hormonic pi ilc

IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS, VOL. 57, NO. 11, NOVEMBER 2010 3767

Feedback-Feedforward PI-Type Iterative LearningControl Strategy for Hybrid Active Power Filter

With Injection CircuitAn Luo, Senior Member, IEEE, Xianyong Xu, Lu Fang, Houhui Fang, Jingbing Wu, and Chuanping Wu

Abstract—In this paper, the configuration characteristic ofHybrid active power filter (APF) with injection circuit (IHAPF)is analyzed, as well as its current closed-loop control model isestablished. Because of the character of reperiod of current har-monics in steady-load power system, the iterative learning controlalgorithm based on the PI-type learning law is presented. Thesystemic robustness is enhanced by using a forgetting factor. Inorder to improve the dynamic performance of a control system,a feedforward based on the D-type learning law of referencedcurrent error by fuzzy reasoning is proposed. The system of theIHAPF with the proposed control strategy has been applied ina steel plant in Guangxi, China. Simulation and industrial ap-plication results show that the IHAPF with the proposed controlmethod is not only easy to calculate and implement but also veryeffective in improving the performance of the filter. Meanwhile,IHAPF shows great promise in reducing harmonics and improvingpower factor with a relatively low capacity of APF.

Index Terms—D-type learning law, forgetting factor, fuzzy ad-justor, hybrid active power filter (APF), PI-type iterative learningcontrol.

I. INTRODUCTION

B ECAUSE nonlinear loads are widely used in industrialapplications and transmission systems, harmonic interfer-

ence problem is becoming increasingly serious [1]–[4]. Con-ventionally, a passive power filter (PPF) composed of tunedL–C filters has been broadly used to suppress harmonic currentbecause of its low initial cost and high efficiency [5], [6]. How-ever, a passive filter has many disadvantages such as large size,parallel and series resonance with load, and utility impedances[7]. With a remarkable progress in speed and capacity of semi-conductor switching devices, an active power filter (APF) is apowerful tool for compensation not only of current harmonicsproduced by distorting loads but also of reactive power andunbalance of nonlinear and fluctuating loads. In some industrialapplications, to complement or enhance the performance of the

Manuscript received June 26, 2009; revised December 11, 2009; acceptedDecember 31, 2009. Date of publication February 8, 2010; date of current ver-sion October 13, 2010. This work was supported in part by the National NaturalScience Foundation of China (No. 60774043), by the National Basic ResearchProgram of China (973 Program) (No.2009CB219706), and by the ScientificResearch Plan of Hunan Provincial Science and Technology Department ofChina (2008SK1004, 2010CK3017 and 2010fj3033).

The authors are with the College of Electrical and Information Engineering,Hunan University, Changsha 410082, China (e-mail: [email protected]; [email protected]; [email protected]; [email protected]; [email protected]; [email protected]).

Digital Object Identifier 10.1109/TIE.2010.2040567

APF or PPF, different combinations of several types of filtersare proposed. Reference [8] shows a combination of a seriesactive filter and a shunt passive filter. In this type, the seriesactive filter overcomes the resonance between the grid and thepassive filter, but the cost of the active filter is higher comparedwith that of the passive filter; moreover, the electrical insulationof the active filter is more difficult. Akagi [9] proposed a newtopology of series active filter together with parallel active filter.The parallel active filter acted as a current source to compensatethe harmonic current of nonlinear load, while the series activefilter worked as a kind of “harmonic isolator” between thesource and the nonlinear load. It provided high impedance forthe harmonics and zero impedance for the fundamental wave,but the capacity of active filters is restricted to high-capacitysemiconductor components. Reference [10] proposed a newHAPF topology in which the APF is connected in series witha C-type PPF to reduce its capacity. To avoid the resonancebetween the grid and the thyristor switched filter (TSF) andto improve the harmonic compensation performance of TSF,Yang et al. [11] proposed a new system of an APF in serieswith the TSF. However, the APF in these two topologiesneeds to endure the fundamental wave voltage. Among theseconfigurations, the active filter in series with a parallel passivefilter, also known as the hybrid APF, is more widely discussedin literatures for its good performance in harmonic suppres-sion. Particularly, hybrid APF with injection circuit (IHAPF)becomes the hotspots of technological research, because it doesnot have to bear a fundamental wave voltage and is suitablefor application in high-voltage grid to reduce harmonics andimprove power factor [12]–[16].

