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energies Article

A Nature-Inspired Optimization-Based Optimum Fuzzy Logic Photovoltaic Inverter Controller Utilizing an eZdsp F28335 Board Ammar Hussein Mutlag 1,2, *, Azah Mohamed 1 and Hussain Shareef 3 1 2 3

*

Department of Electrical, Electronic and Systems Engineering, Faculty of Engineering and Built Environment, Universiti Kebangsaan Malaysia, 43600 Bangi, Selangor, Malaysia; [email protected] College of Electrical and Electronic Engineering Techniques, Middle Technical University, 10022 Baghdad, Iraq Department of Electrical Engineering, United Arab Emirates University, 15551 Al-Ain, UAE; [email protected] Correspondence: [email protected]; Tel.: +6011-2325-1760

Academic Editor: Peter J S Foot Received: 9 December 2015; Accepted: 5 February 2016; Published: 23 February 2016

Abstract: Photovoltaic (PV) inverters essentially convert DC quantities, such as voltage and current, to AC quantities whose magnitude and frequency are controlled to obtain the desired output. Thus, the performance of an inverter depends on its controller. Therefore, an optimum fuzzy logic controller (FLC) design technique for PV inverters using a lightning search algorithm (LSA) is presented in this study. In a conventional FLC, the procedure for obtaining membership functions (MFs) is usually implemented using trial and error, which does not lead to satisfactory solutions in many cases. Therefore, this study presents a technique for obtaining MFs that avoids the exhaustive traditional trial-and-error procedure. This technique is implemented during the inverter design phase by generating adaptive MFs based on the evaluation results of the objective function formulated with LSA. The mean squared error (MSE) of the inverter output voltage is used as an objective function in this study. LSA optimizes the MFs such that the inverter provides the lowest MSE for the output voltage, and the performance of the PV inverter output is improved in terms of amplitude and frequency. First, the design procedure and accuracy of the optimum FLC are illustrated and investigated through simulations conducted in a MATLAB environment. The LSA-based FLC (LSA-FL) are compared with differential search algorithm (DSA)-based FLC (DSA-FL) and particle swarm optimization (PSO)-based FLC (PSO-FL). Finally, the robustness of the LSA-FL is further investigated with a hardware that is operated via an eZdsp F28335 control board. Simulation and experimental results show that the proposed controller can successfully obtain the desired output when different loads are connected to the system. The inverter also has a reasonably low steady-state error and fast response to reference variation. Keywords: lightning search algorithm (LSA); fuzzy logic controller (FLC); inverter; photovoltaic (PV); space vector pulse width modulation (SVPWM); eZdsp F28335

1. Introduction Nowadays, renewable energy (RE) has become the main impetus of the energy sector, primarily because it is environment friendly, clean, and a secure energy source [1]. Among REs, photovoltaic (PV) power generation is one of the most promising technologies that can be utilized in industrial power systems and rural electrification [2]. Given that PV generators can only supply DC power, an inverter is required to connect the load to PV generators [3]. The main feature of a good power inverter is

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its capability to provide clean, high-quality power and constant amplitude sinusoidal voltage and frequency, regardless of the load type to which it is connected. Furthermore, a power inverter must also have the capability to recover quickly from transients caused by external disturbances without causing power quality problems. In the context of a stand-alone PV generator, the output voltage and current waveforms should be controlled based on the reference values. Therefore, an efficient PV inverter controller is required [4]. However, the extensive use of PV generators raises many challenges, such as harmonic pollutions, low efficiency of energy conversion, fluctuation of output power, and reliability of power electronic converters [5]. Numerous PV inverter controllers have been suggested by many researchers to solve these problems. A proportional integral (PI) controller is a widely accepted technique in inverter controls. Selvaraj et al. [6] implemented a digital PI current control algorithm in a PV inverter through a eZdsp F2812 to maintain the current fed into the utility grid network to be sinusoidal. However, this PI controller requires trapezoidal sum approximation to transform the integral term into a discrete-time domain. Similarly, Sanchis et al. [7] proposed a traditional PI controller to control a DC-to-AC boost converter. However, their controller requires the differential equations of the system to obtain good performance. In a related work, PI controllers were implemented for a three-phase inverter utilizing dSPACE DS1104 control hardware [8]. However, the method of tuning the gains of PI controllers has not been elaborated. In recent years, researchers have focused on the utilization of optimization techniques in PI controller tuning to achieve improved performance. An optimal DC bus voltage regulation strategy with PI controllers for a grid-connected PV generator was suggested in [9]. In this research, PI control parameters were optimized through simplex optimization technique. Various other optimization methods, such as particle swarm optimization (PSO), have also been used in PI controller parameter tuning for different applications [10–13]. The performance of a PI controller is limited to small load disturbances. Its design is based on an accurate mathematical model of the real system under consideration, and it needs appropriate setting of its parameters. Artificial intelligence-based controllers have been used in inverters with high efficiency and great dynamics. Various methods, including artificial neural network (ANN), fuzzy logic, and adaptive neuro fuzzy inference system (ANFIS)-based controllers, were reported in the literature. ANN-based maximum power point tracking controller in a PV inverter power conditioning unit was proposed in [14]. In this work, the ANN module was used to estimate the voltages and currents corresponding to a maximum power delivered by PV panels. The module was then utilized to obtain the desirable converter duty cycle. Nonetheless, this proposed controller requires a large amount of training data before it can be trained and implemented in the controller. Fuzzy logic controllers (FLCs) have become increasingly popular in designing inverter controls because of their simplicity and adaptability to complex systems without a mathematical model [15]. Some good examples of FLCs for inverter control can be found in [16,17]. In these studies, two individual FLCs were used to control both the DC–DC and DC–AC converter in a fuel cell grid-connected inverter and stand-alone PV inverter, respectively. The authors claimed that acceptable results can be achieved with seven membership functions (MFs) and that the proposed technique can be implemented easily. In [18], the interval type-II fuzzy rule-based static synchronous compensator (STATCOM) for voltage regulation in a power system has been investigated. The interval type-II fuzzy rule base utilizes the output of the PID controller to tune the signal applied to the STATCOM to mitigate bus voltage variation caused by large changes in load and intermittent generation of PV arrays. Nonetheless, the performance of FLC depends on the rule base, number of rules, and MFs. These variables are determined based a trial-and-error procedure which is time consuming [19]. Therefore, various techniques, such as neuro-fuzzy model and other optimization techniques were proposed in the literature to overcome the limitations of the FLC design. In [20], Collotta et al. developed a neuro-fuzzy model for dynamic and automatic regulation of indoor temperature. The ANN is applied to forecast indoor temperatures that are used to feed a FLC unit to manage the on/off switching of the ventilating and air-conditioning system and the regulation of the inlet air speed. However, neuro-fuzzy model requires extensive

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training data similar to ANN controllers and that training data are difficult to obtain in many cases. In [21], a particle swarm optimization (PSO) algorithm was applied to optimize a FLC for maximum power point tracking of a PV system. The selection of a proper optimization technique is important because PSO is prone to premature convergence. To date, such adaptive MF tuning method has not Energies 2016, 9, 120  3 of 32  been applied in a FLC for PV inverter control. In the proposed research, the LSA is developed to PSO  enhance the performance the fuzzy logic proper  optimization  technique  is  important  because  is  prone  to  premature of convergence.    To date, such adaptive MF tuning method has not been applied in a FLC for PV inverter control.    controller for the three-phase PV inverter. The proposed approach aims to solve the problem In the proposed research, the LSA is developed to enhance the performance of the fuzzy logic  of trial-and-error procedure in obtaining MFs used in the conventional FLC. LSA is a novel controller  the  three‐phase  PV  inverter.  The  both proposed  approach  aims  solve  the  problem  of  nature-inspiredfor technique formulated to solve single-modal and to  multimodal optimization trial‐and‐error  procedure  in  obtaining  MFs  used  in  the  conventional  FLC.  LSA  is  a  novel  problems. This algorithm is particularly recommended to solve multimodal problems, such as for nature‐inspired  technique  formulated  to  solve  both  single‐modal  and  multimodal  optimization  tuning the MFs of the FLC [22]. Therefore, the utilization of the LSA improves the performance of the problems. This algorithm is particularly recommended to solve multimodal problems, such as for  FLC for PV inverters. LSA optimizes the MFs of the FLC based three-phase inverter by minimizing tuning the MFs of the FLC [22]. Therefore, the utilization of the LSA improves the performance of  the objective which isLSA  the mean squared errorof (MSE) of the output voltage.inverter  The system the  FLC  function for  PV  inverters.  optimizes  the  MFs  the  FLC  based  three‐phase  by  is first modeled in the MATLAB environment and then implemented in the eZdsp F28335 control board minimizing the objective function which is the mean squared error (MSE) of the output voltage. The  system is first modeled in the MATLAB environment and then implemented in the eZdsp F28335  (Spectrum Digital Inc, Stafford, TX, USA) to validate the performance of the proposed controller by control board (Spectrum Digital Inc, Stafford, TX, USA) to validate the performance of the proposed  considering perturbation such as change in DC input voltage and load. controller by considering perturbation such as change in DC input voltage and load. 

2. Inverter Control Algorithm 2. Inverter Control Algorithm 

Inverter control aims to regulate the AC output voltage at a desired magnitude and frequency Inverter control aims to regulate the AC output voltage at a desired magnitude and frequency  with low harmonic distortion. This regulation is performed by the controller by implementing a with  low  harmonic  distortion.  This  regulation  is  performed  by  the  controller  by  implementing  a  proper control algorithm to maintain the voltage at a set reference. The structure of the standalone PV proper control algorithm to maintain the voltage at a set reference. The structure of the standalone  inverter used in this study is shown in Figure 1 to illustrate the main control loops for achieving the PV inverter used in this study is shown in Figure 1 to illustrate the main control loops for achieving  aforementioned control objective. This inverter consists of a DC input from the PV source, DC–AC the aforementioned control objective. This inverter consists of a DC input from the PV source, DC–AC  inverter, transformer, and load. This type of inverter with a DC input source is known as a VSI. inverter, transformer, and load. This type of inverter with a DC input source is known as a VSI.  Inverter Inverter

PV PV

Filter

Transformer Loads

G G11

G G66

Controller Controller

V Vaa V Vbb Vc Vc

  Figure 1. Structure circuit of the three‐phase inverter system.  Figure 1. Structure circuit of the three-phase inverter system.

To apply the control algorithm in the inverter system, the three‐phase output voltages in the 

To apply the control algorithm in the inverter system, the three-phase output voltages in the synchronous reference frame must be sensed at the load terminals through the appropriate voltage  synchronous reference frame must be sensed at the load terminals through the appropriate voltage sensors. The three‐phase output voltages of the load terminal ( ,  , and  ) can be represented as:  sensors. The three-phase output voltages of the load terminal (Va , Vb , and Vc ) can be represented as: sin ω  

(1) 

2 Va “ V sin ωt (1) (2)  sin ω π   3 ˆ ˙ 2 2π Vb “ V sin (3)  (2) sin ωωt ´ π   33 ˆ ˙ , , and  ) are  where    is the voltage magnitude, and ω is the output frequency. These voltages ( 2 Vc “ V sin ωt ` π (3) then scaled and transformed into a d–q reference frame to simplify the calculations for controlling  3 the  three‐phase  inverter  [23,24].  The  two  DC  quantities,  namely, 

  and 

,  can  be  obtained  by 

whereapplying  V is thePark’s  voltage magnitude, and ω is the output frequency. These voltages (Va , Vb ,a and V ) are transformation,  as  shown  in  Equation  (4).  This  transformation  employs  50  Hz c then scaled and transformed into a d–q reference frame to simplify the calculations for controlling the synchronization signal from a phase‐locked loop block:  three-phase inverter [23,24]. The two DC quantities, namely, Vd and Vq , can be obtained by applying

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Park’s transformation, as shown in Equation (4). This transformation employs a 50 Hz synchronization signal from a phase-locked loop block: » »

fi

— Vd — — ffi 2 — – Vq fl “ — 3— Energies 2016, 9, 120  – Vo

ˆ

˙ ˆ ˙ 2π 2π cos pωtq cos ωt ´ cos ωt ` 3˙ 3˙ ˆ ˆ 2π 2π ´sin pωtq sin ωt ´ sin ωt ` 3 3 1 1 1 2 2 2 cos ω

cos ω

2π

cos ω

fi ¨ ˛ ffi Va ffi ffi ˚ ‹ ffi ˆ ˝ Vb ‚ ffi fl Vc

(4) 4 of 32 

2π

3 The error E between the measured voltages Vd3and Vq and reference voltages Vdre f and Vqre f 2 2π in error CE2π (4)  the per unit can then be computed. Similarly, the change can be determined by taking sin ω sin ω sin ω 3 3 3 derivative of E. These signals (i.e., E and sent to the1controller at each sampling time Ts to 1 CE) are then 1 compute the missing components in2Vd and Vq and to generate2 the new Vd and Vq signals. The new 2   and    and reference voltages    and    The error E between the measured voltages  Vd and Vq are again converted into the synchronous reference frame voltages Va , Vb , and Vc through per unit can then be computed. Similarly, the change in error CE can be determined by taking the  the following equation: derivative of E. These signals (i.e., E and CE) are then sent to the controller at each sampling time Ts  » fi to compute the missing components in    and to generate the new    and  ˛  signals. The  cos pωtq  and  ´sin pωtq ˙ 1 ¨ » fi ˆ ˙ ˆ — ffi voltages  Vd new    and    V are  into  the  synchronous  reference  frame  , ,  and    2π 2π a again  converted  — ffi 2 — cos ωt ´ ‹ ´sin ωt ´ 1 ffi ffi ˆ ˚ through the following equation:  (5) V ˝ ‚ – Vb fl “ — 3 3 q — ffi

