Elektrotehniški vestnik 76(5): 275-280, 2009 Electrotechnical Review: Ljubljana, Slovenija
Active Power Filter with a Reduced Number of Current Sensors
David Nedeljkovic, Mitja Nemec, Klemen Drobnic, Vanja Ambrozic
University of Ljubljana, Faculty of Electrical Engineering, Trzaska cesta 25, SI-1000 Ljubljana, Slovenia E-mail: davidn@fe.uni-lj.si
Abstract. In this paper, a modification of a parallel active power filter (APF) control is presented. Its purpose is to decrease the cost of the hardware by minimizing the number of current sensors, normally present in conventional topologies. The approach employs the direct current control (DCC), a method for predictive control of currents in polyphase systems, developed by the authors. Since in traditional filter topologies, currents for compensation of distorted load currents are produced by an inverter-like circuit, DCC, as in similar approaches, is used for filter current generation. In this particular case, a variant of DCC with a modulated voltage during a sampling interval is used. However, following a relatively simple algorithm, only a grid current can be used in DCC, without any need for filter and load current measurement, thus eliminating the necessity of installing corresponding current sensors. In addition, robustness of the approach was proved by examining the effect of alteration of the filter model parameters. Simulation results show validity of the proposed method.
Keywords: active power filter, direct current control, current sensors, modulation
Aktivni močnostni filter z zmanjšanim številom tokovnih merilnikov
Povzetek. V članku je predstavljena modifikacija vodenja paralelnega aktivnega močnostnega filtra (APF), ki zniža stroške aparaturne opreme zaradi manjšega števila potrebnih tokovnih sond. Pristop temelji na uporabi metode za neposredno regulacijo toka (angl. direct current control -DCC), namenjene za prediktivno regulacijo tokov v večfaznih sistemih. Tokove za kompenzacijo popačenih bremenskih tokov generira aktivni filter, ki ima razsmerniško topologijo, zato je za regulacijo filtrskega toka možno uporabiti metodo DCC, ki se je že izkazala pri drugih aplikacijah s podobno topologijo. V predstavljenem primeru je uporabljena različica metode DCC, kjer se napetost modulira znotraj intervala vzorčenja. V predlaganem pristopu lahko za DCC zaradi njenega prediktivnega značaja in poznavanja parametrov filtrske veje uporabimo samo omrežne tokove. Zato merjenje filtrskih tokov in pripadajoče tokovne sonde niso več potrebni. V nadaljevanju prispevka je opravljena še analiza robustnosti metode glede na vpliv spremembe parametrov filtrskega modela. Simulacijski rezultati potrjujejo veljavnost predlaganega pristopa.
Ključne besede: aktivni močnostni filter, neposredna regulacija toka, tokovni merilniki, modulacija
1 Introduction
Strict norms imposed on quality of the electrical power supplied by the grid are challenged by an increasing usage of switching power devices in industrial applications and home appliances. As a consequence, different harmonics are present in the current drawn from the grid both due to the converter switching actions and/or the non-linear character of the load. An
Received 12 August 2009 Accepted 16 September 2009
additional problem is caused by unbalanced loads in the three-phase systems. A very effective way of compensating for these distortions is by using shunt (parallel) active power filters (APF). They are basically power electronics, inverter-like devices that act as high-dynamic current sources. These filter currents, added to the load currents, cause the line supply currents to be sinusoidal and in phase with the supply voltages [1-6]. It is needless to say that control of APFs requires fast online tracking of actual currents and fast adaptation according to the implemented algorithm.
In this paper, a method for controlling the three-phase filter currents, based on the previous work by the authors [7-11], is presented. Its main advantage is in reduction of the number of current sensors present in traditional APF topologies, thus decreasing the total cost of the hardware. Therefore, instead of mounting six current sensors, only three are necessary. Still, the current generation algorithm remains fast, thus providing excellent filter current dynamics.