Because harmonic current control is the key to the perfor-mance of APF, many control methods have been proposed.Reference [17] studied a one-cycle control (OCC) methodfor a three-phase APF. Its experimental results show that thesinusoidal output currents of the APF can be realized with theOCC method, whether the three-phase input voltages and/orthe nonlinear loads are balanced or unbalanced. However, itneeds an extra hardware circuit to realize the OCC method.Under unbalanced utility or load, reference [18] proposed thecontrol method of integrators for sinusoidal signals with re-duced computation complexity, by which the zero steady-stateerror of the reference harmonic current is realized. This controlmethod can suppress all order harmonics in theory, but it canonly suppress particular order harmonics in fact. Besides theaforementioned control methods, linear current control such

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3768 IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS, VOL. 57, NO. 11, NOVEMBER 2010

Fig. 1. Topology of a hybrid APF with injection circuit.

as ramp comparison control [19], sinusoidal internal modelcontrol [20], synchronous-frame PI control [21], [22], andnonlinear current control, such as hysteretic control [23] andpredictive control [24], are proposed. Ramp comparison controlusing a PI regulator is a conventional control method, and ithas a steady-state error if the reference current is a harmonicsignal [19]. The sinusoidal internal model control is presentedin [20]. It has good control performance and tracking precision,but its controller parameters are not to be tuned online, and itsrobustness should be improved. In [21], [22], a synchronous-frame PI controller is proposed to guarantee a zero steady-stateerror. If the harmonic current expected to be compensated ismultiple order, it needs several PI regulators. The controllerneeds more hardware or software for significant computation.Hysteretic control has the attraction of simplicity but leads to awidely varying switching frequency. This limitation has beenimproved with variable hysteresis band-switching strategies,but it requires a complex controller to achieve a satisfactoryperformance [23]. Predictive current control offers the bestpotential for precise current control; however, implementationof a practical system can be difficult and complex [24].

In this paper, a feedback-feedforward PI-type iterative learn-ing control strategy is proposed for a hybrid APF with injectionbranch. The topology and operation principle of IHAPF aredescribed in Section II. Section III establishes a current closed-loop control model of the IHAPF. To simplify the closed-loopcontrol model, the disturbance effects of the harmonic voltageof the power grid and the harmonic current of the load are notconsidered. Meanwhile, to improve the dynamic performanceand enhance the robustness of the whole control system, afeedforward based on the D-type learning law of referencedcurrent error by fuzzy reasoning is constructed. The simulationresults have been shown to verify the proposed controller inSection IV. Experimental and industrial application results havebeen shown to confirm the effectiveness of IHAPF with theproposed control strategy in Section V. Finally, the conclusionis given in Section VI.

Fig. 2. Single-phase equivalent circuit of the injection circuit.

II. MAIN CIRCUIT AND PRINCIPLE OF IHAPF

A. Topology of IHAPF Applied to High-Voltage Grid

The configuration of the hybrid APF used in this paper isshown in Fig. 1. This topology is composed of a group of PPFsand an APF based on voltage source inverter (VSI). The APFused in the IHAPF is a voltage source PWM inverter with alarge capacitor at the direct current side and an output filterfor eliminating the high-frequency ripples at the output side.The L1−C1 branch is tuned at the fundamental frequency andthen composes the injection branch with CF . The APF, shuntedto the fundamental resonance circuit, is directly connected inseries with a matching transformer, thus forming the IHAPF.Moreover, the dc-side voltage of IHAPF is supported by anuncontrolled rectifier. PPF sustains the main grid voltage andcompensates the constant reactive power.

The single-phase equivalent circuit of the injection circuit isshown in Fig. 2. U1 is the voltage endured by the fundamentalseries branch. ZR stands for the impedance of the fundamentalwave resonance circuit. The L1−C1 branch is tuned at thefundamental frequency, so it can get the following equations:

ω0L1 =1

ω0C1(1)

ZR = jω0L1 +1

jω0C1+ R1 = R1 (2)

LUO et al.: FEEDBACK-FEEDFORWARD PI-TYPE ITERATIVE LEARNING CONTROL STRATEGY FOR HYBRID APF 3769

where ω0 is the fundamental frequency and R1 is the internalresistance of L1.

