Analysis of Transients in a Three-Level DC–DC Flying Capacitor Converter. Time Domain Approach

Abstract

The paper considers a discrete state-space model for transients in a three-level flying capacitor DC–DC converter. A transition matrix is obtained for a pulse width modulation (PWM) period. The matrix elements are expanded into a power series using a selected small parameter. The matrix eigenvalues that determine the natural balancing dynamics transients are presented in the form of power series as well. Four separate transients are constructed based on four possible PWM period initial states (topologies). Inductor current and capacitor voltage transients are found for the voltage source power-up as the arithmetic average of the four separate transients. The discrete solutions are replaced by continuous ones. The resulting transients that are elementary functions of the circuit parameters, PWM period, and voltage reference demonstrate good agreement with the simulation results.

Analysis of Transients in a 4-Level Flying Capacitor Converter: Time Domain Approach. Part 1: Large Normalised Voltage Command

“…The use of equation 2(the discrete model of the FCC) assumes giving up the details of FCC behaviour within a PWM period. Using the terminology (Reznikov et al, 2019), the FCC behaviour in the "short" time is ignored, and the focus is put on the average behaviour in the "long" time by considering the FCC behaviour at the discrete moments t k . In accordance with the above, let us rewrite equation 2as ( ) ( )…”

“…Time domain approach for average transients in a three-level DC-DC flying capacitor converter (FCC) was first described in detail in Reznikov et al (2019). In that paper, the processes in "short" and "long" time were separated and the strict and detailed analysis was carried out for "long" time process.…”

“…In comparison with the three-level FCC, a four-level one potentially has smaller ripples for steady-state load current and capacitor voltages due to the higher number of output voltage levels. It was previously noted (Reznikov et al, 2019) that the frequency domain approach (Wilkinson et al, 2006a(Wilkinson et al, , 2006bYuang et al, 2001) leads to extremely cumbersome formulas that do not allow to trace the dependence of the transient characteristics on the FCC circuit, load and pulse width modulation (PWM) parameters. The time domain approach to natural balancing dynamics of a four-level FCC was first presented in Reznikov and Ruderman (2009).…”

“…The purpose of this paper was to present a strict and detailed derivation of simple and accurate formulas for average transients that clearly show the dependences of the FCC circuit and PWM period parameters on the basis of ideas presented in Reznikov et al (2019) for a three-level FCC. Figure 1a shows a four-level DC-DC FCC topology.…”

“…Figure 1a shows a four-level DC-DC FCC topology. The transient analysis is carried out under the assumptions accepted for a three-level FCC (Reznikov et al, 2019), namely, the load is represented as a series connection of inductance and resistor, the switches are bi-directional with zero resistance in the conductive state (ON) and infinite in the open-circuit one (OFF) and switching times are negligibly small.…”