SVC Implementation Using Neural Networks For An AC Electrical Railway
SVC Implementation Using Neural Networks For An AC Electrical Railway
SVC Implementation Using Neural Networks For An AC Electrical Railway
WSEAS TRANSACTIONS on CIRCUITS and SYSTEMS Seyed Saeed Fazel, Amir Tahavorgar
Abstract: - This paper presents an on-line method for implementation of a static var compensator (SVC) in a
real ac autotransformer (AT)-fed electrical railway for reactive power compensation using Neural Networks
(NN). Genetic algorithm (GA) can be the off-line minimizing function for reactive power compensation.
Consequently, the nonlinear auto-regressive model with exogenous Inputs networks in series-parallel
arrangement (NARXSP) is implemented as a predictor and methodology in order to diminish calculation time
and making this method practicable. To study load flow and reactive power compensation for this unique
system, forward/backward sweep (FBS) load flow method is applied. MATLAB software is used for
programming and simulations.
Key-Words: - Neural network (NN), reactive power compensation, static var compensator (SVC),
genetic algorithm (GA), AC electrical railways load flow, forward/backward sweep (FBS).
exogenous Inputs network (NARX) [11] is well (C), rail (R), and feeder (F), respectively. So, (2) is
suited for non-linear systems such as heat obtained regarding the variation of x.
exchangers and waste water treatments plants [12],
[13]. In this paper, NARX network in series-parallel ⎡U C ⎤ ⎡ I C ⎤ ⎡U C ( x ) ⎤
arrangement (NARXSP) is considered for ⎢U ⎥ = Z (x ) ⎢ I ⎥ + ⎢U x ⎥
calculation of the exact amount of reactive power ⎢ R⎥ [ ] ⎢ R ⎥ ⎢ R ( )⎥ (2)
which must be injected by the SVC. ⎢⎣U F ⎥⎦ ⎢⎣ I F ⎥⎦ ⎢⎣U F ( x ) ⎥⎦
The remainder of the paper is organized as
follows. The FBS method which is modified for ac
electrical AT-fed railways is presented in section 2. where IC represents catenary current, which can be
Minimizing reactive power and the methodology changed by charging currents of coupling capacitors
using neural network is discussed in sections 3. between the catenary and both the rail and feeder.
Simulation results are given in section 4. Section 5 However, coupling capacitors and consequently
presents the conclusions of this work. charging currents are small enough to be neglected
[14]. PQ busses (trains) move along the track and
consequently x changes. Therefore, load flow
calculations must be iterated for each location, x.
2 Load Flow Calculations
For unbalanced distribution systems, the impedance
matrix consists of the self and mutual equivalent 2.1 AT systems
impedances for the three phases. The model ATs lead to changes in the feeding currents and
depicted in Fig.1 constitutes the fundamental part of flowing currents from the TSS. In the load flow
the computational method that simultaneously calculation, following key points are taken into
analyzes the three lines and their reciprocal account: a) the TSS transformer is modeled as a
interactions. Thus, (1) allows expressing the sending single phase transformer and an AT, whose
voltages, Uai, Ubi, and Uci, with branch currents, Ia, midpoint connected to the rails with zero potential;
Ib, and Ic; and receiving voltages, Uaj, Ubj, and Ucj. b) ATs are regarded as ideal voltage sources whose
voltages will be calculated after load flow
⎡U ai ⎤ ⎡ I a ⎤ ⎡U aj ⎤ calculations. As shown in Fig.2, ATs secondary
⎢U ⎥ = Z (x ) ⎢ I ⎥ + ⎢U ⎥
⎢ bi ⎥ [ ] ⎢ b ⎥ ⎢ bj ⎥ (1) currents, I2n, feed the train according to (3).
