synchronous reference frame method for mitigation of...

International Journal of Innovations in Engineering and Technology (IJIET)

433

Volume 7 Issue 3 October 2016 ISSN: 2319 - 1058

Synchronous Reference Frame method for Mitigation of Current Harmonics with PI and

FLC based Shunt Active Filter under Load Variation

Elavala Satish Dept. of Electrical and Electronics Engineering,

National Institute of Technology Goa.

Suresh Mikkili Dean Students Welfare and Assistant Professor, Dept. of Electrical and Electronics Engineering,


Lav Kumar Gupta, Dept. of Electrical and Electronics Engineering,


Abstract: Recent advancements in power electronics has encouraged large scale use of non-linear loads such as Adjustable Speed Drives (ASD), traction drives etc. Power electronic equipment like frequency drives, computers, SMPS etc. introduce great amount of harmonic content into the power system. Harmonics overheat the power system equipment, increase transmission losses, cause nuisance tripping of circuit breakers and errors in measurements and medical diagnosis. They also interfere in the nearby communication systems. Conventionally, passive filters were used for mitigation of harmonics in the power system. However these L-C filters introduce tuning, aging and resonance (with network impedance) problems. They are suited for fixed harmonics compensation and are large in size. Active filters have been proven to be an efficient, flexible and alternative solution for the problem of power quality. The advantage of active filtering is that it automatically adapts to network and load variations, provides dynamic compensation and eliminates the risk of resonance. Active filters take up very little space compared to passive filters. As a result, active filters have gained much more attention in the recent times. However, active filters seem to have contradictions with different control strategies. Therefore this paper aims at providing a comparative study of Shunt Active Filter with PI and Fuzzy Logic based Controllers. Extensive simulations were carried out; Simulations were performed with PI and FLC with Triangular, Trapezium and Gaussian Membership Functions. Index Terms: Synchronous Reference Frame, PI controller, Fuzzy logic controller, Hysteresis current controller, Harmonics, THD.

Abbreviations:

COA : Centroid of Area. APF : Active Power Filter. PI : Proportional Integral. CT : Current Transformer. MF : Membership Function. VSI : Voltage Source Inverter. FIS : Fuzzy Inference System. FLC : Fuzzy Logic Controller. PWM : Pulse Width Modulation. SMPS : Switch Mode Power Supplies. IGBT : Insulated Gate Bipolar Transistor. SRF : Synchronous Reference Frame. SHAF : Shunt Active Filter.


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Id-Iq : Instantaneous Active and Reactive Current Theory. Notations:

E : Error. : Change in Error.

Is : Source Current. If : Filter Current/Compensation current. IL : Load Current. ILd : Load Current component along d axis ILq : Load current component along q axis I*fabc : Reference filter current. I*fd : Reference filter current along d axis. I*fq : Reference filter current along q axis. Vdc : Actual DC link voltage Vdc_ref : Reference DC link voltage.

I. INTRODUCTION Advancements in Power electronics has encouraged proliferation of numerous non-linear loads such as ASDs, SMPS, traction drives, etc. They generate perilous harmonics and cause enormous economic losses every year. Harmonics overheat power system equipment like transformers, circuit breakers, Electric motors, etc. and reduce their life expectancy. They increase the transmission losses and cause poor system efficiency. They cause errors in measurements, medical diagnosis and also nuisance tripping of circuit breakers. Active filters are eminent solution to power quality issues such as harmonics and reactive power compensation, making the source current in phase with the source voltage. Several control strategies and techniques [1-2] have been developed for the implementation of Shunt Active Filters for the mitigation of Current Harmonics. They still have the contradictions with the performance of Shunt Active Filters. This paper aims at providing a comprehensive study of performance of PI and Fuzzy Logic Controllers based Shunt Active Filters.

The performance of a Shunt Active Filter depends on the control strategy implemented to generate reference compensating currents. In this research paper, we have considered the SRF method for the determination of reference currents in Shunt Active Filters. One of the advantages of this control strategy is that it is frequency independent, avoiding the PLL in the control circuit. Therefore the synchronising problems associated with unbalanced and distorted conditions of main voltages are eliminated. Thus SRF control strategy is limited only by the cut off frequency of the Voltage Source Inverter (VSI). In order to maintain constant DC link voltage, the real power flowing into the active power filter needs to be controlled equal to the losses inside the filter. In order to maintain constant DC link voltage, we have developed PI controller and Fuzzy Logic Controller. We have used three-phase voltage source PWM converter to generate reference compensating currents. Hysteresis based current control technique has been implemented to obtain the control signal for the switching devices of the APF.