η is the ratio of the harmonic current flowing into the gridand into the fundamental series resonance circuit. When theproposed IHAPF works, part of the compensating current willflow into the fundamental series resonance circuit. Therefore,the harmonic current injection ratio becomes an importantcharacteristic of the IHAPF.

If the injection circuit resonances at the nth order frequency,when the mth harmonic current is generated, ZR and theimpedance of the injection capacitance ZC should be

|ZC | =1

mωCF=

(n2 − 1)100πL1

m(3)

|ZR| = |ZL1 − ZC1| =(m2 − 1)100πL1

m(4)

∣∣∣∣ZC

ZR

∣∣∣∣ =(n2−1)100πL1

m(m2−1)100πL1

m

=n2 − 1m2 − 1

(5)

η =∣∣∣∣IAPFh

IRh

∣∣∣∣ =∣∣∣∣ZC

ZR

∣∣∣∣ =n2 − 1m2 − 1

(6)

where IAPFh and IRh, respectively, stand for the currents of theinjection branch and the fundamental wave resonance circuit.The ratio η will increase as the harmonic frequency increases;therefore, most harmonic currents produced by APF can beinjected into the grid.

When only the base frequency of 50 Hz is considered, fromFig. 2 and (1), we can further see that

U1 = IRhZR = IRhR1. (7)

As R1 is very small, U1 will be a low voltage. The systemvoltage is all applied across the injection capacitor CF anddoes not appear on the inverter output terminals, which greatlyreduces the voltage requirements of the VSI of IHAPF andreduces the rating of the semiconductor switching device.

B. Principle of Harmonic Elimination

In order to clarify the compensation principle, a single-phase equivalent circuit is shown in Fig. 2. The active part iscontrolled as a controllable voltage source UFh. The definitionsand vector reference directions of other variables are shown inFig. 3. IPFh, IAPFh, IL0h, and ILh, respectively, stand for thecurrent of the parallel passive branch, the injection branch, theoutput filter inductor branch, and the load harmonic current.I1h is equal to the sum of the output filter capacitance currentIc0h and the fundamental wave resonance circuit current IRh.ZSh, ZPF , ZC , ZR, ZC0, and ZL0 stand for the impedance ofthe power grid, the passive filter, the injection capacitance, thefundamental wave resonance circuit, the output filter capacitorbranch, and the output filter inductance branch, respectively.The transformation ratio of the coupling transformer is n.

In Fig. 3, assuming that Z1h represents the parallel im-pedance of n2ZC0 and ZR, according to the Kirchhoff voltage

Fig. 3. Single-phase equivalent circuit.

Fig. 4. Single equivalent circuit just considering ILh.

and current theorem, the following equations can be obtained:⎧⎪⎪⎪⎪⎪⎨⎪⎪⎪⎪⎪⎩

USh = ULh + ISh × ZSh

IPFh × ZPF = ULh

IAPFh × ZC + I1h × Z1h = ULh

IL0h × n2ZL0 = I1h × Z1h − nUFh

I1h + IL0h = IAPFh

ISh = IAPFh + IPFh + ILh.

(8)

Hence, ISh can be calculated out from (9), shown at thebottom of the next page, where{

K1 = Z1h

Z1h+n2ZL0

K2 = n2Z1hZL0Z1h+n2ZL0

.(10)

When APF is considered as a controlled voltage source

UFh = K × ILh (11)

where K is the controlled gain of ILh. From (9), shown at thebottom of the next page, and (11), the supply harmonic currentshould be

ISh =ZPF (ZC +K2−nK1K)×ILh+(ZC +ZPF +K2)USh

ZSh(ZC +ZPF +K2)+ZPF (ZC +K2).

(12)

According to (12), Fig. 3 can be simplified to an equivalentcircuit shown in Fig. 4. In Fig. 4, where Z ′ = ZPF (ZC +K2)/(ZC + K2 + ZPF ), it can be seen that the characteris-tic of PPFs is optimized as a regulable harmonic impedance−(nKK1Z

′/(Zc + K2))(Ω), which is connected in serieswith PPFs. Meanwhile, a regulable harmonic impedance(nKK1Z

′/(Zc + K2))(Ω) is connected in series with ZSh.


