Download optimal control desi a shunt active power a shunt active power filter

OPTIMAL CONTROL DESIGN OF DC CIRCUIT OF
A SHUNT ACTIVE POWER FILTER
Vlad SURU
University of Craiova
Alexandru BITOLEANU
University of Craiova
Mihaela POPESCU
University of Craiova
Mihăiţă LINCĂ
University of Craiova
REZUMAT. În funcţionarea
funcţionarea filtrelor active atât curentul de la ieşire cât şi tensiunea din circuitul de curent continuu trebuie
reglate la valorile instantanee dorite prin intermediul buclelor de reglare. Uzual, regulatoarele din componenţa acestor bucle
bucle
sunt regulatoare de tip
tip PI, atât pentru reglarea tensiunii cât şi a curentului, deşi pentru reglarea curentului sunt de asemenea
utilizate regulatoare cu histerezis.
histerezis. Această lucrare îş
îşi propune verificarea atât prin simulare, cât şi experimental a algoritmului
de filtrare destinat
destinat unui filtru activ paralel, respectiv, al dependenţ
dependenţei performanţ
performanţelor obţ
obţinute de valoarea tensiunii din circuitul
de curent continuu al filtrului.
Cuvinte cheie:
cheie filtre active, bucle de reglare, distorsiune armonică.
ABSTRACT. The active filter operation
operation involves the use of control loops to obtain both the instantaneous value of the
compensating current and the voltage on the compensation capacitor.
capacitor. Usually, PI controllers are used for these loops for both
current and voltage regulation, although for the
the current regulation, hysteresis regulators are also used.
used. This paper aims to
validate the filtering algorithm for a parallel active filter by simulation and experimental study, and the dependence between
betwee n
the filtering performance and the voltage across the
the compensating capacitor.
Keywords: active filters, voltage control loop, harmonic distorsion.
1. STRUCTURAL SCHEMATIC OF THE
ACTIVE FILTER CONTROL SYSTEM
For the compensating current regulation, and the
DC link voltage regulation, respectively, the closed
loop control system illustrated in figure 1 makes the
subject of this study.
Fig. 1. The block diagram of the automatic control system
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To simplify the tuning process of the voltage
control loop, the current control loop is considered
proportional, with unit amplification factor [11][12].
Thus, from the active filter control block diagram, the
outer voltage loop is extracted in figure 2.
For the specific case of the experimental equipment
used, where: UA = 220 V, UCN = 700 V, C = 1100 µF,
L1 = 0.4 mH (the inverter side coil of the LCL interface
filter), L2 = 4 mH (the grid side coil of the LCL
interface filter), Ci = 0.12 µF (the LCL interface filter
capacitor), Rd = 200 Ω (the LCL interface filter series
damping resistor), the following values of the controller
parameters are found:
- the proportionality constant: KPU = 2.97;
- the integration time constant: TIU = 6 ⋅ 10-3.
Fig. 2. Structural schematic of the voltage control loop
The blocks represents:
- GRU(s) – the voltage regulator transfer function;
- GTI(s) – transfer function of the current
transducer;
- GFu(s) – the voltage transfer function of the
active filter;
- GTU(s) – transfer function of the voltage
transducer.
In order to determine the voltage and current
transducers transfer functions, these can be
approximated by a first-order transfer function:
G TI (s) =
K TU
K TI
; G TU (s) =
(1)
1 + TTI ⋅ s
1 + TTU ⋅ s
Since the transducers proportionality constants and
integration time constants are considered to be known,
the transfer functions of the active filter and voltage
regulator remains to be determined. Starting from the
equality between the active power measured at the the
AC terminals of the active filter and at the DC
terminals, the voltage transfer function of the active
filter can be determined [3].
A classical proportional-integral structure is adopted
for the voltage controller:
G RU (s) =
v ⋅s +1
1
= K PU +
w ⋅s
TIU ⋅ s
(2)
To determine the values for v and w, Kessler’s
Modulus Optimum criterion was used [3][12].
