Experimental Evaluation of Single-Phase Shunt Active Power Filter Based on Optimized Synergetic Control Strategy for Power Quality Enhancement

Nowadays, Single-Phase Pulse Width Modulation (SP-PWM) inverter-based Shunt Active Power Filter (SAPF) plays a vitally important role to generate the required harmonic components to minimize harmonic distortion currents and compensate reactive power in low or medium voltage distribution networks [1]. Single-Phase SAPFs (SP-SAPFs) are characterized by simple control design, small size, high energy efficiency, stable output voltage, improved safety, energy security and great ability to adapt with various forms of linear and non-linear loads. Moreover, the standard SP-SAPFs do not need high-voltage components that are typically required in specially designed three-phase SAPFs [2-5]. Figure 1. presents the schematic diagram of the typical SP-SAPF system. The latter is the subject of many researches over the recent years [6, 7].

These SAPF systems can be used not only as Static Var Generators (SVGs) to stabilize and improve the voltage profile in power systems, but also to compensate the harmonic contents, reactive power and unbalanced load current with a fast-dynamic behavior and flexibility during load variations [6, 8, 9]. One of the key factors for the establishment of the SP-SAPF system is the control mechanism. Faced with the variability over time of SP-SAPF systems, conventional deterministic strategies are not sufficiently resistant to ensure better performance required at the same time in the dynamic and permanent conditions [10]. For the control of the DC link voltage and the harmonic current of SP-SAPF, voltage and current controllers of the Proportional-Integral (PI) type have been used. However, this kind of controller requires exact linear mathematical model of the SP-SAPF system, hardly achievable under nonlinearity, parameter variations, and load disturbances [11-13].

Hysteresis controllers have been introduced in the published works and generated a great deal of interest [14] in SP-SAPF applications [15, 16]. This type of controllers provides over-current protection capability for versatility and simplicity of practical implementation. To validate practically the hysteresis controller, the digital signal processor guarantees a good and fast dynamic response compared to other types of digital controllers [17]. Despite the excellent performance of the hysteresis controller, the latter suffers from the problem of the switching frequency which is variable and high. This phenomenon increases power losses and produces severe electromagnetic compatibility (EMC) noise in the single-phase APF and also complicates the selection of the coupling inductor in hysteresis current controllers [18].

To fix the switching frequency of SP-SAPF system, Wang et al. [19] have proposed an adaptive feed-forward control scheme that varied the hysteresis band in the hysteresis modulator in the event of any change of the current error. The adaptive hysteresis modulator is an efficient method for adjusting the switching frequency. The disadvantage of this modulator lies in the extra input voltage feedback which can lead to an increase in the total cost and the complexity of the employed control system. For these reasons, the adaptive hysteresis modulator is not suitable for SP-SAPF system. In their turn, Antchev et al. [20] have limited the switching frequency of SP-SAPF with calculation of any time interval while maintaining the switching action.

The finite control set model predictive control (FCS-MPC) scheme is suggested by Alhasheem et al. [21] for the harmonic current regulation of the SAPF system. The natural switching action of SP-SAPF is compatible with FCS-MPC feature. This strategy is well recognized for its stability, robustness, fast dynamic reaction, and good regulation properties in a wide range of operating conditions. Furthermore, this method does not require the use of internal current loops, PWM or SVPWM modulators for the control of the single phase APF. According to the FCS-MPC theory, the main objective of the SAPF control is to predict the behavior of this system for all admissible switching states over the prediction horizon in order to solve the optimization problem and guarantee the filter current regulation with low THD in different conditions. However, this control technique is more effective than the hysteresis controllers but its performances are dependent of the accurate prediction of the future behavior of the SAPF system [22]. Using incorrect parameters for the predictive controller may result in an inaccurate prediction of future behavior due to the incorrect system model. This situation can lead to the incorrect choice of switching states resulting in a deterioration of the performance of the applied control, even endangering the stability of the system. Building an exact system model with precise parameters is thus important to avoid these serious anomalies. To estimate the uncertain parameters, an FCS-MPC current control with model parameter mismatch and a fuzzy adaptive control law have been proposed for the governance of the SAPF system in the references of Young et al. [22] and Narongrit et al. [23]. However, it is not possible to estimate all uncertain parameters of the SP-SAPF system model [7].

