Contribution of a Shunt Active Power Filter Control using Double ...

16th International Power Electronics and Motion Control Conference and Exposition

Antalya, Turkey 21-24 Sept 2014

Contribution of a Shunt Active Power Filter Control using Double Fuzzy PI Controller H. Djeghloud, Y. Terriche Laboratory of Electrical Engineering Constantine 1 University Constantine, Algeria

N. Elhaj T. jarou, M. B. Sedra Laboratory of High Energy and Engineering Sciences Ibn Tofail University, Kenitra, Morroco [email protected]

Abstract—This paper presents a contribution to harmonic cancellation using a shunt active power filter (SAPF) based on a voltage source converter. The harmonic producer is a threephase diode bridge feeding a variable DC RL load. The SAPF power circuit is constituted of a IGBTs two-level inverter and an output RL filter. The control circuit contains a hysteresis current controller and a DC bus voltage regulation loop based on a double fuzzy PI (DFPI) controller. The harmonic reference current is extracted using the algorithm of the synchronous reference frame (SRF) and the Double fuzzy PI controller allows the control of the DC voltage so that the SAPF works properly. An additional feature of the paper consists in dimensioning of the SAPF passive elements. To validate the presented work, simulation studies performed under MATLAB/Simulink are provided and a comparison between PI and DFPI controllers performances is dressed. The obtained results seem to be satisfactory and promising even under load current variation. Also, they demonstrate the advantage of a DFPI controller. Index Terms--Shunt power active filter, dc voltage control, Double Fuzzy PI Controller, Synchronous Reference Frame, hysteresis modulator. I.

INTRODUCTION

The power quality concerns became one of the most important preoccupations to researchers of electrical engineering field seeking for a good and reliable electric power [1]. The quality of the distributed power can be affected by various types of disturbances related to the utility voltage (harmonics, unbalance, sags, swells, flickers…), to the utility current (harmonic, unbalance…) and utility frequency (problem of frequency variation especially in isolated sites) [2][3][4]. Then, a good power quality broadly refers to maintaining a near sinusoidal utility voltage at rated magnitude and frequency and where the distributed energy must be uninterrupted from the reliability point of view [5]. Disturbances are usually caused by the connection of nonlinear loads (such as fluorescent bulbs, TV sets, air conditioning systems, computer equipment, diode and thyristor rectifiers, electronic starters, speed variation drives, arc welding machines, arc furnaces,…) to the main grid [6][7].

To deal with this undesired effect of non-linear loads, solutions have been proposed, such as Shunt active Power filters [8] that are effective for elimination of harmonic currents. These filters act as current sources connected in parallel with the non-linear load, generating identical but opposite-phase harmonic currents allowing the compensation of the harmonic components contained in the current absorbed by the disturbing load [9]. The injection of such currents can disturb the DC capacitor voltage, which can result in loss of the ability to control parallel active filter. Therefore, this paper presents a method of control at the base of Double Fuzzy controller [10][11] and a proportional integral controller (PI) to control the voltage of DC capacitor so that the active filter DC voltage follows a baseline which ensure both the possibility of a stable DC voltage capacitor, and control the shunt active filter correctly. A Synchronous Reference Frame method [9] [12] is used for the extraction of reference currents, and the hysteresis band controller is adopted for launching the gating signals of the IGBTs constituting the active filter main switches. This paper is organized as follows. Section II presents a descriptive diagram of the various components of the active power filter system. Section III provides the dimensioning of the SAPF system passive elements. Section IV presents the reference currents identification SRF algorithm. Section V details the control method of DC capacitor voltage based on the DFPI controller associated to a PI controller. Section VI exhibits the hysteresis modulator principle. Section VII presents the simulation results and establishes a brief comparative study between DFPI and PI controllers responses. Finally, a conclusion summarizing the paper contribution, findings and prospects is given. II.

CONSIDERED SYSTEM DESCRIPTION

The studied system, as Fig. 1 shows, is composed of a three-phase power supply (Vs, Rs, Ls), a non-linear load absorbing the reactive power which is a three-phase diode,

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16th International Power Electronics and Motion Control Conference and Exposition

Antalya, Turkey 21-24 Sept 2014

Figure 1. Presentation of the studied system.

loaded by a passive circuit (RL, LL), and a shunt active power filter. The SAPF contains a three wires IGBT half bridge and an output filter (Rf, Lf). This latter serves to damp the cutouts caused by PWM modulator which produce the gating signals. The control of the DC voltage feeding the IGBT bridge is based on a double fuzzy controller associated to a proportional integral (PI) controller. Reference current generation method adopts the synchronous reference frame algorithm. Finally, the hysteresis current controller is used to generate the IGBTs pulses. III.