By applying this method, only the expression which
gives the value for v can be determined. In order to find
the value of the other constant of the voltage regulator
transfer function, the passband of the unity feedback
voltage control loop is imposed. [3].
2. CALCULATION OF THE DC LINK
CAPACITOR
When compensating the nonlinear load reactive and
distorsion power, there is no exchange of active power
beetween the power grid and the shunt active
compensator, therefore the energy storage element can
be purely reactive (generally one large capacitor or a
less common solution, one large inductor).
Starting from the expression of the instantaneous
capacitor voltage, and by imposing the AC voltage
component as a percent of the nominal voltage, and
also, imposing the capacitor electric charge as a
percentage of the charge corresponding to the active
filter rated current, the compensating capacitor capacity
expression is obtained [3]:
C=
3 ⋅ εi ⋅ εS ⋅ U A I FT
U 2 CN ⋅ ε u
(3)
where:
- εi – is the imposed percent of the compensating
capacitor electric charge;
- εS – is the ratio between the AC side active filter
apparent power and the DC side apparent power;
- UA – power grid voltage Laplace transform;
- IF – is the compensating current rated value;
- T – is the averaging period of the capacitor current;
- UCN - the nominal voltage across the capacitor;
- εu – is the imposed percent of the AC voltage
component across the DC link capacitor;
For the specific case described above, using (3)
gives the capacity used for the voltage controller tuning,
which is 1100 µF.
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3. DC LINK VOLTAGE INFLUENCE OVER
EFFICIENCY. THE IMPLEMENTATION OF
CONTROL LOOPS
To study the influence of the active filter DC link
voltage on the compensation performance, the Simulink
model of the active filter shown in Figure 3, was built.
The DC link voltage was set to the imposed value in
the model initial conditions. The nonlinear load whose
current is compensated by the active filter is a threephase AC static converter which absorbs a current
similar to that absorbed by PWM inverter and induction
motor electric drives.
Also, to bring the simulation study as close to
reality, the three-phase power grid has a total harmonic
distortion of 2.51%, by inserting the 5th, 7 th, 11 th and 13
th
order harmonics in the corresponding proportions of a
real measured grid voltage.
The interface filter of the active filter, used in this
study, is a T passive filter, with damping resistors,
mounted in series with the capacitor.
In order to calculate the compensating current, the pq theory was used, valid for sinusoidal voltage [1][3],
and for the gating signals of the power transistors,
hysteresis current controllers and also, PI current
controllers and PWM modulation had been used.
To analyze the dependence of the total harmonic
distortion factor of the compensated current on the DC
link voltage, the following relations based on the p-q
theory, where used [3]:
- the apparent power on the active filter AC side:
S = P2 + Q2 + D2
(4)
Fig. 3. The complete Simulink model of the active filter system
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123
25
- the apparent power on the active filter DC side:
THD i
P I
20
T
SFcc = U C ⋅ I Cef = U C ⋅
1 2
i C ⋅ dt
T ∫0
(5)
15
10
- the distorsion power on the active filter AC side:
T
D=
1
p 2 ~ + q 2 ~ ⋅ dt
∫
T0
(
)
(6)
5
0
600
700
800
900
Uc
[V]
900
Uc
[V]
a)
9000
where p~ and q~ are the AC components of the
complex apparent power, real and imaginary
projections on the fixed orthogonal reference frame.
For the analysis by simulation, the nonlinear load
effective current had been set to 10 A, for which the
total harmonic distortion factor has a value of 126.5%.
For the PI current controllers, the compensated
current minimum total harmonic distortion is obtained
at about 860 V, when it reaches the value of 4.8%. At
lower values of the capacitor voltage, the distortion
factor increases rapidly when the voltage diminishes,
unlike at higher voltage, where the dependence is much
smaller.
8000
7000
D
Sc
a
Sc
c
6000
5000
4000
3000
600
700
800
b)
25
THD i
h y s
20
For the hysteresis current controllers, the resulting
efficiency is much lower, the minimum THD of 8.77%
is obtained for a DC link voltage about 750 V.
