This paper presents a power system harmonic elimination using the mixed adaptive linear neural network and variable stepsize leaky least mean square (ADALINEVSSLLMS) control algorithm based active power filter (APF). The weight vector of ADALINE along with the variable stepsize parameter and leakage coefficient of the VSSLLMS algorithm are automatically adjusted to eliminate harmonics from the distorted load current. For all iteration, the VSSLLMS algorithm selects a new rate of convergence for searching and runs the computations. The adopted shunthybrid APF (SHAPF) consists of an APF and a series of 7
^{th}
tuned passive filter connected to each phase. The performance of the proposed ADALINEVSSLLMS control algorithm employed for SHAPF is analyzed through a simulation in a MATLAB/Simulink environment. Experimental results of a realtime prototype validate the efficacy of the proposed control algorithm.
I. INTRODUCTION
Current harmonics have become a major issue in distribution network because of the wide power electronic device applications in the industry. To overcome the current harmonic related problems, passive filters are connected in different configurations that represent a low cost solution
[1]
,
[2]
. However, this mechanism has few drawbacks, such as resonance, size, instability, and inability to compensate for the changing harmonic current contents, which deject their implementation. To resolve these issues, an active filtering approach called active power filter (APF) was introduced as an advanced technique for harmonics elimination and reactive power compensation
[3]

[7]
. Nonetheless, the main disadvantage in using this approach is that the cost of power electronic inverters is high, especially for high power ratings. Morever, APF is difficult to implement in highvoltage applications. Another harmonic mitigation solution called shunthybrid APF (SHAPF) topology was investigated and introduced
[8]

[10]
. SHAPF is formed by the connection of an APF with one or more passive filters in a series. This type of configuration significantly reduces the rating. Passive filters absorb the harmonics injected by the nonlinear load and suppress the switching ripples generated from APF, which in turn enhances the filtering performance of the passive filter.
The generation of references in the form of voltage or current is the essential aspect of active filter control. The control strategies in frequencydomain include the fast Fourier method
[11]
, the Kalman filter
[12]
, and the wavelet transform. The frequencydomain approach requires large memory, slow response, and additional computational power. Moreover, this method may provide imprecise results during transient conditions. Timedomain approaches, such as dq and pq transformations, are based on the measurements and transformation of threephase quantities
[7]

[10]
. However, these three to twophase transformations fail to work properly under unbalanced conditions
[3]
,
[13]
. A recent study proposed a fast adaptive linear neural network (ADALINE) based timedomain approach for extracting the fundamentals from the distorted current
[3]

[6]
. The weights of ADALINE are generally updated using the least mean square (LMS) recursive algorithm
[14]

[16]
.
This algorithm is commonly used in signal processing and control system application because of its simplicity and robustness. The rate of convergence of LMS algorithm directly depends on the fixed stepsize parameter
[17]
. During steady state operations, a large stepsize leads to a large offset and fast convergence rate, whereas a small stepsize results in a slow convergence rate and small offset. These drawbacks can be addressed by implementing a time varying stepsize. In the variable stepsize LMS (VSSLMS) algorithm, stepsize is dynamically adjusted during convergence
[17]
,
[18]
.
The eigenvalue decomposition of the autocorrelation matrix sometimes produces a zero eigenvalue, which causes the LMS adaptive filter to have undamped modes. These modes make the system unstable and should therefore be pushed to zero. In this event, a leakage factor is introduced in the autocorrelation matrix
[19]

[21]
. Implementing a leaky adjustment technique makes the convergence rate faster than the conventional LMS algorithm in case of a high input eigenvalue spread.
In this study, a new design of SHAPF that employs mixed ADALINEVSSLLMS algorithm is proposed. Three ADALINEs in each phase are used to extract the harmonics and reactive components from the sensed load currents. A pulse width modulation control technique is used to generate gating pulses for the insulated gate bipolar transistors (IGBTs). Extensive simulations are conducted to emphasize the efficacy of the investigative results and the admirable performance of the proposed ADALINEVSSLLMS control algorithm. Finally, the results are verified by implementing the proposed control algorithm in realtime using a SPARTAN3A DSP processor.
