# High-Performance Standalone Photovoltaic Water Pumping System Using Induction Motor

Authors: Mustapha Errouha; Aziz Derouich; Najib El Ouanjli; Saad Motahhir
Journal: International Journal of Photoenergy
 (2020)

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## Abstract

This work is aimed at achieving a simple and reduced-cost configuration of photovoltaic (PV) water pumping system (PVWPS) using an induction motor with high efficiency. The proposed PV system is composed of two stages of converters which the first one ensures the maximum power point by controlling the duty ratio of boost converter using variable step size incremental conductance (VSS INC) technique. Fuzzy logic control based on direct torque control is proposed to serve the purpose of operating an induction motor. Moreover, the combining of these proposed control strategies has been never discussed. The proposed control scheme is modeled and simulated in detail under MATLAB/Simulink software to evaluate its performance under fast variations of irradiance and daily climatic profile. The obtained simulation results using the suggested control strategies are compared to those using the most used method in the literature (variable step size perturb and observe (VSS P&O) algorithm). The simulation results indicate that the proposed PVWPS performed best in terms of the time of response; pumped water, flux ripples, and the stator currents are reduced.


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## Body

## 1. Introduction

With the increasing use of electricity and cost diesel, finding a promising alternative to power a pumping system is required. Water pumping systems based on photovoltaic technology are good solutions for rural areas where the connection to the grid power can be difficult and expensive [1, 2]. Thus, these systems are more reliable than those based on diesel pumps, because they require less maintenance [3].However, the performance of a PV generation system is influenced by three factors which are irradiation, nature of load, and atmospheric temperature [4]. To surmount these drawbacks, maximum power point tracking (MPPT) techniques are used to maximize the PV output power whatever the weather and operating conditions [5]. Various MPPT techniques have been reported in the literature; each method has its specification, limitation, and application. The MPPT algorithms can be classified into three major groups [6]: (i) conventional methods including constant voltage controller (CVC) method, perturb and observe (P&O) method, incremental conductance (IC) method; these kinds of algorithms use PV current, PV voltage, irradiance, and temperature for maximum power extraction and they are characterized by its simple implementation; (ii) artificial intelligence-based methods including fuzzy logic controller technique, artificial neural network control strategy, and adaptive neurofuzzy inference method. These algorithms have fast response and good MPP tracking accuracy and offer better performance than the conventional methods but they are complex to implement; (iii) hybrid methods including modified perturb and observe method (modified P&O), PI-modified fuzzy logic controller (PI-FLC) method, and neural-fuzzy logic (N-FL) method; these algorithms combine the conventional and artificial intelligence-based methods to achieve greater efficiency and tracking accuracy.Artificial intelligent-based methods and the incremental conductance algorithm are the most recommended control strategies for PV water pumping systems [7]. Artificial intelligent-based methods are complex and need a high-speed processor for implementation [4].Different types of motors are used with PV-based water pumping system to drive the pump [8, 9]; the choice depends on the efficiency, the availability, the price, and the reliability. PV pumping systems based on AC motors, particularly induction motors (IM), are more attractive because these types of engines are rugged; they have high efficiency, maintenance-free, and low cost [10, 11]. Field oriented control (FOC) and direct torque control (DTC) are the most used control strategies for induction motor drives [12]. FOC assures a decoupling between the flux and torque of the motor [8, 13]; this decoupling provides very fast torque response and large speed control range. However, this technique is sensitive to the parametric variations of the motor, particularly that of the resistances whose value changes with temperature [14]. DTC technique was proposed by Takahashi to overcome some of the difficulties encountered with FOC [15, 16]. It offers remarkable dynamic performance as well as good robustness to parameter variations. However, two major disadvantages arise: (i) the ripples’ amplitude of the torque and stator flux especially at low speed and (ii) the switching frequency is highly variable [17]. The torque ripples cause additional noise and mechanical vibrations. Different solutions are proposed in the literature to overcome these disadvantages [18, 19]. In this paper, a fuzzy logic controller (FLC) is proposed to improve the performance of DTC. The use of FLC allows fixing the switching frequency. Therefore, the