Harmonic and balance compensation using instantaneous active and reactive power control on electric railway systems
ABSTRACT This work presents a general filtering and unbalance compensation scheme for electric traction systems. The proposed method uses an active filter controlled with the instantaneous active and reactive power, to reduce the harmonic current distortion and the negative sequence obtained by the system under unbalanced operation in steady state. The proposed filter is evaluated using open delta (VV) and Scott transformers in the power substation. The scheme has been simulated and experimentally validated. Experimental and simulation results show the controller advantages and the applicability of the proposed method in railway systems.

Article: A DualLoop Control Strategy of Railway Static Power Regulator Under V/V Electric Traction System
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ABSTRACT: For power quality in V/V traction system of the 350km/h highspeed railway, a kind of railway static power conditioner (RPC) is discussed, which is used to carry out the comprehensive compensation of negative sequence and harmonic currents in the traction substation. In order to improve the control effect and performance of RPC, a dualloop control strategy is constructed for RPC. Taking into account the disturbance and variation of electrified railway environment, a recursive proportionalintegral control based on fuzzy algorithm is adopted to realize a fast and smooth tracking to the reference current. An energybalance control is proposed to suppress the fluctuation of dclink voltage and maintain the stability of RPC, which is an accurate and adaptive feedback control based on corresponding parameters. Finally, the correctness of the analysis proposed in this paper has been confirmed by the simulation and experiment results.IEEE Transactions on Power Electronics 08/2011; · 5.73 Impact Factor  [Show abstract] [Hide abstract]
ABSTRACT: ELECTRIC traction is considered one of the most widely used means of transportation because of its advantages such as being economical, environment friendly etc. Indian Railways has been using electric traction fed by 25kV singlephase AC supply obtained from three phase utility. This paper analyses the harmonic issues of the electric traction system by measuring voltage, current and harmonics at different traction substations. A passive harmonic LC filter is designed to filter out the prominent harmonics in the system.01/2011;
Page 1
Harmonic and Balance Compensation using
Instantaneous Active and Reactive Power Control
on Electric Railway Systems
A. Bueno, J. M. Aller and J. Restrepo
Grupo de Sistemas Industriales de Electrónica de Potencia
Universidad Simón Bolívar
Caracas 1080A, Venezuela
T. Habetler
School of Electrical and Computer Engineering
Georgia Institute of Tecnology
Atlanta, Georgia
Abstract—This work presents a general filtering and unbalance
compensation scheme for electric traction systems. The proposed
method uses an active filter controlled with the instantaneous
active and reactive power, to reduce the harmonic current
distortion and the negative sequence obtained by the system
under unbalanced operation in steady state. The proposed filter
is evaluated using open delta (VV) and Scott transformers
in the power substation. The scheme has been simulated and
experimentally validated. Experimental and simulation results
show the controller advantages and the applicability of the
proposed method in railway systems .
Index Terms—Harmonics, Active filter, Transformer, Locomo
tive, Traction application.
I. INTRODUCTION
Electric traction systems for passengers and goods use
different power transformer configurations, in order to feed
single phase systems from the three phase supply. In gen
eral, threephase to two single phase conversion schemes use
transformers connected in open delta (V − V ), Scott or Le
Blanc configurations [1]. In a practical application, the load
associated with each singlephase circuit does not compensate
each other, due to the variable demands in the transport
system and railroad line profile. Also, the use of uncontrolled
rectification to feed the traction load contribute to the total
unbalance seen from the three phase supply. This unbalance
is due mainly to the injection of current harmonics to the main
threephase system depending on the transformer connection
and harmonic order [2].
It is then required the use of filters and unbalance com
pensators to ensure proper system operation and to raise the
power quality [3].
These problems are usually addressed, in practice, with the
use of passive power quality compensators such as reactive
power compensation capacitors and passive filters, and they
are singlephase equipment installed in each feeder of the
traction substation. Usually, the coupling factor between two
feeders is negligible due to the independent operation of each
passive compensator. Moreover, passive equipment does not
have the dynamic capability to adjust to changes in load, where
over and under compensation happen frequently as a result of
continuous change in load conditions.
Different active power quality compensators have been
proposed in [4]–[6] to solve the unbalance problem. All of
them employ two singlephase converters that have a common
DC bus and the simultaneous compensation of harmonic
content and unbalance can not be achieved with these schemes.
Also, when the compensation is made from the single phase
side, the instantaneous active and reactive power definition is
difficult to use in the compensation of harmonics and power
unbalance [7] [8].
In this work a compensation scheme is proposed to pro
vide simultaneous correction of harmonic content and load
unbalance for railroad systems using open delta or Scott
transformers in the power substation. This scheme is based
on the instantaneous active and reactive power description of
the system [9], using space vector representation of the state
variables, and the application of direct power control (DPC)
to attain the required correction by minimizing a cost function
obtained from the instantaneous active and reactive mismatch
[10]–[12].