The rest of the paper is organized into six sections. Following the Introduction, Section II describes the complete structure of SHAPF. Section III presents the mathematical equations of the proposed control algorithm. Section IV discusses the simulation results of SHAPF under different load conditions. Section V explains the development of a laboratory prototype model and the corresponding experimental results. Finally, Section VI describes the conclusion of the study.
II. SYSTEM DESCRIPTION
Fig. 1
shows the configuration of SHAPF. The lowrated APF and 7
^{th}
tuned passive filters are connected directly to the ACmains without using a coupling transformer. The 7
^{th}
tuned passive filter provides a lower impedance path for the 11
^{th}
and 13
^{th}
harmonic frequencies as compared to 5
^{th}
tuned passive filter, thereby resulting in a satisfactory filtering performance. Moreover, designing the 5
^{th}
tuned passive filter is heavy, bulky, and expensive than the 7
^{th}
tuned because of its large capacitance C
_{p}
value.
Structure of the threephase SHAPF.
APF is a threephase voltage source inverter consisting of six switches and a DClink capacitor (C
_{dc}
). A PI controller is employed to charge the DClink capacitor to the desired voltage level. The nonlinear load comprises a diode bridge rectifier followed by a capacitor with an inductive load (R
_{L}
, L
_{L}
). The SHAPF, which employs the proposed control technique, is designed to detect its harmonics and reactive components and inject a filter current identical with the load harmonic current. The threephase source voltages measured at the point of common coupling are (v
_{a}
, v
_{b}
, and v
_{c}
). The threephase source currents, threephase load currents, and threephase SHAPF currents are denoted as (i
_{sa}
, i
_{sb}
and i
_{sc}
), (i
_{La}
, i
_{Lb}
and i
_{Lc}
), and (i
_{fa}
, i
_{fb}
and i
_{fc}
), respectively.
III. MIXED ADALINEVSSLLMS BASED HARMONIC AND REACTIVE COMPONENT ELIMINATION
The load current i
_{La}
(t), including the harmonics, can be described using a Fourier series as follows:
where i
_{DC,a}
(t) is the fundamental or DC current component, and i
_{AC,a}
(t) is the sum of all harmonics or AC current components of the load current. If the reactive component is simultaneously compensated by APF, then i
_{DC,a}
(t) can be further divided into two terms shown below.
where i
_{xa}
(t) and i
_{ya}
(t) are the active and reactive components of the fundamental load current, respectively. Combining Eqs. (1) and (2) yields the following expression:
The compensating current component i
_{fa}
(t) can be derived as
where W = [w
_{1a}
, w
_{2a}
] is the weight vector of ADALINE.
Fig. 2
shows the block diagram of the ADALINEVSSLLMS control algorithm for reference signal generation. This algorithm is composed of two neurons whose weights w
_{1a}
(n) and w
_{2a}
(n) are updated online by the VSSLLMS algorithm. The input of each neuron is fed by the sinusoidal x
_{1a}
(n) and cosine x
_{2a}
(n) reference inputs collected from the source voltage v
_{a}
(n) by the phase locked loop circuit. The difference between the primary nonlinear load current i
_{La}
(n) and the estimated components i
_{ra}
(n) induces an error signal e
_{a}
(n). The weights of ADALINE are updated based on the VSSLLMS algorithm
[19]

[21]
.
where Δ(n) is the variable stepsize parameter, and γ(k) is the variable leakage factor. When γ(k) = 0, it behaves as a conventional LMS algorithm. The leakage factor is set to be large enough at the transient state to expedite the rate of convergence, but is reduced at the steady state. The variable stepsize can be calculated as
[17]
,
[18]
where α and γ are constant values controlling the convergence time, and R(n) is the autocorrelation of e
_{a}
(n) and e
_{a}
(n  1). This autocorrelation can be expressed as follows:
where β is an exponential weighting parameter. The variable leakage factor γ(k) can be adjusted with the below equations.