2 Active power filter
Figure 1 shows a typical topology of a parallel APF [3]. Independently generated currents in an APF are added to each of the three line phases. Their purpose is to compensate for load harmonics, fundamental reactive power and possible phase unbalances (e.g. loss of one phase, etc.). Unlike the classical scalar approaches, the vector approach deals with vector sums of currents in all phases - space vectors. Therefore, the current vector equation for the filter space vector is
iF = is - i,	(1)
t,..t6
Power Stage
^(1,2,3) (t) =
S (1,2,3)
(t)
VS1 (1,2,3) (t)
(2)
To provide a sinusoidal waveform of supply line current is, it is reasonable to take into account the supply line voltage fundamental v^, since the line voltage is usually heavily distorted. It has been shown, that the line voltage fundamental can be calculated online without any special synchronization to the grid [3, 8].
Since there should be no active power in the filter branch (except for covering losses) and the supply line currents should be balanced, symmetrical substitutive conductance is calculated [7] as:
G(t) = G1(i) = Ü2(t) = G3(i) =
t
j (vS(1)il(1) + VS(2)il(2) + VS(3)il(3) ) dt
= t-T*_
t '
j (v2(1) + VS(2) + V5(3)) dt
Figure 1. Topology of a three-phase, three-wire parallel active power filter.
Filter currents must instantly adapt themselves to the anomalies on the load side so as to produce the grid phase currents iS to be sinusoidal and in phase with the grid voltage, containing only the fundamental harmonic. Consequently, from the grid side, the load behaves as being a pure resistive one.
In the classical approach, in order to fully perform the task of compensating harmonics and phase unbalances, line voltages as well as filter and load currents have to be measured in each phase with an additional measurement of the filter capacitor voltage. Filter currents measurement is also necessary for their effective control through the filter three-phase bridge voltage source inverter (VSI). The capacitor acts like a pseudo-constant voltage DC source that is chopped by the transistors, thus impressing the desired current.
Of course, the amount of the filter compensation current is dictated by the desired line current, determination of which forms a very important part of the APF algorithm. According to the above mentioned demands, the load-filter circuitry should behave like a resistive load with conductance
Sinusoidal line current reference iS is now obtained easily:
4l,2,3)W = %(1,2,3)(t) • G(t) or i S = V S1 ■ G . (4)
In [7], filter current reference iF was further calculated, because the actual filter current iF was measured and controlled directly. Moreover, as it is evident from (3), the load current (i^) measurement was required. The advanced method, proposed in this paper, should rely only upon the measurement of supply line current iS. Assuming fast operating current control, one can expect the actual line currents to be sinusoidal. Therefore, the substitutive conductance becomes
G(t) =
i (vS(1)iS(1) + VS(2)iS(2) + VS(3)iS(3) ) dt
t-T'	(5)
j (v2(1) + V5(2) + ^(3)) dt
However, the supply line current amplitude must be additionally controlled to provide filter capacitor voltage VC to be constant. Thus, the superior control of the active power flow from the supply grid is obtained. It can be carried out simply by the filter capacitor voltage error (VC - Vc) slightly increasing the substitutive conductance G. Certainly, the negative value of the error (when the capacitor voltage VC is too high) decreases the value of G and consequently reduces the active power flow from the supply grid. Some filter control methods rely solely on this approach [2], thus further reducing the number of sensors needed and providing a moderate dynamic response.
After comparing (5) and (3), we can now conclude that the load current measurement becomes obsolete (dashed lines in Figure 1). Instead, line currents have to be measured (dashed-dotted lines), without any gain in cost reduction. In order to achieve this goal, the task of the presented approach will be to eliminate the filter currents measurement needed for current control (solid lines in Figure 1).
As already explained, the main control variables of a parallel APF are the filter currents or their resulting space vector. In the presented approach, these currents are controlled using direct current control (DCC).

s0(n + 1)
v4 7V7'
i(n +1) = i(n)| 1 - R At) + v(n) -A
(6)
io (n +1
Note that currents and voltages are represented by space vectors, which are spatial sums of temporal phase values. Voltage vector v depends on the type of the
supply. In modern three-phase systems, a transistor full bridge is usually used, which gives a possibility of generating six distinct active voltage space vectors [8]. If the load has a passive character, this is the only voltage applied. However, in a variety of applications, additional voltage pseudo sources can be present, e.g. back EMF in electrical drives. The goal of DCC is to minimize the error between the reference current (i.e. supply line current reference in (4)) and the actual current (6) at the end of the sampling interval.
