# Evaluating the Impact of the COVID-19 Pandemic on Residential Energy Use in Los Angeles
## 2 Materials and Methods
### Load Evaluation  
First, individual feeders' average loads were compared on a monthly or weekly basis (using an ISO 8601 defined week--see Table S4) across the period of study without temperature normalization or restriction. Major holidays were excluded from categorization. Analysis of input data and calculations were performed in kW and kWh. For temperature analyses, hourly average temperature values were used along with monthly degree day values, which were assessed from local NWS observation weather station monthly reports (see Table 1 for data source information). Interpolative re-sampling was used to correlate temperature data to load data. Temperature data and derivative units were converted from \({}^{\circ}\)F to \({}^{\circ}\)C for final reporting and rounded to the nearest 0.1 \({}^{\circ}\)C for reported values. Two effects of temperature on load must be distinguished in these analyses. First, the expected effect of temperature on electricity use (particularly cooling on hot days) must be considered when comparing across periods with different temperature patterns. Second, higher residential occupancy rates can increase households' response to temperature, making the effect of hot days stronger during the stay-at-home periods than otherwise. Temperature models to assess sensitivity to load change due to temperature change were created using 2018 and 2019 daily average load data (for counterfactual models) discretely processed with ambient temperatures corresponding to feeder weather station source. As individual household loads are not available, reporting is performed in percent change compared to the counterfactual model used as a baseline for 2020 observed data. Depending on the specific application, temperature data was used as average period temperature or relative to heating or cooling degree days with a customary balance point of 18.3 \({}^{\circ}\)C (65 \({}^{\circ}\)F). In average-temperature regression models, the mean static temperature (MST) temperature was used rather than the customary degree day balance point value in calculation. Processing was performed as an average daily load considering daily average temperature (computed average of all periods as opposed to average of minimum and maximum daily observed temperature approach, which is used with degree-day calculation). Hourly models were used for direct comparison of specific, short-term periods. Being more stable, daily models were used in the linear modeling methods used in this report, consistent with similar observations in previous method comparisons [19; 27]. For the relationship of energy usage to ambient temperature, piecewise regression corresponding to ASHRAE RP-1050 type linear change-point regression [37; 38] was used to determine the 5-parameter models used (corresponding to three segments marked by two change points (CPs)-representing three regressed periods of load versus temperature), see Equation (1):  
\[ \begin{array}{l}y=m_{1}x_{1}+b_{1}\ (\text{inf. to low CP bound, t}_{1}),\\ y=b_{2}\ (\text{low CP bound, t}_{1}\ \text{to high CP bound, t}_{2}),\\ y=m_{2}x_{2}+b_{3}\ (\text{high CP bound, t}_{2}\ \text{to inf}),\end{array}  \tag{1}\]  
where \(y\) is an average feeder load (kW), \(m_{1}\) is a regressed constant (kW/temp), \(x_{1}\) is a period average temperature value (below the low CP bound), \(m_{2}\) is a regressed constant (kW/temp), \(x_{2}\) is a period average temperature value (above the high CP bound), \(b_{1}\) and \(b_{3}\) are a set of regressed intercept values corresponding to load at the CP bounds (kW) and \(b_{2}\) is average constant load (kW) across temperature range between CP bounds. This model accounts for temperature effects on energy use for heating and cooling as well as temperature ranges where load is not substantially affected by temperature.