Because the compensating current calculation was
considered only for the fluctuating real and imaginary
power, only the distorsion power was compensated by
the active filter, thus the reactive power it is still
absorbed from the power grid. It follows that the
apparent power on the active filter AC side is
approximately equal to the distorsion power calculated
for the same measuring point, throughout the capacitor
voltage range, except for the lower voltages, where the
distorsion power transferred by the active filter
decreases with the compensation efficiency.
Regarding the powers transmited between the active
filter and the nonlinear load for the two types of current
regulation, it can be seen from figure 4, that the
compensated curent minimum THD is obtained at about
the voltage across the capacitor at which the apparent
power of the active filter DC side equals to that of the
AC side. This information can be used to create a
control system for the DC link optimal voltage.
15
10
5
0
600
700
800
900
Uc
[V]
900
Uc
[V]
c)
9000
8000
D
Sc
a
7000
Sc
c
6000
5000
4000
3000
600
700
800
d)
Fig. 4. Supply current THD and computed powers versus DC link
voltage for: a, b) the use of PI current controlers
c, d) the use of hysteresis current controlers
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4. DC LINK VOLTAGE CONTROL SYSTEM
PERFORMANCES
To test the performances of the voltage control
system, the block diagram in the Fig. 2 has been
implemented under Matlab - Simulink environment (fig
3). Thus, the control system response has been studied
for the capacitor pre-charging sequence, and also during
the compensation process. In the first sequence of
operation, a sinusoidal charging current is applied at the
input of the current control loop, signal obtained by
multiplying the voltage regulator output with a threephase unitary amplitude current obtained at the output
of a phase-locked loop.
The capacitor voltage evolution is illustrated in
figure 5. It appears that the DC link voltage has a low
deviation from the prescribed voltage, achieving about
0.3% overshoot. It also notes that prescribed voltage
ramp does not start from zero, but from the maximum
rectified grid voltage.
800
700
600
*
uc
500
The capacitor voltage during the compensating
process of a nonlinear load current of 10 A shows a
peak to peak ripple also very low rate of about 0.4% for
a nominal voltage of 700 V(as seen in figure 6).
5. THE IMPLEMENTATION OF THE
CHARGING ALGORITHM FOR THE
DSPACE PLATFORM.EXPERIMENTAL
RESULTS
The correct implementation of the voltage control
loop was verified both by simulation and experimental
testing. The experimental system consists of:
- the hardware component, that includes the static
inverter, and the amplification and protection auxiliary
circuits;
- the configurable interface filter (one first order or
second order filter can be obtained);
- the software control component, implemented on a
dSpace DS1103 acquisition board;
- the nonlinear load (a three-phase AC static converter
which absorbs a current similar to that absorbed by
PWM inverter and induction motor electric drives).
For the implementation of the control algorithm on
the DS1103 board, the Simulink model illustrated in
figure 7 was built and compiled.
uc
400
0.04
0.24
0.44
t [s]
Fig. 5. The DC link voltage during the charging sequence
This is because the closed-loop control system
cannot obtain a voltage value across the capacitor less
than the maximum grid rectified voltage. For this
reason, the capacitor is beeing charged from zero to
about 560 V, via the anti-parallel diodes of the active
filter voltage inverter.
701
700
699
*
uC
698
uC
697
0.45
0.46
0.47
0.48
0.49
t [s]
Fig. 6. Detail of the DC link voltage during compensation
Fig. 7. The active filter control Simulink model for the DS1103
To maintain the equivalence between the Simulink
model of the virtual active filter system (fig 3) and the
experimental equipment which reflects, the active filter
control block was built in a compact and universal
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Buletinul AGIR nr. 4/2011 ● octombrie-decembrie
125
form, which allows the use of the same block for both
experimental and simulation testing.
The capacitor voltage during the active charging
process is illustrated in figure 8.