Block diagram of ADALINEVSSLLMS based reference signal generation in phasea.
ADALINEVSSLLMS aims to minimize the error and determine an optimal weight vector. Hence, i
_{ra}
(n) approximates i
_{xa}
(n). The residual error can be obtained as
The cost function J(n) is defined as follows:
where E{.} is the statistical expectation operator, and i
_{fa}
(n) is uncorrelated with i
_{xa}
(n) and i
_{ra}
(n) because of the orthogonality of trigonometric functions. When i
_{xa}
(n) = i
_{ra}
(n), the following expression is obtained:
The preceding equation is the best mean square estimation of i
_{xa}
(n). When this condition is achieved, the references are estimated successfully
[4]
.
IV. SIMULATION STUDIES
The newly developed ADALINEVSSLLMS control algorithm for harmonics elimination is designed, modeled, and simulated in a MATLAB/Simulink environment. The device parameters employed in the simulation studies are given in the Appendix, and the initial parameters are Δ = 0.001, γ = 0.01, and W = 0.018.
The steady state response of SHAPF is presented in
Fig. 3
. The source voltage v
_{a}
, sinusoidal source current i
_{sa}
, nonlinear load current i
_{La}
, SHAPF current i
_{fa}
, reference voltage v
_{refa}
, output of inverter voltage v
_{a}
′, DClink capacitor voltage v
_{dc}
, and reference current I
_{0}
are depicted in
Figs. 3
(a) to (h), respectively. These figures illustrate that the source waveforms are of pure sinusoids and are in phase. The voltage across the capacitor is well balanced with an average value of 130 V. The maximum and minimum values of v
_{dc}
are 127 and 132 V, respectively. The magnitude of the reference current i
_{0}
is zero.
Steady state waveforms of SHAPF; (a) source voltage v_{a}, (b) source current i_{sa}, (c) load current i_{La}, (d) SHAPF current i_{fa}, (e) reference voltage v_{refa}, (f) output of inverter voltage v_{a}′, (g) DClink capacitor voltage v_{dc}, and (h) DCcurrent I_{0}.
Figs. 4
(a) to (h) depict the dynamic response when a sudden step change of load occurs. The load resistance changes from 32 Ω to 16 Ω and from 16 Ω to 32 Ω at 0.25 and 0.35 S, respectively. The
Fig. 4
evidently demonstrates that i
_{sa}
and v
_{dc}
exhibit a fast transient response, achieving a stable operation using the ADALINEVSSLLMS control algorithm.
Dynamic response under sudden load variations; (a) source voltage v_{a}, (b) source current i_{sa}, (c) load current i_{La}, (d) SHAPF current i_{fa}, (e) reference voltage v_{refa} , (f) output of inverter voltage v_{a}′, (g) DClink capacitor voltage v_{dc}, and (h) DCcurrent I_{0}.
Figs. 5
(a) to (h) show the dynamic response of SHAPF, which adopts the proposed controller, under on and offload switching conditions. A threelevel variation is conducted on i
_{La}
(100% to 0%, steady at 0%, 0% to 100%). The SHAPF exhibits a fast response of onetime period to settle down to a new value. When i
_{La}
is set to zero, i
_{sa}
takes 0.016 S to maintain the equal i
_{fa}
. The DClink capacitor charges to an overshoot voltage of 140 V (7.69%) and to an undershoot voltage of 125 V (3.84%) at the on and offload conditions, respectively.
Dynamic response under on and offload switching conditions; (a) source voltage v_{a}, (b) source current i_{sa}, (c) load current i_{La}, (d) SHAPF current i_{fa}, (e) reference voltage v_{refa}, (f) output of inverter voltage v_{a}′ , (g) DClink capacitor voltage v_{dc}, and (h) DCcurrent I_{0}.