flux ripples and THD currents are minimized.In PV pumping systems, an IM shows good performance as compared to other commercial motors because of its greater robustness, lower cost, higher efficiency, lower maintenance cost, and availability in local markets [20]. In addition to the power exchange from PV to the IM, a DC-DC boost converter is introduced. For good utilization of PV panels, it is necessary to extract maximum power from the PV panels. For this reason, variable step size incremental conductance-based maximum power point tracking control is implemented due to its performance. On the other side, VSS INC can be implemented using the low-cost ATMega328 microcontroller in the Arduino Uno board to propose a low-cost PV system [21]. Also, the proposed PV system operates without a battery. Consequently, not only the initial cost is low but also repairing, maintenance, and replacement cost can be saved.Several configurations of PV water pumping system have been proposed in literature. In [20], an incremental conductance- (INC-) based MPPT control technique is utilized to obtain the peak power from the PV array and scalar control for induction motor drive operation. However, the authors used the INC method based on fixed step size. Incremental conductance algorithm gives a good performance with higher accuracy, but it uses a fixed step; smaller step causes slower response and larger step results in higher oscillations [22, 23]. Therefore, the performance is reduced. The scalar control strategy is characterized by its simple structure, easy design, and low cost. However, this method provides poor response of torque and the speed accuracy is not good enough, particularly at the low speed [24]. In [25], authors have presented standalone photovoltaic water pumping system driven by a brushless DC (BLDC) motor. Perturb and observe and fuzzy logic control algorithms are used to get the maximum power and compared to evaluate the performance of the PV system. BLDC motor has high efficiency and reliability, but the rotor position of this engine is identified by using hall sensors which make the system complex and increase the cost [26]. In [27], an optimization based on genetic algorithms (GA) was effectuated for two MPPT algorithms which are perturb and observe and fuzzy techniques. On the other hand, the permanent magnet DC (PMDC) motor is used to drive the pump. The use of this kind of motor for water pumping is still not popular as it suffers from nonavailability of rare earth magnet and cost constraints [28]. GA is usually utilized to optimize other algorithms based on principles of biological evolution [29]. However, this technique cannot guarantee the identification of global minimum, is not recommended for optimizing excessively complex or very large problems, and requires much time to fine tune all parameters and achieve convergence [30].In this paper, two control strategies are introduced to propose a simple and efficient PV water pumping system. The first strategy is based on a controller that consists of variable step size incremental conductance algorithm, in which the step is adjusted automatically depending on each operational condition in order to achieve satisfactory tradeoff between the oscillations and dynamics, which leads to obtain better performance than that of incremental conductance based on fixed step. On the other hand, the second strategy is based on fuzzy DTC technique to control the induction motor. This type of motor provides good performance as compared to other commercial motors due to its rugged construction. Moreover, DTC allows to achieve better efficiency and performance than scalar control strategy.Different authors have treated variable step size incremental conductance algorithm to extract the maximum power from the PV panel [22] and DTC based on the fuzzy logic controller to improve the performance of the IM separately [31, 32]. However, to the authors’ best knowledge, the combining of these proposed control strategies has never been discussed. This allows us to propose a PV water pumping system based on the combining of variable step size incremental conductance technique and fuzzy DTC control for the first time in the literature.Moreover, the proposed system is evaluated under real daily climatic conditions and sudden changes in solar radiation. A comparison with one of the most used MPPT in the literature (variable step size perturb and observe) is achieved. Hence, the main contribution of this work is the effective reduction of flux ripples and THD of the output currents and increasing the pumped water.This work is structured as follows: the PVWPS components are modeled in Section2. The control strategies which are VSS P&O, VSS INC, and FDTC are detailed in Section 3. The results and discussion are illustrated in Section 4. Finally, Section 5 summarizes the conclusions of the paper.


## 2. Modeling of Component PV Pumping Systems

The PV pumping system (Figure1) is composed of a PV panel, DC-DC converter controlled by MPPT algorithms, voltage source inverter (VSI) at two-level, and a centrifugal pump driven by IM.Figure 1
Synoptic diagram of the pumping system.


