Research ArticleCascade Control of Grid-Connected PV Systems UsingTLBO-Based Fractional-Order PID

Afef Badis ,1 Mohamed Nejib Mansouri,1 and Mohamed Habib Boujmil2

1Electronics and Microelectronics Laboratory (EμE), The National Engineering School of Monastir (ENIM),University of Monastir, Tunisia2Higher Institute of Technological Studies of Nabeul, Nabeul, Tunisia

Correspondence should be addressed to Afef Badis; badis.afef@gmail.com

Received 4 December 2018; Revised 20 February 2019; Accepted 13 March 2019; Published 16 May 2019

Academic Editor: Huiqing Wen

Copyright © 2019 Afef Badis et al. This is an open access article distributed under the Creative Commons Attribution License,which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Cascade control is one of the most efficient systems for improving the performance of the conventional single-loop control,especially in the case of disturbances. Usually, controller parameters in the inner and the outer loops are identified in a strictsequence. This paper presents a novel cascade control strategy for grid-connected photovoltaic (PV) systems based onfractional-order PID (FOPID). Here, simultaneous tuning of the inner and the outer loop controllers is proposed. Teaching-learning-based optimization (TLBO) algorithm is employed to optimize the parameters of the FOPID controller. The superiorityof the proposed TLBO-based FOPID controller has been demonstrated by comparing the results with recently publishedoptimization techniques such as genetic algorithm (GA), particle swarm optimization (PSO), and ant colony optimization(ACO). Simulations are conducted using MATLAB/Simulink software under different operating conditions for the purpose ofverifying the effectiveness of the proposed control strategy. Results show that the performance of the proposed approachprovides better dynamic responses and it outperforms the other control techniques.

1. Introduction

In recent years, solar energy has become one of the mostpotential renewable and environmentally friendly resourcesof energy thanks to its free gas emission, abundance, and lowmaintenance cost [1]. Usually, the solar energy is exploitedeither for stand-alone systems or for grid-connected photo-voltaic (PV) systems. Several papers in the literature are tar-geting the issue of grid-connected PV generator (PVG) [2],and studies are carried out in this issue in order to improvethe overall efficiency of the system. In fact, the nonlinearityof the PV power systems and the unpredictable intrinsicand atmospheric changes, which make the operating pointvary due to the control unit and the parametric errors, arethe two key factors that should be thoroughly examined.Thus, the main objective in a grid-connected PV system isto ensure high performance with low cost by choosing theappropriate control strategy.

The control chain consists of two main parts, includingthe PVG-side control which ensures maximum extractionof PVG power using the appropriate MPPT algorithm andthe grid-side control by controlling the DC bus voltage andinjecting the desired power into the grid.

A considerable progress has been made over the lastdecade in optimization techniques. Among these methods,proportional-integral-derivative (PID) controllers are knownto be the most widely used in many studies of grid-connectedPV systems since they perform well in linear systems as com-pared to many new advanced control strategies, namely,model predictive control [3], neural control [4], and fuzzyPI control [5–7]. However, for nonlinear systems or withvarying parameters, PID controllers become insufficientand unreliable, especially, when the performance require-ments of the system are rigorous.

To overcome the weaknesses of the already cited controlstrategies, metaheuristic has recently emerged in the literature

HindawiInternational Journal of PhotoenergyVolume 2019, Article ID 4325648, 17 pageshttps://doi.org/10.1155/2019/4325648

with new evolutionary techniques. Particle swarm optimiza-tion (PSO) was first developed in [8], and since then, it hasgained much attention and become largely exploited in sev-eral fields [9–12]. PSO has the advantage of generating ahigh-quality solution within shorter calculation time andstable convergence characteristics in designing and tuning aPID controller [13]. Nowadays, teaching-learning-basedoptimization (TLBO) is a new optimization technique whichoutperforms the conventional methods. TLBO has beenimmersed in the literature for the purpose of tuning thePID parameters.

Moreover, performances of the classical PID controllercan be further improved by setting the appropriatefractional-I and fractional-D actions. The fractional-orderPID (FOPID) was firstly reported in [14] for a fractional-order system. Since then, FOPID controllers concern moreresearchers to reach the most robust performance of varioussystems [15, 16].

