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Improved Active Power Filter Performance for Distribution Systems with Renewable Generation
P. Acufia*, L. Monin*, IEEE Fellow Member, M. Riverat, IEEE Member, J. Rodriguez t, IEEE Fellow Member, and J. Dixon+, IEEE Senior Member
*Dep. of Electrical
Engineering
Univ. de Concepci6n
Concepcion, CHILE
tDep. of Electronics
Engineering
+Dep. of Electrical
Engineering
Pontificia Univ. Cat6lica de
Chile
Univ. Tecnica Federico Santa
Maria
Valparaiso, CHILE
Santiago, CHILE
Ahstract-A predictive control algorithm specially devel
oped for shunt active power filters aimed to compensate
reactive power and current harmonics components is
presented and analyzed. The proposed predictive control
algorithm is implemented in a three-phase four-leg voltage
source inverter (4L-VSI). The use of a 4L-VSI allows
the compensation of current harmonics, reactive power
and neutral current harmonics generated by single-phase
non-linear loads. A detailed mathematical model of the
filter, including the effect of the power system equivalent
impedance is derived and used to design the proposed
predictive control algorithm. The proposed active power
filter and associated control scheme performance and
compensation effectiveness are demonstrated by simulation
and with experimental results.
Index Terms-Active power filter, Current control, Fi
nite control set model predictive control, Four-leg inverters.
I. NOMENCLATURE
AC Alternating current
DC Direct current
PWM Pulse width modulation
VSI Voltage source inverter
Vdc DC voltage
iL Load current vector [iLu iLv iLw]T
Vs System voltage vector [vsu Vsv vsw]T
i� Reference current vector [i�u i�v i�w]T
Zn Neutral line current
L f Filter inductance
Rf Filter resistance
II. INTRODUCTION
Renewable generation affects power quality due to its
nonlinear characteristic. Solar generation plants and wind
power generators must be connected to the grid through
high power static PWM converters. Moreover, the non
uniform nature of power generation affects directly volt
age regulation and distortion in power systems. This new
scenario in power distribution systems will force the use
of more accurate compensation schemes.
Although active power filters implemented with three
phase four-leg voltage-source inverters have already been
presented in the technical literature [1], [2], the principal
contribution of this paper is the development of the
predictive control algorithm for this specific application.
Traditionally, active power filters have been controlled
using PI controllers, for the current as well as for the
DC voltage loops. The PI controllers must be designed
based on a linear model.
The active power filter is a non linear system; therefore
compensation effectiveness as well as transient response
depends on how accurate is the associated developed
linear model. A good design using linear PI controllers
reflects in the transient performance of the active power
filter, specially its ability to follow the current reference,
and the capacity to keep the DC voltage constant and
equal to the reference signal [2]-[7].
So far, predictive control implemented in power con
verters has been used mainly in induction motor drive
applications [8]-[ 15]. In case of active power filter,
predictive control algorithm has the advantage that the
converter output impedance is constant and well known,
since the output ripple filter is part of the active power
filter design, simplifying the non linear model and the
predictive control implementation. Therefore, a detailed
discrete time model that includes system nonlinearities
of the output power filter can be developed and used to
978-1-4673-2421-2/12/$31.00 ©2012 IEEE 1344
[*fj ')\ Vs Z s pee - -
� Static Step-up ZL I PWM Transformer Converter
Ls io t Renewable System Loads
Energy Lj Zj Sources
-( j-( �-( f-( Rj Vdc �
-( f-( j-( f-t Shunt Active Power Filter
Figure 1. Standalone hybrid power system with Shunt Active Power Filter.
derive the predictive control algorithm.
The proposed non-linear model predicts the future
value of the injected current for all possible voltage
vectors generated by the 4L-VSI. The predictions are
evaluated with a cost function that minimizes the output
current error at the end of each sampling time. This
strategy allows fast current tracking with minimum error,
and without the necessity to use tuned controllers or
complicated control strategies. Modulators are no re
quired in this control technique.
The current reference signal is obtained from the load
current using the dq-based transformation. This block
calculates the active power required by the converter and
delivers the current reference to the current predictive
controller. A discrete mathematical model of the con
verter is obtained using its 16 feasible switching states.
