.  4   . The x-axis  81  represents time of day. The y-axis  82  represents temperature in ° F. The testing period is divided into an unheated period that occurs from time t 0  to time t 1 , a heated period that occurs from time t 1  to time t 2 , and a stabilizing period that occurs from time t 2  to time t 3 . At a minimum, indoor temperature  83  is measured at times t 0 , t 1 , and t 3 , although additional indoor temperature measurements will increase the accuracy of the controlled test. Outdoor temperature  84  may optionally be measured at times t 0  and t 3  and additional outdoor temperature measurements will also increase the controlled test&#39;s accuracy. Additionally, an expected final indoor temperature  85  is estimated based on a projection of what the indoor temperature would have been at time t 3 , had the heating source not been turned back on at time t 1 . 
     The starting time t 0  of the unheated period should start when the indoor temperature has stabilized due to the effects of thermal mass. The unheated period is of a duration sufficient to allow for measurable heat loss, such as a period of around 12 hours, although other periods of time are possible. The heating source is run for a short duration during the heated period, such as for an hour or so, preferably early in the morning before the sun rises. The stabilizing period provides a time lag for a short duration, such as an hour or so, to allow the indoor temperature to stabilize due to the effects of thermal mass. Other factors can be included in the controlled test, such as heat gain from occupants or other heat sources inside the building. 
     Referring back to  FIG.  4   , a baseline indoor temperature T 0  is recorded at the outset of an unheated period at time t 0  (step  61 ), at which time operation of the heating source is also stopped (step  62 ). The method pauses during the unheated period from time t 0  to time t 1  (step  63 ). A starting indoor temperature T 1  is recorded at the outset of a heated period at time t 1  (step  64 ), at which time operation of the heating source is also temporarily resumed (step  65 ). The method pauses during the heated period from time t 1  to time t 2  (step  66 ). Operation of the heating source is again stopped at the end of the heated period at time t 2  (step  67 ). The method pauses during a stabilizing period from time t 2  to time t 3  (step  68 ). A final indoor temperature T 3  is recorded at the end of a stabilizing period at time t 3  (step  69 ). 
     Next, the amount of energy consumed over testing period from time t 0  to time t 3  is measured (step  70 ). The energy is assumed to equal the total amount of heat gained inside the building from internal sources of heat (Q Internal ); inclusion of independent sources of heat gain, such as from occupants, will increase accuracy. Finally, the overall thermal performance of the building UA Total  and distribution efficiency are estimated (step  71 ), as follows. 
     First, the heat loss over the unheated period from time t 0  to time t 1  is calculated, that is, by setting Δt to around 12 hours. Solving Equation (21) yields:
 
 Q   Δt   Total   =UA   Total (   T   Δt   Indoor   −   T   Δt   Outdoor   )Δ t    (24)
 
where  T Δt   Indoor    is the average indoor temperature and  T Δt   Outdoor    is the average outdoor temperature.
 
     Next, the heat gain by operating the heating source over the heated period from time t 1  to time t 2  is calculated using Equation (8). The amount of energy required to return the building to the baseline indoor temperature T 0  can be approximated by dividing the delivered heat by the percent of heat loss that was restored using the controlled heat source. The amount of heat restored is assumed to be proportional to three temperatures, the baseline indoor temperature T 0 , the final indoor temperature T 3 , and an expected final indoor temperature T 3   No Heat  which is an estimated temperature based on a projection of what the indoor temperature would have been at time t 3 , had the heating source not been turned back on at time t 1 . Assuming that T 0 ≠T 3   No Heat , the percentage of energy lost provided by the heat source equals: 
     
       
         
           
             
               
                 
                   
                     Percent 
                     ⁢ 
                         
                     Restored 
                   
                   = 
                   
                     
                       
                         T 
                         3 
                       
                       - 
                       
                         T 
                         3 
                         
                           No 
                           ⁢ 
                               
                           Heat 
                         
                       
                     
                     
                       
                         T 
                         0 
                       
                       - 
                       
                         T 
                         3 
                         
                           No 
                           ⁢ 
                               
                           Heat 
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   25 
                   ) 
                 
               
             
           
         
       
     
     The hours of operation of the heating source equal t 2  minus t 1 . Thus, the heat gain required to replace the lost heat equals Equation (8) divided by Equation (25), expressed as: 
     
       
         
           
             
               
                 
                   
                     Q 
                     
                       Heat 
                       ⁢ 
                           
                       Delivered 
                       - 
                       Furnace 
                     
                   
                   = 
                   
                     
                       ( 
                       
                         R 
                         Furnace 
                       
                       ) 
                     
                     ⁢ 
                     
                       ( 
                       
                         
                           η 
                           Furnace 
                         
                         ⁢ 
                         
                           η 
                           Delivery 
                         
                       
                       ) 
                     
                     ⁢ 
                     
                       ( 
                       
                         
                           t 
                           2 
                         
                         - 
                         
                           t 
                           1 
                         
                       
                       ) 
                     
                     ⁢ 
                     
                       ( 
                       
                         
                           
                             T 
                             3 
                           
                           - 
                           
                             T 
                             3 
                             
                               No 
                               ⁢ 
                                   
                               Heat 
                             
                           
                         
                         
                           
                             T 
                             0 
                           
                           - 
                           
                             T 
                             3 
                             
                               No 
                               ⁢ 
                                   
                               Heat 
                             
                           
                         
                       
                       ) 
                     
                   
                 
               
               
                 
                   ( 
                   26 
                   ) 
                 
               
             
           
         
       
     
     In addition, heat was gained inside the building from internal sources of heat. Set Equation (33) plus heat delivered through internal gains Q Internal  equal to Equation (24) and solve for overall thermal performance UA Total : 
     
       
         
           
             
               
                 
                   
                     UA 
                     Toal 
                   
                   = 
                   
                     
                       
                         [ 
                         
                           
                             
                               
                                 
                                   
                                     ( 
                                     
                                       R 
                                       Furnace 
                                     
                                     ) 
                                   
                                   ⁢ 
                                   
                                     ( 
                                     
                                       η 
                                       Furnace 
                                     
                                     ) 
                                   
                                   ⁢ 
                                   
                                     ( 
                                     
                                       η 
                                       Delivery 
                                     
                                     ) 
                                   
                                 
                               
                             
                             
                               
                                 
                                   
                                     ( 
                                     
                                       
                                         t 
                                         2 
                                       
                                       - 
                                       
                                         t 
                                         1 
                                       
                                     
                                     ) 
                                   
                                   ⁢ 
                                   
                                     ( 
                                     
                                       
                                         T 
                                         0 
                                       
                                       - 
                                       
                                         T 
                                         3 
                                         
                                           No 
                                           ⁢ 
                                               
                                           Heater 
                                         
                                       
                                     
                                     ) 
                                   
                                 
                               
                             
                           
                           
                             ( 
                             
                               
                                 T 
                                 3 
                               
                               - 
                               
                                 T 
                                 3 
                                 
                                   No 
                                   ⁢ 
                                       
                                   Heater 
                                 
                               
                             
                             ) 
                           
                         
                         ] 
                       
                       + 
                       
                         Q 
                         Internal 
                       
                     
                     
                       
                         ( 
                         
                           
                             
                               T 
                               
                                 Δ 
                                 ⁢ 
                                 t 
                               
                               Indoor 
                             
                             _ 
                           
                           - 
                           
                             
                               T 
                               
                                 Δ 
                                 ⁢ 
                                 t 
                               
                               Ambient 
                             
                             _ 
                           
                         
                         ) 
                       
                       ⁢ 
                       
                         ( 
                         
                           
                             t 
                             3 
                           
                           - 
                           
                             t 
                             0 
                           
                         
                         ) 
                       
                     
                   
                 
               
               
                 
                   ( 
                   27 
                   ) 
                 
               
             
           
         
       
     
     The controlled test approach has been empirically validated. The testing procedure was conducted at approximately the same time of day on two separate days with different weather conditions for a house in Napa, Calif. The first test was started on Jan. 12, 2014 and the second test was started on Jan. 13, 2014. There was a difference of about 15° F. in outdoor temperature at the start of the testing on the two days. In addition, the heating source was only operated for the amount of time necessary to return the house to the baseline temperature for the first test, while the heating source was not operated for a sufficiently long time to return the house to the baseline temperature for the second test. The recorded indoor and outdoor temperatures for the test conducted on Jan. 12, 2014 is shown in  FIG.  5   . Similarly,  FIG.  6    is a graph depicting, by way of example, the controlled, short-duration test of  FIG.  4    for Jan. 13, 2014. As before, the x-axis represents time of day and the y-axis represents temperature in ° F. Assuming an 80% delivery efficiency η Delivery  results indicate that the house&#39;s overall thermal performance UA Total  was 525 for the first test and 470 for the second test. These results are within approximately 10 percent of each other. In addition, an independent Certified Home Energy Rating System (HERS) rater was hired to perform an independent energy audit of the house. The results of the HERS audit compared favorably to the results of the empirical approach described supra with reference to  FIG.  4   . 
     The methods described herein can be used to equip consumers with the kinds of information necessary to make intelligent energy decisions. An example of how to apply the results to a particular situation will now be presented. 
     Example: A residential homeowner has an old heating, ventilation, and air conditioning (HVAC) system that is on the verge of failure. The consumer is evaluating two options: 
     Option 1: Replace the existing HVAC system with a system that has the same efficiency and make no other building envelope investments in the house, at the cost of $9,000. 
     Option 2: Take advantage of a whole house rebate program that the consumer&#39;s utility is offering and simultaneously upgrade multiple systems in the house. The upgrades include increasing ceiling insulation, replacing ductwork, converting the natural gas-powered space heating furnace and electric air conditioner to electric-powered air source heat pumps, and providing enough annual energy to power the heat pump using a photovoltaic system. 
     In this example, the following assumptions apply:
         The consumer&#39;s annual natural gas bill is $600, 60 percent of which is for space heating. The natural gas price is $1 per therm.   The existing furnace has an efficiency of 80 percent and the existing ductwork has an efficiency of 78 percent.   Adding four inches of insulation to the 1,100 ft 2  ceiling, to increase the R-Value from 13 to 26, will cost $300.   Photovoltaic power production costs $4,000 per kW DC , produces 1,400 kWh/kW DC -yr, and qualifies for a 30-percent federal tax credit.   The heat pump proposed in Option 2 has a Heating Season Performance Factor (HSPF) of 9 Btu/Wh and a Seasonal Energy Efficiency Ratio (SEER) identical to the existing air conditioner. The heat pump will cost $10,000.   The ductwork proposed in Option 2 will be 97 percent efficient and will cost $3,000.   The consumer will receive a $4,000 rebate from the utility for the whole house upgrade under Option 2.       

