Implementation of Sparse LMS Control Algorithm in Mrutyunjaya Mangaraj 1, Student Member, IEEE, Trilochan Penthia, Student Member, IEEE, and Anup Kumar Panda, Senior Member, IEEE Department of Electrical Engineering, NIT Rourkela, India 1 Email: mmangaraj.ee@gmail.com Abstract: Nowadays, the selection of a suitable adaptive controller for a Distribution STATic COMpensator () is a tough job for the researchers due to the complexity of the power system. The performance of the depends on the effectiveness of the control algorithm. This paper presents a Sparse Least Mean Square (SLMS) control algorithm for a threephase to mitigate the power quality problems. Specifically, the control algorithm is implemented to compensate current harmonics, reactive power and load unbalancing. The reference source currents are generated followed by extracting the weighted values of fundamental active and reactive power components of harmonic rich three-phase load current. The intention of the proposed control algorithm is to generate appropriate switching signals for the Voltage Source Converter (VSC) of the in order to maintain its DC-link voltage constant. The simulation is performed in the MATLAB software. Index Terms distribution static compensator (); sparse least mean square (SLMS) control algorithm; power quality. I. INTRODUCTION The electric grid is being complex day by day due to the massive use of advanced technology based power electronic devices and other semiconductor devices in the system [1]. The presence of such type of devices in the system causes several problems such as harmonics in the current, current unbalance, voltage unbalance, overvoltage, under voltage, voltage sag/swell, voltage flickering, etc. [2-4]. These problems can generate overheating, motor vibration, poor power factor, excessive neutral current, capacitor blowing and communication interference in the system. Finally, the power system goes under severe damages and make the system worse. Generally, custom power devices are used to solve such problems in a power system. Distribution static compensator () is one of the most widely used custom power devices to mitigate power quality issues [5-8]. Besides the selection of an appropriate custom power device, the selection of a suitable control algorithm is essential. Because its performance solely depends on the adaptability and flexibility of a control algorithm [9]. Mainly, control techniques are used to extract the fundamental, active and reactive components of the load current to make the supply harmonic free. The using different control techniques has been implemented in a power system for power quality improvement. The most recently used adaptive control algorithms in the to generate switching signals for the voltage source converter (VSC) are presented in the following publications [1-12]. In this article, the uses the widely used least mean square (LMS) algorithm based on the concept of sparse updating technique is called sparse least mean square (SLMS) control algorithm. In general, the convergence behaviour of the SLMS algorithm depends on the correlation of supply signals and load signals of the system. It has better stability due to the high rate of convergence. It shows excellent performance for the task like harmonic mitigation, load compensation, etc. Moreover, during faults, transient or dynamic conditions in the system, the conventional LMS algorithm performs less effective because of its poor data convergence operation whereas SLMS is not. To achieve the higher convergence rate, the weight updating of the LMS control algorithm is carried out using the sparse technique. The technique uses a sparse factor in order to attain both higher convergence rate and stability of the system. II. SYSTEM TOPOLOGY The three-phase three-leg VSC based is connected at the point of common coupling (PCC) of the three phase utility through an interfacing impedance ( ), as shown in Fig.1. A three-phase supply is coupled with a three-phase nonlinear load via a source impedance ( ). 978-1-4799-5141-3/14/$31. 216 IEEE