Fig. 5. Single-phase control equivalent circuit of the IHAPF.

If |nKK1Z′/(Zc + K2)| � |ZSh|, all the harmonic currents

produced by the load would sink into the filter branch.

III. PI-TYPE ITERATIVE LEARNING CURRENT

CONTROLLER FOR IHAPF

A. Mathematic Model of IHAPF

The single-phase control equivalent circuit of IHAPF inharmonic domain is shown in Fig. 5. IC represents the currentof the output filter. According to the Kirchhoff voltage andcurrent theorem, the following equations can be obtained:

⎧⎪⎪⎪⎨⎪⎪⎪⎩

IC = nUF h−IRh×ZR

n2ZL0− IRh×ZR

n2ZC0USh = ISh × ZSh + IPFh × ZPF

IAPFh × ZC + IRh × ZR = IPFh × ZPF

ISh = IAPFh + IPFh + ILh

IC = IRh − IAPFh.

(13)

Hence, IC can be calculated out from (14), shown at the bottomof the page, where

{K3 = nZC0

ZC0+ZL0

K4 = n2ZC0ZL0ZC0+ZL0

.(15)

In the frequency domain, (14), shown at the bottom of thepage, can be re-expressed as

IC(S) = GC(S)UFh(S) − GS(S)USh(S) + GL(S)ILh(S)(16)

where UFh(S) represents the controlled quantity and USh(S)and ILh(S) can be regarded as periodic disturbances.

Defining that⎧⎪⎪⎪⎪⎪⎪⎪⎨⎪⎪⎪⎪⎪⎪⎪⎩

GC(S)= K3(ZShZP F +ZCZP F +ZCZSh+ZRZP F +ZRZSh)

(K3+ZR)(ZShZP F +ZCZP F +ZCZSh)+K4ZR(ZSh+ZP F )

GS(S)= ZP F ZR

(K3+ZR)(ZShZP F +ZCZP F +ZCZSh)+K4ZR(ZSh+ZP F )

GL(S)= ZShZP F ZR

(K3+ZR)(ZShZP F +ZCZP F +ZCZSh)+K4ZR(ZSh+ZP F ) .

(17)

Consequently, according to (16), the closed-loop controlfunctional block diagram of the harmonic current of the IHAPFis shown in Fig. 6.

In Fig. 6, Gcon(S) denotes the transfer function of thePI-type iterative learning controller, and Ginv(S) denotes thetransfer function of VSI. I∗C(S) denotes the reference currentof IHAPF.

Due to the nonlinear characteristic of VSI, it is very difficultto attain an enough accurate transfer function of VSI just bytheoretical analysis. Many scholars consider that the approxi-mate transfer function of three-phase VSI is one order inertiallink, as shown in

Ginv(S) =Kinv

TinvS + 1(18)

where Kinv is the gain constant and Tinv is the time constant.According to [25], in industrial applications, the amplitudes

of GS(S) and GL(S) are very small in the fundamental waveand low-order harmonics current given out by VSI. Therefore,the disturbance is also very small to the controlled currentIC(S), which is caused by the harmonic voltage of the powergrid USh(S) and harmonic current of the load ILh(S). Mean-while, the closed-loop control functional block diagram of theharmonic current of the IHAPF can be predigested as Fig. 7.

According to Fig. 7 and the superposition principle, theclosed-loop transfer function of current IC(S) can be derivedas

Gclose(S) =IC(S)I∗C(S)

=Gcon(S)Ginv(S)GC(S)

1 + Gcon(S)Ginv(S)GC(S). (19)

In order to get an ideal control effect, it is necessary to designa reasonable controller which has a fast response speed and agood tracking precision.

ISh =(ZCZPF + K2ZPF ) × ILh + (ZC + ZPF + K2)USh − nK1ZPF UFh

ZCZPF + ZShZC + ZShZPF + K2(ZPF + ZSh)(9)

IC =ZShZPF ZRILh − ZPF ZRUSh + K3(ZShZPF + ZCZPF + ZCZSh + ZRZPF + ZRZSh)UFh

(K3 + ZR)(ZShZPF + ZCZPF + ZCZSh) + K4ZR(ZSh + ZPF )(14)


Fig. 6. Current closed-loop control of the IHAPF.