This paper is organised as follows: Section II deals with Basic Architecture of SHAF; Section III deals with reference current determination using SRF method; Section IV discusses with Hysteresis current control of VSI for generation of filter currents; Section V deals with DC link voltage regulation using PI controller; Section VI deals with basics of FLC; Section VII deals with DC link voltage regulation with FLC and section VIII deals with simulation results; Section IX deals with THD analysis and finally conclusion is given in section-X.

II. BASIC ARCHITECTURE OF SHAF

Shunt Active Filter [2] is used to mitigate current harmonics in three-phase three-wire power system with balanced non-linear load. Fig. 1 shows the basic block diagram of SHAF. A three phase balanced sinusoidal voltage source is connected to a non-linear load through a transmission line. The load current is non-sinusoidal (IL). Shunt Active Filter injects filter current (If) such that the source current (Is) is sinusoidal. The Shunt Active Filter consists of a three-phase PWM Voltage Source Inverter, generating filter currents. The gating signals of IGBT switches of VSI are generated using hysteresis controller. Reference filter currents are the harmonic component of load currents, estimated using SRF control strategy. DC link voltage of VSI is maintained constant using PI or FLC for satisfactory performance of the filter. Fig. 2 shows the entire shunt active filtering using SRF strategy. The DC link voltage of the VSI is to be maintained constant in order to obtain satisfactory operation of the active filter. The actual voltage of the DC link capacitor is compared with the reference voltage and the error signal is used by the PI or Fuzzy Logic Controller to


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control the active power component flowing into the filter, maintaining the DC link voltage at the reference value.

Fig.1 Block Diagram of Shunt Active Filter

Fig.2 Shunt Active Filtering with SRF method

III. REFERENCE CURRENT DETERMINATION USING SRF CONTROL STRATEGY

Control methods of Shunt Active Filter in the time domain are based on instantaneous derivation of compensating currents from distorted or harmonic polluted load current signals. The SRF strategy, also known as the Instantaneous active reactive current control strategy (Id-Iq) [3-5] is used in this research paper. In this method, current signals are transformed into an SRF, in which fundamental quantities become DC quantities and then harmonic compensation currents are estimated. Advantages of SRF method is that it is independent of harmonics frequency and also provides reactive power compensation. Fig. 3 shows reference current extraction with SRF strategy using PI or FLC.


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Fig.3. SRF approach for extraction of reference filter currents using PI or FLC.

In this approach, Load currents are sensed using CTs. Load currents in phase a, b and c are transformed into d-q components using Park’s transformation. The formula for conversion from a,b,c to d-q reference frame using Parks transformation is shown in eq. 1.

(1)

Where w=2*pi*f, where f is the synchronous or fundamental frequency. The ILo of the load current along zero-component of the d-q-o reference frame is not considered as it is a three phase three wire system. Each current component (ILd, ILq), as shown in eq. 2 has an average value or DC component and an oscillating value or AC component.

; (2)

The compensation strategy of SAF for harmonic reduction and reactive power compensation assumes that the source must only deliver the mean value of the direct-axis component of the load current. Therefore, the reference filter current will be given by eq. 3 and 4. (3)

(4) Where represents the average or dc component and represents oscillating component of d axis load current. The negative sign in eq. 3 and 4 are used to cancel out harmonics and reactive power component of the load current. The power loss component of the DC bus is regulated using PI or Fuzzy controller and the loss correction component Ik is added to . This will be discussed in detail in the next sections. Therefore the reference filter currents, considering the DC voltage regulation are given in eq. 4 and 5.

(5)

The reference filter currents are transformed into a, b, c components using Inverse Park’s transformation. The formula for inverse Park’s transformation of reference filter currents is given in eq. 6.

(6)

Where w=2*pi*f; f=fundamental frequency.

The reference filter currents must be controlled using a current limiter to the large amount of currents during load variation. The filter currents are then generated using a VSI [6].

IV. FILTER CURRENT GENERATION USING HYSTERESIS CURRENT CONTROL OF VSI.

Current control of PWM converters is one of the most important techniques of power electronics due to its extremely good dynamics and high accuracy. The Hysteresis band current control (HCC) is characterised by unconditioned stability, very fast response and good accuracy. In HCC, the actual filter currents are


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monitored instantaneously and compared to the reference filter currents (eq.6) estimated using SRF strategy. Fig. 4 shows the control strategy used in HCC.