Cascade control is one of the most commonly usedcomplex control structures in industrial processes. It isimplemented to enable faster disturbance rejection. Althoughsophisticated cascade control schemes have been proposed[17–19], the basic scheme still includes two nested loops withtwo controllers. Since this configuration requires the tuningof two controllers, cascade tuning systems are more complexthan single-loop tuning systems. The usual approach is tofirst optimize the secondary regulator. The primary control-ler is then adjusted by evaluating the action of the secondarycontroller on the internal loop. Such a setting proceduretakes a long time because at least two tests are usually neces-sary [20, 21]. However, the sequential tuning procedure hasbeen improved so that only one test is performed to adjustboth controllers simultaneously [22].

Very limited studies are available in the literature for howto tune cascade control systems, andmost of them change theoriginal structure of the cascade control system. In [23], theauthors have proposed a technique to tune the P/PI control-lers and PID/PID simultaneously for the internal and exter-nal loop. It consists in finding the ideal parameters by theMaclaurin series. This method is compared with the methodin [24, 25]. The method in reference [23] outperforms theother methods.

In [26], GA is used to tune the P/PI and PID/PID con-trollers for the internal and external loops simultaneously.This method enables the user to select the performance cri-teria, which is not the case in [23]. GA has proven to be veryeffective in finding the optimal gains [27]. The GA-basedmethod is compared to the method in [28]. Simulationresults show the superiority of GA over the other methods.

Owing to the control design, this paper presents a com-parative study of different metaheuristic-based control strat-egies to control the entire system which includes fourcascaded controllers designed on the basis of the nonlinearsystem. On this topic, a TLBO-based FOPID controller isproposed to design a control strategy which is insensitive toparameter variations, perturbations, and nonlinearity andits parameters’ gain is varying accordingly.

In the conventional cascade control, the controllerparameters in the primary and secondary loops are tuned

sequentially which makes the control more difficult andtime-consuming. This paper describes a simultaneous tuningmethod for both GPV and grid-side cascade subsystemsusing the TLBO algorithm to estimate the appropriateparameters of the primary and secondary loop controllers.The control technique takes advantage of a simple but accu-rate control design technique.

The paper is organized as follows. Section 2 covers the PVsystemmodeling. Section 3 encompasses the different controlstrategies. In section 4, simulation results are discussed forvarious operating conditions. Comparison and commentssupporting the performance and robustness of the TLBO-FOPID control strategy are given. Finally, Section 5 drawsthe conclusion followed by References.

2. Modeling of the Grid-ConnectedPhotovoltaic System

The PV interface configuration consists of two conversionstages. The first stage is made up of a PV generator and aDC-DC boost converter which executes the maximum powerpoint tracking (MPPT) and follows the power reference whilethe second stage includes a three-phase inverter connectedbetween the DC bus and the grid via a low-pass filter.

The Energetic Macroscopic Representation (EMR) for allcomponents has been used for description and modeling ofthe PV conversion system as shown in Figure 1, while theMaximum Control Structure (MCS) allows modeling thecontrol loops [29]. The EMR is interconnected in order toframe the EMR of the entire system. The used representationhelps to understand the relations between all the systemparameters and to design controllers for the system by char-acterizing the tuning chains. The MCS is generated by inver-sion of the EMR [29, 30].

In order to implement the control strategy, it is essentialto provide control circuits either for the PVG voltage or forthe currents injected into the grid, while maintaining theDC bus voltage, so as to obtain good module and phase accu-racy and a rapid dynamic response.

The EMR model and its inverse MCS allow not only todecompose the system into two or more first-order subsys-tems but also to make its modeling systematic in view of itssetting. Moreover, thanks to this decomposition, the systemand its chain of control thus obtained lead to a structure con-sisting of nested loops which require a cascade control. Thiscontrol provides good dynamic performance and is charac-terized by the following properties [31]:

(i) Cascading of two or more controllers of any type

(ii) Since the subsystems are of the first order, it is easierto stabilize the control circuits

(iii) The choice and dimensioning of the controller arefacilitated. Conventionally, first is the control circuitof the inner loop in which the static converter con-trol unit is treated, and then, the superposed controlloop and so on are processed. In the current study,the two loops are tuned simultaneously. The blockdiagram of Figures 2 and 3 is obtained

2 International Journal of Photoenergy

3. Presentation of the ProposedControl Strategy

The main objective in a grid-connected PV system is toensure high performances with low costs by choosing theadequate control strategy. Furthermore, the simplicity ofthe control algorithm is very crucial. This section deals withthe presentation of the proposed control technique used forcontrolling the whole system. The control chain consists of

two main subsystems including the PVG-side control whichensures the maximum power extraction from the PVG byusing the appropriate MPPT and the grid-side control bycontrolling the DC link voltage and injecting the desiredpower to the grid.