Fig. 7. Simplified closed-loop control diagram.

B. Proposed Feedback-Feedforward PI-Type IterativeLearning Control Method

The character of the harmonic current of the steady powergrid has a fundamental wave period. The period of the fun-damental wave is T . The subscript k = 0, 1, . . . represents therepeatable operating times. In the time domain, I∗C(t), ICk(t),uk(t), ufb

k (t), and uffk (t), respectively, stand for the expected

tracking current, output current, output signal of the controller,feedback signal, and feedforward signal in the Kth iterativetime. I∗Ck(t) is the periodic quantity between the time interval[0, kT].

The whole control system’s output signal uk+1(t) can beexpressed as

uk+1(t) = ufbk+1(t) + uff

k+1(t). (20)

The whole control system’s input signal current error ek(t)can be expressed as

ek(t) = I∗C(t) − ICk(t). (21)

The output signal of the PI-type iterative learning controllerufb

k+1(t) can be expressed as

ufbk+1(t) = ufb

k (t) + Lek(t) + ψ

t∫0

ek(t)dτ (22)

where L and ψ are steady gains.In order to reduce the systemic initial tracking offset, to

accelerate the speed of iterative convergence and to improve

TABLE IRULE OF Γk(t)’s FUZZY CONTROL

TABLE IISIMULATION PARAMETERS OF IHAPF

the systemic robustness, an initial correction term u0(t) isintroduced into (22). Therefore, the (22) can be re-expressed as

ufbk+1(t)=(1−λ)ufb

k (t)+λu0(t)+Lek(t)+Ψ

t∫0

ek(t)dτ.

(23)

where λ is the forgetting factor.


Fig. 8. Simulation results of the dynamic response characteristics with different control strategies. (a) Simulation results with the conventional PI control strategy.(b) Simulation results with the proposed control strategy.

The purpose of introducing λ is to ensure the convergenceof iterative learning and reduce the influence produced by theinitial correction term u0(t) as the iterative time is increased.When the systemic tracking accuracy is enough (|ek(t)| <|emin|), λ is attenuated to zero.

On the effect of the feedback controller, the feedforwardD-type learning law is introduced to correct the feedback con-trol signal ufb

k+1(t), so the controller can realize the complete

tracking task quickly. The feedforward signal uffk (t) can be

expressed as

uffk+1(t) = Γk(t)ek(t) (24)

where Γk(t) is obtained by fuzzy inference rules.Fuzzy inference mechanism can real-timely determine Γk(t)

according to the calculation of ek(t) and its change rateeck(t) = [ek(t) − ek−1(t)]. Assuming the fuzzy sets of e andec, both are {NB,NS,ZO,PS,PB}, and the fuzzy set of Γk(t)is {NVB,NB,NM,NS,ZO,PS,PM,PB,PVB}. The membershipfunctions of e, ec, and Γk(t) all obey normal distribution. TheΓk(t)’s fuzzy control rule is shown in Table I.

From (23) and (24), (20) can be re-expressed as

uk+1(t) = (1 − λ)uk(t) + λuo(t) + Lek(t)

+ψ

t∫0

ek(t)dτ + Γk(t)ek(t). (25)

The sample period is h. In the mth sample period, thediscrete expression of (25) can be written as

uk+1(m) = (1 − λ)uk(m) + λu0(m) + Lek(m)

+ψ

m∑j=0

ek(j) + Γk(m) (ek(m + 1) − ek(m)) (26)

where m = 0, 1, . . . , T/h − 1. If |ek(m)| is less than |emin|,the best control u∗

k(m) can be chosen after m times iterativelearning under the effect of (26). The iterative learning does notstop until the expected tracking current I∗C(t) is not changed.


Fig. 9. Simulation results of the steady-state performance with different control strategies. (a) Simulation current waves and spectrum with the conventional PIcontrol strategy. (b) Simulation current waves and spectrum with the proposed control strategy.


