**5. Medial operation mode of the converter**

124 Power Quality Harmonics Analysis and Real Measurements Data

*СS* and *С*0, the smaller this area is. However, the increase of the snubber capacitors leads to a decrease in the commutation losses in the transistors as well as to limiting the

The expression (51) defines the borders, beyond which the converter stops working because of the breakage in the conditions for natural switching the controllable switches on at zero voltage (ZVS). Exemplary boundary curves have been drawn in the plane of the output characteristics (fig.8) at *а*1=0.10. Four values have been chosen for the other parameter: *а*2 = 0.05; 0.1; 0.2 and 1.0. When the capacity of the capacitor *С*0 is smaller or equal to that of the snubber capacitors *CS* ( ) 1 2 *a a* ≥ , then the converter is fit for work in the area between the curve *L*1 or *L*2 and the x-axis (the abscissa). Only the main operation mode of the converter is possible in this area. The increase in the load resistance or in the operating frequency leads to stopping the operation of the converter before it has accomplished a transition

When *C*0 has a higher value than the value of *CS* ( ) 1 2 *a a* < then the boundary curve of the area of converter operation with ZVS is displaced upward (curve *L*3 or *L*4). It is possible now

**4.2 Output characteristics and boundary curves at the boundary operation mode** 

consecutive substitution of expressions (35)÷(42) in equations (43)÷(45) as well as of expressions (43)÷(46) in equation (22), a dependence of the kind *U*0 0 12

obtained. Its solving enables with a possibility to build the outer (output) characteristics of the converter in relative units at the boundary operation mode under consideration and at regulation by changing the operating frequency. Such characteristics are shown in fig. 7-а for ν = 3.0; 3.3165; 3.6 and *а*1=0.1; *а*2=0.2 and in fig. 7-b for ν =1.5; 1.6; 1.8 and *а*1=0.1; *а*2=1.0. At the boundary operation mode, the diodes of the rectifier have to start conducting after opening the freewheeling diodes of the inverter. This is guaranteed if the following

′ is eliminated. After that, by a

′ ′ = *f* ( ) *I aa* ,, , ν

is

electromagnetic interferences in the converter.

towards the medial and the boundary modes of work.

Fig. 8. Borders of the converter operation capability

condition is fulfilled:

Applying expression (47) for equations (35)÷(42) *UCm*

to achieve even a no-load mode.

At this operation mode, the diodes of the rectifier start conducting during the commutation in the inverter. The equivalent circuits, corresponding to this mode for a cycle, are shown in fig.9. In this case, the sinusoidal quantities have four different angular frequencies:

$$\begin{aligned} \text{so}\_0 &= \mathbb{1} \Big/ \mathbb{L}\mathbb{C} \quad \text{for stages 4 and 8;}\\ \text{so}\_0' &= \mathbb{1} \Big/ \overline{\mathbb{L}\mathbb{C}\_{E1}} \quad \text{where} \quad \mathbb{C}\_{E1} = \text{CC}\_S \Big/ \left(\mathbb{C} + \mathbb{C}\_S\right), \text{ for stages 3 and 7;}\\ \text{so}\_0'' &= \mathbb{1} \Big/ \overline{\mathbb{L}\mathbb{C}\_{E2}} \quad \text{where } \mathbb{C}\_{E2} = \text{CC}\_0 \Big/ \left(\mathbb{C} + \mathbb{C}\_0\right), \text{ for stages 1 and 5;}\\ \text{so}\_0''' &= \mathbb{1} \Big/ \overline{\mathbb{L}\mathbb{C}\_{E3}} \quad \text{where } \mathbb{C}\_{E3} = \text{CC}\_S \mathbb{C}\_0 \Big/ \left(\mathbb{C}\mathbb{C}\_S + \mathbb{C}\mathbb{C}\_0 + \mathbb{C}\_S \mathbb{C}\_0\right), \text{ for stages 2 and 6.} \end{aligned}$$

