2.4.1. Miles Driven

Electrical, natural gas, and gasoline monthly demands are estimated based on average monthly driving distance (per user specifications) and user input parameters for vehicle mpg and mpkWh. StepM leverages forecasts from publicly available information of the Energy Information Administration [46] to assign costs based on miles driven, mpg, and mpkWh (see author-proposed Equation (2):

> *Variable Fuel Costs* = *Grid* × *% Battery* × *(\$*/*kWh Electricity)* × *(kWh*/*mile)* × *miles* + *(1-GRID) % Natural Gas* × *% Battery* × *(\$*/*kWh Natural Gas)* × *(kWh*/*mile)* × *miles* + *% Solar x 0* + *(1* − *% Battery)* × *(\$*/*gl)* × *(gl*/*mile)* × *miles.* (2)

In Equation (2), *GRID* is an indicator variable identifying that the residence relies on an electrical grid for recharging the vehicle rather than natural gas. *% Battery* is the percent of vehicle power generated by the battery for PHEVs and BEVs. *% Natural Gas* is the percentage residential battery recharge from natural gas. Electric car costs are then calculated by taking the estimated cost per kWh, multiplying by kWh per mile and the distance driven in miles. *Solar* charging assumes away gray power, power produced when solar is not active, and is set to zero. This is an artificial simplification. Cars that are not fully electric generate costs based on dollars per gallon times gallons per mile and distance in miles for the percentage, not powered by batteries.

### 2.4.2. Natural Gas, Electricity, and Regular Gasoline Prices

Monthly natural gas residential price data from the Energy Information Administration (EIA) in dollars per 1000 cubic feet (converted to dollars per kWh) were used to estimate costs for BEV and PHEV re-charging from residences using. The data were state-dependent with Hawaii being an obvious outlier. To account for seasonality in natural gas costs, simple error, trend, seasonality (ETS) models implemented using the *fpp2* library in R were used [47]. These models proved reasonable versus ARIMA (auto-regressive, integrated, moving average models), as well as random walks for this data in previous research [5].

Grid electricity costs from the EIA in dollars per kWh have trended slowly upwards since 2001 and vary largely by state, with Hawaii having the most expensive residential costs [46]. Due to the large cost variability, ETS models by state were used to forecast costs over the vehicles' lifespans. A previous study also found that ARIMA and ETS models performed nearly identically for this variable [5].

The EIA does not publish gasoline prices for each of the states but rather only U.S. averages, U.S. petroleum regions, and data for nine selected states and cities. All states in petroleum production regions were then assigned the regional cost for regular gasoline, unless the state had its own estimates from the EIA.

Figure 2 compares the costs of natural gas, electricity, and regular gasoline per kWh for the United States based on the publicly available EIA data discussed and shows the values used for forecasting from ETS modeling. About 1000 cubic feet of natural gas is 293.07 kWh, and 1 gallon of regular gasoline is equivalent to about 36 kWh, so for comparison, the *y*-axis is shown in dollars per kWh. The data exhibit significant seasonality and illustrate that natural gas is the cheapest alternative of the three.

**Figure 2.** Actual energy costs and Error, Trend, Seasonality forecasts by source.
