# Capacitor Sizing, Balancing, and Pre-Charge for Flying-Capacitor Boosters

## This article focuses on the challenges the flying-capacitor topology may encounter and solutions to tackle capacitor sizing, balancing and pre-charge.

This article is the second part of article series about flying-capacitors boosters (first part “The Advantages and Operation of Flying-Capacitor Boosters” was published in October 2020 edition of Bodo’s Power). The first part described the advantage of it, which is increasing the efficiency while being still low at system cost. The second part focuses on the challenges the flying-capacitor topology may encounter. Solutions to tackle capacitor sizing, balancing and pre-charge are introduced here.

## Introduction

Using high-efficiency solar inverters is reaching more and more popularity in a design, however, it is not the most economical. To achieve a cost efficient solution, not only the inverter has to be low cost and high efficient, but also the booster stage. The flying-capacitor booster solution can increase the efficiency while being still cost-efficient. However, it has also some challenges as capacitor sizing, balancing and the pre-charge. This article will describe the solution for this challenges.

## Sizing of the Flying-Capacitor

The voltage supplied by a flying-capacitor has a key role in this topology. To keep the voltage ripple on the capacitor low, a suitable capacitor size is needed. To determine the needed capacitance, the switching frequency and the maximum allowed voltage ripple need to be considered. The size of the capacitance can be calculated as:

$$C_{FC} = \frac{I_{peak}}{\Delta U_{FC} \cdot 2f_{SW}}$$

where is the maximum allowed voltage ripple, is the maximum current, and is the switching frequency of the transistors.

## The Balancing of the Capacitor Voltage

For the appropriate operation the flying-capacitor, voltage has to be half of the output voltage. To achieve this, it must be regulated at all time. This can be done by changing the operation modes. As it can be seen in Table 1, Mode 1 and Mode 4 have no effect for the flyingcapacitor, so for regulation Mode 2 and Mode 3 have to be used. The regulation state diagram can be seen on Figure 1.

Mode |
Transistors |
Inductor Current |
FC Voltage |
DC-link Voltage |
||

T25 |
T27 |
D<0.5 |
D>0.5 |
|||

Mode 1 | OFF | OFF | decreasing | - | - | increasing |

Mode 2 | OFF | ON | increasing | decreasing | increasing | decreasing |

Mode 3 | ON | OFF | increasing | decreasing | decreasing | increasing |

Mode 4 | ON | ON | - | increasing | - | decreasing |

*Table 1: Output and FC voltage states*

*Figure 1: The flying-capacitor regulation*

The needed modes are depending on the duty cycle. In case of ≤ 0.5, the operation will be the following:

… → Mode 1 → Mode 2 → Mode 1 → Mode 3 → …

If the flying-capacitor voltage exceeds the set point, the operation can be modified to decrease the voltage:

… → Mode 1 → Mode 3 → Mode 1 → Mode 3 → …

If the flying-capacitor voltage is less than the set point:

… → Mode 1 → Mode 2 → Mode 1 → Mode 2 → …

In case of ≥ 0.5, the needed modification will be the same, only Mode 4 will be used instead of Mode 1:

… → Mode 4 → Mode 3 → Mode 4 → Mode 3 → …

to decrease the voltage

… → Mode 4 → Mode 2 → Mode 4 → Mode 2 → …

to increase the voltage

## The Pre-Charge of the Flying Capacitor

This section describes the details of the method proposed by Mitsubishi Electric Corporation [1] to protect the flying capacitor booster, when there are no control signals (e.g.: during startup). In case when all the control signals of the transistors are low, the flying-capacitor voltage cannot be regulated. In that operation an extra effort is needed to keep the flying-capacitor voltage on the safe side. Failing to eliminate the overvoltage on the semiconductors may cause a fatal error in the system. There are two operation modes, when all the transistors are OFF: 1) When the input is applied and the output is equal with the input (e.g.: startup), and 2) when the input is zero and the output is not. This happens, for example, when one string is not connected to the circuit and other boosters are working. In both two cases the voltage of the flying-capacitor is zero, and the voltage sharing of the two transistors is not defined. To keep the voltage level of the semiconductors below the breakdown voltage, additional balancing has to be used.

During startup the current flows through the two diodes and charge the output capacitance. In this case the output voltage is equal to the input voltage, while the flying-capacitor voltage is zero. This is dangerous for the lower switch. To eliminate this problem, another current path has to be added, in which the current can charge also the flyingcapacitor. For this a diode can be used, a cathode of which has to be connected to a capacitive voltage divider, where the lower point of the flying-capacitor is clamped at the half of the DC-link voltage. This can be seen on Figure 2.