3–

ˆ

˙

ˆ

˙

Vo ω 2π sin ωt ω ` 2π1 1 ´sin cos cos ωt ` 3 3 2π 2π 2 cos ω sin ω 1 (5)  3 3 3 These voltages can be applied in generating the pulse2π width modulation (PWM) to drive the 2π cos ω sin ω 1 3 in the inverter3block in Figure 1. As a result of inverter insulated-gate bipolar transistor IGBT switches Vc

fl

switching, a series of pulsating DC input voltage Vdc appears at the output terminals of the inverter. These voltages can be applied in generating the pulse width modulation (PWM) to drive the  Given that the output voltages of the inverter arein pulsating DCblock  voltages, an appropriate low-pass insulated‐gate  bipolar  transistor  IGBT  switches  the  inverter  in  Figure  1.  As  a  result  of  appears at the output terminals of the  filter inverter switching, a series of pulsating DC input voltage  must be used (Figure 1) before importing PV-generated electrical energy to the load. The design inverter.  that  the  output  voltages  inverter  are  pulsating  DC  voltages, an appropriate  procedure of Given  the filter circuits can be foundof inthe  [25]. low‐pass filter must be used (Figure 1) before importing PV‐generated electrical energy to the load.  The design procedure of the filter circuits can be found in [25].    3. Inverter Control Using FLC Strategy

In consideration of the nonlinearity of  the power conversion process in PV inverters, fuzzy logic 3. Inverter Control Using FLC Strategy  is a convenient method to adopt in a PV inverter control system. An FLC represents the human expert In consideration of the nonlinearity of the power conversion process in PV inverters, fuzzy logic  decision in the problem solving mechanism. The main advantages of FLC are: is  a  convenient  method  to  adopt  in  a  PV  inverter  control  system.  An  FLC  represents  the  human  i expert decision in the problem solving mechanism. The main advantages of FLC are:  FLC can be used in many applications especially for control and modeling of non-linear i. [19]. FLC can be used in many applications especially for control and modeling of non‐linear  systems systems [19].  ii FLC is less dependent  on a mathematical model and system parameters [26]. FLC is less dependent on a mathematical model and system parameters [26].  iii FLC ii. is based on linguistic rules with an if-then general structure, which is the basis of human iii. FLC is based on linguistic rules with an if‐then general structure, which is the basis of  logic [27]. human logic [27]. 

Figure 2 shows the inverter control concept with FLC as a control strategy. Figure 2 shows the inverter control concept with FLC as a control strategy. 

  Figure 2. Inverter voltage control with FLC.  Figure 2. Inverter voltage control with FLC.

The  first step  in  FLC is  to select  the  number  of  inputs  and  outputs.  In  this  work,  where FLC  serves as a PV inverter controller, E and CE are used as inputs, whereas the missing component of    or    defined  as  O  is  used  as  the  output  of  the  FLC.  The  two  inputs  for  the  FLC  depicted  in  Figure 2, namely, E and CE, at the tth sampling step that corresponds to    can be described as follows: 

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The first step in FLC is to select the number of inputs and outputs. In this work, where FLC serves as a PV inverter controller, E and CE are used as inputs, whereas the missing component of Vd or Vq defined as O is used as the output of the FLC. The two inputs for the FLC depicted in Figure 2, namely, E and CE, at the tth sampling step that corresponds to Vd can be described as follows: E ptq “ Vdre f ´ Vd ptq Energies 2016, 9, 120 

(6) 5 of 32 

CE ptq “ E ptq ´ E pt ´ 1q

(7)

The output O for this case can be obtained at the last stage of the FLC design, which is(6)  explained in the next section. The FLC design must pass through the (7)  1   following steps, namely, fuzzification, inference engine design, and defuzzification [28,29]. The output O for this case can be obtained at the last stage of the FLC design, which is explained  in  the  next  section.  The  FLC  design  must  pass  through  the  following  steps,  namely, fuzzification, 

3.1. Fuzzification inference engine design, and defuzzification [28,29]. 

After the inputs and outputs are defined, the next stage involves the fuzzification of inputs. 3.1. Fuzzification  This step represents the inputs with suitable linguistic value by decomposing every input into a set After  the  inputs  and  outputs  are  defined,  the  next  stage  involves  the  fuzzification  of  inputs.  and by defining a unique MF label, such as “big” or “small”. Thus, the number of MFs used in the FLC This step represents the inputs with suitable linguistic value by decomposing every input into a set  depends on the linguistic label. The MFs of E and CE for the FLC can be defined as trapezoidal and and by defining a unique MF label, such as “big” or “small”. Thus, the number of MFs used in the  triangular MFs. This process translates the crisp values of “E” and “CE” as the fuzzy set “e” and “ce”, FLC depends on the linguistic label. The MFs of E and CE for the FLC can be defined as trapezoidal  respectively, through the MF degrees µe (E) and µce (CE), which range from 0 to 1, as shown in Figure 3 and triangular MFs. This process translates the crisp values of “E” and “CE” as the fuzzy set “e” and  “ce”, respectively, through the MF degrees μ e(E) and μ for triangular MFs. In Figure 3a, the MF of error (MFE)ce(CE), which range from 0 to 1, as shown in  is defined by three elements, namely, X1 , X2 , Figure  3  for  triangular  MFs.  In  Figure  3a,  the  MF  of  error  is  defined  three  elements,  and X3 , whereas the MF of change of error (MFCE) in Figure(MFE)  3b is defined byby  another three elements namely, X1, X2, and X3, whereas the MF of change of error (MFCE) in Figure 3b is defined by another  represented by X4 , X5 , and X6 . 1

MFE

0.5

0 0X 1

X12

X23

Error (E)

Degree of membership function

Degree of membership function

three elements represented by X4, X5, and X6. 

MFCE

1

0.5

0 0X 4

X15

X26

Change of Error (CE)

(a) 

(b)  Figure 3. Membership functions for (a) E and (b) CE. 

Figure 3. Membership functions for (a) E and (b) CE. After defining the MFs, μe(E) and μce(CE) can be calculated with a basic straight line equation  that consists of two points. For example, μ e(E) and μ ce(CE) for the MFs in Figure 3 can be expressed  After defining the MFs, µe (E) and µce (CE) can be calculated with a basic straight line equation as follows:  that consists of two points. For example, µ (E) and µ (CE) for the MFs in Figure 3 can be expressed e

as follows:

ce

E ´ X1 X1 ď E ă X2 (8)  X ´ X1 µe pEq “ 1 2 X ´E ’ % 1` 2 X2 ď E ă X3 X3 ´ X2 $ CE ´ X4 μ (9)  ’ & X4 ď CE ă  X5 X ´ X 1 5 4 µce pCEq “ ’ % 1 ` X5 ´ CE X5 ď CE ă X6 In a standard FLC design, the selection of the number of MFs and the boundary values of each  X6 ´ X5 μ

$ ’ &

MF must be adjusted by the designer by using the trial‐and‐error method until the FLC provides a 

(8)

(9)

In a standard FLC design, the selection of the number of MFs and the boundary values of each satisfactory  result.  However,  this  process  is  time  consuming  and  laborious.  After  the  inputs  are  MF must be adjusted by the designer by using the trial-and-error method until the  FLC provides fuzzified, the fuzzy inputs are subjected to an inference engine to generate a fuzzy output.  a satisfactory result. However, this process is time consuming and laborious. After the inputs are 3.2. Inference Engine Design  fuzzified, the fuzzy inputs are subjected to an inference engine to generate a fuzzy output. This stage represents the decision making process based on the information from a knowledge  base, which contains linguistic labels and control rules. Two types of inference systems mainly exist, 

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3.2. Inference Engine Design This stage represents the decision making process based on the information from a knowledge base, which contains linguistic labels and control rules. Two types of inference systems mainly exist, namely, Mamdani type and Sugeno type. The Mamdani-type inference system is adopted in this study Energies 2016, 9, 120  6 of 32  because of its simple implementation steps. The rules with two inputs for the Mamdani type can be written as follows: namely,  Mamdani  type  and  Sugeno  type.  The  Mamdani‐type  inference  system  is  adopted  in  this  study because of its simple implementation steps. The rules with two inputs for the Mamdani type  R : IF E is “label” AND CE is “label, ” THEN u is “label.” can be written as follows: 

The quantity of rulesR: IF E is “label” AND CE is “label,” THEN u is “label.”  depends on the number of inputs and MFs used in the FLC [28,29]. An FLC with a large rule base demands great computational effort in terms memory and computation The  quantity  of  rules  depends  on  the  number  of  inputs  and ofMFs  used  in  the  FLC  [28,29]. time.   An  FLC  with  a  large  rule  base  demands  great  computational  effort  in  terms  of  memory  and 

3.3. Defuzzification computation time. 

The final step in the FLC is the selection of the defuzzification method. This process generates a 3.3. Defuzzification  fuzzy control action as a crisp value. Several methods can be used to generate the crisp value. The most common The final step in the FLC is the selection of the defuzzification method. This process generates a  methods include the center of area (COA) and the mean of maximum (MOM) methods. fuzzy control action as a crisp value. Several methods can be used to generate the crisp value. The  The widely used COA method generates the center of gravity of the MFs. In this study, the COA most  common  methods  include  the  center  of  area  (COA)  and  the  mean  of  maximum  (MOM)  method given in Equation (10) is used to generate the crisp value because it is more accurate than methods. The widely used COA method generates the center of gravity of the MFs. In this study, the  MOMCOA method given in Equation (10) is used to generate the crisp value because it is more accurate  method [28]: řn i “1 w i ¨ u i than MOM method [28]:  (10) COA “ ř n i “1 w i ∑

.

(10)  where n is the number of rules, and wi is the weighted ∑ factor that can be calculated with Mamdani-MIN between µe (E) and µce (CE), as expressed by: where  n  is  the  number  of  rules,  and    is  the  weighted  factor  that  can  be  calculated  with  Mamdani‐MIN between μe(E) and μce(CE), as expressed by: 

wi “ MI N rµe pEq , µce pCEqs μ

,μ

(11)

(11) 

The implementation steps of the standard FLC are illustrated in Figure 4. The implementation steps of the standard FLC are illustrated in Figure 4. 

Figure 4. Encoding of the FLC. 

Figure 4. Encoding of the FLC.

4. Proposed Optimum FLC Design Procedure 

4. Proposed Optimum FLC Design Procedure

As  noted  in  the  standard  FLC  design  procedure,  the  main  drawback  of  FLC  design  is  the 

time‐consuming  to  adjust  the  boundary  values  MFs  in  the  As noted in thetrial‐and‐error  standard FLCprocess  designused  procedure, the main drawback of of  FLC design is the fuzzification process. Improper selection of MF boundaries may lead to the poor performance of the  time-consuming trial-and-error process used to adjust the boundary values of MFs in the fuzzification overall system. Therefore, this work presents a methodology to optimize MFs through a heuristic  optimization algorithm. A heuristic optimization algorithm is used to solve complex and intricate  problems  that  are  otherwise  difficult  to  solve  with  classical  methods.  It  is  a  population‐based 

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process. Improper selection of MF boundaries may lead to the poor performance of the overall system. Therefore, this work presents a methodology to optimize MFs through a heuristic optimization algorithm. A heuristic optimization algorithm is used to solve complex and intricate problems that are otherwise difficult to solve with classical methods. It is a population-based method designed to solve a problem quickly or to determine an approximate solution when classic methods fail to determine a solution particularly with multimodal optimization problems. LSA has been developed as a heuristic optimization tool to adjust the boundary values of MFs adaptively because of its suitability for multimodal problems, such as the FLC design for PV inverter control. 4.1. Overview of LSA LSA is a nature-inspired metaheuristic optimization algorithm [22]. LSA is based on the natural phenomenon of lightning. The probabilistic nature and tortuous characteristics of lightning discharges originate from a thunderstorm. The proposed optimization algorithm is generalized from the mechanism of step leader propagation. It considers the involvement of fast particles known as projectiles in the formation of the binary tree structure of a step leader. Three projectile types are used to represent the transition projectiles that create the first step leader population N, the space projectiles that attempt to become the leader, and the lead projectile that represents the best positioned projectile that originated among N number of step leaders. The details of the LSA, including its basic concepts and algorithms, can be found in [22]. 4.2. Optimal FLC Problem Formulation The three basic components that are considered in any optimization method are input vectors, objective function formulation, and constraints. Each component is developed and clarified to obtain the optimal MFs. The optimization technique searches the optimal solution as formulated in the objective function through manipulation of the input vector subject to the constraints in each generation of the iterative process. 4.2.1. Input Vector As the first step in FLC design, the number of MFs must be defined to provide the solution from the optimization technique. Depending on the number of MFs, the input vector Z can be described by: ” ı 1 2 n Zi,j “ Xi,j Xi,j . . . Xi,j

(12)

k is the kth element where Zi,j represents the jth solution in the population during the ith iteration, Xi,j of Zi,j , and n is the total number of parameters. For example, the input vector Zi,j should contain six parameters indicating the boundaries of MFs that should be optimized to represent the MFs in Figure 3.