The involves six insulated gate bipolar transistors (IGBTs), a DC-link capacitor ( ) and the SLMS control unit. Fig.1: Schematic block diagram of the proposed III. PROPOSED SLMS CONTROL ALGORITHM The SLMS is a new efficient technique in the reduction of distortion and power quality improvement through the proper learning process. The main purpose of this control algorithm is to extract the fundamental-weighted active as well as reactive load current component by choosing the correlated signals such as rate of convergence ( =.4), step size ( =.1), estimation error ( =.2), associated weight ( ) and sparse constant ( =.1). Simply, the system sparsity is defined as the ratio of the numerator and denominator of the system transfer function. The smaller the numerator makes the system more sparsity. The Sigmoidal function, including the divisional operator, provides about the sparsity-information-aided of the LMS control algorithm. Mainly, the SLMS algorithm involves three steps to generate the appropriate switching signals for the VSC of the, The steps are (a) Extraction of weighting values of active and reactive component of the load current (b) generation of direct and quadrature vector components (c) generation of active and reactive components of the reference source current and (d) generation of six switching signals for the VSC. Fig.2: Generation of switching signals using the proposed SLMS control algorithm
The schematic block diagram of the proposed SLMS control algorithm is shown in Fig.2. The governing equations [13-14] of the SLMS are presented as follows: a) Extraction of weighting values of active and reactive component of the load current using the sparse concept The extraction of weighting values of fundamental active component from three-phase load current (,, ) are: + (1) + (2) + (3) The mean value( ) of the weighting values of the a, b and c- phase is calculated as follows: = + + (4) 3 Similarly, the extraction of weighting values of fundamental reactive component of the three-phase load current (,, ) are computed based on the SLMS control algorithm as follows: + (5) + (6) + (7) The mean value( ) of the weighting values of the a, b and c- phase is calculated as follows: = + + 3 (8) The mean weighting values of the both active and reactive are passed through a half band filter (HBF) having frequency of 75 Hz, to get the active and reactive components ( & ) of the reference source current. b) Generation of direct and quadrature vector components The direct unit vector (,, ) can be calculated from the three-phase source voltages (,, ) & amplitude of the PCC voltage ( ) estimated as given below: = ; = ; = (9) Similarly, the quadrature unit vectors (,, ) are calculated as: = 1 3 (1) = 1 2 3 + +3 (11) = 1 2 3 + 3 (12) Where can be expressed as = 2 ( 2 + 2 3 + 2 (13) c) Generation of active and reactive components of the reference source current An error is generated by subtracting the sensed DC voltage from the reference DC voltage, and it can be given as = ( ) (14) Then the error ( ) is processed through the proportionalintegral (PI) controller to control the constant DC bus voltage. The output of PI controller can be expressed as = + (15) The total magnitude of the active components of the reference source current is calculated by adding the output of the PI controller ( ) and the output of the HBF used for the active components of the load current ( ), as shown in Fig.2 and it can be stated as = + (16)
Again, an error is generated by subtracting the sensed AC bus voltage from the reference AC bus voltage and the error ( ) can be expressed as = ( ) (17) The error is allowed through a PI controller to maintain the constant AC bus voltage. The output of the PI controller can be given as = + (18) The total magnitude of the reactive components of the reference source current is calculated by subtracting the output of the HBF used for extraction of active components of the load current ( ), from the output of the PI controller ( ) and it can be written as = (19) The component is included in control section which is responsible for compensation of distortion presence in the supply voltage. In addition, firstly, the sensed dc-link voltage and PCC voltage of the system are passed through a low pass pass filter (LPF) of 2Hz, in order to eliminate the distortions present in the signal as presented in