Equations Flashcards
General Equation for Determining Savings
Savings = (Baseline Period Energy - Reporting Period Energy) +/- Adjustments
Energy, demand, water, greenhouse gas emissions, or other savings in a facility cannot be directly measured because savings represent the absence of energy/water consumption or demand. Instead, savings are determined by comparing measured energy consumption or demand before and after implementation of an energy efficiency measure (EEM), making suitable adjustments for changes in conditions. The comparison of before and after energy consumption or demand must be made on a consistent basis, using the above general M&V equation.
pg.22 for figure
Primary IPMVP Savings Equation
Savings = (Baseline Period Energy - reporting Period Energy) +/- Routine Adjustments +/- Non-routine Adjustments
Note that baseline data consist of real facts about energy and independent variables as they existed during the baseline period.
Non-routine adjustments can potentially have a significant impact on reported savings; the rationale and calculation for non-routine adjustments should be agreed upon between the parties and documented.
Therefore, savings can be expressed as shown in the above equation, which is the primary IPMVP equation.
Fundamental Equation for Avoided Energy Consumption Using Forecasting
Avoided Energy Consumption = (Baseline Period Energy +/- Routine Adjustments to reporting period conditions +/- Non-routine adjustments to reporting period conditions) - Reporting period energy
The term forecasting is used to describe the adjustment of baseline period energy to reporting period conditions. This common style of estimating savings can be stated as shown in the above equation.
The adjusted baseline energy is frequently found by first developing a mathematical model that correlates actual baseline period energy data with appropriate independent variables in the baseline period. Each reporting period’s independent variables are then inserted into this baseline mathematical model to produce the adjusted baseline energy. This procedure is called forecasting.
Simplified Equation for Avoided Energy Consumption using Forecasting
Avoided Energy Consumption = Routinely Adjusted Baseline Energy
– Reporting Period Energy
± Non-Routine Adjustments to Reporting Period Conditions
The adjusted baseline energy is frequently found by first developing a mathematical model that correlates actual baseline period energy data with appropriate independent variables in the baseline period. Each reporting period’s independent variables are then inserted into this baseline mathematical model to produce the adjusted baseline energy. This procedure is called forecasting.
Fundamental Equation for Avoided Energy Consumption Using Backcasting
Avoided Energy Consumption = Baseline Period Energy
− (Reporting Period Energy ± Routine Adjustments to Baseline Period Conditions ± Non-Routine Adjustments to Baseline Period Conditions)
This process of calculating savings may be used in reverse, where the reporting period energy is adjusted to baseline period conditions and savings are determined under baseline conditions. The term backcasting is used to describe this adjustment of reporting period energy to baseline period conditions. Although rare, it can make sense to use this approach when more data are available in the reporting period than in the baseline period to develop mathematical models of energy consumption or demand (e.g., utility meter is upgraded to provide more frequent data). Since backcasting may introduce risk due to the unknown accuracy of modeling future energy consumption, it is best practice to use it as an optional method to forecasting.
Simplified Equation for Avoided Energy Consumption using Backcasting
Avoided Energy Consumption = Baseline Period Energy
− Routinely Adjusted Reporting Period Energy
± Non-Routine Adjustments to Baseline Period Conditions
This process of calculating savings may be used in reverse, where the reporting period energy is adjusted to baseline period conditions and savings are determined under baseline conditions. The term backcasting is used to describe this adjustment of reporting period energy to baseline period conditions. Although rare, it can make sense to use this approach when more data are available in the reporting period than in the baseline period to develop mathematical models of energy consumption or demand (e.g., utility meter is upgraded to provide more frequent data). Since backcasting may introduce risk due to the unknown accuracy of modeling future energy consumption, it is best practice to use it as an optional method to forecasting.
Another less common method of determining Avoided Energy Consumption may be considered when reporting period conditions are out of range of the baseline conditions and hinder making routine adjustments as planned. In these cases, the basis of adjustment may need to shift to some interim period conditions that include the full range of conditions (chaining)1.
Fundamental Equation for Normalized Energy Savings
Normalized Energy Savings = (Baseline Period Energy
± Routine Adjustments to Fixed Conditions
± Non-Routine Adjustments to Fixed Conditions)
− (Reporting Period Energy
± Routine Adjustments to Fixed Conditions
± Non-Routine Adjustments to Fixed Conditions)
Normalized energy savings use conditions other than those of the reporting or baseline periods as the basis for adjustment. The conditions may be those of an agreed-upon representative period or a typical, average or normal set of conditions as the basis of adjustment. Adjustments to a fixed set of conditions such as typical meteorological year (TMY) weather data provide a type of savings called normalized energy savings. In this method, the reporting period energy and the baseline period energy are adjusted from their actual conditions to the common fixed or normal set of meaningful conditions.
Normalized energy savings:
Require routine adjustments to the reporting period energy and the baseline period energy to a fixed set of conditions that are established once and are not changed.
