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Research Article

LMS Algorithm Based Fundamental Current Detection for Shunt Hybrid Filter

R. Sriranjani and S. Jayalalitha
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An adaptive control technique is used to extract the fundamental current for the active filter. The Shunt Hybrid Filter (SHF) comprises passive filter (resonant filter) and active filter. The passive filter is tuned to suppress dominant harmonics and the active filter is tuned to reduce harmonics and reactive power of the supply mains. The Least mean Square (LMS) algorithm is used for implementing Hysteresis current control. The dc bus voltage is regulated using Proportional-Integral controller which improves the dynamic characteristics of SHF. The Shunt Hybrid filter with the dc bus voltage control is analysed by the MATLAB simulink and the results are compared.

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  How to cite this article:

R. Sriranjani and S. Jayalalitha, 2014. LMS Algorithm Based Fundamental Current Detection for Shunt Hybrid Filter. Journal of Applied Sciences, 14: 1612-1617.

DOI: 10.3923/jas.2014.1612.1617

Received: August 28, 2013; Accepted: December 18, 2013; Published: April 17, 2014


The growth of the power converters raises the issue of the power quality problems. The major power quality problem is the harmonics which distorts the supply voltage, derating the electrical equipment and there is a mal functioning of the protective devices (Bashi et al., 2006). This load also consumes reactive power from the mains. The bank of capacitors is connected to reduce the reactive power (Q) so that power factor is reduced. But there is harmonic amplification caused by the capacitor and the line impedance. The diode rectifier with boost converter improves the power factor (Bashi et al., 2005). But the THD does not meet the IEEE standard. The side filter such as passive filter and active filter reduces the harmonics as well as improves power factor (Vahedi, 2012). The Shunt Active Filter (SAF) was used to reduce the supply current harmonics and also minimizes Q. But the active filter cost is high and it is difficult to construct the filter with quick current response (Kouzou et al., 2010; Singh and Verma, 2006). Various hybrid filter topology was investigated in the recent years. The hybrid filters are connected to the supply line through a transformer. By removing the transformer, the expenditure of the active filter is reduced to 10% (Mattavelli, 2001). Series hybrid filter carriers the fundamental reactive current (iq) and the total harmonic current (Sriranjani and Jayalalitha, 2011). But in the Shunt hybrid filter (Rahmani et al., 2012) the SAF carries the (iq) and the other harmonic current. The dominant harmonic current is flowing in tuned passive filter which is connected to supply as shown in Fig. 1.

Fig. 1: Schematic representation of shunt hybrid filter

This study presents a SHF without transformer is used to decrease the rating of the SAF (Luo et al., 2009).

The control of active filter is done by detecting the harmonics by the theory of instantaneous reactive power or synchronous reference frame (Sriranjani and Jayalalitha, 2012a). This theory needs more computation and also Phase locked loop has many disadvantages. Many control strategy uses harmonic detection methods (Tao et al., 2009). In this study, the fundamental current is detected from the supply using Least mean square algorithm which simplifies the control circuit (Sriranjani and Jayalalitha, 2012b). There is no intermediate transformer between the supply line and the active filter. This reduces the cost of the filter design. The inverter losses are minimized by managing the dc bus voltage using PI.

Fig. 2: Shunt hybrid filter equivalent circuit

Hysteresis current controller based Shunt hybrid filter is analysed in MATLAB simulink.


Non linear load: The 3φ full bridge rectifier with RL load act as a non linear load which distorts the line current.

Source voltage is given by:


Due to the diode rectifier load, the supply current contains fundamental component and harmonics component:




I1 = Fundamental current
Ik-kth = Harmonic current
Vm = Peak supply voltage
ωs = Fundamental frequency at rad/sec
φk = Phase angle between the supply voltageand current of the kth harmonic component

Shunt hybrid filter: The Shunt Hybrid filter contains the passive filter which is tuned for the dominant harmonic frequency of the line current. The SAF provides the reactive power compensation and harmonic compensation. The equivalent circuit of the system is shown in Fig. 2. The switching ripples are reduced by the inductance coupled with the active filter.

The distorted current is given by:


For harmonic compensation and power factor improvement, the supply current should have the fundamental component and it should be in phase with the supply mains.

Thus the line current is:


where, Im is the maximum fundamental component current of the mains and ω1 is the supply frequency (50 Hz). In this study the resonant filter is tuned for the fifth order harmonic frequency:


where, Lr and Cr are the inductor and capacitor of the resonant filter.

The resonant filter current and the active filter current is given by:




where, Ir1 is the fundamental reactive current component, Id is the dominant harmonic current, d is the dominant harmonic order and Ihr represents the remaining harmonic component of the line current. n denotes the phase angle between the current and supply voltage. The Zpf is the passive filter tuned for the dominant frequency so that it will inject the ipf to the supply mains. The shunt active filter will inject the Ihr and Ir1 current so that the supply is free from harmonics and reactive power is minimized.