DIMENSIONING OF SAPF PASSIVE ELEMENTS

(1)

B. Dimensioning of the DC Capacitor Transitory changes in the instantaneous power absorbed by the load cause fluctuations of capacitor DC voltage. The amplitude of these fluctuations can be controlled by a relevant choice of the capacitor value. The maximum voltage that can be supported by the capacitor is given by (2) [13]: ୢୡ୫ୟ୶ ൌ 

ଵ ஼೏೎

ಐమ

ሺ

ሻ

Ǥ ‫ ׬‬ಐభಡ ‹ୢୡ ሺ–ሻ†– ൅ ୢୡ ሺ

ಡ

ሻ

(2)

Where ș1, ș2 are two angles belonging to the interval [0,2ʌ], and Ȧ is the angular frequency of the power supply (Ȧ = 2.ʌ.f, f is the fundamental frequency). The capacitance Cdc is then expressed by:

PEMC 2014

ଵ ୼୚ౚౙ

ಐమ

ሺ

ሻ

Ǥ ‫ ׬‬ಐభಡ ‹ୢୡ ሺ–ሻ†– ሺ

ಡ

ሻ

(3)

ΔVdc is the DC voltage fluctuation (ΔVdc = Vdcmax-Vdc) that should not exceed 5% of Vdc. The mean value of the current idc absorbed by the capacitor is given in (4): ಐమ

ಐమ

ሺ ሻ

ሺ ሻ

ሺ ሻ

ሺ ሻ

‫ ׬‬ಐభಡ ‹ୢୡ ሺ–ሻ†– ൌ ‹୊୫ୟ୶ Ǥ ‫ ׬‬ಐమಡ ൣ•‹ሺɘ–ሻ ൅  •‹൫ɘ– ൅ ʹɎൗ͵൯൧†–(4) ಡ

A. Dimensioning of the DC Voltage The DC voltage Vdc feeding the inverter of the SAPF system can be dimensioned according to the RMS value of the fundamental component contained in the inverter output voltage. Knowing that the maximum value of the output voltage is ൅ܸ݀ܿȀʹ, then the RMS value of the fundamental voltage is ൅ܸ݀ܿȀሺʹξʹሻ. Thus, Vdc will be dimensioned from (1). ܸௗ௖ ൌ ʹξʹǤ ܸ௦ோெௌ

ୢୡ ൌ 

ಡ

‹୊୫ୟ୶ is the maximum amplitude of SAPF output current. If Ʌଵ  ൌ Ͳ rad and Ʌଶ ൌ  ߨൗ͸ rad, the capacitance can be dimensioned from: ୢୡ ൌ 

୧ూ ଶǤனǤ୼୚ౚౙ

(5)

C. Dimensioning of the Output Filter Impedance The output filter is a series Lf, Rf circuit. The value of Lf can be extracted from (6), accordin to fig. 1 and neglecting the resistor Rf: ୤ ൌ ሺ୊ െ ୱ ሻǤ

ୢ୧ూ ୢ୲

(6)

The design of Lf is performed out with the constraint that for a given switching frequency, the slope of the current iF ሺ݀݅ி Τ݀‫ݐ‬ሻ is smaller than the slope of a triangular carrier (in the case of a carrier-based PWM modulator) defining the switching frequency. The slope of a bipolar triangular waveform is defined by: ߛ ൌ ͶǤ

஺೎ ்೎

(7)

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16th International Power Electronics and Motion Control Conference and Exposition

Where Ac and Tc are the amplitude and the period of the triangular waveform, so that the switching frequency fs equals ͳȀܶ஼ as it is well known in carrier-based PWM. Consequently the maximum value of Lf should satisfy: ሺ୚ూ ି୚౩ ሻ

୤ ൐

(8)

ସǤ୅ౙ Ǥ୤౩

Knowing that VAF varies from Ȃ ܸ݀ܿȀʹ to ൅ܸ݀ܿȀʹ and that Lf can’t take negative values, then the maximum value of Lf might be obtained from (9) ୤୫ୟ୶ ൐ °