     Analysis of the options requires determining the overall thermal characteristics of the existing building, evaluating the effects of switching fuel sources, comparing furnace efficiency, and determining fuel requirements. For purposes of illustration, the calculation in the example will only include the heating characteristics. 
     In this example, the consumer performed the empirical approach described supra with reference to  FIG.  4    to empirically estimate overall thermal performance of a building and determined that the UA Total  for his house was 450. Option 2 presents multiple changes that need to be considered. First, Option 2 would require switching fuels from natural gas to electricity. Assume conversion factors of 99,976 Btu per therm and 3,412 Btu per kWh. Converting current energy usage, as expressed in therms, to an equivalent number of kWh yields: 
     
       
         
           
             
               
                 
                   
                     Q 
                     F 
                   
                   = 
                   
                     
                       
                         ( 
                         
                           600 
                           ⁢ 
                               
                           thems 
                         
                         ) 
                       
                       ⁢ 
                       
                         ( 
                         
                           
                             99 
                             , 
                             976 
                             ⁢ 
                                 
                             Btu 
                           
                           therm 
                         
                         ) 
                       
                       ⁢ 
                       
                         ( 
                         
                           
                             1 
                             ⁢ 
                                 
                             kWh 
                           
                           
                             3 
                             , 
                             412 
                             ⁢ 
                                 
                             Btu 
                           
                         
                         ) 
                       
                     
                     = 
                     
                       17 
                       , 
                       581 
                       ⁢ 
                           
                       kWh 
                     
                   
                 
               
               
                 
                   ( 
                   28 
                   ) 
                 
               
             
           
         
       
     
     Second, the heat pump is 264 percent efficient at converting electricity to heat. The equivalent furnace efficiency {circumflex over (η)} Furnace  of the heat pump is: 
     
       
         
           
             
               
                 
                   
                     
                       η 
                       ^ 
                     
                     Furnace 
                   
                   = 
                   
                     
                       
                         ( 
                         
                           
                             9 
                             ⁢ 
                                 
                             Btu 
                           
                           Wh 
                         
                         ) 
                       
                       ⁢ 
                       
                         ( 
                         
                           
                             1 
                             , 
                             000 
                             ⁢ 
                                 
                             Wh 
                           
                           kWh 
                         
                         ) 
                       
                       ⁢ 
                       
                         ( 
                         
                           
                             1 
                             ⁢ 
                                 
                             kWh 
                           
                           
                             3 
                             , 
                             412 
                             ⁢ 
                                 
                             Btu 
                           
                         
                         ) 
                       
                     
                     = 
                     
                       264 
                       ⁢ 
                       % 
                     
                   
                 
               
               
                 
                   ( 
                   29 
                   ) 
                 
               
             
           
         
       
     
     Third, the annual amount of electricity required to power the heat pump can be determined with Equation (42), as further described infra, with the superscript changed from ‘F’ (for natural gas fuel) to ‘E’ (for electricity): 
     
       
         
           
             
               
                 
                   
                     
                       
                         
                           
                             Q 
                             ^ 
                           
                           
                             E 
                             - 
                             Heating 
                           
                         
                         = 
                           
                         
                           
                             ( 
                             0.6 
                             ) 
                           
                           ⁢ 
                           
                             
                               ( 
                               
                                 17 
                                 
                                   , 
                                   TagBox[&#34;,&#34;, &#34;NumberComma&#34;, Rule[SyntaxForm, &#34;0&#34;]] 
                                 
                                 581 
                               
                               ) 
                             
                             [ 
                             
                               1 
                               - 
                               
                                 
                                   
                                     ( 
                                     
                                       
                                         1 
                                         13 
                                       
                                       - 
                                       
                                         1 
                                         26 
                                       
                                     
                                     ) 
                                   
                                   ⁢ 
                                   
                                     ( 
                                     
                                       1 
                                       
                                         , 
                                         TagBox[&#34;,&#34;, &#34;NumberComma&#34;, Rule[SyntaxForm, &#34;0&#34;]] 
                                       
                                       100 
                                     
                                     ) 
                                   
                                 
                                 450 
                               
                             
                             ] 
                           
                           ⁢ 
                           
                             ( 
                             
                               0.8 
                               2.64 
                             
                             ) 
                           
                           ⁢ 
                              
                           
                             ( 
                             
                               0.78 
                               0.97 
                             
                             ) 
                           
                         
                       
                     
                   
                   
                     
                       
                         = 
                           
                         
                           2 
                           
                             , 
                             TagBox[&#34;,&#34;, &#34;NumberComma&#34;, Rule[SyntaxForm, &#34;0&#34;]] 
                           
                           351 
                           ⁢ 
                               
                           kWh 
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   30 
                   ) 
                 
               
             
           
         
       
     
     Fourth, in addition to switching from natural gas to electricity, the consumer will be switching the source of the fuel from utility-supplied electricity to on-site photovoltaic power generation. The number of kW DC  of photovoltaic power required to provide 2,329 kWh to power the heat pump can be found as: 
                     PV   ⁢         Capacity   ⁢         Required     =         2     ,   TagBox[&#34;,&#34;, &#34;NumberComma&#34;, Rule[SyntaxForm, &#34;0&#34;]]     351   ⁢         kWh   /   yr       1     ,   TagBox[&#34;,&#34;, &#34;NumberComma&#34;, Rule[SyntaxForm, &#34;0&#34;]]     400   ⁢         kWh   /   yr       =     1.68           kW     D   ⁢   C                   (   31   )               
Expected photovoltaic production can be forecast, such as described in commonly-assigned U.S. Pat. Nos. 8,165,811; 8,165,812; 8,165,813, all issued to Hoff on Apr. 24, 2012; U.S. Pat. Nos. 8,326,535 and 8,326,536, issued to Hoff on Dec. 4, 2012; U.S. Pat. No. 8,335,649, issued to Hoff on Dec. 18, 2012; U.S. Pat. No. 8,437,959, issued to Hoff on May 7, 2013; U.S. Pat. No. 8,577,612, issued to Hoff on Nov. 5, 2013; and U.S. patent application Ser. No. 14/058,121, filed Oct. 18, 2013, pending, the disclosures of which are incorporated by reference.
 
     Finally, as shown in Table 1, Option 2 will cost $14,025. Option 1 is the minimum unavoidable cost of the two options and will cost $9,000. Thus, the net cost of Option 2 is $5,025. In addition, Option 2 will save $360 per year in natural gas bills because 60-percent of the $600 natural gas bill is for space, which represents a cost avoided. As a result, Option 2 has a 14-year payback. 
     
       
         
           
               
               
               
               
             
               
                 TABLE 1 
               
               
                   
               
               
                   
                   
                   
                 Combined 
               
               
                 Item 
                 Cost 
                 Incentive 
                 Cost 
               
               
                   
               
             
            
               
                 Increasing Ceiling Insulation 
                   $300 
                   
                   
               
               
                 Replace Ductwork 
                  $3,000 
                   
                   
               
               
                 Electric-Powered Air Source Heat 
                 $10,000 
                   
                   
               
               
                 Pump (Added Cost) 
                   
                   
                   
               
               
                 Photovoltaic Power Generation (1.68 
                  $6,720 
                   
                   
               
               
                 kW DC  @ $4,000 per kW DC ) 
                   
                   
                   
               
               
                 Tax Credit for Photovoltaic Power 
                   
                 ($1,995) 
                   
               
               
                 Generation 
                   
                   
                   
               
               
                 Utility-Offered Whole House Rebate 
                   
                 ($4,000) 
                   
               
               
                 Total 
                 $20,020 
                 ($5,995) 
                 $14,025 
               
               
                   
               
            
           
         
       
     
     A building&#39;s overall thermal performance can be used to quantify annual energy consumption requirements by fuel type. The calculations described supra assumed that energy prices did not vary with time of day, year, or amount of energy purchased. While this assumption is approximately correct with natural gas and gasoline consumption, electricity prices do vary, with electric rate structures often taking into consideration time of day, year, amount of energy purchased, and other factors. 
     Overall thermal performance, annual fuel consumption, and other energy-related estimates can be combined with various data sets to calculate detailed and accurate fuel consumption forecasts, including forecasts of electric bills. The fuel consumption forecasts can be used, for instance, in personal energy planning of total energy-related costs C Total , as well as overall progress towards ZNE consumption.  FIG.  7    is a screen shot showing, by way of example, the graphical user interface (GUI)  90  of an energy investment choices analysis tool. Total energy-related costs C Total  include electricity cost (C E ), fuel for heating cost (C F ), gasoline (or other automobile fuel) cost (C G ), and maintenance cost (C M ), as described supra with reference to Equation (1), or for other energy planning purposes. Through the upper section  91  of the GUI  90 , a user can select current and planned energy-related equipment and parameters. As applicable, the equipment and parameters are evaluated in light of current energy data, including consumption data, building thermal characteristics, and historical solar resource and weather data, from which proposed energy data can be generated as investment analysis results in the lower section  92  of the GUI  90 . 
     For instance, in the lower left-hand corner, current  93 , proposed  94 , and proposed after PV  95  energy consumption statistics are provided. These energy consumption statistics reflect energy costs incurred for transportation, space heating, water heating, and other electrical devices, such as lighting, appliances, and electrical devices. In addition, net energy consumption  96 , which is net electricity consumption based only upon the energy purchased from the power utility, that is, provided from a source external to the building, and proposed photovoltaic power production  97 , are provided, albeit in a traditional “before” and “after” manner, where current energy consumption  93  is first improved through increased energy efficiencies, as reflected by the proposed energy consumption  94 , and later improved through the addition of on-site photovoltaic power generation  95 . Utility-provided net energy consumption  96  statistics, though, can mask the overall efficiency of a building, particularly where on-site power generation has been installed first, as further described infra beginning with  FIG.  10    et seq. Where photovoltaic power generation has already been installed, current energy consumption  93  would instead include both net energy consumption  96  and (already-installed) photovoltaic power production  97  to yield a combined indication of gross energy consumption upon which other types of energy investment choices, such as replacing a gasoline-fueled vehicle with an electrical vehicle, can be considered in the proper context of overall energy consumption. 
     The forecasts can be used to accurately model one or more energy-related investment choices, in terms of both actual and hypothesized energy consumption and, in some cases, on-site energy production. The energy investment choices analysis tool described with reference to  FIG.  7    can be implemented through software.  FIG.  8    is a process flow diagram showing a computer-implemented method  100  for evaluating potential energy investment scenarios from a user&#39;s perspective, in accordance with one embodiment. Execution of the software can be performed on a computer system, such as further described infra with reference to  FIG.  29   , as a series of process or method modules or steps. The user interactively inputs energy-related investment selections and can view analytical outputs through a graphical user interface. 
     As an initial step, using the GUI  90 , a user makes selections  101  of energy-related equipment investments and parameters in the form of energy-consuming or (on-site) energy-producing equipment that are currently owned or that are under consideration for acquisition. The analysis tool helps the user to explore the various aspects of the total energy-related costs C Total  in terms of price and quantity, as described supra with reference to Equation (2). If the user is interested in just determining incurred capital cost or forecasting an electric bill, the user need only enter information about existing equipment. If an energy equipment investment is being considered, the user will need to select both the equipment currently in use and the equipment proposed to replace or upgrade the current equipment. Note that the term “equipment” as used in the context of the analysis tool non-exclusively includes multi-component systems, machinery, fixtures, appliances, and building structure, materials and components, any of which could form the basis of an energy-related investment. Additionally, the term “parameters” refers to aspects of an investment related more to operational use, than to the nature of the equipment proper. For instance, energy consumption of a fixture, such as lighting, may be reduced by parametrically decreasing the hours of operation, in addition to (or in lieu of) choosing a more energy-efficient form of lighting fixture. 
     A pair of databases respectively store listings of equipment  104  and their prices  105 . The two databases  104 ,  105  could be combined into a single database. In addition, the information stored in the two databases  104 ,  105  is expected to be continually evolving and can be supplemented or revised with new data through automatic or manual updates, which allows the analysis tool to model personal energy-related equipment that is new to the market and other kinds of changes. 
     Each listing in the equipment database  105  lists a type of equipment and the type of fuel used, including, for example, electricity, heating gas or oil, gasoline (or diesel), or solar. The user makes selections of equipment for both current and proposed personal equipment investments. Each equipment listing also includes energy-related characteristics, including classifying each listed equipment as affecting one or more of personal electricity cost, heating cost, transportation cost, or maintenance cost; and an energy affect that can be quantitatively expressed as measures of one or more of personal energy-consumption, energy-conservation, or (on-site) energy-production. For instance, a non-EV (electric vehicle) car consumes gasoline (or diesel) and the energy affect can be expressed as average miles per gallon. The annual or periodic cost of fuel can thus be projected by multiplying annual or periodic mileage by the average miles per gallon. Note that some types of equipment neither consume nor produce energy, such as different kinds of building envelope investments, which indirectly conserve energy by preventing infiltration of ambient conditions. However, their energy-related affect can be indirectly expressed based on insulative contributions to a building envelope, from which a cost (or savings) can be derived. As well, each equipment listing specifies energy-related and general characteristics that include, as applicable, name; model number; model year; fuel type: and energy (fuel) consumption, conservation or production characteristics, operational parameters, and other related performance specifications. Equipment information for energy investments that specifically affect building envelope, furnace, and heat delivery and suitable for use in the equipment database  105  is described infra with reference to  FIG.  9   . Other equipment information could also be included in each listing. The equipment database  105  can include:
         1. Electricity-related equipment investments, including lighting, appliances, and other devices that consume electricity.   2. Building envelope equipment investments, including windows, window shades, ceiling and wall insulation, radiant barriers, roof ridge vents, and other fixtures that conserve energy within a building envelope.   3. Space conditioning equipment investments, including natural gas furnaces, air conditioning units, heat pumps, stand-alone heaters, and other units that consume energy for space conditioning.   4. Water heating equipment investments, which can either be units that consume energy or conserve energy for heating water.   5. Vehicle and transportation equipment investments, which can be conveyances or use of conveyances that consume energy for transportation, conserve energy for transportation, or both, as in the case of a hybrid automobile.   6. On-site energy producing equipment investments relating to source of electricity, including photovoltaic power generation, or, less commonly, small wind, small hydroelectric, or other distributed or standalone power generation technologies, all of which produce electricity.
 
