## E C B1 B3 T B2 T

where

C = the energy use at the change point, B1 = the coefficient or slope that describes the linear dependency on temperature below the change point, B2 = the coefficient or slope that describes the linear dependency on temperature above the change point B3 = the change-point temperature, T = the temperature for the period of interest,

+ = positive values only for the parenthetical expression.

### F. Five-parameter Model

Five-parameter change-point linear models are useful for modeling the whole-building energy use in buildings that contain air conditioning and electric heating. such models are also useful for modeling the weather dependent performance of the electricity consumption of variable air volume air-handling units. The basic form for the weather dependency of either case is shown in Figure 27.7f, where there is an increase in electricity use below the change point associated with heating, an increase in the energy use above the change point associated with cooling, and constant energy use between the heating and cooling change points. Five-parameter change-point linear models can be described using variable-based degree day models, or a five-parameter model. The equation for describing the energy use with variable-based degree days is

where

C = the constant energy use between the heating and cooling change points, B1 = the coefficient or slope that describes the linear dependency on heating degree-days, B2 = the coefficient or slope that describes the linear dependency on cooling degree-days, DDth = the heating degree-days (or degree hours), which are based on the balance-point temperature.

DDtc = the cooling degree-days (or degree hours), which are based on the balance-point temperature.

The five-parameter change-point linear model that is based on temperature is

where

C = the energy use between the heating and cooling change points, B1 = the coefficient or slope that describes the linear dependency on temperature below the heating change point, B2 = the coefficient or slope that describes the linear dependency on temperature above the cooling change point B3 = the heating change-point temperature, B4 = the cooling change-point temperature, T = the temperature for the period of interest, + = positive values only for the parenthetical expression.

### G. Whole-building Peak Demand Models

Whole-building peak electric demand models differ from whole-building energy use models in several respects. First, the models are not adjusted for the days in the billing period since the model is meant to represent the peak electric demand. Second, the models are usually analyzed against the maximum ambient temperature during the billing period. Models for whole-building peak electric demand can be classified according to weather-dependent and weather-independent models.

### G-l. Weather-dependent

Whole-building Peak Demand Models Weather-dependent, whole-building peak demand models can be used to model the peak electricity use of a facility. Such models can be calculated with linear and change-point linear models regressed against maximum temperatures for the billing period, or calculated with an inverse bin model.155'156

### G-2. Weather-independent

Whole-building Peak Demand Models Weather-independent, whole-building peak demand models are used to measure the peak electric use in buildings or sub-metered data that do not show significant weather dependencies. ASHRAE has developed a diversity factor toolkit for calculating weather-independent whole-building peak demand models as part of Research Project 1093-RP. This toolkit calculates the 24-hour diversity factors using a quartile analysis. An example of the application of this approach is given in the following section.

Example: Whole-building energy use models

Figure 27.8 presents an example of the typical data requirements for a whole-building analysis, including one year of daily average ambient temperatures and twelve months of utility billing data. In this example of a residence, the daily average ambient temperatures were obtained from the National Weather Service (i.e., the average of the published min/max data), and the utility bill readings represent the actual readings from the customer's utility bill. To analyze these data several calculations need to be performed. First, the monthly electricity use (kWh/month) needs to be divided by the days in the billing period to obtain the average daily electricity use for that month (kWh/day). Second, the average daily temperatures need to be calculated from the published NWS min/max data. From these average daily temperatures the average billing period temperature need to be calculated for each monthly utility bill.

The data set containing average billing period temperatures and average daily electricity use is then analyzed with ASHRAE's Inverse Model Toolkit (IMT)157 to determine a weather normalized consumption as shown in Figures 27.9 and 27.10. In Figure 27.9 the twelve monthly utility bills (kWh/period) are shown plotted against the average billing period temperature along with a three-parameter change-point model calculated with the IMT. In Figure 27.10 the twelve monthly utility bills, which were adjusted for days in the billing period (i.e., kWh/day) are shown plotted against the average billing period temperature along with a three-parameter change-point model calculated with the IMT. In the analysis for this house, the use of an average daily model improved the accuracy of the unadjusted model (i.e., Figure 27.9) from an R2 of 0.78 and CV (RMSE) of 24.0% to an R2 of 0.83 and a CV (RMSE) of 19.5% for the adjusted model (i.e., Figure 27.10), which indicates a significant improvement in the model.

In another example the hourly steam use (Figure

27.11) and hourly electricity use (Figure 27.13) for the U.S. DOE Forrestal Building is modeled with a daily weekday-weekend three-parameter, change-point model for the steam use (Figure 27.12), and an hourly weekday-weekend demand model for the electricity use (Figure 27.14). To develop the weather-normalized model for the steam use the hourly steam data and hourly weather data were first converted into average daily data, then a three-parameter, weekday-weekend model was calculated using the EModel software,158 which contains similar algorithms as ASHRAE's IMT. The resultant model, which is shown in Figure 27.12 along with the daily steam, is well described with an R2 of 0.87 an RMSE of 50,085.95 kBtu/day and a CV (RMSE) of 37.1%.