3.1. Fractional-Order PID Controller. The FOPID controllerpresents a generic control loop feedback mechanism whichattempts to reduce the error between a measured variable

Command

Maximum control structure PVG side

Photovoltaic generator Cl filterBoost DC link Three-phase Three-phaseFilter

inverter gridconverter

Maximum control structure grid side

MPPT

Command

PVG

upv iLum

mREG

ipv upv iLim udc vm_dq

ir_dq ir_123

gq

vr_123

mdq_REG

vr_dq

ir_dq_ref

imr_ref

udc_ref

upv_ref iL_ref um_ref

udc

Process

12

Control

udcimr

Grid

CPQ

Figure 1: The EMR and its reverse MCS of the overall system.

upv

+−

+−

+− +

−

+−+

upv_ref

upv

C2 (s) C1 (s)' '

ˆ ipvˆ iLˆ upvˆ udcˆ

udc

OCM

×

÷

mg

umh1+sT1

Ki

1+sT2

Capacitor C Inductance L

KuiL

ipvupv

iL_ref 'uL_ref 'mg_reg

Figure 2: Block diagram of the PVG side.

3International Journal of Photoenergy

and the desired set point of a process. The generalized trans-fer function is given by

C s =U sE s

= KP +KI

sλKDs

μ  λ, μ ≥ 0 , 1

where C s represents the controller output; U s and E sare the control signal and the error signal, respectively; KP,KI , and Kd are the proportional, integral, and derivative con-stant gains, respectively; λ is the order of integration; and μ isthe order of differentiator [31].

If λ = 1 and μ = 1, a classical PID controller is recovered.The FOPID controller generalizes the PID controller andexpands it from point to plane by moving in the quarterplane defined by selecting the values of λ and μ instead ofjumping between four points. In general, researchers areusing a range of 0 to 2 as the order of the FOPID.

3.2. TLBO-Based FOPID Tuning. This optimization tech-nique was firstly invented by Rao et al. in 2011 [32]. Sincethen, TLBO has been rapidly emerged as a powerful optimi-zation tool owing to the high-quality solutions and the goodconvergence it gives. It imitates the teaching and learningprocess between the teacher and learners in the class.

TLBO is based on a randomly generated populationwhich consists of a class of students and it relies on twomodes:

(i) Teacher mode where teachers learn students in aperfect way

(ii) Learners’ mode where learning is made throughinteraction between learners

Initially, a matrix of N rows and D columns is randomlygenerated where N represents the random initial populationof initial solutions and D is the dimension of each vector(number of subjects).

The jth parameter of the ith vector in the first generation ischosen randomly using the equation below:

x1i,j = xminj + rand i,j xmax

j − xminj , 2

with rand i,j ∈ 0 1 .The ith learner’s vector for the gth generation can be

expressed by

Xgi = Xg

i,1 , Xgi,2 ,… , Xg

i,j ,… , Xgi,D 3

In the teacher mode, the student’s result of an exam in asubject represents the fitness function to be optimized andthe best learner becomes the teacher. The learners are moti-vated by the teacher and try to improve their own perfor-mance. Thus, the performance of each learner improvescontinuously through the process of information sharingbetween the teacher and learners.

imo_ref P_ref

udc

udc imo p

q

q=0~

' ir_ref' um_ref'mg_reg'

ir̂ urˆ

ur+

ur

um mgir

udcˆ

udc

udcˆ urˆ

×

Command

Process

+− −−

−−

+ +

++

++×

×

CPQ−1

CPQ K31+st3

OCMC2(s)C2 (s)udc_ref' '

imh

udcˆimhˆ

÷

÷K41+st4

Figure 3: Block diagram of the grid side.