### 2.1. Modeling of PV Cell

Various mathematical models explain the behavior and operation of the PV cell [33]. In this work, the single diode model is adopted (Figure 2):Figure 2
Equivalent circuit of a photovoltaic cell.From the equivalent circuit above, the output current can be calculated as follows [34, 35]:(1)IPV=Iph-IOexpqVPV+RsIaKTNs-1-VPV+IRsRsh,Iph=Isc+KiT-298.15G1000,Io=Isc+KiT-298.15expqVoc+KvT-298.15/aKTNs-1.


### 2.2. Boost Converter

The DC-DC converter is placed between the PV panel and the inverter to increase the voltage and maximizing the power from the panel (Figure3).Figure 3
Boost converter.The following equation represents the mathematical model of the DC-DC converter:(2)dVdcdt=1Cdc1−α⋅Ipv−Iinv,dIpvdt=1Lpv−1−α⋅Vdc+Vpv.


### 2.3. Voltage Source Inverter

The voltage source inverter (VSI) model is composed of six IGBT switches and controlled by analog values [36]. The structure of VSI is illustrated in Figure 4.Figure 4
General structure of VSI.Equation (3) represents the mathematical model of VSI as follows:(3)VaVbVc=Vdc3⋅2−1−1−12−1−1−12⋅SaSbSc,where Sa, Sb, and Sc are the logic control signals and Vdc is the input DC voltage.


### 2.4. Induction Motor

The model of the IM suitable for direct torque controls which is the two-phase model (α, β) is described by the following equation:(4)dIαsdt=−Rsσls−RrσlrIαs−wrIβs+Rrσlrlsψαs+wrσlsψβs+1σlsVαs,dIβsdt=−Rsσls−RrσlrIβs−wrIαs+Rrσlrlsψβs−wrσlsψαs+1σlsVβs,dψαsdt=Vαs−RsIαs,dψβsdt=Vβs−RrIβs,where σ, τs, and τr are given as follows: σ=1−M2/LsLr, τs=Rs/Ls, and τr=Rr/Lr,where Iαs,Iβs are the stator current components, ψαs, ψβs are the stator flux components, Rs, Rr are the stator and rotor resistances, ls, lr are the stator and rotor inductances, Mis the mutual stator-rotor inductance, and wr is the rotor speed.The electromagnetic torque in the reference frameα,β and the movement are expressed as follows:(5)Tem=32Pψαsiβs−ψβsiαs,JdΩdt+fΩ=Tem−Tr,where p is the number of pole pairs, and f is the coefficient of friction.


### 2.5. Centrifugal Pump

As shown in Equation (6), the centrifugal pump load torque Tr is given as follows:(6)Tr=K⋅Ω2,where K is the pump constant.Using the similarity laws (Equation (7)), the characteristic of the centrifugal pump can be obtained for any rotation speed [37].(7)Q′=Q⋅N′N,(8)H′=H⋅N′N2,(9)P′=P⋅N′N3.


## 2.1. Modeling of PV Cell

Various mathematical models explain the behavior and operation of the PV cell [33]. In this work, the single diode model is adopted (Figure 2):Figure 2
Equivalent circuit of a photovoltaic cell.From the equivalent circuit above, the output current can be calculated as follows [34, 35]:(1)IPV=Iph-IOexpqVPV+RsIaKTNs-1-VPV+IRsRsh,Iph=Isc+KiT-298.15G1000,Io=Isc+KiT-298.15expqVoc+KvT-298.15/aKTNs-1.


## 2.2. Boost Converter

The DC-DC converter is placed between the PV panel and the inverter to increase the voltage and maximizing the power from the panel (Figure3).Figure 3
Boost converter.The following equation represents the mathematical model of the DC-DC converter:(2)dVdcdt=1Cdc1−α⋅Ipv−Iinv,dIpvdt=1Lpv−1−α⋅Vdc+Vpv.


## 2.3. Voltage Source Inverter

The voltage source inverter (VSI) model is composed of six IGBT switches and controlled by analog values [36]. The structure of VSI is illustrated in Figure 4.Figure 4
General structure of VSI.Equation (3) represents the mathematical model of VSI as follows:(3)VaVbVc=Vdc3⋅2−1−1−12−1−1−12⋅SaSbSc,where Sa, Sb, and Sc are the logic control signals and Vdc is the input DC voltage.