The control strategies presented in this work are both,
simulated using a state variables model representation and
experimentally validated using a DSP based modular power
electronic system able to emulate the electric traction system
operating conditions, the open delta, the Scott transformer, the
filtering and the load balancing converters [13].
The generality of the proposed filtering technique using
instantaneous active and reactive power can be extended to
any other transformer configuration in the power substation.
Multilevel converter technology can facilitate the industrial
implementation because reduces the specifications of the
power electronics switches and the voltage stress (dv
the magnetic components like coupling transformers and/or
inductors [14].
dt) on
II. HARMONIC AND UNBALANCE COMPENSATION SYSTEM
Figure 1 shows the proposed control scheme. A shunt active
filter is used, directly connected to the power system using
a voltage rising transformer. The active filter uses a power
converter configured as an active threephase PWM rectifier,
connected to the threephase side.
9781424447831/10/$25.00 ©2010 IEEE 1139
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Figure 1: Proposed compensation scheme
(a) VV Transformer(b) Scott Transformer
Figure 2: Proposed compensation scheme.
Figure 2 shows the open delta (V − V ) and Scott trans
formers used frequently to connect a traction substation to the
electric grid. These connection schemes generate two single
phase networks from the threephase power system. Each
singlephase circuit is used to feed a 60 to 100 km rail track.
The simulation of the steady state and dynamic behavior
for the traction system under unbalance conditions and with
harmonic current injection uses a space vector model of the
open delta and Scott transformer, uncoupling the differential
equations in the transformer model [7]. Additionally, the filter
and its control have been modeled using a space vector
representation [15].
The power invariant space vector transformation is defined
as,
? x =
?
2
3
?xa(t) + αxb(t) + α2xc(t)?
α = ej2π
3
(1)
A. VV Transformer space vector model
For the ideal V − V transformer configuration shown in
Fig. 2a, its model can be obtained considering the transformer
ratio and using Ampere and Faraday Laws [1]:
vab=N1
N2vT1; vbc=N1
N2vT2; ia=N2
N1iT1; ic=N2
N1iT2
(2)
The voltage and current space vectors calculated in the
transformer’s primary winding as function of the secondary
winding voltages and currents are:
?
?is=
3
N1
? vs=
?
2
3
N1
N2
?vT1− α2vT2
?
2
N2
?(1 − α)iT1+?α − α2?iT2
?
(3)
B. Scott Transformer space vector model
For the ideal Scott transformer shown in figure 2b, its model
can be obtained considering the transformer ratio and using
Ampere and Faraday Laws [1]:
vab=N1
√3
2
N2vT1; vco=
N2ic= iT2;1
√3
2
N1
N2vT2;
N1
2
N1
N2(ia− ib) = iT1
(4)
The voltage and current space vectors calculated in the
transformer’s primary winding as function of the secondary
winding voltages and currents are:
?
?is=
3
N1
? vs=
?
3
2
N1
N2
?(1 − α)iT1+√3α2iT2
1
1−α2(vT1− jvT2)
2
N2
?
(5)
C. Active and reactive power control
The DPC controller is based in the instantaneous apparent
power from the current and voltage space vectors definitions
[7]:
? s = ? vs·?i∗
From Fig. 1, the active filter can be modeled as,
s= (vsα+ j vsβ) · (isα+ j isβ)∗= p + jq
(6)
? vs= ? vr+ R?is+ Ld?is
dt
(7)
A discrete time version of this equation is obtained by
replacing the derivative with a first order Euler approximation,
and the estimated supply current for the next control cycle
becomes
??is(k + 1) =?is(k) + ∆??is(k)
∆??is(k) =Ts
From (6), the estimated active and reactive power for the
next sampling period can be written as,
(8)
where
ˆL
??? vs(k) −?? vr(k) −ˆR?is(k)
?
(9)
? s(k + 1) = ? s(k) + ∆? s(k) = ? s(k) + ∆p(k) + j∆q(k) =
= ? vs(k) ·?is(k)∗+ ∆?? vs(k) ·?is(k)∗+?? vs(k + 1) · ∆??is(k)∗
Replacing (9) in (10), the change in apparent power is:
(10)
∆? s(k)=∆?? vs(k) ·?is(k)∗+ ···
(11)
?∗
···+
?? vs(k + 1) ·Ts
ˆL
??? vs(k) −?? vr(k) −ˆR?is(k)
For a sinusoidal voltage source power supply, the estimated
?? vs(k + 1) is obtained by rotating in ∆θ = ωTsrads.
