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Shiuly Mukherjee et al Int. Journal of Engineering Research and Applications www.ijera.com 
ISSN : 2248-9622, Vol. 4, Issue 7( Version 2), July 2014, pp.60-63 
www.ijera.com 60 | P a g e 
Power System Harmonic Compensation Using Shunt Active Power Filter. Shiuly Mukherjee1, Nitin Saxena2, A K Sharma3 1,2,3Jabalpur Engineering College, Jabalpur, Madhya Pradesh, India. Abstract This paper shows the method of improving the power quality using shunt active power filter. The proposedtopic comprises of PI controller, filter hysteresis current control loop, dc link capacitor. The switching signal generation for filter is fromhysteresis current controller techniques. With the all these element shunt active power filter reduce the total harmonic distortion. Thispaper represents the simulation and analysis of the using three phase three wire system active filter to compensate harmonics .Theproposed shunt active filter model uses balanced non-linear load. This paper successfully lowers the THD within IEEE norms and satisfactorily works to compensatecurrent harmonics. Keywords-Power system Harmonics, shunt active filters, power quality, non linear loads 
I. Introduction 
Shunt technology has brought drastic increase in the use of power electronic equipments resulting in the increase of harmonics in source current or ac mains current. intensive use of power converters, various non linear loads and increasing use of office equipments like computers ,faxes ,printers are reasons for the increasing harmonics resulting in deterioration if sources current and source voltage. Harmonics causes very serious damage in powers system. Problems like resonance; overheating of neutral wire, low power factor, damaging microprocessor based equipment. Traditionally, L-C passive filters were used to solve the problem of harmonics to filter out current harmonics to get sinusoidal supply current .Passive filters are classified as single tune filter and high pass filter. To overcome the problems of passive filters, active filters were developed and used to solve the problem of harmonics the technology of the active filter has improved a lot thereby giving very good results to reduce the problem of harmonics. The power semiconductor devices improved the active filters a lot. Active filters solve the problem of harmonic in industrial area as well as utilityPower distribution. The active power filter working performance is based on the techniques used for the generation of reference current. With the development various technologies results the lowering of harmonics below 5% as specifies by IEEE. Efficient ways of generating reference current are p-q theory, synchronous reference current theory (SRF method). In this paper SRF method has been used. We have many current control technologies for active power filter, but theHysteresis current controller is proved to be very efficient in terms of fast current controllability and it also very easy to 
apply when compared to other method like sinusoidal PWM. We can detect harmonics in two ways or two main forms first in time domain and second in the frequency domain the paper deals with Fast Fourier Transform (FFT) is used to find harmonics in frequency domain. Other frequency domain techniques are discrete Fourier transform (DFT); recursive discrete Fourier transform (RDFT).our main target is to reduce THD of supply current with the help of hysteresis band current controller. There are two type of hysteresis Current controller namely, adaptive hysteresis current controller and fixed band current controller. Our paper deals with the use of fixed band hysteresis current controller. The model of shunt active power filter using hysteresis current controller has been used in mat lab/simulink. Results have been successfully retrieved from model and followed by conclusion. 