ష౒ౚౙ ି୚౩ౣ౗౮ ሻ మ

ሺ

ସǤ஺೎ Ǥ௙ೞ

°

(9)

Where ܸ௦௠௔௫ ൌ ܸ௦ோெௌ Ǥ ξʹ and VsRMS can be obtained from (1). Thus, ୤୫ୟ୶  ൐ 

௏೏೎

(10)

ସǤ஺಴ Ǥ௙ೞ

ܴ௦ ൑ ͳͲΨǤ ܴ௕௔௦௘ , ‫ܮ‬௦ ൑ ͳͲΨǤ ‫ܮ‬௕௔௦௘

୚౎౜ ୧ూ౗

ǡ ‹୊ୟ ൎ ͷͲΨǤ ‹୐

E. Dimensioning of the Rectifier Upstream Impedance The upstream impedance is the impedance insterted between the PCC and the rectifier entry (Fig. 1). The principle of dimensioning this impedance is the same as the preceding impedances (filter and source impedances), the voltage drop should be kept inferior to 10% of the input voltage (the PCC voltage in this case). ο ൌ  ୡ Ǥ ‹୐ ൅ ୡ Ǥ

(11)

Where VRf is the resistive voltage drop in the output filter which should be less that 10% of the point of common coupling RMS voltage as expressed in (12). iL is the RMS value of the load current. ˜ ୖ౜ ൏

ଵ଴ ଵ଴଴

Ǥ ˜ୖ୑ୗ

(12)

୚౎౉౏

(13)

(16)

Where Vs and is are RMS values of fundamental supply voltage and current, f is the power system frequency. is value can be obtained from the harmonic spectrum of iL obtained in the frequency domain using Fourier block in Simulink (the Fourier block performs a Fourier analysis of the input signal over a running window of one cycle of the fundamental frequency. First and second outputs return respectively the magnitude and phase of the harmonic component specified.

Now, for dimensioning Rf the following method is used: ୤ ൌ

Antalya, Turkey 21-24 Sept 2014

ୢ୧ై ୢ୲

ൌ ୱ െ ୐

(17)

Rc and Lc should be dimensioned in such a way to maintain ο ൑ ͳͲΨǤ ୱ . Therefore, all values of Rc and Lc that satisfy this condition are acceptable. As depicted in the voltage diagram of Fig. 2, one can deduce the values of Rc and Lc geometrically using (18) and (19).

Then  ୤ ൏ ͲǤʹ

୧ై

D. Dimensioning of the Source Impedance The insertion of impedance in series with the source terminals makes it possible to block undesirable harmonics components that are caused by the nonlinear load to pass through the tuned filters. The source impedance value is typically dimensioned from (14) and (15) assuming that the drop voltage in the impedance is less than 10% of the given line voltage (as was done with Rf). For dimensioning source impedance (Rs and Ls), basic value of the source impedance is calculated at first using (13). Then Rbase and Lbase are deduced from (14). Finally, following the imposed constraint on the voltage drop in the source impedance terminals, Rs and Ls can be obtained from (15). ܼ௕௔௦௘ ൌ ܴ௕௔௦௘ ൌ ܼ௕௔௦௘ , Thus,

PEMC 2014

௏ೞ

(14)

௜ೞ

‫ܮ‬௕௔௦௘ ൌ

௓್ೌೞ೐ ଶǤగǤ௙

(15)

Figure 2. Geometrical dimensioning of the upstream impedance.

 ୡ ൌ οǤ …‘•ሺɔሻ Ǥ and ଵ

ଵ

(18)

୧ై

ୡ ൌ οǤ •‹ሺɔሻ Ǥ Ǥ

ଵ

(19)

୧ై ଶ஠୤

ɔ is extracted from the Fourier of iL. IV.

