Download ii. ii. finite-difference time-domain method

CE 1
Finite-Difference Time-Domain Method
used in Transient Analysis of Wave Processes
Denisa Duma, Calin Munteanu and Dan D. Micu
Electrotehnics Department, Technical University of Cluj-Napoca
G. Baritiu 26-28, 400027 Cluj-Napoca, Romania
E-mail [email protected]
Abstract— The aim of this paper is to made an analysis of wave
processes of voltage and current distributed along the MTLs with
branches in a substation, caused by the switching operation due
to the circuit breakers and the disconnect switchers. The wave
processes of voltage and current distributed along the busbars
and the power lines without load in the substation are calculated
with the finite-difference time-domain method (FDTD) when the
circuit breakers and the disconnect switchers are closed.
Keywords—Finite-Difference Time-Domain, transmission line,
transient analysis, wave processes, electromagnetic field
I.
INTRODUCTION
In a substation, the switching transients are a very
important problem because the frequency spectrum of the
transient process is very wide and the electromagnetic field at
the high frequency domain is radiated from the busbars and the
power lines.
Wave processes caused by the switching operation due to
the circuit breakers and the disconnect switchers can seriously
disturb the secondary equipment in the substation and the
consumer devices nearby.
The wave processes of voltage and current distributed
along the busbars and the power lines in a substation are
calculated with Finite-Difference Time-Domain Method in
order to develop an effective numerical algorithm.
II. II. FINITE-DIFFERENCE TIME-DOMAIN METHOD
The Finite Difference Time Domain (FDTD) method has
been widely used to simulate various electromagnetic
problems because of its flexibility and versatility. Many
variations and extensions of the FDTD exist, and the literature
on the FDTD technique is extensive.
This technique involves the Maxwell’s equations in time
domain by approximating the space and time derivatives by
finite differences. Taking the x-components:
E y
z

H x H y H z
E x
E z

 E x  
;
 
z
y
t
y
t
(1)
The FDTD method involves a time-stepping procedure
from inputs which are time-sampled analogue signals. The
modeled region is represented by two interleaved grids of
discrete points, one containing the points at which the
magnetic field is evaluated, the other the electric field. One
cell of these grids is shown in Fig. 1.
Fig. 1. FDTD of Element Space
The derivatives are replaced by finite differences. For
example, using the shown nomenclature, the first equation are
reduces to
 E y 2 t   E y1 t    E z 2 t   E z1 t  


 

 
z
y


 
(2)
H x 0 t  t   H x 0 t  t 
 
t
In this equation, the only unknown quantity is Hx0(t+Δt).
Hence the electric field values at time t are used to find the
magnetic field values at time t+Δt. A similar approach can then
be used to evaluate the electric field values at time t + 2Δt.
Fields can therefore be propagated through the whole grid by
alternately evaluating the electric and magnetic field strengths
at each time step. This time stepping is continued until either a
steady-state response is found or the desired response is
obtained.
It can be seen that using this technique it is not necessary to
solve a system of linear equations, however the computer
storage and running time is dependent upon the electrical
volume being modeled and the necessary grid resolution.
FDTD has been used successfully over a wide range of
modeling problems its chief advantage being its flexibility. It
is possible to model arbitrary waveforms as they propagate
through complex configurations of conductors, dielectrics and
even lossy non-linear and nonisotropic materials.
III. APLICATION
As an example, is applied the FDTD method on a MTLs
model in a three-phase substation, shown in Figure 2.
CE 2
Fig. 2. An MTLs Model in a Substation
In this model, the MTLs are assumed as uniform, so the
per- unit-length parameters are independent to the position z
for each MTLs.
We will use an iterative formula to determine the boundary
conditions at the node of the branches for the MTLs with
branches. Based on these formulae, the wave processes of
voltage and current distributed along the busbars and the
power lines without load in the substation have been calculated
with FDTD method during the switching operation.
IV. CONCLUSIONS
The FDTD method demonstrated to be the most
appropriate technique to analyze the wave processes of voltage
and current distributed along the busbars and the power lines
in the substations in comparison with other methods (MOM)
used in literature, because of his applied flexibility for
complex configurations and for non linear processes.
V. REFERENCES
[1]
[2]
[3]
[4]
T. Lu, X. Cui, “Transient Analysis o Wave Processes for Multiconductor Transmission Lines with Branches Using FDTD”, IEEE
Trans. on EMC, pp. 699-703, 2000.
A. Adascalitei, R. Ball, M. Cretu, V. David, Electromagnetic
Compatibility Testing and Measurement-Theory Manual, The
University of Warwick United Kingdom, 2002
Wiggins, C.M. and Wright, S.E., “Switching Transient Fields in
Substation”, IEEE Trans. on Power Delivery, Vo1.6, No.2, pp.591-600,
1991.
A. Orlandi, C.R. Paul, “FDTD Analysis of Lossy Multiconductor
Transmission Lines Terminated in Arbitrary Loads”, IEEE Trans. on
EMC, Vol.5 No.3, pp.388-399, 1996.