Design and Implementation of Sliding Mode and PI ... - Science Direct

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ScienceDirect Energy Procedia 50 (2014) 504 – 511

The International Conference on Technologies and Materials for Renewable Energy, Environment and Sustainability, TMREES14

Design and Implementation of Sliding Mode and PI Controllers based Control for Three Phase Shunt Active Power Filter M.T Benchouia a, I.Ghadbanea, A.Golea a, K.Srairi b, M.H Benbouzid c a

Biskra University ,BP. 145, Laboratory LGEB, Department of Electrical Engineering, ALGERIA Biskra University, BP. 145, Laboratory LMSE, Department of Electrical Engineering, ALGERIA Université de Bretagne Occidentale, LBMS Laboratory, CS 93837 - 29238 Brest Cedex 03, FRANCE e-mail: [email protected] b

c

Abstract─ This paper presents a simulation and experimental comparative study of Sliding Mode Controller (SMC) and Proportional Integral (PI) regulator based the control of the DC bus voltage of three phase shunt Active Power Filter (APF). The capacitor that feeds the active filter plays the role of a voltage source. This tension must be kept constant, so as not to degrade the filter performances, and not to exceed the voltage of semiconductors. The main cause of the variation of this voltage is the change in the pollutant load, which creates an active power exchange with the network (if the inverter provides power active, then the average voltage across the capacitor will decrease and if the inverter consumes power active, then the average voltage across the capacitor will increase). The algorithm used to identify the reference currents is based on the Self Tuning Filter (STF). This study was verified experimentally, using a hardware prototype based on dSPACE-1104. Keywords ─ Active Power Filter (APF), Sliding Mode Controller (SMC), Self Tuning Filter (STF), Proportional Integral (PI) Controller.

1. Introduction Industrial and domestic equipments actually use a large variety of power electronic circuits such as switch mode power converters, adjustable speed drives, rectifiers and dimmers. These ones lead to significant energy savings and productivity benefits. But unfortunately, they also present non-linear impedance to the supply network and therefore generate non-sinusoidal currents. The outcome of these wide-band current harmonics includes substantially higher losses for the transformers and the power lines, possible over voltages and overheating destroying equipments and disturbances of communication equipments and precision instruments [1]. So, it is necessary to develop techniques Corresponding author. Tel./ fax: +21333543158. E-mail : [email protected]

1876-6102 © 2014 Elsevier Ltd. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/3.0/). Selection and peer-review under responsibility of the Euro-Mediterranean Institute for Sustainable Development (EUMISD) doi:10.1016/j.egypro.2014.06.061

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to reduce all the harmonics as it is recommended in the IEEE 519-1992. The first approach consists in the design of LC filters. Traditionally, passive LC filters have been used to eliminate line current harmonics, and to improve the load power factor [1]. However, in many practical applications, this passive second order filters present many disadvantages such as tuning problems, series and parallel resonance. They can also lead to resonance phenomena. In recent years, shunt active power filters, based on current controlled PWM converters have been widely investigated. The APF can solve the problems of harmonics and reactive power simultaneously. The theories and applications of active power filters have become more popular and have attracted great attention since two decades ago. Since its introduction some twenty years ago, the APF presents a good solution for disturbance treatment, particularly for harmonic currents and/or voltages. The APF allows the compensation of current harmonics and unbalance, together with the power factor correction, and can be a much better solution than the conventional approach [2], [4]. The identification approach is based on the Phase Locked Loop (PLL), which is not sensitive to the disturbances, specifically to the harmonic and unbalanced voltage [3], [10]. Moreover, the Self Tuning Filter (STF) is proposed for extracting harmonic currents instead of classical harmonics extraction based on High Pass or Low Pass Filters [5]. The sliding mode strategy provides a systematic approach to the problem of maintaining stability and performance in the presence of modeling uncertainty. The most advantage of a sliding mode control is its insensitivity to parametric uncertainty and external disturbances. Therefore, the sliding mode control is suitable for the closed loop control of power converters. Many researchers have paid attention to the application of sliding mode control to power converters witch improving the dynamic behavior of the system, endowing it with robustness against changes in the load, uncertain system parameters and simple implementation [6] ,[7], [8]. These hybrid controllers try to ensure the asymptotical stability and to reduce the chattering by combining sliding mode control with other techniques, such as adaptive control techniques, fuzzy control techniques and ANN-Based Predictive [9] ,[10], [11]. The regulation of this voltage is necessary to keep its value constant, and to limit the fluctuations of this voltage. The control of the DC bus voltage of the APF is associated in several studies with different regulators [8], [9] [10], [11], [12]. In this paper, first the circuit configuration of the APF system is presented. Second, the control strategy is developed according to the circuit configuration. After this, the SMC and PI design are presented taking in consideration the stability conditions. Finally, detailed simulation and experimental results of the developed APF system are given and discussed to demonstrate their dynamic performances and their ability for harmonic elimination and reactive power compensation. 2. System Configuration Fig. 1 shows the fundamental building block of the APF. The last one is composed of a standard 3-phase IGBT based VSI bridge with an input AC inductors (L F ,R F) and a DC bus capacitor C to provide a self-supporting DC bus. The three phase AC supply system with the line impedance Ls, Rs is feeding a three-phase diode bridge rectifier with Rl, Ll load. This nonlinear load generates harmonic currents in the supply system. The current drawn from the power system at the coupling point of the APF will result in sinusoidal waveform. The source current is is the result of summing the load current iL and the compensating current iF. The control strategy can be divided in three parts: The first part is the harmonic isolator (reference current generation). It consists in generating the harmonic current references using the Self Tuning Filter (STF). This Filter is proposed for extracting harmonic currents instead of classical harmonics extraction based on High Pass or Low Pass Filters [5].