*Figure 2: The additional current path during startup*

As the voltage of the capacitor can be calculated from the following expression: $$V = \frac{O}{C}$$ and the charge will be the same for C_{out1} and C_{out2} + C_{FC}, the flying-capacitor voltage will be the following:

$$V_{FC} = V_{OUT} \frac{C_{out1}}{C_{out1}+C_{out2}+C_{FC}}$$

where V_{OUT} is equal with V_{In} (If the forward voltage of the diodes are not considered).

*Figure 3: The additional diode when Vin is zero*

If the capacitance of Cout1 and Cout2 is equal and the capacitance of CFC is significantly smaller than the capacitance of Cout1 and Cout2, the voltage of the flying-capacitor is half of the output.

$$C = C_{out1} = C_{out2}, C_{FC} \ll C, V_{FC} \approx \frac{V_{in}}{2}$$

When the string is not used and other boosters are working, the input voltage is zero, while the output voltage is not. In this case another diode has to be added to charge the flying-capacitor. As it can be seen on Figure 3, the current path is the following:

$$C_{out2} \rightarrow Dh \rightarrow C_{FC} \rightarrow D45 \rightarrow L \rightarrow C_{in}$$

In this case the sum of the flying-capacitor voltage and the input voltage can be calculated as the following:

$$V_{fci} = V_{OUT} \frac{C_{out2}}{C_{out1} + C_{out2} + C_{FC} \times C_{in}}$$

As in the last expression, if Cout1 and Cout2 is equal and CFC and Cin is negligible compared to Cout1 and Cout2 , the voltage is half of the output voltage.

$$C = C_{out1} = C_{out2}, C_{FC} \times C_{in} \ll C, V_{fci} \approx \frac{V_{OUT}}{2}$$

This voltage is divided on the two capacitors. If the capacitance of the CFC is much smaller than the Cin capacitor, then the voltage of the capacitor is as low as it can be considered zero, and the voltage of the flying-capacitor is near to the half of the output voltage.

This method can be improved by closing the T27 switch. In this case the voltage is not divided by Cin and CFC capacitors and the current path will be the following:

$$C_{out2} \rightarrow Dh \rightarrow C_{FC} \rightarrow T27$$

And the flying-capacitor voltage:

$$V_{FC} = V_{OUT} \frac{C_{out2}}{C_{out1}+C_{out2}+C_{FC}}$$

## Design Considerations

During normal operation T27 creates an overvoltage spike at turn-off. If Df turns on to clamp this spike, T27 switch will be loaded with the reverse recovery of Df. To avoid Df clamping this overvoltage spike, an additional Zener diode (Dz) can be added in series with Df. The Zener voltage of the Zener diode should be higher than the spike of turn-off. This can be seen on Figure 4.

*Figure 4: The additional Zener diode*

If the voltage of flying capacitor is extremely higher than $$\frac{V_{OUT}}{2}$$ an additional current ripple will appear on the inductor. This ripple causes increased losses and noise. This ripple can be also moderated with this Zener diode.

If the voltage of C_{FC} is less than the voltage of C_{out2} an equalization current will flow between C_{FC} and C_{out2} resulting an unbalance between Cout1 and C_{out2}.

This unbalance can be decreased with a current limiting resistor (Rf) which can be seen on Figure 5.

*Figure 5: The current limiting resistor In is zero*

## Conclusion

The flying-capacitor booster is a high-efficient, low cost solution for solar inverter applications. The main advantages are the frequency multiplication, the lower semiconductor voltage, the lower voltage and current ripple, the lower switching losses, and the low EMI emission. The flying-capacitor size is significantly smaller than the required DC-link capacitor used in traditional booster topologies with the same power rating. The challenge is to regulate the voltage of the flying-capacitor especially when all the transistors are in OFF state (i.e.: before the converter is turned on). The balancing can be achieved by state regulation. Also the pre-charge challenge can be solved easily by additional diodes based on Mitsubishi Electric Corporation’s patent. With these diodes the flying-capacitor booster is a cost efficient alternative for the other booster solutions with higher efficiency.

#### About the Author

**Viktor Antoni** holds a Master's Degree and a Bachelor's Degree in Power Electronics at Obuda University. He is specialized in electronics, semiconductors and product development. Currently, he works as a Development Engineer at Vincotech since July 2017.

#### References

- T. Okuda and H. Ito, "DC/DC POWER CONVERSION APPARATUS". United States Patent US 2013/0021011 A1, 24 01 2013.

This article originally appeared in the Bodo’s Power Systems magazine.

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