Design and real time implementation of fuzzy switched controller for ...

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Design and real time implementation of fuzzy switched controller for single phase active power filter Hamza Afghoul a,n, Fateh Krim b, Djamel Chikouche a, Antar Beddar c a

Laboratoire d'analyse des signaux et systèmes (LASS), Département d'électronique, Faculté de technologie, Université de Mohamed Boudiaf M’sila, Algeria Laboratoire LEPCI, Département d'électronique, Faculté de technologie, Université de Ferhat Abbas Sétif-1, Algeria c Département de Génie Electrique, Faculté de technologie, Université de Skikda, Algeria b

art ic l e i nf o

a b s t r a c t

Article history: Received 13 January 2015 Received in revised form 22 June 2015 Accepted 4 July 2015 This paper was recommended for publication by Jeff Pieper.

This paper proposes a novel fuzzy switched controller (FSC) integrated in direct current control (DCC) algorithm for single phase active power filter (SPAPF). The controller under study consists of conventional PI controller, fractional order PI controller (FO-PI) and fuzzy decision maker (FDM) that switches between them using reduced fuzzy logic control. The proposed controller offers short response time with low damping and deals efficiently with the external disturbances while preserving the robustness properties. To fulfill the requirements of power quality, unity power factor and harmonics limitations in active power filtering an experimental test bench has been built using dSPACE 1104 to demonstrate the feasibility and effectiveness of the proposed controller. The obtained results present high performance in steady and transient states. & 2015 ISA. Published by Elsevier Ltd. All rights reserved.

Keywords: Fractional calculus (FC) Power quality (PQ) Total harmonic distortion (THD) dSPACE 1104 Single phase active power filter (SPAPF)

1. Introduction Recently, current harmonics become a serious problem in power distribution systems caused by connecting nonlinear loads to the electrical grid; especially power electronics converters in industry fields as well as by domestic consumers [1–5]. These harmonics fed from nonlinear loads pollute the grid by affecting the current and voltage waveforms and leading to a reduction of the power factor [6]. Thus, several standards were proposed to avoid deterioration of power quality such as IEEE harmonic standard 519 that strictly imposes a value less than 5% of the global THD [7]. Traditional solutions based on RLC circuits were designed to face these problems regarding to their advantages presented in simplicity and low cost [1]. Moreover, these kinds of passive filters eradicate particularly low order frequencies (3th, 5th, 7th, 11th…) but they are susceptible to originate series and parallel resonances between the power supply and load [8–10]. Thus, active power filters are often used to compensate reactive power by reducing distortions of current due to nonlinear loads [11,12]. n

Corresponding author. E-mail addresses: [email protected] (H. Afghoul), [email protected] (F. Krim), [email protected] (D. Chikouche), [email protected] (A. Beddar).

In the literature, active power filters are presented with several topologies. Among them, single phase active power filter (SPAPF) is widely used in medium and low power installations due to its low cost and high efficiency [13]. Indeed, SPAPFs are allowing an easier installation without the need to interrupt the power supply or loads [13]. A number of new control techniques have been proposed to control SPAPFs with regard to the integration of control and sensorless methods [11]. The majority of techniques based on complicated calculus of instantaneous active and reactive power lead to slow computing time and need powerful calculation units (such as DSPs) [8]. For this reason, this paper improves the regulation side of the direct current control (DCC) which is a simple algorithm consisting of two control loops [13]. An outer voltage loop used for DC-bus voltage regulation while an inner current loop is used to generate switching command signals. In industrial fields, the PI controller with fixed parameters is known as good solution in regulation loops and continued to be the most widely used process control technique for many decades because the simple structure is easier for engineering design [14]. This controller is good in steady state but has some weakness in dynamic state [15]. Indeed, the conventional PI controller is sensitive to parameters variation and external disturbances [16]. Unfortunately, this kind of controllers cannot satisfy the requirements in DC-bus regulation loops and leads to degradation in control performance. Nowadays, using fractional order PI

