Methodology

This page describes the methodology for estimating the average annual energy burden for census tracts in the Fairbanks North Star Borough.

Note

This methodology was originally developed in 2024, resulting in a static report. The findings and methods for that paper can be found here: Kaczmarski, J., Pride, D., &; Trochim, E. (2024). Spatial Energy Burden Analysis of the Fairbanks North Star Borough (1.0.0). Zenodo.

Tool Overview

With this tool, we define energy cost burden as the share of a household's income that is spent on space heating and electricity. This allows comparison across different geographies because it accounts for differences in incomes, energy prices, and use by households. In this study, we aim to estimate the average annual energy cost burden for households within each census tract. Doing this requires two main steps:

1. Estimating the average space heating and electricity load of a residential unit in the census tract of question.
2. Calculating the average space heating and electricity costs of meeting those energy loads.

Step 1 is an in-depth process that required combing through the property tax database for single and multi-family residential structures and estimating their energy load based on the structure's age and size. Each census tract in the borough contains a unique mix of structures based on age, size, and amount, which allows for some variation (i.e., tracts with newer construction may have less energy load than tracts with older construction). This is an oversimplification of the process taken, which we detail in the above mention 2024 study, and we encourage users to familiarize themselves with the estimation strategy and its limitaions. This tool does not recalculate energy loads and it is assumed that the energy load is fixed. This means that the data used for the energy load is from the 2023 property tax database.

Step 2 is what this tool allows users to interact with. Given that we have the energy load from step 1, we can change assumptions when calculating the energy cost burden, which are primarily energy prices, household income, and occupancy rates for each census tract. Since energy prices fluctuate widely, this tool allows you to set prices per unit for energy sources such as heating fuel oil, cord wood, pellets, coal, district steam, natural gas, electricity, etc (the default prices are from the 2024 study).

When you submit your assumptions for calculation, then the map will update to reflect the new estimates for average annual energy cost burden for each census tract in the borough.

Mathematical Appendix

This section includes details on how each component of the model is calculated.

Weighted Average Space Heating Costs

The borough has a number of homes that use different primary sources of fuel. To best represent what the average household spends on space heating, we build an average space heating cost ($/MMBtu) that is weighted by the distribution of households using each fuel type as their primary, which we call the market share. The market share of each fuel use type is based on Carlson, T., Zhang, W. Analysis of Fairbanks 2013-2015 Home Heating Surveys. Sierra Research. Sierra Research. 2015, pp 1–39. The following formula describes how the price inputs make their way into calculating the weighted average space heating price,

$$P^{SpaceHeat} = \sum_j \left( P^j\cdot MarketShare_j \right)$$

where,

• $P^j$ is the price per MMBtu of useful energy for fuel $j$.
• $MarketShare_j$ is the share of borough survey respondents using fuel $j$ as their primary fuel source.

The prices input into the calculator are represented in different units (e.g., $/gallon or $/ton, etc.) and must be converted to $/MMBtu of useful energy. Since different fuels pass through appliances with different conversion efficiencies, we use the average fuel use efficiency as reported by the FNSB's Fall 2023 Community Research Quarterly.[^1] The following functional form describes this conversion process,

$$P^j = \frac{1,000,000}{UnitBtu_j \cdot AFUE_j}\cdot P^u_j$$

where,

• $UnitBtu_j$ is the conversion from the unit provided (e.g., gallons of heating fuel oil, tons of coal, tons of pellets, etc.) to MMBtu.
• $AFUE_j$ is the average fuel use efficiency (0 to 1) of converting BTUs to useful heat (see FNSB's Fall 2023 Community Research Quarterly).
• $P^u_j$ is the price per unit that the user provided.

The following conversion factors were used in this study and were found from the FNSB's Fall 2023 Community Research Quarterly,

• 1 gallon of heating fuel oil (No. 1) = 137,400 Btu
• 1 cord of split wood = 17,750,000 Btu
• 1 ton of pellets = 16,000,000 Btu
• 1 CCF of natural gas = 101,000 Btu
• 1 ton of coal = 15,200,000 Btu
• 1,000 lbs of district heat (steam) = 1,066,000 Btu

[^1]: Fairbanks North Star Borough, Department of Community Planning, Community Research Quarterly, Vol. XLVI, No. 3, 2023.

Average Electricity Costs

The total annual electricity consumption costs within census tract $i$ are calculated as follows,

$$ElecCost_i = P_e \cdot ElecMMBtu_i$$

where,

• P_e is the average electricity cost per MMBtu. This is converted from the user provided electricity price ($/kWh) with the following formula: $P_e = \frac{1,000,000}{3412}\cdot P_e^u$ where $P_e^u$ is the price of electricity per kWh.
• $ElecMMBtu_i$ is the total estimated electricity load for single and multi-family residential structures in the census tract.

Space Heating Costs

The total annual space heating costs within census tract $i$ are calculated as follows,

$$SpaceHeatCost_i = P^{SpaceHeat}*SpaceHeatMMBtu_i$$

where,

• $P^{SpaceHeat}$ is the weighted average space heating costs. The definition of this is provided in Weighted Average Space Heating Costs.
• $SpaceHeatMMBtu_i$ is the total estimated heat load for single and multi-family residential structures in the census tract.

Average Annual Household Energy Cost

The average annual household space heating and electricity costs for census tract $i$ are defined as follows,

$$EnergyCosts_i = \left(\frac{SpaceHeatCost_i + ElecCost_i}{OccupiedUnits_i}\right)$$

where,

• $SpaceHeatCost_i$ is total estimated expenditures on space heating for all single and multi-family residential properties within the census tract.
• $ElecCost_i$ is the total estimated expenditures on electricity for all single and multi-family residential properties within the census tract.
• $OccupiedUnits_i$ is the number of occupied housing units within the the census tract as reported by the census.

The result is the average space heating and electricity expenditures per occupied household within the census tract.

Average Annual Energy Cost Burden

The average annual household energy cost burden for census tract $i$ is defined as follows,

$$EnergyBurden_i = \frac{EnergyCosts_i}{Y_i}$$

where,

• $EnergyCosts_i$ is the average annual household space heating and electricity costs.
• $Y_i$ is the median household income as reported by the census.

The result is a measure of the average amount of a household income that is spent on space heating and electricity.