3.4. DC or HV differential-mode filter subsystem¶
This subsystem represents a differential mode filter connected to a DC bus (high-voltage side in the case of the DC-DC converter) from one side and the macrocells on the other side. The purpose of this filter is to absorb the high-frequency current harmonics created by the macrocells.
3.4.1. Operating point consideration¶
In the case of the DC-DC converter, for some specific configurations of hybrid multilevel converters (flying capacitor converters in parallel, where \(2π / n_{cell(par)}\) and \(2π / n_{cell(fc)}\) are relatively prime numbers), if the ratio \({U_{LV}}/{U_{HV}}\) is multiple of \({1}/{n_{cell(par)}}\), interleaving produces a constant DC current from the macrocell, cancelling the theoretical voltage ripple across the capacitor of the DC filter. However, any disturbance will cause voltage harmonics that need to be filtered. To take into account this specific behaviour, the ratio is shifted to \(\dfrac{U_{LV}}{U_{HV}} - \dfrac{\Delta t}{T_{sw}}\) where \(\Delta t\) is the minimum time step and \(T_{sw}\) is the switching period.
Figure below shows the voltage ripple across the capacitor depending on the voltage ratio \({U_{LV}}/{U_{HV}}\) and the small disturbance of the ratio which is considered to design the filter.
3.4.2. Design and electrical parameters¶
Two model variants are available for this subsystem:
a damped L-C filter composed by an inductor and a capacitor, and a R-C damping system composed by a resistor and a capacitor (in charge of limiting the instabilities created by the resonance of the second order L-C filter);
a 1st order C filter composed by a capacitor.
Convention to number the capacitors of different stages: (Capacitor \(1,2,...,n_{stack}\))
3.4.3. Design algorithm in auto design mode¶
For the 1st order C filter, the algorithm considers the specified operation point and computes capacitance values to meet the required voltage ripple.
For the damped LC filter, the algorithm considers the specified operation point and two requirements to compute inductance and capacitance values:
a frequency requirement which will impose a maximal frequency of the filter (i.e. a minimal value for the LC product), which is issued from:
the “outer” ripple (current ripple for a high-voltage filter),
or the frequency domain limit line;
an “inner” ripple requirement (voltage ripple for a high-voltage filter), which will impose a minimal capacitance.
These requirements - which are detailed below - can be represented on a graph \(L_{HV}\) vs \(C_{HV}\) for an “equivalent” 2nd order LC filter, considering a damped LCRC filter will have the same principles:
This figure shows an area of feasible points. PowerForge will propose a design with the minimal values of inductance and capacitance.
Yet, for the same amount of stored energy, the inductor mass can be 2 to 10 times higher than the capacitor mass. Thus, it can be interesting to try solutions with a higher capacitance and lower inductance. The designer is then able to decrease the inner voltage ripple (i.e. move the constraint line “voltage ripple” to the right) to try such solutions.
3.4.3.1. Frequency requirement¶
The frequency requirement is given by \(f_c = min(f_{ripple}, f_{freq-limit})\) and imposes a minimum value for the \(LC\) product, such as:
where \(f_c\) would be the highest cut-off frequency of the filter.
3.4.3.2. “Inner” ripple requirement¶
The “inner” ripple requirement is the voltage ripple requirement across the capacitor. This ripple is considered to be low enough to assume the whole DC voltage as constant to compute the voltage at the low voltage side. It imposes a minimum value of the high voltage capacitance \(C_{HV}\).
3.4.3.3. Design of the damping circuit¶
1- The value of the damping capacitance if assumed to be equal to 4 times to the main capacitance \(C_{HV}\):
2- Then the value of the damping resistance is calculated to set a damping factor of 0.7.