Fig.4 HCC for generation of switching pulses.

When the error exceeds the positive tolerance value, the upper IGBT switch of VSI is turned off and the lower switch is turned on so that the actual current decreases and the error decreases. Similarly, when the error exceeds negative tolerance value, the upper IGBT switch is turned on and the lower switch is turned off. Hence the actual filter current is forced to track the reference current within the hysteresis band. The upper and the lower switches in one leg of VSI are switched in complimentary manner to avoid short circuit across the DC bus. Fig. 5 shows the block diagram of HCC technique for generation of switching pulses and filter currents in SHAF. In this scheme, each phase of the converter is controlled independently with three hysteresis comparators in a manner that reduces the error between the reference and actual currents.

Fig. 5 Generation of Filter Currents using HCC.

V. DC LINK VOLTAGE REGULATION OF SHAF USING PI CONTROLLER. APF adapts to changes in the network and load parameters. It is controlled to supply compensating currents to cancel out load harmonics as well as to control the reactive power flow making source current in phase with the source voltage. When the load changes the real power balance between the supply and the load will be disturbed. This real power difference is compensated by using DC capacitor of the VSI. Due to this the error voltage between reference DC link voltage and actual DC link voltage increases. For satisfactory operation of the SHAF, the reference filter current must be adjusted to proportionately change the real power drawn from the source. The real power absorbed or delivered by the capacitor compensates the power difference between the load and the source and also accounts for the losses in the filter. If the actual DC link voltage is recovered to its reference value, then real power supplied by the source equals the power consumed by the load. DC link voltage can be maintained by using PI Controller as shown in Fig. 6.

Fig.6. DC Voltage Regulation of SHAF using PI Controller.

The actual DC link voltage is compared with the reference value by control circuit and the error (E) is fed to PI controller. The PI controller estimates the amount of active current (Ik) needed to attain constant DC link


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voltage. It is used as a part of the reference filter current, which is generated using a VSI [7] with hysteresis controller.

VI. INTRODUCTION TO FUZZY LOGIC CONTROLLERS.

The concept of Fuzzy Logic was introduced by Professor Lofti Zadeh in 1965 as a way of processing data by allowing partial set Membership Functions rather than crisp membership [8]. In this research paper, we have compared the performance of FLC with PI controller. FLC is advantageous over PI controller as it does not require an accurate mathematical model, can work with imprecise inputs, can handle non-linearity and is more robust. The block diagram of FLC is shown in Fig. 7, and it involves three main steps: Fuzzification, Fuzzy Inference System and De-fuzzification.

Fig.7. Block diagram of FLC

Fuzzification involves conversion of crisp input values into membership functions, where the membership of an input value in a Fuzzy set is indicated by its membership grades. Fuzzy sets, expressed in terms of MFs describe the fuzzy variables. Fig. 8 shows Triangular membership function.

Fig. 8 Triangular MF.

The mathematical representation of Triangular MF is given in eq. 7.

(7)

Fig. 9 shows input variable expressed as Trapezium MF.

Fig. 9 Trapezium MF

The mathematical representation of Trapezium MF is given in eq. 8


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(8)

Fig.10 shows Gaussian MF. The mathematical representation of Gaussian MF is given in eq. 9. ) (9)

Where c=centre; m=fuzzification factor; and .

The inputs are error and change in error in the DC link voltage and the output is active current component in the d-axis needed to attain constant DC link voltage.

Fig.10 Gaussian MF.

In this research paper, we have considered Triangular, Trapezium and Gaussian MFs. For better performance of FLC, each of the input and output variables are characterised by seven Fuzzy sets namely, Negative Big (NB), Negative Medium (NM), Negative Small (NS), Zero Error (ZE), Positive Small (PS), Positive Medium (PM), Positive Big (PB). Fig. 11 shows the input-‘error’ expressed in Triangular Fuzzy sets. The seven membership functions are same for inputs and outputs each time.

Fig.11 7X7 Triangular MF. Similarly, both the inputs- error, change in error and the output are expressed in Triangular, Trapezium and Gaussian MFs respectively. FIS consists of rule base, data base and reasoning mechanism. Rule base consists of selection of conditional rules to be followed by the FLC based on its inputs. Table 1 shows the rule base used in this research paper.

