Home EV Charging Losses: Level 1 vs Level 2 and Cold Weather

The energy boundary is the home meter to additional usable battery energy. Source power is $VI\,PF$, wiring loss is $I^2R_w$, and EVSE electronics are accounted separately. The actual AC current falls when the charger rating, battery acceptance or taper limits the demand.

With $x=P_{AC}/P_r$, charger loss is $P_r(f_0+f_1x+f_2x^2)+\delta_1P_{AC}$; $\delta_1$ applies only to Level 1. The default coefficients fit 22 points in TI PMP22650/TIDT249 (September 2021), section 3.4, printed p. 9, at approximately 240 V input, 350 V output and 20 °C coolant, excluding the two reference-case points. Those held-out checks allow 0.7% relative efficiency error. The measured curve excludes external 12 V bias; the awake-load input includes its DC-equivalent demand.

The pack uses $U_{oc}=V_n(0.9+0.2s)$ and $R_b=R_{20}\exp[\beta(20-T)]\{1+(2s-1)^2\}$. At every step, the stable positive root of $P_b=U_{oc}I_b+R_bI_b^2$ gives battery current. Accepted current is the smaller of available-power current and a warm pack-current limit, derated linearly between the minimum charging temperature and heating setpoint and tapered linearly above the chosen charge percentage to a finite termination fraction. Stored-energy fraction obeys $\dot s=U_{oc}I_b/E_{usable}$.

The heater has priority over charging, with $K_h=C_{th}/(900\,\mathrm{s})$. Its requested power is $\max[0,K_h(T_{set}-T)+G(T-T_a)]$, bounded by heater capacity and available DC power. Thermal dynamics are $C_{th}\dot T=P_h+I_b^2R_b-G(T-T_a)$. Midpoint integration advances energy fraction and temperature, accumulating every energy flow with the same quadrature and shortening the last step at the target. Both electrical and thermal balances are checked.

Annual cost scales the weighted cold/reference-session wall energy by annual stored energy divided by the exact requested positive session stored energy. Every contributing warm session must complete, including a separately selected current. C-rate is battery current divided by nominal Ah capacity $E_{usable}/V_n$. Kieldsen et al. (2016), section 3.4, supports separating battery and auxiliary losses. Unlike the sample averages in their equations 4–5, session efficiency here is a ratio of integrated energies, including taper.

The household supply is single phase with constant RMS source voltage, power factor and operating-temperature loop resistance. The EVSE’s electronics load is supplied at the meter boundary. The battery heater is resistive with unity electrical-to-thermal conversion, with no heat recovery from the charger.

The pack is one lumped cell-temperature node. SOC means fraction of stored usable energy, not an exact coulomb-counted cell SOC. Pack resistance, thermal capacity, heat conductance, temperature coefficient, voltage curve and BMS acceptance are adjustable illustrative assumptions, not a calibration of a production EV. Charger fixed and quadratic losses scale with rated power; transplanting a 7 kW test curve to another rating is an assumption.

The additional Level 1 penalty defaults to zero. INL's 2012 Volt results compare different powers as well as different voltages and therefore cannot isolate a universal voltage-only penalty. Set an additional penalty only from appropriate measurements. Charging stops at the target; balancing dwell, parked high-SOC exposure, cabin heat and subsequent standby are excluded. Warm reference sessions begin at 20 °C outdoors and in the pack.

For comparative AC home-charging scenarios, not a vehicle-specific range, battery-life or installation certification. The TI fit is grounded in 240 V, 350 V DC, 20 °C coolant tests; other ratings, 120 V operation, very low loads and other pack voltages are extrapolations. Coefficients and the optional Level 1 correction should be calibrated to measured vehicle data. The curve checks validate the conversion subsystem only, not complete winter charging sessions.

Default integration steps are at most 60 s, shortened for thermal control, short sessions and the final target; cold-case wall energy and duration are checked against 30 s steps. Display curves use shape-preserving interpolation of solved samples, with 241 display points per trajectory; the schematic linearly interpolates the selected trajectory. Integration ends at seven days or a stalled heating equilibrium. If an entered-temperature session or a contributing 20 °C annual reference cannot reach the target, results are withheld and the inputs must be changed. Warm references are excluded from completion validation only when the cold-session share is 100%. Annual session count divides annual stored energy by the exact positive session increment; no denominator floor is applied.

The pack model omits entropy heat, spatial hot/cold spots, changing capacity, detailed electrochemistry and active cooling. A conditional message flags temperatures above 45 °C because those cases need a cooling model. The BMS cutoff and taper are assumed controls, not cell charging instructions. Peak lumped cell temperature, current and time above 90% do not determine a percentage of battery wear. Electrical losses become heat; heater energy may remain temporarily stored as pack sensible heat and is not counted as usable battery energy.

SAE J1772 terminology follows US AC charging levels as summarized by DOE AFDC; this calculator implements no installation-code sizing rules. Tariffs are user inputs, with an illustrative default dated 6 November 2026.