Other types of equipment are possible.
       

     Each listing of price in the equipment prices database  105  corresponds to a listing of equipment in the equipment database  105  and includes, as applicable, cost of acquisition, whether by purchase, lease, rental, or other form; installation cost; maintenance cost; costs of ownership, such as annual registration, emissions compliance, and taxes; rebates, discounts, or other incentives; and, optionally, current valuation, such as depreciated value, residual value, resale value, trade-in value, or salvage value. Other price information could also be included. 
     Based upon the types of energy-related investments selected, up to three sets of current data  102  may be maintained. First, for all investments, current electricity, fuel, and gasoline consumption data  106  are collected for each equipment selection  101  for a recent time period, which will generally be for the past year. The consumption data  106  is formed into time series, which is particularly important for electricity and fuel, specifically, fuel used for space conditioning and water heating. The source, quantity, and type of consumption data will depend upon the nature of the equipment selection. For instance, net electricity consumption is available from power utility bills, although the amount of electricity consumed for a particular purpose, such as space or water heating, would need to be identified or estimated from net consumption. In a further embodiment, where a consumer has already made a switch to an alternative energy source (or knows with specificity the expected amount of energy to be provided by an alternative energy source), such as on-site photovoltaic power generation, the net electricity consumption data is combined with on-site power generation (and consumption) to yield gross energy load, as further described infra with reference to  FIG.  17   . Fuel consumption depends upon the form of delivery. Bulk fuels, such as heating oil, are delivered en masse to an on-site tank; for analysis purposes, consumption can be equated to amount purchased. Consumption of metered fuels, like natural gas, is also available from fuel bills and, like electricity, use for a specific purpose, may need to be identified or estimated, such as described supra with reference to Equation (10) for the case of fuel for space heating. Gasoline (or diesel) consumption can be estimated by dividing annual miles driven by average miles per gallon, or similar metric. 
     Second, when the proposed energy investments relate to changes to the building&#39;s thermal envelope, the thermal characteristics  107  of the building are collected. The overall thermal properties of a building (UA Total ) may already be available from an energy audit, or could be determined using the empirical approach described supra with reference to  FIG.  4   . 
     Third, when the proposed energy investments relate to on-site energy production, historical solar resource, if photovoltaic energy production is being considered, and weather data  108  are collected for the same recent time period as the consumption data  106 . In addition, if necessary, the historical solar resource and weather data  108  are converted into time series using the same time resolution as applicable to the consumption data  106 . Weather data can be obtained from weather reporting services. Solar resource data is discussed in further detail infra. The equipment selections  101  are combined with the current data  102  to generate proposed data  103  for indicating annual consumption  109 , by fuel type, which are calculated for both the equipment currently in use and the equipment proposed for use to replace or upgrade the current equipment. Fuel consumption and gasoline (or diesel) consumption are converted into electricity-equivalent units, as further described infra. The electricity consumption time series data is submitted to a bill calculator  110  and is combined with electric rate structure information to calculate an estimated annual cost  112 . The estimated annual cost  112  is combined with the electricity-equivalent units to forecast a total annual cost, and the initial capital cost is compared to the total annual cost to determine an estimated system payback  113 . 
     From a non-technical person&#39;s perspective, a sufficient amount of information is presented in a single screen to help a consumer in making informed energy investment decisions.  FIG.  9    is a detail of the GUI  90  of  FIG.  7    showing, by way of example, an annotated graph  120  of power consumption. The x-axis  121  represents time. They-axis  122  represents power, expressed in kW. Both current power consumption  123 , which is limited to net electricity consumption based only upon the energy purchased from the power utility, that is, provided from a source external to the building, and proposed power consumption  124 , following the implementation of energy efficiencies and installation of on-site photovoltaic power generation, are depicted, respectively based on the electricity demand profiles for the current and proposed investments. Proposed power consumption  124  reflects the effect of electric vehicle (“EV”) charging; operation of water and space heating pumps; efficiency investments in the form of load reduction achieved by replacing existing constant load, “Always On” electric devices with more energy efficient electric devices and modifying operating schedule parameters; and fuel switching from natural gas, supplemented with on-site photovoltaic power generation. 
     Power utilities and energy agencies have become increasingly proactive in assisting their customers with making informed energy investment decisions and by urging their customers to lower their energy consumption through improved efficiency and adoption of renewable energy sources. To help educate customers, they often provide periodic energy consumption statistics, which reflect the net energy purchased from the utility.  FIG.  10    is a graph showing, by way of example, monthly net energy consumption statistics  130 . The x-axis  131  represents months and the y-axis  132  represents electricity consumption, expressed in kilowatt hours (kWh). Net electricity usage  133  is plotted for each month. Net electricity usage  133  represents energy purchased from a power utility, which invariably implies energy provided from a source external to the building, as opposed to energy generated (and consumed) on-site. Frequently, such monthly net energy consumption statistics are provided by power utilities or energy agencies to their customers through informational Web sites and printed form. In this Web page example, a pull down menu enables a user to view electricity consumption by utility bill  134 , which also corresponds to each month of consumption over the past twelve months. Other types of user input controls are possible. Here, the energy consumer both purchases electricity from a power utility and generates electricity on-site with a photovoltaic power generation system. The net usage  133 , though, only reflects the net amount of energy purchased from the power utility; energy generated (and consumed) on-site is implicitly included in the monthly net energy consumption statistics by virtue of a lowering of the amount of energy purchased. 
     The effect of implicitly including on-site energy generation can be misleading to the consumer because the monthly net energy consumption statistics only provide a partial picture of total energy consumption. The consumption of energy generated on-site decreases the net amount of energy that must be purchased from the utility, yet based on the utility&#39;s periodic energy consumption statistics, the consumer remains unaware of how much on-site energy was consumed during the same reporting period. Inefficiencies in home energy consumption are effectively masked from view. Here, during the late spring through early fall months, photovoltaic power generation contributes significantly to the gross energy available for home consumption, which creates negative net usage  133 . During the winter months, energy consumption reflects a substantial seasonal increase, which, in most cases, could be expected, as heating fixtures, specifically, furnaces, will consume significant amounts of energy, while photovoltaic power generation can suffer a seasonal decline in output. 
     Such periodic energy consumption statistics can send a mixed message. If a consumer sees a lowered monthly energy bill, the consumer may believe that they have succeeded in lowering their energy consumption. However, a lower monthly energy bill may not necessarily be due to improved efficiency in those situations where the consumer has also implemented an on-site renewable energy source that lowers a consumer&#39;s dependence on utility-supplied energy, and thus lowers their monthly energy bill. 
     Monthly net energy consumption bins together daily electricity use into approximately 30-day intervals. Finer-grained energy consumption statistics can help a consumer better identify energy wasting habits.  FIG.  11    is a graph showing, by way of example, average daily net energy consumption statistics  135 , including on-site photovoltaic power generation. The x-axis  136  represents months and they-axis  137  represents average daily electricity consumption, expressed in kilowatt hours per day (kWh/day). Average daily net electricity usage  138  is plotted for each month with energy generated on-site included. In this Web page example, the pull down menu enables the user to view electricity consumption by average day  139 . Here, net usage  138  shows scaled down negative net usage during the late spring to early fall months as the energy consumption requirements of the building are met (and exceeded) by the on-site photovoltaic power generation. A similarly scaled down increase in net energy consumption occurs during the winter months. 
     With only monthly net energy purchases reflected, the net usage  133  may create a misperception that a home is energy efficient, as other forms of inefficiencies, such as large “vampire” loads, are effectively disguised. (Vampire loads refer to the electricity consumed by appliances while they are switched off or in a standby mode. For example, a remote control receiver or a text or light display still consumes electricity, even though the appliance is turned off and not performing its primary function.)  FIG.  12    is a graph showing, by way of example, average daily gross energy consumption statistics  140 , excluding on-site photovoltaic power generation. The x-axis  141  represents months and the y-axis  142  represents average daily electricity consumption, expressed in kilowatt hours per day (kWh/day). Average daily gross energy load  143  is plotted for each month. In this Web page example, a pair of pushbuttons  144  enable the user to view electricity consumption by either net load  145 , which includes on-site photovoltaic power generation, or gross load  146  (selected). Other types of user input controls are possible. Gross energy load  143  combines both the net energy purchased from the power utility and estimated net energy generated (and consumed) on-site by photovoltaic power generation, as further described infra with reference to  FIG.  17   . Here, the difference between the lowest and highest average daily net load is only about five kWh/day, yet peak average usage occurs in the winter, as expected, as well as in June and August. Depiction of the gross energy load  143  shows that energy consumption is fairly consistent throughout the year, particularly when the slightly higher energy consumptions caused by summertime cooling and wintertime heating are factored out. The true average daily energy consumption is exposed, and the need to make improvements in energy conservation are more readily understood by the consumer, especially as the contributions to gross energy load attributable to on-site photovoltaic power generation as opposed to utility-supplied energy do little to lower the overall amount of energy consumed, independent of seasonal changes in power generation output. 
     The average daily gross energy consumption statistics, such as shown in  FIG.  12   , can be supplemented with energy investment planning tools, such as shown in  FIG.  7   , to help customers find ways to improve their energy efficiency, which can be particularly persuasive when provided to a customer through an interactive informational Web site.  FIG.  13    is a graph showing, by way of example, average daily gross energy consumption statistics  147 , excluding on-site photovoltaic power generation with light emitting diode (LED) lighting fixtures and lighting usage reduction. The x-axis  148  represents months and the y-axis  149  represents average daily electricity consumption, expressed in kilowatt hours per day (kWh/day). Average daily gross energy load  150  is plotted for each month. In this Web page example, a pair of option boxes  151  enable the user to view electricity consumption with an electric vehicle (EV)  152  in place of a gasoline-powered vehicle and light emitting diode (LED) fixtures in place of conventional lighting, plus energy usage pattern reductions  153  (selected). Other types of user input controls are possible. Here, switching to LED fixtures and reducing energy consumption by turning off unnecessary lights and curtailing wasteful habits decreases average daily electricity by about ten kWh/day, which amounts to an average decrease of about 50% per day. 
     Overall energy consumption can be decreased by replacing inefficient forms of transportation with electric-powered vehicles.  FIG.  14    is a graph showing, by way of example, average daily gross energy consumption statistics  154 , excluding on-site photovoltaic power generation with electric vehicle usage. The x-axis  155  represents months and they-axis  156  represents average daily electricity consumption, expressed in kilowatt hours per day (kWh/day). Average daily gross energy load  147  is plotted for each month. Although recharging an electric vehicle noticeably increases monthly electricity consumption, when viewed on a holistic level with respect to all forms of energy consumed annually, replacing a gasoline-powered vehicle with an electric vehicle actually saves a significant amount of energy annually, as further explained infra beginning with  FIG.  22   . 
     When the option boxes  151  for an electric vehicle  152  and light emitting diode fixtures, plus energy usage pattern reductions  153  are both selected, average daily gross energy load is only slightly higher than the gross energy load, such as shown in  FIG.  12   , without any energy conservation steps.  FIG.  15    is a graph showing, by way of example, average daily gross energy consumption statistics  158 , excluding on-site photovoltaic power generation with light emitting diode lighting fixtures, lighting usage reduction, and electric vehicle usage. The x-axis  159  represents months and the y-axis  160  represents average daily electricity consumption, expressed in kilowatt hours per day (kWh/day). Average daily gross energy load  161  is plotted for each month. The energy costs for recharging the electric vehicle are effectively absorbed by the light emitting diode fixtures and energy usage pattern reductions, while the costs of gasoline are entirely avoided. Finally,  FIG.  16    is a graph showing, by way of example, average daily net energy consumption statistics  158 , including on-site photovoltaic power generation with light emitting diode lighting fixtures, lighting usage reduction, and electric vehicle usage. The x-axis  159  represents months and the y-axis  160  represents average daily electricity consumption, expressed in kilowatt hours per day (kWh/day). Average daily net energy load  161  is plotted for each month. The differences in average daily load before switching to an electric vehicle and LED fixtures, plus improved energy usage patterns, such as shown in  FIG.  11   , and after are minimal. 
     Gross energy load is determined by combining net electricity consumption data, such as provided by a power utility or energy agency, with on-site power generation, such as photovoltaic power generation, as produced over the same time period.  FIG.  17    is a process flow diagram showing a routine  170  for estimating gross energy load for use in the method  100  of  FIG.  8   . The process is explained with reference to photovoltaic power generation and can be applied mutatis mutandis to other types or combinations of on-site renewable energy sources, including small wind, small hydroelectric, or other distributed power generation technologies. 
     Net load data is first obtained for a known time period (step  171 ). Typically, net load data is provided by a power utility or energy agency in increments of one month. Daily average net load can be estimated by taking an average of the net load data over a 30-day or other appropriate time period. 
     Photovoltaic production data is then simulated for the customer&#39;s location with the same time resolution as each point of net load data (step  172 ), whether based on monthly consumption, average daily consumption, or other consumptive time period. The simulation must be performed using time- and location-correlated solar resource data, as well as specific information about the orientation and other characteristics of the photovoltaic system, such as can be provided by the Solar Anywhere service (http://www.SolarAnywhere.com), a Web-based service operated by Clean Power Research, L.L.C., Napa, Calif. The operational specifications of the photovoltaic system may be available from the manufacturer or installer. Otherwise, the operational specifications can be inferred through evaluation of historical measured system production data and measured solar resource data, such as described in commonly-assigned U.S. Pat. No. 8,682,585, issued to Hoff on Mar. 25, 2014, or with net load data and measured solar resource data, such as described in commonly-assigned U.S. Pat. No. 9,880,230, Issued Jan. 30, 2018, the disclosures of which are incorporated by reference. The simulated photovoltaic production data can be normalized to a daily average by taking an average over the same 30-day (or other appropriate) time period as used with the net load data. 
     Briefly, the photovoltaic production data is simulated by first obtaining a time series of solar irradiance data for a set of locations representative of the geographic region within which the building is located. Each time series contains solar irradiance observations electronically recorded at fixed time intervals over successive time periods. The solar irradiance observations can include direct irradiance measured by a representative set of ground-based weather stations, which are assembled as point statistics as an average of all values of raw measured irradiance. The solar irradiance observations can also include inferred irradiance based on power statistics collected for existing photovoltaic systems. Apparent irradiance is inferred as area statistics based on a performance model selected for each of the systems and the time series of power statistics. Finally, the solar irradiance observations can include area solar irradiance observations based on a set of pixels from satellite imagery for the geographic region in which the building is located. The area solar irradiance statistics are first converted into irradiance statistics for an average point within the set of pixels and measured irradiance is determined as average point statistics as an average of all values of the set of pixels. Other sources of the solar irradiance data are possible. 
     Next, the solar irradiance data in the time series is converted over each of the fixed time intervals, such as at half-hour intervals, into a set of clearness indexes, which are calculated relative to clear sky global horizontal irradiance. The set of clearness indexes are interpreted as irradiance statistics. A time lag correlation coefficient for an output time interval can also be determined to enable the generation of an output time series at any time resolution, even faster than the input data collection rate. The time lag correlation coefficient captures the relationship between the power output by the photovoltaic system at one point of time and the power output by the photovoltaic system at one time interval later. 
     Finally, a time series of the power statistics for the photovoltaic system is generated as a function of the irradiance statistics and the photovoltaic system&#39;s operational specification, including power rating. The resultant high-speed time series performance data can be used to predictably estimate power output and photovoltaic production variability. 
     The high resolution time series of power output data is determined in the context of a photovoltaic fleet, whether for an operational fleet deployed in the field, by planners considering fleet configuration and operation, or by other individuals interested in photovoltaic fleet variability and prediction. Time series power output data for a photovoltaic fleet is generated using observed field conditions relating to overhead sky clearness. Solar irradiance relative to prevailing cloudy conditions in a geographic region of interest is measured. Direct solar irradiance measurements can be collected by ground-based weather stations. Solar irradiance measurements can also be inferred by the actual power output of existing photovoltaic systems. Additionally, satellite observations can be obtained for the geographic region. Both the direct and inferred solar irradiance measurements are considered to be sets of point values that relate to a specific physical location, whereas satellite imagery data is considered to be a set of area values that need to be converted into point values, such as described in commonly-assigned U.S. Pat. Nos. 8,165,811; 8,165,812; 8,165,813, cited infra. Still other sources of solar irradiance measurements are possible. 
     The net load data and simulated photovoltaic production data are then combined at each point in the known time period (step  173 ) to yield gross energy load  174 . Gross energy load is expressed in kilowatt hours, although other units of energy could be used. The gross energy load can then be presented in graphical form, such as described supra with reference to  FIG.  12    to  FIG.  15   , or in other written form. 
     The effects current and proposed energy investments and reductions are ultimately reflected as a payback on investment, which helps to provide a consumer with answers on personal energy consumption and an understanding what options and alternatives work best for the consumer&#39;s energy needs.  FIG.  18    is a process flow diagram showing a routine  180  for evaluating potential energy investment payback for use in the method  100  of  FIG.  8   . The process uses the equipment selections  101  in combination, as applicable, with current electricity, fuel, and gasoline consumption data  106 ; building thermal characteristics  107 ; and historical solar resource and weather data  108 . 
     By way of example, potential energy investments that affect electricity cost (C E ), fuel for heating cost (C F ), and gasoline (or other automobile fuel) cost (C G ), per Equation (1), as discussed supra, are modeled, but other costs, including maintenance cost (C M ), could also be weighed in the evaluation of total energy-related costs C Total . Initially, as applicable, an initial capital cost  185 , as discussed supra, and annual consumption, by fuel type, are calculated (step  181 ). The annual consumption values are determined for both the equipment currently in use and the equipment proposed to replace or upgrade the current equipment. In this example, the total energy-related costs C Total  include gasoline (or other automobile fuel) cost (C G ), so the energy consumed by the person&#39;s mode of transportation is determined. This example assumes that the form of transportation is a personal car. Other forms of transportation are possible, such as trains, buses, bikes, walking, and so forth. 
     