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Fig. 1. Basic compensation principle of the shunt APF.

3. Control of the APF 3.1. Identification of reference currents The quality of the compensation of current harmonics depends heavily on the performance of the identification method chosen. Indeed, a control system, even very effective, cannot alone make a good filter if the harmonic currents are poorly identified. For this reason, many identification methods have been developed in the literature. There are many control algorithms available for the generation of reference source currents for the control of proposed active power filter in the literature, synchronous reference frame theory[13], [14], instantaneous reactive power theory (p–q theory) [7], [15], power balance theory. A block diagram of the controlling algorithm is shown in Fig. 2. The feedback signals are sensed from the load currents, AC source voltages and DC bus voltages of APF. The three phase currents iLa, iLb and iLc are transformed from three phase (a-b-c) reference frame to two phase’s α-β stationary reference frame currents iα and iβ using:

iLa  i  2 1 1/ 2 1/ 2     iLb  i    3 0 3 / 2 3 / 2     i   Lc 

(1)

The instantaneous current can be written as the sum of a fundamental component and an alternative component:

i  iˆ  ~ i  ~ i  iˆ  i

(2)

Then, the STF extracts the fundamental components at the pulsation ωc directly from the currents in the α-β axis. Then, the α-β harmonic components of the load currents are computed by subtracting the STF input signals from the corresponding outputs (see Fig.3). The resulting signals are the AC components, ĩα and ĩβ , which correspond to the harmonic components of the load currents iLa, iLb and iLc in the stationary reference frame. Using a PLL (Phase

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Locked Loop), we can generate cos(θ) and sin(θ) from the phase voltage source Vsa, Vsb and Vsc. The currents expression ĩα and ĩβ in d-q reference frame are given by:

~ ~ id  sin( )  cos( ) i  ~     ~  iq  cos( ) sin( )  i 

(3)

The reference currents in the (a-b-c) frame are given by:

0  1 i* Fa   1 3  * *  2  i   i Fb    2 2   *  3 1 i i* Fc    3       2 2  

(4)

Fig. 2: Synchronous reference frame control strategy.

The STF in Fig. 3 is used in the harmonic isolator instead of classical extraction filters. Hong-sock Song in [5] had presented that the integration in the synchronous reference frame is defined by:

Vxy (t)  e jt  e jtUxy (t)dt

(5)

The equation (5) can be expressed as follows: following transfer function [5], [12]:

K i (s)  i (s)  c i (s) s s  K i  ( s )  i  ( s )  i  ( s )  c i ( s ) s s i ( s ) 

(6) (7)

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Fig 3. Self Tuning Filter tuned STF.