With this model, the corresponding predicted values are
used to evaluate a cost function which deals with the
control objectives. After that, the valid switching state
that produces the minimum value of the cost function is
selected for the next sampling period.
This paper is organized as follows, in section III
the mathematical model of the 4L-VSI is presented; in
section IV the proposed control algorithm is introduced.
In section V, the current reference generation is detailed.
The proposed active power filter and associated control
scheme are validated thought simulation and experimen
tal results in section VI. Finally, our conclusions are
given in section VII.
III. FOUR-LEG INVERTER MODEL
In Fig. 1 is shown the typical standalone hybrid power
system which consists of renewable energy sources,
AC/ AC static PWM converter for voltage conversion,
battery banks for long-term energy storage, active power
filter and arbitrary loads. The AC/ AC converters perform
maximum power point tracking to extract maximum
possible energy from the sun and wind respectively.
The loads are unknown and can be of single-phase or
three-phase, balanced or unbalanced, linear or non-linear
nature. The four-leg inverter is used as an active filter.
Four-Leg Inverter P r---.---.---.---,
+
N �--�--�--�--�
io R Leq -+ eq
VxN Vo
Figure 2. Two-level four-leg inverter topology.
The power converter topology for the four-leg inverter
is shown in Fig. 2. The connection format is similar to
the conventional three-phase inverter with the fourth leg
connected to the neutral point of the system. The fourth
leg increases switching states from 8 (23) to 16 (24)
and thus offers control flexibility and improved output
voltage quality [16].
The voltage in any leg x of the inverter, measured
from the negative point of the DC voltage (N) can be
expressed in terms of switching states as,
VxN = Sx vdc, x = u, v, w, n. (1)
The mathematical model of the filter is:
R · L d io Vo = vxN - eq 10 - eq dt (2)
where Req and Leq are Thevenin equivalent filter
parameters, located to the output of the 4L-VSI.
IV. DIGITAL PREDICTIVE CURRENT CONTROL
The proposed digital predictive current control scheme
is shown in Fig. 3. This control scheme is basically an
optimization algorithm and thus it has to be implemented
digitally in the microprocessor based hardware. Conse
quently, the analysis has to be developed using discrete
1345
mathematics in order to consider additional restrictions
such as delays and approximations, etc. [9], [17]. The
main characteristic of predictive control is the use of
the system model to predict the future behavior of the
variables to be controlled. The controller uses this infor
mation to obtain the optimal actuation, according to a
predefined optimization criterion. The predictive control
algorithm is very easy and intuitive to understand. It
consists of three main steps as follows:
1) References and Measurements: the control objec
tives are obtained and the necessary variables to obtain
the prediction model are measured or calculated. In this
case, the measurements of output currents, load currents
and DC-side voltage are obtained, while the neutral
output current and neutral load current are given as
explain in section V.
2) Prediction Model: as a second consideration, it is
important to obtain the converter system model for the
output current prediction. Since the controller operates in
discrete time, both the controller and the system model
need to be represented in a discrete time domain [17].
The discrete time model consists of a recursive matrix
equation that allows the system prediction. This means,
for a given sampling time Ts, it is possible to predict the
system states at any instant [k+1]Ts, with the knowledge
of system states and control variables at instant kTs. Due to the first order nature of the state equations that
describe the model in (1 )-(2), a first order approximation
for the derivative which provides sufficient accuracy is
considered in this paper:
dx x[k + 1] - x[k] dt Ts (3)
The 16 possible output current predictions can be
obtained from (2) and (3) as:
io[k + 1] = !l (VXN[k]- Yolk]) + (1 _ Req TS ) io[k]. Leq Leq (4)
As shown in (4), the output current predictions require
the output current and voltage (which is a function of
the switching signals and the DC voltage) values. The
algorithm calculates all the 16 possible conditions that
the state variables can achieve.