II. Shunt Active Power Filter 
The large scale use of power electronics equipment has led to increase in harmonics in the power system. The nonlinear loads generate harmonic current which distorts the voltage waveform at PCC. These current harmonics will result in a power factor reduction, decrease in efficiency, power system voltage fluctuations and communications interference [3]. So harmonics can be considered as a pollutant which pollutes the entire power system. Traditionally a bank of tuned LC filters was used as a solution for the problems caused by the system harmonics, since they are easy to design, have simple structure, low cost and high efficiency. [7] Phase advancers synchronous capacitors etc. were also employed for the power system quality enhancement. However traditional controllers have many drawbacks. It provides only 
RESEARCH ARTICLE OPEN ACCESS
Shiuly Mukherjee et al Int. Journal of Engineering Research and Applications www.ijera.com 
ISSN : 2248-9622, Vol. 4, Issue 7( Version 2), July 2014, pp.60-63 
www.ijera.com 61 | P a g e 
fixed compensation, generates resonance problems 
and are bulky in size [6]. To overcome these 
disadvantages, active power filters are introduced 
which compensate for the current harmonics and 
reduces the total harmonic distortion. The SAPF is 
connected in parallel with the line through a coupling 
inductor. Its main power circuit consists of a three 
phase three-leg current controlled voltage source 
inverter with a DC link capacitor. An active power 
filter operates by generating a compensating current 
with 180 degree phase opposition and injects it back 
to the line so as to cancel out the current harmonics 
introduced by the nonlinear load. This will thus 
suppress the harmonic content present in the line and 
make the current waveform sinusoidal. So the 
process comprises of detecting the harmonic 
component present in the line current, generating the 
reference current, producing the switching pulses for 
the power circuit, generating a compensating current 
and injecting it back to the line. In this paper a 
nonlinear load supplied by a three phase voltage 
source is projected. An active power filter is 
introduced in parallel to this system for the 
compensation of current harmonics caused by the 
nonlinear loads. Here SRF algorithm is used for the 
reference current extraction from the distorted source 
current, which is being explained in section II. The 
switching pulses for the power circuit are generated 
using the Hysteresis Current Control technique as 
explained in section III and is found to be very 
effective. Figure 1 shows a three phase shunt active 
power filter. 
Figure 1 three phase shunt active filter 
III. Working principle of Shunt APF 
The schematic diagram of the single phase load 
compensator is shown in Figure 25. In this diagram a 
voltage source is supplying a load that could be 
nonlinear as well. The point of connection of the load 
and the source is the point of common coupling 
(PCC). Since there is no feeder joining the source and 
the load, we shall designate the source to be stiff. 
Here the compensator consists of an H-bridge 
inverter and an interface inductor (Lf). The resistance 
Rf represents the resistance of the interface inductor 
due to its finite Q-factor as well as the losses in the 
inverter. One end of the compensator is connected at 
the PCC through the interface inductor while the 
other end is connected with the load ground. The dc 
side of the compensator is supplied by a dc capacitor 
Cdc. The inverter is expected to be controlled to 
maintain a voltage Vdc across the capacitor. Let us 
assume that the load is nonlinear and draws a load 
current has a poor power factor. The instantaneous 
load current then can be decomposed as 
iL = iLp + iLq + iLh …(1) 
Where iLp and iLq are respectively the real and 
reactive parts of the current required by the load and 
iLh is the harmonic current drawn by the load. The 
purpose of the compensator is to inject current ic 
such that it cancels out the reactive and harmonic 
parts of the load current. 
Now applying KCL at the PCC we get 
iL = is + ic => is = iL – ic …(2) 
We assume that the compensator operates in a 
hysteresis current control loop in which the 
compensator current tracks a reference current ic*. 
Let us now choose this reference current as 
ic* = iLq + iLh …(3) 
If the inverter accurately tracks this reference 
current, then the source current will be equal to the 
unity power factor current drawn by the load. Since 
the compensator does not draw any real current, the 
average power consumed by the compensator is zero. 
Figure 2: Basic Scheme of shunt active filter 
Implementation:- The hysteresis band current 
control (HBCC) technique is used for pulse 
generation in current controlled VSIs. The control 
method offers good stability, gives a very fast 
response, provides good accuracy and has got a 
simple operation [5]. The HBCC technique employed 
in an active power filter for the control of line current 
is shown in Figure 3. It consists of a hysteresis band 
surrounding the generated error current. The current 
error is obtained by subtracting the actual filter 
current from the reference current. The reference 
current used here is obtained by the SRF method as 
discussed earlier which is represented as Iabc*. The 
actual filter current is represented asIfabc. The error 
signal is then fed to the relay with the desired
Shiuly Mukherjee et al Int. Journal of Engineering Research and Applications www.ijera.com 
ISSN : 2248-9622, Vol. 4, Issue 7( Version 2), July 2014, pp.60-63 
www.ijera.com 62 | P a g e 
hysteresis band to obtain the switching pulses for the 
inverter. 