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Please cite this article as: Afghoul H, et al. Design and real time implementation of fuzzy switched controller for single phase active power filter. ISA Transactions (2015), http://dx.doi.org/10.1016/j.isatra.2015.07.008i

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controller (FO-PI) in control systems received more and more attention of scientists to increase the control accuracy [16,17]. λ μ First, the fractional order PI D controller was proposed by Poblubny in [18], where a better control performance was demonstrated in comparison with the conventional PID controller because of the extra real parameters λ and μ [16]. The FO-PI controller solves the drawbacks of the conventional one in dynamic state by giving extra degree of freedom to the controller, offering faster response [19,20] and being robust to the parameters variation due to its flat phase around the crossover frequency as demonstrated in the Ref. [20]. However, FO-PI controllers have bad effects on the power quality in active filtering in steady state. Especially, the need of the approximation method when building these controllers as demonstrated in [21]. Recently, using soft computing techniques such as fuzzy logic [22–24], neural networks [25] and genetic algorithm [26,27] have successfully been used in many control applications [23] and in regulation loops especially such as variable order fractional PID controller based on fuzzy logic to deal with parameters variation of the system has been proposed in [28], the robustness of a fractional PID controller using neural network has been enhanced in [29], a novel fractional order (FO) fuzzy Proportional-IntegralDerivative (PID) controller has been proposed in [27], which used a genetic algorithm to optimize their parameters, an IP controller to reduce the first overshoot of DPC technique has been integrated in voltage regulation loop in [10,19], a higher order sliding mode controller based on super twisting algorithm has been used in [30]. But the complexity of these controllers is far beyond the fixed parameters PI controller that leads to high online calculation ability and increases the cost of hardware as well as software of the system [14]. Nevertheless, all mentioned controllers have improved the control performance from some aspects and ignore the other aspects. The main contribution of this paper is to propose a new robust controller named fuzzy switched controller (FSC) in the outer voltage regulation loop of the DCC technique regarding to the steady and dynamic performance. The proposed FSC consists of conventional PI controller, FO-PI controller and fuzzy decision maker (FDM) that switches between the conventional and the fractional order controllers based on a reduced fuzzy logic (FL) rules to guarantee low cost. FL has become common application to deal with complex nonlinear processes and to enhance the closed loop performance [31]. The implementation of FL control is rather difficult and leads to high cost. Thus, a reduced FL rules is used to decrease the calculation [14]. PI and FO-PI controllers are selected from one to another depending on their performance under certain operating conditions. When the error between the actual value and its reference is considered small; the FDM switches to the conventional PI controller. Elsewhere, the FDM switches to the FO-PI controller to deal with the abnormal condition. The FO-PI

Fig. 1. Scheme of the power system under study.

controller is designed to bring the DC-bus voltage closer to the reference as faster as possible. Thus, the FSC guarantees high performance and low cost with less calculation and complexity. All obtained results prove that the FSC outperforms the use of conventional or fractional order controller. This paper presents a procedure to design a robust fuzzy switched controller to enhance the DC-bus regulation of SPAPF. The validity of the proposed DCC approach (FSC-DCC) has been investigated through real time bench implementation. The steady state and dynamic behavior of FSC-DCC algorithm have been presented with the robustness tests in practice.

2. Power system and control algorithm 2.1. Power system configuration The single phase compensation system shown in Fig. 1 is composed of an electrical grid supplying a nonlinear load represented by a single phase bridge rectifier feeding RC load and a SPAPF which is a voltage source inverter (VSI) with 4 IGBTs including a capacitor Cdc in the DC part and an inductance Lf in the other part. The configuration of the SPAPF is able to compensate current harmonics, to ensure a power factor (PF) correction and to eliminate voltage distortions. 2.2. DCC technique Fig. 2 shows the proposed direct current control algorithm for SPAPF. It is composed of two control loops, the first one is the outer voltage loop, which is responsible to keep the measured capacitor voltage (Vdc) oscillating around a desired reference ðV ndc Þ and generate the maximum source current amplitude (Isamx). The second is the inner current loop that compares the calculated reference current ðI ns Þ with the measured reference current. Finally, the error Δis passed through a hysteresis band ( 70.1 A) to obtain the switching command signals.