3) Cost Function Optimization: as a final stage, the
predicted values are used to evaluate a cost function
which deals with the control objective. To choose the
optimal switching state to be applied to the inverter, the
16 predictions obtained for io[k + 1] are compared with
their references using a cost function 9 as follows:
g[k + 1] = (i�u[k + 1] - iou[k + 1])2 + (i�v[k + 1] - iov[k + 1])2 + (i�w[k + 1] - iow[k + 1])2 + (i�n[k + 1] - ion[k + 1])2 (5)
The output current equals its reference when 9 = O. Therefore the optimization goal of the cost function is to
achieve 9 value close to zero. The voltage vector v 0 that
minimizes the cost function is chosen and then applied at
the next sampling instant. During each sampling instant,
the minimum value of 9 is selected from the 16 function
values. The algorithm selects a switching state which
produces this minimal value and then applies it during
the whole k + 1 period.
V. CURRENT REFERENCE GENERATION
The phase current reference signals are obtained from
the corresponding load currents using the dq-based
scheme shown in Fig. 4. This block calculates the active
power required by the converter and delivers the current
reference to the predictive current controller.
The dq-based scheme operates in a rotating reference
frame, therefore the measured current signals must be
multiplicated by the sin(wt) and cos(wt) signals. By
using dq-transformation, the d current component is
synchronized with the corresponding phase-to-neutral
system voltage and the q current component is phase
shifted by 90°. The synchronized sin(wt) and cos(wt)
signals are obtained from a synchronous reference frame
Phase-Locked-Loop [18]. Equation (6) shows the rela
tion between the current in the stationary frame iLx(t)
(x = u, v, w), and its dq components (id and iq).
[::l � JH �:��t :���:l [� 1 �� 1 m:l (6)
A low-pass filter (LFP) extracts the DC components
of the line curr�nts id, resulting in harmonics references
components -id, with the corresponding negative value.
The reactive reference components of the line currents
are obtained inverting the corresponding ac and DC
components of iq. In order to keep the DC voltage
under control it is necessary to modify the amplitude
of the inverter reference current, by adding an active
power reference signal (ie) into the d-component. The
resulting signal i'd, together with i� are transformed back
to a three-phase system by the inverse Park and Clark
1346
Figure 3. Proposed predictive digital current control scheme.
io
SRF PLL
io
sin (wt)
cos (wt)
Figure 4. dq-based Current Reference Generator.
transformations as shown in (7). The cutoff frequency of
the LPF used in this paper was 20 Hz. [i�U] f2 [11 0 1 [1 0 0] [iO] ��v =Y"3 �-t13 Osinwt- :oswt �dq*' Zow v'2 -2" -1 Ocoswt smwt •
(7)
The current that flows through the neutral lines is
compensated by injecting the same instantaneous value,
obtained from the others line currents, phase-shifted by
1800, as shown in (8).
(8)
VI. SIMULATION AND EXPERIMENTAL RESULTS
A simulation model for the three-phase four-leg con
verter with the parameters as indicated in Table I, has
been developed using MATLAB-Simulink. The objec
tive is to verify the effectiveness of the proposed con
trol scheme in harmonic current compensation under
different operating conditions. The active power filter
Variable
Vs f Vdc Cdc Lf Rf Ts Te
Table I SPECIFICATION PARAMETERS
Description Value a
Source voltage 55 [V] System frequency 50 [Hz] DC voltage 162 [V] DC capacitor 2200 [p,F] (2.0 pu)
Filter inductor 5.0 [mH] (0.5 pu)
Internal resistance within L f 0.6 [12] Sampling time 20 [J.is] Execution time 16 [J.is]
a Note: Vbase = 55 V and Sbase = I kVA.
was tested compensating a 6-pulse rectifier. The pro
posed predictive algorithm was programmed using an S
function block that allows simulation of a discrete model
to be implemented easily in a Real-Time Interface (RT!)
on the dSPACE DSII04 R&D controller board. Simula
tions were performed considering a discrete sample time
of 20 [J-Ls],
In the simulated results shown in Fig. 5, the active
1347
Su
Sv
Sw
Sn
iL
vs
io
io
io∗
iok+1
Four–legInverter
3
4
CurrentReferenceGenerator
CostFunction
Optimizationgk+1
PredictiveModel
vdc
_ :�� ,-_._. _. '_'--,' .L-' _. _ ._. _ '_' ..J..'._' ._ ._ ._. _. _'_'.L. •. _._. _ . . _ ._ ._. --,' .---,' Vsu
5� . . . o . . .. ' . . . .... . . . . '. .... . iLu . . .