3.2. Sliding Mode controller of DC voltage The sliding mode control has been widely applied to power converters [10], due to its operation characteristics such as fastness, robustness, and stability under large load variations. A simple form of the control action using sliding mode theory is a relay function which is given by equation (8),

s ( x )  k .sign ( s ( x ))

(8)

The Lyapunov function must be decreases to zero; for this purpose, it is sufficient to assure that its derivative is negative. In order to reduce the chattering phenomenon due to the discontinuous nature of the controller, a smooth function is defined in some neighborhood of the sliding surface with a threshold. If a representative point of the state trajectory moves within this interval, a smooth function replaces the discontinuous part of the control action. Thus, the controller becomes,

 kC  .s ( x) if s ( x)    0 un    k C .sign( s ( x)) if s ( x)   

(9)

Where, kc takes the admissible value. In order to regulate the DC voltage Vdc and to compensate the losses using an SMC, the block diagram of the regulation is given by Fig. 4. According to Fig.4, the sliding surface σc is used to synthesis a command current I*. In this case I* is given by,

I *  k C .sign ( C )

(10)

Fig. 4: Bloc diagram for voltage regulation

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3.3. PI Controller design The transfer function for PI controller is defined as:

H PI ( s )  K P 

KI s

(11)

The proportional gain is derived using KP = 2.ξ.ωn.C that determines the dynamic response of the DC-side voltage control. Similarly, the integral gain is derived using KI =Cωn2 that determines it’s settling time [2], [10]. The PI controller for the DC-link voltage sets the amplitude of the active current of the APF inverter to regulate the DC-link voltage based on its reference value covering the inverter losses. Subtracting the measured load current, the reference value of the APF current is obtained. Hence, K P = 2.ξ.ωn.C and KI =Cω n2 , for ξ = 0,707 and C=1100×106 F , Kp and KI can be determined. 4. Simulation and experimental Results To simulate the SMC or PI controlled shunt active power filter, a model in Matlab\Simulink and SimPowerSystems Blockset is developed. The same experimental test bench parameters are used for simulation. The performances of SMC of the DC bus voltage of three phase shunt active power filter are compared to conventional PI regulator by extensive simulation and experimentation for various operating conditions and parameters variation at permanent and transit response. The same experimental test bench parameters are used for simulation: Vm = 120 V , RS = 0.42 Ω, LS = 2.3 mH, LC = 1 mH, Lf = 3 mH, Rl = 45 Ω Ll= 1.3 mH, V*dc = 420 V, C = 1100 μF, Δi (hysteresis band) = 0.2 A, Kc= 1.5. First simulation is done on fixed load, we see that after the connection of the APF, the mains current has a sinusoidal form (see Fig. 5). In permanent response (see Fig. 6), it is clear that the DC-voltage is regulated well around the reference V*dc = 420 V, the source current has a sinusoidal form and in phase with supply voltage (it is confirmed for the two controllers), which minimizes the reactive power consumed by the inverter, allowing a high power factor operation and with low THD Total Harmonic Distortion (the THDSMC=3.53% and the THDPI=3.82%) in current.

Fig.5 Experimental results during the connection of the APF: Ch1 scale 5 A/div: load current iL (A); Ch3 scale 5 A/div: filter current iF (A) and Ch4 scale 5 A/div: source current iS (A). Time scale: 20 ms/div.

Fig.6 Experimental APF results at permanent response: Ch1 scale 80V/div: source voltage Vs (V); Ch2 scale 100 V/div: capacitor voltage; Ch3 scale 5 A/div: filter current iF (A) and Ch4 scale 5 A/div source current iS (A). Time scale: 10 ms/div.

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Secondly, in order to prove the dynamical response of the controllers at a transient condition, the DC side resistance is changed from RL to RL/2. It can be seen from simulation (Fig. 7 and 8), and experimental results (Fig.9 and Fig.10), that the voltage controlled by the SMC joined quickly his reference compared to the DC voltage regulated by the PI.

Fig.7. Simulation APF with PI: capacitor voltage Vdc (V); source current iS (A) and load current iL(A).

Fig.9. Simulation APF with SMC: capacitor voltage V dc (V); source current iS (A) and load current iL(A).

Fig.8. Experimental results APF with PI: Ch1 scale 10 A/div: load current iL (A); Ch2 scale 10 A/div: source current iS (A); Ch3 and Ch4 scale 60 V/div: capacitor and reference voltage. Time scale: 40 ms/ div.

Fig.10. Experimental results APF with SMC: Ch3 and Ch4 scale 60 V/div: capacitor and reference voltage; Ch2 scale 10 A/div: source current iS (A) and Ch1 scale 10 A/div: load current iL (A). Time scale: 40 ms/div.