Fig. 6
demonstrates the active and reactive powers on the load and source sides of the distorted power system. With SHAPF, the instantaneous active power is 1.48×10
^{4}
W, and the reactive power is zero. The simulated waveforms of the system power factor are depicted in
Fig. 7
. The power factor is upgraded from 0.81 to 0.98 when SHAPF is connected.
Simulated waveforms; (a) instantaneous active power P_{L} on load side, (b) instantaneous reactive power Q_{L} on load side, (c) instantaneous active power P_{S} on source side, and (d) instantaneous reactive power Q_{S} on source side.
Simulated waveforms of the system power factor; (a) before compensation, (b) after compensation.
The harmonic distortions of i
_{La}
and i
_{sa}
with the application of SHAPF are depicted in
Figs. 8
(a) to (b), respectively. During the steady state operation, the harmonic levels of i
_{La}
and i
_{sa}
are 2.64% and 40.98%, respectively. These values are well below the restrictions imposed by the IEEE standard 5191992.
Total harmonic distortion; (a) load current, (b) source current.
Table I
presents the performance comparison of the individual harmonic amplitude (peak value) using the conventional ADALINELMS and the proposed ADALINEVSSLLMS algorithm. The harmonic component elimination that employs the ADALINEVSSLLMS algorithm exhibits better precision than that, which uses the conventional approach. Moreover, the computational time needed for the proposed algorithm is lesser than that for the conventional one.
PERFORMANCE COMPARISON
V. REALTIME FPGA IMPLEMENTATION
To evaluate the performance of the proposed ADALINEVSSLLMS control algorithm applied for SHAPF, a prototype model is developed using a SPARTAN3A XC3SD1800A DSP processor and is certified in the laboratory as shown in
Fig. 9
. The experimental setup is composed of an SKKD 101/16 diode bridge rectifier fed inductive load that acts as a nonlinear load. A balanced threephase supply is fed to the load through an autotransformer and IGBT module PM25RSB120, which acts as a voltage source inverter. In this experimental setup, the source inductor, filter inductor, filter capacitor, and DClink capacitor are set as 120 μH, 1500 μH, 137 μF, and 2200 μF respectively. The load resistance and inductance values are 100 Ω and 36 mH, respectively. The switching frequency for the IGBT inverter is 10 KHz. LEM LV25P and LEM LTS25NP sensors are used to track the load currents and DClink capacitor voltage, respectively. A signal conditioning circuit is designed to amplify and provide the necessary offset required by the analog to the digital converter circuit used.
Table II
describes the device utilization summary of the SPARTAN3A XC3SD1800A DSP processor.
Photograph of FPGA based experimental setup for implementing the proposed algorithm.
DEVICE UTILIZATION SUMMARY
DEVICE UTILIZATION SUMMARY
Figs. 10
(a) to (f) show the steady state waveforms of the threephase source voltages, threephase load currents, threephase source currents, threephase compensated currents, switching signals, and DClink capacitor voltage, respectively.
Fig. 10
(f) indicates that the DClink capacitor voltage is regulated with regard to its reference value, and the output current of PI controller is set as zero. These conditions satisfy the essential requirements of SHAPF. The reactive power and harmonic components of the load currents are almost compensated by the generated SHAPF currents depending on the feedback signal fed to the control circuit. Therefore, the source current waveforms are almost pure sinusoidal with an input power factor of 0.96.
Experimental results of SHAPF under the steady state condition; (a) source voltages (v_{a}, v_{b}, v_{c}), (b) load currents (i_{La}, i_{Lb}, i_{Lc}), (c) source currents (i_{sa}, i_{sb}, i_{sc}), (d) compensating currents (i_{fa}, i_{fb}, i_{fc}), (e) gating signals (g_{a}, g_{b}, g_{c}), and (f) DC current (I_{0}) and DClink capacitor voltage (V_{dc}).
