**6. Methododlogy for designing the converter**

During the process of designing the *LCC* resonant *DC/DC* converter under consideration, the following parameters are usually predetermined: power in the load *Р*0, output voltage *U*<sup>0</sup> and operating frequency *f*. Very often, the value of the power supply voltage *Ud* is predefined and the desired output voltage is obtained by adding a matching transformer. The design of the converter could be carried out in the following order:

1. Choice of the frequency distraction ν

For converters, operating at frequencies higher than the resonant one, the frequency distraction is usually chosen in the interval ν =1.1÷1.3. It should be noted here that if a higher value of ν is chosen, the exchange of reactive energy between the resonant circuit and the energy source increases, i.e., the current load on the elements in the circuit increases while the stability of the output characteristics decreases. It is due to the increase in the impedance of the resonant circuit of the converter.

2. Choice of the parameter 2 0 *a CC* =

The choice of this parameter is a compromise to a great extent. On the one hand, to avoid the considerable change of the operating frequency during the operation of the converter from nominal load to no-load mode, the capacitor *С*0 (respectively the parameter *а*2) should be big enough. On the other hand, with the increase of *С*0 the current in the resonant circuit increases and the efficiency of the converter decreases. It should be noted that a significant increase in the current load on the elements in the scheme occurs at 2 *a* > 1 (Malesani et al., 1995).

3. Choice of the parameter 1 *<sup>S</sup> a CC* =

The parameter *а*1 is usually chosen in the interval *а*1 = 0.02÷0.20. The higher the value of *а*<sup>1</sup> (the bigger the capacity of the damping capacitors), the smaller the area of natural commutation of the transistors in the plane of the output characteristics is. However, the increase in the capacity of the snubber capacitors leads to a decrease in the commutation losses and limitation of the electromagnetic interferences in the converter.

4. Choice of the coordinates of a nominal operating point

The values of the parameters *а*1 and *а*2 fully define the form of the output characteristics of the converter. The nominal operating point with coordinates 0*I*′ and *U*<sup>0</sup> ′ lies on the characteristic, corresponding to the chosen frequency distraction ν. It is desirable that this point is close to the boundary of natural commutation so that the inverter could operate at a high power factor (minimal exchange of reactive energy). If the converter operates with sharp changes in the load and control frequency, however, it is then preferable to choose the operating point in an area, relatively distant from the border of natural commutation. Thus, automatic switching the converter off is avoided – a function, integrated in the control drivers of power transistors.

5. Defining the transformation ratio of the matching transformer

The transformation ratio is defined, so that the required output voltage of the converter at minimal power supply voltage and at maximum load is guaranteed:

$$k \geq \frac{\mathcal{U}\_0' \cdot \mathcal{U}\_{d\min}}{\mathcal{U}\_0},\tag{54}$$

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

6. Calculating the parameters of the resonant circuit

The values of the elements in the resonant circuit *L* and *C* are defined by the expressions related to the frequency distraction and the output current in relative units:

$$\mathbf{v} = \mathbf{a}/\mathbf{a}\_0 = 2\mathbf{n}f\sqrt{\mathbf{L}\mathbf{C}}\qquad\qquad\vdots\qquad I\_0' = \frac{I\_0/\mathbf{k}}{\mathbf{U}\_d\sqrt{\mathbf{L}/\mathbf{C}}} = \frac{P\_0/\mathbf{k}}{\mathbf{U}\_d\mathbf{L}l\_0\sqrt{\mathbf{L}/\mathbf{C}}}\tag{55}$$

Solving the upper system of equations, it is obtained:

$$L = \frac{k\nu L I\_d \mathcal{U}\_0 I\_0'}{2\pi f P\_0} \qquad ; \qquad C = \frac{\nu P\_0}{2\pi f k \mathcal{U}\_d \mathcal{U}\_0 I\_0'} \tag{56}$$

#### **7. Experimental investigations**

126 Power Quality Harmonics Analysis and Real Measurements Data

During the process of designing the *LCC* resonant *DC/DC* converter under consideration, the following parameters are usually predetermined: power in the load *Р*0, output voltage *U*<sup>0</sup> and operating frequency *f*. Very often, the value of the power supply voltage *Ud* is predefined and the desired output voltage is obtained by adding a matching transformer.