## 2.4. Induction Motor

The model of the IM suitable for direct torque controls which is the two-phase model (α, β) is described by the following equation:(4)dIαsdt=−Rsσls−RrσlrIαs−wrIβs+Rrσlrlsψαs+wrσlsψβs+1σlsVαs,dIβsdt=−Rsσls−RrσlrIβs−wrIαs+Rrσlrlsψβs−wrσlsψαs+1σlsVβs,dψαsdt=Vαs−RsIαs,dψβsdt=Vβs−RrIβs,where σ, τs, and τr are given as follows: σ=1−M2/LsLr, τs=Rs/Ls, and τr=Rr/Lr,where Iαs,Iβs are the stator current components, ψαs, ψβs are the stator flux components, Rs, Rr are the stator and rotor resistances, ls, lr are the stator and rotor inductances, Mis the mutual stator-rotor inductance, and wr is the rotor speed.The electromagnetic torque in the reference frameα,β and the movement are expressed as follows:(5)Tem=32Pψαsiβs−ψβsiαs,JdΩdt+fΩ=Tem−Tr,where p is the number of pole pairs, and f is the coefficient of friction.


## 2.5. Centrifugal Pump

As shown in Equation (6), the centrifugal pump load torque Tr is given as follows:(6)Tr=K⋅Ω2,where K is the pump constant.Using the similarity laws (Equation (7)), the characteristic of the centrifugal pump can be obtained for any rotation speed [37].(7)Q′=Q⋅N′N,(8)H′=H⋅N′N2,(9)P′=P⋅N′N3.


## 3. Control Strategies

### 3.1. MPPT Algorithms

In this paper, two MPPT algorithms have been chosen for comparison: variable step size perturb and observe (VSS P&O) and variable step size incremental conductance (VSS INC).


#### 3.1.1. Variable Step Size Perturb and Observe

The P&O algorithm is used by the majority of authors because it is easy and simple to implement and is low-cost [38]. Based on the measuring of PV voltage and current, the PV power is calculated; this latter is compared with the previous power to deduce the value of the duty cycle α. The perturb and observe algorithm is functioned as follows:(i)
IfdPpv/dVpv≻0, the working point is on the left of the MPP(ii)
IfdPpv/dVpv≺0, the working point is on the right of the MPP(iii)
IfdPpv/dVpv≈0, the working point is at the MPPThe conventional P&O MPPT is based on the fixed step; smaller step causes slower response and larger step results in higher oscillations. To overcome this drawback, the variable step size is used which consists to choose automatically the step. The step size is determined by Equation (10). Figure 5 shows the flowchart of the VSS P&O algorithm.(10)Offset=Ofseet0∗ΔPΔV.Figure 5
Variable step size P&O.


#### 3.1.2. Variable Step Size Incremental Conductance

The incremental conductance algorithm has been proposed which is based on the derivative of thePpv with respect to Vpv to avoid the disadvantages of the P&O algorithm. The principal advantage of the incremental conductance (INC) algorithm is that it provides good performance under rapidly changing atmospheric conditions. This technique uses the slope of the Ppv characteristics to track MPP [39]. Therefore, incremental conductance algorithm is operated as follows:(i)
Vpv/Ipv=−ΔVpv/ΔIpv at MPP(ii)
Vpv/Ipv≺−ΔVpv/ΔIpv left to MPP(iii)
Vpv/Ipv≻−ΔVpv/ΔVpv right to MPPThe drawback of the incremental conductance method is the use of a fixed tracking step size. For this, the variable step size incremental conductance is used in this paper. Figure6 shows the flowchart of VSS INC algorithm.Figure 6
Variable step size incremental conductance.


### 3.2. Fuzzy Direct Torque Control for Induction Motor

The concept of fuzzy direct torque control (FDTC) is similar to classical DTC. It consists in regulating the flux and torque of the IM by the selection of one of the eight voltage vectors generated by each voltage inverter; this choice is made by switching the table. However, this table is elaborated by the reasoning of fuzzy logic from the flux error, torque error, and position of flux vector. This technique is characterized by good precision, stability, a good torque response, robustness, and simplicity of implementation. The principle of FDTC for the IM is shown in Figure7.Figure 7
Synoptic scheme of FDTC for induction motor.