The recently introduced synergistic control has been widely accepted by the control community as well as by the industrialists. The success of its implementation has been proven in several areas such as: the battery charging system where Eghtedarpour et al. [24] have used the synergetic approach for the local control of the power converters; the flexible satellites with a desired attitude achievement have been presented by Sabatini et al. [25]; the output voltage control of the DC/DC buck converter system with an approximation of the unknown parameters has been studied by Babes et al. [26] and Hamouda et al. [27]; the speed control of the PMDC motor has been proposed by Hamouda et al. [28]; the hydraulic turbine regulating system with a stable frequency for small and medium-size power stations has been treated by Huang et al. [29] and Bouchama et al. [30] present the design of power system stabilizers insensitive to parameters variation. The principle of the synergistic control strategy is similar to that of the sliding mode control (SMC) but devoid of the chattering problem. This robust approach is based on the concept of forcing a system under control to operate according to a preselected designer constraint. Based on a continuous control law and a macro-variable that can be a simple combination of state variables, synergistic control is more suitable to a real-time implementation. The main benefit of this approach is that once system states reach the attractor, the system dynamics remain insensitive to a class of parameter variation and external disturbances [30, 31]. Thanks to the high performance of the synergistic control technique, several research articles were published in the literature. However, in much of this research, the synergistic control law was designed based on an asymptotic stability analysis where the trajectories of the system evolve towards a specified attractor reaching equilibrium in an infinite time [31, 32]. This research work discusses the subject of power quality improvement by the SP-SAPF via the synergistic technique. The proposed controller has many advantages such as: ease of practical implementation; asymptotic stability ensured with respect to the required operating conditions; operation under a fixed switching frequency reducing the burden of the filtering device design as well as insurance of robustness characteristics of the SMC technique with low chattering [31]. These advantages offered by this advanced technique have a positive influence on the operation of SP-SAPF through rapid dynamics on the controlled quantities and effective compensation of harmonics, thus leading to a quality of energy recognized by international standards.

The proposed synergetic control algorithm is designed to master the switching states of the SAPF device is based on two gains T and λ imposed and identified by the experience of the designer. To properly determine the two aforementioned gains during the development of the synergistic controller, these latter will undergo an adjustment by the particle swarm optimization (PSO) algorithm. In order to effectively control the SP-SAPF system, two control loops must be governed. To do this and in addition to the application of the synergistic non-linear controller for the internal current control loop of the single-phase APF, another classical PI type controller has been reserved for calculating the reference current in the external loop of the DC bus voltage of SP-SAPF. This paper discusses the simulation by MATLAB/Simulink and the practical validation via the dSPACE 1104 card of the advanced SP-SAPF system which is based on a PI controller and Synergetic Control (SC) law optimized by PSO algorithm. The PI regulator ensures the control of the output voltage of the studied SP-SAPF on the one hand and the calculation of the reference current on the other hand. In turn, the role of the optimized synergistic strategy is to govern the switching states for the switches of the single-phase filtering device after application of the current command. The proposed control strategy has confirmed its superiority through the comparison of the simulation results of the latter with those of the classical strategy (classical PI and classical Hysteresis regulators) as well as of the classical synergistic not optimized method (classical PI and synergistic control law). In addition, the practical validation of the SP-SAPF based on the optimized synergetic control ensures a total harmonic distortion (THD) rate of the source current fully meeting the IEEE international standard. In the case of a healthy and distorted power source, a THD of 3.3% and of 5.3% have been recorded respectively. The obtained results are satisfactory and the objective of improving energy quality has largely been achieved.

3.1 DC link voltage regulator

PI controller is offered to decrease the instability and variations of the DC link voltage, such as indicated in Figure 1. The DC link voltage regulator consists of the proportional gain (K_p) for enhancing the rise time and the integral gain (K_i) for smooth operation, eliminating the error between the sensed DC link voltage (V_C) and its reference (V_C^*) in steady state [33].

