A current control scheme based on multiple ...

A Current Control Scheme Based on Multiple Synchronous

Reference Frames for Parallel Hybrid Active Filter Sukin Park, Soo-Bin Han, Bong-Man Jung, Soo-Hyun Choi, Hak-Geun Jecag Electric Energy Conservation Team,Korea Institute of Energy Research, 71-2, Jang-Dong, Yusong-Ku, Taejon, 305-343, Korea. Phone: +82-42-860-3721 Fax: +8242-860-3 102 E-mail: [email protected]

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Abstract A control algorithm is developed with the objective of eliminating the harmonics and reactive power for the parallel hybrid active filters. In this problem set, the load current is assumed to have the 5th and 7th harmonics along with the fundamental component. We utilize the three synchronous reference fiames(SRF) and the low pass filters to measure the finchmental, Sth, 7th components separately In the SRF rotating at the fundamentaljkquencj the q-axis current is contmlled to regulate the reactive power and d-axis current is contmlled to keep constant the DC link voltage of the convertex In the SRF's rotating at thejkquencies of 5th and 7th harmonics, the $Iter currents are controlled to cancel out the 5th and 7th harmonics of the load In each contmller; the cross-coupling current control scheme is utilized for decoupling d-q current dynamics interaction Key words: Parallel hybrid active filter, harmonic isolation, reactive power compensation, cross coupling control.

1. Introduction Nonlinear loads, such as diode and thyristor rectifiers and uninterruptible power supplies are proliferated in various areas, thus without proper compensation, the quality of power in transmissiddistribution systems can be deteriorated. Passive filters are broadly used to reduce the harmonics for their low cost. However, they have some drawbacks: Source impedance strongly affects the compensation characteristics of passive filters. Passive filters are susceptible to undesirable series and parallel resonance with source and loads. Active filters were developed for its flexibility and adaptability to the varying situation. But the use of active filter is limited, due to the limits in semi-conductor switch rating and its high construction cost.

Combining the advantages of passive filter and active filter, the hybrid active filter topologies have been developed which enable the use of significantly small rated active filters, compared to pure parallel or series active filter solutions. In other words, they are cost effective while offering line voltage regulation, reactive power compensation, and hannonic isolation between supply and load. Another advantage is the easy protection, since possible failwes in the active filter do not affect much the load[l]. The parallel hybrid active filter in which the active filter is connected to the shunt passive filters through a transformer. In the parallel hybrid active filter, the active filter provides a low impedance for harmonics so that all the harmonics flow into the passive unit[l]. Divan et al. [2,3] used the multiple synckuonous reference fiames (SRF) and low pass filters in extracting the desired harmonic signals and made varying positive or negative inductances with the aim of providing the tuned harmonic sinks. Interesting fact in their work is that the tuning action at each harmonic component is totally independent fiom the other, although one inverter is utilized. The impedance variation techniques are basically developed based on the steady state model. Therefore, their dynamic properties are .very limited. Furthermore, the perspective of compensating the reactive power has not been considered seriously with the parallel hybrid active filter except the work of Uceda[l]. Uceda utilized a phase and magnitude control, method to compensate the reactive power and harmonics in the abc fiame. But, the phase and magnitude detecting circuit is dependent on the system environments. In this paper, we propose a control scheme for parallel hybrid active filter with the purpose of isolating the 5th and 7th load harmonics from source side and correcting the power factor(PF). The treatment of this work is similar to the previous work of Divan[2] in that the 218 -

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converter filter capacitor C, is so small that it is ignored in the analysis, The equivalent circuit per phase is shown in Fig. I@), fiom which we obtain

Supply Voltage (60 Hz) R,

_._

-'lA

Es

= RSiS

dis

+Ls - + R F i f dt

dif

+Lc -+Vc dt

+ V F , (1) (2)

is = i , + i f ,

w

IC!

(d)

Fig 1. (a) A parallel hybrid active filter, (b) the qui-, valent circuit, (c) the equivalent circuit for the fimdmental fiequency, (d) the equivalent circuit for the harmonics multiple SRF's and low pass filters are used in extracting the harmonic signals. But the differences are that the closed loop current controllers are constructed in the canceling out the harmonics, and that another closed loop current controller is added for the unity power factor in the SRF rotating at the fundamental fiequency. Hence, the dynamic response is fast and superior is performance even in the varying environments. In each controller, we utilize the QOSS coupling controller in decoupling d-q axis dynamics. We demonstrate its performance through computer simulation.