#### 3.2.1. Stator Flux and Torque Estimation

FDTC of the IM relies on the estimation of the magnitude to be controlled, namely, the stator flux and electromagnetic torque.The components of stator flux can be estimated as follows:(11)φ^sα=∫0tvsα−Rs⋅isα⋅dt,φ^sβ=∫0tvsβ−Rs⋅isβ⋅dt.The modulus and angle of the stator flux are calculated as follows:(12)φ^s=φ^sα2+φ^sβ2,θs=arctgφ^sβφ^sα.The torque is found by the estimated flux and currents as follows:(13)Tem=p⋅φ^sα⋅isβ−φ^sβ⋅isα.The currentsisα and isβ are obtained from the measurement of the real currents isa, isb, and isc, and by the application of the transformation of Concordia, we obtain the following:(14)isα=23isa,isβ=12isb−isc.The stator voltage depends on the switches state (Sa, Sb, Sc) and the DC voltage Vdc; applying the Concordia transformation, we obtain the following:(15)vsα=23Vdc⋅Sa−12Sb+Sc,vsβ=12VdcSb−Sc.


#### 3.2.2. Fuzzy Switching Table

The switching table used in conventional DTC and the hysteresis controllers are replaced by a fuzzy switching table; the latter is built using a FLC; the inputs of this fuzzy controller are the error of the stator fluxεφs, electromagnetic torque error εTem, and flux position θs (Figure 8).Figure 8
Fuzzy logic switching table.Generally, the control by fuzzy logic is done in three steps: fuzzification, the establishment of rules binding the outputs to the inputs called fuzzy inference, and defuzzification.


#### 3.2.3. Fuzzification

The purpose of fuzzification is to convert physical input variables into fuzzy variables, by defining membership functions for different input variables; the fuzzy system performance is described using a fuzzy rule base. Approximate reasoning will be done by associating the input variable with fuzzy rules using a fuzzy inference engine.The first input of FLC is stator flux error; its universe of discourse is composed of three fuzzy variables: positive (P), zero (Z), and negative (N). The (Z) variable is represented by a triangular membership function, while (P) and (N) variables are represented by two trapezoidal membership functions (Figure 9(a)).Figure 9
Membership functions of (a) flux error, (b) torque error, and (c) flux position.
(a)(b)(c)The torque error is composed of five fuzzy variables: positive small (PS), positive large (PL), zero (Z), negative large (NL), and negative small (NS). The membership function of torque error is represented by two symmetric trapezoidal and three triangular (Figure 9(b)).The last input of FLC is the stator flux angle; its universe of discourse is divided into 12 fuzzy sets. This input is represented by twelve membership functions triangular of 60° wide and an overlap of 30° with neighborhood fuzzy sets which each fuzzy set works for an angle of 30° (Figure9(c)).Figure9 gives the membership functions for the input variables of the switching table. The output variable is illustrated in Figure 10, which is represented in our case by the switching state of the voltage inverter and defined by three output groups (Sa, Sb, Sc); the discourse universe of each output is divided into two fuzzy sets (0 and 1).Figure 10
Membership functions of output variables.


#### 3.2.4. Fuzzy Control Rule

The optimal switching state is given by fuzzy rules, which are established using expert knowledge and intuition to govern the behavior of FLC. The control algorithm has 180 rules; the method adopted is the Max–Min inference (Mamdani method).(16)αi=minμAiεφ,μBiεTem,μCiθ,μ′ViV=maxαi,μViV,where μAiεφ, μBiεTem, and μCiθ represent the membership values of torque error, flux error, and stator flux angle and αi is the weighting factor for its rules.The fuzzy rules which determine the output variables of controller depending on input variables are presented in Table1.Table 1
Fuzzy control rules.
εφsεTemθ1θ2θ3θ4θ5θ6θ7θ8θ9θ10θ11θ12PLPV2V3V3V4V4V5V5V6V6V1V1V2PSV2V2V3V3V4V4V5V5V6V6V1V1ZV0V7V0V7V0V7V0V7V0V7V0V7NSV1V1V2V2V3V3V4V4V5V5V6V6NLV6V1V1V2V2V3V3V4V4V5V5V6PLZV2V3V3V4V4V5V5V6V6V1V1V2PSV2V3V3V4V4V5V5V6V6V1V1V2ZV7V0V7V0V7V0V7V0V7V0V7V0NSV7V0V7V0V7V0V7V0V7V0V7V0NLV6V1V1V2V2V3V3V4V4V5V5V6PLNV3V4V4V5V5V6V6V1V1V2V2V3PSV4V4V5V5V6V6V1V1V2V2V3V3ZV7V0V7V0V7V0V7V0V7V0V7V0NSV5V5V6V6V1V1V2V2V3V3V4V4NLV5V6V6V1V1V2V2V3V3V4V4V5