Fig.2. d) Generation of six switching signals for the VSC Three phase instantaneous reference source active component is estimated by multiplying in phase unit voltage template and active power current component and these are obtained as =, =, = (2) Similarly, three-phase instantaneous reference source reactive component is estimated by multiplying quadrature unit voltage template and reactive current component and these are obtained as =, =, = (21) The addition of the corresponding active and reactive components of the reference source current is the desired threephase reference source current (, & ) and they can be obtained as = +, = +, = + (22) The current error signals are generated by subtracting the actual source currents (,, ) from the respective reference phase source currents (,, ) and then the errors are fed to a hysteresis current controller (HCC) each. After that the outputs of the HCCs (HCC1, HCC2 & HCC3) are fed to the six IGBTs of the VSC. IV. MATLAB RESULTS The simulation of the system is accomplished in MATLAB/Simulink to observe the performance under the two conditions such as without and with. The stability of the system is also analysed, and it is found satisfactory. The Bode plot analysis of the system using the proposed control algorithm is shown in Fig.3. The stability of the system is found at the points of 22.2 db magnitude and -23 phase angle. The control algorithm confirmed excellent performance in the. Before compensation, the total harmonic distortion (THD) of the load current and supply current are observed 25.86% and 25.89% respectively. Similarly, after compensation by the, THD of the load current and supply current are found 3.83% and 25.86% respectively. Table-1 and table-2 illustrate the performance parameters and system parameters of the system. Phase (deg) Magnitude (db) 25 2 15 1 5-45 -9-135 -18-225 Bode Diagram System: sys Frequency (rad/sec):.211 Magnitude (db): 22.2 System: sys Frequency (rad/sec):.211 Phase (deg): -23-27 1-2 1-1 1 1 1 1 2 1 3 Frequency (rad/sec) Fig.3: Bode plot to analyse the stability of the system The waveforms of the a-phase source current before compensation and after compensation using the is compared in the Fig.4. The filter currents or the compensating currents (, & ) and DC-link voltage of the VSC are illustrated in Fig.5. Comparison of the source voltage and source of the both cases, i.e. without and with, are shown in Fig.6 and Fig.7 in order
to observe the phase displacement between them. Fig.7 endorses almost unity input power factor of the system. Also, the corresponding THD spectra of PCC voltage, load current and source current are depicted in Fig.8 and table-1. For information, the SLMS controller is taking not more than 5 cycle to achive staedy state operation. Here, the THD of the signals are taken 3 cycles from the beginning of the simulation i.e. from. sec onwards. i sa 8 4-4 -8.5.52.54.56.58.6 Fig.4: Source current ( ) of the system with and without i ca i cb i cc v dc (V) 8 4-4 -8 8 4-4 -8 8 4-4 -8 6 with without Fig.5: Waveform of three phase compensating current (, & ) and DClink voltage ( ) v sa (V), i sa 4 2.5.52.54.56.58.6 4 2-2 voltage -4.5.52.54.56.58.6 current Fig.6: Phase difference between source voltage and source current before v sa (V), i sa 4 2-2 -4.5.52.54.56.58.6 Fig.7: Phase difference between source voltage and source current after Mag (% of Fundamental) Mag (% of Fundamental) Mag (% of Fundamental) 1.5.5 4 2 1 1 5 voltage (a) (b) (c) Fig.8: Harmonic spectra of (a) PCC voltage, (b) load current (c) source current. Table.1: Performance parameters of the proposed system current Fundamental (5Hz) = 299.8 V, THD= 1.55% 2 4 6 8 1 Harmonic order Fundamental (5Hz) = 52.11 A, THD= 25.86% 2 4 6 8 1 Harmonic order Fundamental (5Hz) = 55.16 A, THD= 3.83% 2 4 6 8 1 Harmonic order Performance parameter Without With Load current, THD 52.11, 25.86 (%) 52.11, 25.86 (%) PCC voltage, THD 292.7 (V), 5.27 (%) 299.8 (V), 1.55 (%) Source current, THD 54.2, 3.83 (%) 55.16, 3.83 (%)