2. The Structure of Hybrid Active

where Esb v c = [ v ~VCb VcclTdenote the source voltage and the converter output voltage, respectively. Further, we denote by RF the equivalent series resistor of the L-C filter, and by VF the voltage $,,i,the source over the L-C filter. We also denote by is current, the filter current and the load current respectively. We assume that the source voltage E, do not contain any harmonic voltage other than the fundamental component. The load current represented as a current sink, can be decomposed into firndamental and harmonic components such that iL= iJL + PL, where iIL is the fundamental component and is the sum of harmonic components. In many practical converters such as diode and thyristor converters, the 5th and 7th order components are the major harmonics to be compensated. We assume that the load current iL contains only 5th and 7th order harmonics along with the fimdamental components, i.e., PL = i', + i7L,where isL,i'L are the 5th and 7th order harmonit currents, respectively. In the case of diode and thyristor converters, the 5th order harmonic current constitutes a negative sequence, while the fundamental and 7th order components form a positive sequence. We also assume that the converter output voltage is controlled to be such that Vc= Vc + V",, where V c and P, are the fundamental and harmonic components. Further, the spectral components of P", is the Same as those of i.e., V", = Pc + VC,where Pc, VCare the 5th and 7th harmonic voltages, respectively. Then, the filter currents are represented as iF i$ + Pp where i$ i", are the hdamental and harmonic components. Therefore, it follows fiom (1) that

eL,

Es = Rs(ij$ +i:)+Ls -(& d +i:)+RF(i; +$) dt (3) +L, -(i' d +i')+@ +v: +v; + ~ , h 7

Filter and its Model The proposed hybrid active filter is depicted in Fig l(a), in which the 5th and 7th passive L-C filters are serially connected with the converter output through the transformer. The PWM switching harmonics of the converter output is filtered by L, and C, However, the

dt f f Using the spectral decomposition we obtain fi-om (3) that

Es = Rsij$ +LA

dik dt

RFi> +Lc

di>

: V: + V i , (4)

dt

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Fig 2. The overall control block diagram using three SRF'S dish

O=Rsis +Ls-+R dt

h

di; dt

h +YF,(5) h

i +Lc-+Yc

F f

where ilS= ilL + i'Jsfs=f L + fpand h=5,7. Therefore, we obtain two equivalent circuits for the fundamental fiequency and the harmonics as shown in Fig. l(c), (d). Note at the fundamental Srequency that the filter impedance is nonzero, and further that capacitive impedance is dominant over the inductive impedance. Hence, only capacitor appears in the equivalent circuit for the fundamental fiequency.

3. Independent Control Using

Multiple SRF's In this section, we describe the proposed control scheme that controls each spectral component independently utilizing different SRF's. In the complex plane, iLcan be described as FW= fm +j f&= JlLda+"+ PLe +17Lt?7a+87, where I'D f L , PL>O and U is the electric angular fiequency. Note that the negative s i 5 of 5th order component reflects that the 5th harmonic constitutes the negative sequence. We utilizes three SRF's that rotate at the fundamental, 5th, and 7th order fiequencies. The currents in the SRF's are obtained by multiplying fw by ka,t@, e-17a,i.e.,

S iWe -j7d = Iie-j6d+e, I~e-j12mt+65 17e6, L +

+

*

(8)

We will call, in the rest of the paper, the SRF rotating

at fundamental ffequencyfindamental SRF for short. In the same way, we will use the terms, 5th order SRF and 7th order SRF. Note in the fiundamental SRI? that only the fundamental component appears as DC,while the 5th, 7th harmonics appear as 6th order components. Similarly, in the synchronous reference jiame tuned to dSa, the 5th and 7th harmonics appear as DC, respectively. Hence applying low pass filter to the currents in each SRF, one can obtain fL,PL,17Lseparately based on the assumption that e,, e,, O7 are known. Fig. 2 shows the block diagram of the proposed current control scheme. In which the same measurement procedure and notational convention are applied to the filter current i/. The three components are controlled independently with different objectives. The main function of each controllers is summarized in the following: In the fundamental SRF, we choose d-axis aligned with the source voltage vector E,. The q-axis current is controlled to compensate the reactive power, and the da x i s current is controlled to keep constant converter DC link voltage. In the 5th order SRF, the 5th order harmonic current is generated by feedback so that it cancels out the 5th order load harmonic current Pw.Since the 5th order harmonics appear as DC in the 5th order SRF, the harmonic elimination problem turns out to be DC level adjustment, and it can be achieved by PI controllers in the 5th order SRF. In the 7th order SRF, the 7th order harmonic currents i7'@is generated by feedback so that it cancels out the 7th order load harmonic cwrrent i7=* The voltage commands coming out from the current controllers are transformed back into the stationary f i m e and summed. The s i m e d voltage is spthesized by a voltage source converter switching legs. Since the plant is linear, the superposition law holds, i.e., the fundamental component ofthe voltage input induces d-q axis currents of the hdamental Srequency for controlling DC link voltage and the power factor, while 5th, 7th order voltage components produce 5th, 7th currents for harmonic canicellation, respectively. Fact is that each of them does not interfere the others' control function. That is, the three controllers behave independently. In PWM converter, active filter and UPS, the coupling d i d are much larger than the ohmic drops voltages di,, Rib Ri, due to a large electrical fiequency w In such a case,the cross coupling omtroller may be a better choice for its good decoupling action and robustness. In the cross coupling controller, the d-axis voltage is used to control q-axis current, while the q-axis voltage is used to