#### 3.2.5. Defuzzification

This step converts the fuzzy values back into a numerical value at the output, which is one zero voltage (V0 or V7) and six nonzero voltage vectors. For this step, the max method is used and expressed by Equation (17). From this method, the fuzzy output value which has the maximum possibility distribution is used as a control output.(17)μ′VoutV=maxi=1180maxμ′VoutV,where μ′Vout is a membership degree of the output variable.


### 3.3. Rotation Speed Controller by Fuzzy Logic

To overcome the troubles of classical speed controller, such as static error, sensitivity, and overshoot, we propose a FLC with as input the error and the derivation of speed error. The two fuzzy controller inputs are the speed error and its variation [40].The speed error notede is defined as follows:(18)ek=Ωrefk−Ωk.The variation of the speed error notedΔe is defined as follows:(19)dek=ek−ek−1.The controller output corresponds to the torque notedΔu. The three magnitudes, e, Δe, and Δu, are normalized as follows:(20)E=K1·e,ΔE=K2·ΔE,Δu=K3·Δu,where K1, K2, and K3 are scale or standardization factors and play a decisive role in the static and dynamic performance of the control.Figure11 illustrates the schema of the fuzzy speed controller. The control rules must be expressed in terms of the input and output variables using the decision table; the decision rules are described as if E is A and ΔE is B, then Δu is C. The internal structure of the fuzzy speed controller is shown in Figure 12.Figure 11
Structure of fuzzy logic controller.Figure 12
Internal structure of fuzzy speed controller.


## 3.1. MPPT Algorithms

In this paper, two MPPT algorithms have been chosen for comparison: variable step size perturb and observe (VSS P&O) and variable step size incremental conductance (VSS INC).


### 3.1.1. Variable Step Size Perturb and Observe

The P&O algorithm is used by the majority of authors because it is easy and simple to implement and is low-cost [38]. Based on the measuring of PV voltage and current, the PV power is calculated; this latter is compared with the previous power to deduce the value of the duty cycle α. The perturb and observe algorithm is functioned as follows:(i)
IfdPpv/dVpv≻0, the working point is on the left of the MPP(ii)
IfdPpv/dVpv≺0, the working point is on the right of the MPP(iii)
IfdPpv/dVpv≈0, the working point is at the MPPThe conventional P&O MPPT is based on the fixed step; smaller step causes slower response and larger step results in higher oscillations. To overcome this drawback, the variable step size is used which consists to choose automatically the step. The step size is determined by Equation (10). Figure 5 shows the flowchart of the VSS P&O algorithm.(10)Offset=Ofseet0∗ΔPΔV.Figure 5
Variable step size P&O.


### 3.1.2. Variable Step Size Incremental Conductance

The incremental conductance algorithm has been proposed which is based on the derivative of thePpv with respect to Vpv to avoid the disadvantages of the P&O algorithm. The principal advantage of the incremental conductance (INC) algorithm is that it provides good performance under rapidly changing atmospheric conditions. This technique uses the slope of the Ppv characteristics to track MPP [39]. Therefore, incremental conductance algorithm is operated as follows:(i)
Vpv/Ipv=−ΔVpv/ΔIpv at MPP(ii)
Vpv/Ipv≺−ΔVpv/ΔIpv left to MPP(iii)
Vpv/Ipv≻−ΔVpv/ΔVpv right to MPPThe drawback of the incremental conductance method is the use of a fixed tracking step size. For this, the variable step size incremental conductance is used in this paper. Figure6 shows the flowchart of VSS INC algorithm.Figure 6
Variable step size incremental conductance.