Figure 3: Hysteresis band current controller. 
The operation of APF depends on the sequence 
of pulse generated by the controller. Figure 4 shows 
the simulation diagram of the hysteresis current 
controller.A band is set above and below the 
generated error signal. Whenever this signal crosses 
the upper band, the output voltage changes so as to 
decrease the input current and whenever the signal 
crosses the lower band, the output voltage changes to 
increase the input current. Accordingly switching 
signals are generated. [5] 
Figure 4: Simulation diagram of hysteresis current 
control. 
The switching signals thus generated are fed to 
the power circuit which comprises of a three phase 
three leg VSI with a DC link capacitor across it. 
Based on these switching signals the inverter 
generates compensating current in phase opposition 
to the line current. The compensating current is 
injected back into the power line at the PCC and thus 
suppressing the current harmonics present in the line 
[1]. The overall simulation block diagram is shown in 
Figure 5. 
Figure 5: simulation diagram of shunt active filter 
IV. Simulation Results and Discussion 
The harmonic current compensation is 
implemented in a three-phase power system using a 
shunt active power filter. The rms value of source 
voltage of the system is set as 480V and a 
combination of three-phase universal bridge rectifier 
with an RLC load across it constitutes the nonlinear 
load which introduces the harmonics into the 
system.The source current waveform without filter in 
a-phase is shown in Figure 6. The Total Harmonic 
Distortion (THD) spectrum in the system without 
filter is shown in Figure 9, which indicate a THD of 
25.75%. The compensating current waveform in a 
phase is illustrated in Figure 8. The source current 
after the injection of compensating current is shown 
in Figure 10. The THD with active power filter 
included is observed to be 4.87% which is within the 
allowable harmonic limit. Figure 10 shows the THD 
spectrum with active power filter in the circuit. 
Fig. 6. Load current of the phase “a”. 
Fig. 7. Source current when the passive filter is 
connected. 
Fig. 8. Source current when the active filter is 
connected.
Shiuly Mukherjee et al Int. Journal of Engineering Research and Applications www.ijera.com 
ISSN : 2248-9622, Vol. 4, Issue 7( Version 2), July 2014, pp.60-63 
www.ijera.com 63 | P a g e 
Figure 9: THD spectrum without filter 
Figure 10: THD Spectrum with active power filter. 
V. Conclusions 
The SAPF explained in this paper compensate 
the line current harmonics generated due to the 
nonlinear loads in the system. HBCC technique used 
for the switching pulse generation was found to be 
effective and its validity is proved based on 
simulation results. Thus SAPF has been proved to be 
effective to keep the harmonic content in power lines 
within the permissible limit. 
References 
[1] S. Sivanagaraju, and V.C.Veera 
Reddy(2011), “Design of Shunt Active 
Power Filter to eliminate the harmonic 
currents and to compensate the reactive 
power under distorted and or imbalanced 
source voltages in steady state”, IJETTVol. 
2 Issue 3 
[2] Y. P. Obulesh and Y. KusumaLatha(2011), 
“Control strategy for 3phase shunt active 
power filter with minimum current 
measurements”, IJECE 
[3] A. Chandra and B. Singh (1999), “A Review 
on Active Filters for Power Quality 
Improvement”, IEEE Trans. on IET, 46,5 
[4] Kamal Al-Haddad andNassar M 
(2000),“Modeling and Nonlinear Control of 
Shunt Active Power Filter in the 
Synchronous Reference Frame”. IEEE Intl 
[5] Murat K. and EnginOzdhemier(2005), “An 
adaptive hysteresis band current controller 
for shunt active power filters”, Electric 
Power Systems Research, 73, pp113–119 
[6] G. Bhuvaneswariand Charles. S(2010), 
“Comparison of Three Phase Shunt Active 
Power Filter Algorithms”,IJCEE, 2, 
[7] G. Gurusamy and P.M. Balasubramaniam,. 