Can be directly compared with savings from other time periods and EEMs where savings are predicted under the same set of fixed conditions.
Can only be reported after a full cycle of reporting period operating conditions so that the mathematical correlation between reporting period energy and operating conditions can be derived.
The calculation of the reporting period routine adjustment term usually involves the development of a mathematical model correlating reporting period energy with the independent variables of the reporting period. This model is then used to adjust reporting period energy to the chosen fixed conditions. Further, a mathematical model of baseline energy is also used to adjust baseline period energy to the chosen fixed conditions.
Simplified Equation for Normalized Energy Savings
Normalized Energy Savings = (Routinely Adjusted Baseline Period Energy to Fixed Conditions
± Non-Routine Adjustments to Fixed Conditions)
− (Routinely Adjusted Reporting Period Energy to Fixed Conditions
± Non-Routine Adjustments to Fixed Conditions)
Normalized energy savings use conditions other than those of the reporting or baseline periods as the basis for adjustment. The conditions may be those of an agreed-upon representative period or a typical, average or normal set of conditions as the basis of adjustment. Adjustments to a fixed set of conditions such as typical meteorological year (TMY) weather data provide a type of savings called normalized energy savings. In this method, the reporting period energy and the baseline period energy are adjusted from their actual conditions to the common fixed or normal set of meaningful conditions
The calculation of the reporting period routine adjustment term usually involves the development of a mathematical model correlating reporting period energy with the independent variables of the reporting period. This model is then used to adjust reporting period energy to the chosen fixed conditions. Further, a mathematical model of baseline energy is also used to adjust baseline period energy to the chosen fixed conditions.
Option A/B Savings when Adjustments are not required
Savings = SUMtime (Baseline Period Rate of Energy Consumption
x Baseline Hours of Use)
−
(Reporting Period Rate of Energy Use
x Reporting Period Hours of Use)
These equations are conceptual in nature, and the exact savings equations will be more complex because savings are the sum of the conditions over time, the hours at a specific rate.
Generally, using Option A: Key Parameter(s) Measurement would be appropriate for Scenarios 1 and 2, but not for Scenario 3 or 4. Option B: All Parameter Measurement is more suitable for EEMs impacting variable loads or EEMs impacting both loads and operating hours.
Simplified Equation for Avoided Energy Consumption Using Option D in New Construction
Avoided Energy Consumption = Baseline Period Energy from the Calibrated Model updated to Baseline Conditions
− Reporting Period Energy from the Calibrated Model
If the baseline period does not exist or baseline data are not available (e.g., new construction or repurposing of a building), the calibrated reporting period model can be used to develop the baseline model. For projects that develop a hypothetical baseline model (e.g., code-compliant baseline energy for a new construction project), the baseline model for M&V must be developed from the calibrated reporting period model with EEMs removed, as described above. In all situations, the models’ input parameters and measured energy data must be under the same set of operating conditions, similar to Option C.
Since the model is only calibrated to one period, the calibration error is assumed to equally affect the baseline period and reporting period models. For new construction, the calibration error is the actual reporting period energy minus the energy predicted by the calibrated model for the reporting period, which can be either positive or negative.
Cost Savings Using Total Costs Method
To calculate the difference in total costs of energy consumption and/or demand, the appropriate price schedule is applied to the energy consumption and/or demand. The same price schedule should be applied in computing both Cb and Cr using Equation below:
Cost Savings = Cb – Cr
Where:
Cb = Cost of the baseline energy plus any adjustments (i.e., cost of adjusted baseline energy)
Cr = Cost of the reporting period energy plus any adjustments (i.e., cost of adjusted reporting period energy)
The costs used in the equation are determined for the adjusted reporting period energy, including all routine and non-routine adjustments, and the adjusted baseline period energy, including all routine and non-routine adjustments.
This method can be best when actual costs are based on complex rate schedules, includes demand costs, or includes rate changes resulting from reduced consumption due to the installation of EEMs.
Calculate baseline gas use for those HDD into baseline model
Gas = slope *HDD+ Intercept
Calculate savings from a model with known baseline model and HDD
Fix (intercept) : 111,358
Variable : 173.27 (slope) x 420 (HDD) = 72,773
Total : 11,358 + 72773 = 184,131
Savings : 184,131 - 122,111 (consumption during reporting period)
= 62,020 mcf
62,020 mcf x 6.232 (price $)
= $386,511 value
Rate of heat transfer (kW)
= Mass flow rate (kg/s or LPM) x Temperature difference in Kelvin x Specific heat at constant pressure (kJ/kg K)
What error is better error: 12 observations at 4MWh +/-2 with 90% CL or 52 observations at 1MWh +/-0.9 with 90%CL?
2 x SQRT12 = 6.93 standard error
OR
0.9 x SQRT52 = 6.49 standard error
Therefore the second option has a lower standard error