IV. SIMULATION RESULTS

To confirm the effectiveness of the proposed IHAPF andto testify the superiority of the feedback-feedforward PI-typeiterative learning control strategy proposed in this paper, sim-ulation results of a 10-kV system have been carried out withsoftware PSIM6.0. The main frequency of the power system is50 Hz. The system parameters are listed in Table II. The PPFsare turned at 11th and 13th, respectively. The injection circuitis turned at sixth. In this simulation, ideal harmonic currentsources are applied. The control signal of switching is obtainedthrough pulsewidth modulation, taking a triangle wave as thecarrier wave whose amplitude and frequency are −12 ∼ +12 Vand 12.8 kHz, respectively. In the simulation, in order to avoidthe impact of the oscillating high voltage which is brought inwhen the injection circuit is connected into the power grids,the PPFs are put into the power grids first. Then, after 0.2 s,the APF is switched into the power grids. The simulationresults with the conventional PI controller and the proposedcurrent controller are shown in Figs. 8 and 9. i_La, i_Sa,i_Ca, and Error represent the A phase load current, A phasesupply current, current through APF, and the error betweenthe output harmonic current of the APF and the referencecurrent.

A. Dynamic Response Characteristics

Fig. 8 shows the dynamic response characteristics of IHAPFwhen different control strategies are adopted. After the IHAPFis adopted, the supply current i_Sa has already approximated toa sinusoidal wave. When the conventional PI control strategyis used, the Error can be reduced from ±120 to ±100 A at0.2 s. At 0.3 s, the Error can be reduced to ±70 A, and then,the Error is reduced from ±70 to ±20 A in 0.22 s. However,there is an obvious steady-state error at 1.0 s all the same. Whenthe proposed control strategy is used, the Error can be reducedfrom ±120 to ±20 A at 0.2 s, and the Error is reduced to ±15A in 0.1 s. It is observed that, compared to the conventionalPI control strategy, the proposed feedback-feedforward PI-typeiterative learning control strategy has a better dynamic responsecharacteristics.

B. Steady-State Performance

Fig. 9 shows the steady-state performance of IHAPF at aperiod of 0.96–1 s when different control strategies are adopted.From Fig. 9 and Table III, it can be seen that, after the IHAPFwith the conventional PI control strategy is run, the trackingerror of the harmonic current is between 0.5 and 0.7 A. Mean-while, the current total harmonic distortion (THD) reduces to3.6% from 19.7%. When the proposed control strategy is used,the tracking error of the harmonic current is between 0 and0.3 A. The current THD reduces to 2.1% from 19.7%, andthe power factor is increased from 0.64 to 0.93. Therefore, itcan be observed that the proposed feedback-feedforward PI-type iterative learning control strategy exhibits a much bet-ter steady-state performance than the conventional PI controlstrategy.

TABLE IIISPECTRUM DATA OF THE TRACKING HARMONIC

CURRENT ERROR IN FIG. 9

V. EXPERIMENTAL AND INDUSTRIAL

APPLICATION RESULTS

A. Experimental Results

To confirm the effectiveness of IHAPF with the proposedcontrol strategy, some experiments have been made, employinga laboratory test system. The specifications of the laboratorytest system and the parameters of the simulated LC filter arelisted in Table II. The PPFs are composed of 11th and 13thorder LC filters, and a voltage-source IGBT inverter is used asthe main circuit of the APF. Fig. 10 shows the local experimentequipments of IHAPF, which consists of active and passiveparts.

Fig. 11 shows the waveform of the supply current IS usingdifferent control strategies when the load current IL of A phaseis increased from ±40 to ±60 A suddenly. ComparingFig. 11(a) with Fig. 11(b), it can be seen that the supply currentIS achieved the steady state in 30 ms under the conventional PIcontrol strategy. However, when the proposed control strategyis adopted, the supply current IS achieved the steady state in10 ms, and its waveform is approximately a perfect sinusoidalwave. Fig. 12 shows the current tracking Error under differentcontrol strategies when the load current IL is ±40 A. Compar-ing Fig. 12(a) with Fig. 12(b), it can be seen that the Error is±10 A under the conventional PI control strategy. When theproposed control strategy is adopted, the Error is only ±5 A.

From the experimental results, it can be seen that the iterativelearning control method is better than the conventional PIcontrol method. It can be analyzed from the following aspects.