“Evaluation and Implementation of Three 
Phase Shunt Active Power Filter for Power 
Quality Improvement”, IJCE.Vol. 5, No. 7 - 
2012. 
[8] E. J. Acordi, A. Goedtel. and L. C. B. 
Nascimento, “A Study of Shunt Active Power 
Filters Applied to Three-Phase Four-Wire 
Systems”, ICREPQ’12 - Spain, 28 - 30 
March, 2012 
[9] H. Akagi, Y. Kanazawa, A. Nabae, 
Generalized Theory of the Instantaneous 
Reactive Power in Three-Phase Circuits, 
IPEC'83 - Int. Power Electronics Conf., 
Tokyo, Japan, 1983, pp. 1375-1386. 
[10] H. Akagi, Y. Kanazawa, A. Nabae, 
Instanataneous Reactive Power 
Compensator Comprising Switching Devices 
without Energy Storage Compenents”, IEEE 
Trans. Industry Applic., vol. 20, May/June 
1984. 
[11] E. H. Watanabe, R. M. Stephan, M. Aredes, 
New Concepts of Instantaneous Active and 
Reactive Powers in Electrical Systems with 
Generic Loads, IEEE Trans. Power 
Delivery, vol. 8, no. 2, April 1993, pp. 697- 
703. 
[12] M. Aredes, E. H. Watanabe, New Control 
Algorithms for Series and Shunt Three- 
Phase Four-Wire Active Power Filters, 
IEEE Trans. Power Delivery, vol 10, no. 3, 
July 1995, pp. 1649-1656. 
[13] J. Afonso, C. Couto and J. Martins, “Active 
Filters with Control Based on the p-q 
Theory”, IEEE Industrial Electronics 
Society Newsletter, vol. 47, nº 3, Set. 2000, 
pp. 5-10. 
[14] MATLAB: High-Performance Numeric 
Computation and Visualization Software – 
Reference Guide, The MathWorks Inc., April 
1993. 
[15] SIMULINK: The Dynamic System 
Simulation Software-User’s Guide, The 
MathWorks Inc., April 1993. 
[16] J. Afonso, “Filtro Ativo Paralelo com 
Controlo Digital para a Melhoria da 
Qualidade de Energia Eléctrica”, Ph.D. 
dissertation, University of Minho, 2000. 
[17] J. Afonso, M. Aredes, E. Watanabe e J. 
Martins, “Shunt Active Filter for Power 
Quality Improvement”, Conference UIE 
2000, Lisboa, 2000, pp. 683- 691.

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Power System Harmonic Compensation Using Shunt Active Power Filter

  • 1. Shiuly Mukherjee et al Int. Journal of Engineering Research and Applications www.ijera.com ISSN : 2248-9622, Vol. 4, Issue 7( Version 2), July 2014, pp.60-63 www.ijera.com 60 | P a g e Power System Harmonic Compensation Using Shunt Active Power Filter. Shiuly Mukherjee1, Nitin Saxena2, A K Sharma3 1,2,3Jabalpur Engineering College, Jabalpur, Madhya Pradesh, India. Abstract This paper shows the method of improving the power quality using shunt active power filter. The proposedtopic comprises of PI controller, filter hysteresis current control loop, dc link capacitor. The switching signal generation for filter is fromhysteresis current controller techniques. With the all these element shunt active power filter reduce the total harmonic distortion. Thispaper represents the simulation and analysis of the using three phase three wire system active filter to compensate harmonics .Theproposed shunt active filter model uses balanced non-linear load. This paper successfully lowers the THD within IEEE norms and satisfactorily works to compensatecurrent harmonics. Keywords-Power system Harmonics, shunt active filters, power quality, non linear loads I. Introduction Shunt technology has brought drastic increase in the use of power electronic equipments resulting in the increase of harmonics in source current or ac mains current. intensive use of power converters, various non linear loads and increasing use of office equipments like computers ,faxes ,printers are reasons for the increasing harmonics resulting in deterioration if sources current and source voltage. Harmonics causes very serious damage in powers system. Problems like resonance; overheating of neutral wire, low power factor, damaging microprocessor based equipment. Traditionally, L-C passive filters were used to solve the problem of harmonics to filter out current harmonics to get sinusoidal supply current .Passive filters are classified as single tune filter and high pass filter. To overcome the problems of passive filters, active filters were developed and used to solve the problem of harmonics the technology of the active filter has improved a lot thereby giving very good results to reduce the problem of harmonics. The power semiconductor devices improved the active filters a lot. Active filters solve the problem of harmonic in industrial area as well as utilityPower distribution. The active power filter working performance is based on the techniques used for the generation of reference current. With the development various technologies results the lowering of