Reference current extraction: With the intention of tuning the active filter, the reference current at the fundamental frequency is extracted by the least mean square algorithm from the line current.

Fig. 3: Adaptive linear combiner

Fig. 4: Block diagram of generation of pulses for Mosfet

The distorted line current is filtered out by the adaptive linear combiner shown in Fig. 3. Pulse generation of SAF is shown in Fig. 4. In this proposed control circuit, the fundamental current is detected from the supply current.

The actual output is the fundamental current If determined by the LMS algorithm (Bernard and Stearns, 2002).

The harmonic current is:


The adaptive linear combiner with desired output and error signal is given by:




Fig. 5:
Comparison of supply current and reference current using hysteresis controller

Weight matrix is updated by:


where, εn is error signal, dn is the desired output, yn is the actual output and μ is gain constant. From Eq. 1, 3, 10 and 12:


So the fundamental current is extracted by updating the weight matrix wn+1.

Inverter dc bus voltage control: The capacitor is charged or discharged due to the switching of the Mosfet. The increasing of the capacitor voltage is limited by PI controller and while switching pattern are formed by considering the reference voltage of the dc bus shown in Fig. 4. This minimizes the losses of the inverter.


where, k is the controller gain and If is the fundamental reference current.

Hysteresis current control (HCC): The switching patterns for the each leg is obtained by comparing the instantaneous value of the line current and the fundamental current at supply frequency is shown in Fig. 5. The fixed band HCC is used because of fast response and high accuracy compare to PWM control (Abedi and Vahedi, 2013). The Switching pattern for leg -1, the upper switch is ON when the supply current is more than the reference current within the hysteresis band and the lower switch is ON when the supply current is less than the reference current.

Design of SAF: The ripples of the SAF is filtered by an inductor which is designed by:


Table 1: Specification shunt hybrid filter

Fig. 6: Supply voltage waveform

Fig. 7: Supply current waveform without filter

and the active filter capacitor is given by:


where, IL is load current, T is the switching period, V*dc is the reference active filter dc voltage. Vdc is the actual voltage.


Shunt Hybrid filter is simulated in Matlab. Power gui is used to measure THD. Here the full bridge rectifier with RL load is used and power is measured. The passive filter is designed in such way that it will reduce the Fifth order harmonics. Finally the SAF is connected and the power, power factor and harmonics are measured. The rating of the active filter is calculated. Table 1, shows Selection of parameters.


Figure 6 and 7 shows supply voltage waveform and the supply current waveform before the connection of SHF.

Fig. 8: Active filter current

Fig. 9:
Fifth order Harmonic current waveform of the passive filter

Fig. 10:
Suply crrunt waveform after compesation

The current waveform is distorted and the power factor is less than 0.95. Figure 8 and 9 shows the passive filter current waveform and active filter current waveform. The passive filter injects the fifth order harmonics to the load and the active filter injects the fundamental reactive current and other harmonic current. The HSAF gives near to unity power factor and reduces the current harmonics which is shown in Fig. 10. When the Hysteresis controlled SHF is connected, the supply is free from harmonics. Figure 11 and 12 shows the frequency spectrum of supply current before and after connection of the filter. The Total harmonic distortion of the line current is trim down from 20.85 to 0.15% and there is an improvement in power factor. The KVA rating of the active filter is 1.3 KVA. Figure 13 shows the dc bus voltage waveform. It finally settled to its reference dc voltage value. When the reference voltage is reduced below the set value (300 V), the harmonics are increased. Thus the shunt hybrid filter overcomes the drawbacks of the resonant filter and SAF.

Fig. 11(a-b): Frequency spectrum of the line current without SHF

Fig. 12(a-b): Frequency spectrum of the line current with SHF

Fig. 13: Dc bus voltage of the active filter

Table 2: Individual harmonics of the supply current

Table 2 shows the results of power, harmonics and power factor before and after the connection of SHF. The nonlinear load absorbs very high reactive power from the supply line. After the Shunt Hybrid filter is implemented in the supply line, the reactive power is reduced from 272 to 3 VAR. Thus the harmonic and reactive power compensation is done by Shunt Hybrid filter with LMS algorithm.


Using Hysteresis controlled Shunt Hybrid filter the reactive power and current harmonics becomes scanty. The Least mean square algorithm is used for extracting the fundamental reference current for hysteresis current control. By balancing the active filter dc voltage using the PI controller reduces the losses of SAF. The proposed filter achieves 0.99 power factor and current harmonics are reduced to less than 5%. The dominant harmonic of the supply current is five. So passive filter is tuned for the fifth order harmonics and SAF balances the reactive power and other harmonics. The burden of the SAF is very much diminished.

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13:  Sriranjani, R. and S. Jayalalitha, 2011. Improvement of the dc bus voltage of shunt active filter using controllers. Proceedings of the IEEE International Conference on Recent Advancements in Electrical, Electronics and Control, Engineering, December 15-17, 2011, Sivakasi, pp: 187-191.

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