To calculate the PI controller's gains, firstly we must determine the transfer function of the studied system with PI controller through the Eq. (1) [34]:

$\frac{{{V}_{C}}}{V{{_{C}^{{}}}^{*}}}=\frac{\left( {{{K}_{P}}}/{C}\; \right)\left( s+{{{K}_{i}}}/{{{K}_{P}}}\; \right)}{s{}^\text{2}+\left( {{{K}_{P}}}/{C}\; \right)\cdot s+{{{K}_{i}}}/{C}\;}$      (1)

We notice from the Eq. (1) that the closed loop system is presented by a canonical second order transfer function.

$\frac{{{V}_{C}}}{V_{C}^{*}}=\frac{\omega {}^\text{2}}{s{}^\text{2}+2\xi {{\omega }_{n}}\cdot s+\omega _{n}^{2}}$      (2)

Through the equalization of the two denominators of Eqns. (1) and (2), the controller's gains (K_p and K_i) are quantified as follows:

$\left\{ \begin{align}  & {{\text{K}}_{\text{P}}}\text{=2 }\!\!\xi\!\!\text{ }{{\text{ }\!\!\omega\!\!\text{ }}_{\text{n}}}\text{C} \\ & {{\text{K}}_{\text{i}}}\text{=C}{{\text{ }\!\!\omega\!\!\text{ }}_{\text{n}}}\text{ }\!\!{}^\text{2}\!\!\text{ } \\\end{align} \right.$       (3)

3.2 Design of synergetic control law

The basic procedure of synergetic control synthesis for SAPF is shown below. The choice of function of the system state variables (macro-variable) is the first step to design the synergetic controller’s synthesis as shown in Eq. (4).

$\psi =\psi (x,t)$      (4)

The main focus of the controller requires the system to have the attractor ψ=0. The characteristics of the macro-variable according to performance and control specifications can be selected by the designer. Also, the desired dynamic evolution of the macro variable is usually chosen by the Eq. (5).

$T\frac{d\psi }{dt}+\psi =0{{,}^{{}}}{{^{{}}}^{{}}}T>0$      (5)

T is a positive constant to be imposed by the designer. In our paper, its value is optimized by PSO algorithm.

The designer chooses speed convergence to the target equilibrium point. Eq. (6) is given by the chain rule of differentiation as follows:

$\frac{d\psi }{dt}=\frac{\partial \psi (x,t)}{\partial x}\frac{dx(t)}{dx}$      (6)

Making deference between the macro-variable Eq. (4) and Eq. (5) leads to Eq. (7).

$T\frac{\partial \psi (x,t)}{\partial x}f(x,U,t)+\psi (x,t)=0$      (7)

The law of the proposed SC can be found by solving Eq. (7) as follows.

${{U}_{SC}}={{U}_{d}}(x,t,\psi (x,t),T)$       (8)

The differential equations form of nonlinear dynamic for SP-SAPF system is given by the Eq. (9).

$\left\{ \begin{align}  & {{{\dot{x}}}_{1}}=\frac{-1}{{{L}_{f}}}{{x}_{2}}(1-2{{U}_{d}})+\frac{{{V}_{SS}}}{{{L}_{f}}} \\ & {{{\dot{x}}}_{2}}=\frac{1}{C}{{x}_{1}}(1-2{{U}_{d}}) \\\end{align} \right.$       (9)

As reminder: x(t) represents the state coordinate; x₁ represents the current filter (i_f); x₂ represents the DC link voltage (V_C); U_d is the control input (the duty ratio); L_fis the inductor of SP-SAPF and C is the capacitor of the DC link voltage.

The synergetic control synthesis of the system that we have presented in Eq. (9) started by demonstrating a designer that is been chosen as macro-variable and given in Eq. (10).