£o(n +1) = i* (n +1) - i (n +1)
(7)
Figure 2. Principle of current generation using DCC II.
3 Direct current control
Direct current control is a predictive method developed for the fastest possible current control. The method was also altered for stator flux control that is more suitable for application in electrical drives, where back EMF occurs [10].
DCC is ideal for passive R-L three-phase loads where only the inverter voltage is impressed. However, it works equally well if additional voltages (e.g. back EMF, additional sources) are present, providing their easy detection/measurement. Besides the high dynamics, minimization of the current ripple is of a great concern. However, this goal is achieved on account of a higher switching frequency of inverter transistors leading to higher switching losses. For this purpose, two variants have been proposed; one suitable for loads with lower dynamics (higher time constants) yielding low switching losses, and the other with a reduced current ripple but with higher switching frequency (suitable for high dynamic loads). In the presented paper, only the second variant (DCC II) will be examined.
Due to the discrete nature of the microprocessor used for control, the basic current equation for a three-phase R-L load, when fed by voltage v, has to be written in its discretized form. Thus, the current at the end of sampling interval At can be generally written as [8]
Figure 2 shows relations between space vectors. Since the current vector at instant (n+1) hardly matches the desired (reference) current in direction and size when one of the six active voltage vectors is applied, DCC II offers a possibility of minimizing the initial current error e0. From (6), this task is performed by first selecting the voltage vector pointing into direction of the current error (v3 in Figure 2) and then calculating the optimal time ton, in which the active vector should be applied, yielding the final current error ev. The approach was explained in detail in [8-11].
4 APF with a reduced number of current sensors
According to Figure 1, equation (6) applied to the active power filter can be re-formulated as
R,
L
At
iF(n +1) = iF(n)| 1 --FAt I + vS(n) • —+ vF(n)
(8)
L
L
i f o(n +1)
Here, the impressed voltage (v in (6)) consists of two parts: the first part is sinusoidal grid voltage vS applied throughout entire sampling interval At, whereas the second part is filter (inverter) voltage vF, through which the filter current is to be controlled. The latter is applied throughout pre-calculated interval ton. Although changing, the grid voltage is measurable and predictable. Therefore, it will be aggregated to the first part of (8) under the term denoted as iF0(n+1).
Now, the first simplification can be made. The right term in brackets containing an R-L time constant represents a natural decrease of the filter current. Due to the short microprocessor sampling interval At, low filter resistance RF and relatively high filter inductance LF, it can be neglected (in experimental setup: At = 78.125 |ms, Rf = 90 mW and LF = 2.6 mH yield 0.0027-iF(n)).
An additional simplification, crucial for the elimination of the filter current sensors, is introduced by presuming that the change of load current il during the sampling interval is negligible due to the usually much higher load time constant vs. short sampling interval. Therefore, from (1):
a
v v
5 ' 6
Vsi(n)
£o(n+1)
, , At vs (n) —
v\
Figure 3. DCC approach with a modulated active voltage vector minimizes the predicted current error e^n+1).
if (n) = is (n) - il (n)
if (n +1) » is (n +1) - il (n)
(9)
After inserting (9) into (8), an important conclusion can be drawn: the value of is0(n+1) can be predictably controlled without measuring the filter current:
is(n +1) = is(n) + vs(n) + vF(n) • ^f-
(10)
(n +1)
The first part of (10) - i^, like in (8), is a term that can be established at the beginning of the sampling interval through the measurement of grid currents and voltages. If there is no filter voltage impressed (ton = 0), this will be the final supply line current at the end of the interval, producing an error
£ o (n +1) = i S (n +1) - i so (n +1)
(11)
Among six possible filter (inverter) active voltage space vectors to form vF, the one pointing nearest to the direction of the initial pre-calculated error e0(n+1) should be chosen. As described in [7, 11], after adapting the nomenclature to its application in APF, voltage application interval ton is calculated as
t„„ =-
9Ln
4Vr
eoa (n +1) • + eob (n +1) ~
V
V
(13)
c y
with respect to the reference current calculated from (4), as shown in Figure 3.
