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This research presents a study of the ringing and voltage overshoot analysis of a proposed DC/AC converter. This overvoltage is generated due to the resonance between three passive components: transformer leakage inductances, switch capacitances, and wiring resistances. By applying simple RLC circuit equations, it proves possible to determine the analytic equations and reproduce the voltage across the switche s to predict the overvoltage and resonance frequency. The circuit is built and tested experimentally to validate the theoretical concept.

In this paper the current and voltage ringing of the DC/AC converter, proposed by the author in [

It is convenient to use the circuit shown in

The circuit can be seen as a conventional voltage source inverter when v_{SA} is positive and not zero and when S_{B}_{18}, S_{B}_{20}, S_{B}_{22}, and S_{B}_{24} are switched on. On the other hand, when switches S_{B}_{17}, S_{B}_{19}, S_{B}_{21}, and S_{B}_{23} are switched on and v_{SA} is negative and not zero, it can also be seen as a conventional inverter. Therefore, it can be modulated as a conventional inverter in each half period. This converter is similar to a high frequency link DC/AC converter [

To carry out the ringing analysis a parasitic capacitor is placed in parallel with each switch, as shown in

The circuit in

As shown in _{SA} during the first half-period, which are also repeated in the second half-period. Each oscillation has a different path, and the three paths are highlighted in

The first oscillation type appears when v_{SA} changes from −U_{SB} to +U_{SB}. _{LS} (shown in _{B}_{17}, S_{B}_{18}, S_{B}_{21}, and S_{B}_{22}); therefore, there is no current through the transformer. The resulting circuit loop consists of resistors, inductances, and capacitors, where the oscillating current passes through the capacitors in parallel with the switches S_{B}_{19} and S_{B}_{23}. Since the upper switches are conducting the load current, the voltages across S_{B}_{19} and S_{B}_{23} are the same. Because the capacitor C_{SB} has a high value, its internal resistance R_{CSB} is quite low (2 mΩ); thus, the SB port can also be seen as a short circuit at high frequencies.

In order to predict the behavior of the voltage across the snubber capacitors in parallel with S_{B}_{19} and S_{B}_{23} a formulation is developed in the following. To carry out the calculations, the well-known relationship for a RLC network is applied.

The oscillation frequency of a weakly-damped parallel resonant RLC network is known to be

Using the parameters from [

Using the parameters shown in [

resulting in ζ = 0.05. A system with a damping factor lower than unity is expected to be underdamped.

The general expression for the capacitor voltage in a RLC network [

where v_{f} is the DC voltage component, and s_{1} and s_{2} are, respectively,

The coefficients A_{1} and A_{2} are determined by the boundary conditions. For the specific situation in _{1} and A_{2} are given by, respectively,

where C is the equivalent capacitance of C_{SB}_{19} and C_{SB}_{23} in parallel, i_{PA} is the initial current through the transformer leakage inductance, and v_{oC} is the initial voltage across the capacitor C.

For the first oscillation mode, the initial current through the transformer leakage inductance and the initial voltage across C_{SB}_{19} and C_{SB}_{23} are both zero. Under these initial conditions, the voltage waveform across the switches S_{B}_{19} and S_{B}_{23} is determined by (3). The results were plotted with MATLAB software and they are similar to the simulation outcome from the PSIM software, which is shown in the

Independent of the current value that circulates through the load, the voltage waveform across the switches S_{B}_{19} and S_{B}_{23} never changes in the first oscillation mode because the initial conditions are always the same. The resonant frequency of the circuit was calculated and confirmed by simulation to be 3.3 MHz.

The second oscillation mode in _{SB} starts sending energy to the load, as shown in _{B}_{19} is clamped with the load voltage (v_{SG}). The voltage v_{SG} can be calculated because the current through the load at this moment is known. Therefore, the initial conditions in this case are the voltage value of v_{SG} (at that specific moment) and zero current through the transformer leakage inductance. Using these quantities and (3), a theoretical voltage waveform across S_{B}_{19} for the second oscillation mode can be determined. The voltage waveforms across S_{B}_{19} and S_{B}_{21} are the same in this case.

The third oscillation mode starts when the power source U_{SB} stops sending energy to the load, as shown in _{PA} and L_{SA}) are equal to the load current i_{LS}, the voltage across S_{B}_{21} is equal to U_{SB}, and the voltage across S_{B}_{17} is zero. Thus, the currents coming from the leakage inductances and from the capacitor in parallel with S_{B}_{21} start charging the capacitor in parallel with S_{B}_{17}. When the voltages across S_{B}_{21} and S_{B}_{17} reach the same value, oscillation starts. Under these initial conditions, the theoretical voltage waveform across the switches S_{B}_{17} and S_{B}_{21} can be calculated. When the load current is negative, the same overvoltage is generated across the switches S_{B}_{20} and S_{B}_{24}. As such, the highest overvoltage will always occur on the outer switches S_{B}_{17}, S_{B}_{20}, S_{B}_{21}, and S_{B}_{24}, as shown in