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?? vs(k + 1) = ? vs(k) · ejωTs
∆?? vs(k) = ? vs(k)?ejωTs− 1?
(12)
(13)
The complex apparent power? s(k) is a function of the supply
voltage, and also changes with the rectifier voltage?? vr(k) that
j qref. Defining ∆? s0(k) as an independent voltage vector term
in?? vr(k), the following change in active and reactive power is
Ts
ˆL
can be manipulated to obtain the commanded value pref+
obtained
∆? s0(k)=
? vs(k)2· ejωTs+ ···
(14)
?
··· +? vs(k) ·?is(k)∗
??
1 −TsˆR
ˆL
?
ejωTs− 1
For a given reference in active and reactive power the
change in power for proper compensation becomes a function
of the converter voltage?? vr(k). The apparent power variation
the following sampling period, prefand qref, are given by the
following expressions
needed to change from the actual to the demanded value in
∆? s(k) = ∆? s0(k) −Ts
ˆL
??? vs(k + 1) ·?? vr(k)∗?
+j qref− ℑm{? s(k)}
?
(15)
? ǫs(k) = pref− ℜe{? s(k)}
?
In the OVSS algorithm, also known as predictive direct
power control, a cost function is evaluated for a set of the
converter voltages ? vr, and the value of this voltage providing
the minimum value for the cost function is employed in the
next control cycle [16]–[18]. In this case the cost function is
???
ǫp(k)
???
ǫq(k)
(16)
J(k) = ηp(ǫp(k) − ℜe∆? s(k))2+ηq(ǫq(k) − ℑm∆? s(k))2
(17)
where ηpand ηqcontrol the relative importance of the active
and reactive parts in the system.
The proposed control technique is based in the selection
of the voltage vector that minimized the cost function (17)
expressed by the active and reactive power errors. However,
since zero is the global minimum for the cost function, instead
of testing among several candidate vectors for the best choice,
the proposed techniques computes with a closed form formula,
the voltage vector for this minimum. Forcing to zero the cost
function (17), J(k) = 0,
? ǫs(k) − ∆? s(k) = 0
(18)
Replacing (15) and (16) in (18)
∆? s0(k) −Ts
ˆL
??? vs(k + 1) ·?? vr(k)∗?
= ǫp(k) + jǫq(k)
(19)
Finally, replacing (12) into (19), the absolute optimum
converter voltage required to attain the commanded active and
reactive power becomes
?? vr(k) = ? vrα(k) + j ? vrβ(k) =
This voltage is synthesized in the converter using standard
space vector modulation (SVM) [19]. As with other DPC
algorithms, the reactor parameters are required for computing
the estimated value of the power system voltages, the active
and reactive power and the update value for the converter
voltage indicated in (20).
The proposed algorithm has many advantages over existing
methods, among them it provides an instantaneous correction
of the active and reactive power flowing into the converter,
reduces the ripple in the instantaneous power and currents,
resulting in a low harmonic distortion and have low computa
tional demands.
ˆL
Ts
?∆? s0(k) −? ǫs(k)
? vs(k) · ejωTs
?∗
(20)
III. SIMULATION RESULTS
The scheme shown in Fig. 1 has been modeled using the
space vector representation of the state variables [7]. Both,
the V − V and Scott transformers have been included in
these simulations. The rail road system is represented using
the measured harmonic currents distribution, injected to the
power system in the secondary side of each transformer [20].
The three phase power system is modeled using a space vector
Thevenin equivalent. Also, space vector representations of the
power transformer (V − V or Scott), IGBT converter and
the filter inductor are used in the simulation. The per unit
parameter used in simulations are shown in Table I.
Table I: Parameters of the filter scheme model
Lth
0.037
RTrx
0.01
LTrx
0.1
Rtrx
0.01
Ltrx
0.1
Rrec
0.005
Lrec
0.05
VDC
3
Table II shows the current Total Harmonic Distortion
(THD) and the unbalance relation between positive and
negative sequences (I2/I1) [21], for uncompensated and com
pensated cases using V − V and Scott transformer. The
simulation uses maximum unbalance by operating on one
single phase circuit with the other under no load, which is the
most demanding operating condition. The active filter injects
the harmonic content used by the single phase rail road load.
The proposed control scheme reduces by more than 50% the
THD for both transformer connections.
Table II: Simulated total harmonic distortion and unbalance
Uncompesated
THD
.4065
.2054
.4015
.2264
Compensated
THD
.1804
.1110
.1228
.0747
Simulated Cases
V − V rectifier
V − V rail road
Scott rectifier
Scott rail road
I2/I1
.9238
.9216
.9235
.9384
I2/I1
.0835
.0732
.0838
.0813
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Figure 3 shows the simulated instantaneous currents flowing
into the power system without compensation and with the
proposed active and reactive compensation. The simulations
show the balancing effect on the power system current as
well as the THD reduction obtained with the active filter
controlled by the instantaneous active and reactive power.