750
700
650
600
*
uC
550
uC
500
9
10
11
12
13
t [s]
Fig. 8. The real DC link voltage during the charging sequence
As mentioned, the capacitor is passively charged to
the power grid peak rectified voltage, then (manually
or automaticaly) the active charging can be triggered.
7. DC LINK VOLTAGE INFLUENCE OVER
EFFICIENCY. EXPERIMENTAL RESULTS
To analyze the experimental dependence of the
filtration efficiency on the DC link voltage value, two
cases of 660 V and 700 V have been considered. For
the control algorithm of the active filter, hysteresis
current regulators had been chosen. For the
compensating current calculation, the p-q theory was
adopted, valid under sinusoidal grid voltage.
In the first case, the resulted compensated current
THD was 11.2%, giving a 8.04 filtration efficiency, for
a nonlinear load current THD of 90.1%.
For the DC link voltage of 700 V, the compensated
current THD diminished to 10.94%, leading to a
filtration efficiency of 8.26. Because of the grid current
THD reduction, the grid voltage THD also diminished
from 2.32% to 2.15%.
40
715
ir
710
is
20
u r /8
705
700
0
695
*
uC
690
-20
uC
685
13
13.02 13.04 13.06 13.08 t [s]
-40
0
0.02
Fig. 9. Detail of the steady state real DC link voltage
Although the voltage control loop is the same as the
simulation study, because of the long charging time, the
resulted overshoot is nonexistent. Also, the steady state
real DC link voltage without compensation, has a ripple
about 1% (fig 9), and during the compensation process
of a 10 A nonlinear load current, the DC link voltage
ripple reaches 2.82% (fig 10).
0.04
t [s]
a)
40
ir
is
20
u r /8
0
-20
715
710
-40
0
705
0.02
0.04
t [s]
b)
700
695
*
uC
690
Fig.11. The power grid voltage and current before and after the
active filtering for a DC link voltage of: a) 660 V, b) 700 V
uC
685
0
0.02
0.04
t [s]
Fig. 10. Detail of the DC link voltage when the compesation is on
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11. CONCLUSION
The voltage regulation system of the active filter
was tuned by means of the modulus optimum criterion.
Also, the compensating capacity of the filter reactive
DC link was determined.
The simulations performed using the MatlabSimulink environment, and the experimental testing,
respectively, illustrates a very good behavior of the
control system regarding reference tracking.
The results also showed that there is an optimum
value of the DC link voltage, depending on the nonactive compensated power, which minimizes the
compensated current total current harmonic distorsion.
REFERENCE
[1]
[2]
[3]
[4]
[5]
AKAGI H,
WATANABE EH, AREDES
M,„
Instantaneous Power Theory and Applications to Power
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is key. Harmonic detection methods for active power filter
applications, IEEE Industry Applications Magazine, July /Aug.
2007, pag. 22-33
BITOLEANU A, POPESCU M., Filtre Active de Putere, Ed.
Universitaria, Craiova, 2010, ISBN 978–606–14–0039-3.
BITOLEANU A, POPESCU Mh, Convertoare statice şi
Structuri de comandă Performante, Ed Sitech, Craiova, 2000,
ISBN 973-657-016-9.
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[6] BITOLEANU A, POPESCU Mh, MARIN D,
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[7] BITOLEANU A, POPESCU Mh, SURU V, p-q Power
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Lagow, Poland, ISBN 978-1-4244-7894-1.
[8] Control Desk Experiment Guide for release 5.2, dSpace
Gmbh, 2006
[9] DS1103 Hardware Instalation and Configuration for release
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[10] KEVIN J TORY, RICH POPE, Eliminating harmonics from
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[11] POPESCU Mh, BITOLEANU A, DOBRICEANU M,
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[12] POPESCU Mh, BITOLEANU A, DOBRICEANU M, SURU
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[13] POPESCU Mh, BITOLEANU A, MARIN D, On the DCCapacitance and Control of Voltage Across the Compensating
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