## 3.1.1. Variable Step Size Perturb and Observe

The P&O algorithm is used by the majority of authors because it is easy and simple to implement and is low-cost [38]. Based on the measuring of PV voltage and current, the PV power is calculated; this latter is compared with the previous power to deduce the value of the duty cycle α. The perturb and observe algorithm is functioned as follows:(i)
IfdPpv/dVpv≻0, the working point is on the left of the MPP(ii)
IfdPpv/dVpv≺0, the working point is on the right of the MPP(iii)
IfdPpv/dVpv≈0, the working point is at the MPPThe conventional P&O MPPT is based on the fixed step; smaller step causes slower response and larger step results in higher oscillations. To overcome this drawback, the variable step size is used which consists to choose automatically the step. The step size is determined by Equation (10). Figure 5 shows the flowchart of the VSS P&O algorithm.(10)Offset=Ofseet0∗ΔPΔV.Figure 5
Variable step size P&O.


## 3.1.2. Variable Step Size Incremental Conductance

The incremental conductance algorithm has been proposed which is based on the derivative of thePpv with respect to Vpv to avoid the disadvantages of the P&O algorithm. The principal advantage of the incremental conductance (INC) algorithm is that it provides good performance under rapidly changing atmospheric conditions. This technique uses the slope of the Ppv characteristics to track MPP [39]. Therefore, incremental conductance algorithm is operated as follows:(i)
Vpv/Ipv=−ΔVpv/ΔIpv at MPP(ii)
Vpv/Ipv≺−ΔVpv/ΔIpv left to MPP(iii)
Vpv/Ipv≻−ΔVpv/ΔVpv right to MPPThe drawback of the incremental conductance method is the use of a fixed tracking step size. For this, the variable step size incremental conductance is used in this paper. Figure6 shows the flowchart of VSS INC algorithm.Figure 6
Variable step size incremental conductance.


## 3.2. Fuzzy Direct Torque Control for Induction Motor

The concept of fuzzy direct torque control (FDTC) is similar to classical DTC. It consists in regulating the flux and torque of the IM by the selection of one of the eight voltage vectors generated by each voltage inverter; this choice is made by switching the table. However, this table is elaborated by the reasoning of fuzzy logic from the flux error, torque error, and position of flux vector. This technique is characterized by good precision, stability, a good torque response, robustness, and simplicity of implementation. The principle of FDTC for the IM is shown in Figure7.Figure 7
Synoptic scheme of FDTC for induction motor.


### 3.2.1. Stator Flux and Torque Estimation

FDTC of the IM relies on the estimation of the magnitude to be controlled, namely, the stator flux and electromagnetic torque.The components of stator flux can be estimated as follows:(11)φ^sα=∫0tvsα−Rs⋅isα⋅dt,φ^sβ=∫0tvsβ−Rs⋅isβ⋅dt.The modulus and angle of the stator flux are calculated as follows:(12)φ^s=φ^sα2+φ^sβ2,θs=arctgφ^sβφ^sα.The torque is found by the estimated flux and currents as follows:(13)Tem=p⋅φ^sα⋅isβ−φ^sβ⋅isα.The currentsisα and isβ are obtained from the measurement of the real currents isa, isb, and isc, and by the application of the transformation of Concordia, we obtain the following:(14)isα=23isa,isβ=12isb−isc.The stator voltage depends on the switches state (Sa, Sb, Sc) and the DC voltage Vdc; applying the Concordia transformation, we obtain the following:(15)vsα=23Vdc⋅Sa−12Sb+Sc,vsβ=12VdcSb−Sc.


### 3.2.2. Fuzzy Switching Table

The switching table used in conventional DTC and the hysteresis controllers are replaced by a fuzzy switching table; the latter is built using a FLC; the inputs of this fuzzy controller are the error of the stator fluxεφs, electromagnetic torque error εTem, and flux position θs (Figure 8).Figure 8
Fuzzy logic switching table.Generally, the control by fuzzy logic is done in three steps: fuzzification, the establishment of rules binding the outputs to the inputs called fuzzy inference, and defuzzification.