4.2.2. Objective Function An objective function is required to determine and evaluate the performance of Zi,j for the MFs. Thus, the objective function to determine the optimal values is formulated in such a way that Zi,j generates the best fuzzy control action as a crisp value according to Equation (10) described in the defuzzification process. In the FLC design for the PV inverter control, E and CE at the tth sampling step that corresponds to Vd (which is the transformed inverter output voltage) indicate the goodness of the crisp value of the fuzzy control action. Therefore, the MSE (13) obtained from the reference values Vdre f and the measured values Vd are used as the objective function: ř` MSE “

i “1

´ Vdre f ´ Vd

`

¯2 (13)

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where Vdre f is the reference value that is equal to (1 p.u.), Vd is the measured value, and ` is the number of the samples used to evaluate MSE. In the optimization process, Equation (13) needs to be minimized. 4.2.3. Optimization Constraints The optimization algorithm must be implemented while satisfying all constraints used to determine the optimal values of MF parameters. The boundaries of these parameters should not k should be between X k´ 1 and X k`1 . If the 8 of 32  k overlap. InEnergies 2016, 9, 120  other words, the element Xi,j element Xi,j i,j i,j k`1 k ´1 is greater than Xi,j or less than Xi,j , this,  element should be, regenerated within its boundaries. overlap. In other words, the element  should be between    and  , . If the element  ,   is    or  less  than  ,  this  element to should  be  that regenerated  within  its  boundaries.  greater  than  , restriction Therefore, the following must fulfilled ensure each MF parameter is within the , be Therefore, the following restriction must be fulfilled to ensure that each MF parameter is within the  prescribed boundaries: prescribed boundaries:  k ´1 k `1 k Xi,j ă Xi,j ă Xi,j (14) ,

,

,

 

Figure 5. Proposed LSA‐based optimum FLC design procedure. 

Figure 5. Proposed LSA-based optimum FLC design procedure.

(14) 

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4.3. Implementation Steps of LSA to Obtain the Optimal FLC Design  4.3. Implementation Steps of LSA to Obtain the Optimal FLC Design The implementation starts by resetting the LSA parameters, namely, number of iterations (T),  The implementation starts by resetting the LSA parameters, namely, number of iterations (T), population size (N), problem dimension (D), and channel time. The initial populations for the MFs  population size (N), problem dimension (D), and channel time. The initial populations for the MFs are then generated and encoded according to Equation (12). The next step involves the evaluation of  are then generated and encoded according to Equation (12). The next step involves the evaluation the objective function through Equation (13). A suitable running time Tr is required to populate the  of the objective function through Equation (13). A suitable running time Tr is required to populate FLC output for the evaluation of MSE in population N. After the initial population is evaluated, the  the FLC output for the evaluation of MSE in population N. After the initial population is evaluated, direction and position are updated with Equations (15) and (16), respectively: After updating all the  the direction and position are updated with Equations (15) and (16), respectively: After updating all values of  , in the population, the procedure re‐evaluates the objective function, and the process  the values of Zi,j in the population, the procedure re-evaluates the objective function, and the process continues to the next iteration. This updating and objective function reevaluation process is repeated  continues to the next iteration. This updating and objective function reevaluation process is repeated until the maximum iteration count is reached, as explained in Figure 5.  until the maximum iteration count is reached, as explained in Figure 5. μ _ S pi_new “ piS ˘ exprand pµi q μ ,σ   L L p “ p ` normrand pµ Lq L , σprojectile,  new   is  the  new  space  projectile,    is  the  old  space  and 

(15)  (15) (16) 

(16) where  _   is  the  new  lead  S After  L in  space the  population,  the pprocedure  re‐evaluates  the  projectile.  updating  all projectile, the  values  where pi_new is the new space piS of  is the, old projectile, and new is the new lead projectile. objective  function,  and  the  process  continues  to  the  next  iteration.  This  updating  and  objective  After updating all the values of Zi,j in the population, the procedure re-evaluates the objective function, function reevaluation process is repeated until the maximum iteration count is reached, as explained  and the process continues to the next iteration. This updating and objective function reevaluation in Figure 5.  process is repeated until the maximum iteration count is reached, as explained in Figure 5. 5. FLC Design for PV Inverter Control Using the Proposed Method 5. FLC Design for PV Inverter Control Using the Proposed Method  A 3 kW,  3 kW, 240 V,  240 V, 50 Hz  50 Hz PV  PV inverter  inverter system  system is  is modeled  modeled in  in the  the Matlab  Matlab Simulink  Simulink environment  environment A  (Figure 6) to demonstrate the application of an optimum FLC design by supplying various types of (Figure 6) to demonstrate the application of an optimum FLC design by supplying various types of  loads continuously. As depicted in Figure 6, the output voltages (Va, , Vb, and  , and Vc) are measured and  ) are measured and loads continuously. As depicted in Figure 6, the output voltages ( converted to  to Vd  and  and Vq  at  at each  each sampling  sampling time  time Tss  =  = 2 μs.  2 µs. The  Thecontroller  controllerblock  blockshown  shownin  in the  the figure  figure converted  contains two FLCs that correspond to Vd  and in the d–q reference frame. The controllers require E contains two FLCs that correspond to  and Vq in the d–q reference frame. The controllers require E  and CE to generate new Vd  and  and Vq  and to convert to  and to convert to Va, , Vb, and  , and V c . The converted signals are then  . The converted signals are then and CE to generate new  utilized to create the PWM for driving the IGBT switches of the inverter. utilized to create the PWM for driving the IGBT switches of the inverter.   

Figure 6. Simulation model for the three-phase inverter. Figure 6. Simulation model for the three‐phase inverter. 

As explained previously for each input, seven MFs defined as trapezoidal and triangular MFs are As explained previously for each input, seven MFs defined as trapezoidal and triangular MFs  1 to X 7 ) are used to define the used according to the illustration in Figure 7. Seven parameters (i.e., Xi,j are  used  according  to  the  illustration  in  Figure  7.  Seven  parameters  (i.e., i,j , , )  are  used  to  8 to X 14 ) are used to define the second input first input (E), whereas the seven other parameters (i.e., X i,j i,j define the first input (E), whereas the seven other parameters (i.e.,  , , are used to define the  second  input  (CE).  Therefore,  each  controller  input    in  the  optimum  FLC  design  contains  14  parameters. Thus, the FLC control rule for the PV inverter control system includes 49 rules (Table 1). 

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MFE

1

MFE

MFE

MFE

MFE

Degree of membership function

Degree of membership function

(CE). Therefore, each controller input Z in the optimum FLC design contains 14 parameters. Thus, the Energies 2016, 9, 120  10 of 32  FLC control rule for the PV inverter control system includes 49 rules (Table 1). MFE

MFE

0.5

0 0

1 ,

2 ,

3

,

4

,

5

Error (E)

,

6 ,

7 ,

8

1

MFCE MFCE MFCE MFCE MFCE

MFCE

MFCE

0.5

0 0

1

,

2

,

3

,

4 ,

5 ,

Change of error (CE)

(a) 

6 ,

7 ,

8

(b)  Figure 7. FLC with seven MFs for (a) E and (b) CE.  Figure 7. FLC with seven MFs for (a) E and (b) CE. Table 1. Fuzzy control rules based on seven MFs.  Table 1. Fuzzy control rules based on seven MFs.

Error  Error(E)  (E) MFE1  MFE MFE 1 2  MFE 2 3  MFE MFE3 MFE4  MFE4 MFE 5  MFE 5 MFE MFE 6 6  MFE 7 7  MFE

MFCE1  MFCE ONB 1 ONB ONB  ONB ONB  ONB ONB  ONB ONM  ONM ONS ONS  OZ OZ 

MFCE2  MFCE ONB 2 ONB ONB  ONB ONB  ONB ONM  ONM ONS  ONS OZ OZ  OPS OPS 

Change of Error (CE) Change of Error (CE) MFCE3 MFCE4 MFCE5 MFCE MFCE MFCE5 3 4 ONB  ONB  ONM ONB ONB ONM ONB  ONM  ONS  ONB ONM ONS ONM  ONS  OZO  ONM ONS OZO ONS  OZ  OPS  ONS OZ OPS OZ  OPS  OPM  OZ OPS OPM OPS OPM OPB OPS  OPM  OPB  OPM OPB OPB OPM  OPB  OPB 

MFCE6  MFCE ONS  6 ONS OZ  OZ OPS  OPS OPM  OPM OPB  OPB OPB OPB  OPB OPB 

MFCE7  MFCE OZ  7 OZ OPS  OPS OPM  OPM OPB  OPB OPB  OPB OPB OPB  OPB OPB 

ONB == output negative big, ONM output=  negative ONS = output negative OZnegative  = output zero, ONB  output  negative big,  =ONM  output medium, negative  medium,  ONS  = small, output  small,    OPS = output positive small, OPM = output positive medium, and OPB = output positive big. OZ  =  output  zero,  OPS  =  output  positive  small,  OPM  =  output  positive  medium,  and    OPB = output positive big. 

The input vector and control rules are then defined. The optimization process described in The input vector and control rules are then defined. The optimization process described in the  the previous section can be performed by evaluating the objective function given in Equation (13) previous section can be performed by evaluating the objective function given in Equation (13) with  with the Simulink model shown in Figure 6 for a suitable running time of Tr = 0.2 s. In this design the  Simulink  shown  in  Figure  6  for  a  suitable  running  time  of the Tr  =  0.2  s.  In parameters: this  design  illustration, the model  optimization process based on LSA is started by initializing following illustration,  optimization  process  on  LSA (N) is  as started  by  initializing  the  following  the number of the  iterations (T) as 100, numberbased  of populations 20, dimension of the problem (D) as parameters: the number of iterations (T) as 100, number of populations (N) as 20, dimension of the  14, and maximum channels as 10. After the creation of the initial population and the calculation of the problem (D) as 14, and maximum channels as 10. After the creation of the initial population and the  corresponding objective function for each input vector in the population, LSA updates the population calculation  of  the  corresponding  objective  function  for  each  input  vector  in  the  population,  LSA  and initiates a new iteration. If LSA reaches the maximum iteration, then the FLC with the best MF is updates the population and initiates a new iteration. If LSA reaches the maximum iteration, then the  obtained (Figure 5). This result indicates that the proposed approach provides a systematic and easy FLC  with  the  best  MF  is  obtained  (Figure  5).  This  result  indicates  that  the  proposed  approach  way to design FLCs for PV inverter control systems. provides a systematic and easy way to design FLCs for PV inverter control systems.  6. Fuzzy Logic PV Inverter Controller Implementation Based eZdsp F28335 6. Fuzzy Logic PV Inverter Controller Implementation Based eZdsp F28335  The implementation in the hardware of the developed optimized FLC for PV inverter using eZdsp implementation  in  the  of  the  developed  FLC  inverter  using  F28335The  control board is essential tohardware  appraise the performance ofoptimized  the controller infor  realPV  time. Therefore, eZdsp F28335 control board is essential to appraise the performance of the controller in real time.  the implementation to test the optimized FLC-based PV inverter is performed in the laboratory. Therefore,  the  implementation  to  test  the  optimized  FLC‐based  PV  inverter  is  performed  in    6.1. eZdsp F28335 Controller the laboratory.  The eZdsp F28335 board is appropriate for the inverter control platform because of its ability 6.1. eZdsp F28335 Controller  to link the MATLAB/Simulink inverter model to the real-time hardware. It is an inexpensive The eZdsp F28335 board is appropriate for the inverter control platform because of its ability to  standalone digital controller that contains an analog-to-digital converter (ADC), a digital input/output, link the MATLAB/Simulink inverter model to the real‐time hardware. It is an inexpensive standalone  and a TMS320F28335 floating-point DSP. In the controller, Code Composer Studio (CCS) and digital  controller  that  contains  an analog‐to‐digital  converter  (ADC),  a  digital  input/output,  and a  TMS320F28335  floating‐point  DSP.  In  the  controller,  Code  Composer  Studio  (CCS)  and  MATLAB/Simulink  should  be  operated  properly.  The  Simulink  PV  inverter  model  is  compiled,  converted  to  C‐code,  and  then  automatically  linked  to  the  real‐time  TMS320F28335  processor 

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MATLAB/Simulink should be operated properly. The Simulink PV inverter model is compiled, converted to C-code, and then automatically linked to the real-time TMS320F28335 processor through MATLAB/Simulink. During the linking process, a user should include eZdsp input–output (I/O) interface blocks, such as ADC, and the enhanced PWM (ePWM) in the Simulink models. The Energies 2016, 9, 120  11 of 32  behavior and performance of the inverter can be monitored in real time by applying the CCS through MATLAB/Simulink. During the linking process, a user should include eZdsp input–output  software. The most important features of the eZdsp F28335 board include a TMS320F28335 digital signal(I/O) interface blocks, such as ADC, and the enhanced PWM (ePWM) in the Simulink models. The  controller, 150 MHz operating speed, 68 Kb on-chip RAM, 512 Kb on-chip flash memory, 256 behavior  and  performance  of  the  inverter  can  ADC be  monitored  real  channels. time  by  applying  CCS  Kb off-chip SRAM memory, and on-chip 12-bit with 16in  input These the  components software. The most important features of the eZdsp F28335 board include a TMS320F28335 digital  constitute the eZdsp F28335 board, which is suitable for prototype development and cost-sensitive, signal  controller,  150 MHz  operating  speed,  68 Kb  on‐chip  RAM,  512 Kb  on‐chip  flash  memory,  rapid-control prototyping. 256 Kb off‐chip SRAM memory, and on‐chip 12‐bit ADC with 16 input channels. These components  constitute the eZdsp F28335 board, which is suitable for prototype development and cost‐sensitive,  6.2. Control Algorithm Implementation rapid‐control prototyping. 