-5 �
J' �� _: 1 0AJj iW
_: 1 r" H·n -:� ;. :::� =. ,----, �
........ ---,---.�------,---....• ... '------,---, ......•.. Vdc
(50ms/div)
Figure 5. Simulation waveforms for the proposed control scheme.
filter starts to operate at t = tl. At this time, the active
power filter injects an output current io to compensate
current harmonic components, current unbalanced, and
neutral current simultaneously. Compensated system cur
rents (is) show sinusoidal waveform, with low distortion
(T H D < 5%). At t = t2, a three-phase balanced load
change is introduced from 0.6 to 1.0 p.u. Compensated
system currents remain sinusoidal despite the change in
the load. Finally, at t = t3, a single-phase load change
is introduced in the phase u from 1.0 to 1.3 p.u. As
expected on the load side, a neutral current flows through
the fourth leg (iLn), but on the source side, no neutral
current is observed (isn). Simulated results show that
the proposed control scheme effectively eliminate current
unbalanced. Additionally, Fig. 5 shows that the DC
voltage remains constant through the whole active power
filter operation. Experimental results corroborate the successful oper
ation of the active filter shown in the simulations. The
dynamic performance of the active filter is tested under
balanced and unbalanced load conditions. Fig. 6 shows
the transient response when APF starts to operate. The
line current immediately becomes sinusoidal and the
capacitor-voltage behavior is as expected. The T H Di is reduced from 27.09% to 4.54%.
Tek JL • Acq Complete M Pos: O,OOOs
iLu ...
VVV
TRIGGER
Type
11m Source
I!il Slope
1m '.\J\J\J'vV a;.m Vdc Coupling -.pa:akt "Vill""� �,�! L. \t.; • �",. .\, f ,. .... 1 l J' II iii "'-CH1 50.0V CH2 SO.OV M 10.0ms Eit..r 312mV
CH3 SO.OV CH4 10.0V 10-Mar-12 03:25 <10Hz
Figure 6. Experimental transient response under APF connection.
In Fig. 7, the response of the series active filter under
load change is shown. The line current remains sinu
soidal and the capacitor voltage returns to its reference
in two cycles, with minimum variation when the load
changes. In this case, a step change is introduced from
0.6 to 1.0 p.u.
Tek JL
"'-
• Acq Complete M Pos: O,OOOs ...
TRIGGER
Type
11m Source
!iii Slope
1m Mode
WllIiIlI Coupling
IiI! CH1 50.0V CH2 SO.OV M 10.0ms
CH3 50.0V CH4 S.OOV 10-Mar-12 04:49
CH1 ..r 32.0V
<10Hz
Figure 7. Experimental results under balanced load change (0.6 to 1.0 p.u.)
In the last case, the phase u load was increased from
1348
1.0 to 1.3 p.u. The corresponding waveforms are shown
in Fig. 8. This figure shows that the active filter is able
to compensate current flow in the neutral wire and has
fast transient performance. Moreover, results show that
the four wire output current ion is effectively controlled,
and the neutral current of the system remains close to
zero even if a unbalance of 30% is applied.
Tek • Acq Complete M Pos: O.OOOs
Vsu I ( II'
TRIGGER
Type
m Source
!!iii Slope
IiII:IliE Mode
I1a Coupling
iii! CH1 50,OV CH2 50,OV M 10,Oms CH1 f 58,OV
CH3 50,OV CH4 50,OV 11-Mar-12 04:41 <10Hl
Figure 8. Experimental results under unbalanced phase u load change (1.0 to 1.3 p.u.)
VII. CONCLUSION
An improved dynamic compensation scheme for
power distribution systems with renewable generation
with a prediction time of one sample has been proposed
to improve the distribution system current quality. The
proposed predictive control algorithm has proved to be
good alternative for active power filter applications.
The advantages of the proposed control scheme re
lated with simplicity, modeling and implementation have
proved that predictive control schemes are a good alter
native to classical methods proposed previously. Sim
ulated and experimental results have shown that com
pensation effectiveness of the active power filter is well
achieved with predictive techniques.
ACKNOWLEDGMENT
The authors wish to thank the financial support from
the the Chilean Fund for Scientific and Technological
Development (FONDECYT) through project 11 10592 Basal Project FB0821.
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