harmonics below 5% as specifies by IEEE. Efficient ways of generating reference current are p-q theory, synchronous reference current theory (SRF method). In this paper SRF method has been used. We have many current control technologies for active power filter, but theHysteresis current controller is proved to be very efficient in terms of fast current controllability and it also very easy to apply when compared to other method like sinusoidal PWM. We can detect harmonics in two ways or two main forms first in time domain and second in the frequency domain the paper deals with Fast Fourier Transform (FFT) is used to find harmonics in frequency domain. Other frequency domain techniques are discrete Fourier transform (DFT); recursive discrete Fourier transform (RDFT).our main target is to reduce THD of supply current with the help of hysteresis band current controller. There are two type of hysteresis Current controller namely, adaptive hysteresis current controller and fixed band current controller. Our paper deals with the use of fixed band hysteresis current controller. The model of shunt active power filter using hysteresis current controller has been used in mat lab/simulink. Results have been successfully retrieved from model and followed by conclusion. II. Shunt Active Power Filter The large scale use of power electronics equipment has led to increase in harmonics in the power system. The nonlinear loads generate harmonic current which distorts the voltage waveform at PCC. These current harmonics will result in a power factor reduction, decrease in efficiency, power system voltage fluctuations and communications interference [3]. So harmonics can be considered as a pollutant which pollutes the entire power system. Traditionally a bank of tuned LC filters was used as a solution for the problems caused by the system harmonics, since they are easy to design, have simple structure, low cost and high efficiency. [7] Phase advancers synchronous capacitors etc. were also employed for the power system quality enhancement. However traditional controllers have many drawbacks. It provides only RESEARCH ARTICLE OPEN ACCESS
  • 2. Shiuly Mukherjee et al Int. Journal of Engineering Research and Applications www.ijera.com ISSN : 2248-9622, Vol. 4, Issue 7( Version 2), July 2014, pp.60-63 www.ijera.com 61 | P a g e fixed compensation, generates resonance problems and are bulky in size [6]. To overcome these disadvantages, active power filters are introduced which compensate for the current harmonics and reduces the total harmonic distortion. The SAPF is connected in parallel with the line through a coupling inductor. Its main power circuit consists of a three phase three-leg current controlled voltage source inverter with a DC link capacitor. An active power filter operates by generating a compensating current with 180 degree phase opposition and injects it back to the line so as to cancel out the current harmonics introduced by the nonlinear load. This will thus suppress the harmonic content present in the line and make the current waveform sinusoidal. So the process comprises of detecting the harmonic component present in the line current, generating the reference current, producing the switching pulses for the power circuit, generating a compensating current and injecting it back to the line. In this paper a nonlinear load supplied by a three phase voltage source is projected. An active power filter is introduced in parallel to this system for the compensation of current harmonics caused by the nonlinear loads. Here SRF algorithm is used for the reference current extraction from the distorted source current, which is being explained in section II. The switching pulses for the power circuit are generated using the Hysteresis Current Control technique as explained in section III and is found to be very effective. Figure 1 shows a three phase shunt active power filter. Figure 1 three phase shunt active filter III. Working principle of Shunt APF The schematic diagram of the single phase load compensator is shown in Figure 25. In this diagram a voltage source is supplying a load that could be nonlinear as well. The point of connection of the load and the source is the point of common coupling (PCC). Since there is no feeder joining the source and the load, we shall designate the source to be stiff. Here the compensator consists of an H-bridge inverter and an interface inductor (Lf). The resistance Rf represents the resistance of the interface inductor due to its finite Q-factor as well as the