How to calculate the filter capacitor capacitance?

When the motor driver is designed to use an AC power supply, the designed circuit needs to rectify the AC power supply and then filter, to produce a DC power supply for the motor drive circuit. The selection of a filter capacitor in the circuit needs to consider several aspects: capacitor voltage, working temperature, capacity, and so on.

The selection of the capacitance of the input filter is directly related to the driving voltage and maximum power of the driver, which needs to be calculated. If this capacitance capacity is too small, the driver behaves as an insufficient driving force. And if the capacity is too large, it will increase the manufacturing cost.

In engineering applications, there is such a rule of thumb: the value of the filter capacitance is equal to the value of the drive power. However, it should be noted that this is only for single-phase 220V AC full-wave rectifier driver applications, and can not be taken out of context.

The following through a simple calculation derivation, introduces the process of capacity calculation, only as a reference.

First of all, starting from the capacitor, resistance RC time constant τ: τ=R×C

The larger the τ, the more stable the voltage at both ends of R, and the less ripple voltage for pulsating power supplies. In engineering, when the RC time constant meets the following conditions, it can meet the ripple requirements: τ≥5T, T is the period of the pulsating power supply, and the period T after the full-wave rectification of 50Hz mains is: 10mS.

Therefore, from the above two formulas can be obtained:

                                             R×C≥5T                                         

R is equivalent load resistance; C is the filter capacitance.

The following diagram is the circuit diagram:

 

Therefore, as long as the equivalent load resistance of the motor driver is obtained, the capacity required for the filter capacitor can be calculated.

U is the input voltage of the motor driver, and the unit is (V);

P is the motor drive power, in (W);

R_L is the equivalent load resistance of the motor driver, in Ω.

Combine the above types:

Using frequency f instead of period T, the calculation formula of filter capacitance can be obtained as follows:

P is the rated output power of the motor driver, in unit (W), such as P=750W;

U is the effective value of the rated input AC voltage of the motor driver, and the unit is (V), such as domestic power U=220V (AC);

f is the frequency of the pulsating power supply after rectification, the unit is (Hz), such as single-phase power after full wave rectification, f=100Hz;

C is the capacitive capacity of the driver input filter, in unit (F).

For Example

Suppose that the driver we design uses a single-phase power supply from the mains, and the circuit design is full wave rectification, we can get: U = 220V; f=100Hz

Back into the calculation formula:

 

Therefore, the numerical size of the input filter capacitance (unit uF) is about equal to the numerical size of the rated power of the driver (unit W). That is if the power required by the driver is 2.2KW, the value of the filter capacitance is 2200uF. Similarly, if the driver input voltage is 110VAC,then the filter capacitance C should be:

I.e. if your drive requires 300W of power, then the filter capacitance value is 1200uF.

Three-Phase Power

Because the power pulsation frequency of single-phase electricity after full wave rectification is 100Hz; And for three-phase electricity after full wave rectification, its pulsation frequency is 300Hz. Therefore, when using a three-phase power supply, the input filter capacitance capacity of the driver can be reduced by three times than that of single-phase power, so the use of a three-phase power supply for medium and high-power motor drivers can reduce the capacity of the input filter capacitance, which can reduce the volume of the capacitor and save space.

Power Grid Fluctuation

Generally, the design expects the motor driver to operate within a certain fluctuation range of the grid voltage (e.g., ±15%) and be able to deliver full power output. At this time, when the filter capacitance is calculated, the voltage is not the rated voltage, but the lowest voltage for the driver to work. Such as (220V±15%) driver, calculation with 220V, but (1+15%) *220V, is 187V. In addition, to make the drive your design work reliably within the voltage fluctuations of the grid, in addition to calculating the capacity, also consider the withstand voltage value of the capacitor.