3. The proposed controller design This paper presents a new systematic design of switched controllers by proposing a fuzzy switched controller (FSC) as shown in Fig. 3. The FSC composed of conventional PI controller, fractional order PI controller (FO-PI) and switches between them using fuzzy decision maker (FDM). The FDM selects the best controller according to the value of ε(t) (the error between the actual capacitor voltage Vdc and its reference V ndc ) when persistent external disturbances are detected. The closed loop of DC-link voltage of the SPAPF is shown in Fig. 4. Where, Fig. 4a is the equivalent closed loop in the steady state when the conventional PI controller has been selected. On the other hand, Fig. 4b is the equivalent closed loop regulation when the FO-PI

Fig. 2. Proposed control scheme (FSC-DCC technique) for SPAPF.

Please cite this article as: Afghoul H, et al. Design and real time implementation of fuzzy switched controller for single phase active power filter. ISA Transactions (2015), http://dx.doi.org/10.1016/j.isatra.2015.07.008i

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controller is selected in dynamic state. The FO-PI controller is capable to stand the parameters variations because of its flat phase around the crossover frequency as demonstrated in Fig. 5.

4. Steps to design the proposed FSC The procedure for developing the FSC of Fig. 3 is summarized as follows: Step 1: calculate the proportional and integral gains of the conventional PI controller (kpc, kic), (selected in steady state). Step 2: calculate the proportional and integrator gains (kif, kpf) and the real order of integration α of the FO-PI controller (selected in dynamic state). Then, approximate the term s  α using Oustaloup continuous approximation to a transfer function (to be implemented in practical tests). Step 3: build the FDM to select the best controller.

4.1. Conventional PI controller The conventional PI controller is designed to determine appropriate control parameters kp and ki to obtain the expected control performance in steady state. The system TF and the conventional controller TF can be described respectively by Eqs. (1) and (2), P ðsÞ ¼

1

ð1Þ

C dc s

C c ðsÞ ¼ kpc þ

kic s

ð2Þ

The TF of closed loop regulation (Fig. 4a) is calculated and given by Eq. (3) GðsÞ ¼

V dc ¼ V ndc

kpc kic C dc s þ C dc k pc s2 þ C dc s þ Ckdcic

ð3Þ

3

Eq. (3) is a second order and then it is similar to Eq. (4) GðsÞ ¼

V dc 2ξωn s þ ω2n n ¼ 2 V dc s þ 2ξωn s þ ω2n

ð4Þ

By identification of Eqs. (3) and (4), we get Eq. (5) to calculate the parameters of the conventional controller ( kic ¼ C dc :ω2n ð5Þ kpc ¼ 2ξωn C dc The parameters of the conventional PI controller are given in Appendix A. 4.2. Fractional order PI controller design The regulation loop of the FO-PI controller is presented in Fig. 4b with an extended integration order from integer value ð1=sÞ to real value ð1=sα Þ. 4.2.1. Parameters calculus of FO-PI controller The method to calculate the parameters kif, kpf and α of the FOPI controller has been given is this brief section and has been well detailed in the Ref. [21]. The FO-PI controller has the following TF: kif C ðsÞ ¼ kpf þ α s

ð6Þ

Assume gain crossover frequency ωc and phase margin φm are given. From the basic definition of gain crossover frequency and phase margin, we get the following specifications [32]: 1) phase margin specification:   Arg ½Gðωc Þ ¼ Arg Cf ðjωc ÞP ðjωc Þ ¼  π þ φm 2) robustness to gain variations of the plant:   dðArgðCf ðjωÞPðjωÞÞÞ ¼0 dω ω ¼ ωc

ð7Þ

ð8Þ

with the condition that the phase derivative at ωc the frequency is zero, i.e., the phase Bode plot is flat at the gain crossover frequency; it means that the system is more robust to gain changes and being the overshoots of the responses are almost the same. 3) amplitude specification:     Gðjωc Þ ¼ Cf ðjωc ÞP ðjωc Þ ¼ 1 ð9Þ

Fig. 3. The proposed fuzzy switched controller (FSC).