Finally, to confirm the effectiveness of the control of DC voltage using SMC and PI controllers, a double change of the reference is shown 450-300 and 450V. It can be noted that after the transient response, the DC voltage regulated by the SMC follows its reference, there is no overshoot and the settling time is very small (see Fig. 11. and 12.). However the results in transient response obtained by the PI controller, show oscillations around voltage reference.

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Fig.11. Experimental results APF with PI: capacitor and reference voltage [100 V/div], Time scale: 2s/div.

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Fig.12. Experimental results APF with SMC: capacitor and reference voltage [100 V/div], Time scale: 2s/div.

6. Conclusion Two different control strategies for a three-phase shunt active power filter employing a digital signal processor DSP were presented in this paper. The first is based on sliding mode control SMC and the second uses a single proportional-integral controller PI. These controllers are used in order to regulate the DC voltage of the three phase shunt active power filter and improving the dynamical performances. Several tests have been performed in order to prove the efficiency of the type of the control. The results obtained by simulations and Experimental, show that the SMC controller offers better performances than the PI. References [1] Das J.C (2004), “Passive filters- Potentialities and limitations”, IEEE-Transactions on industry applications; 40(1): 232– 241. [2] Wei Zhao, An Luo, Ke Peng, Xia Deng “Current control for a shunt hybrid active power filter using recursive integral PI” Journal of Control Theory and Applications, February 2009, Volume 7, Issue 1, 77-80. [3] Mekri F, Machmoum M, Mazari B and Ahmed N A.( 2007) “Determination of voltage references for series active pow er filter based on a robust PLL system”. In: IEEE International Symposium on Industrial Electronics. p.473 – 78. [4] Karimi S. ,Poure P. ,Saadate S. , Gholipour E. (2008), ‘FPGA-based fully digital controller for three-phase shunt active filters’, International Journal of Electronics, 95( 8), 805–818. [5] Abdusalam M, Poure P, Saadate S. (2008) “Study and experimental validation of harmonic isolation based on Self -Tuning-Filter for threephase active filter”, In: IEEE International Symposium on Industrial Electronics,166 – 71. [6] Saetieo, S, Devaraj, R, Torrey, D. A. (1995)“The design and implementation of a three phase active power filter based on sliding mode control” IEEE Transactions Industry Appl.; 31(5): 993–99. [7] Mendalek, N, Al-haddad, K, Fnaeich, F., Dessaint, L. A.(2002) “Sliding mode control of 3 -phase shunt active filter in the d-q frame” In: Proceeding of the Conference on Power Electronics Specialists Conference, 369 – 75. [8] Guo L, Hung J.Y, Nelms R.M.(2011) “Comparative evaluation of sliding mode, fuzzy controller and PID controller for a boost converter”; Original Research Article Electric Power Systems Research , 81(1): 99 -106. [9] Bhattacharya A, Chakraborty C.(2011) “A Shunt Active Power Filter with Enhanced Performance Using ANN -Based Predictive and Adaptive Controllers”. IEEE Transactions on Industrial Electronics; 58(2): 421 -426. [10] Karuppanan P, KamalaKanta M.(2010) “PLL with PI, PID and Fuzzy Logic Controllers based Shunt Active Power Line Conditioners”, In: IEEE International Conference on Power Electronics, Drives and Energy Systems. PEDES, 1-6. [11] Saad L, Zellouma L. (2009) “Fuzzy logic controller for three-level shunt active filter compensating harmonics and reactive power. Electric Power Systems Research “; 79(10):1337–41. [12] A Ghamri, M.T Benchouia, A.Golea.,Sliding-mode Control Based Three-phase Shunt Active Power Filter: Simulation and Experimentation; Electric Power Components and Systems Journal, 2012, 40( 4): 383-398. [13] Leszek S, zarnecki C. (2006) “Instantaneous Reactive Power p -q Theory and Power Properties of Three-Phase Systems”. IEEE Transactions on Power , 21(1): 362-367. [14] Akagi H, Kanazawa Y, Nabae A. (1984) “Instantaneous Reactive Power Compensators Comprising Switching Devices without Energy Storage Components”, IEEE Transactions on Industry Applications ; 20(3):625 – 630. [15] S. Bhattacharya, D. M. Divan, B. Banerjee, (1991) “Synchronous frame harmonic isolator using active series filter. EPE -Firenze”, 3: 30-35.