It is now obvious that the supply line currents can be controlled directly by the filter voltage vectors, necessitating no filter current measurement. Therefore, if an active filter voltage vector is impressed during pre-calculated interval ton, the final predicted supply line current error becomes
Vectors vp and e0 are decomposed into their components in an a-b stationary reference frame. Lp and VC are the filter inductance and voltage across the capacitor, respectively (Figure 1).
5 Results
The proposed filter control with the advanced DCC method was simulated with the filter parameters Cp = 1000 pF, Lp = 2.6 mH and Rp = 90 mW. The supply grid line-to-neutral voltage VS was 230 V (RMS). Filter capacitor voltage VC was controlled at 720 V. As a nonlinear load a single-phase thyristor rectifier was used connected between two phase terminals, thus simulating an extremely unbalanced load. Figure 4 shows the supply line voltages and load currents, where unbalance is obvious since there is no current in phase 3 of the nonlinear load. Harmonic distortion of load currents is significant (THD = 21.4%).
In Figure 5, the filter branch currents and compensated supply line currents are presented. Since there is no current in phase 3 of the load, the current in phase 3 of the filter branch takes a sinusoidal form and actually represents the supply line current in phase 3. As the compensated supply line currents are sinusoidal (harmonic distortion is reduced to THD = 2.6%) and synchronized with the corresponding supply line voltages, the fundamental reactive power is successfully compensated as well.
Figure 6 presents the trajectory of compensated supply line current iS for steady-state conditions within one grid cycle (20 ms). It is clearly shown how individual active/zero filter voltage vectors vp are activated. The circular shape of the trajectory meets the requirements.
£v(n +1) = 14 +1)-iso(n+1)-VF(n) •
£o(n +1)	F
V
a
Vc v
5	' 6
VS(3)
VS (2)
m <u m ra
o
>
<
m
vs (1)
'm
'm
'i(i)
'F(3)
'm
'm
~ 'S(3)
O
> 's(2)
C
O 'S(1)
3
O
0.05 0.06 0.07 0.0
Time (s)
Figure 4. Supply line voltages (vS(i), vS(2), vS(3)) and load currents (ij(i), i/(2), ij(3)) during the load transient (kv = 400 V/div, A, = 50 A/div).
6	Sensitivity to parameter variations
Although the initial values of the parameters are known, the main problem arises from their possible alteration during the filter operation. The filter inductance and resistance are the only parameters that can be altered while not being directly measured.
Inductance can change due to saturation and resistance due to temperature. Although these effects are not as drastic as those in electrical drives, it is still interesting to observe their possible impact on the presented method. Figure 7 shows the performance of the filter with its model parameters exceeding the actual ones by 20% (e.g. in saturation). As it can be seen when compared to Figure 6, the method still proves to be very robust, showing practically no difference.
7	Conclusion
In this paper, an approach to predictive current control in APF is presented. Unlike the standard topologies with load and filter currents measurement, the proposed one requires only measurement of line currents through corresponding sensors, thus reducing the hardware cost. A fairly precise calculation of conductance, needed for line reference current
Time (s)
Figure 5. Filter currents (iF(i), iF(2), iF(3)), compensated supply line currents (iS(i), iS(2), iS(3)) and filter capacitor voltage (VC) during the load transient (kv = 400 V/div, A, = 50 A/div).
determination, can also be provided through the line current measurement. Moreover, instead of directly controlling the filter currents, line currents can be indirectly controlled, providing a fast and accurate current control algorithm. For this purpose, the already verified method, called the direct current control, was applied. The issue of parameter variation during filter operation was also addressed, showing no significant
iSa (A)
Figure 6. Orthogonal components of compensated supply line currents (iSa, iSb) in steady-state during one grid cycle (20 ms).
iSa (A)
Figure 7. Orthogonal components of compensated supply line currents (iSa, iSb) in steady-state during one grid cycle (20 ms) for LFmodel = 1.2 L/Ctual.
impact on the performance of the method. Our future work in this field will be focused on confirming the obtained results on a specially adapted experimental setup.