The control algorithm described in Section 2 is implemented with the eZdsp F28335 board. 6.2. Control Algorithm Implementation  This algorithm initially reads the measured voltages Va , Vb , and Vc through LEM LV25-P sensors. Therefore,The control algorithm described in Section 2 is implemented with the eZdsp F28335 board. This  three sensors are utilized to interface the output voltages of the inverter with the eZdsp F28335 board. These three sensors decrease the voltages to a level suitable for the eZdsp F28335 working algorithm initially reads the measured voltages  , , and    through LEM LV25‐P sensors. Therefore,  three  sensors  are  utilized  to  interface  the  output  voltages  of  the  inverter  with  eZdsp  F28335  voltages, and these voltages are fed to the ADC channels of the eZdsp F28335 for the  additional processing. board.  These  three  sensors  decrease  the  voltages  to  a  level  suitable  for  the  eZdsp  F28335  working  in Va , Vb , and Vc are then transformed into the d–q reference frame, and E and CE are calculated voltages, and these voltages are fed to the ADC channels of the eZdsp F28335 for additional processing.    to per unit according to Equations (6) and (7), respectively. The resulting E and CE are fed to the FLC , , and    are then transformed into the d–q reference frame, and E and CE are calculated in  control the steady-state error and the output voltage. per unit according to Equations (6) and (7), respectively. The resulting E and CE are fed to the FLC to  Space vector PWM (SVPWM) is employed in the inverter control algorithm to produce sinusoidal control the steady‐state error and the output voltage.  AC waveforms thePWM  three-phase voltage source inverter output signal to  cycle is divided Space from vector  (SVPWM)  is  employed  in  the  [30,31]. inverter Each control  algorithm  produce  into six sections that resemble a hexagon (Figure 8). Vre f and α in each sector are the products of two sinusoidal AC waveforms from the three‐phase voltage source inverter [30,31]. Each output signal  adjacent nonzero and zero vectors, respectively. The hexagon consists of six nonzero vectors, namely, cycle is divided into six sections that resemble a hexagon (Figure 8).    and α in each sector are the  V 1 , Vproducts of two adjacent nonzero and zero vectors, respectively. The hexagon consists of six nonzero  2 , . . . , V 6 , and two zero vectors, particularly V 0 and V 7 [32]. The PWM control includes the vectors, index namely,  , … , is ,  and  two  zero  vectors,  particularly    [32].  The the PWM  control  modulation (MI),, which necessary to improve the accuracy and by decreasing total harmonic includes the modulation index (MI), which is necessary to improve the accuracy by decreasing the  distortion (THD) of the output signals from the inverter [33]. The MI is computed as follows: total  harmonic  distortion (THD)  of  the output  signals  from  the  inverter  [33].  The  MI  is  computed    Vp1 as follows:   

MI “

(17)

Vp1six

 

(17) 

where Vp1 is the maximum fundamental voltage, and Vp1six is the maximum fundamental voltage where  V   is the maximum fundamental voltage, and  V   is the maximum fundamental voltage  2 through a six-step operation. Thus, V “ V , where V is the DC-link voltage [30]. The remainder p1six dc dc through a six‐step operation. Thus,  V π V ,  where  V   is the DC‐link voltage [30]. The remainder  of Ts of T is filled with the zero space vectors V0 and V7 . . The time shares are calculated as follows [34]:  The time shares are calculated as follows [34]: s is filled with the zero space vectors    and 



  Figure 8. Space vector PWM diagram.  Figure 8. Space vector PWM diagram.

√3 ∙

∙

sin

3

π

α

(18) 

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? T1 “

ˇ ˇ ˇ ˇ 3¨ Ts ¨ ˇVre f ˇ

sin

´n

¯ π´α

(18)

Vdc 3 ˇ ˇ ? ˇ ˇ ˆ ˙ 3¨ Ts ¨ ˇVre f ˇ n´1 T2 “ √3 ∙ ∙ sin α ´ π Vdc 3 1π sin α 3 T0 “ Ts ´ pT1 ` T2 q

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(19) (19) 

(20) (20)  where n = 1 to 6 are the sectors at 0 ď α ď π/3; T1 , T2 , and T0 are the time vectors of the respective where n = 1 to 6 are the sectors at  0 time; α and π⁄3; α is,  the, and    are the time vectors of the respective  voltage vectors; Ts is the switching angle of the reference vector relative to the voltage vectors;  T   is the switching time; and  α  is the angle of the reference vector relative to the  space vector. space vector.    uses the optocoupler in the driver circuit to establish the interface of the SVPWM to The inverter The inverter uses the optocoupler in the driver circuit to establish the interface of the SVPWM  the IGBT. The voltage values of the produced SVPWM switching signals are appropriate for the IGBT to the IGBT. The voltage values of the produced SVPWM switching signals are appropriate for the  working voltage to achieve an effective inverter switching operation. IGBT working voltage to achieve an effective inverter switching operation.  7. Experimental PV Inverter Control System 7. Experimental PV Inverter Control System  The real-time model shown in Figure 9 is utilized to implement the PV inverter control system The real‐time model shown in Figure 9 is utilized to implement the PV inverter control system  through eZdsp F28335 board. In this model, the employed eZdsp F28335 I/O blocks include through  eZdsp  F28335  board.  this  model,  the  employed  eZdsp  output F28335 voltages, I/O  blocks  include  C280x/C28x3x ADC, unit16, and In  C280x/C28x2833x ePWM. The inverter particularly C280x/C28x3x ADC, unit16, and C280x/C28x2833x ePWM. The inverter output voltages, particularly  V , V , and V , are sampled via C280x/C28x3x ADC. These voltages are then converted to digital a c b , , and  , are sampled via C280x/C28x3x ADC. These voltages are then converted to digital values  values for processing. The C280x/C28x2833x ePWM block produces the PWM switching signals for for processing. The C280x/C28x2833x ePWM block produces the PWM switching signals for the IGBTs.  the IGBTs.

  Figure 9. Real‐time implementation of the eZdsp F28335 inverter system algorithm.  Figure 9. Real-time implementation of the eZdsp F28335 inverter system algorithm.

Referring to Figure 9, the first block is the ADC C280x/C28x3x. The ADC module which has 16  Referring to Figure 9, the first block is the ADC C280x/C28x3x. The ADC module which has channels,  is  configurable  as  two  independent  8‐channel  modules  (module  A  and  module  B)  to  16 channels, is configurable as two independent 8-channel modules (module A and module B) to service service  the  ePWM  modules.  The  two  independent  8‐channel  modules  can  be  cascaded  to  form  a  the ePWM modules. The two independent 8-channel modules can be cascaded to form a 16-channel 16‐channel  module.  Multiple  input  channels  and  two  sequencers  are  available  with  only  one  module. Multiple input channels and two sequencers are available with only one converter in the converter in the ADC module. The two 8‐channel modules can auto sequence a series of conversions  ADC module. The two 8-channel modules can auto sequence a series of conversions with each module with each module having the choice of selecting any one of the respective eight channels available  having the choice of selecting any one of the respective eight channels available through an analog through an analog MUX. In the cascaded mode, the auto sequencer functions as a single 16‐channel  MUX. In the cascaded mode, the auto sequencer functions as a single 16-channel sequencer. On each sequencer. On each sequencer, once the conversion is completed, the selected channel value is stored  sequencer, once the conversion is completed, the selected channel value is stored in its respective in  its  respective  ADCRESULT  register.  Auto  sequencing  allows  the  system  to  convert  the  same  ADCRESULT register. Auto sequencing allows the system to convert the same channel multiple times. channel multiple times. Functions of the ADC module include a 12‐bit ADC core with built‐in dual  Functions of the ADC module include a 12-bit ADC core with built-in dual sample-and-hold (S/H), sample‐and‐hold (S/H), and analog input from 0 V to 3 V. The analog input for the ADC is in the  range of 0 to 3 V. As the ADC is 12‐bit, the digital value of the input analog voltage is calculated as:  0

4096



3

0

0 3

 

(21) 

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and analog input from 0 V to 3 V. The analog input for the ADC is in the range of 0 to 3 V. As the ADC is 12-bit, the digital value of the input analog voltage is calculated as: $ ’ 0 ’ &

input ď 0 V

Input Analog Voltage Digital Value “ 4096 ˆ ’ 3 ’ % 4095

0 V ă input ă 3 V

(21)

input ě 3 V

From Equation (21), the digital output is from 0 to the 4095. To remove the bias from the digital signal and get the actual signal, it must be subtracted from half of the highest value (4095). Experimentally, the half of the highest value is found to be 2058. As the control procedure is working in per unit (p.u.), therefore the actual signal should be converted to p.u. signal. The actual signal should be divided by the highest value for converting to p.u. signal. Therefore, the actual signal is dived by 1240 to get the p.u. signal. The C280x/C28x2833x ePWM block is one of the most important blocks in the eZdsp F28335 control board for PV inverter control. As shown in Figure 9, three ePWM blocks are used. Each ePWM block is responsible to generate the switching for the switching devices (IGBTs) in each inverter leg. The dead-time which is the time delay between the upper switch (e.g. IGBT1) turning ON time and lower switch (e.g., IGBT4) turning OFF time should be taken into account. The dead-band sub-module supports independent values for rising-edge (RED) and falling-edge (FED) delays. The amount of delay is programmed using the dead-band RED (DBRED) and dead-band FED (DBFED) registers. Since the DBRED and DBFED are 10-bits, they can be set to values from 0 to 1023. The rising-edge-delay and falling-edge-delay can be calculated as: RED “

DBRED CPU clock

(22)

FED “

DBFED CPU clock

(23)

where DBFED is the dead-band FED and DBRED is the dead-band RED. In the experiment, 25 SolarTIFSTF-120P6 PV modules with a peak capacity of 3 kW are utilized to supply the load. The modules are subsequently arranged in a series-connected configuration; thus, a DC output voltage of 435 V is produced. The characteristics of the SolarTIFSTF-120P6 PV module are shown in Table 2. Solar irradiation and temperature are the two main parameters responsible for the output power of the solar cell. The mathematical model of the PV electrical circuit is represented by the output of the cell current, which is obtained as follows [35–38]: ˛ qpV ` I. Rs q ‹ V ` I.Rs ˚ p ´ 1‚´ “ I ph ´ Io ˝e n.K B .T Rsh ¨

IPV

(24)

where IPV is cell output current (A), I ph is the light-generated current (A), Io is the cell reverse saturation current or dark current (A), q is the electronic charge (1.6 ˆ 10´19 C), V is the cell output voltage (V), n is the ideality factor, KB is the Boltzmann’s constant (1.38 ˆ 10´23 J/K), T is the cell temperature (K), and RS is the internal resistance of the stack. The short-circuit current Isc,n under the nominal condition and that at the short-circuit current temperature coefficient α are provided in Table 2. The PV characteristics are programmed in the PV simulator Chroma 62050H-600s to represent the actual variation of voltage and current.