Figs. 11
(a) to (c) demonstrate the experimental waveforms under the steady and dynamic states of load. The waveforms in each figure, from top to bottom, represent the source voltage v
_{a}
, source current i
_{sa}
, load current i
_{La}
, and filter current i
_{fa}
, respectively.
Fig. 11
(b) shows the waveforms of SHAPF under the sudden changes of load from 2 KW to 1 KW, and
Fig. 11
(c) depicts the load changes from 1 KW to 2 KW. It has been observed that i
_{sa}
exhibits a fast transient response to settle down to a new value within a halftime period. The figures illustrate that both i
_{sa}
and V
_{a}
are maintained with pure sinusoidal and same phase by employing the proposed control technique.
Experimental waveforms of source voltage, source current, load current, and filter current (all values in phasea); (a) steady state response of load, (b) and (c) dynamic response of SHAPF under sudden load variations (a) (b)
The harmonic spectra of i
_{La}
and i
_{sa}
are presented in
Figs. 12
(a) to (b), respectively. These figures indicate that the amplitude of the individual harmonics is reduced significantly by employing SHAPF based on the ADALINEVSSLLMS control algorithm.
Harmonic spectra; (a) load current, (b) source current.
VI. CONCLUSION
A novel mixed ADALINEVSSLLMS control algorithm is presented for reference signal generation. The SHAPF based on proposed control algorithm has ability to compensate reactive power and eliminate harmonic components from the load currents. Both simulation and experimental results are analyzed to validate the efficacy of the proposed control algorithm. The findings reveal that the novel ADALINEVSSLLMS approach is accurate, has fast convergence, and is stable at the dynamic changes of load in the power system. Given these advantages, the proposed control strategy can be a good solution for SHAPF, which requires adaptive characteristics and integrated functionalities.
BIO
Priyabrat Garanayak was born in Odisha, India. He received his B.Tech degree in Electronics and Telecommunication Engineering from Biju Patnaik University of Technology, India and his M.Tech degree in VLSI and Embedded System Design from the Centre for Micro Electronics, Biju Patnaik University of Technology, India, in 2009 and 2011, respectively. He is presently working toward his Ph.D. degree in the Department of Electrical Engineering at National Institute of Technology Meghalaya, India. His research interests are power system harmonic estimation and its elimination in a distribution network.
Gayadhar Panda was born in Odisha, India in 1970. He received his bachelor’s degree from the Institute of Engineers, India in 1996. Consequently, Gayadhar obtained his master’s degree from Bengal Engineering College, India and his Ph.D. degree from Utkal University, India, in 1998 and 2007, respectively. He has 17 years of teaching experience in the field of Electrical Engineering. Since January 2013, he has been with the Department of Electrical Engineering, National Institute of Technology Meghalaya, India as an associate professor and department head. His research interests include automatic generation control, stability improvements using FACT devices, power quality, power electronic converters, and renewable energy.
Akagi H.
“Active harmonic filters,”
in Proc. of the IEEE 93
Dec. 2005
Vol. 93, No. 12
2128 
2141
Singh B.
,
AlHaddad K.
,
Chandra A.
1997
“A review of active power filters for power quality improvement,”
IEEE Trans. Ind. Electron.
46
(5)
960 
971
DOI : 10.1109/41.793345
Singh B.
,
Solanki J.
2008
“An improved control approach for DSTATCOM with distorted and unbalanced AC mains,”
Journal of Power Electronics
8
(2)
131 
140
Wang Q.
,
Wu N.
,
Wang Z.
2001
“A neuron adaptive detecting approach of harmonic current for APF and its realization of analog circuit,”
IEEE Trans. Instrum. Meas.
50
(1)
77 
84
DOI : 10.1109/19.903881
Pereira R. R.
,
Silva C. H.
,
Silva L. E.
,
Torres G. L.
,
Pinto J. P.
2011
“New strategies for application of adaptive filters in active power filters,”
IEEE Trans. Ind. Applicat.
47
(3)
1136 
1141
DOI : 10.1109/TIA.2011.2125931
Li Z.