$\psi ={{e}_{if}}+\lambda \int{{{e}_{if}}}=({{x}_{1}}-x_{1}^{*})+\lambda \int{({{x}_{1}}-x_{1}^{*})dx(t)}$      (10)

$\begin{align}  & \dot{\psi }={{{\dot{e}}}_{if}}+\lambda {{e}_{if}} \\ & \dot{\psi }=\left[ \frac{1}{{{L}_{f}}}{{x}_{2}}(2\,{{U}_{d}}-1)+\frac{{{V}_{ss}}}{{{L}_{f}}}-\dot{x}_{1}^{*} \right]+\lambda ({{x}_{1}}-x_{1}^{*}) \\\end{align}$     (11)

Moreover, having Eq. (5) and Eq. (11), the resulting control law U_d is given by Eq. (13):

$T\left[ \frac{1}{{{L}_{f}}}{{x}_{2}}(2\,{{U}_{d}}-1)+\frac{{{V}_{ss}}}{{{L}_{f}}}-\dot{x}_{1}^{*} \right]+T.\lambda ({{x}_{1}}-x_{1}^{*})+\psi =0$      (12)

$U_{S C}=U_{d}=\frac{\frac{\psi}{\mathrm{T}}+\lambda\left(x_{i f}-x_{i f}^{*}\right)-x_{i f}^{*}+\frac{1}{L_{f}} V_{s s}}{\frac{2}{L_{f}} x_{2}}+\frac{1}{2}$    (13)

To confirm stability, we use the following Lyapunov function candidate:

$V=\frac{1}{2}{{\psi }^{T}}\psi $     (14)

Therefore:

$\dot{V}={{\psi }^{T}}\dot{\psi }$     (15)

The use of Eq. (16) leads to:

$\dot{V}=-\frac{1}{\mathrm{~T}}\left(e_{i f}+\lambda \int e_{i f}\right)^{2}$     (16)

Form Eq. (16) it can be found that $\dot{V}<0$.

On the basis of Lyapunov theory, the stability of the SP-SAPF system is assured via the synergetic control law.

3.3 Implementation of PSO for Synergetic controller (SC-PSO)

3.3.1 Formulation of the problem to be optimized

The formulation of the problem to be optimized is mainly concerned with minimizing the error ERR = i_f – i_f* where the objective function F(X) can be written as fellow:

$Min~F(x)=Min(ERR)$      (17)

With: X the control parameter set which can be written in the following form:

$X=\left[ T,\text{ }\!\!\lambda\!\!\text{ } \right]$        (18)

The objective function is subjected to inequality constraints as shown below:

$\begin{align}  & {{T}^{\min }}<\text{T}<{{T}^{\max }} \\ & {{\text{ }\!\!\lambda\!\!\text{ }}^{\min }}<\text{ }\!\!\lambda\!\!\text{ }<{{\text{ }\!\!\lambda\!\!\text{ }}^{\max }} \\\end{align}$       (19)

3.3.2 Particle swarm optimization

J. Kennedy & R. Eberhart have been proposed the PSO algorithm in 1995 [35]. It is one of the stochastic search algorithms. In PSO, the population is made up of solution candidates named particles [36, 37].

Each particle having a position ${{X}_{i}}=(x_{i}^{1},x_{i}^{2},...,x_{i}^{l})$ and a flight velocity ${{V}_{i}}=(v_{i}^{1},v_{i}^{2},...,v_{i}^{l})$. In fact, every particle has a best position $P_{ibest}^{{}}=(P_{ibest}^{1},P_{ibest}^{2},...,P_{ibest}^{l})$ and a global best position $G_{best}^{{}}=(G_{best}^{1},G_{best}^{2},...,G_{best}^{l}).$

The update of position and velocity is obtained by the following equations:

$X_{r}^{iter+1}=X_{r}^{iter}+\theta \times V_{r}^{iter+1}$     (20)

$\begin{align}  & V_{r}^{iter+1}=\theta \times {{w}_{{}}}.V_{r}^{iter+1}+{{\theta }_{1}}.rand1.(P_{best}^{iter}-X_{r}^{iter})+ \\ & {{\theta }_{2}}.rand2.(G_{best}^{iter}-X_{r}^{iter}) \\\end{align}$     (21)

where: w represents the inertia weight factor; θ₁ and θ₂ are the acceleration factors; rand is a uniform random value between [0,1]; V^iter and X^iter denote the velocity and the position of one particle i at iteration k, respectively.

The acceleration coefficients are considered as fixed values as follow: θ₁=θ₂=2.05 [38].

2.png

Figure 2. Flowchart of SC strategy optimised by PSO

The main optimization steps of the SC-PSO strategy are illustrated on the flowchart illustrated by Figure 2.