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Table 2. PV module characteristics. PV Module Type: SolarTIFSTF-120P6

Values

No. of modules in series (NS ) No. of modules in parallel (NP ) Maximum Power (P MPP ) Open circuit voltage (Voc ) Short circuit current (Isc ) Voltage at maximum power (V MPP ) Current At maximum power (I MPP ) Current temperature coefficient (α) Voltage temperature coefficient (β)

25 1 3 kW 537.5 V 7.63 A 435 V 6.89 A 6.928 mA/˝ C ´0.068 V/˝ C

In the inverter input stage, the configuration of the PV modules in series, parallel, or combination is responsible for the current IPV and voltage VPV of the PV system. In the proposed PV system, IPV and VPV are expressed as follows: ” ı VPV “ NS Vre f ´ β pT ´ Tn q ´ Rs pT ´ Tn q

(25)

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„ IPV “ NP Ire f ´ α pT α

β ´

G Tn q ` ISC Gn

ˆ

G ´1 Gn

˙

1  

(25) 

(26)

(26) 

where NS is the series module number, Vre f is the PV reference voltage, β is the voltage temperature where  the  series  module  number,    is  the  PV  reference  voltage,  β   is  the  voltage  coefficient, T is the stack  is temperature, Tn is the nominal temperature, NP is the parallel module number, temperature  coefficient,    is  the  stack  temperature,    is  the  nominal  temperature,    is  the  Ire f is the PV reference current, G is the irradiance, and irradiance. The inverter parallel module number,    is the PV reference current,   G is the irradiance, and  n is the nominal  is the nominal  irradiance.  The  prototype  is  developed  and experimental verified  on  based  setup on  the  experimental  prototype is developed andinverter  verified on based on the shown insetup  Figure 10. shown in Figure 10. 

  Figure 10. Experimental setup for the proposed PV inverter control system. 

Figure 10. Experimental setup for the proposed PV inverter control system. 8. Results and Discussion  The PV inverter system depicted in Figure 6 is used to evaluate the proposed LSA‐based FLC 

8. Results and(LSA‐FL)  Discussion optimization  method  and  the  robustness  of  the  overall  system.  Figure  11  shows  the 

convergence  characteristics  of  LSA‐FL  to  determine  the  best  optimal  solution  for  the  test  system, 

The PV inverter system depicted Figure 6 isFLC  used to evaluate the proposed LSA-based FLC along  with  the  results  obtained  in with  DSA‐based  (DSA‐FL)  and  PSO‐based  FLC  (PSO‐FL)  optimization methods. For a fair comparison, all optimization algorithms used the same parameters  (LSA-FL) optimization method and the robustness of the overall system. Figure 11 shows the (i.e., problem dimension, population, and iteration). Figure 11 shows that LSA‐FL converges faster  convergence characteristics of LSA-FL to determine the best optimal solution for the test system, along than  DSA‐FL  and  PSO‐FL.  The  optimal  solution  generated  with  LSA‐FL  is  also  better  than  those  with the resultsgenerated with DSA‐FL and PSO‐FL. The optimum performance of LSA‐FL shown in Figure 11 is  obtained with DSA-based FLC (DSA-FL) and PSO-based FLC (PSO-FL) optimization when  both  FLCs  that  represent    and    accomplish  the  MFs  shown  in  Figure  12.  In  methods. For aobtained  fair comparison, all optimization algorithms used the same parameters (i.e., problem consideration of its effectiveness, only FL‐LSA is used to evaluate the performance of the overall PV  dimension, population, and iteration). Figure 11 shows that LSA-FL converges faster than DSA-FL and inverter system when subjected to different types of loads.  PSO-FL. The optimal solution generated with LSA-FL is also better than those generated with DSA-FL

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and PSO-FL. The optimum performance of LSA-FL shown in Figure 11 is obtained when both FLCs that represent Vd and Vq accomplish the MFs shown in Figure 12. In consideration of its effectiveness, only FL-LSA is used to evaluate the performance of the overall PV inverter system when subjected to differentEnergies 2016, 9, 120  types of loads. 15 of 32  15 of 32 

Mean Meanobjective objectivefunction function

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LSA-FL LSA-FL DSA-FL DSA-FL PSO-FL

0.3 0.3

PSO-FL

0.25

0.25

0.2

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0.2

0.15

LSA-FL DSA-FL PSO-FL

Mean objective function

0.15

0.1 0.3

0.1

0.050.25

0.05 0.2 0

20

0

20

0.15

40

60

80

40 Iteration 60

100

80

100  

Iteration   Figure 11. Performance comparisons based on LSA‐FL, DSA‐FL, and PSO‐FL.  0.1

Figure 11. Performance comparisons based on LSA-FL, DSA-FL, and PSO-FL. MFE4

MFE5 MFE6

0 MFE5

MFE4

Degree of membership function Degree of membership function

1

MFE3

MFE3

MFE7

MFE620 MFE7

1

MFCE2

MFCE1 60

MFCE3

MFCE4 MFCE5 MFCE6 MFCE7

MFCE280 MFCE3

100MFCE4 MFCE5

MFCE6 MFCE7

 

0.8 Figure 11. Performance comparisons based on LSA‐FL, DSA‐FL, and PSO‐FL.  0.6

0.60.4

1

0.40.2

0.8

0.2 0

0.6

0 -4

0.4

-4

MFCE1

0.8 Iteration

0.8

0.80.6

1

40

MFE1 MFE2

MFE3

MFE4

MFE5 MFE6

0.6 MFCE1 0.4 1

MFE7

Degree of membership function

1

MFE1 MFE2

Degree of membership function

Degree of membership function

Degree of membership function

Figure 11. Performance comparisons based on LSA‐FL, DSA‐FL, and PSO‐FL.  0.05

MFE1 MFE2

MFCE2

MFCE3

MFCE4 MFCE5 MFCE6 MFCE7

0.4 0.2 0.8

-2

-2

0 Error (E)

2

(a)  0 Error (E)

2

4

4

0.2 00.6 -1

0.4 0

-0.5 0 0.5 Change of error (CE)

-1

-0.5

(b)  0

Change of error (CE) 0.2 Figure 12. Optimized MFs of (a) E and (b) CE using LSA.  (a)  (b)  0 0 -4 -2 0 2 4 -1 -0.5 0 0.5 8.1. Results with Resistive Load (R)  Figure 12. Optimized MFs of (a) E and (b) CE using LSA.  Error (E) Change of error (CE) 0.2

1

0.5

1

1

Figure 12. Optimized MFs of (a) E and (b) CE using LSA.

(a)  (b) s  as  can  be  shown  in  A  simulation  is  conducted  with  a  resistive  load  of  1500 W  for  0.1  Figure 13a.  Furthermore,  the  experiment  is  conducted  in  the  laboratory  to  evaluate  the  overall  Figure 12. Optimized MFs of (a) E and (b) CE using LSA.  8.1. Results with Resistive Load (R) performance  of  the  fuzzy  logic  PV  inverter  controller.  Experimental  A  simulation  is proposed  conducted  with  a  resistive  load  of  1500 W  for  0.1  s voltage  as  can waveforms  be  shown  in  8.1. Results with Resistive Load (R)  are measured with differential probes with a scale (X200), as depicted Figure 13b.    shownthe  AFigure 13a.  simulation is conductedthe  with a resistive of 1500 forlaboratory  0.1 s as can in Figure Furthermore,  experiment  is  load conducted  in W the  to  be evaluate  overall  13a.

8.1. Results with Resistive Load (R) 

performance  of  the  proposed  fuzzy  logic  PV  inverter  controller.  Experimental  voltage  waveforms  A experiment simulation  is  is conducted  with in a  resistive  load  of  1500 W  for  0.1 the s  as overall can  be  shown  in  Furthermore, the conducted the laboratory to evaluate performance of Va Vb Vc 400 Furthermore,  the  experiment  is  conducted  in  the  laboratory  Figure 13a.  to  evaluate  the  overall  are measured with differential probes with a scale (X200), as depicted Figure 13b.    the proposed fuzzy logic PV inverter controller. Experimental voltage waveforms are measured with 300 of  the  proposed  fuzzy  logic  PV  inverter  controller.  Experimental  voltage  waveforms  performance  differential probes with a scale (X200), as depicted Figure 13b. Voltage (V)

are measured with differential probes with a scale (X200), as depicted Figure 13b.  200 Va Vb   Vc 400 100

300

Va

0 400

Vb

Vc

-100 300

100

-200 200

0

Voltage (V)

Voltage (V)

200

-300

100

-100

0

-200

-100

-400

-300 -400 0

0

-200

0.01

0.02

0.03

0.04

-300 -400

0.01

0

0.05 0.06 Time (s)

0.07

0.08

0.09

0.1

 

(a)  0.02

0.01

0.03

0.02

0.04

0.05

0.06

0.03 Figure 13. Cont.  0.04Time0.05 0.06 (s) Time (s)

(a)  (a) 

Figure 13. Cont.  Figure 13. Cont.  Figure 13. Cont.

0.07 0.07

0.08

0.08

0.09

0.09

0.1

0.1

 

 

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  (b)  Figure 13. Output voltage waveforms (i.e., 

, , and ) of the three‐phase inverter with R load for 

  Figure 13.(a) simulation and (b) experimental.  Output voltage waveforms (i.e., Va , Vb , and Vc ) of the three-phase inverter with R load for (b)  (a) simulation and (b) experimental. Both the simulation and experimental output voltage waveforms of the inverter, namely,  , ,  Figure 13. Output voltage waveforms (i.e.,  , , and ) of the three‐phase inverter with R load for  and  , are sinusoidal with 50 Hz, and no negative effect exists, such as overshoot or oscillation. The  (a) simulation and (b) experimental.  Both shift is 120° between each phase. The controller distinctly succeeds in regulating the magnitude of  the simulation and experimental output voltage waveforms of the inverter, namely, Va , phase  voltage  waveform  approximately  339 V  and  the exists, rms  voltage  V.  This  result  Vb , and Vcthe  ,Both the simulation and experimental output voltage waveforms of the inverter, namely,  are sinusoidal with 50 at  Hz, and no negative effect suchof as240  overshoot or oscillation. , ,  ˝ between confirms  that  the  proposed  FLC  is  in  accordance  with  the  exact  voltage  reference;  therefore,  the  The shift is 120 each phase. The controller distinctly succeeds in regulating the magnitude and proposed inverter control algorithm is efficient. The three‐phase load current waveforms should also  , are sinusoidal with 50 Hz, and no negative effect exists, such as overshoot or oscillation. The  of the shift is 120° between each phase. The controller distinctly succeeds in regulating the magnitude of  phase voltage waveform at approximately 339 V and the rms voltage of 240 V. This result be recorded analysis. The load current waveforms are measured, as shown in Figure 14. Similar to  confirms the proposed FLC is accordance 339 V  with and  the exact voltage reference; the that phase  voltage  waveform  at  in approximately  the  rms  voltage  of  240  V. therefore, This  result the the three‐phase output voltage waveform, the phase load current waveforms in the simulation and  confirms  that control the  proposed  FLC isis efficient. in  accordance  with  the  exact  voltage  reference;  therefore,  the  the experimental are successfully regulated through the proposed controller within approximately  proposed inverter algorithm The three-phase load current waveforms should also 3.3 A.  The  load  current  waveforms  are  purely  sinusoidal  with  50  Hz,  and  a  120°  shift  is  proposed inverter control algorithm is efficient. The three‐phase load current waveforms should also  be recorded analysis. The load current waveforms are measured, as shown in Figure 14. Similar to demonstrated between each phase.  be recorded analysis. The load current waveforms are measured, as shown in Figure 14. Similar to 

Current (A)

the three-phase output voltage waveform, the phase load current waveforms in the simulation and the three‐phase output voltage waveform, the phase load current waveforms in the simulation and  the experimental are successfully regulated through the proposedIacontroller Ib Ic within approximately 4 the experimental are successfully regulated through the proposed controller within approximately  3.3 A. The load current3 waveforms are purely sinusoidal with 50 Hz, and a 120˝ shift is demonstrated 3.3 A.  The  load  current  waveforms  are  purely  sinusoidal  with  50  Hz,  and  a  120°  shift  is  between each phase. 2 demonstrated between each phase.  1 0

4 -1

Ia

Ib

0.09

0.1

Ic

3 -2 Current (A)

2 1

-3 -4

0

0

0.01

0.02

0.03

0.04

-1

0.05 Time (s)

0.06

0.07

0.08

 

(a) 

-2 Figure 14. Cont. 

-3 -4 0

0.01

0.02

0.03

0.04

0.05 Time (s)

0.06

(a)  Figure 14. Cont. Figure 14. Cont.  