Fig. 9. Equivalent circuits at the medial operation mode of the converter

Therefore, the analysis of the medial operation mode is considerably more complex. The area in the plane of the output characteristics, within which this mode appears, however, is completely defined by the boundary curves *A* and *B* for the main and the boundary modes respectively. Having in mind the monotonous character of the output characteristics for the other two modes, their building for the mode under consideration is possible through linear interpolation. It is shown in fig. 7-а for ν = 3.0; 3.3165 as well as in fig. 7-b for ν=1.5; 1.6; 1.8. The larger area of this mode corresponds to the higher capacity of the snubber capacitors *CS* and the smaller capacity of the capacitor *C*0.

Study of LCC Resonant Transistor DC / DC Converter with Capacitive Output Filter 127

The values of the elements in the resonant circuit *L* and *C* are defined by the expressions

′ <sup>=</sup> ; <sup>0</sup>

For the purposes of the investigation, a laboratory prototype of the LCC resonant converter under consideration was designed and made without a matching transformer and with the following parameters: power supply voltage 500 *Ud* = V; output power 0*P* = 2.6 кW, output voltage 0 *U* = 500 V; operating frequency and frequency distraction at nominal load *f* = 50 kHz and ν = 1.3 ; 1*a* = 0.035 ; 2 *a* = 1 ; coordinates of the nominal operating point - <sup>0</sup>*I*′ = 1.43 and 0 *U*′ = 1 . The following values of the elements in the resonant circuit were obtained with the above parameters: 570 *L* = μH; 0 *C C*= = 30 nF. The controllable switches of the inverter were IGBT transistors with built-in backward diodes of the type IRG4PH40UD, while the diodes of the rectifier were of the type BYT12PI. Snubber capacitors *С*1÷*С*4 with capacity of 1 nF were connected in parallel to the transistors. Each transistor possessed an individual driver control circuit. This driver supplied control voltage to the gate of the corresponding transistor, if there was a control signal at the input of the individual driver circuit and if the collector-emitter voltage of the transistor was practically

Experimental investigation was carried out during converter operation at frequencies *f* = 50 kHz ( ν = 1.3 ) and *f* = 61.54 kHz ( ν = 1.6 ). The dotted curve in fig.10 shows the theoretical output characteristics, while the continuous curve shows the output

A good match between the theoretical results and the ones from the experimental investigation can be noted. The small differences between them are mostly due to the losses in the semiconductor switches in their open state and the active losses in the elements of the

Oscillograms, illustrating respectively the main and the boundary operation modes of the converter are shown in fig. 11 and fig. 12. These modes are obtained at a stable operating frequency *f* = 61.54 kHz ( ν = 1.6 ) and at certain change of the load resistor. In the oscillograms the following quantities in various combinations are shown: output voltage (*ua*) and output current (*i*) of the inverter, input voltage (*ub*) and output current (*i0*) of the rectifier.

0

*U L C <sup>I</sup> <sup>k</sup> <sup>I</sup>*

*<sup>P</sup> <sup>C</sup>*

π

*d d* 0 0 0

0 0 2 *<sup>d</sup>*

*fkU U I* ν

*U Ud <sup>k</sup> U*

where *Ud* min is the minimal permissible value of the input voltage *Ud*.

related to the frequency distraction and the output current in relative units:

0 0 <sup>0</sup> 2 *<sup>d</sup> kUUI <sup>L</sup> fP*

6. Calculating the parameters of the resonant circuit

ν = ω ω<sup>0</sup> = 2π*f LC* ;

ν

π

Solving the upper system of equations, it is obtained:

characteristics, obtained in result of the experiments.

**7. Experimental investigations** 

zero (ZVC commutation).

resonant circuit.

0 min 0

′ <sup>⋅</sup> <sup>≥</sup> , (54)

*U U L C P k*

′ = = (55)

<sup>=</sup> ′ (56)