Both transformers (V − V and Scott) have a similar current
behavior when a single phase rectifier load is connected in one
secondary.
IV. EXPERIMENTAL RESULTS
For the experimental test, the proposed algorithm was
implemented on a custom build floating point DSP (ADSP
2106140 MHz) based testrig. The power stage uses six 50A,
1200V, IGBTs with two 2200 µF 400 V series connected ca
pacitors in the DC link. The input inductors have an 7mH; the
PWM signals are provided by a motion coprocessor ADMC
201 operating at 10 kHz. The rail road load was implemented
in only one single phase circuit using a single phase rectifier
bridge with an RL (50200 Ω, 40 mH) load in the DC side.
The sampling frequency is synchronized by the motion co
processor at the beginning of each PWM cycle. Fig. 4 shows
the power module and the DSP based processing unit. The
electrical parameters for the power circuit in the experimental
tests are the same to those used in the simulations, and shown
in Table III. The V − V and Scott transformer connections
were built using two singlephase – 480 : 240 – 120 V, 1
kVA transformers. The Scott transformer was built with two
additional single phase variable transformers.
Table III: Parameter testrig
Rrec
20mΩ
Lrec
7.0mH
CVDC
Ts
V
1100µF
200 ∼ 600V
100µs
LLOAD
17mH
208V
ffs
RLOAD
50Ω
CLOAD
2200µF
60Hz
100kHz
A. V − V Transformer
Figures 5a to 5d show the current waveforms and spectrums
measured on a three phase V − V transformer test bench
feeding a nonlinear load, with and without the proposed
compensation scheme. The measurements were obtained us
ing a power quality analyzer type “B” [22]. Comparing the
compensated and the uncompensated results, it can be ob
served that the compensator reduces unbalance and harmonic
distortion in the system. The unbalance is reduced from 94.7%
(uncompensated value) to 16.8% (compensated value), and the
system’s current THD to values below 18.4% in all phases,
with a significant reduction in the third and seventh harmonics
which are the more significant components present in the
harmonic spectra generated by vector controlled converters
used in locomotives.
(a) Uncompensated (V − V transformer)
(b) Compensated (V − V transformer)
(c) Uncompensated (Scott transformer)
(d) Compensated (Scott transformer)
Figure 3: Simulated active filter effect on power system
currents feeding a single phase rectifier load
1142
Page 5
Figure 4: Experimental rig
B. Scott Transformer
Figures 5e to 5h show the current waveforms and the
harmonic spectrum, measured on a three phase Scott trans
former test bench feeding a nonlinear load, with and without
the proposed compensation scheme. The nonlinear load was
the same used in the V − V transformer case. Comparing
the compensated and the uncompensated results, it can be
observed that the compensator reduces harmonic content and
balance the three phase load. The compensator reduces the cur
rent unbalance from 94.7% (uncompensated value) to 16.8%
(compensated value), and the system’s current THD to values
below 18.4% in all phases, with a significant reduction in the
third and seventh harmonics which are the more significant
components present in the harmonic spectra generated by
vector controlled converters used in locomotives.
V. CONCLUSIONS
The proposed compensation scheme reduces negative se
quence currents that circulate in the uncompensated system
feeding an electric traction system using a power system trans
former connected in V −V or Scott configuration. The scheme
reduces the current THD to values allowed by international
regulations, and regulates the power factor observed in the
common coupling point between the traction substation and
the power system. The proposed compensation scheme im
plementation using an instantaneous power control algorithm
with direct space vector representation, reduces the system’s
current THD to allowable ranges (< 20%) and reduces the
overall unbalance from 97% to 18% for worse case operation.
The compensation algorithm is able to control the power factor
measured at the coupling point under all considered conditions.
From the simulation and experimental results it is found that
there is a compromise between the amount of unbalance
correction and harmonic reduction that can be achieved. This
is due to the finite amount of energy stored by the active filter
in its input inductance and dclink capacitor.
(a) Uncompensated (V − V )(b) Harmonics uncompensated (V −
V )
(c) Compensated (V − V )(d) Harmonics compensated (V − V )
(e) Uncompensated (Scott) (f) Harmonics uncompensated (Scott)
(g) Compensated (Scott)(h) Harmonics compensated (Scott)
Figure 5: Experimental active filter effects on power system
currents feeding a single phase rectifier load
ACKNOWLEDGMENT
The authors want to express their gratitude to the Dean
of Research and Development Bureau (DID) of the Simón
Bolívar University, for the annual financial support provided
to the GSIEP (registered as GID04 in the DID) to perform
this work.
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