For converters, operating at frequencies higher than the resonant one, the frequency distraction is usually chosen in the interval ν =1.1÷1.3. It should be noted here that if a higher value of ν is chosen, the exchange of reactive energy between the resonant circuit and the energy source increases, i.e., the current load on the elements in the circuit increases while the stability of the output characteristics decreases. It is due to the increase in the

The choice of this parameter is a compromise to a great extent. On the one hand, to avoid the considerable change of the operating frequency during the operation of the converter from nominal load to no-load mode, the capacitor *С*0 (respectively the parameter *а*2) should be big enough. On the other hand, with the increase of *С*0 the current in the resonant circuit increases and the efficiency of the converter decreases. It should be noted that a significant increase in the current load on the elements in the scheme occurs at 2 *a* > 1 (Malesani et al.,

The parameter *а*1 is usually chosen in the interval *а*1 = 0.02÷0.20. The higher the value of *а*<sup>1</sup> (the bigger the capacity of the damping capacitors), the smaller the area of natural commutation of the transistors in the plane of the output characteristics is. However, the increase in the capacity of the snubber capacitors leads to a decrease in the commutation

The values of the parameters *а*1 and *а*2 fully define the form of the output characteristics of

characteristic, corresponding to the chosen frequency distraction ν. It is desirable that this point is close to the boundary of natural commutation so that the inverter could operate at a high power factor (minimal exchange of reactive energy). If the converter operates with sharp changes in the load and control frequency, however, it is then preferable to choose the operating point in an area, relatively distant from the border of natural commutation. Thus, automatic switching the converter off is avoided – a function, integrated in the control

The transformation ratio is defined, so that the required output voltage of the converter at

′ lies on the

losses and limitation of the electromagnetic interferences in the converter.

the converter. The nominal operating point with coordinates 0*I*′ and *U*<sup>0</sup>

4. Choice of the coordinates of a nominal operating point

5. Defining the transformation ratio of the matching transformer

minimal power supply voltage and at maximum load is guaranteed:

**6. Methododlogy for designing the converter** 

impedance of the resonant circuit of the converter.

1. Choice of the frequency distraction ν

2. Choice of the parameter 2 0 *a CC* =

3. Choice of the parameter 1 *<sup>S</sup> a CC* =

drivers of power transistors.

1995).

The design of the converter could be carried out in the following order:

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 zero (ZVC commutation).

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 characteristics, obtained in result of the experiments.

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 resonant circuit.

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.

Study of LCC Resonant Transistor DC / DC Converter with Capacitive Output Filter 129

From fig. 11-b and fig. 12-b the difference between the main and the boundary operation mode of the converter can be seen. In the first case, the commutations in the rectifier (the process of recharging the capacitor *С*0) end before the commutations in the inverter (the process of recharging the capacitor *С*S). In the second case, the commutations in the rectifier complete after the ones in the inverter. In both cases during the commutations in the rectifier, all of its diodes are closed and the output current *i*0 is equal to zero (fig. 11-с and

Fig. 12-b confirms the fact that at certain conditions the output voltage can become higher

At no-load mode, the converter operation is shown in fig. 13. In this case, the output voltage

ua 500V/div; ub 500V/div; х=5µs/div

The operation of an LCC transistor resonant DC/DC converter with a capacitive output filter and working above the resonant frequency has been investigated, taking into account the influence of snubber capacitors and a matching transformer. The particular operation modes of the converter have been considered, and the conditions under which they are obtained have been described. The output characteristics for all operation modes of the converter have been built including at regulation by means of changing the operating frequency. The boundary curves between the different operation modes of the converter as well as the area of natural commutation of the controllable switches have been shown in the plane of the output characteristics. Results from investigations carried out by means of a laboratory prototype of the converter have been obtained and these results confirm the ones

The theoretical investigations show that the conditions for ZVS can be kept the same for high-Ohm loads and the converter can stay fit for work even at a no-load mode. For the purpose, it is necessary to have the natural capacity of the matching transformer bigger than

The output characteristics show that in the zone of small loads the value of the normalized output voltage increases to reach a value higher than unit what is characteristic for

than the power supply voltage without using a matching transformer.

is more than two times higher than the power supply one.

Fig. 13. Oscillograms, illustrating no-load mode of the converter

fig. 12-с).

**8. Conclusions** 

from the analysis.

the one of the snubber capacitors.

х=5µs/div

Fig. 10. Experimental output characteristics of the converter.

х=5µs/div

Fig. 11. Oscillograms illustrating the main operation mode of the converter

х=5µs/div

Fig. 12. Oscillograms illustrating the boundary operation mode of the converter

From fig. 11-b and fig. 12-b the difference between the main and the boundary operation mode of the converter can be seen. In the first case, the commutations in the rectifier (the process of recharging the capacitor *С*0) end before the commutations in the inverter (the process of recharging the capacitor *С*S). In the second case, the commutations in the rectifier complete after the ones in the inverter. In both cases during the commutations in the rectifier, all of its diodes are closed and the output current *i*0 is equal to zero (fig. 11-с and fig. 12-с).

Fig. 12-b confirms the fact that at certain conditions the output voltage can become higher than the power supply voltage without using a matching transformer.

At no-load mode, the converter operation is shown in fig. 13. In this case, the output voltage is more than two times higher than the power supply one.

ua 500V/div; ub 500V/div; х=5µs/div

Fig. 13. Oscillograms, illustrating no-load mode of the converter