E/∆E NB NM NS Z PS PM NB

NB NB NB NB NB NM NM Z

NM NB NB NB NM NS Z PS

NS NB NB NM NS Z PS PM

Z NB NM NS Z PS PM PB

PS NM NS Z PS PM PB PB

PM NS Z PS PM PB PB PB

PB Z PS PM PB PB PB PB

Table 1. Rule base.

( )xA


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A rule base is constructed to control the output variable. A fuzzy rule is a simple IF-THEN rule with a condition and a conclusion. Data base defines the membership functions used in the Fuzzy rules. Reasoning mechanism performs the inference procedure upon the rules and given inputs to derive required output. We have used Mamdani FIS using max-min composition scheme i.e. aggregation is maximum operation and implication is minimum operation. The output of Fuzzy Logic systems is generally in Fuzzy values. But Fuzzy controllers generally need crisp outputs. Therefore Fuzzy values are converted into crisp values by defuzzification techniques. Fig. 12 shows various defuzzification techniques generally employed.

Fig.12 De-fuzzification methods.

In this research paper, we have considered Centroid of Area (COA) method of de-fuzzification. It returns the centroid of are under the curve. The Mathematical representation of COA is given in eq. 10.

(10)

VII. DC LINK VOLTAGE REGULATION OF SHAF USING FLC. The DC link voltage regulation of SHAF using FLC is shown in Fig. 13. In this method, the actual DC link voltage is compared with the reference voltage. The error and change in error signals are inputs to FLC. The FLC converts the crisp inputs into Fuzzy inputs through Fuzzification, estimates the output signal based on the rule base, data base and reasoning mechanism and provides crisp outputs through de-fuzzification. We have considered centroid method of de-fuzzification. The output of FLC (Ik), used as a part of reference filter currents (If*), is the active current component needed to maintain constant DC link voltage. The filter currents are generated using a VSI with hysteresis controller.

Fig. 13 DC Voltage regulation with FLC

VIII. RESULTS AND ANALYSIS.

8.1 Without Filter:

Initially, the system performance is analysed without using filter. Fig. 14a, 14b, 14c, 14d, 14e and 14f show source voltage, load current, compensation current, source current, DC link voltage and THD of source current respectively. Three phase balanced sinusoidal voltage is shown in Fig. 14(a). The load current of system is non-sinusoidal due to non-linear load which is shown in Fig.14 (b).


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0 0.005 0.01 0.015 0.02 0.025 0.03 0.035 0.04-400

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Time (sec)

Sour

ce V

olta

ge (v

olt)

Source Voltage

Fig.(14a) Source Voltage.

0.2 0.25 0.3 0.35 0.4 0.45 0.5-40

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Load CurrentLoad current under increased load condition

Load current under light load condition

Fig.(14b) Load Current

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Filter Current under Disconnected condition

Fig.(14c) Filter Current Without Filter

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Fig.(14d) Source Current Without Filter


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0 0.1 0.2 0.3 0.4 0.5 0.6 0.7-1

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Fig.(14e) DC link voltage Without Filter

0 5 10 15 20 25 30 35 400

5

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20

Harmonic order

THD= 30.59%

Mag

(% o

f Fun

dam

enta

l)

Fig. (14f) THD of source current without filter

Fig. 14. 3-phase, 3-wire system response without filter.

The load is kept constant from t=0s to t=0.4s. The load is doubled at t=0.4s and then kept constant at the increased value from t=0.4s to 0.7s. Due to absence of filter there is no compensation current (Fig.14c). Due to this, the source current (Fig.14d) is same as load current without harmonic compensation. The real power exchange with the filter is zero and hence DC link voltages is zero (Fig.14e). Fig.14f shows the THD of source current without filter. It can be seen that the source current has a large THD of 30.59%. As per IEEE standards, the THD must be below 5%. So to reduce the harmonics and to maintain the THD within the limits we have developed PI controller based SHAF. 8.2 PI controller based SHAF:

Source voltage and load current remain the same. Fig. 15a, 15b, 15c, 15d and 15e show filter current, source current, DC link voltage and THD of source current under normal and increased load respectively.

0.2 0.25 0.3 0.35 0.4 0.45 0.5-60

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Filte

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Filter Current with PI Controllar

Filter Current under lncreaseload condition

No Filter

Filter Current underlight load condition

Fig. (15a) Filter Current with PI based SHAF.


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Source Current with PI Controllar

source current with filterunder light load condition

source current without filterunder light load condition

source current with filter underIncrease load condition

Fig. (15b) Source Current with PI based SHAF.

