MCS Truck Charging: Cable Heat, Losses and Charge Time

The DC circuit has two identical copper conductors and two identical contact paths. For each cable pole, $R_{20}=\rho_{20}Lk/A$ and $R(T)=R_{20}[1+\alpha(T-20\,°C)]$. Copper resistivity 0.017241 Ω·mm²/m and temperature coefficient 0.00393 K⁻¹ follow NBS Handbook 100 (1966), PDF p. 9. Density is 8890 kg/m³; the 385 J/(kg·K) heat capacity follows the Kanthal C11000 ETP datasheet (2021).

Each pole has a cable thermal node and a separate contact node, both connected to a fixed effective sink; there is no direct thermal coupling between the nodes. The per-pole cable equation is $C_w\,d\Delta T_w/dt=I^2R(T)-\Delta T_w/\theta_w$, where $\theta_w=R_{line}/L$ and $C_w=m_{Cu}c_{Cu}k_{mass}$. Define $b=1-\theta_w I^2R_{20}\alpha$. For $b>0$, $\Delta T_{w,\infty}=\theta_w I^2R(T_{sink})/b$ and $\tau_w=\theta_w C_w/b$. The rise is $\Delta T_{w,\infty}(1-e^{-t/\tau_w})$. Contact rise is $\theta_j I^2R_j(1-e^{-t/(\theta_j C_j)})$ with fixed measured contact resistance.

Total cable/contact loss is $2I^2[R_w(t)+R_j]$. Integrating dispenser power minus these losses gives vehicle-terminal energy. A bracketed root solves for the time at which storage efficiency times that energy equals the requested capacity increment. The continuous-current ceiling solves the steady heat balance at each entered temperature limit; the lower result is reported. Current is not automatically derated.

The circuit, thermal ODE and its analytical integral are derived here. NBS wire-table cases verify resistance and temperature correction; the manufacturer case verifies DC power only. These references do not validate the illustrative thermal parameters against an MCS assembly.

Constant charging current and representative constant dispenser voltage; stored-energy state of charge is proportional to usable battery energy. Two equal copper poles, uniform cable temperature per pole, constant specific heat and cooling parameters. All nodes initially equal the cooling sink temperature. Cable thermal mass includes copper multiplied by the entered factor. Contact resistance is an operating-condition value held constant and covers the same path as its thermal node. No axial or cable-to-contact heat transfer is resolved.

Defaults for contact resistance, cooling, thermal mass and temperature limits are transparent example inputs, not measured MCS product data. Fit thermal resistance from steady temperature rise divided by node heat and fit heat capacity from the measured time constant. For the cable, include copper resistance feedback when fitting.

Use for comparative electrical-loss and first-order thermal studies of DC truck charging with a stable cable equilibrium, positive vehicle-terminal power, and modeled node temperatures up to 200 °C. Short pulses and local hot spots may need a distributed model; coolant warming and flow dependence are absorbed only into the user-supplied effective sink and thermal resistances. A copper-only thermal mass is not a prediction of the full assembly's measured transient.

The reported thermal ceiling checks the entered node temperature limits only. It does not establish ampacity, connector surface temperature, touch safety, protection response, cooling-loss behavior, or permitted charging current. The charge-time scenario excludes BMS taper, changing pack voltage, power limits and charging interruptions. Storage efficiency describes vehicle-terminal energy to stored energy; upstream AC/DC and cooling auxiliary losses are excluded.

IEC TS 63379:2026, edition 1.0, is relevant context for MCS assemblies, not the source of this model or its example temperature limits. Check actual manufacturer ratings and check against the standard in force.