       
         
           
               
             
               
                 TABLE 2 
               
             
            
               
                   
               
               
                 Vehicle Fuel Consumption 
               
            
           
           
               
               
               
               
            
               
                   
                   
                 Current 
                 Proposed 
               
               
                   
                   
               
            
           
           
               
               
               
               
            
               
                   
                 Annual Mileage 
                 12,000 
                 12,000 
               
               
                   
                 Miles Per Gallon 
                 16 
                 129 
               
               
                   
                 Vehicle Is Included In Analysis? 
                 TRUE 
                 TRUE 
               
               
                   
                 Gasoline Consumption (gallons per year) 
                 750 
                 93 
               
               
                   
                 Miles Per kWh 
                 0.47 
                 3.83 
               
               
                   
                 Electricity Consumption (kWh per year) 
                 25,275 
                 3,135 
               
               
                   
                 Vehicle Is Electric Powered? 
                 FALSE 
                 TRUE 
               
               
                   
                 EV Charging Efficiency 
                 N/A 
                 85% 
               
               
                   
                 Electricity Purchases (kWh-eq. per year) 
                 25,275 
                 3,688 
               
               
                   
                 Gasoline Purchases (gallons per year) 
                 750 
                 0 
               
               
                   
                 Electricity Purchases (kWh per year) 
                 0 
                 3,688 
               
               
                   
                   
               
            
           
         
       
     
     Referring to Table 2, the consumer currently drives a 2004 Honda Odyssey EX minivan about 12,000 miles per year primarily for city driving. For this type of usage, the vehicle has a stated fuel economy of 16 miles per gallon and will consume 750 gallons of gasoline annually. There are 33.7 kWh of energy per gallon of gasoline, so the vehicle&#39;s annual fuel consumption represents an electricity-equivalent of 25,275 kWh annually. 
     The consumer is proposing to replace the current vehicle with a 2013 Nissan Leaf SV, which is plug-in charging all-electric vehicle. The Leaf SV achieves a gasoline-equivalent of 129 miles per gallon for city driving, which converts to 3.8 miles per kWh. An inefficiency occurs when the vehicle is charged, which can be assumed to be around 15 percent. For the same type of usage, about 12,000 miles per year primarily for city driving, the Leaf SV, at 3.8 kWh per mile with an 85 percent charging efficiency, would require 3,688 kWh annually, which compares quite favorably to the electricity-equivalent of 25,275 kWh used by the Odyssey EX under identical driving conditions. 
     Electric energy efficiency investments reduce annual electricity consumption. In every building, there is typically some percentage of electricity drawn on a continuous basis by devices that are always turned on. These constant load devices may be, for example, electric hot water heaters, clocks, electric timers for operating lights, uninterruptible power supplies for computer equipment, and appliances placed on a standby mode. 
     The electric load consumed by “Always On” devices can be reduced by replacing existing “Always On” electric devices with more energy efficient electric devices and modifying operating schedule parameters or by unplugging unused devices. Referring to Table 3, a reduction in “Always On” loads from 150 Watts to 50 Watts translates to a savings of 876 kWh per year [(0.15 kW−0.05 kW)×8,760 hours]. 
     In addition, other electric efficiency investments are possible, such as energy efficient appliances and efficient lighting. In this example, replacing fifty 15-Watt CFLs with 6-Watt LEDs that are operated for only six hours per day translates to a savings of 986 kWh per year [50×(0.015 kW−0.006 kW)×(6 hours per day)×(365 days per year)]. 
     
       
         
           
               
             
               
                 TABLE 3 
               
             
            
               
                   
               
               
                 Electrical Efficiency Savings and Capital Cost 
               
            
           
           
               
               
               
               
            
               
                   
                 Savings (kWh/yr) 
                 Savings (kWh/hour) 
                 Cost 
               
               
                   
               
            
           
           
               
               
               
               
            
               
                 Always On Loads 
                 876 
                 0.10 
                  $0 
               
               
                 Lights 
                 986 
                 0.11 
                 $250 
               
               
                 Total 
                 1,862 
                 0.21 
                 $250 
               
               
                   
               
            
           
         
       
     
     Improvements to a building can change the overall thermal performance of the building UA Total . Improvements can affect how heat loss or gain occurs by conduction through each unique building surface and through infiltration. In Equation (42), as further described infra, these effects can be calculated by incrementally changing the building&#39;s thermal characteristics. Referring to Table 4, the house in this example has R-6 wall insulation, that is, insulation with an R-value of 6. Adding R-13 insulation increases the overall insulation to R-19. The change in UA Total  for 225 ft 2  of R-19 insulation equals 26 Btu/hr-° F. [(⅙− 1/19)×225]. The total of all UA Total  changes equals 218 Btu/hr-° F. 
     
       
         
           
               
             
               
                 TABLE 4 
               
               
                   
               
               
                 Building Improvements 
               
               
                   
               
             
            
               
                   
               
            
           
           
               
               
               
               
               
               
            
               
                   
                 Current 
                 Proposed 
                 Area  
                   
                 Change  
               
            
           
           
               
               
               
               
               
            
               
                   
                 R-Value 
                 (ft 2 ) 
                 Cost 
                 in UA 
               
               
                   
               
            
           
           
               
               
               
               
               
               
            
               
                 Wall Insulation 
                 6 
                 19 
                 225 
                   $60 
                 26 
               
               
                 Attic Insulation 
                 13 
                 26 
                 900 
                   $266 
                 35 
               
               
                 Window Insulation 
                 2 
                 6.7 
                 319 
                 $4,500 
                 112 
               
               
                   
               
            
           
           
               
               
               
               
               
            
               
                   
                 ACH @ Standard  
                 Volume  
                   
                   
               
               
                   
                 Pressure 
                 (ft 2 ) 
                 Cost 
               
               
                   
               
            
           
           
               
               
               
               
               
               
            
               
                 Seal Building 
                 0.25 
                 0.15 
                 25,500 
                   $100 
                 46 
               
               
                 Total Building  
                   
                   
                   
                 $4,926 
                 218 
               
               
                 Improvement 
                   
                   
                   
                   
                   
               
               
                   
               
            
           
         
       
     
     Several ratios are calculated based on current and proposed efficiencies and UA Total  values, as further discussed infra with reference to Equation (38), Equation (42), and Equation (43). Referring to Table 5, the efficiency ratio equals the current value divided by the proposed value. The relationship is reversed for the UA Total  values, where the UA Total  ratio equals the proposed UA Total  value divided by the current UA Total  value. The current UA Total  value of the building is a required input and can be obtained by the empirical approach described supra with reference to  FIG.  4   . The efficiency ratios in Table 5 will now be discussed. 
     
