The calculation of the smoothing filter
First of all it is necessary to find the smoothing parameter qf that is defined by the formula:
(2.11)
where
and
are the smoothing parameters on the input
and output of the smoothing filter. The value
is taken from the table 1.1. The value
is determined according to the following formula:
,
(2.12)
,
[grad]
The values of α and β depend on m (in other words on the scheme of rectifier). Its values are shown in the table 2.10.
Table 2.10 – Calculated coefficients
m |
α |
β |
2 |
200 |
1,5 |
3 |
100 |
4 |
6 |
120 |
12,5 |
If qf > 60 then for the smoothing filter it is used multisection filter that consists of n LC-filters.
To chose the optimal number of the section nопт for smoothing filter it is defined by the formula:
(2.13)
In this case the smoothing parameter qf that is defined by the formula:
(2.14)
If all sections of filter are done from the same elements (L1 = L2 = …= Lзв; C1 = C2 = …= Cзв), then q1 = q2 = …= qфп = qзв:
(2.15)
where qзв is the smoothing coefficient of the separated section;
Lзв and Cзв are inductance and capacitance of the separated section;
n is number of sections;
kпос1, kпос2, kпосn = kпо pulsing coefficients of capacitor’s voltage corresponding to 1-st, 2- nd, …, n-th section.
As the smoothing filter it will be used the single linked smoothing filter to decrease the mass of filter and dynamical overrating voltage on the output.
To provide the continuous mode of the work of smoothing filter it is used the inductance of the fist link in the following way:
,
where Lmin is the boundary value of the throttle’s inductance of the first filter’s link.
The calculation is started from the definition of minimal allowed throttle’s inductance according to the following formula:
(2.16)
The value of capacity is defined by the formula:
where 1
i
n
(1.17)
According to the calculated capacitance of the capacitor’s i-th section Cзвi it is calculated the type of capacitor, whose standard value of capacitance and allowed voltage is more on 20-30% than calculated one. When there is no capacitors with such values then it is used several ones that are connected in parallel way.
The value of maximum voltage on the capacitor of the first link of smoothing filter is defined by the formula:
(2.18)
where
is the value of overvoltage on the capacitor.
The overvoltage on the capacitor becomes in the moment of switching the rectifier and in the moment of abrupt change in current loading from the nominal I0 to IC1.
To calculate the overvoltage on the capacitor of
filter it is necessary to find the ratio of attenuation coefficient
to the natural frequency of the filter ωf
:
(2.19)
(2.20)
where In
can have the value In
= I0
(while
=
and
=
).
According to the obtained ratio
/
it is possible to define Q1
and according to the obtained ratio
/
it is possible to define Q2.
(2.21)
(2.22)
Them it is calculated the values
and
by the following formulas:
;
(1.18)
But with respect to the values and it is chosen Ucm (by the formula 2.18) it is chose the biggest value that is working voltage of the smoothing filter
The obtained results have to be shown in the following table.
Table 2.11 – The parameters of smoothing filter
Calculated units |
γ, grad |
qф |
Lф, H |
Cф, μF |
ωф, rad/s |
Uc max, V |
Lф1, H |
Cф1, μF |
Results of calculations |
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