THE SRF ALGORITHM

The block diagram of a current reference generator using the SRF algorithm is shown in Fig. 3 [9][12]. In this case, the real currents are transformed into a d-q synchronous reference frame. This latter is being synchronized with the voltage source (using a PLL), and rotates at the same frequency. This transformation is performed on the basis of initial Park matrix expressed in (20). ଶగ ଶగ ݅௅௔ •‹ሺ߱Ǥ ‫ݐ‬ሻ •‹ሺ߱Ǥ ‫ ݐ‬െ ሻ •‹ሺ߱Ǥ ‫ ݐ‬൅ ሻ ‹ୢ ଶ ଷ ଷ ൩Ǥ ൥݅௅௕ ൩ ൤‹ ൨ ൌ ൥ ଶగ ଶగ ଷ ୯ …‘•ሺ߱Ǥ ‫ݐ‬ሻ …‘•ሺ߱Ǥ ‫ ݐ‬െ ሻ …‘•ሺ߱Ǥ ‫ ݐ‬൅ ሻ ݅௅௖ ଷ

(20)

ଷ

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16th International Power Electronics and Motion Control Conference and Exposition

Antalya, Turkey 21-24 Sept 2014

As for the theory of the instantaneous reactive power, d and q terms are constituted by a DC component and a sum of AC components [14].

Figure 4. Proposed DFPI Controller

Figure 3. Block diagram required to obtain current reference using the synchronous reference frame algorithm.

‹ୢ  ൌ  ‹ୢୢୡ  ൅  ‹ୢୟୡ ൜‹  ൌ  ‹  ൅  ‹ ୯ ୯ୢୡ ୯ୟୡ

The synoptic scheme of the fuzzy logic controller is shown in Fig. 5 where all steps are mentioned (fuzzification, inference engine, and défuzzication) [15].

(21)

The compensation reference signals are obtained from the following expressions: ݅ ‫  כ‬ൌ  ݅ௗ െ ‹ୢୢୡ ൜ ௗ‫כ‬ ݅௤  ൌ  ‹୯ି ‹୯ୢୡ



(23)

One of the most remarkable features of this algorithm is that the reference currents are obtained directly from the load currents, regardless of mains voltages. This is an important advantage since the compensating current generation will be affected by either distortions or by imbalances present in the source voltages, thereby enhancing the robustness and performance of the compensation. However, the synchronization with the voltages of the network is required and can be ensured using a PLL. V.

error derivative (ǻe)

NB NM NS Z PS PM

NB NB NB NB NB NM NS

NM NB NB NB NM NS Z

error (e) NS Z NB NB NB NM NS NS Z Z PS PS PM PM

PS NM NS Z PS PM PB

PB NS Z PS PM PB PB

(a)

(b)

THE DFPI CONTROLLER PRESENTATION

Fuzzy logic controller is used for complicated systems and allows translating knowledge and human reasoning to simple rules that a computer can use, while intelligence artificial and PI Control are used to achieve this objective. The diagram of Fig. 4 shows the control algorithm of the capacitor voltage Vdc of the SAPF based on a dual fuzzy controller, the DC bus voltage capacitor is compared with the reference to obtain the error e given by the following equation: ‫כ‬ ሺ–ሻ െ ୢୡ ሺ–ሻ ‡ሺ–ሻ ൌ  ୢୡ

(24)

the derivative of the error is given by (24) ο‡ሺ–ሻ ൌ ‡ሺ–ሻ െ ‡ሺ– െ ͳሻ

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Synoptic scheme of fuzzy logic controller TABLE I. FUZZY RULES TABLE

(22)

Then, the reference currents can be obtained in the a-b-c frame using the inverse of the matrix given in equation (20). •‹ሺ߱Ǥ ‫ݐ‬ሻ …‘•ሺ߱Ǥ ‫ݐ‬ሻ ‫כ‬ ݅ி௔ ‫כ‬ ଶగ ଶ •‹ሺ߱Ǥ ‫ ݐ‬െ ଶగ ሻ ‫כ‬ …‘•ሺ߱Ǥ ‫ ݐ‬െ ሻ൪ Ǥ ൤݅ௗ‫ כ‬൨ ቎݅ி௕ ቏ ൌ ଷ ൦ ଷ ଷ ݅௤ ‫כ‬ ଶగ ଶగ ݅ி௖ …‘•ሺ߱Ǥ ‫ ݐ‬൅ ଷ ሻ …‘•ሺ߱Ǥ ‫ ݐ‬൅ ଷ ሻ

Figure 5.

(25)

(c) Figure 6. Membership function used in fuzzification for a) input variable e, b) input variable de, and c) output variable idc.