       
         
           
               
             
               
                 TABLE 5 
               
             
            
               
                   
               
               
                 Efficiencies 
               
            
           
           
               
               
               
               
            
               
                   
                 Current 
                 Proposed 
                 Ratio 
               
               
                   
               
            
           
           
               
               
               
               
            
               
                 Water Heating Energy Factor 
                 62% 
                 245% 
                 25% 
               
               
                 Building UA (Btu/hr-° F.) 
                 583     
                 365    
                 63% 
               
               
                 Duct Efficiency 
                 77% 
                  94% 
                 82% 
               
               
                 Furnace Efficiency 
                 80% 
                 249% 
                 32% 
               
            
           
           
               
               
               
            
               
                 Total Space Heating (UA * Ducts * Furnace) 
                   
                 16% 
               
               
                   
               
            
           
         
       
     
     The Water Heating Energy Factor Ratio is used to determine the proposed total annual energy required for water heating. Current annual water heating fuel consumption was calculated using the approach summarized in Equation (12), which is 199 therms of natural gas. There are 3,412 Btu per kWh. Thus, the current consumption of fuel for water heating can be expressed as 5,820 kWh of natural gas. The proposed consumption of fuel for water heating equals 5,820 kWh times the Water Heating Energy Factor Ratio and is 1,473 kWh per year (5,820×0.25). Referring to Table 6, the installed cost for the heat pump water heater is $1,899. 
     
       
         
           
               
             
               
                 TABLE 6 
               
               
                   
               
               
                 Water Heating 
               
               
                   
               
             
            
               
                   
               
            
           
           
               
               
               
            
               
                   
                 Capital 
                 $1,199 
               
               
                   
                 Installation 
                   $700 
               
               
                   
                 Total Cost 
                 $1,899 
               
               
                   
                   
               
            
           
         
       
     
     Space heating requirements are calculated in a two-step process. The sizing of the heating source is first estimated, after which cost can be determined. One approach to sizing the heating source is provided in Manual J, cited supra. However, that sizing approach does not take into account historical information about the building&#39;s consumption nor is the sizing approach dynamic. 
     Here, an alternate approach to sizing of the heating source is applied. First, historical fuel consumption requirements are evaluated to determine worst-day situations, rather than simply assuming worst day conditions. Second, the approach dynamically incorporates the effect of investment decisions across technologies and fuel types and their various interactions. For example, the decision to add insulating window shades reduces a building&#39;s rate of heat loss and thus reduces the required size of the space conditioning heat pump, which, in turn, reduces capital cost. This decision also reduces the total amount of heat that needs to be provided by the heat pump, which, in turn, reduces the size of the photovoltaic system needed to supply energy to the heat pump. These interactions are automatically calculated. 
     Referring to Table 7, the maximum daily natural gas purchased for the building in this example for space heating purposes, as determined using daily water heating consumption from Equation (12) combined with total daily natural gas purchases, was 5.71 therms. In other words, the peak day over the year analyzed required a purchase of 5.71 therms of natural gas. Based on the proposed energy investments, the building envelope and duct losses will respectively be lowered to 63 percent and 82 percent, per Table 5. The product of these two ratios is 51 percent, which means that proposed energy investments would require 2.93 therms on the worst day, assuming the same furnace efficiency, η Furnace  48,836 Btu of natural gas must be purchased per hour, given a maximum daily operation of six hours. Since the current furnace is 80 percent efficient, 39,069 Btu of heat are actually delivered per hour. 
     The proposed space heating source is a heat pump that has a Heating Season Performance Factor (HSPF) of 8.5 Btu/Wh, which means that the heat pump will consume 4.6 kW per hour (39,069 Btu/8,500 Btu/kWh). The rating of this heat pump can also be expressed in tons by dividing by 12,000. The cost for the heat pump equals the product of the rating, expressed in in tons, times the cost, expressed in dollars per ton, plus the fixed cost, installation cost, and ductwork cost. The total proposed space heating cost is $11,256. 
     
       
         
           
               
             
               
                 TABLE 7 
               
               
                   
               
             
            
               
                 Space Heating Sizing 
               
            
           
           
               
               
               
               
            
               
                   
                   
                 UA Ratio *  
                   
               
               
                   
                 Current 
                 Duct Ratio 
                 Proposed 
               
               
                   
               
               
                 Max Daily Consumption (therms/day) 
                 5.71 
                 51% 
                 2.93 
               
               
                 Max Daily Operation (Hours) 
                 6 
                   
                 6 
               
               
                 Max Hourly Operation (Btu/hour) 
                 95,242 
                   
                 48,836 
               
               
                 Delivered Heat (Btu/hour) 
                 76,193 
                   
                 39,069 
               
               
                 Furnace FISPF (Btu/Wh) 
                   
                   
                 8.50 
               
               
                 Furnace AFUE 
                   
                   
                 0% 
               
               
                 Furnace Is Heat Pump 
                   
                   
                 TRUE 
               
            
           
           
               
               
               
            
               
                 Max Hourly Space Heating Consumption (kW/hr) 
                   
                 4.60 
               
               
                 Max Hourly Space Heating Consumption (tons) 
                   
                 3.26 
               
               
                   
               
            
           
           
               
            
               
                 Space Heating Cost 
               
            
           
           
               
               
               
               
            
               
                   
                 Required  
                 Cost  
                   
               
               
                   
                 Tons 
                 per Ton 
                 Cost 
               
               
                   
               
               
                 Capacity Cost 
                 3.26 
                 $1,000 
                 $3,256 
               
               
                 Fixed Cost 
                   
                   
                 $3,000 
               
               
                 Capacity + Fixed Cost 
                   
                   
                 $6,256 
               
               
                 Installation Cost 
                   
                   
                 $2,000 
               
               
                 Duct Cost 
                   
                   
                 $3,000 
               
               
                 Total Cost 
                   
                   
                 $11,256  
               
               
                   
               
            
           
         
       
     
     Installing a photovoltaic system allows a consumer to offset purchased electricity consumption with on-site power generation. In the interactive energy investment choices analysis tool, the consumer could simply explicitly size the photovoltaic system. Alternatively, the consumer can specify the percentage of purchased electricity consumption to offset by on-site power generation. 
     Referring to Table 8, in this example, annual consumption is estimated at 9,682 kWh. The consumer has indicated that the photovoltaic system should provide 80 percent of annual consumption, or 7,746 kWh. Historical photovoltaic power production was analyzed for the location and time period of interest. Here, a 1-kW-DC, south-facing photovoltaic system would produce 1,521 kWh per year; however, a 5.09 kW-DC photovoltaic system is needed to produce 7,746 kWh. A photovoltaic system of this capacity would cost $20,376 and would be eligible to receive 30-percent federal tax credit of $6,113. 
     
       
         
           
               
             
               
                 TABLE 8 
               
               
                   
               
               
                 PV System Sizing and Cost 
               
               
                   
               
             
            
               
                   
               
            
           
           
               
               
               
            
               
                   
                 Proposed Consumption (kWh/yr) 
                 9,682 
               
               
                   
                 Percent Cons. to be Supplied by PV 
                 80% 
               
               
                   
                 PV Supplied Energy (kWh/yr) 
                 7,746 
               
               
                   
                 Historical Production (kWh/kW-DC/yr) 
                 1,521 
               
               
                   
                 Required PV Size (kW-DC) 
                      5.09 
               
               
                   
                 Per Unit PV Cost ($/kW) 
                 $4,000  
               
               
                   
                 Total PV Cost 
                 $20,376  
               
               
                   
                 Federal Tax Credit 
                 $6,113  
               
               
                   
                   
               
            
           
         
       
     
     Referring back to  FIG.  10   , annual electric consumption is then converted into time series consumption (step  182 ), which allocates annual electric consumption into time-series values on an hourly, or other time interval, basis. For any particular end-use, the distribution of annual energy must satisfy the requirement that the sum of all 8,760 hours in a year (or all 8,784 hours in a leap year), as factored, equals 1, in accordance with: 
                       ∑     m   =   1     12         ∑     d   =   1       28   ⁢        to   ⁢        31           ∑     h   =   1     24       hf     m   ,   d   ,   h             =   1           (   32   )               
where m, d, and h respectively represent month, day, and hour; and hf represents the percent of total annual energy being consumed in a given hour. A daily factor for each month and day is defined, such that the sum of the daily factors for a particular month and day equals:
 
                     d   ⁢     f     m   ,   d         =       ∑     Hour   =   1       2   ⁢   4         h   ⁢     f       h   |   m     ,   d                   (   33   )               
where hf h|m,d  signifies the hourly factor for hour h, given month m and day d.
 
     A new term, called normalized hourly factors, is defined, which equals the original hourly factor divided by the daily factor for that month and day, expressed as: 
                   =           h   ⁢     f       h   |   m     ,   d           d   ⁢     f     m   ,   d           ⁢         for   ⁢         h     =     1   ⁢         to   ⁢         24               (   34   )               
Rearranging Equation (34) and substituting into Equation (32) yields:
 
                       ∑     m   =   1     12         ∑     d   =   1       28   ⁢        to   ⁢        31           df     m   ,   d       ⁢       ∑     h   =   1     24             =   1           (   35   )               
Repeat the same process to define a daily factor/monthly factor relationship:
 
     
       
         
           
             
               
                 
                   
                     
                       ∑ 
                       
                         m 
                         = 
                         1 
                       
                       12 
                     
                     
                       
                         mf 
                         m 
                       
                       ⁢ 
                       
                         
                           ∑ 
                           
                             d 
                             = 
                             1 
                           
                           
                             28 
                             ⁢ 
                                
                             to 
                             ⁢ 
                                
                             31 
                           
                         
                         
                           
                             
                               d 
                               ❘ 
                               m 
                             
                           
                           
                             
                               ∑ 
                               
                                 h 
                                 = 
                                 1 
                               
                               24 
                             
                           
                         
                       
                     
                   
                   = 
                   1 
                 
               
               
                 
                   ( 
                   36 
                   ) 
                 
               
             
           
         
       
     
     The benefit of Equations (35) and (36) is that they can be used to create load profiles for which detailed hourly data is unavailable. Suppose, for example, that total daily water heating consumption is available for each day of the year, but hourly data are unavailable. In this case, the consumption profiles distribution within any given day of the year could be assumed to be the same as every other day, as would be the case if the status of the water heater was always either on or off during the same time of the day. This assumption does not require that the total water heater load be the same for every day of the year. 
     Here, Equation (35) simplifies to the following equation: 
                       ∑     m   =   1     12         ∑     d   =   1       28   ⁢        to   ⁢        31           df     m   ,   d       ⁢       ∑     h   =   1     24             =   1           (   37   )               
Equation (37) can be used in the context of current Green Button natural gas data. A similar approach can be taken to define constant load profiles for a day within a given month.
 
     The hourly distribution factors for a proposed energy investment scenario can be depicted.  FIG.  19    is a graph depicting, by way of example, assumed hourly distribution factors, as used in the routine of  FIG.  8   . The x-axis represents time of day. The y-axis represents percentage. The assumed hourly distribution factors in the example for water heating, space heating, and electric vehicle charging are used in this example. Electric vehicle charging is assumed to follow the same pattern every day of the year. The daily factors for the water and space heating are based on measured natural gas purchase data. Table 9 presents projected hourly electricity consumption by end-use for one day. The columns present electricity by Other Consumption, Water Heating, Space Heating, and EV Charging. The sum of these four columns is Total Consumption. 
     