8 References
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[3]	D. Nedeljkovic, J. Nastran, D. Vončina and V. Ambrožič. Synchronization of Active Power Filter Current Reference to the Network, IEEE Trans. on Industrial Electronics, vol. 46 (2), pp. 333-339, April 1999.
[4]	B.-R. Lin and C.-H. Huang. Implementation of a Three-Phase Capacitor-Clamped Active Power Filter Under Unbalanced Condition, IEEE Trans. on Industrial Electronics, vol. 53 (5), pp. 1621-1630, Oct. 2006.
[5]	J. Rodriguez, J. Pontt, C.A. Silva; P. Correa, P. Lezana, P. Cortes and U. Ammann. Predictive Current Control of a Voltage Source Inverter, IEEE Trans. on Industrial Electronics, vol. 54 (1), pp. 495-503, Feb. 2007.
[6]	R. Grino, R. Cardoner, R. Costa-Castello and E. Fossas, Digital Repetitive Control of a Three-Phase Four-Wire Shunt Active Filter, IEEE Trans. on Industrial Electronics, vol. 54 (3), pp. 1495-1503, June 2007.
[7]	D. Nedeljkovic, M. Nemec, V. Ambrožič. Application of Direct Current Control in a Three-Phase Parallel Active Power Filter. Elektrotehniški vestnik = Electrotechnical Review, vol. 76, no. 3, pp. 85-91, 2009.
[8]	V. Ambrožič, R. Fišer, D. Nedeljkovic. Direct Current Control - a New Current Regulation Principle. IEEE Trans. on Power Electronics, vol. 18, no. 1, pp. 495-503, Jan. 2003.
[9]	V. Ambrožič, D. Nedeljkovic. Primerjalna analiza metode neposredne regulacije toka = Comparative Analysis of the Direct Current Control Method. Elektrotehniški vestnik = Electrotechnical Review, vol. 70, no. 4, pp. 172-177, 2003.
[10]	K. Drobnič, M. Nemec, D. Nedeljkovic, V. Ambrožič. Predictive Direct Control Applied to AC Drives and Active Power Filter. Trans. on Industrial Electronics, vol. 56, no. 6, pp. 1884-1893, Jun. 2009.
[11]	D. Nedeljkovic, M. Nemec, K. Drobnič, V. Ambrožič. Direct Current Control of Active Power Filter without Filter Current Measurement. 9th Speedam 2008, Ischia (Italy), pp. 72-76, June 11th-13th, 2008.
David Nedeljkovic received his B.S., M.S., and Ph.D. degrees from the Faculty of Electrical Engineering, University of Ljubljana, Slovenia, in 1991, 1996, and 1998, respectively. He joined the same faculty in 1993, where he is now an Assistant Professor and Vice-Dean for financial affairs. In 2001 he was a Guest-scientist with the Institut für Regelungstechnik, Technische Universität Braunschweig, Germany. His main research interest concerns active power filters, pulse magnetizing devices, solid-state power converters, and control of electrical drives.
Mitja Nemec received his M.S. and Ph.D. degrees in electrical engineering from the Faculty of Electrical Engineering, University of Ljubljana, Slovenia, in 2003 and 2008, respectively. He is currently working as an assistant at the same institution. His scientific and pedagogical work is oriented towards power electronics and motion control.
Klemen Drobnic received his B.S. degree in electrical engineering from the Faculty of Electrical Engineering, University of Ljubljana, Slovenia, in 2007. He is currently working towards his Ph.D. degree at the same faculty. His research interests include motor control, predictive control and power electronics.
Vanja Ambrozic received his B.S., M.S. and Ph.D. degrees from the Faculty of Electrical Engineering, University of Ljubljana, Slovenia, in 1986, 1990 and 1993, respectively. In 1986 he joined the Laboratory of Control Engineering at the same faculty, first as a junior researcher, then as an assistant and assistant professor. He is currently an associate professor and the head of the Department of Mechatronics. His main research interests include control of electrical drives and power electronics.