The paper is focused on the electromagnetic analysis of the Toroidal Field superconducting coils (TFCs) of the Divertor Tokamak Test facility (DTT) when electrical transients occur in the TFCs system: for example, during the operations of the Fast Discharge Units (FDUs) and considering also, the simultaneous occurrence of a fault condition. During the FDU intervention, a transient voltage excitation lasting few milliseconds occurs at the TFC terminals and it electrically stresses the insulations of TFCs itself. To investigate the voltage distribution across, inside and between different Double Pancakes (DPs) of each TFC, a lumped parameters circuital model has been developed and implemented in Ansys Simplorer simulation environment. This model includes both the detailed sub-model of each TFC and FDU. The transient analyses have been carried out for two different scenarios: a reference one and a failure scenario, considering three different fault resistance values and also two different values of the resistance connecting the TF case to ground. In order to verify the correct sizing of the coil insulation and the TF case-to-ground resistance value inserted in the circuit of each TFC, the voltages of each TFC (terminal-to-terminal, terminal-to-ground, across of adjacent DPs and between other circuit points) were computed in the time domain (in the range of milliseconds) for both scenarios. An overview of calculations and simulation results is presented and discussed, pointing out a high sensitivity of fault conditions and of overvoltage values and addressing mitigation strategies.