       
         
           
               
               
               
               
               
               
               
               
               
               
             
               
                 TABLE 9 
               
             
            
               
                   
               
               
                   
                   
                   
                 Projected Hourly Electricity 
                   
                   
                   
                   
                   
                   
               
            
           
           
               
               
               
               
               
               
               
               
            
               
                   
                   
                   
                 (KWh) 
                   
                   
                 Rate Structure 
                   
               
            
           
           
               
               
               
               
               
               
               
               
               
               
            
               
                   
                 Other 
                 Water 
                 Space 
                 EV 
                 Total 
                 PV 
                 Net 
                 Information 
                   
               
            
           
           
               
               
               
               
               
               
               
               
               
               
               
               
            
               
                 DST Start Time 
                 Consumption 
                 Heating 
                 Heating 
                 Charging 
                 Consumption 
                 Production 
                 Consumption 
                 Season 
                 Period 
                 Rate 
                 Cost 
               
               
                   
               
            
           
           
               
               
               
               
               
               
               
               
               
               
               
               
            
               
                 Jan. 1, 2013 12:00 AM 
                 0.32 
                 0.00 
                 0.0 
                 2.02 
                 2.34 
                 0.00 
                 2.34 
                 Winter 
                 Off Peak 
                 $0.10 
                 $0.24 
               
               
                 Jan. 1, 2013 1:00 AM 
                 0.42 
                 0.00 
                 0.0 
                 2.02 
                 2.44 
                 0.00 
                 2.44 
                 Winter 
                 Off Peak 
                 $0.10 
                 $0.25 
               
               
                 Jan. 1, 2013 2:00 AM 
                 0.85 
                 0.00 
                 0.0 
                 2.02 
                 2.87 
                 0.00 
                 2.87 
                 Winter 
                 Off Peak 
                 $0.10 
                 $0.29 
               
               
                 Jan. 1, 2013 3:00 AM 
                 0.87 
                 0.00 
                 0.0 
                 2.02 
                 2.89 
                 0.00 
                 2.89 
                 Winter 
                 Off Peak 
                 $0.10 
                 $0.29 
               
               
                 Jan. 1, 2013 4:00 AM 
                 0.85 
                 0.00 
                 0.0 
                 2.02 
                 2.87 
                 0.00 
                 2.87 
                 Winter 
                 Off Peak 
                 $0.10 
                 $0.29 
               
               
                 Jan. 1, 2013 5:00 AM 
                 0.85 
                 0.00 
                 2.1 
                 0.00 
                 2.93 
                 0.00 
                 2.93 
                 Winter 
                 Off Peak 
                 $0.10 
                 $0.30 
               
               
                 Jan. 1, 2013 6:00 AM 
                 1.21 
                 1.35 
                 2.1 
                 0.00 
                 4.64 
                 0.00 
                 4.64 
                 Winter 
                 Off Peak 
                 $0.10 
                 $0.47 
               
               
                 Jan. 1, 2013 7:00 AM 
                 0.85 
                 1.35 
                 2.1 
                 0.00 
                 4.28 
                 −0.21 
                 4.08 
                 Winter 
                 Partial 
                 $0.16 
                 $0.66 
               
               
                   
                   
                   
                   
                   
                   
                   
                   
                   
                 Peak 
                   
                   
               
               
                 Jan. 1, 2013 8:00 AM 
                 1.14 
                 0.00 
                 2.1 
                 0.00 
                 3.22 
                 −0.98 
                 2.25 
                 Winter 
                 Partial 
                 $0.16 
                 $0.37 
               
               
                   
                   
                   
                   
                   
                   
                   
                   
                   
                 Peak 
                   
                   
               
               
                 Jan. 1, 2013 9:00 AM 
                 0.83 
                 0.00 
                 0.0 
                 0.00 
                 0.83 
                 −1.94 
                 −1.11 
                 Winter 
                 Partial 
                 $0.16 
                 ($0.18) 
               
               
                   
                   
                   
                   
                   
                   
                   
                   
                   
                 Peak 
                   
                   
               
               
                 Jan. 1, 2013 10:00 AM 
                 0.52 
                 0.00 
                 0.0 
                 0.00 
                 0.52 
                 −2.63 
                 −2.12 
                 Winter 
                 Partial 
                 $0.16 
                 ($0.35) 
               
               
                   
                   
                   
                   
                   
                   
                   
                   
                   
                 Peak 
                   
                   
               
               
                 Jan. 1, 2013 11:00 AM 
                 0.22 
                 0.00 
                 0.0 
                 0.00 
                 0.22 
                 −3.01 
                 −2.79 
                 Winter 
                 Partial 
                 $0.16 
                 ($0.46) 
               
               
                   
                   
                   
                   
                   
                   
                   
                   
                   
                 Peak 
                   
                   
               
               
                 Jan. 1, 2013 12:00 PM 
                 −0.18 
                 0.00 
                 0.0 
                 0.00 
                 −0.18 
                 −3.07 
                 −3.25 
                 Winter 
                 Partial 
                 $0.16 
                 ($0.53) 
               
               
                   
                   
                   
                   
                   
                   
                   
                   
                   
                 Peak 
                   
                   
               
               
                 Jan. 1, 2013 1:00 PM 
                 −0.32 
                 0.00 
                 0.0 
                 0.00 
                 −0.32 
                 −2.81 
                 −3.13 
                 Winter 
                 Partial 
                 $0.16 
                 ($0.51) 
               
               
                   
                   
                   
                   
                   
                   
                   
                   
                   
                 Peak 
                   
                   
               
               
                 Jan. 1, 2013 2:00 PM 
                 −0.13 
                 0.00 
                 0.0 
                 0.00 
                 −0.13 
                 −2.21 
                 −2.35 
                 Winter 
                 Peak 
                 $0.27 
                 ($0.63) 
               
               
                 Jan. 1, 2013 3:00 PM 
                 1.18 
                 0.00 
                 0.0 
                 0.00 
                 1.18 
                 −1.41 
                 −0.23 
                 Winter 
                 Peak 
                 $0.27 
                 ($0.06) 
               
               
                 Jan. 1, 2013 4:00 PM 
                 2.11 
                 0.00 
                 0.0 
                 0.00 
                 2.11 
                 −0.48 
                 1.62 
                 Winter 
                 Peak 
                 $0.27 
                 $0.43 
               
               
                 Jan. 1, 2013 5:00 PM 
                 1.29 
                 1.35 
                 0.0 
                 0.00 
                 2.64 
                 0.00 
                 2.64 
                 Winter 
                 Peak 
                 $0.27 
                 $0.71 
               
               
                 Jan. 1, 2013 6:00 PM 
                 1.60 
                 0.00 
                 2.1 
                 0.00 
                 3.68 
                 0.00 
                 3.68 
                 Winter 
                 Peak 
                 $0.27 
                 $0.99 
               
               
                 Jan. 1, 2013 7:00 PM 
                 1.96 
                 0.00 
                 2.1 
                 0.00 
                 4.04 
                 0.00 
                 4.04 
                 Winter 
                 Peak 
                 $0.27 
                 $1.08 
               
               
                 Jan. 1, 2013 8:00 PM 
                 0.24 
                 0.00 
                 0.0 
                 0.00 
                 0.24 
                 0.00 
                 0.24 
                 Winter 
                 Peak 
                 $0.27 
                 $0.06 
               
               
                 Jan. 1, 2013 9:00 PM 
                 0.33 
                 0.00 
                 0.0 
                 0.00 
                 0.33 
                 0.00 
                 0.33 
                 Winter 
                 Partial 
                 $0.16 
                 $0.05 
               
               
                   
                   
                   
                   
                   
                   
                   
                   
                   
                 Peak 
                   
                   
               
               
                 Jan. 1, 2013 10:00 PM 
                 0.35 
                 0.00 
                 0.0 
                 0.00 
                 0.35 
                 0.00 
                 0.35 
                 Winter 
                 Partial 
                 $0.16 
                 $0.06 
               
               
                   
                   
                   
                   
                   
                   
                   
                   
                   
                 Peak 
                   
                   
               
               
                 Jan. 1, 2013 11:00 PM 
                 0.72 
                 0.00 
                 0.0 
                 0.00 
                 0.72 
                 0.00 
                 0.72 
                 Winter 
                 Off Peak 
                 $0.10 
                 $0.07 
               
               
                   
               
            
           
         
       
     
     Referring back to  FIG.  10   , net consumption is calculated using time-correlated production data (step  183 ), which requires combining time series total consumption data with time- and location-correlated production data. In many cases, photovoltaic production data may be of interest. As a result, historical photovoltaic production data needs to be simulated for the location of interest. The simulation must be performed using time- and location-correlated solar resource data, as well as specific information about the orientation and other characteristics of the photovoltaic system, such as can be provided by the Solar Anywhere service (http://www.SolarAnywhere.com), a Web-based service operated by Clean Power Research, L.L.C., Napa, Calif. The time series photovoltaic production data is subtracted from the time series consumption data to yield time series net consumption data. Photovoltaic production and net consumption for one day are presented in Table 9. 
     Finally, an electric bill is calculated (step  184 ), from which annual cost  186  can be forecast and upon which payback  187  can be determined. Electric bill calculation involves combining the net consumption data with the applicable electric rate structure information, including details about fixed, demand, tier, and time-of-day charges. In Table 9, the right columns present results for one day using a Pacific Gas and Electric EV-A tariff rate structure. Importantly, different rates can be used for “Before” and “After” calculations because a rate switch may be financially beneficial. The net consumption profile should be run through the detailed electric bill calculator for all possible rate structures to select the one that provides the greatest benefit. 
     The interactive energy investment choices analysis tool, described supra with reference to  FIG.  7   , provides a consumer with the information necessary to evaluate the economic savings or costs of new energy-related equipment investments for existing buildings. In a similar manner, energy investments that specifically affect building envelope, furnace, and heat delivery can also be evaluated.  FIG.  20    is a flow diagram showing a computer-implemented method for evaluating potential energy investment scenarios specially affecting a building&#39;s envelope, heating source, or heating delivery  190 , in accordance with a further embodiment. The method  190  can be implemented in software and execution of the software can be performed on a computer system, such as further described infra with reference to  FIG.  29   , as a series of process or method modules or steps. 
     Initially, the amount of total fuel purchased annually Q F  is obtained, which can be found in a utility bill, and the ratio Hof the amount of fuel consumed annually for heating Q F-Heating  over the amount of the total fuel purchased annually Q F  is calculated (step  191 ). The amount of fuel consumed annually for heating Q F-Heating  can be derived empirically based on the fuel consumed during non-heating season months, as described supra with reference to Equation (2), or from the building&#39;s thermal performance and heating and delivery equipment characteristics, as described supra with reference to Equation (14) (step  191 ). The ratio H can be used to identify the initial cost  195  of the fuel consumed annually for heating based on the total cost of the fuel purchased annually. To evaluate energy investments mainly affecting heating efficiency or delivery efficiency, a modified version of Equation (10) can be used. Depending upon the energy investments being evaluated, one or more of the existing thermal performance of the building UA Total  existing furnace efficiency η furnace  and existing delivery efficiency η delivery  may be needed and can be estimated, if not available (step  192 ). To represent the costs after investment, each variable in Equation (10) that corresponds to a new energy investment is labeled with a caret symbol ( Λ ) (step  193 ). Equation (15) is substituted into the Equation (10), which is then simplified and solved (step  194 ) to yield the new amount of fuel used strictly for space heating {circumflex over (Q)} F-Heating . 
                         Q   ^       F   -   Heating       =       (   H   )     ⁢     (     Q   F     )     ⁢     (       U   ⁢     A   Total         )     ⁢     (       η   furnace         η   ˆ     furnace       )     ⁢       η   delivery         η   ˆ     delivery           )           (   38   )               
Note that the variables in Equation (15) do not have caret symbols because the variables represent the values for the existing building before the investment is made. Based on {circumflex over (Q)} F-Heating , the new cost  196  of the fuel consumed annually for heating based on the new energy-related equipment investments can be found, and the investment payback  197  can be evaluated by comparing the initial cost  195  to the new cost  196 .
 