losses in the inverter. One end of the compensator is connected at the PCC through the interface inductor while the other end is connected with the load ground. The dc side of the compensator is supplied by a dc capacitor Cdc. The inverter is expected to be controlled to maintain a voltage Vdc across the capacitor. Let us assume that the load is nonlinear and draws a load current has a poor power factor. The instantaneous load current then can be decomposed as iL = iLp + iLq + iLh …(1) Where iLp and iLq are respectively the real and reactive parts of the current required by the load and iLh is the harmonic current drawn by the load. The purpose of the compensator is to inject current ic such that it cancels out the reactive and harmonic parts of the load current. Now applying KCL at the PCC we get iL = is + ic => is = iL – ic …(2) We assume that the compensator operates in a hysteresis current control loop in which the compensator current tracks a reference current ic*. Let us now choose this reference current as ic* = iLq + iLh …(3) If the inverter accurately tracks this reference current, then the source current will be equal to the unity power factor current drawn by the load. Since the compensator does not draw any real current, the average power consumed by the compensator is zero. Figure 2: Basic Scheme of shunt active filter Implementation:- The hysteresis band current control (HBCC) technique is used for pulse generation in current controlled VSIs. The control method offers good stability, gives a very fast response, provides good accuracy and has got a simple operation [5]. The HBCC technique employed in an active power filter for the control of line current is shown in Figure 3. It consists of a hysteresis band surrounding the generated error current. The current error is obtained by subtracting the actual filter current from the reference current. The reference current used here is obtained by the SRF method as discussed earlier which is represented as Iabc*. The actual filter current is represented asIfabc. The error signal is then fed to the relay with the desired
  • 3. Shiuly Mukherjee et al Int. Journal of Engineering Research and Applications www.ijera.com ISSN : 2248-9622, Vol. 4, Issue 7( Version 2), July 2014, pp.60-63 www.ijera.com 62 | P a g e hysteresis band to obtain the switching pulses for the inverter. Figure 3: Hysteresis band current controller. The operation of APF depends on the sequence of pulse generated by the controller. Figure 4 shows the simulation diagram of the hysteresis current controller.A band is set above and below the generated error signal. Whenever this signal crosses the upper band, the output voltage changes so as to decrease the input current and whenever the signal crosses the lower band, the output voltage changes to increase the input current. Accordingly switching signals are generated. [5] Figure 4: Simulation diagram of hysteresis current control. The switching signals thus generated are fed to the power circuit which comprises of a three phase three leg VSI with a DC link capacitor across it. Based on these switching signals the inverter generates compensating current in phase opposition to the line current. The compensating current is injected back into the power line at the PCC and thus suppressing the current harmonics present in the line [1]. The overall simulation block diagram is shown in Figure 5. Figure 5: simulation diagram of shunt active filter IV. Simulation Results and Discussion The harmonic current compensation is implemented in a three-phase power system using a shunt active power filter. The rms value of source voltage of the system is set as 480V and a combination of three-phase universal bridge rectifier with an RLC load across it constitutes the nonlinear load which introduces the harmonics into the system.The source current waveform without filter in a-phase is shown in Figure 6. The Total Harmonic Distortion (THD) spectrum in the system without filter is shown in Figure 9, which indicate a THD of 25.75%. The compensating current waveform in a phase is illustrated in Figure 8. The source current after the injection of compensating current is shown in Figure 10. The THD with active power filter included is observed to be 4.87% which is within the allowable harmonic limit. Figure 10 shows the THD spectrum with active power filter in the circuit. Fig. 6. Load current of the phase “a”. Fig. 7. Source current when the passive filter is connected. Fig. 8. Source current when the active filter is connected.