0.07

0.08

0.09

0.1

 

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  (b)    Figure 14. Output current waveforms (i.e.,  , , and ) of the three‐phase inverter with R load for  Figure 14. Output current waveforms (i.e., Ia , Ib , and (b) Ic ) of the three-phase inverter with R load for (a) (a) simulation and (b) experimental.  simulation and (b) experimental. Figure 14. Output current waveforms (i.e., 

, , and ) of the three‐phase inverter with R load for 

Power  factor  is  essential  for  the  three‐phase  inverter  design  to  indicate  the  efficiency  of  the  (a) simulation and (b) experimental.  proposed inverter and its control algorithm. The goal of the design is to obtain a unity power factor.  Power factor is essential for the three-phase inverter design to indicate the efficiency of the Therefore, the voltage and the load current waveforms are measured simultaneously (Figure 15) to  Power  factor  for  the  three‐phase  inverter  the  efficiency  of  the  proposed inverter and is  itsessential  control algorithm. The goal of the design  designto  is indicate  to obtain a unity power factor. depict the phase difference between these signals. The voltage and the current waveforms exhibit  proposed inverter and its control algorithm. The goal of the design is to obtain a unity power factor.  Therefore, the voltage and the load current waveforms are measured simultaneously (Figure 15) to the same phase angle, which is in accordance with the  power factor  operation, as  expected.  Therefore, the voltage and the load current waveforms are measured simultaneously (Figure 15) to  depict the phase difference between these signals. The unity  voltage and the current waveforms exhibit The phase relationship of load current and voltage signals in the simulation and the experimental  depict the phase difference between these signals. The voltage and the current waveforms exhibit  the same phase angle, which is in accordance with the unity power factor operation, as expected. indicates high efficiency (Figure 15).  the same phase angle, which is in accordance with the  unity  power factor  operation, as  expected.  The phase relationship of load current and voltage signals in the simulation and the experimental The phase relationship of load current and voltage signals in the simulation and the experimental  400 (Figure 15). indicates high efficiency indicates high efficiency (Figure 15).  300

2

200 0

04

100 -100

-22

-200 0

-40

-100 -300 -200 -400 0 -300 -400 0

Current (A) Current (A)

4

300 100

Voltage (V) Voltage (V)

400 200

-2 0.01

0.02

0.01

0.03

0.02

0.03

0.04 0.04

0.05 0.06 Time (s)

(a) 

0.05 0.06 Time (s)

0.07

0.08

0.09

0.1

-4

  0.07

0.08

0.09

0.1

 

(a) 

  (b)  Figure 15. Output voltage  and (b) experimental.  Figure 15. Output voltage 

  and current load 

(b) 

  and current load 

    of the inverter with R load for (a) simulation    of the inverter with R load for (a) simulation 

Figure 15. Output voltage (Va ) and current load (Ia ) of the inverter with R load for (a) simulation and and (b) experimental.  (b) experimental.

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The THD of the voltage and current signals are measured in the simulation and the experimental THD  of ofthe  and  current  signals  are The measured  the  to verify The  the quality thevoltage  inverter output waveforms. qualityin ofthe  thesimulation  waveformand  is inversely experimental to verify the quality of the inverter output waveforms. The quality of the waveform is  proportional to the THD percentage. Figures 16 and 17 show the THD percentages of the voltages and inversely proportional to the THD percentage. Figures 16 and 17 show the THD percentages of the  currents obtained for the R load analyzed in this study. Figure 16a,b shows that the THD of the voltage voltages and currents  obtained for  the R  load analyzed in  this study.  Figure 16a,b  shows  that  the  waveform is 0.56% and 2.1% for the simulation and the experimental, respectively, which satisfies the THD  of  the  voltage  waveform  is  0.56%  and  2.1%  for  the  simulation  and  the  experimental,  IEEE-929-2000 international standard [39]. respectively, which satisfies the IEEE‐929‐2000 international standard [39].    Fundamental (50Hz) = 584.7 , THD= 0.56%

Mag (% of Fundamental)

100 80 60 40 20 0

0

50

100 Harmonic order (a) 

(b) 

150

200

 

 

Figure 16. THD for the phase voltage of the three‐phase inverter with R load for (a) simulation and 

Figure 16. THD for the phase voltage of the three-phase inverter with R load for (a) simulation and (b) experimental.  (b) experimental.

Figures 17a,b shows that the THD of the current waveform is 0.57% and 3% for the simulation  and the experimental, respectively, which complies with the IEEE‐929‐2000 international standard.  Figure 17a,b shows that the THD of the current waveform is 0.57% and 3% for the simulation The low THD in the voltage and current waveforms is mainly achieved with the robustness of the  and the experimental, respectively, which complies with the IEEE-929-2000 international standard. proposed FLC. Two tests are conducted to appraise the proposed fuzzy logic PV inverter controller.  The low THD in the voltage and current waveforms is mainly achieved with the robustness of the The robustness and efficiency of any controller are indicated prominently when perturbation occurs  proposed FLC. Two tests are conducted to appraise the proposed fuzzy logic PV inverter controller. in  DC  input  voltage  or  when  a  change  in  the  value  of  load  occurs.  Therefore,  two  tests  were  The robustness and efficiency of any controller are indicated prominently when perturbation occurs in performed, namely, changing R load and changing DC input voltage, to determine the validity and  DC input voltage or when a change in the value of load occurs. Therefore, two tests were performed, ability of the proposed fuzzy logic PV inverter controller. 

namely, changing R load and changing DC input voltage, to determine the validity and ability of the proposed fuzzy logic PV inverter controller.

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Mag (% of Fundamental)

Fundamental (50Hz) = 3.395 , THD= 0.57%

100 80 60 40 20 0

0

50

100 Harmonic order (a) 

(b) 

150

200  

 

Figure 17. THD for the phase current of the three‐phase inverter with R load for (a) simulation and 

Figure 17. THD for the phase current of the three-phase inverter with R load for (a) simulation and (b) experimental.  (b) experimental.

8.1.1. Step Change in R Load 

8.1.1. Step Change in R Load

The effect of a large step change in the load should also be investigated. A change in the load  usually disturbs the voltage, and the controller regulates this disturbance by controlling the MI. The  The effect of a large step change in the load should also be investigated. A change in the load load disturbs decreases  from  1500 W and to  750 W  at  0.4  s.  Figure  18a,b  this illustrates  the  simulation  voltage  and  usually the voltage, the controller regulates disturbance by controlling the MI. current signals, respectively. Meanwhile, Figure 18c illustrates the experimental voltage and current  The load decreases from 1500 W to 750 W at 0.4 s. Figure 18a,b illustrates the simulation voltage and signals.  Figure  18  illustrates  that  the  decrease  in  load  results the in  experimental an  increase  in voltage output  voltage  current signals, respectively. Meanwhile, Figure 18c illustrates and current waveform, which changes the E and CE signals. The controller possibly detects these signals, and  signals. Figure 18 illustrates that the decrease in load results in an increase in output voltage waveform, suitable control signals are supplied to regulate the inverter output waveforms. 

which changes the E and CE signals. The controller possibly detects these signals, and suitable control signals are supplied to regulate the inverter output waveforms.

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Voltage (V)

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500 400 300 200 100 0 -100 -200 -300 -400 -500 0.1

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Va

0.2

0.3

0.4 Time (s)

0.5

Vb

Vc

0.6

0.7

 

(a) 

Ia

4

Ib

Ic

3 Current (A)

2 1 0 -1 -2 -3 -4 0.1

0.2

0.3

0.4 Time (s) (b) 

(c) 

0.5

0.6

0.7

 

 

Figure 18. Output waveforms with R load decreasing from 1500 W to 750 W. (a) Simulation voltage 

Figure 18. Output waveforms with R load decreasing from 1500 W to 750 W. (a) Simulation voltage waveforms; (b) simulation current waveforms; and (c) experimental voltage and current waveforms  waveforms; (b) simulation current waveforms; and (c) experimental voltage and current waveforms (Ch. 1, Ch. 2, Ch. 3, and Ch. 4 for  , ,  , and  , respectively).  (Ch. 1, Ch. 2, Ch. 3, and Ch. 4 for Va , Vb , Vc , and Ia , respectively).

Figure 19a,b illustrates the simulation voltage and current, respectively, for load that increases  from 750 W to 1500 W at 1 s. Figure 19c shows the experimental voltage and current signals. The  Figure 19a,b illustrates the simulation voltage and current, respectively, for load that increases change in the load disturbs the voltage and the current waveforms.  from 750 W to 1500 W at 1 s. Figure 19c shows the experimental voltage  and current signals. The change

in the load disturbs the voltage and the current waveforms.

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Voltage (V)

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500 400 300 200 100 0 -100 -200 -300 -400 -500 0.7

4 3

Va

0.8

Ia

Ib

0.9

1 Time (s) (a) 

1.1

1 Time (s) (b) 

1.1

Vb

1.2

Vc

1.3

 

Ic

Current (A)

2 1 0 -1 -2 -3 -4 0.7

0.8

0.9

(c) 

1.2

1.3

 

 

Figure 19. Output waveforms with R load increasing from 750 W to 1500 W. (a) Simulation voltage 

Figure waveforms; (b) simulation current waveforms; and (c) experimental voltage and current waveforms  19. Output waveforms with R load increasing from 750 W to 1500 W. (a) Simulation voltage waveforms; (b) simulation current waveforms; and (c) experimental voltage and current waveforms , ,  , and  , respectively).  (Ch. 1, Ch. 2, Ch. 3, and Ch. 4 for  (Ch. 1, Ch. 2, Ch. 3, and Ch. 4 for Va , Vb , Vc , and Ia , respectively). The controller regulates the inverter output waveforms successfully. Therefore, the inverter  output responses indicate that the proposed controller is sufficiently robust to achieve a favorable  The controller regulates the inverter output waveforms successfully. Therefore, the inverter response to a change in step load. 

output responses indicate that the proposed controller is sufficiently robust to achieve a favorable response to a change in step load.   8.1.2. Step Change in Vdc

The intermittent PV characteristics should be appraised to determine the effectiveness of the proposed controller. The PV system suffers from a fluctuating DC voltage. Therefore, the change in the step DC voltage, Vdc , should also be examined to analyze the proposed controller. Vdc is increased

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Voltage (V)

The  intermittent  PV  characteristics  should  be  appraised  to  determine  the  effectiveness  of  the  proposed controller. The PV system suffers from a fluctuating DC voltage. Therefore, the change in  ,  should  be  examined  to  analyze  proposed  controller.    is  and from the  200 step  V to DC  300 voltage,  V at 1.6 s to test thealso  proposed controller. Figurethe  20a,b illustrates the voltage increased  from  200 V  to  300 V  at  1.6 s  to  test  the  proposed  controller.  Figure  20a,b  illustrates  the  current waveforms, respectively. Meanwhile, Figure 20c illustrates the experimental voltage and voltage  and  current  waveforms,  respectively.  Meanwhile,  Figure  20c  illustrates  the  experimental  current signals. An increase in Vdc also increases the voltage and current waveforms. Therefore, voltage and current signals. An increase in    also increases the voltage and current waveforms.  the proposed controller regulates the inverter output waveforms successfully; thus, the proposed Therefore, the proposed controller regulates the inverter output waveforms successfully; thus, the  controller is implemented successfully. proposed controller is implemented successfully.  700 600 500 400 300 200 100 0 -100 -200 -300 -400 -500 1.3

Va

Vb

Vc

1.4

Vdc=200V

1.5

1.6 Time (s)

Vdc=300V

1.7

1.8

1.9

 

Current (A)

(a)  7 6 5 4 3 2 1 0 -1 -2 -3 -4 -5 1.3

Ia

Ib

Ic

1.4

Vdc=200V

1.5

1.6 Time (s)

Vdc=300V

1.7

1.8

1.9

 

(b) 

(c)  Figure 20. Output waveforms with 

 

  increasing from 200 V to 300 V with R load. (a) Simulation 

Figure 20. Output waveforms with Vdc increasing from 200 V to 300 V with R load. (a) Simulation voltage  waveforms;  (b)  simulation  current  waveforms;  and  (c)  experimental  voltage  and  current  voltage waveforms; (b) simulation current,  waveforms; and (c) experimental voltage and current , and  , respectively).  waveforms (Ch. 1, Ch. 2, and Ch. 3 for  waveforms (Ch. 1, Ch. 2, and Ch. 3 for Vdc , Va , and Ia , respectively).

Vdc is decreased from 300 V to 200 V at 2.2 s to evaluate further the proposed controller. The voltage and current waveforms are illustrated in Figure 21a,b, respectively. Meanwhile, Figure 21c shows the experimental voltage and current waveforms. The decrease in Vdc decreases the inverter voltage and current output waveforms. The proposed FLC successfully regulates the voltage and current

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  is decreased from 300 V to 200 V at 2.2 s to evaluate further the proposed controller. The  Energies 2016, 9, 120 23 of 32 voltage and current waveforms are illustrated in Figure 21a,b, respectively. Meanwhile, Figure 21c 

Current (A)

Voltage (V)

shows the experimental voltage and current waveforms. The decrease in    decreases the inverter  voltage  and  current  output  waveforms.  The  proposed  FLC  successfully  regulates  the  voltage  and  waveforms. This finding indicates that the proposed controller can deal with the change in Vdc with current waveforms. This finding indicates that the proposed controller can deal with the change in  different  with different loads, and it can be efficiently used in PV systems.  loads, and it can be efficiently used in PV systems. 700 600 500 400 300 200 100 0 -100 -200 -300 -400 -500 1.9

7 6 5 4 3 2 1 0 -1 -2 -3 -4 -5 1.9

Vdc=200V

Vdc=300V

2

2.1

2.2 Time (s)

2.3

Va

Vb

Vc

2.4

2.5

 

(a)  Vdc=200V

Vdc=300V

2

2.1

2.2 Time (s) (b) 

(c)  Figure 21. Waveforms with 

2.3

Ia

Ib

Ic

2.4

2.5

 

 

  decreasing from 300 V to 200 V with R load. (a) Simulation voltage 

Figure 21. Waveforms with Vdc decreasing from 300 V to 200 V with R load. (a) Simulation voltage waveforms; (b) simulation current waveforms; and (c) experimental voltage and current waveforms  waveforms; (b) simulation current and (c) experimental voltage and current waveforms ,  waveforms; , and  , respectively).  (Ch. 1, Ch. 2, and Ch. 3 for  (Ch. 1, Ch. 2, and Ch. 3 for Vdc , Va , and Ia , respectively).