00

500

1000

1500

50 100 150 200PV voltage (v)

PV p

ower

(w)

250 300 350

Figure 4: P-V curve with P&O.

00

1

2

3

PV cu

rren

t (A

)

4

5

6

50 100 150 200PV voltage (v)

250 300 350

Figure 5: I-V curve with P&O.

4 International Journal of Photoenergy

iL_refUpv

C

+−OCM L

Inner loop G1(s)

Superposed loop Upv G2(s)

C2 (s) i

i + iTp

C1 (s)' 'Upv_ref +−k1 tL

i + iT1

k2i + iT2

Figure 6: The simplified block diagram of the process.

0 5 10 15Iteration

Best

fitne

ss

20 25 30

10–3

10–4

10–5

10–2

10–1

100

101

102

X: 30Y: 6.058e-05

Function fitness per TLBO

(a)

Iteration

Best

fitne

ss

0

10–3

10–2

10–1

100

101

102

5 10 15 20 25 30

X: 29Y: 0.003447

Function fitness per TLBO

(b)

Figure 7: Convergence of the fitness function of the inner loop iL (a) and the outer loop Upv (b).

Table 1: Controller parameters of the Upv loop.

Parameters P I D Λ Μ

PSO-PID 0.3448 0.0869 0 _ _

TLBO-FOPID 1.45974 0.03948 0.00597 0.88048 0.46836

ACO-PID 0.6232 2.3787 0 _ _

GA-FOPID 0.2783 0.0095 0 1.1049 0.3005

Table 2: Controller parameters of the iL loop.

Parameters P I D Λ Μ

PSO-PID 166.7585 617.1194 0 _ _

TLBO-FOPID 22.40959 0.14503 0 0.10325 0

ACO-PID 0.67797 0.89969 0.18383 _ _

GA-FOPID 228.1800 18.7110 0 0.1768 0.4135

5International Journal of Photoenergy

Time (seconds)

PV

vol

tage

(W)

0

50

100

150

200

250

300

350

0 0.5 1 1.5 2 2.5 3

UPV-ACOPID

UPV-PSOPID

UPV-GAFOPID

UPV-ref

UPV-TLBO

0.05 0.06 0.07 0.08 0.09 0.1285

290

295

300

1.98 1.985 1.99 1.995 2 2.005 2.01 2.015 2.02239

240

241

242

243

244

245

Figure 8: Upv voltage at varying irradiation.

50 10 15 20

Iteration

25 3010−2

10−0

10−1

Best

fitne

ss

Function fitness-per TLBO

(a)

5010−2

10−1

10−0

10−1

Best

fitne

ss

10−2

10−3

10 15 20

Iteration

25 30

Function fitness-per TLBO

(b)

Figure 9: Convergence of the fitness function of the inner loop idq (a) and the outer loop Udc (b).

6 International Journal of Photoenergy

The vector below contains the learners’mean in the classfor each subject at the gth iteration. The teacher has alwaysthe best mean.

Mg = 〠N

i=1

xgi,1N

N

i=1

〠N

i=1

xgi,2N

N

i=1

… 〠N

i=1

xgi,jN

N

i=1

… 〠N

i=1

xgi,DN

N

i=1

4

A randomly weighted differential vector is formed andadded to the existing population of learners according tothe actual mean and the desired mean vector in order to geta new set of improved learners.

Xnew i

g = Xgi + randg Xg

teacher − TFMg , 5

where TF is randomly selected at each iteration (1 or 2). Eachteacher improves the mean result of the class in the subject incharge of. Bad learners of the population are replaced by thebest learners found through this phase.

Udc

link

vol

tage

(V)

694

696

698

700

702

704

706

708

UDC-ref

UDC-ACO

UDC-GA

UDC-PSO

UDC-TLBO

699.51.45 1.5 1.55 1.6

700

700.5

Time (seconds)0 0.5 1 1.5 2 2.5 3

Figure 10: Udc link voltage at varying irradiation.

Table 3: Controller parameters of the Udc loop.

Parameters P I D Λ Μ

PSO-PID 10 10 0 _ _

TLBO-FOPID 1.35201 1.08842 0.018702 0.30639 0.044487

ACO-PID 0.4633 0.5796 0 _ _

GA-FOPID 0.50140 0.0068 0 1.0748 0.08004

Table 4: Controller parameters of idq loop.