2011
“Consistency between two adaptive detection methods for harmonic and reactive currents,”
IEEE Trans. Ind. Electron.
58
(10)
4981 
4983
DOI : 10.1109/TIE.2011.2114315
Garanayak P.
,
Panda G.
,
Ray P. K.
2015
“Harmonic estimation using RLS algorithm and elimination with improved current control technique based SAPF in a distribution network,”
Electr. Power & Energy Syst.
73
209 
217
DOI : 10.1016/j.ijepes.2015.04.023
Rahmani S.
,
Hamadi A.
,
Mendalek N.
,
AlHaddad K.
2009
A new control technique for threephase shunt hybrid power filter,”
IEEE Trans. Ind. Electron.
56
(8)
2904 
2914
DOI : 10.1109/TIE.2008.2010829
Corasaniti V. F.
,
Barbieri M. B.
,
Arnera P. L.
,
Valla M. I.
2009
“Hybrid power filter to Enhance power quality in a mediumvoltage distribution network,”
IEEE Trans. Ind. Electron.
56
(8)
2885 
2893
DOI : 10.1109/TIE.2009.2014369
Kumar S.
,
Sensarma P. S.
2008
“A multiband shunt hybrid active power filter with sensorless control,”
Journal of Power Electronics
8
(4)
317 
324
Girgis A. A.
,
Chang W. B.
,
Makram E. B.
1991
“A digital recursive measurement scheme for online tracking of harmonics,”
IEEE Trans. Power Del.
6
(3)
1153 
1160
DOI : 10.1109/61.85861
Kennedy K.
,
Lightbody G.
,
Yacamini R.
“Power system harmonic analysis using the Kalman Filter,”
IEEE Power Engg. Society General Meeting
2003
752 
757
Malengret M.
,
Gaunt T.
2008
“Decomposition of currents in three and four wire systems,”
IEEE Trans. Instrum. Meas.
57
(5)
963 
972
DOI : 10.1109/TIM.2007.911705
Dash P. K.
,
Swain D. P.
,
Liew A. C.
,
Rahman S.
1996
“An adaptive linear combiner for online tracking of power system harmonics,”
IEEE Trans. Power Syst.
11
(4)
1730 
1735
DOI : 10.1109/59.544635
Joorabian M.
,
Mortazavi S.S.
,
Khayyami A.A.
2008
“Harmonic estimation in a power system using a novel hybrid least squareAdaline algorithm,”
Electric Power Syst. Res.
79
107 
116
DOI : 10.1016/j.epsr.2008.05.021
Sarkar A.
,
Choudhury S.R.
,
Sengupta S.
2011
“A selfsynchronized ADALINE network for online tracking of power system harmonics,”
Measurement
44
(4)
784 
790
DOI : 10.1016/j.measurement.2011.01.009
Pradhan A. K.
,
Routray A.
,
Basak A.
2005
“Power system frequency estimation using least mean square technique,”
IEEE Trans. Power Del.
20
(3)
1812 
1816
DOI : 10.1109/TPWRD.2004.843453
Aboulnasr T.
,
Mayyas K.
1997
“A robust variable stepsize LMStype algorithm: analysis and simulations,”
IEEE Trans. Signal Process.
45
(3)
631 
639
DOI : 10.1109/78.558478
Subudhi B.
,
Ray P. K.
,
Ghosh S.
2012
“Variable leaky least meansquare algorithmbased power system frequency estimation,”
IET Science, Meas. & Tech.
6
(4)
288 
297
DOI : 10.1049/ietsmt.2011.0103
Mayyas K.
,
Aboulnasr T.
1997
“Leaky LMS algorithm: MSE analysis for Gaussian data,”
IEEE Trans. Signal Process.
45
(4)
927 
934
DOI : 10.1109/78.564181
Kememetsky M.
,
Widrow B.
“A variable leaky LMS adaptive algorithm,”
in Proc., 38th IEEE Asilomar Conference on Signals, System and Computers
2004
125 
128