8.2. Results with Resistive and Inductive Load (RL) Another type of load is used to test the robustness of the controller. In this case, RL load represented by a motor with a capacity of 1 hp is used. The equivalent circuit for this motor is equal to (89.9161 + j57.509). Therefore, the values of the RL load are R = 89.9161 Ω and L = 183.1 mH.

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Another  type  of  load  is  used  to  test  the  robustness  of  the  controller.  In  this  case,  RL  load  represented by a motor with a capacity of 1 hp is used. The equivalent circuit for this motor is equal  to (89.9161 + j57.509). Therefore, the values of the RL load are R = 89.9161 Ω and L = 183.1 mH. The  The simulation is performed for 0.1 s, as depicted in Figure 22a. Figure 22b shows the experimental simulation  is of performed  for  0.1 s, inverter, as  depicted  in  Figure  22a.  Figure  22b  shows  the  experimental  voltage waveforms the three-phase namely, Va , V b , and Vc . The voltage waveforms are voltage waveforms of the three‐phase inverter, namely,  , , and  . The voltage waveforms are  not affected by a change in the load type. The controller still succeeds in preserving the magnitude of not affected by a change in the load type. The controller still succeeds in preserving the magnitude of  the AC voltage signals for the three-phase inverter at approximately 339 V. The waveforms are stable, the  AC  voltage  signals  for  the  three‐phase  inverter  at  approximately  339 V. ˝ The  waveforms  are  clean, and balanced at 50 Hz. The displacement between each two phase is 120 . stable, clean, and balanced at 50 Hz. The displacement between each two phase is 120°.  400

Va

Vb

0.08

0.09

Vc

300 Voltage (V)

200 100 0 -100 -200 300 -400 0

0.01

0.02

0.03

0.04

0.05 0.06 Time (s)

0.07

0.1

 

(a) 

(b)  Figure 22. Output voltage waveforms (i.e., 

 

, , and ) of the three‐phase inverter with RL load for 

Figure 22. Output voltage waveforms (i.e., Va , Vb , and Vc ) of the three-phase inverter with RL load for (a) simulation and (b) experimental.  (a) simulation and (b) experimental.

The  simulation  and  experimental  three‐phase  load  current  waveforms  are  presented  in  Figure 23a,b, respectively, to observe the effect of RL load on the current waveform. The change in  The simulation and experimental three-phase load current waveforms are presented in load type does not affect the quality of the current waveforms. The waveforms remain stable, and  Figure 23a,b, respectively, to observe the effect of RL load on the current waveform. The change the  controller  a  constant  level  with  waveforms. approximately The 1.95 A  and  an  approximately  in load type does notachieves  affect the qualitypeak  of the current waveforms remain stable, 1.37 A·rms. The waveforms remain balanced at 50 Hz, and they are displaced by 120° between each  and the controller achieves a constant peak level with approximately 1.95 A and an approximately two phases.    ˝

1.37 A¨ rms. The waveforms remain balanced at 50 Hz, and they are displaced by 120 between each two phases.

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Current (A) (A) Current

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Ia

Ib

Ic

Ia

Ib

Ic

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21 10 0 -1 -1 -2 -2 -3 0

0.01

0.02

0.03

-3 0

0.01

0.02

0.03

0.04

0.05 0.06 Time (s) 0.04 0.05 (a)  0.06 Time (s)

0.07

0.08

0.09

0.1

0.07

0.08

0.09

0.1

   

(a) 

 

(b) 

 

Figure 23. Output current waveforms (i.e.,  , , and ) of the three‐phase inverter with RL load for  (b) Ic ) of Figure 23. Output current waveforms (i.e., Ia , Ib , and the three-phase inverter with RL load for (a) simulation and (b) experimental.  (a) simulation and (b) experimental. Figure 23. Output current waveforms (i.e.,  , , and ) of the three‐phase inverter with RL load for  (a) simulation and (b) experimental.  The phase shift between the voltage and current with RL load is also measured to evaluate the 

300 400 200 300 100 200 0 100 -100 0 -200 -100 -300 -200 -400 -300 0

0.01

0.02

0.03

0.04

0.07

0.08

0.09

-400 0

0.05 0.06 Time (s)

3 4 2 3 1 2 0 1 -1 0 -2 -1 -3 -2 -4 0.1 -3

0.01

0.02

0.03

0.04

(a)  0.06 0.05 Time (s)

0.07

0.08

0.09

-4 0.1

Current (A) (A) Current

Voltage (V) (V) Voltage

controller further. Figure 24a,b illustrates the simulation and experimental output voltage    and the The phase shift between the voltage and current with RL load is also measured to evaluate The phase shift between the voltage and current with RL load is also measured to evaluate the  current load  . The figure indicates that the power factor of the RL load is 84.2%, which means  controller further. Figure 24a,b illustrates the simulation and experimental output voltage (Va ) and controller further. Figure 24a,b illustrates the simulation and experimental output voltage    and  that the load current lags behind the voltage waveform by 32.6°.  currentcurrent load  load (Ia ). The figure indicates that the power factor of the RL load is 84.2%, which means that . The figure indicates that the power factor of the RL load is 84.2%, which means  ˝ the load current lags that the load current lags behind the voltage waveform by 32.6°.  400 behind the voltage waveform by 32.6 . 4

(a)  Figure 24. Cont.  Figure 24. Cont.  Figure 24. Cont.

   

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(b)  Figure 24. Output voltage 

  and current load 

  of the inverter with RL load for (a) simulation 

  Figure 24. Output voltage (Va ) and current load (Ia ) of the inverter with RL load for (a) simulation and and (b) experimental.  (b)  (b) experimental. Figure 24. Output voltage    and current load    of the inverter with RL load for (a) simulation  The  THD  for  the  inverter  output  waveforms  are  also  measured  to  verify  the  quality  of  the  and (b) experimental. 

(% of Fundamental) Mag (%Mag of Fundamental)

signals  when  connected with  RL are load.  Figure  25a,b  shows  the the voltage  THD for  The THD for the inverter is  the inverter output waveforms also measured to verify quality of thethe  signals simulation and the experimental. Figure 25 clearly shows that the controller succeeds in maintaining  when the The  inverter is connected with RL load. Figure 25a,b shows the voltage THD for the simulation THD  for  the  inverter  output  waveforms  are  also  measured  to  verify  the  quality  of  the  the voltage THD at a small percentage of 0.54% and 2.7% for the simulation and the experimental,  and the experimental. Figure 25connected with  clearly shows RL  thatload.  the controller succeeds in maintaining the the  voltage signals  when  the inverter is  Figure  25a,b  shows  the  voltage  THD for  respectively. The current THDs for the simulation and the experimental are shown in Figure 26. The  THD simulation and the experimental. Figure 25 clearly shows that the controller succeeds in maintaining  at a small percentage of 0.54% and 2.7% for the simulation and the experimental, respectively. controller also succeeds in maintaining the current THD of 1.15% and 3.6% for the simulation and  the voltage THD at a small percentage of 0.54% and 2.7% for the simulation and the experimental,  The current THDs for the simulation and the experimental are shown in Figure 26. The controller also the experimental, respectively. This finding indicates that the controller can successfully deal with RL  respectively. The current THDs for the simulation and the experimental are shown in Figure 26. The  succeeds in maintaining the current THD of 1.15% and 3.6% for the simulation and the experimental, load, and clean waveforms can be supplied, thereby meeting the IEEE‐929‐2000 international standard.  controller also succeeds in maintaining the current THD of 1.15% and 3.6% for the simulation and  respectively. This finding indicates that the controller can successfully deal with RL load, and clean the experimental, respectively. This finding indicates that the controller can successfully deal with RL  (50Hz) = 584 , THD=international 0.54% waveforms can be supplied, therebyFundamental meeting the IEEE-929-2000 standard. load, and clean waveforms can be supplied, thereby meeting the IEEE‐929‐2000 international standard.  100 Fundamental (50Hz) = 584 , THD= 0.54%

80 100 60 80 40 60 20 40 0 20 0 0

0

50 50

100 Harmonic order (a) 

100 Harmonic order Figure 25. Cont.  (a) 

Figure 25. Cont.  Figure 25. Cont.

150

200

  150

200

 

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(b) 

(b) 

 

Figure 25. THD for the phase voltage of the three‐phase inverter with RL load for (a) simulation and 

Mag (% of Fundamental)

Figure 25. THD for the phase voltage of the three-phase inverter with RL load for (a) simulation and Figure 25. THD for the phase voltage of the three‐phase inverter with RL load for (a) simulation and  (b) experimental.  (b) experimental. (b) experimental.  Fundamental (50Hz) = 1.953 , THD= 1.15%

100 Fundamental (50Hz) = 1.953 , THD= 1.15%

Mag (% of Fundamental)

100

80

8060 6040 4020 20 0 0 0

0

50

50

100 Harmonic order (a) 

100 Harmonic order (a) 

(b) 

150

200

  150

200

 

 

Figure 26. THD for the phase current of the three‐phase inverter with RL load for (a) simulation and  (b) experimental. 

 

(b) 

 

Figure 26. THD for the phase current of the three‐phase inverter with RL load for (a) simulation and  Figure 26. THD for the phase current of the three-phase inverter with RL load for (a) simulation and (b) experimental.  (b) experimental.

 

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Step Change Vdc Step Change in 

 

Voltage (V)

The step change in Vdc is also implemented for RL load to appraise the robustness of the proposed The  V step  change  in    is  also  implemented  for  RL  load  to  appraise  the  robustness  of  the  FLC controller. dc is increased from 250 V to 350 V to determine the effect of a step change in the DC proposed  FLC  controller.  is  increased  from  250  V  to  350  V toto an determine  effect  a  step the on the inverter output waveforms  when the inverter is connected RL load. the  Figure 27of  shows change in the DC on the inverter output waveforms when the inverter is connected to an RL load.  inverter response with DC step change. Figure 27a,b illustrates the simulation voltage and current Figure 27 shows the inverter response with DC step change. Figure 27a,b illustrates the simulation  signals when Vdc increased from 250 V to 350 V at 0.4 s. Meanwhile, Figure 27c shows experimental voltage and current signals when    increased from 250 V to 350 V at 0.4 s. Meanwhile, Figure 27c  voltageshows experimental voltage and current waveforms.  and current waveforms.   700 600 500 400 300 200 100 0 -100 -200 -300 -400 -500 0.1

5 4

Va

Vb

Vc

0.2

0.3

0.4 Time (s)

Vdc=350V

0.5

0.6

0.7

 

(a)  Ia

Ib

Ic Vdc=250V

3 Current (A)

Vdc=250V

Vdc=350V

2 1 0 -1 -2 -3 0.1

0.2

0.3

0.4 Time (s)

0.5

0.6

0.7

 

(b) 

(c)  Figure 27. Output waveforms with 

 

  increasing from 250 V to 350 V with RL load. (a) Simulation 

Figure 27. Output waveforms with Vdc increasing from 250 V to 350 V with RL load. (a) Simulation voltage  waveforms;  (b)  simulation  current  waveforms;  and  (c)  experimental  voltage  and  current  voltagewaveforms (Ch. 1, Ch. 2, and Ch. 3 for  waveforms; (b) simulation current waveforms; and (c) experimental voltage and current ,  , and  , respectively).  waveforms (Ch. 1, Ch. 2, and Ch. 3 for Vdc , Va , and Ia , respectively).

Figure 27 shows that the DC step change leads to an increase in voltage and current waveforms.  In this case, the controller succeeds in regulating the inverter output waveforms, and the effect of the  Figure 27 shows that the DC step change leads to an increase in voltage and current waveforms.

In this case, the controller succeeds in regulating the inverter output waveforms, and the effect of the overshoot is limited with a short time. Figure 28a,b illustrates the voltage and current signals when

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Voltage (V)

overshoot is limited with a short time. Figure 28a,b illustrates the voltage and current signals when  Vdc changes from 350 V to 250 V at 1 s with RL load. Figure 28c shows the experimental voltage and   changes from 350 V to 250 V at 1 s with RL load. Figure 28c shows the experimental voltage and  current waveforms. Figure 28 clearly shows that the proposed FLC controller succeeds in regulating current waveforms. Figure 28 clearly shows that the proposed FLC controller succeeds in regulating  the voltage and current waveforms with a slight drop. Figure 28 indicates that the proposed FLC can the voltage and current waveforms with a slight drop. Figure 28 indicates that the proposed FLC can  also effectively deal with RL load with high efficiency. also effectively deal with RL load with high efficiency.  700 600 500 400 300 200 100 0 -100 -200 -300 -400 0.7

Vdc=350V

0.8

0.9

Vdc=250V

1 Time (s) (a) 

1.1

Current (A)

3

Vb

1.2

Ia Vdc=350V

Vc

1.3

 

5 4

Va

Ib

Ic

Vdc=250V

2 1 0 -1 -2 -3 0.7

0.8

0.9

1 Time (s) (b) 

(c)  Figure 28. Waveforms with 

1.1

1.2

1.3

 

 

  decreasing from 250 V to 350 V with RL load. (a) Simulation voltage 

Figure 28. Waveforms with Vdc decreasing from 250 V to 350 V with RL load. (a) Simulation voltage waveforms; (b) simulation current waveforms; and (c) experimental voltage and current waveforms  waveforms; (b) simulation current waveforms; and (c) experimental voltage and current waveforms (Ch. 1, Ch. 2, and Ch. 3 for  ,  , and  , respectively).  (Ch. 1, Ch. 2, and Ch. 3 for Vdc , Va , and Ia , respectively).