Parameters P I D Λ Μ

PSO-PID 156.4459 2.3633 0 _ _

TLBO-FOPID 8.0678 37.2269 6.6273 0.3780 0.0879

ACO-PID 0.0803 1.07 0.3727 _ _

GA-FOPID 0.2783 0.0095 0 1.1049 0.3005

7International Journal of Photoenergy

0 0.5 1 1.5 2 2.5 3

Time (seconds)

−3

−2

−1

0

1

2

3

4

5

6

Grid

curr

ents

(A)

1.98 21.99 2.022.02−2

−1

0

1

2

ir1refir1

0 0.04 0.06 0.080.02−2

−1

0

1

2

ir1refir1ir2ref

ir2ir3refir3

Figure 11: Grid currents (GA-FOPID control).

0 0.5 1 1.5 2 2.5 3

Time (seconds)

−3

−2

−1

0

1

2

3

4

5

6

Grid

curr

ents

(A)

1.48 1.49 1.511.5 1.52−2

−1

0

1

2

ir1refir1

ir1refir1ir2ref

ir2ir3refir3

Figure 12: Grid currents (ACO-PID control).

8 International Journal of Photoenergy

Grid

curr

ents

(A)

−3

−2

−1

0

1

2

3

4

5

6

ir1ref

ir1ir2ref

ir2ir3ref

ir3

1.45 1.5 1.55−2

−1

0

1

2

Time (seconds)0 0.5 1 1.5 2 2.5 3

Figure 13: Grid currents (TLBO-FOPID).

Grid

curr

ents

(A)

–3

–2

–1

0

1

2

3

4

5

6

ir1ref

ir1ir2ref

ir2ir3ref

ir3

1.48 1.49 1.5 1.51 1.52–2

–1

0

1

2

ir1refir1

Time (seconds)0 0.5 1 1.5 2 2.5 3

Figure 14: Grid currents (PSO-PID).

9International Journal of Photoenergy

In the learner mode, learners interact with each other aswell as with the teacher in order to boost their proficiencyand facilitate the knowledge sharing.

This process of mutual interaction is randomly made. Infact, two learners Xg

i and Xgr are randomly chosen (i ≠ r).

The ith vector of the Xnew matrix is given by

Xnew i

g =Xg

i + randgi X gi − Xg

r si Ygi < Yg

r ,

Xgi + randgi Xg

r − Xgi

6

In this proposed work, the optimal values of the FOPIDcontrollers’ gains are obtained using the TLBO algorithm.Theperformanceofmanyoptimization techniques in the liter-ature depends on the appropriate setting of certain controlparameters. In thedifferential evolution algorithm, the controlparameters are the scale factor and the crossing rate; in thePSOalgorithm, the control parameters are the inertia weight ω,social and cognitive parameters (c1 and c2, respectively).The selection of these parameters is crucial to the perfor-mance of the algorithms. However, the TLBO algorithm

does not require any control parameters. As it is aparameter-free algorithm, it is simple, efficient, and fast.

The proposed TLBO-based control ensures the optimumpower transfer from the PVpanel to the grid. In order to proveits reliability, themodel of thewhole systemhas been designedusing MATLAB/Simulink software. The model has been thentested under different operating conditions. The control strategyis designed to tune the parameters (Kp, Ki, Kd, λ, and μ) of theFOPID/FOPID cascade controllers simultaneously in order tomaintain the stability of the entire control system.The algorithmsearches for thefive controller parameters thatmostoptimize thepower transfer from the PVG to the grid. The optimization algo-rithm gradually and iteratively minimizes the integral perfor-mance index while finding the optimal set of parameters forFOPID/FOPID controllers following the steps described above.Thealgorithmends if the valueof thefitness function is kept con-stant appreciably over a few successive iterations.