1) Steady Characteristics: I∗C is composed of multiharmon-ics. The conventional PI controller has different frequencyresponding to different harmonic waves, respectively, so it ishard to realize zero steady-state error control with all frequencywaves. The PI-type iterative learning control method uses therepeatability of the load current and accumulates to correctthe control signal. This method can eliminate the influence ofrepeated load harmonic current, and when the system is stable,the static error is zero, and the feedforward link also enhancesthe tracking accuracy. The results show that the waveformshave better sinusoidal characteristics under the PI-type iterativelearning control.

2) Systemic Robustness: A linear regulator can only controlin a certain extent. If the load is changed greatly, the control ca-pability of a linear regulator will be decreased significantly. ThePI-type iterative learning control method admits greater controlmode mismatch, so when the load is changed greatly or otherfactors are affected, the controller also has effectively controlrobustness. As shown in Figs. 11 and 12, the conventional PIcontroller has a good effect when the load current is unchanged.The supply current has a good sinusoidal characteristic. When


Fig. 10. Local experiment equipments of the IHAPF. (a) Active part of theIHAPF. (b) PPF of the IHAPF.

Fig. 11. Supply current IS with different control strategies when the loadcurrent IL is increased. (a) Supply current IS with the conventional PI controlstrategy. (b) Supply current IS with the proposed control strategy.

the load current is changed, the supply current loses the sinu-soidal characteristics. However, the PI-type iterative learningcontroller has a good sinusoidal characteristic no matter if theload current is changed or not.

Fig. 12. Current tracking Error with different control strategies when the loadcurrent IL is kept invariant. (a) Current tracking Error with the conventional PIcontrol strategy. (b) Current tracking Error with the proposed control strategy.

TABLE IVPARAMETERS OF THE IHAPF

3) Dynamic Response Characteristics: In (25), uk(t) is ac-cumulated in the last K cycles, and it is obtained in Kth itera-tion to correct uk+1(t). The PI-type iterative learning controlcan feedback current information and summarize the formercontrol experience. The feedforward control loop based onD-type learning regulation can accelerate the response speed


Fig. 13. Industrial wiring diagram of the IHAPF.

of the controller, so its dynamic response speed is more quickthan that of the conventional PI controller.

B. Industrial Application Results

The control strategy proposed in this paper has been appliedin an IHAPF of a steel plant in Guangxi, China. The PPFsare composed of 7th and 11th order LC filters. Parameters of

the IHAPF system are shown in Table IV. A 16-b fixed-pointTMS320 F240 is used on the controller board to implement thefeedback-feedforward PI-type iterative learning control strat-egy in industrial applications. Fig. 13 shows the industrialwiring diagram of the IHAPF.

The load current, supply current, and their spectrums areshown in Fig. 14. From Fig. 14(a), it can be seen that thedistortion of the 5th, 7th, 11th, 13th, and 17th of the load current


Fig. 14. Industrial application results. (a) Load current and spectrum beforecompensated. (b) Supply current and spectrum when only the PPFs are adopted.(c) Supply current and spectrum when the IHAPF is adopted.

are 19.02%, 12.67%, 9.52%, 7.32%, and 6.04%, respectively,before the compensation, while the THD is 26.7%. FromFig. 14(b), it can be seen that, with the use of the PPFs only,the current distortions turn out to be 18.01%, 2.93%, 3.28%,6.83%, and 5.37%, respectively. The THD is 20.3%. Whereas

Fig. 14. (Continued.) Industrial application results. (c) Supply current andspectrum when the IHAPF is adopted.

after the whole IHAPF is adopted, from Fig. 14(c), it can beseen that they are decreased to 1.28%, 1.21%, 1.14%, 1.12%,and 1.03%, respectively. The power factor is increased from0.46 to 0.94. Moreover, the supply current waveform has al-ready approximated to a sinusoidal wave. In conclusion, all theapplication results have validated the practicability of IHAPFwith the proposed feedback-feedforward PI-type iterative learn-ing control strategy.