     In Equation (38), the new amount of fuel required for heating {circumflex over (Q)} F-Heating  equals the amount of total fuel purchased annually Q F , as fractionally adjusted by the ratio H multiplied by three additional interrelated ratios, each term in the ratio representing, as applicable, characteristics of both existing and proposed equipment:
         New thermal performance of building   divided by existing thermal performance of building UA Total .   Existing furnace efficiency η furnace  divided by new furnace efficiency {circumflex over (η)} furnace .   Existing delivery efficiency η delivery  divided by new delivery efficiency {circumflex over (η)} delivery .
 
Equation (38) is quite useful. For example, suppose that a consumer is considering an investment in a new furnace. The existing furnace has an 80-percent efficiency η furnace  and the delivery system has a 78-percent efficiency η delivery . If the building had a $1,000 annual bill for fuel required for heating, Equation (38) allows the consumer to determine the fuel cost for a new 96-percent efficient furnace with 95-percent efficient ductwork. Since there is no change to the building&#39;s thermal characteristics, Equation (38) suggests that the new annual fuel cost will be $1,000×(0.80/0.96)×(0.78/0.95)=$684.
       

     In addition to assessing the benefits associated with a new furnace and delivery system, a consumer may want to understand the effect of building envelope improvements, such as new windows or increased insulation, which can be determined by evaluating both the building&#39;s original thermal characteristics (UA Total ) and its new thermal characteristics ( ). The typical approach to obtaining the existing and new thermal characteristics of a building is to perform a detailed energy audit that requires fully modeling the building by taking physical measurements of the surface areas of all non-homogeneous exterior-facing surfaces or verifying non-exposed surfaces. Once calculated, the existing UA Total  is then parametrically adjusted to quantify new thermal characteristics. 
     Although comprehensive and customized to a specific building under consideration, there are notable weaknesses to energy audits. First, energy audits can be quite expensive, costing over a thousand dollars for the pre- and post-inspections and the filing of the necessary paperwork to obtain utility rebates. Second, equipment problems during testing can require multiple site visits. Third, energy audit results become less valid as new energy investments are made, which change the baseline thermal characteristic findings. 
     Consider an alternative method. Assume that the original overall thermal characteristic UA Total  of a building is known. UA Total  can be determined, for instance, using the empirical approach described supra with reference to  FIG.  4   . Suppose that energy investments are made for only one portion of the building that only affect heat transfer through the building envelope due to conduction. For example, the building owner is considering an investment in new windows, which can be called the j th  surface area. The new thermal characteristics of the building   equal the original building characteristics UA Total , minus the thermal characteristics of the original windows, plus the thermal characteristics of the new windows, which can be expressed as:
 
 = UA   Total −( U   j   A   j   −Û   j   A   j )= UA   Total −( U   j   −Û   j ) A   j   (39)
 
where U j  and Û j  respectively represent the existing and proposed U-values of surface j, and A i  represents the surface area of surface j.
 
     Equation (39) can be restated in a generalized form when there are M investments being made in a building: 
     
       
         
           
             
               
                 
                   = 
                   
                     
                       UA 
                       
                         T 
                         ⁢ 
                         o 
                         ⁢ 
                         t 
                         ⁢ 
                         a 
                         ⁢ 
                         l 
                       
                     
                     + 
                     
                       
                         ∑ 
                         
                           j 
                           = 
                           1 
                         
                         M 
                       
                       
                         
                           ( 
                           
                             
                               U 
                               j 
                             
                             - 
                             
                               
                                 U 
                                 ^ 
                               
                               j 
                             
                           
                           ) 
                         
                         ⁢ 
                         
                           A 
                           j 
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   40 
                   ) 
                 
               
             
           
         
       
     
     Suppose further that energy investments are made that affect heat losses due to infiltration. As discussed supra with reference to Equation (18), infiltration losses are based on the density of air (ρ), specific heat of air (c), number of air changes per hour (n), and volume of air per air change (V). The volume of a building can be approximated by multiplying building square footage by average ceiling height. Equation (40) can be modified to account for “Before” and “After” infiltration heat transfer: 
     
       
         
           
             
               
                 
                   = 
                   
                     
                       UA 
                       
                         T 
                         ⁢ 
                         o 
                         ⁢ 
                         t 
                         ⁢ 
                         a 
                         ⁢ 
                         l 
                       
                     
                     + 
                     
                       
                         ∑ 
                         
                           j 
                           = 
                           1 
                         
                         M 
                       
                       
                         
                           ( 
                           
                             
                               U 
                               j 
                             
                             - 
                             
                               
                                 U 
                                 ^ 
                               
                               j 
                             
                           
                           ) 
                         
                         ⁢ 
                         
                           A 
                           j 
                         
                       
                     
                     + 
                     
                       ρ 
                       ⁢ 
                       
                         c 
                         ⁡ 
                         ( 
                         
                           n 
                           - 
                           
                             n 
                             ˆ 
                           
                         
                         ) 
                       
                       ⁢ 
                       V 
                     
                   
                 
               
               
                 
                   ( 
                   41 
                   ) 
                 
               
             
           
         
       
     
     Substituting Equation (41) into Equation (38): 
     
       
         
           
             
               
                 
                   
                     
                       Q 
                       ˆ 
                     
                     
                       F 
                       - 
                       Heating 
                     
                   
                   = 
                   
                     
                       ( 
                       H 
                       ) 
                     
                     ⁢ 
                     
                       ( 
                       
                         Q 
                         F 
                       
                       ) 
                     
                     ⁢ 
                     
                       ( 
                       
                         1 
                         - 
                         
                           
                             
                               
                                 ∑ 
                                 
                                   j 
                                   = 
                                   1 
                                 
                                 M 
                               
                               
                                 
                                   ( 
                                   
                                     
                                       U 
                                       j 
                                     
                                     - 
                                     
                                       
                                         U 
                                         ˆ 
                                       
                                       j 
                                     
                                   
                                   ) 
                                 
                                 ⁢ 
                                 
                                   A 
                                   j 
                                 
                               
                             
                             + 
                             
                               ρ 
                               ⁢ 
                               
                                 c 
                                 ⁡ 
                                 ( 
                                 
                                   n 
                                   - 
                                   
                                     n 
                                     ˆ 
                                   
                                 
                                 ) 
                               
                               ⁢ 
                               V 
                             
                           
                           
                             U 
                             ⁢ 
                             
                               A 
                               Total 
                             
                           
                         
                       
                       ) 
                     
                     ⁢ 
                     
                       ( 
                       
                         
                           η 
                           furnace 
                         
                         
                           
                             η 
                             ˆ 
                           
                           furnace 
                         
                       
                       ) 
                     
                     ⁢ 
                     
                       ( 
                       
                         
                           η 
                           
                             d 
                             ⁢ 
                             e 
                             ⁢ 
                             l 
                             ⁢ 
                             i 
                             ⁢ 
                             ν 
                             ⁢ 
                             e 
                             ⁢ 
                             r 
                             ⁢ 
                             y 
                           
                         
                         
                           
                             η 
                             ˆ 
                           
                           
                             d 
                             ⁢ 
                             e 
                             ⁢ 
                             l 
                             ⁢ 
                             i 
                             ⁢ 
                             ν 
                             ⁢ 
                             e 
                             ⁢ 
                             r 
                             ⁢ 
                             y 
                           
                         
                       
                       ) 
                     
                   
                 
               
               
                 
                   ( 
                   42 
                   ) 
                 
               
             
           
         
       
     
     Equation (42) implies that only the following information is required to quantify the energy impact of building envelope investments:
         Percentage of fuel bill used for heating purposes (M, which can be obtained from monthly fuel bill data.   Existing fuel bill (Q F ), which can be obtained from the local utility bill records.   Existing overall thermal properties of building (UA Total ), which can be determined using the empirical approach described supra with reference to  FIG.  4   .   Existing furnace efficiency (η furnace )) This value is based on manufacturer and furnace model and is often listed directly on the furnace chassis or manufacturer specifications.   New furnace efficiency ({circumflex over (η)} furnace ) This value is based on manufacturer and furnace model and is often listed directly on the furnace chassis or manufacturer specifications.   Existing delivery system efficiency (η delivery ). This value typically ranges between 70 and 95 percent. η delivery  can be estimated or can be measured directly using a duct blast (or duct leakage) test, which is a detailed, on-site test. Alternatively, delivery system efficiency can be measured empirically using temperature tests in the spaces in which the ducts are located.   New delivery system efficiency ({circumflex over (η)} delivery ) This value can be specified as a requirement as part of ductwork replacement. Verification involves a detailed, on-site test.   Areas of building surfaces to be replaced or upgraded. These values can be determined using a tape measure and a calculator, or software.   Existing U-values of thermal properties of building surfaces to be replaced or upgraded. These values can be estimated.   New U-values of thermal properties of building surfaces to be replaced or upgraded. These values are reported by the surface manufacturer.   Number of air changes before and after energy investment. This number is required for energy investments that affect infiltration, but not for many other building envelope-implicating energy investments. Verification involves a detailed, on-site test.
 
The foregoing parameters are substituted into Equation (42) (step  193 ), which is then simplified (step  194 ) to find the annual cost  196  and payback  197 .
       

     In some special cases, Equation (42) can be simplified to: 
                       Q   ^       F   -   Heating       =       (   H   )     ⁢     (     Q   F     )     ⁢     (     1   -         (       U   j     -       U   ^     j       )     ⁢     A   j         U   ⁢     A   Total           )               (   43   )               
which applies when the heating source is not being replaced, the delivery system is not being upgraded, the investment does not affect the number of air changes per hour, or there is only one investment under consideration. Similar to Equation (42), the foregoing parameters are substituted into Equation (43) (step  193 ), which is then simplified (step  194 ) to find the annual cost  196  and payback  197 .
 
     Consider two examples that show how Equation (43) can be used. In both examples, assume that the buildings overall thermal performance UA Total  is 800, the natural gas bill is $1,000 annually, 60 percent of the natural gas consumed is for heating, and that natural gas costs $1 per therm. 
     Example: A homeowner is considering a $10,000 investment to upgrade single-pane windows with an R-value of 0.8 to triple-pane, low-e, argon gas-filled windows with an R-value of 6.7. The homeowner has 300 ft 2  of windows. How much would the homeowner save on heating? 
     The homeowner currently purchases 1,000 therms per year of natural gas based on an annual heating bill of $1,000 and natural gas price of $1 per therm. Assuming that 400 therms are for non-heating purposes, leaving 600 therms for heating. According to Equation (43), the new heating fuel consumption will be: 
     
       
         
           
             
               
                 
                   
                     
                       Q 
                       ˆ 
                     
                     
                       F 
                       - 
                       Heating 
                     
                   
                   = 
                   
                     
                       
                         ( 
                         
                           0 
                           . 
                           6 
                         
                         ) 
                       
                       ⁢ 
                       
                         ( 
                         
                           1 
                           
                             , 
                             TagBox[&#34;,&#34;, &#34;NumberComma&#34;, Rule[SyntaxForm, &#34;0&#34;]] 
                           
                           000 
                         
                         ) 
                       
                       ⁢ 
                       
                         ( 
                         
                           1 
                           - 
                           
                             
                               
                                 ( 
                                 
                                   
                                     1 
                                     
                                       0 
                                       . 
                                       8 
                                     
                                   
                                   - 
                                   
                                     1 
                                     
                                       6 
                                       . 
                                       7 
                                     
                                   
                                 
                                 ) 
                               
                               ⁢ 
                               3 
                               ⁢ 
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                               ⁢ 
                               0 
                             
                             
                               8 
                               ⁢ 
                               0 
                               ⁢ 
                               0 
                             
                           
                         
                         ) 
                       
                     
                     = 
                     
                       352 
                       ⁢ 
                           
                       therms 
                     
                   
                 
               
               
                 
                   ( 
                   44 
                   ) 
                 
               
             
           
         
       
     
     The $10,000 investment will save the homeowner $248 per year ($1/therm)×(600 therms−352 therms). 
     Example: The same homeowner decided to look into a different energy investment. The home currently has a 2,500 ft 2  ceiling with R-6 insulation. The homeowner is considering spending $1,000 to upgrade to R-30 insulation. According to Equation (43), the new heating fuel consumption will be: 
     
