The goal of the paper is in studying modern high-energy density multilayer ceramic capacitors (MLCCs) with nonlinear dielectrics such as X7R, Y5V, Z5U. The charging-discharging modes of MLCCs as well as the frequency spectra of dielectric characteristics such as admittance and equivalent series resistance (ESR) have been investigated. We have proposed an approach to estimating the dielectric loss in pulsed modes based on ESR frequency spectrum averaging. The capacitance dependencies on DC bias voltage have been obtained. A mathematical model for analytical calculation of the circuit electrical parameters is proposed. The model takes into account the capacitance dependence on applied voltage. The adequacy of the model is confirmed by the numerical calculations and experimental studies results.