In Figure 27.14 hourly weather-independent 24hour weekday-weekend profiles have been created for Figure 27.8: Example Data for Monthly Whole-building Analysis (upper trace, daily average temperature, F, lower points, monthly electricity use, kWh/day). Figure 27.9 Example Unadjusted Monthly Whole-building Analysis (3P Model) for kWh/period (R2 = 0.78, CV (RMSE) = 24.0%).

Figure 27.10. Example Adjusted Whole-building Analysis (3P Model) for kWh/day (R2 = 0.83, CV (RMSE) = 19.5%).

the whole-building electricity use using ASHRAE's 1093-RP Diversity Factor Toolkit.159 These profiles can be used to calculate the baseline whole-building electricity use (i.e., using the mean hourly use) by multiplying times the expected weekdays and weekends in the year. The profiles can also be used to calculate the peak electricity use (i.e., using the 90th percentile).

### Calculation of Annual Energy Use

Once the appropriate whole-building model has been chosen and applied to the baseline data, the annual energy use for the baseline period and the post-retrofit period are then calculated. Savings are then calculated by comparing the annual energy use of the baseline with the annual energy use of the post-retrofit period.

### Whole-building Calibrated Simulation Approach

Whole-building calibrated simulation normally requires the hourly simulation of an entire building, including the thermal envelope, interior and occupant loads, secondary HVAC systems (i.e., air handling units), and the primary HVAC systems (i.e., chillers, boilers). This is usually accomplished with a general purpose simulation program such as BLAST, DOE-2 or EnergyPlus, or similar proprietary programs. Such programs require an hourly weather input file for the location in which the building is being simulated. Calibrating the simulation refers to the process whereby selected outputs from the simulation are compared and eventually matched with measurements taken from an actual building. A number of papers in the literature have addressed techniques for accomplishing these calibrations, and include results from case study buildings where calibrated simulations have been developed for various purposes.

170, 171,172,173,174,175

Applications of Calibrated Whole-building Simulation.

Calibrated whole-building simulation can be a useful approach for measuring the savings from energy conservation retrofits to buildings. However, it is generally more expensive than other methods, and therefore it is best reserved for applications where other, less costly approaches cannot be used. For example, calibrated simulation is useful in projects where either pre-retrofit or post-retrofit whole-building metered electrical data are not available (i.e., new buildings or buildings without meters such as many college campuses with central facilities). Calibrated simulation is desired in projects where there are significant interactions between retrofits, for example lighting retrofits combined with changes to HVAC systems, or chiller retrofits. In such cases the whole-building simulation program can account for the interactions, and in certain cases, actually isolate interactions to allow for end-use energy allocations. It is useful in projects where there are significant changes in the facility's energy use during or after a retrofit has been installed, where it may be necessary to account for additions to a building that add or subtract thermal loads from the HVAC system. In other cases, demand may change over time, where the changes are not related to the energy conservation measures. Therefore, adjustments to account for these changes will be also be needed. Finally, in many newer buildings, as-built design simulations are being delivered as a part of the building's final documents. In cases where such simulations are properly documented they can be calibrated to the baseline conditions and then used to calculate and measure retrofit savings.

Unfortunately, calibrated, whole-building simulation is not useful in all buildings. For example, if a building cannot be readily simulated with available simulation programs, significant costs may be incurred in Figure 27.11: Example Heating Data for Daily Whole-building Analysis. Figure 27.12: Example Daily Weekday-weekend Whole-building Analysis (3P Model) for Steam Use (kBtu/ day, R2 = 0.87, RMSE = 50,085.95, CV (RMSE) = 37.1%). Weekday use (x), weekend use ([]). Figure 27.13: Example Electricity Data for Hourly Whole-building Demand Analysis. Figure 27.14: Example Weekday-weekend Hourly Whole-building Demand Analysis (1093-RP Model) for Electricity Use.

modifying a program or developing a new program to simulate only one building (e.g., atriums, underground buildings, buildings with complex HVAC systems that are not included in a simulation program's system library). Additional information about calibrated, whole-building simulation can be found in ASHRAE's Guideline 14-2002.

Figure 27.15 provides an example of the use of calibrated simulation to measure retrofit savings in a project where pre-retrofit measurements were not avail able. In this figure both the before-after whole-building approach and the calibrated simulation approach are illustrated. On the left side of the figure the traditional whole-building, before-after approach is shown for a building that had a dual-duct, constant volume system (DDCV) replaced with a variable air volume (VAV) system. In such a case where baseline data are available, the energy use for the building is regressed against the coincident weather conditions to obtain the representative baseline regression coefficients. After the retrofit is installed, the energy savings are calculated by comparing the projected pre-retrofit energy use against the measured post-retrofit energy use, where the projected pre-retrofit energy use calculated with the regression model (or empirical model), which was determined with the facility's baseline DDCV data.