⎢⎣U ci ⎥⎦ ⎢⎣ I c ⎥⎦ ⎢⎣U cj ⎥⎦ Yn
I 2n = Il (3)
∑
N
Y
i =1 i
where x, in Fig.1, represents the distance between
sending and receiving points.
where
Pl − jQl
Il = (4)
V∗
as U1', U2', and U3', respectively. Node voltages for calculation must be in a loop considering each
this distance can be calculated in the same way as system current effects on the other. Four iterations
the previous distance. This forward sweep is can minimize the differences.
followed until the last AT so that the first step of b) The TSS current is equal to half of the
iteration will be completed. Afterwards, the summation of the loads currents in the AT system
calculated voltages will be used in the next iterative whereas this current for the SM equals to loads
step. Therefore, this procedure is followed like a summation. In addition, power losses in the AT
recursive calculation until the difference between system are directly related to the number of ATs,
the calculated node voltages for two consecutive length of tracks, and the Overhead Catenary System
steps gets low enough. (OCS) parameters. But, power losses in the SM
While more trains are in the track, the solving depends only on the OCS parameters and distance
method is almost the same, but some consideration between the load and TSS.
must be applied: a) for current calculations,
superposition is used; so, the currents for ATs are
summed up; b) each train adds tree nodes in the 3 Minimizing Reactive Power
distance between two consecutive ATs which must The power consumption of the electric railway
be considered for KVL calculation while using (2); systems depend on the headway, status, and power
c) while two or more trains are between two consumption of trains. Thus, if both on-line data of
consecutive ATs, current of the section which is the trains position and power consumption profiles
situated between PQ buses must be calculated by are available, a central processing system, located at
using KCL and this issue must be considered while the control room, can specify how much reactive
(2) is used as shown in (9): power must be injected to the grid. It is achieved by
sending remotely controlled signals from the
⎡U 4 ( x , n ) ⎤ ⎡U 4 ( x ′, n −1) ⎤ processing center to compensators to implement
⎢ ⎥ ⎢ ⎥ reactive power compensation.
⎢U 5 ( x , n ) ⎥ = ⎢U 5 ( x ′, n −1) ⎥ In this paper, the main objective of the SVC
⎢U 6 ( x , n ) ⎥ ⎢U 6 ( x ′, n −1) ⎥ exploitation is minimizing the power losses revealed
⎣ ⎦ ⎣ ⎦
(9) in (10). To obtain this function, the power losses
⎡ I Cn ,n −1 ⎤ corresponding to the imaginary component of the
⎢ ⎥ current must be compensated to zero as shown in
− ⎡⎣ Z (x − x ′) ⎤⎦ ⎢ I Rn ,n −1 ⎥
(11).
⎢ I Fn ,n −1 ⎥
⎣ ⎦
th th
where n train is farther than the (n-1) train from
Ploss = ∑ n R n I n
2
(
= ∑ n R n I nx
2 2
+ I ny ) (10)
the TSS and x' is the distance between the (n-1)th ∀ n , I ny = 0 ⇒ min ( Ploss ) = ∑ n R n I nx
2
(11)
train from the predecessor AT (x, and x' < d).
where Rn and In are the resistance and current of the
nth branch of the railway system, respectively. Also,
2.2 Combined System y and x indices indicate the imaginary and real part
The left side of Tehran-Golshahr network has no of the current, respectively.
installed AT. The distance between TSS and
Golshahr station is supplied by SM layout as shown
in Fig.4. Power feeding system parameters are given 3.1 Off-line Methodology
in Appendix. While two systems are connected, load To reach the global minimum a constrained GA is
flow calculation should be combined. Following used. The population consists of initial random set
points must be considered to analyze the load flows of constrained injected reactive powers due to the
for this combined system: SVC. The potential injected reactive powers are the
a) SM has no feeder wire. Thus, load flow chromosomes forming the population. The
calculation in SM is easier and the FBS method as arithmetic crossover is shown in (12) in which λ is a
mentioned in subsection A can be implemented. random number between 0 and 1, Q represents the
Voltage drop for the loads which are in the AT chromosome (reactive power), and Q ′ is the
region must be considered for the loads in SM
system and vice versa. For both systems, load flow offspring [15].
For mutation (13) is implemented as follows: where u(t) and yˆ (t ) describe the input and output
of the network at time t. Du and Dy are the input and
X K′ = X K ± Δ (t , X KU − X K ) (13) output orders. The schematic diagram of NARXSP
is illustrated in Fig.5.
where Δ(t , y ) can be defined as below:
U(t)
t
Δ(t, y) = y.r.( 1- ) b (14)
T Ŷ(t)
where
Fig.6 (a) up-line time table, (b) downn-line time table, (c) speed of the first train, and (dd) power of the first train.
Fig.11 (a) generated reactive power by GA and (b) results of training in NN (NARXSP).
Fig.12 (a) generated reactive power by GA and (b) output of the trained NN (NARXSP) for the corresponding
current as the predictor.
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