Instrumentation & Measurement Magazine 26-2 - 7

elements. In this way, the
simple solution method
of lumped parameter circuit
can be used for further
calculation.
Fig. 5. Diagram of the train passing through the neutral section (from [1], ©2021 IEEE).
Fig. 6. The model of the train passing through the neutral section.
◗ Part ⑤ is the distributed parameter model of the catenary,
whose range is from the neutral line to the traction substation
(the B-phase).
◗ Part ⑥ is the distributed parameter model of the secondary
side of the traction substation (the B-phase).
is a simplified model of the PCA, which shows the PCA
position in the neutral section. The PCA is generated between
the power supply line and the neutral line. Also, uA
Rarc
(t) and uB
(t)=27500cos(314t)V and uB
(t)
are the voltages at the secondary side of traction transformer,
uA
(t)=27500cos(314t+120°)V. Part
①, Part ②, Part ③, Part ⑤, and Part ⑥ are consistent with the
situation of the train passing through the common section, so
they will not be illustrated here again. As for Part ④, the relevant
electrical parameters of the neutral line in high-speed
electrified railway are listed in Table 3.
The distributed parameter model can be solved by the
Bergeron numerical algorithm. In this method, the distributed
parameter circuit and energy storage elements (inductances
and capacitances) are changed to resistive circuits before calculating
the transient characteristics. Namely, the distributed
parameter elements are converted to the lumped parameter
Improvement of
the PCA Model in
Different Sections
The traditional arc models
include Mayr Model
and Cassie Model, but their
applicable scenarios are
different. The later Habedank
model expands the
scope of application by
combining the above two
models [17]. The voltage
and dissipative power of
the PCA are assumed as
constants in the Habedank
Model. However, because
the separation distance and
the PCA shape will change
under the influence of train
speed, the voltage and dissipative
power are not
constant. Moreover, the states of PCA generated in different
sections (common section and neutral section) are different.
Therefore, the existing model of PCA needs to be improved.
Firstly, as for the PCA generated in the common section,
the separation distance (d) between the pantograph and the
power supply line is short. Therefore, the arc length of the PCA
(Larc
) and d are basically equal. Secondly, as for the PCA generated
in the neutral section, the separation situation here is
more serious than that in the common section, and the d is longer.
As a result, the angle between the PCA and the horizontal
plane of the train roof cannot be ignored, so Larc
equal. When the PCA is in a stable state, the PCA voltage (Earc
is only related to the Larc, and Earc
and d are not
)
=15Larc. According to the measurement
results and the calculation method of the dissipative
power, the improved models of the PCA in the common and
neutral sections can be derived [18]-[21].
Existing Works on this Topic
Establishment of Distributed Parameter Model of the Highspeed
Train: Some scholars have focused on the distributed
Table 3 - Electrical parameters of the neutral line
Parameter Name
Equivalent resistance (Rz
Equivalent inductance (Lz
)
)
April 2023
Parameter
Value
0.038 Ω
Parameter Name
Equivalent capacitance (Cz
)
0.3 mH Coupling capacitance between the neutral line and the catenary (CJz
IEEE Instrumentation & Measurement Magazine
)
Parameter
Value
1.12 μF
1.43 nF
7
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