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control d-axis current. The cross coupling controller is known to be more robust than the feedforward decoupling controller when there are parameter mismatches[4]. In this work we utilize the cross coupling controller for all three cases.

I

I

--_I

eLs&!+R$ UIlayprmrerf

i L 7

Gmtrdl0

3.1 DC Link Voltage and Power Factor Correction Control

Fig 3. The controi block diagram for the unity power factor and DC link voltage regulation in the fundamental SRF.

In the fundamental SRF, the &xis is chosen to be aligned with the source voltage vector E* Therefore, E,=Es and Esq=O. From Fig. l(c) and (4), we obtain the following voltage equations in the fundamental SRF dig LT -- - - R ile +d iIe -Rsi& +wLsi&, dt fd f9 +(E: -VGd -V;d)

for hndamental frequency w = 377. Since the capacitor voltages P F d , PFq in (9),(10).are assumed to be unknown, they are treated as DC disturbances, and compensated by the integral action of the PI controller. The fundamental components of the currents, being appeared as DC in the SRF, are extracted by a second-order low pass filter.

(9)

3.2 The 5th and 7th Harmonic Isolation where L,=Lc+L, RT=RF+RS, w is the fundamental an@lar fiqUenv, EdiS d-axis Source Voltage, YFd, Y F ~ are &axis voltages over the filter capacitor (C, 11 Cm), and Fa Tpcq are the converter terminal dq-axis voltages. In the fundamental SRF, the d-axis is chosen to be aligned with the source voltage vector E* Then, nullifying the source q-axis current iss implies maintaining the unity power factor. From the Kirchhoffs current law, this can be achieved by making il>= - iIew On the other hand, from the perspective of power the daxis filter current il> is effective for controlling the converter DC-link voltage. The controller aiming at the unity power factor and a constant DC link voltage is constructed such that V& = (pI)(-i& - i i ) ,

V& = ( P I ) ( ( P Z ) ( V ~ vdc

Controllers in the 5th and 7th SRF's For the Sth, 7th harmonics, the equivalent circuit is given as Fig. l(d). In the 5th order SRF, only the 5th order harmonic current and voltage appear in the low fiequency range. In the 5th order SRF, we obtain from ( 5 ) that

(11)

-i g ,

(12)

where @I) denotes a proportional-integral controller. Fig. 3 shows the detailed control block diagram for the control in the fundamental SRF.One can notify the cross coupling control fiom the fact that the q-axis controller output voltage is applied to the input of d-axis subsystem, and that the d-axis controller output voltage is applied to the input of q-axis subsystem. The cross coupling control is feasible, since the coupling gain d ,is relatively large -221

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1:5e

I

where L,=LT + LFS. It should be noted that k5peFd, ksvs',, imply the detuned voltage, i.e., the voltage which is caused by the filter mismatch fiom the 5th ordler resonance condition. In other words, if the passive filttx is tuned exactly to the 5th order harmonics, then ks = 0, thus no voltage drops over the passive filter. The control objective is to isolate the harmonic current fiom the source, and it is achieved by making F'= -PM is"f i -- -P4 The cross coupling control scheme is also used here such that Pa=(Pr>(-i",-P,q), Pcq=(Pl)(pLb p@).There is more reascm to use it since the coupling gain j d ~ = 1 8 8 4 &is five times larger than the case of the fundamental fiequency. Similarly, we obtain for the 7th harmonic component that

I

I

m Fig 4. The harmonic current controllersusing the cross coupling algorithm. (a) 5th order SRF(negative sequence), (b) 7th order SRF@ositive sequence)

whFe pH pfi are the 5th order harmonic filter currents. LFS, CFs are the equivalent inductance and capacitance of the filter for 5th order harmonics. VFdand VFqare the d-q axis voltages over the 5thpassive filter, while VFd and VFq are the d-q axis voltages over the filter capacitor. Using (17), (18), we obtain the following equation fiom (15), (16).