Considering these specifications, we can solve Eqs. (10)–(12) to get kif, α and kpf   tan 2π þ φm   ð10Þ kif ¼   α  α cos απ tan  π þ φ ωc sin απ m 2  ωc 2 2

Fig. 4. Closed loop capacitor voltage regulation using (a) conventional PI, (b) FO-PI controller.

Please cite this article as: Afghoul H, et al. Design and real time implementation of fuzzy switched controller for single phase active power filter. ISA Transactions (2015), http://dx.doi.org/10.1016/j.isatra.2015.07.008i

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FO -PI PI

FO -PI

PI

Fig. 5. Bode diagram of both PI and FO-PI controllers.

Table 1 Fuzzy rules table showing change in control output. ε(t) Δε(t)

N F F C

N ZE P

Fig. 6. Fuzzy decision maker (FDM) block diagram.



h i 1 0 k ω  α sin απ  d  tan  1 1 þ ik cω  α cos2 απ  π2 dðArgðGðjωÞÞÞ if c 2 A ¼@ dω dω ω ¼ ωc

¼0 ω ¼ ωc

ð11Þ C dc U ω kpf ¼ qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi  2  2 þ kif ω  α sin απ 1 þ kif ω  α cos απ 2 2

ð12Þ

The parameters of the proposed FO-PI controller are calculated and given in Appendix A. However, in simulation and practical test, α the integration term s  should be approximated and given as a TF. 4.2.2. Oustaloup continuous approximation α In order to approximate the term s  , several methods have been used, like the predictor–corrector approach [33], analytical and numerical calculation of the inverse Laplace transform [34] and Oustaloup continuous approximation (OCA) [20] which is largely used to approximate the fractional order of the PI controller [20]. The fractional PI λ Dμ controller which was proposed by Podlubny [18] is described in Eq. (13) by its TF C ðsÞ ¼ kpf þ kif U s  λ þkdf Usm

λ; m 4 0

ð13Þ

Oustaloup presented the approximation algorithm used when a frequency band of interest is given by ½ωb ; ωh , the term sα can be substituted by Eq. (14) [32] s þ ωk' ð14Þ s þ ωk α The Oustaloup's approximation model of the term s is given in [32], where s is Laplace transform variable and α is a real number sα ¼ K

N

∏

k ¼ N

ZE F C F

P C F F

in the range of ( 1, 1). sα is called a fractional order differentiator if 0 o α o 1 and a fractional-order integrator if 1 o α o0. The transfer function of the term sα is given by Eq. (15)  α N 1 þ s ωb ω'k ð15Þ H ðsÞ ¼ K ∏ ωh k ¼  N 1 þ ωsk where

ωk' ¼ ωb



ωh ωb

k þ N2Nþ þ12ð11  αÞ

; ωk ¼ ωb



ωh ωb

k þ N2Nþ þ12ð11 þ αÞ

and K ¼ ωαh . ωk' and ωk are respectively the zeros and the poles of rang k, and 2N þ1 is the order of approximation function [32]. Eq. (15) can be written as Eq. (16) sα ¼ K

ðs  Z 0 Þðs Z 1 Þðs  Z 2 Þðs  Z 3 Þðs  Z 4 Þðs  Z 5 Þðs  Z 6 Þ ðs  P 0 Þðs P 1 Þðs  P 2 Þðs  P 3 Þðs  P 4 Þðs  P 5 Þðs  P 6 Þ

ð16Þ

The approximated controller ðC TF ðsÞÞ has the following form:  α N 1 þ s0 ωk ωb ð17Þ C TF ðsÞ ¼ kpf þ kif nK ∏ ωh k ¼  N 1 þ ωsk 4.3. Fuzzy decision maker Fuzzy logic was created by Zadeh [35] and applied in several fields of research and developed later in many works [22–24]. The proposed FDM of Fig. 3 is obtained by incorporating human experience or expert knowledge into a fuzzy controller through reduced linguistic rules (N, Z and P) which makes the control process easily to be understood [31,24]. To realize a systematic switching process based on previous knowledge about the conventional and the FO-PI controllers, a Takagi–Sugeno model is employed. Fig. 6 displays the basic function of the proposed FDM. Note that global error ε(t) is the sum between the error εp(t) passed through the conventional PI controller in steady state and the

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Fig. 7. Membership functions, (a) error, (b) derivative error, (c) output switching signal.

