Method and system for determining a capacitance value
A method for determining a capacitance value of a capacitor is provided. The method includes receiving a current signal flowing through the capacitor and receiving a voltage signal applied across the capacitor. The received voltage signal and the received current signal are filtered with a low pass filter. The filtered voltage signal and the filtered current signal are then discretized. The discretized voltage signal and the discretized current signal are transformed into a frequency domain. The capacitance value of the capacitor is determined from the transformed voltage signal and the transformed current signal.
1 . A method for determining a capacitance value of a capacitor, the method comprising:
measuring, by a current sensor, a current signal flowing through the capacitor;
measuring, by a voltage sensor, a voltage signal applied across the capacitor;
receiving, by a first low pass filter connected to the current sensor, the current signal;
filtering, by the first low pass filter, the received voltage signal at a dominant frequency, wherein the dominant frequency is a frequency with a maximum amplitude, and wherein the first low pass filter attenuates current signals with frequencies higher than the dominant frequency;
receiving, by a second low pass filter connected to the voltage sensor, the voltage signal;
filtering, by the second low pass filter, the received current signal at the dominating frequency, wherein the second low pass filter attenuates voltage signals with frequencies higher than the dominant frequency;
discretizing, by an Analog to Digital Converter (ADC) connected to the first low pass filter and the second low pass filter, each of the filtered voltage signal and the filtered current signal, wherein discretizing each of the filtered voltage signal and the filtered current signal comprises measuring a value of the current signal and the voltage signal over a sampling interval;
transforming each of the discretized voltage signal and the discretized current signal into frequency domain, wherein transforming each of the discretized voltage signal and the discretized current signal into frequency domain comprises determining currents and voltages present in each of the discretized voltage signal and the discretized current signal at different frequencies; and
determining the capacitance value of the capacitor from the transformed voltage signal and the transformed current signal.
2 . The method of claim 1 , wherein determining the capacitance value of the capacitor from the transformed voltage signal and the transformed current signal comprises:
determining an impedance of the capacitor from the transformed voltage signal and the transformed current signal;
determining a capacitive reactance of the capacitor from an imaginary part of the impedance; and
determining the capacitance value of the capacitor from the capacitive reactance.
3 . The method of claim 2 , further comprising:
determining a series resistance of the capacitor from a real part of the impedance.
4 . The method of claim 1 , wherein determining the impedance of the capacitor from the transformed voltage signal and the transformed current signal further comprises determining the impedance of the capacitor from the transformed voltage signal and the transformed current signal transformed at the dominant frequency.
5 . The method of claim 1 , wherein transforming each of the discretized voltage signal and the discretized current signal into the frequency domain comprises performing a fast Fourier transform of each of the discretized voltage signal and the discretized current signal.
6 . The method of claim 1 , further comprising windowing the discretized voltage signal and the discretized current signal.
7 . The method of claim 1 , wherein each of the discretized voltage signal and the discretized current signal are transformed into the frequency domain in parallel.
8 . The method of claim 1 , wherein determining the impedance of the capacitor from the transformed voltage signal and the transformed current signal comprises determining the impedance as
Z
(
kf
df
)
=
(
real
(
V
(
kf
df
)
)
+
imag
(
V
(
kf
df
)
)
)
(
real
(
I
(
kf
df
)
)
+
imag
(
I
(
kf
df
)
)
)
where V(kf df ) and I(kf df ) are the voltage and current values obtained from the transformed discretized current signal I[n] and the transformed discretized voltage signal V[n] at the dominating frequency and where k is {1, 2, 3, 4, 5, . . . }.
9 . The method of claim 8 , further comprising determining the capacitive reactance of the capacitor from the imaginary part of the impedance as:
X C (kf df )=imag(Z(kf df )).
10 . The method of claim 9 , further comprising determining the capacitance value of the capacitor from the capacitive reactance as:
C
estm
1
(
kf
df
)
=
1
2
π
kf
df
X
C
(
kf
df
)
where f df is the dominating frequency.