  • 4. Shiuly Mukherjee et al Int. Journal of Engineering Research and Applications www.ijera.com ISSN : 2248-9622, Vol. 4, Issue 7( Version 2), July 2014, pp.60-63 www.ijera.com 63 | P a g e Figure 9: THD spectrum without filter Figure 10: THD Spectrum with active power filter. V. Conclusions The SAPF explained in this paper compensate the line current harmonics generated due to the nonlinear loads in the system. HBCC technique used for the switching pulse generation was found to be effective and its validity is proved based on simulation results. Thus SAPF has been proved to be effective to keep the harmonic content in power lines within the permissible limit. References [1] S. Sivanagaraju, and V.C.Veera Reddy(2011), “Design of Shunt Active Power Filter to eliminate the harmonic currents and to compensate the reactive power under distorted and or imbalanced source voltages in steady state”, IJETTVol. 2 Issue 3 [2] Y. P. Obulesh and Y. KusumaLatha(2011), “Control strategy for 3phase shunt active power filter with minimum current measurements”, IJECE [3] A. Chandra and B. Singh (1999), “A Review on Active Filters for Power Quality Improvement”, IEEE Trans. on IET, 46,5 [4] Kamal Al-Haddad andNassar M (2000),“Modeling and Nonlinear Control of Shunt Active Power Filter in the Synchronous Reference Frame”. IEEE Intl [5] Murat K. and EnginOzdhemier(2005), “An adaptive hysteresis band current controller for shunt active power filters”, Electric Power Systems Research, 73, pp113–119 [6] G. Bhuvaneswariand Charles. S(2010), “Comparison of Three Phase Shunt Active Power Filter Algorithms”,IJCEE, 2, [7] G. Gurusamy and P.M. Balasubramaniam,. “Evaluation and Implementation of Three Phase Shunt Active Power Filter for Power Quality Improvement”, IJCE.Vol. 5, No. 7 - 2012. [8] E. J. Acordi, A. Goedtel. and L. C. B. Nascimento, “A Study of Shunt Active Power Filters Applied to Three-Phase Four-Wire Systems”, ICREPQ’12 - Spain, 28 - 30 March, 2012 [9] H. Akagi, Y. Kanazawa, A. Nabae, Generalized Theory of the Instantaneous Reactive Power in Three-Phase Circuits, IPEC'83 - Int. Power Electronics Conf., Tokyo, Japan, 1983, pp. 1375-1386. [10] H. Akagi, Y. Kanazawa, A. Nabae, Instanataneous Reactive Power Compensator Comprising Switching Devices without Energy Storage Compenents”, IEEE Trans. Industry Applic., vol. 20, May/June 1984. [11] E. H. Watanabe, R. M. Stephan, M. Aredes, New Concepts of Instantaneous Active and Reactive Powers in Electrical Systems with Generic Loads, IEEE Trans. Power Delivery, vol. 8, no. 2, April 1993, pp. 697- 703. [12] M. Aredes, E. H. Watanabe, New Control Algorithms for Series and Shunt Three- Phase Four-Wire Active Power Filters, IEEE Trans. Power Delivery, vol 10, no. 3, July 1995, pp. 1649-1656. [13] J. Afonso, C. Couto and J. Martins, “Active Filters with Control Based on the p-q Theory”, IEEE Industrial Electronics Society Newsletter, vol. 47, nº 3, Set. 2000, pp. 5-10. [14] MATLAB: High-Performance Numeric Computation and Visualization Software – Reference Guide, The MathWorks Inc., April 1993. [15] SIMULINK: The Dynamic System Simulation Software-User’s Guide, The MathWorks Inc., April 1993. [16] J. Afonso, “Filtro Ativo Paralelo com Controlo Digital para a Melhoria da Qualidade de Energia Eléctrica”, Ph.D. dissertation, University of Minho, 2000. [17] J. Afonso, M. Aredes, E. Watanabe e J. Martins, “Shunt Active Filter for Power Quality Improvement”, Conference UIE 2000, Lisboa, 2000, pp. 683- 691.