Fig. 8. (a) Error between the measured capacitor voltage and its reference (ε(t)), (b) error through PI controller (εp(t)), (c) error through FO-PI controller (εf(t)).

error εf(t) passed through the FO-PI controller in transient state. r is a nonzero positive constant less than one. In this paper, an expert control strategy involving only few rules can realize the switching mechanism of Table 1 and described as follows: Rulei if ε(t) is Mj and Δε(t) is Tk then u(t) Where: Mj and Tk are fuzzy terms of the rulei corresponding to the error ε(t) and its derivative Δε(t), i¼1, 2,…, 9 and j¼ 1, 2, 3,

k¼ 1, 2, 3. u(t) is the switching command signal which is equal to 1 or 0 to select the proper controller. The fuzzy logic controller of Fig. 6 translates numeric input data into verbal or linguistic variables through membership functions as shown in Fig. 7, uses fuzzy rules to evaluate these variables, after the defuzzification process, the switching signal u(t) is obtained and has two values 0 or 1 (Fig. 7c). The error and its derivative consist of three fuzzy sets, positive (P), negative (N) and zero (Z) as illustrated in

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Fig. 7a and b. The normalized ε(t) and Δε(t) fall within the range [ 1, 1] and adjusted by the gains Kε and KΔε which are responsible to control the sensibility bandwidth of the FDM to the external changes. After building the FSC, several practical tests have been developed to validate the proposed FSC-DCC algorithm.

5. Results

Fig. 9. Photo of the experimental set-up components: (1) PC with dSPACE 1104, (2) transformer, (3) oscilloscope, (4) power analyzer, (5) filter inductance, (6) voltage sensors, (7) current sensors, (8) voltage source inverter (VSI).

As application of the proposed controller, active power filtering is the system used to test the robustness of the FSC by imposing severe changes on the load. On the other hand, the SPAPF is used as intermediate elements to connect different renewable sources to the grid which lead to instable capacitor voltage reference ðV ndc Þ. Thus, building a powerful controller with high performance leads to reduction of the cost without invest in additional equipments. Due to the limitation of the paper presentation, only the FSC performance is presented in simulation section and the other tests have been made experimentally. 5.1. Simulation results The simulation example is incorporated to explain the switching mechanism from one controller to another one depending on the external uncertainties. As shown in Fig. 8, the global error ε(t) of Fig. 8a is the sum of the error εp (t) passed through the conventional PI controller (Fig. 8b) and the error εf(t) passed through the FO-PI controller (Fig. 8c). In more details, when the error is out of the desired band, the FDM switches to FO-PI controller to push the capacitor voltage into the band in short time with low overshoot. Note that we can regulate the limit range of this band by adjusting the gains (Kε, KΔε) of the FDM (see Fig. 6). 5.2. Experiment results

Fig. 10. Experimental results with capacitive load in steady state.

Fig. 9 presents the experimental set-up of 1.5 kW developed in laboratory, in order to examine the validity of the proposed algorithm to control the SPAPF. The proposed FSC-DCC algorithm is implemen-

Fig. 11. Experimental measures obtained from power quality analyzer: (a) THDi–v of Is and Vs before filtering, (b) THDi–v after filtering using well-tuned PI controller, (c) THDi–v after filtering using FO-PI controller.