VI. CONCLUSION

Because a fundamental resonance circuit has a small fun-damental impedance, the active part of IHAPF does not haveto bear the fundamental voltage, which reduces the requiredcapability of the active part greatly and makes the device moreefficient in high-voltage systems. Since the reference currentsignal of IHAPF is a reperiodic quantity in steady-load powersystem which is superposed with different multifrequency har-monic waves, the conventional PI will generate a steady-stateerror. Therefore, the iterative learning control algorithm basedon the PI-type learning law is proposed in this paper. Thismethod can enhance systemic robustness by using a forgettingfactor. Meanwhile, the proposed control method constructs afeedforward based on the D-type learning law of referencedcurrent error by fuzzy reasoning to improve the dynamic per-formance of the whole control system. It is implemented inan IHAPF system in a steel plant in Guangxi, China, and itdemonstrates a good performance for harmonic elimination.Simulation, experimental, and industrial application resultsproved the feasibility and validity of IHAPF and the proposedcontrol method.


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An Luo (M’09–SM’09) was born in Changsha,China, on July 21, 1957. He received the B.S. andM.S. degrees from Hunan University, Changsha,in 1982 and 1986, respectively, and the Ph.D. de-gree from Zhejiang University, Hangzhou, China,in 1993.

Between 1996 and 2002, he was a Professor withCentral South University, Changsha. Since 2003, hehas been a Professor with the College of Electri-cal and Information Engineering, Hunan University,Changsha. He is engaged in research on power con-

version systems, harmonics suppression and reactive power compensation,and electric power saving. He has published over 100 journal and conferencearticles.

Dr. Luo currently serves as the Associate Board Chairperson of the HunanSociety of Electrical Engineering. He also serves as the Chief of the HunanElectric Science and Application Laboratory. He is a recipient of the 2006National Scientific and Technological Awards of China and the 2007 Scientificand Technological Awards from Hunan, China.

Xianyong Xu was born in Henan, China, on July 30,1981. He received the B.S. degree from the Collegeof Electrical and Information Engineering, HunanUniversity, Changsha, China, in 2001, where he hasbeen working toward the Ph.D. degree since 2005.

He engaged in research on harmonics suppressionand reactive power compensation for power elec-tronic devices and active power filters, power qualityof microgrid, UHV ac test system and its applica-tion for UHV ac devices, and electric power saving.He has published over ten journal and conference

articles.Dr. Xu is a recipient of the 2007 Scientific and Technological Awards from

the National Mechanical Industry Association of China.

Lu Fang was born in Hunan, China, on August 22,1983. She received the B.S. degree from the Collegeof Electrical and Information Engineering, HunanUniversity, Changsha, China, in 2001, where she hasbeen working toward the Ph.D. degree since 2006.

She engaged in research on harmonics suppressionand reactive power compensation, power quality ofmicrogrid, and electric power saving.


Houhui Fang was born in Changsha, China, onMay 19, 1956. He received the B.S. and M.S. degreesfrom Hunan University, Changsha, in 1977 and 1991,respectively.

Since 2005, he has been a Professor with theCollege of Electrical and Information Engineering,Hunan University. He is engaged in research onbuilding electrical and power conversion systems,harmonics suppression and reactive power compen-sation, and electric power saving. He has publishedover 30 journal and conference articles.

Prof. Fang has been serving as the Associate Chairperson of the ElectricalResearch Society in Hunan colleges and universities since 2007. Between 2003and 2007, he also served as the Director of the Electrical Research Society inChina colleges and universities. He was a recipient of the 2005 Scientific andTechnological Awards from the National Mechanical Industry Association ofChina and the 2005 Scientific and Technological Awards from Hunan, China.

Jingbing Wu was born in Hubei, China, on April 11,1982. He received the M.S. degree from the Collegeof Mathematics and Econometrics, Hunan Univer-sity, Changsha, China, in 2005, where he has beenworking toward the Ph.D. degree in the College ofElectrical and Information Engineering since 2008.

His research interests include electric power sav-ing, reactive power compensation, and active powerfilters.

Chuanping Wu was born in Hunan, China, onMarch 20, 1984. He received the B.S. degree fromthe College of Electrical and Information Engineer-ing, Hunan University, Changsha, China, in 2003,where he has been working toward the M.S. degreesince 2007.

His research interests include harmonics suppres-sion and reactive power compensation, and activepower filters.

hormonic pi ilc

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