Table.2: System parameter for simulation studies Load side Supply side Three-leg VSC: =.32Ω =1.56mH ( ) =55V =25μF Three-phase nonlinear (RL) load: = 1Ω, =2mH Supply voltage: =23V (rms)/phase, 5Hz Source impedance: =.36 Ω+j2.85mH Hence, from the simulation study, it has been clear that the SLMS control algorithm based is attained excellent performance in the compensation process. Moreover, it can also implemented in a 3-phase 4-wire (3P4W) topology and under faulty condition (transient) for power quality improvement. Harmonic mitigation of the source current and power factor improvement of the supply is achieved successfully. The DC-link voltage of the VSC is also maintained almost constant to ensure low power loss across the. However, SLMS is quite complicated regarding the learning due to the association of its computational complexity. V CONCLUSION The proposed SLMS control algorithm has been implemented in the successfully, and it has achieved excellence performance. In the paper, the stability of the system is analysed using the Bode plot concept. Harmonics of the source current is mitigated by the. THD of the source current is obtained well below 5%, thus satisfying the IEEE-519 standard on the harmonic limit. Not only the harmonic of the source current alleviated but also the input power factor of the system is improved, and it is found almost unity. [3] SJ. Shi, A. Noshadi, A. Kalam and P. Shi, "Fuzzy logic control of for improving power quality and dynamic performance," Power Engineering Conference (AUPEC-215), 215 Australasian Universities, Wollongong, NSW, pp. 1-6 Sept. 215. [4] T. Penthia, A. K. Panda, S. K. Sarangi and M. Mangaraj, "ANN controlled 4-leg VSC based for power quality enhancement," 215 Annual IEEE India Conference (INDICON), New Delhi, pp. 1-6, Dec. 215. [5] V. C. Sekhar, K. Kant and B. Singh, " supported induction generator for improving power quality," in IET Renewable Power Generation, vol. 1, no. 4, pp. 495-53, April 216. [6] M. Mangaraj, A. K. Panda and T. Penthia, "Supercapacitor supported for harmonic reduction and power factor correction," 216 IEEE Students' Conference on Electrical, Electronics and Computer Science (SCEECS), Bhopal, pp. 1-6, March 216. [7] T. Penthia, A. K. Panda, S. K. Sarangi and M. Mangaraj, "ADALINE based LMS algorithm in a three phase four wire distribution system for power quality enhancement," 216 IEEE 6th International Conference on Power Systems (ICPS), New Delhi, pp. 1-5, March 216. [8] M. Mangaraj, A. K. Panda and T. Penthia, "Investigating the performance of using ADALINE based LMS algorithm," 216 IEEE 6th International Conference on Power Systems (ICPS), New Delhi, pp. 1-5, March 216. [9] S. R. Arya and B. Singh, "Performance of Using Leaky LMS Control Algorithm," in IEEE Journal of Emerging and Selected Topics in Power Electronics, vol. 1, no. 2, pp. 14-113, June 213. [1] W. Gao, J. Huang, J. Han and Q. Zhang, "Theoretical convergence analysis of complex Gaussian kernel LMS algorithm," in Journal of Systems Engineering and Electronics, vol. 27, no. 1, pp. 39-5, Feb. 216. [11] M. Mangaraj, A. K. Panda and T. Penthia, "Neural network control technique based sensorless for the power conditioning," 215 Annual IEEE India Conference (INDICON), New Delhi, 215, pp. 1-6, Dec. 215. [12] M. Farhoodnea, A. Mohamed, H. Shareef and H. Zayandehroodi, "Optimum D-STATCOM placement using firefly algorithm for power quality enhancement," 213 IEEE 7th International Power Engineering and Optimization Conference (PEOCO-213), Langkawi, pp. 98-12, June 213. [13] Kun Shi, Peng Shi, Convergence analysis of sparse LMS algorithms with l1-norm penalty based on white input signal, in Signal Processing (Elsevier), vol. 9, pp. 3289 3293, Dec. 21. [14] W. Lei, Y. Meng, Y. Wu, S. Zhe and X. Wang, "Sparsityinformation-aided least mean squares method for sparse channel estimation," International Conference on Wireless Communications & Signal Processing (WCSP-215), Nanjing, pp. 1-5, Oct. 215. REFERENCES [1] M. Barghi Latran, A. Teke and Y. Yoldaş, "Mitigation of power quality problems using distribution static synchronous compensator: a comprehensive review," in IET Power Electronics, vol. 8, no. 7, pp. 1312-1328, July 215. [2] Om Prakash Mahela, Abdul Gafoor Shaik, Power quality improvement in distribution network using with battery energy storage system, International Journal of Electrical Power & Energy Systems, vol. 83, pp. 229 24, Dec. 216