11 . A method for determining a capacitance value of a capacitor, the method comprising:
measuring, by a current sensor, a current signal flowing through the capacitor;
receiving, from the current sensor, the current signal flowing through the capacitor;
measuring, by a voltage sensor, a voltage signal applied across the capacitor;
receiving, from the voltage sensor, the voltage signal applied across the capacitor;
receiving, by a first low pass filter connected to the current sensor, the current signal;
filtering, by the first low pass filter, the received voltage signal at a dominant frequency, wherein the dominant frequency is a frequency with a maximum amplitude, and wherein the first low pass filter attenuates current signals with frequencies higher than the dominant frequency;
receiving, by a second low pass filter connected to the voltage sensor, the voltage signal;
filtering, by the second low pass filter, the received current signal at the dominant frequency, wherein the second low pass filter attenuates voltage signals with frequencies higher than the dominant frequency;
sampling, by a sampler connected to the first low pass filter and the second low pass filter, each of the filtered voltage signal and the filtered current signal;
performing a fast Fourier transform of each of the sampled voltage signal and the sampled current signal, wherein performing the fast Fourier transform for each of the filtered voltage signal and the filtered current signal comprises measuring a value of the current signal and the voltage signal over a sampling interval;
transforming each of the discretized voltage signal and the discretized current signal into frequency domain, wherein transforming each of the discretized voltage signal and the discretized current signal into frequency domain comprises determining currents and voltages present in each of the discretized voltage signal and the discretized current signal at different frequencies
determining an impedance of the capacitor from the transformed voltage signal and the transformed current signal;
determining a capacitive reactance of the capacitor from an imaginary part of the impedance; and
determining the capacitance value of the capacitor from the capacitive reactance.
12 . The method of claim 11 , wherein filtering each of the received voltage signal and the received current signal with the low pass filter comprises further filtering each of the received voltage signal and the received current signal with the low pass filter at the dominant frequency.
13 . The method of claim 11 , wherein determining the impedance of the capacitor from the transformed voltage signal and the transformed current signal comprises determining the impedance as
Z
(
k
f
d
f
)
=
(
r
e
a
l
(
V
(
k
f
d
f
)
)
+
i
m
a
g
(
V
(
k
f
d
f
)
)
)
(
r
e
al
(
I
(
kf
d
f
)
)
+
i
m
ag
(
I
(
kf
d
f
)
)
)
where V(kf df ) and I(kf df ) are the voltage and current values obtained from the transformed discretized current signal I[n] and the transformed discretized voltage signal V[n] at the dominating frequency and where k is {1, 2, 3, 4, 5, . . . }.
14 . The method of claim 13 , further comprising determining the capacitive reactance of the capacitor from the imaginary part of the impedance as: X C (kf df )=imag(Z(kf df )).
15 . The method of claim 14 , further comprising determining the capacitance value of the capacitor from the capacitive reactance as:
C
e
s
t
m
1
(
k
f
d
f
)
=
1
2
π
k
f
d
f
X
C
(
k
f
d
f
)
where f df is the dominating frequency.
16 . The method of claim 11 , wherein determining the impedance of the capacitor from the transformed voltage signal and the transformed current signal comprises determining the impedance as
Z
(
kf
df
)
=
(
real
(
V
(
kf
df
)
)
+
imag
(
V
(
kf
df
)
)
)
(
real
(
I
(
kf
df
)
)
+
imag
(
I
(
kf
df
)
)
)
where V(kf rf ) and I(kf rf ) are the voltage and current values obtained from the transformed current signal I[n] and the transformed voltage signal V[n] at a ripple frequency and where k is {1, 2, 3, 4, 5, . . . }.
17 . The method of claim 11 , wherein a rate of sampling of each of the filtered voltage signal and the filtered current signal is predetermined.
18 . The method of claim 11 , wherein each of the filtered voltage signal and the filtered current signal are sampled in parallel.
19 . The method of claim 11 , wherein the Fast Fourier transform for the filtered voltage signal and the filtered current signal is performed in parallel using a dedicated Fast Fourier transform operator.
20 . The method of claim 11 , wherein further comprising:
determining a series resistance of the capacitor from a real part of the impedance.