In cases where the baseline data are not available (i.e., the right side of the figure), a simulation of the building can be developed and calibrated to the post-retrofit conditions (i.e., the VAV system). Then, using the calibrated simulation program, the pre-retrofit energy use (i.e., DDCV system) can be calculated for conditions in the post-retrofit period, and the savings calculated by comparing the simulated pre-retrofit energy use against the measured post-retrofit energy use. In such a case the calibrated post-retrofit simulation can also be used to fill-in any missing post-retrofit energy use, which is a common occurrence in projects that measure hourly energy and environmental conditions. The accuracy of the post-retrofit model depends on numerous factors.

Methodology for Calibrated Whole-building Simulation

Calibrated simulation requires a systematic approach that includes the development of the whole-building simulation model, collection of data from the building being retrofitted and the coincident weather data. The calibration process then involves the comparison of selected simulation outputs against measured data from the systems being simulated, and the adjustment of the simulation model to improve the comparison of the simulated output against the corresponding measurements. The choice of simulation program is a critical step in the process, which must balance the model appropriateness, algorithmic complexity, user expertise, and degree of accuracy against the resources available to perform the modeling.

Data collection from the building includes the collection of data from the baseline and post-retrofit periods, which can cover several years of time. Building data to be gathered includes such information as the building location, building geometry, materials characteristics, equipment nameplate data, operations schedules, temperature settings, and at a minimum whole-building utility billing data. If the budget allows, hourly whole-

When Baseline Measured Data are Available

When Baseline Measured Data are Available When Post-Installation Measured Data are Available Figure 27.15: Flow Diagram for Calibrated Simulation Analysis of Air-Side HVAC System.176

When Baseline Measured Data are Not Available

When Baseline Measured Data are Not Available When Post-Installation Measured Data are Available Figure 27.15: Flow Diagram for Calibrated Simulation Analysis of Air-Side HVAC System.176

building energy use and environmental data can be gathered to improve the calibration process, which can be done over short-term, or long-term period.

Figure 27.16 provides an illustration of a calibration process that used hourly graphical and statistical comparisons of the simulated versus measured energy use and environmental conditions. In this example, the site-specific information was gathered and used to develop a simulation input file, including the use of measured weather data, which was then used by the DoE-2 program to simulate the case study building. Hourly data from the simulation program was then extracted and used in a series of special-purpose graphical plots to help guide the calibration process (i.e., time series, bin and 3-D plots). After changes were made to the input file, DoE-2 was then run again, and the output compared against the measured data for a specific period. This process was then repeated until the desired level of calibration was reached, at which point the simulation was proclaimed to be "calibrated." The calibrated model was then used to evaluate how the new building was performing compared to the design intent.

A number of different calibration tools have been Figure 27.16: Calibration Flowchart. This figure shows the sequence of processing routines that were used to develop graphical calibration procedures.178

reported by various investigators, ranging from simple X-Y scatter plots to more elaborate statistical plots and indices. Figures 27.17, 27.18 and 27.19 provide examples of several of these calibration tools. In Figure 27.17 an example of an architectural rendering tool is shown that assists the simulator with viewing the exact placement of surfaces in the building, as well as shading from nearby buildings, and north-south orientation. In Figure 27.18 temperature binned calibration plots are shown comparing the weather dependency of an hourly simulation against measured data. In this figure the upper plots show the data as scatter plots against temperature. The lower plots are statistical, temperature-binned box-whisker-mean plots, which include the super positioning of measured mean line onto the simulated mean line to facilitate a detailed evaluation. In Figure 27.19 comparative three-dimensional plots are shown that show measured data (top plot), simulated data (second plot from the top), simulated minus measured data (second plot from the bottom, and measured minus simulated data (bottom plot). In these plots the day-of-the-year is the scale across the page (y axis), the hour-of-the-day is the scale projecting into the page (x axis), and the hourly Figure 27.17: Example Architecture Rendering of the Robert E. Johnson Building, Austin, Texas.179,180

Figure 27.16: Calibration Flowchart. This figure shows the sequence of processing routines that were used to develop graphical calibration procedures.178

Figure 27.17: Example Architecture Rendering of the Robert E. Johnson Building, Austin, Texas.179,180

electricity use is the vertical scale of the surface above the x-y plane. These plots are useful for determining how well the hourly schedules of the simulation match the schedules of the real building, and can be used to identify other certain schedule-related features. For example, in the front of plot (b) the saw-toothed feature is indicating on/off cycling of the HVAC system, which is not occurring in the actual building.

Table 27.17 contains a summary of the procedures used for developing a calibrated, whole-building simulation program, as defined in ASHRAE's Guideline 14-2002. In general, to develop a calibrated simulation, detailed information is required for a building, including information about the building's thermal envelope (i.e., the walls, windows, roof, etc.), information about the building's operation, including temperature settings, HVAC systems, and heating-cooling equipment that existed both during the baseline and post-retrofit period. This information is input into two simulation files, one for the baseline and one for the post-retrofit conditions. Savings are then calculated by comparing the two simulations of the same building, one that represents the baseline building, and one that represents the building's operations during the post-retrofit period.

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