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Decrease load

Vdc [100V/div] Increase load

Q [100VAR/div]

P [100W/div]

50ms

Decrease load

Vdc [100V/div] Increase load

7

P [100W/div]

Q [100VAR/div]

50ms

Fig. 12. Experimental results for two changes of load, (a) using well-tuned PI controller, (b) using proposed FSC.

ted on real time board (dSPACE RTI 1104) with a sampling time Ts¼40 ms. The controller is executed at 20 kHz. A SEMIKRON inverter is used as VSI. The variation in the load is obtained by connecting or disconnecting a parallel load. The system parameters used in practical tests are given in Appendix B and the results are shown in Figs. 10–12. The SPAPF is capable of cleaning up the grid-side from current harmonics generated by a nonlinear load. Fig. 10 shows the voltage and currents waveforms using FSC-DCC algorithm in steady state. This figure confirms the efficiency of SPAPF by injecting filter current (If) to compensate the load current (IL) which is rich of harmonics, then leading to a sinusoidal waveform of the source current (Is). Fig. 11 shows Is and Vs of Fig. 10 obtained from the power quality analyzer. Before filtering in Fig. 11a, the nonlinear load is considered as a high polluting load with a THDi equal to 55.8% and a THDv equal to 7.5% compared to the widely used inductive load (THDi ¼26%) in the literature. Thus, use of a high polluted load can be a strong challenge to the enhanced algorithm in steady state. After filtering, the SPAPF compensates the harmonic currents by reducing them less than 5% to respect the IEEE 519 standard. Fig. 11b and c shows the THDs using conventional controller and FO-PI controller respectively. It can be seen that the conventional solution with a THD equal to 2.4% is better than the fractional order controller with a THD equal to 5%. According to the experimental results and the previous knowledge about the behavior of both controllers, the FDM is obliged to select the well-tuned controller to ensure better power quality in steady state. To verify the robustness of the proposed controller in dynamic state, another test was done and clearly presented in Fig. 12 where we compare the performance of our proposed FSC with a welltuned PI controller. Obviously, with severe changes of the load, the control performance gets worse when using the conventional PI controller as shown in Fig. 12a while the FSC reduces the overshoots and achieves its references in short time by switching to the FO-PI controller to deal with abnormal condition (Fig. 12b). According to Fig. 12, we can design the FDM to select the FO-PI controller in dynamic state. All experimental results confirm the robustness of the FSC in both dynamic and steady states, the efficiency in compensation of reactive power by reducing the THD less than 3% of the SPAPF permits the proposed algorithm (FSC-DCC) to be an interesting solution algorithm for active power filtering. While developing a simple algorithm with powerful performance, it means a reduction of the size, cost, and volume of the overall power installation, also reducing power losses in equipments.

6. Conclusion In this paper, a novel fuzzy switched controller (FSC) for DC-bus voltage regulation of SPAPF is proposed. The FSC consists of conventional PI controller, fractional order PI controller and fuzzy decision maker (FDM) switches between them using reduced fuzzy logic

control. The benefits of the FSC is that, if the conventional PI controller failed to follow quickly its reference when an external disturbance has been detected; the FDM switches to fractional order controller that is designed for better dynamic state to deal with the abnormal working conditions. Thus, the proposed controller is dedicated to enhance the closed loop regulation performance for linear model in steady and dynamic states. The experimental results show that the integration of FSC improves the power quality by respecting the harmonics limitations (THDi ¼ 2.4%, THDv ¼2.4%), putting the power factor closer to unity and standing the load variations with short settling time. All obtained results satisfy IEEE harmonic standard 519 (THDo5%). All the tests of robustness have been done proving the superiority of proposed FSC-DCC algorithm which could become an interesting alternative to standard DCC techniques for active power filtering.

Appendix A

Control parameters kpc ¼ 1:4, kic ¼ 217, kp ¼ 0:4, ki ¼ 30, α ¼ 0:8 , ωb ¼ 10  2 rad=s,

ωh ¼ 106 rad=s, N ¼ 3

Appendix B

Circuit parameters Vs RL CL Lf C dc

50 V 25 Ω 1100 mF 4 mH 1100 mF

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Please cite this article as: Afghoul H, et al. Design and real time implementation of fuzzy switched controller for single phase active power filter. ISA Transactions (2015), http://dx.doi.org/10.1016/j.isatra.2015.07.008i