9. Conclusions 

9. Conclusions

This paper has presented a novel nature‐inspired optimization technique called as the LSA to  enhance the performance of the three‐phase PV inverter and its practical implementation using the  This paper has presented a novel nature-inspired optimization technique called as the LSA to

enhance the performance of the three-phase PV inverter and its practical implementation using the eZdsp F28335 controller board. The LSA is applied to optimally tune the MFs of the FLC based PV inverter instead of manual tuning. To optimize the MFs of the FLC, a suitable objective function is

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formulated by minimizing the MSE of the inverter output voltage. A comparative study with DSA and PSO techniques was performed to validate and compare the performance of the LSA. The simulations results showed that the FLC with optimally tuned MFs using the LSA performs well in tracking the reference value and regulating the output voltage waveforms at the desired amplitude for various loads. In addition, the LSA gives better results with high convergence rate compared to the DSA and PSO techniques. To demonstrate the functionality of the proposed method, a hardware prototype of the optimal FLC based PV inverter is developed and compiled using the eZdsp F28335 controller board. The real-time model for the optimized FLC using LSA was first developed in the MATLAB environment to generate PWM switching signals for the IGBTs of the inverter. Thereafter, the developed controller was implemented in hardware using the eZdsp F28335 controller board in a prototype three-phase voltage source inverter. The developed PV inverter model was compiled, converted to the C-code, and automatically linked to the real-time TMS320F28335 processor board. The performance and behavior of the inverter was monitored in real-time by developing a GUI program in the CCS software. The experimental results with the prototype PV inverter showed that the proposed controller successfully regulated the inverter output waveform when connected to the resistive and combined resistive and inductive loads and also demonstrated the ability to handle changing DC input voltage and changing load. High quality inverter output voltage waveforms were obtained with low voltage THD values of 2.1% and 2.7% for the resistive and combined resistive and inductive loads, respectively. Furthermore, low current THD values of 3% and 3.6% are obtained for the resistive and resistive inductive loads, respectively. Therefore, the developed prototype optimum fuzzy logic based PV inverter controller implemented using the eZdsp F28335 control board is considered a useful device to be use in stand-alone and grid-connected PV systems. Acknowledgments: The authors are grateful to Universiti Kebangsaan Malaysia for supporting this research financially under grant no. ETP-2013-044. Author Contributions: Ammar Hussein Mutlag is a PhD student implementing the project and he is the corresponding author of the manuscript. Azah Mohamed is the main supervisor of the student who leads the project and edits the manuscript. Hussain Shareef is the co-supervisor of the student who has edited the manuscript and given valuable suggestions to improve the manuscript. Conflicts of Interest: The authors declare no conflict of interest.

References 1.

2. 3. 4.

5. 6. 7. 8.

Sperati, S.; Alessandrini, S.; Pinson, P.; Kariniotakis, G. The Weather Intelligence for Renewable Energies Benchmarking Exercise on Short-Term Forecasting of Wind and Solar Power Generation. Energies 2015, 8, 9594–9619. [CrossRef] Chel, A.; Tiwari, G.N.; Chandra, A. Simplified method of sizing and life cycle cost assessment of building integrated photovoltaic system. Energy Build. 2009, 41, 1172–1180. [CrossRef] Blaabjerg, F.; Chen, Z.; Kjaer, S. Power electronics as efficient interface in dispersed power generation systems. IEEE Trans. Power Electron. 2004, 19, 1184–1194. [CrossRef] Ortega, R.; Figueres, E.; Garcerá, G.; Trujillo, C.L.; Velasco, D. Control techniques for reduction of the total harmonic distortion in voltage applied to a single-phase inverter with nonlinear loads: Review. Renew. Sust. Energ. Rev. 2012, 16, 1754–1761. [CrossRef] Ryu, T. Development of Power Conditioner Using Digital Controls for Generating Solar Power. Oki Tech. Rev. 2009, 76, 40–43. Selvaraj, J.; Rahim, N.A. Multilevel Inverter for Grid-Connected PV System Employing Digital PI Controller. IEEE Trans. Ind. Electron. 2009, 56, 149–158. [CrossRef] Sanchis, P.; Ursaea, A.; Gubia, E.; Marroyo, L. Boost DC-AC Inverter: A New Control Strategy. IEEE Trans. Power Electron. 2005, 20, 343–353. [CrossRef] Ghani, Z.A.; Hannan, M.A.; Mohamed, A. Simulation model linked PV inverter implementation utilizing dSPACE DS1104 controller. Energy Build. 2013, 57, 65–73. [CrossRef]

Energies 2016, 9, 120

9. 10. 11. 12. 13.

14. 15.

16. 17.

18. 19. 20. 21. 22. 23.

24. 25. 26. 27. 28. 29. 30.

31. 32.

31 of 32

Daud, M.Z.; Mohamed, A.; Hannan, M.A. An Optimal Control Strategy for DC Bus Voltage Regulation in Photovoltaic System with Battery Energy Storage. Sci. World J. 2014, 2014, 271087. [CrossRef] [PubMed] Liserre, M.; Dell’Aquila, A.; Blaabjerg, F. Genetic Algorithm-Based Design of the Active Damping for an LCL-Filter Three-Phase Active Rectifier. IEEE Trans. Power Electron. 2004, 19, 76–86. [CrossRef] Li, W.; Man, Y.; Li, G. Optimal parameter design of input filters for general purpose inverter based on genetic algorithm. Appl. Math. Comput. 2008, 205, 697–705. [CrossRef] Sundareswaran, K.; Jayant, K.; Shanavas, T.N. Inverter Harmonic Elimination through a Colony of Continuously Exploring Ants. IEEE Trans. Ind. Electron. 2007, 54, 2558–2565. [CrossRef] Mohamed, Y.A.I.; El Saadany, E.F. Hybrid Variable-Structure Control with Evolutionary Optimum-Tuning Algorithm for Fast Grid-Voltage Regulation Using Inverter-Based Distributed Generation. IEEE Trans. Power Electron. 2008, 23, 1334–1341. [CrossRef] Rai, A.K.; Kaushika, N.D.; Singh, B.; Agarwal, N. Simulation model of ANN based maximum power point tracking controller for solar PV system. Sol. Energy Mater. Sol. Cells 2011, 95, 773–778. [CrossRef] Ali, J.A.; Hannan, M.A.; Mohamed, A. A Novel Quantum-Behaved Lightning Search Algorithm Approach to Improve the Fuzzy Logic Speed Controller for an Induction Motor Drive. Energies 2015, 8, 13112–13136. [CrossRef] Sakhar, A.; Davari, A.; Feliachi, A. Fuzzy logic control of fuel cell for stand-alone and grid connection. J. Power Sources 2004, 135, 165–176. [CrossRef] Thiagarajan, Y.; Sivakumaran, T.S.; Sanjeevikumar, P. Design and Simulation of FUZZY Controller for a Grid connected Stand Alone PV System. In Proceedings of the EEE Conference on Computing, Communication and Networking (ICCCn’08), St. Thomas, VI, USA, 18–20 December 2008; pp. 1–6. Hong, Y.-Y.; Hsieh, Y.-L. Interval Type-II Fuzzy Rule-Based STATCOM for Voltage Regulation in the Power System. Energies 2015, 8, 8908–8923. [CrossRef] Altin, N.; Sefa, I. dSPACE based adaptive neuro-fuzzy controller of grid interactive inverter. Energy Conv. Manag. 2012, 56, 130–139. [CrossRef] Collotta, M.; Messineo, A.; Nicolosi, G.; Pau, G. A Dynamic Fuzzy Controller to Meet Thermal Comfort by Using Neural Network Forecasted Parameters as the Input. Energies 2014, 7, 4727–4756. [CrossRef] Cheng, P.C.; Peng, B.R.; Liu, Y.H.; Cheng, Y.S.; Huang, J.W. Optimization of a Fuzzy-Logic-Control-Based MPPT Algorithm Using the Particle Swarm Optimization Technique. Energies 2015, 8, 8534–8561. [CrossRef] Shareef, H.; Mutlag, A.H.; Mohamed, A. A novel approach for fuzzy logic PV inverter controller optimization using lightning search algorithm. Neurocomputing 2015, 168, 435–453. [CrossRef] Nasiri, R.; Radan, A. Pole-placement control strategy for 4 leg voltage source inverters. In Proceedings of the IEEE Conference on Power Electronic & Drive Systems & Technologies (PEDSTC‘10), Tehran, Iran, 17–18 February 2010; pp. 74–82. Thandi, G.S.; Zhang, R.; Zhing, K.; Lee, F.C.; Boroyevich, D. Modeling, control and stability analysis of a PEBB based DC DPS. IEEE Trans. Power Deliv. 1999, 14, 497–505. [CrossRef] Mohan, N.; Undeland, T.M.; Robbins, W.P. Power Electronics: Converters, Applications, and Design, 3rd ed.; John Wiley and Sons: Hoboken, NJ, USA, 2003. Altin, N.; Ozdemir, S. Three-phase three-level grid interactive inverter with fuzzy logic based maximum power point tracking controller. Energy Conv. Manag. 2013, 69, 17–26. [CrossRef] Hazzab, A.; Bousserhane, I. K.; Zerbo, M.; Sicard, P. Real Time Implementation of Fuzzy Gain Scheduling of PI Controller for Induction Motor Machine Control. Neural Process. Lett. 2006, 24, 203–215. [CrossRef] Cheng, C.H. Design of output filter for inverters using fuzzy logic. Expert Syst. Appl. 2011, 38, 8639–8647. [CrossRef] Elmas, C.; Deperlioglu, O.; Sayan, H.H. Adaptive fuzzy logic controller for DC–DC converters. Expert Syst. Appl. 2009, 36, 1540–1548. [CrossRef] Rajkumar, M.V.; Manoharan, P.S.; Ravi, A. Simulation and an experimental investigation of SVPWM technique on a multilevel voltage source inverter for photovoltaic systems. Int. J. Electr. Power Energy Syst. 2013, 52, 116–131. [CrossRef] Rajkumar, M.V.; Manoharan, P.S. FPGA based multilevel cascaded inverters with SVPWM algorithm for photovoltaic system. Sol. Energy 2013, 87, 229–245. [CrossRef] Behera, S.; Das, S.P.; Doradla, S.R. Quasi-resonant inverter-fed direct torque controlled induction motor drive. Electr. Power Syst. Res. 2007, 77, 946–955. [CrossRef]

Energies 2016, 9, 120

33. 34. 35.

36. 37. 38.

39.

32 of 32

Durgasukumar, G.; Pathak, M.K. Comparison of adaptive Neuro-Fuzzy-based space-vector modulation for two-level inverter. Int. J. Electr. Power Energy Syst 2012, 38, 9–19. [CrossRef] Saribulut, L.; Teke, A.; Tumay, M. Vector-based reference location estimating for space vector modulation technique. Electr. Power Syst. Res 2012, 86, 51–60. [CrossRef] Yazdani, A.; Fazio, A.R.D.; Ghoddami, H.; Russo, M.; Kazerani, M.; Jatskevich, J.; Strunz, K.; Leva, S.; Martinez, J.A. Modeling guidelines and a benchmark for power system simulation studies of three phase single stage photovoltaic systems. IEEE Trans. Power Deliv. 2011, 26, 1247–1264. [CrossRef] Lijun, G.; Roger, A.; Shengyi, D.L.; Albena, P.I. Parallel-connected solar PV system to address partial and rapidly fluctuating shadow conditions. IEEE Trans. Ind. Electron. 2012, 56, 1548–1556. [CrossRef] El Amrani, A.; Mahrane, A.; Moussa, F.Y.; Boukennous, Y. Solar module fabrication. Int. J. Photoenergy 2007, 2007, 27610. [CrossRef] Young-Hyok, J.; Doo-Yong, J.; Jun-Gu, K.; Jae-Hyung, K.; Tae-Won, L.; Chung-Yuen, W. A real maximum power point tracking method for mismatching compensation in PV array under partially shaded conditions. IEEE Trans. Power Electron. 2011, 26, 1001–1009. IEEE Std 929-2000. Recommended Practices for Utility Interface of Photovoltaic System. The Institute of Electrical and Electronics Engineers: New York, NY, USA, 2000. © 2016 by the authors; licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons by Attribution (CC-BY) license (http://creativecommons.org/licenses/by/4.0/).