0 0.1 0.2 0.3 0.4 0.5 0.6 0.70

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DC

_LIn

k Vo

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DC Link Voltage with PI Controllar

Fig. (15c) DC link Voltage with PI based SHAF.

0 5 10 15 20 25 30 35 400

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THD= 4.51%

Mag

(% o

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Fig. (15d) THD with PI based SHAF under normal load condition.

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Fig. (15e) THD with PI based SHAF under increased load condition.

Fig.15 System response with PI based SHAF.


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Fig. 15a shows the compensation current of the filter. The filter is connected to the system under two different load conditions. Initially it is connected from t=0s to 0.3s under light load condition. It is disconnected from t=0.3s to 0.4s. It is reconnected from t=0.4s to 0.7s to see its performance with increased load. Fig. 15b shows the source current. It can be seen that the source current is sinusoidal whenever filter is connected to the system. It is non-sinusoidal when the filter is disconnected. Fig. 15c shows the DC link voltage. The DC link voltage is close to the value of reference voltage. There is a fall in DC link voltage from t=0.3s to 0.4s since the filter is disconnected from the supply and the capacitor discharges through snubber resistances of the inverter switches. Note that there is an overshoot in DC link voltage with PI controller with increased load. Figures 15d and 15e show that the THD of source current reduced from 30.68% to 4.51% under normal load and 4.08% under increased load condition using SJAF with PI controller. The THD levels are within the IEEE standards 519. 8.3 FLC Triangular MF based SHAF:

In order to further reduce the THD, we have developed an FLC triangular MF based SHAF. Figures 16a, 16b, 16c, 16d and 16e show filter current, source current, DC link voltage, THD of source current under normal load and increased load conditions respectively. It can be seen that the performance of FLC based SHAF is better than that of PI based SHAF. Fig.16a shows that under increased load, source current in FLC based SHAF reaches steady state faster than that of PI based SHAF.

0.2 0.25 0.3 0.35 0.4 0.45 0.5-60

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Filte

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Filter Current with FLC with Triangular MF

Filter Current under lightload condition

Filter Current under lncreaseload condition

N0 Filter

Fig. (16a) Filter current with triangular FLC.

0.2 0.25 0.3 0.35 0.4 0.45 0.5-100

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Source Current with FLC with Triangular MF

Source Current with Filterunder light load condition

Source Current without Filterunder light load condition

Source Current with Filterunder lncrease load condition

Fig. (16b) Source Current with triangular FLC.

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Fig. (16c) DC link voltage with triangular FLC.


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0 5 10 15 20 25 30 35 400

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THD= 3.70%

Mag

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Fig. (16d) THD with FLC Triangular MF based SHAF under normal load condition.

0 5 10 15 20 25 30 35 400

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THD= 3.40%

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Fig. (16e) THD with FLC Triangular MF based SHAF under increased load condition.

Fig.16 System response with FLC Gaussian MF based SHAF.

The steady state error in DC link voltage is lesser and the transient response of DC link voltage (Fig.16c) has improved using SHAF with Triangular MF. The THD has reduced to 3.7% under normal load and 3.4% under increased load using Triangular MF. 8.4 FLC Trapezium MF based SHAF:

The performance of FLC based MF with Trapezium MF is shown in Figure 17. Fig.18a, 18b, 18c, 18d and 18e show filter current, source current, DC link voltage, THD of source current under normal load and THD of source current with increased load respectively. It can be seen that the performance of FLC with Trapezium MF based SHAF is better than that of PI and FLC Triangular MF based SHAF. The Source is more sinusoidal in nature. The DC link voltage is closer to the reference value. The THD reduced to 3.63% under normal load and 3.31% under increased load condition.

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Filter Current with FLC with Trapezodial MF

No Filter

Filter current under lncrease load conditionFilter current under light

load condition

Fig. (17a) Filter Current with trapezoidal FLC.


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source current with filter underlight load condition

source current with filter underincrease load condition


Fig. (17b) Source Current with trapezoidal FLC.

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Fig. (17c) DC link Voltage with trapezoidal FLC.

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THD= 3.63%

Mag

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Fig. (17d) THD with FLC Trapezium MF based SHAF under normal load condition.


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0 5 10 15 20 25 30 35 400

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10

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THD= 3.31%

Mag

(% o

f Fun

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enta

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Fig. (17e) THD with FLC Trapezium MF based SHAF under increased load condition.

Fig.17 System Performance with FLC Trapezium based SHAF.

