(Left) Percentage breakdown of panel sizes in four census regions [12]. (Right) Number of panels (in millions) that require an upgrade in the case of full electrification with backup heat and electrical vehicle adoption.

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... Midwest, and Northeast are all-electric, compared to 44% in the South. This finding echoes the Electric Power Research Institute's (EPRI's) recent report [12], which found that of homes in the U.S. with 100 A or less, 80% have three or fewer large electrical appliances. The breakdown of panel sizes by the four census regions is summarized in Fig. ...

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... will require a panel upgrade (35.8% in the Midwest). Extrapolation of EPRI's analysis should be done with care due to the relatively small sample size. However, applying these results to the number of single-family units in each region, the number of single-family homes that could require panel upgrades in the U.S. is about 23 million households. Fig. 2 shows the geographical breakdown of these estimates. With the average cost of upgrading each panel around $2,000 -$10,000, the total cost to upgrade electrical panels in single-family homes could well be in the tens or hundreds of billions. These estimates exclude multi-family homes, which generally have lower panel capacities per unit ...

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... draws up to 22 A during normal heating operation and up to 7 A during defrost cycles. The HP has three stages of backup resistance heat. Stages I, II and III draw 40, 60, and 80 A, respectively. The WH draws 18.7 A. In combination, all other devices in the house rarely draw more than 20 A and never more than 40 A (see the righthand plot in Fig. ...

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... of the test house do not follow typical workday routines. Therefore, rather than attempting to predict the exact uncontrolled load, historical data were used to compute 99% confidence intervals for each hour of the day. The supervisory controller was then designed to be robust to these (nearly) worst-case realizations of the uncontrolled load. Fig. 12 shows historical data and confidence intervals for the whole-house current (left plot) and the current from the uncontrolled loads (right plot). These plots show that the current from uncontrolled loads (∼10-20 A at the 99th percentile) is a relatively small part of the whole-house current (∼70-110 A). The controlled HP and WH make up ...

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... q α (k) is the α-quantile of I u (k). The righthand plot of Fig. 12 shows empirical estimates of q α (k) with α = 0.99. In practice, enforcing these constraints often led to infeasible MPC problems. Furthermore, as discussed in Section 2.3, rare violations of the current limit may be acceptable, but the violations must not be too large or the main circuit breaker may trip. For these reasons, the MPC ...