3.3. Fitness Function. In order to prove the reliability of theproposed cascade control, it is implemented in the grid-connected PV system. Very limited researches which developguidelines for tuning a FOPID controller are available. Refer-ence [33] highlights the relationships between the order ofdifferentiation (μ) and integration (λ) and the time domainspecifications. The existence of a particular relationship

Grid

curr

ent i

r1 (A

)

0.7 0.75 0.8 0.85 0.9 0.95 1−6

−4

−2

0

2

4

6

ir1PSOir1ref

(a)

Grid

curr

ent i

r1 (A

)

ir1TLBOir1ref

0.7 0.75 0.8 0.85 0.9 0.95 1−6

−4

−2

0

2

4

6

(b)

0.7 0.75 0.8 0.85 0.9 0.95 1

Grid

curr

ent i

r1 (A

)

−4

−2

0

2

4

6

ir1ACOir1ref

(c)

Grid

curr

ent i

r1 (A

)

0.7 0.75 0.8 0.85 0.9 0.95 1−5

0

5

ir1GAir1ref

(d)

Figure 15: Voltage dip effect on grid currents without limitation by using (a) PSO-PID; (b) TLBO-FOPID; (c) ACO-PID; (d) GA-FOPID.

10 International Journal of Photoenergy

between μ and the maximum overshoot has been proven.That is why the maximum overshoot is an important charac-teristic of a control system, and it is used as a measure of per-formance for optimization of the FOPID controller.

For each loop in the subsystem, controller performancesare evaluated according the following fitness function asillustrated in equation (7) and equation (8).

overshoot = max Yout − Y ref , 7

F = α overshoot + β ITAE 8

As there is no preference between the two objectives,α = β = 0 5.

4. Results and Discussion

The instantaneous average model of the overall systemis developed, and results of simulation of different

strategies are carried out under the same conditionsas follows:

P = 1 kW,

C = 220 μF,

R = 100 kΩ,

L = 23mH,

C1 = 5000 μF,

R1 = 10 kΩ,

r1 = 0 0002Ω,L1 = 1mH,

Ur = 380V,

f = 50Hz

9

0.7 0.75 0.8 0.85 0.9 0.95 1

Time (seconds)

−400

−300

−200

100

0

100

200

300

400

Grid

vol

tage

s (V

)

Vr1Vr2Vr3

Figure 16: Voltage dip at t = 0 8 s, 0 9 s .

11International Journal of Photoenergy

This section presents the control response of theproposed TLBO-based cascade control compared toPSO-PID, ACO-PID, and GA-FOPID for autotuning ofthe gains for each cascade control loop for sudden irradia-tion variations, sudden parametric variations, and undervoltage dips of the grid.

4.1. Control under Sudden Irradiation Variations. Five irradi-ation step signals were simulated in order to evaluate the per-formance of the proposed algorithm. The ability of MPPtracking is demonstrated for the P&O method after everystep change, and the maximum PV current and voltage areconsequently extracted. Figures 4 and 5 show the good track-ing results obtained in case of fast-changing conditions.

4.1.1. Stage 1: Cascade Control across the PVG. The simplifiedblock diagram of the process and its control on the GPV sideis shown in Figure 6. It shows that the Upv voltage control ofthe PVG leads to a structure made up of two nested loops. Asit can be seen, there are also two regulators C1 s and C2 swhich, respectively, intervene on the current iL and the volt-age Upv. These two controllers are cascaded.

The Upv voltage loop is the outer loop while the iL cur-rent loop is an inner loop. The inner loop has been

designed to have a relatively short response time in orderto promptly correct the error. The outer loop can be config-ured to be slower.

First, the performance of the proposed algorithm is testedin each subsystem. The search for the parameters of theFOPID-FOPID controllers is carried out simultaneously,and the response corresponding to each set of gains is evalu-ated. The TLBO algorithm must gradually and iterativelyminimize the integral performance index to find the optimalparameters for the FOPID-FOPID controllers of the innerand outer loop in order to find the best performance. Thealgorithm ends if the value of the fitness function is kept con-stant over a few successive iterations as shown in Figures 7(a)and 7(b) for the inner and outer loop, respectively, on thePVG side.

The TLBO algorithm is simulated with a small popula-tion size. This specification is important in order to allow afaster adjustment. In this study, the size of the initial popula-tions is set at 20 for all control loops while the maximumnumber of iterations is set at 30.

The gains of the controllers used for all loops on the GPVside are shown in Table 1. By providing better performance,FOPI controllers can be used instead of FOPID controllers,thanks to the reduced order of the inner loop subsystem.