PSO based SC approach is applied to adjust the optimal control variables in order to minimize the ERR while satisfying a good control of the switching states of the SP-SAPF inverter switches.

To give more confidence to our study, an experimental test bench is carried out using a dSPACE 1104 board as presented in Figure 8. The performance of considered synergetic approach based on PSO algorithm and PI controller for the SP-SAPF has been tested for several conditions. For assess the studied control strategy, our SP-SAPF system is experienced in transient and steady states.

Furthermore, coverage of changes affecting the nonlinear load, the DC link voltage (V_C) and the power source (V_S) has been taken into consideration in this section. Using the power quality analyzer (Chauvin ArnouxC.A.8335) and the digital oscilloscope (GwinstekGDS-3504), the obtained practical results are recorded and presented in the following sections.

8.jpg

Figure 8. Photograph of platform of the experiment test

5.1 SP-SAPF performance in transient and steady states

The start transient of the SP-SAPF at the reference point of DC link voltage V_C^* of 110V accompanied by the currents i_s, i_L and if responds smoothly without overshooting as shown in Figure 9.

9.png

Figure 9. Transient response of SP-SAPF during increment of DC link voltage from V_C=0V to V_C=110V

Figure 10 shows the steady-state responses of the suggested control law under non-linear RC load. The source current has a nearly perfect waveform sine and in phase with the supply voltage thanks to the filter current. For its part, the load current is presented in steady state by its usual form.

10.png

Figure 10. Steady-state performance of the proposed control of the SP-SAPF under a nonlinear RC load condition

Before connecting and commissioning the SP-SAPF, the source current is distorted and its THD is rated at 38% as shown in Figure 11.

11.png

Figure 11. Power quality analysis of i_s without SP-SAPF

12.png

Figure 12. Power quality analysis of i_s with SP-SAPF controlled by SC-PSO strategy

After activation of SP-SAPF controlled by the synergistic strategy optimized by PSO, the source current has become sinusoidal in phase with the source voltage and its THD is 3.3% as shown in Figure 12.

5.2 Performance of the SP-SAPF during change in the DC link voltage reference

The variation of the DC link reference voltage for the following values 110V, 140V and 110V was used to verify the performance of the SP-SAPF as shown in Figure 13. The DC voltage of the filter quickly reaches and easily follows the various imposed references with recording of acceptable overshoots. In addition, the source, load and filter currents maintained their appropriate values during the changes made in the DC link voltage.

131.png

132.png

133.png

Figure 13. Dynamic response of the proposed control of the SP-SAPF under the DC voltage reference sudden change from 110V to 140V and inversely

5.3 Performance of the SP-SAPF during change in the nonlinear load

A nonlinear load change is implemented by connecting/disconnecting an additional load in parallel of the old load. The real-time test results are shown in Figure 14. Because of step change in nonlinear load, source current increases/decreases smoothly. DC link voltage remains fairly constant and does not experience the variations in nonlinear load. With the exception of certain distortions due to the change in the source current, the DC link voltage is maintained at a constant value of 110 V during the change in the nonlinear load. The load and filter currents react correctly to this established test.

141.png

142.png

143.png

Figure 14. Dynamic response of the SP-SAPF under a nonlinear load variation

5.4 Performance of the SP-SAPF under a polluted power source

In this section, the aim is to prove the robustness of the proposed optimized synergetic control in case of a polluted power source with a THD of 20%. The obtained practical results in steady state of the source, load and filter currents are given in Figure 15. Without SP-SAPF of the deformed power source, the THD of the measured source current is equal to 47.6% as indicated in Figure 16. In the event that the SP-SAPF is activated and the power source is deformed, the saved THD in Figure 17 of the source current is 5.3%. This experience has proved the ability of SC-PSO control law to enhance the shape form current in case of the degraded quality of the power source [39].

15.png

Figure 15. Steady-state performance of the proposed control of the SP-SAPF under distorted source voltage condition

16.png

Figure 16. Power quality analysis without SP-SAPF under distorted source voltage condition

17.png

Figure 17. Power quality analysis of i_s with SP-SAPF controlled by SC-PSO strategy under distorted source voltage condition