where k ~ = l - ( j w ) 2 L ~ s c ~ j . In the 5th order SRF, the FeF&and PFqvaries slowly since c F 5 is large. Regarding PFd,PFqas constants, We Can approximate Such that dVS',, /dt = d P F d /dt 0. Then, substituting (19), (20) into (13), (14), we obtain that di$ L~~ -= -R T i 5fde dt

- 5mL~i;- - 5 m L s i z

-Vse - k V5e Cd 5 Fcd

- Rsi$ 421)

where k7=1-(7w)2L&m and L,=L, + LP Comparing (21), (22) with (23), (24), one notice there is a sign change due to sequence difference. Similarly to the 5th order harmonic control, we choose Y'"cd=(~r>(-i7eQ-i7>),Y'"G=(Pr)(-i7eLbi7>). Detailed block diagrams for the harmonic isolation control methods are shown in Fig. 4(a),(b). If the passive filters are mistuned, then the effects are reflected by the disturbance VOltageS, ksvs",, k5PFq, k 7 p ~ d k7V7",, , since they are Dc in thek SWS, the detuned effects can be compensated by the integral action of the PI controllers. If the 5th order passive filter is off-tuned, i.e., the actual resonant fiequency is below the 5th harmonic, then k5 has a. negative value. In the opposite case, it has a positive value. In general, the harmonic current is minor in magnitude compared with the fundamentall one. Thus, if we just want to isolate the load harmonics, then the size of converter(active filter) needs not to be big. But, if we want to consider seriously the power factor correction, then the size of converter shwld be big enough to accommodate the fundamental cuurent.

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TABLE 1. The parameters of the simulation

4. Simulation Results Performances of the proposed control scheme are demonstrated by computer simulation. Table 1 shows the parameters of the simulation. Note that the 5th and 7th passive filters are mistuned at 4.5 and 6.5, respectively. For the simulation, we assume that the load current is 45" lagging: i,

5 =100cos(cd-~)+20cos(5cd--~)

7 + lOc0~(7Ws- R)

4

.

4 Note that the 5th harmonic component has negative sequence whereas the 7th harmonic component has positive sequence. Fig. 5(a) shows the result when the converter is doing nothing but keeping DC link voltage constant. Fig. 5(b) shows the result after the proposed harmonic isolation control is applied. One can notice fiom the second plot of Fig. 5(b) that the source current is, became remarkably clean. It is because the load harmonics were canceled by the injected current fiom the converter, thus the harmonics did not appear in the source line side. Fig. 5(c) shows the result with the power factor correction. The lagghig load current ih was compensated by the leading filter current iM and as a result, the phase angle of the source current coincided with that of the source voltage. Fig. 5(d) shows simulation result when there were sudden step changes in load current: The load current was set to be down by 50% for 5 cycles, and up by 100%. From Fig. 5(d), one can note that the proposed controller did not show any unstable behavior during each transition.

w

Fig 5. Simulation results with 45" lagging load current: (a) with only DC link control, (b) with harmonic isolation, (c) with harmonic isolation and power factor control, (d) step changes in load current the coupling terms are large, the cross coupling algorithm is applied for its robustness to the errors in the parameters. Through simulation results, its pdormance was demonstrated. The result can be extended to isolate the higher order harmonics than 5th and 7th.

References F. B. Libano and J. Uceda, "Simplified Control Strategy for Hybrid Active Filters", in IEEE PESC Rec., 1997, pp. 1102-1108. S . Bhattacharya and D. M. Divan, "Hybrid Solutions for Improving Passive Filter Performance in High Power Applications", IEEE Trans. Indus. Appl., Vol. 33, NO. 3, pp. 1312-1321, 1997. D. M. Divan, "Non dissipative switched networks for high power applications", Electron Lett.,Vol. 20, NO.7, pp. 277-279, Mar. 1984. Q. Yu and T. Underland, "Investication of Dynamic Controllers for a Unified Power Flow Controller", in IEEE PESC Rw., pp. 1764-1769,1996. F. Z. Peng, H. Akagi and A. Nabae "A new approach to harmonic compensation in power systems-A combined system of shunt passive and series active filters", in IEEE ,Trans. Indus. Appl., Vol. 26, pp. 983-990, 1990.

5. Conclusions We developed a control scheme for parallel hybrid active filter that has power factor correction capability, as well as harmonic isolation. This control strategy can be distinguished from the previous works in that three independent current feedback control loops are employed in three different SRF's. Since it eliminates harmonic load currents by injecting the negative of them, the results look superior to the previous methods. Since - LLJ

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