The error e and its derivative Δe are the numerical entries that are converted to the linguistic variables across fuzzifucation step, and the processing of these variables is made through the process of inference mechanism sing triangular membership functions (Fig. 6). Defuzzification is the last step which linguistic variable are converted into numerical variables. Seven linguistic variables are used from the universe of discourse, and are summarized in Table I. The linguistic values are defined as follows: {Positive Big (PB), Positive Medium (PM), Positive Small (PS), Zero (ZO), Negative Small (NS), Negative Medium (NM), Negative Big (NB)}

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16th International Power Electronics and Motion Control Conference and Exposition

e, ǻe, and idc={NB,NM,NS,ZO,PS,PM,PB}

VI.

A. Design of PI Controller Current harmonics generated by the non-linear load influence on the stability of the capacitor voltage. To compensate this effect, a control for the capacitor voltage is necessary. In this work, a PI controller associated to the DF controller is used to generate a current idc that restores capacitor voltage. The transfer function in an open loop is expressed by the product of the transfer function of current and voltage as given in (26) [16].Open Loop):  ୵୧୲୦୭୳୲୔୍ ൌ   ୧ ሺ’ሻ ൈ  ୳ ሺ’ሻ Where,

 ୧ ሺ’ሻ ൌ 

୧ూ౗ ሺ୮ሻ

 ୳ ሺ’ሻ ൌ 

and

୚ూ౗ ሺ୮ሻ

୚ౚౙ

(27)

୧ూ౗

The passing band of the voltage loop is inferior to that of the current loop, the pole of TFi(p) will not intervene in the voltage loop stability, so, one can consider TFi(p) = 1. By neglecting the switching losses in the active filter and in the output filter, the energy is the same in the DC and in the AC side. Thus: ‫כ‬ ‫ כ‬ୢ Ǥ ୢୡ Ǥ ୢୡ Ǥ †– ൌ ୅େ Ǥ †– (28) †ୢୡ ൌ ୢୡ ୢ୲

େౚౙ Ǥ୚ౚౙ Ǥ୮Ǥξଶ

 ୵୧୲୦୭୳୲୔୍ ൌ  ୳ ሺ’ሻ ൌ 

ଵ ୏ᇲ Ǥ୮

, with Ԣ ൌ 

Now,

୏

ଵ

୮

୏ᇲ Ǥ୮

 ୵୧୲୦୔୍ ൌ  ሺ ୮ ൅ ౟ ሻǤ So,  ୵୧୲୦୔୍ ൌ ɒଵ ൌ

With:

୏౦ ୏౟

‫כ‬

ξଶǤେౚౙ Ǥ୚ౚౙ Ǥ୮ ଷǤ୚ూ౎౉౏

ଵାதభ Ǥ୮ தమ Ǥ୮మ ୏ᇲ

, ɒଶ ൌ

୏౟

(29)

(30) (31) (32) (33)

Now, in the periodical state, TFwith PI is expressed by:  ୳ା୔୍ ൌ So that:ɘ଴ ൌ

ଵ ξதమ

and ɘଵ ൌ

ଵ தభ

ಡ Ǥ୮ ಡభ ಡ ୨మ ሺ ሻమ ಡబ

ଵା୨

(34)



according to Bode diagram, ω0 and ω1can be deduced from the cutting frequencyɘୡ ൌ ʹǤ ɎǤ ˆୡ using (34), taking into account a phase margin of 60°. ɘ଴ ൌ

னౙ ξଶ

 and ɘଵ ൌ

னౙ ξଷ

Generally, the cutting frequency is set at 20 Hz [16].

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Figure 7. Principle of hysteresis current controller. VII.

SIMULATION RESULTS

To validate the previous study, simulation works using MATLAB/Simulink were done. The parameters adopted in this section are listed in Table II. TABLE II. SIMULATION PARAMETERS Parameter AC supply voltage and frequency AC supply impedance Rectifier load

ଷ

Where ୅େ ൌ ͵Ǥ ୊ୖ୑ୗ Ǥ ‹୊ୟୖ୑ୗ ൌ Ǥ ୊ୖ୑ୗ Ǥ ‹୊ୟ୫ୟ୶  ξଶ Therefore, ୚ౚౙ ଷǤ୴ూ౎౉౏ ൌ ‫כ‬ ୧ూ౗ౣ౗౮

THE HYSTERESIS MODULATOR

The hysteresis control unit aims to force the filter current iF to follow its reference current ݅ி‫ כ‬matching to the optimal conditions. The obtained error passes through the hysteresis comparator which falls over towards the active state when the negative error reaches the lower limit of the hysteresis band ‫כ‬ ݅ி௔ and remains there until the error becomes positive and inferior to the upper limit ip of the hysteresis band where the comparator falls over towards 0. The hysteresis modulator bloc is depicted in Fig. 7.