       
         
           
             
               
                 
                   
                     
                       Q 
                       ˆ 
                     
                     
                       F 
                       - 
                       Heating 
                     
                   
                   = 
                   
                     
                       
                         ( 
                         
                           0 
                           . 
                           6 
                         
                         ) 
                       
                       ⁢ 
                       
                         ( 
                         
                           1 
                           
                             , 
                             TagBox[&#34;,&#34;, &#34;NumberComma&#34;, Rule[SyntaxForm, &#34;0&#34;]] 
                           
                           000 
                         
                         ) 
                       
                       ⁢ 
                       
                         ( 
                         
                           1 
                           - 
                           
                             
                               
                                 ( 
                                 
                                   
                                     1 
                                     6 
                                   
                                   - 
                                   
                                     1 
                                     
                                       3 
                                       ⁢ 
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                               ⁢ 
                               2 
                               
                                 , 
                                 TagBox[&#34;,&#34;, &#34;NumberComma&#34;, Rule[SyntaxForm, &#34;0&#34;]] 
                               
                               500 
                             
                             
                               8 
                               ⁢ 
                               0 
                               ⁢ 
                               0 
                             
                           
                         
                         ) 
                       
                     
                     = 
                     
                       350 
                       ⁢ 
                           
                       therms 
                     
                   
                 
               
               
                 
                   ( 
                   45 
                   ) 
                 
               
             
           
         
       
     
     This $1,000 investment will save the homeowner $250 per year ($1/therm)×(600 therms−350 therms). 
     Note that Equation (38), Equation (42), and Equation (43) can all be used in the evaluation of energy investments affecting building envelope, furnace, and heat delivery. Choosing the appropriate equation depends upon the form of energy investment under consideration.  FIG.  21    is a process flow diagram showing a routine for selecting energy investment scenario parameters  200  for use in the method  190  of  FIG.  20   . In all three cases, the annual payback  197  on fuel savings for space heating from proposed energy investments can be determined. However, depending upon the energy investment, different parameters are required and, in some cases, a simpler form of evaluation by choosing an equation requiring fewer parameters might be used (step  201 ). If the proposed energy investments mainly affect heating efficiency or delivery efficiency (step  202 ), Equation (38) is the most appropriate form of evaluation. If the proposed energy investments only affect heat transfer due to conduction through only one portion of a building (step  203 ), Equation (42) is better suited to the task. Finally, when the heating source is not being replaced, the delivery system is not being upgraded, the investment does not affect the number of air changes per hour, or there is only one investment under consideration (step  204 ), Equation (43) can be used. 
     A typical household in California consumes about 6,875 kWh of electricity annually. A 4.5 kW-DC photovoltaic power generation system can provide enough power generating capacity to meet that level of consumption. Electricity, however, is only a part of overall energy consumption. Providing only net energy consumption data creates a misperception that a home is energy efficient. Gross energy load data is helpful in dispelling that concern, yet gross energy load remains principally focused on electricity consumption. A holistic view of all forms of energy consumption is more apt to enable a consumer to identify opportunities to improve energy conservation across-the-board and to realize a zero net energy consumption paradigm, including transportation and denoted by ZNET (Zero Net Energy including Transportation), by specifically highlighting all forms of energy consumption, whether electricity or other energy sources, and the amount of on-site power generation required to meet those energy consumption needs.  FIG.  22    is a block diagram depicting, by way of example, annual energy consumption by an average household in California with gasoline and natural gas consumption expressed in kilowatt hours. The area of the rectangles for the different forms of energy consumption shown are drawn to scale. Such energy consumption modeling could be provided as a trusted energy advisor tool included through informational Web sites provided by power utilities or energy agencies to their customers, as well as in printed form. 
     Here, the 6,875 kWh of annual electricity consumption is viewed in perspective to energy consumed to fulfill personal transportation, water heating, and space heating needs. Each of these types of energy consumption can be normalized to kilowatt hours, or other units of energy, for purposes of comparison. The 729 gallons of gasoline converts into approximately 24,564 kWh, using a conversion of 33.7 kWh per gallon of gasoline. The 219 therms of natural gas (NG) for water heating and 238 therms of NG for space heating respectively convert into approximately 6,417 kWh and 6,973 kWh, using a conversion of 29.3 kWh per therm of natural gas. The total energy consumption, when thus considered, is around 44,829 kWh or about 85% more than annual electricity consumption alone. 
     Space heating and simple electricity consumption can be effectively reduced through traditional forms of energy efficiency.  FIG.  23    is a block diagram depicting, by way of example, the annual energy consumption of  FIG.  22    reflecting energy efficiencies implemented through traditional methodologies. Here, energy consumption for both space heating and other electricity have respectively been reduced by around 40%. Other electricity consumption has been reduced to 4,125 kWh by implementing electricity efficiency measures, which includes cutting down on and avoiding wasteful energy use, for instance, turning off unnecessary lights or appliances, and by switching to energy efficient fixtures, such as LED lighting fixtures. Space heating consumption has been reduced to 4,184 kWh by implementing thermal efficiency, which includes improving the thermal efficiency and performance of a building, as described supra with reference to  FIG.  8   . 
     Non-traditional forms of energy efficiency are less familiar to most consumers, yet can save a significant amount of energy annually. For instance, replacing a gasoline-powered vehicle with an electric vehicle is a major energy saver, as well as being instrumental in reducing greenhouse emissions and other environmental harms.  FIG.  24    is a block diagram depicting, by way of example, the annual energy consumption of  FIG.  22    reflecting a switch to an electric vehicle. An electric vehicle will increase electricity consumption due to the need for regular recharging, yet will also reduce overall energy use. Here, energy consumption for personal transportation has been reduced to 4,913 kWh by switching to an electric vehicle, which is about 20% of the energy required by a gasoline-powered vehicle. 
     Another form of non-traditional energy efficiency is fuel switching from a water heater fueled by natural gas to a heat pump water heater.  FIG.  25    is a block diagram depicting, by way of example, the annual energy consumption of  FIG.  22    reflecting a switch to a heat pump water heater. The annual water heating capacity for the building is first determined, from which an appropriately-sized heat pump water heater can be selected. Here, energy consumption for water heating has been reduced to 1,540 kWh by switching to a heat pump water heater of equivalent capacity as the natural gas unit that was replaced. 
     The same type of fuel switch can be made for a space heating.  FIG.  26    is a block diagram depicting, by way of example, the annual energy consumption of  FIG.  22    reflecting a switch to a heat pump space heater. The annual space heating capacity for the building is first determined, from which an appropriately-sized heat pump space heater can be selected. Here, energy consumption for space heating has been further reduced to 1,339 kWh by switching to a heat pump space heater of equivalent capacity as the natural gas unit that was replaced, resulting in a total energy savings of about 20% of the pre-energy conservation amount of 6,973 kWh. 
     Total energy savings adds up.  FIG.  27    is a block diagram depicting, by way of example, the annual energy consumption of  FIG.  22    with cumulative revised energy consumption expressed in kilowatt hours. With both traditional and non-tradition energy efficiencies, annual energy consumption is about 11,917 kWh, which is nearly a 75% reduction in energy. To achieve a ZNE household, on-site power generation capacity would need to be increased.  FIG.  28    is a block diagram depicting, by way of example, the cumulative revised energy consumption of  FIG.  27    overlaying a 20% efficient photovoltaic power generation system. On-site power generation can be simulated for different photovoltaic power generation system configurations based on solar irradiance data for a set of locations representative of the geographic region within which the building is located, such as described supra with reference to  FIG.  17   . Here, based on current photovoltaic technology, a solar array with a 20% efficiency rating that takes up only a small portion of a 30 feet by 50 feet roof would generate about 11,917 kWh, which is enough to satisfy the new energy needs. 
     Fractionally inferring the percentage of the total fuel purchased for space heating purposes, as described supra with reference to  FIG.  2   ; empirically estimating overall thermal performance of a building through a short-duration controlled test, as described supra with reference to  FIG.  4   ; evaluating potential energy investment scenarios, as described supra with reference to  FIG.  10   ; determining gross energy load, as described supra with reference to  FIG.  17   ; and evaluating new energy investments specifically affecting building envelope, heating source, or heating delivery, as described supra beginning with reference to  FIG.  20   , can be performed with the assistance of a computer, or through the use of hardware tailored to the purpose.  FIG.  29    is a block diagram showing a computer-implemented system  210  for empirically estimating overall thermal performance of a building through a short-duration controlled test, in accordance with one embodiment, which can also be used for fractionally inferring the percentage of the total fuel purchased for space heating purposes and evaluating potential energy investment scenarios. A computer system  211 , such as a personal, notebook, or tablet computer, as well as a smartphone or programmable mobile device, can be programmed to execute software programs  212  that operate autonomously or under user control, as provided through user interfacing means, such as a monitor, keyboard, and mouse. The computer system  211  includes hardware components conventionally found in a general purpose programmable computing device, such as a central processing unit, memory, input/output ports, network interface, and non-volatile storage, and execute the software programs  212 , as structured into routines, functions, and modules. In addition, other configurations of computational resources, whether provided as a dedicated system or arranged in client-server or peer-to-peer topologies, and including unitary or distributed processing, communications, storage, and user interfacing, are possible. 
     The computer system  211  remotely interfaces to a heating source  216  and a thermometer  217  inside a building  213  that is being analytically evaluated for overall thermal performance UA Total  In a further embodiment, the computer system  211  also remotely interfaces to a thermometer  218  outside the building  213 , or to a remote data source that can provide the outdoor temperature. The computer system  211  can control the heating source  216  and read temperature measurements from the thermometer  217  throughout the short-duration controlled test, during which the baseline indoor temperature T 0 , the starting indoor temperature T 1 , and the final indoor temperature T 3  are recorded. In a further embodiment, a cooling source (not shown) can be used in place of or in addition to the heating source  216 . The expected final indoor temperature T 3   No Heat  is also estimated by the computer system  211 , based on a projection of what the indoor temperature would have been at the end of the test, had the heating source not been turned back on. The computer system  211  executes a software program  212  to determine overall thermal performance UA Total  based on the empirical approach described supra with reference to  FIG.  4   . 
     In a further embodiment, the computer system  211  may be remotely interfaced with a server  220  operated by a power utility or other utility service provider  221  over a wide area network  219 , such as the Internet, from which fuel purchase data  222 , as well as period net consumption statistics, can be retrieved. The computer system  211  executes a software program  212  to fractionally infer the percentage of the total fuel purchased for space heating purposes, as described supra with reference to  FIG.  4   , and also to determine gross energy load, as described supra with reference to  FIG.  17   . 
     In a still further embodiment, the UA Total  can be used as part of the building thermal characteristics. Optionally, the computer system  211  may also monitor electricity  214  and other metered fuel consumption, where the meter is able to externally interface to a remote machine, as well as monitor on-site power generation, such as generated by a photovoltaic system  215 . The monitored fuel consumption and power generation data can be used to create the electricity, fuel, and gasoline consumption data  96  and historical solar resource and weather data  98 . The computer system  211  executes a software program  212  to evaluate potential energy investment scenarios, and provide a payback estimate 217, as described supra with reference to  FIG.  10   . 
     In a yet further embodiment, the computer system  211  includes a storage device within which is stored one or more of the following data: the percentage of fuel bill used for heating purposes, an existing fuel bill, existing overall thermal properties UA Total  of the building  213 , existing furnace efficiency, new furnace efficiency, existing delivery system efficiency, new delivery system efficiency, areas of building surfaces to be replaced or upgraded, existing U-values of thermal properties of building surfaces to be replaced or upgraded, new U-values of thermal properties of building surfaces to be replaced or upgraded, and number of air changes before and after energy investment. The computer system  211  executes a software program  212  to evaluate new energy investments specifically affecting building envelope, heating source, or heating delivery, and provide a payback estimate  187 , as described supra with reference to  FIG.  20   . 
     While the invention has been particularly shown and described as referenced to the embodiments thereof, those skilled in the art will understand that the foregoing and other changes in form and detail may be made therein without departing from the spirit and scope.