The three oscillation modes can be summarized as follows. Once the equivalent RLC circuit parameters are determined, the first oscillation mode is dependent on the voltage U_{SB}, the second oscillation mode is imposed by the load current i_{LS} and voltage v_{SG}, and the third oscillation mode is based on i_{LS} and U_{SB}. For the parameters shown in _{LS} = 40 A, the maximum overvoltage is approximately 1500 V, as shown in

Consequently, with the method described in this section it is possible to determine the maximum peak voltage across the matrix converter switches for the maximum load current (i_{LS} = 40 A). The results in _{B}_{17}, S_{B}_{20}, S_{B}_{21}, and S_{B}_{24}). The outer switches have the most stress because they are switched off when the load current is at its highest value. Thus, snubber capacitors should be connected in parallel with these switches. The design of these snubber capacitors is described in the following section. The inner switches (S_{B}_{18}, S_{B}_{19}, S_{B}_{22}, and S_{B}_{23}) do not need snubber capacitors

Parameter | Value |
---|---|

Leakage inductance of the primary and secondary winding | 1 μH |

Resistance of the primary and secondary winding at 3.3 MHz | 1.9 Ω |

Total cable resistance at 3.3 MHz | 600 mΩ |

Transformer turn ratio | 1 |

Capacitor in parallel with each matrix converter switch | 580 pF |

Resistance in parallel with each matrix converter switch | 2.5 Ω |

Switching frequency | 10 kHz |

Load resistance | 10 Ω |

Load inductance | 2 mH |

Capacitor at SB port (C_{SB}) | 820 μF |

Voltage at SB port (U_{SB}) | 400 V |

because in the worst conditions (i_{LS} = 40 A) the voltage across the switches is lower than 800 V, as can be seen in

To reduce the overvoltage across the matrix converter switches, snubber capacitors can be placed in parallel with the switches.

The proposed DC/AC converter requires snubber capacitors to limit the overvoltage across the outer switches (S_{B}_{17}, S_{B}_{20}, S_{B}_{21}, and S_{B}_{24}). The snubber capacitors are placed in parallel with the IGBTs to absorb the energy accumulated in the stray inductances, present in the transformer and cables of the circuit shown in

For the AC/AC converter proposed in this chapter, the energy from the leakage inductances (shown in

The power dissipated in the IGBTs due to the snubber capacitors is determined by [

where C_{sn} is a snubber capacitor value, f_{s} the switching frequency, and V_{sn} is the voltage across C_{sn} just before the switch is switched on. The value of C_{sn} can be determined using (3), to guarantee that the overvoltage across the outer switches will not be higher than a desired maximum value.

In the implemented converter (_{LS}) is 40 A. The goal is to reduce the peak voltage to 800 V to allow the use of IGBTs which can support a maximum voltage of 1000 V. Therefore, using (3) is possible to determine the peak voltage across the outer switches for different values of C_{sn}. However, when a different capacitor is placed in parallel with the IGBTs, the ringing frequency changes and, consequently, the resistance of the transformer and cables of the prototypes also change (see

facilitate the choice of the snubbers, for different values of C_{sn}, the corresponding transformer and cable resistances were obtained from the oscillation frequencies as given by (1) and the impedance characteristics in _{B}_{17} has a peak value lower than 800 V. For safety margin reasons a capacitor of 22 nF was implemented. The proposed AC/AC converter was simulated again with the chosen snubber connected in parallel to each outer switch (S_{B}_{17}, S_{B}_{20}, S_{B}_{21}, and S_{B}_{24}) and the results are shown in _{B}_{17} of 650 V and ringing frequency of 759 kHz. The inner switches (S_{B}_{18}, S_{B}_{19}, S_{B}_{22}, and S_{B}_{23}) also have overvoltage lower than 800 V, as requested.

The extra power losses in the switches can be calculated with (8), resulting a dissipation of 17.6 W per switch. Because snubber capacitors are placed only across the outer switches (S_{B}_{17}, S_{B}_{20}, S_{B}_{21}, and S_{B}_{24}), and the proposed converter has 12 switches. As a result, the total snubber loss is 211.2 W. When these losses are added to the total losses, the efficiency of the proposed AC/AC converter reduces to 93.2%.

The converter was experimentally tested to validate the theoretical

The ringing and overvoltage across the switches of the proposed DC/AC converter is described. This overvoltage is generated due to the resonance between three passive components: transformer leakage inductances, switch capacitances, and wiring resistances. By applying simple RLC circuit equations, it proves possible to determine the analytic equations and reproduce the voltage across the switches to predict the overvoltage and resonance frequency. The analysis shows that the switches connected directly to the high-frequency transformer encounter higher voltage spikes compared to those connected directly to the load. Snubber capacitors are designed to decrease the peak voltage based on the theory developed in this paper.

Gierri Waltrich, (2016) Ringing and Voltage Overshoot Analysis of a Proposed DC/AC Converter. Open Access Library Journal,03,1-9. doi: 10.4236/oalib.1102821