0.7 0.75 0.8 0.85 0.9 0.95 1698

699

700

701

702

703

UdcrefUdc

(a)

0.750.7 0.8 0.85 0.9 0.95 1698

699

700

701

702

703

UdcrefUdc

(b)

0.750.7 0.8 0.85 0.9 0.95 1698

699

700

701

702

703

UdcrefUdc

(c)

0.750.7 0.8 0.85 0.9 0.95 1698

699

700

701

702

703

UdcrefUdc

(d)

Figure 17: Voltage dip effect on DC link voltage without limitation by using (a) PSO-PID; (b) TLBO-FOPID; (c) ACO-PID; (d) GA-FOPID.

12 International Journal of Photoenergy

For the tuning of the Upv loop, cascade control isobtained by controlling the two processes where the outputof the inner process feeds the external process. The value ofthe fitness function reaches a minimal value after 28 itera-tions. The MPP search is performed simultaneously usingthe P&O algorithm. Controller gains of the current loop areshown in Table 2.

The simulation results are shown in Figure 8 for thePVG-side control. The results in the figure below show thatthe TLBO-based FOPID offers good performance for refer-ence tracking. When the irradiation changes from one levelto another, the FOPID-FOPID controller is able to quicklytrack the new power level for each subsystem.

ACO-PID is less reliable than the PSO-PID and GA-FOPID. When the irradiation moves from one level toanother, the TLBO-based FOPID tracks quickly the newpower level. However, ACO-PID takes more time to findthe steady state (T rise = 0 5 s).

4.1.2. Stage 2 Grid-Side Control. The purpose of the control isto keep the DC bus voltage constant regardless of the powervariation. The tuning of the Udc outer loop by the TLBO-based FOPID controller is completed after 30 iterations asshown in Figure 9. The value of the fitness function reachesa minimum value after 27 iterations (outer loop).

Figure 10 validates the DC bus controller which ensures agood monitoring of the DC voltage measured in relation to

its reference. It can be seen that when the power increases,the DC voltage tries to increase simultaneously.

The FOPID controller very quickly reduces the error andalways maintains the DC bus voltage at the same constantvalue (700V).

Table 3 indicates the controller gains of the DC link volt-age loop while Table 4 enumerates the controller gains of thegrid current loop.

Figures 11–14 show the behavior of the grid current thatis controlled in the inner loop with adequate control simulta-neously with the DC bus voltage of the outer loop. The sim-ulation is performed for a unity power factor under variableatmospheric conditions. No reactive power will be suppliedto the grid since the voltage and current will be in phase witheach other.

From Figure 13, it is clear that the TLBO cascade controlis capable of generating the desired current. There is no phasedifference between the grid voltage and the voltage for thedesigned controller. Indeed, the current loop regulator is val-idated and we can see that the measured current signals fol-low their references.

4.2. Control under Voltage Dips without Current Limitation.The target of the TLBO-FOPID control consists on keepingthe DC link voltage stable independently of the power varia-tion. Figure 15 highlights the impact of a grid voltage dipas depicted in Figure 16 for a constant irradiation G =1000 G/m2 on the grid currents.

−30.7 0.75 0.8 0.85

Grid

curr

ents

(A)

0.9 0.95 1

−2

−1

0

1

2

3

Time (seconds)ir1PSOir1ref

(a)

−30.7 0.75 0.8 0.85

Grid

curr

ents

(A)

0.9 0.95 1

−2

−1

0

1

2

3

Time (seconds)ir1GAPIDir1ref

(b)

−30.7 0.75 0.8 0.85

Time (seconds)

Grid

curr

ents

(A)

0.9 0.95 1

−2

−1

0

1

2

3

ir1ACOir1ref

(c)

−30.7 0.75 0.8 0.85

Time (seconds)

Grid

curr

ents

(A)

0.9 0.95 1

−2

−1

0

1

2

3

ir1FOPIDir1ref

(d)

Figure 18: Voltage dip effect on grid currents with limitation by using (a) PSO-PID; (b) GA-FOPID; (c) ACO-PID; (d) TLBO-FOPID.