(26)

Where iFa and VFa are active components of the SAPF output current and voltage.

Then,

Antalya, Turkey 21-24 Sept 2014

(35)

Output filter impedance Upstream filter impedance DC link capacitor DC link reference voltage PI coefficients Saturation limits Hysteresis limits

Value 380V-50Hz Rs = 0.1 Ÿ, Ls = 0.15 mH RL = 10 Ÿ, LL = 50 mH (from 0 to 0.06 s) RL = 5 Ÿ, LL = 25 mH (from 0.06 to 0.12 s) RF = 10 mŸ, LF = 1 mH Rc = 0.387 Ÿ, Lc = 0.3 mH Cdc = 3.1 mF V*dc = 550 V Kp = 0.1, Ki = 7.287 ± 1A ± 0.15A

Fig. 8 shows respectively the DC voltage Vdc, the threephase load currents with the introduction of a load variation at 0.06s, the source current after the compensation, the active filter currents and the source voltages. After application of the double fuzzy PI control, it is observed that the capacitor voltage follows the reference voltage (550V) and a satisfying stability is noted. This demonstrates the robustness of the proposed control. Besides, the source filter has sinusoidal waveform which shows the effectiveness of SAPF system proposed in this paper. Fig. 9 illustrates the harmonic spectrum of the source current where one can read a THD (total harmonic distortion) of 1.61% which is an acceptable value if compared with limits imposed by the international standardization [2][4]. Fig. 10 presents the SAPF current following its reference, which means a good response provided by the hysteresis modulator. Finally Fig. 11 is added to give a comparative study between DFPI and PI controller responses. In fact, the harmonic spectrum of Fig. 11 shows a THD of 1.88%. Thus, one can conclude that the DFPI controller has better response than that PI controller implemented alone.

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V d c (V )

16th International Power Electronics and Motion Control Conference and Exposition

VIII. 0.02

0.04

0.06

0.08

0.1

0.12

IL a b c (A )

0.02

0.04

0.06

0.08

0.1

0.12

is a b c (A )

100 0 -100 0

0.02

0.04

0.06

0.08

0.1

0.12

100 0 -100 0 400 200 0 -200 -400 0

0.02

0.04

0.06

0.08

0.1

0.12

0.02

0.04

0.06 Time(s)

0.08

0.1

0.12

V s a b c (V )

0 0 100 0 -100 0

iF a b c ( A )

500

REFERENCES [1]

140

Harmonic magnitude/Fundamental

120

[2]

100 80

THD isa % = 1.61 %

[3]

60

[4]

40 20

0 0

10

20

30

harmonic row

40

50

60

[5]

Figure 9. Harmonic spectrum and THD of the source current delivered by a DFPI controller. 100

i*Fa

iFa

80

[6] [7]

60

Amplitude ( A )

40

[8]

20 0 -20

[9]

-40 -60

[10]

-80 -100 0

0.02

0.04

0.06 Time (s)

0.08

0.1

0.12

[11]

Figure 10. The SAPF current following its reference current. 140

[12]

120

100

[13]

80

THD isa % = 1.88 % 60

40

[14]

20

0

0

10

20

30

40

50

60

harmonic row

[15] Figure 11. Harmonic spectrum and THD of source current delivered by a PI controller. [16]

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CONCLUSION

This paper suggests control of shunt active power filter that can compensate harmonic currents generated by a nonlinear load. The performance of the SAPF has been improved by the inclusion of a control loop which maintains the voltage across the capacitor voltage of the DC link at a constant level. In this way, the voltage gain of the inverter is increased and the ripple current at high frequency is reduced. The proposed control strategy is based on a DFPI controller which proved to be more efficient than PI controller implemented alone. The presented and discussed simulation results confirm the validity of the analysis and the feasibility of the proposed system. Also the section of dimensioning helped to construct a strong simulation model which permitted to experience the influence of the adopted DFPI controller on SAPF performance.

Figure 8. Temporal analysis of the DFPI control response of the SAPF.

Harmonic magnitude/Fundamental

Antalya, Turkey 21-24 Sept 2014

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