8.4 FLC Gaussian MF based SHAF: Figure 19 shows the performance of SHAF with Gaussian MF. Figures 19a, 19b, 19c, 19d and 19e show Filter current, Source Current, DC link voltage, THD of source current with normal load and THD of source current with increased load respectively. The source current is more sinusoidal in nature and reached steady state faster with FLC Gaussian MF based SHAF. The DC link voltage attained reference value quickly and with least steady state error. The THD of source current has reduced to 3.55% under normal load and 3.28% under increased load.

0.2 0.25 0.3 0.35 0.4 0.45 0.5-60

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Filte

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Filter Current with FLC with Gaussian MF

No Filter

Filter current underlight Load condition

Filter current underlncreased Load condition

Fig. (18a) Filter Current with Gaussian FLC.

0.2 0.25 0.3 0.35 0.4 0.45 0.5-100

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Source Current with FLC with Gaussian MF


source current with filter underincreased load load condition

source current with filter under light load condition

Fig. (18b) Source Current with Gaussian FLC.


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0 0.1 0.2 0.3 0.4 0.5 0.6 0.70

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DC

_Lin

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Fig. (18c) DC link Voltage with Gaussian FLC.

0 5 10 15 20 25 30 35 400

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THD= 3.55%

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Fig. (18d) THD with FLC Gaussian MF based SHAF under normal load condition.

0 5 10 15 20 25 30 35 400

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THD= 3.28%

Mag

(% o

f Fun

dam

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Fig. (18e) THD with FLC Gaussian MF based SHAF under increased load condition.

Fig.18 System response with FLC Gaussian MF based SHAF.

IX. CONCLUSION Nonlinear loads introduce large amount of harmonics into power system. Without SHAF, source current is highly distorted/non-sinusoidal. To improve the THD, we have developed a PI controller based SHAF. The THD reduced to within IEEE limits. Further to reduce the THD, we have designed FLC based SHAF with Triangular, Trapezium and Gaussian MFs. The performance of FLC based SHAFs are found to be superior to PI controller based SHAF. Fig. 20 shows the bar graph of THD analysis of source current under different load conditions. Fig.21 shows the line graph representation of THD analysis of source current under different load conditions.


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Fig.20 Bar graph THD analysis.

Fig.21 Line graph THD analysis.

It can be seen that the THD of Source current reduced from 30.68% in case of without filter to 4.51% with normal load and 4.08% with increased load with PI based SHAF. The THD further reduced to 3.70% with FLC Triangle, 3.63% with Fuzzy Trapezium and 3.55% with Fuzzy Gaussian MF based SHAF under normal load conditions. Similarly the THD is reduced to 3.4% with Fuzzy Triangular MF, 3.31% with Fuzzy Trapezium and 3.28% with Fuzzy Gaussian MF based SHAF. The THD of source current is less than 5% in all the above cases with SHAF as per the IEEE standards 519. System Parameters: The following are the system parameters used

System Parameter Value Supply Voltage(phase) 220 V rms

Source Resistance 0.0001mΩ Source Inductance 0.01 mH

DC link capacitance 3000 µF DC link voltage 800 V Hysteresis Band 0.05

Load Diode Rectifier Snubber Resistance 500 Ω

Load Resistance 30 Ω Load Inductance 60 mH


450


REFERENCE

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[4] V. Soares, P. Verdelho and G. D. Marques, “An Instantaneous Active and Reactive Current Component Method for Active Filters,” IEEE Trans. Power Electron.,Vol. 15, No. 4, pp. 660-669, 2000.

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[6] J. L. Willems, “Current compensation in three-phase power systems,” Eur. Trans. Elect. Power Eng., vol. 3, no. 1, pp. 61–66, Jan./Feb.1993.

[7] Suresh Mikkili, A. K. Panda, “PI and Fuzzy Logic Controller based 3-phase 4-wire Shunt active filter for mitigation of Current harmonics with Id-Iq Control Strategy,” Journal of power Electronics (JPE), vol. 11, No. 6, Nov. 2011.

[8] M. Takeda, K. Ikeda, and Y. Tominaga, “Harmonic current compensation with active filter,” in Proc. 1987 IEEUlAS Annual Meeting, 1987.

[9] Parmod Kumar, and Alka Mahajan, “Soft Computing Techniques for the Control of an Active Power Filter,” IEEE Transactions on Power Delivery, Vol. 24, No. 1, Jan. 2009.

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