13International Journal of Photoenergy

DC

link

volta

ge (V

)

0.7 0.8 0.9 1

700

705

710

715

720

UdcrefUdc

(a)

DC

link

volta

ge (V

)

UdcrefUdc

0.7 0.8 0.9 1

700

705

710

715

720

(b)

0.7 0.75 0.8 0.85 0.9 0.95 1 Time (seconds)

700

705

710

715

720

DC

link

volta

ge (V

)

UdcrefUdc

(c)

DC

link

volta

ge (V

)

0.7 0.75 0.8 0.85 0.9 0.95 1

700

705

710

715

720

UdcrefUdc

(d)

Figure 19: Voltage dip effect on DC link voltage with limitation by using (a) PSO-PID; (b) GA-FOPID; (c) ACO-PID; (d) TLBO-FOPID.

20 0.2 0.4 0.6 0.8 1

Time (seconds)1.2 1.4 1.6 1.8 2

345678

T1 =

L1/

r1

9101112

Figure 20: Time constant of the line.

14 International Journal of Photoenergy

Figure 17 validates the DC link voltage controller whichis able to force the measured DC link voltage to track itsreference when the system experiences a 50% voltage dipwithout limitation of the grid current amplitude at t = 0 8 s,0 9 s . This defect involves an increase in the grid currentsas portrayed in Figure 15, whereas Udc remains constant

thanks to the MPPT algorithm. Results of the control strate-gies are approximately similar.

4.3. Control under Voltage Dips with Current Limitation.Similarly, Figures 18 and 19 highlight the impact of the samevoltage dip of the grid on the DC link voltage and the grid

0.7 0.75 0.8 0.85 0.9 0.95 1−5

0

5

ir1ref

ir1

Time (seconds)

Grid

curr

ent i

r1 (A

)

(a)

0.7 0.80.75 0.85 0.950.9 1−5

0

5

ir1ref

ir1

Time (seconds)

Grid

curr

ent i

r1 (A

)

(b)

0.7 0.80.75 0.85 0.950.9 1−200

−150

−100

−50

0

50

100

150

200

ir1ref

ir1

Time (seconds)

Grid

curr

ent i

r1 (A

)

(c)

ir1ref

ir1

0.7 0.80.75 0.85 0.950.9 1

Time (seconds)

−5

0

5

Grid

curr

ent i

r1 (A

)

(d)

Figure 21: The effect of line resistance sudden decrease on the grid currents by using (a) PSO-PID; (b) TLBO-FOPID; (c) ACO-PID;(d) GA-FOPID.

15International Journal of Photoenergy

currents with limitation of their amplitudes. This limitationprovokes an increase in DC link voltage as illustrated inFigure 19. Results are close and the robustness of the controltechniques is proven if such a defect occurs.

4.4. Control under Parametric Variation. A reduction of 50%of resistance r1 leads to an increase of 100% of the time con-stant (T1 = L1/r1) as shown in Figure 20. The results of sim-ulation given in Figure 21 prove the reliability of thecascade TLBO-FOPID control to sudden parametric varia-tions of the system as compared to the other controllers. Infact, only the TLBO-FOPID controller shows ability todeliver the desired output power to the grid with a unitypower factor; in other words, TLBO-FOPID keeps the outputcurrent in phase with the grid voltage. However, the ACO-PID controller is unable to address this defect since thesteady state has not been reached yet when the resistancevalue varies.

5. Conclusion

A comparative assessment between the proposed TLBO-FOPID and three controllers is presented in this paper,namely, GA-FOPID, PSO-PID, and ACO-PID for a grid-connected PV system. For superior tracking efficiency, aP&O-based MPPT algorithm is employed to extract the max-imum power from PV panels. All of the control strategies aredesigned for controlling all cascade loops in the conversionchain in order to eliminate the grid current harmonics. Per-formances of the controllers are compared when fast-changing solar irradiation, voltage dip, and parametric varia-tions of the system are experienced. The TLBO-FOPIDaddresses all the already quoted challenges. Simulations havebeen conducted using MATLAB/Simulink validating thefunctionality, robustness, and simplicity of the algorithmcompared with the other metaheuristic techniques.

Data Availability

The data used to support the findings of this study areavailable from the corresponding author upon request.

Conflicts of Interest

The authors declare that there is no conflict of interestregarding the publication of this paper.

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