The following calculator can aid in the design of a precharge circuit for an electric vehicle. It will compute the precharge resistance required to achieve a desired percent charge of the system capacitance in a desired time.

The results provided herein are for reference only. Please contact Sensata applications engineering to review the calculation results and assist with product selection.

For more technical details on precharging, please refer to this whitepaper. **THE CALCULATOR AND ITS RESULTS ARE PROVIDED “AS IS” AND SENSATA HEREBY DISCLAIMS ALL WARRANTIES, WHETHER EXPRESSED OR IMPLIED, STATUTORY, OR OTHERWISE, INCLUDING BUT NOT LIMITED TO ALL IMPLIED WARRANTIES OF FITNESS FOR A PARTICULAR PURPOSE.**

## Definitions

Euler's Constant | e | 2.71828 | Numerical constant. |

Battery Voltage | Vb | System/battery voltage (DC). | |

Time Elapsed | t | Time elapsed since precharging started. | |

Precharge Time Desired (MAX) | T_{max} | Maximum time acceptable to get the system to the desired level of charge. | |

% Precharge Desired | q | Charge percentage of the system capacitance required before closing the main contactor. | |

System Capacitance | C | Capacitance of the system/load that needs to be precharged. | |

Number of Time Constants Required | n | n=-ln|1-q| | Number of time constants required to precharge the load capacitance to the desired percentage. |

MAX Precharge Resistance | R_{1,max} | R_{1,max} = \frac {T_{max}} {nC} | Maximum precharge resistance that will charge the load capacitance to the desired level in the desired time. The actual precharge resistance used can be less than this, which will result in faster precharging, but also higher power dissipation through the resistor. |

Chosen Resistor Value | R_1 | Chosen precharge resistor value. The maximum resistance calculated above can be used for this by checking the box, but any other value can also be plugged in, for example, to experiment with resistors that are readily available on the market, or to try precharging faster. | |

Total Series Resistance in Main Circuit | R_2 | Total resistance of the load(s), conductors, contact resistances of switches and connectors, etc. in the main circuit. This can be determined as follows: With your system fully assembled and connected, the positive main contactor (K_2) in the open state, and both the negative main contactor (K_1) and precharge contactor (K_3) in the closed state, use an ohmmeter to measure the resistance across the positive main contactor (K_2) power terminals. This is used to determine the inrush current through the main contactor (K_2) when it is closed after precharging is done. R_2 should be much less than R_1, otherwise, the precharge circuit would not be needed. | |

Time Constant | τ | τ=R_1C | Time constant for the RC circuit. This is the amount of time it would take to charge the capacitor to 63.2% SOC. Five-time constants are a good rule of thumb for fully charging a capacitor. Anything less could put the main contactor at risk of welding. This can be adjusted by changing the precharging time input 'T_{max}'. |

Actual Precharge Time | T | T = nR_1C | The actual time it takes to precharge the system to the desired level using the chosen resistor value. If R1max is used, this time should equal the desired precharge time input. |

Precharge Circuit Inrush Current | I(0) | I(t) = \frac{V_b}{R_1}e^ \frac{-t}{R_1C} Evaluated at t=0 I(0) = \frac{V_b}{R_1} |
Peak current at t=0, right when the precharge contactor is closed. This is important for checking the capability of the precharge contactor to close under load. The precharge contactor will need to close into this current every time the system is precharged. |

Capacitor Voltage | V_c(t) | V_c(t) = V_b(1-e^{\frac{-t}{R_1C}}) | Voltage across the load capacitance at a time 't' after precharging starts. This increases as the capacitance is charged. |

Energy Dissipated by Precharge Resistor | E(T) | E(t) = \frac{CV_b^2}{2}(1-e^{\frac{-2t}{R_1C}}) Evaluated at t=T E(\infin) = \frac{CV_b^2}{2} |
Cumulative energy that will be dissipated by the precharge resistor during precharging. If the precharge time is very large (>5 time constants), this will approach \frac{CV_b^2}{2}, which is equal to the total energy stored in the capacitance when it is fully charged. |

Power | P(t) | P(t) = I(t)^2R_1 | Power dissipated through the resistor at a time 't' after precharging starts. |

Average Power | P_{avg} | P_{avg} = \frac{E(T)}{T} | Total energy dissipated by the precharge resistor divided by the actual precharge time. When selecting a precharge resistor, make sure it can handle 'P_{avg}' for 'T' time. |

Peak Power | P_p | P_p = I(0)^2R_1 | Peak instantaneous power that the precharge resistor will see. This occurs at the instant when the precharge contactor is closed. When selecting a precharge resistor, make sure it can handle 'P_p' for very short durations, \lll T. |

Voltage Delta Remaining After Precharge | V_d(T) | V_d(t) = V_b-V_c(t) V_d(t) = V_be^{\frac{-t}{R_1C}} Evaluated at t=T |
Voltage drop remaining across the main contactor after precharging. This, along with the series resistance in the main circuit, will determine the inrush current through the main contactor when it is closed. |

Main Contactor Inrush Current After Precharging | I_m | I_m = \frac{V_d(T)}{R_2} | Once precharging is complete, this is the inrush current the main contactor will be exposed to when it is closed. |

**The results provided herein are for reference only. Please contact Sensata applications engineering to review the calculation results and assist with product selection.**