### 3.2.3. Fuzzification

The purpose of fuzzification is to convert physical input variables into fuzzy variables, by defining membership functions for different input variables; the fuzzy system performance is described using a fuzzy rule base. Approximate reasoning will be done by associating the input variable with fuzzy rules using a fuzzy inference engine.The first input of FLC is stator flux error; its universe of discourse is composed of three fuzzy variables: positive (P), zero (Z), and negative (N). The (Z) variable is represented by a triangular membership function, while (P) and (N) variables are represented by two trapezoidal membership functions (Figure 9(a)).Figure 9
Membership functions of (a) flux error, (b) torque error, and (c) flux position.
(a)(b)(c)The torque error is composed of five fuzzy variables: positive small (PS), positive large (PL), zero (Z), negative large (NL), and negative small (NS). The membership function of torque error is represented by two symmetric trapezoidal and three triangular (Figure 9(b)).The last input of FLC is the stator flux angle; its universe of discourse is divided into 12 fuzzy sets. This input is represented by twelve membership functions triangular of 60° wide and an overlap of 30° with neighborhood fuzzy sets which each fuzzy set works for an angle of 30° (Figure9(c)).Figure9 gives the membership functions for the input variables of the switching table. The output variable is illustrated in Figure 10, which is represented in our case by the switching state of the voltage inverter and defined by three output groups (Sa, Sb, Sc); the discourse universe of each output is divided into two fuzzy sets (0 and 1).Figure 10
Membership functions of output variables.


### 3.2.4. Fuzzy Control Rule

The optimal switching state is given by fuzzy rules, which are established using expert knowledge and intuition to govern the behavior of FLC. The control algorithm has 180 rules; the method adopted is the Max–Min inference (Mamdani method).(16)αi=minμAiεφ,μBiεTem,μCiθ,μ′ViV=maxαi,μViV,where μAiεφ, μBiεTem, and μCiθ represent the membership values of torque error, flux error, and stator flux angle and αi is the weighting factor for its rules.The fuzzy rules which determine the output variables of controller depending on input variables are presented in Table1.Table 1
Fuzzy control rules.
εφsεTemθ1θ2θ3θ4θ5θ6θ7θ8θ9θ10θ11θ12PLPV2V3V3V4V4V5V5V6V6V1V1V2PSV2V2V3V3V4V4V5V5V6V6V1V1ZV0V7V0V7V0V7V0V7V0V7V0V7NSV1V1V2V2V3V3V4V4V5V5V6V6NLV6V1V1V2V2V3V3V4V4V5V5V6PLZV2V3V3V4V4V5V5V6V6V1V1V2PSV2V3V3V4V4V5V5V6V6V1V1V2ZV7V0V7V0V7V0V7V0V7V0V7V0NSV7V0V7V0V7V0V7V0V7V0V7V0NLV6V1V1V2V2V3V3V4V4V5V5V6PLNV3V4V4V5V5V6V6V1V1V2V2V3PSV4V4V5V5V6V6V1V1V2V2V3V3ZV7V0V7V0V7V0V7V0V7V0V7V0NSV5V5V6V6V1V1V2V2V3V3V4V4NLV5V6V6V1V1V2V2V3V3V4V4V5


### 3.2.5. Defuzzification

This step converts the fuzzy values back into a numerical value at the output, which is one zero voltage (V0 or V7) and six nonzero voltage vectors. For this step, the max method is used and expressed by Equation (17). From this method, the fuzzy output value which has the maximum possibility distribution is used as a control output.(17)μ′VoutV=maxi=1180maxμ′VoutV,where μ′Vout is a membership degree of the output variable.


## 3.2.1. Stator Flux and Torque Estimation

FDTC of the IM relies on the estimation of the magnitude to be controlled, namely, the stator flux and electromagnetic torque.The components of stator flux can be estimated as follows:(11)φ^sα=∫0tvsα−Rs⋅isα⋅dt,φ^sβ=∫0tvsβ−Rs⋅isβ⋅dt.The modulus and angle of the stator flux are calculated as follows:(12)φ^s=φ^sα2+φ^sβ2,θs=arctgφ^sβφ^sα.The torque is found by the estimated flux and currents as follows:(13)Tem=p⋅φ^sα⋅isβ−φ^sβ⋅isα.The currentsisα and isβ are obtained from the measurement of the real currents isa, isb, and isc, and by the application of the transformation of Concordia, we obtain the following:(14)isα=23isa,isβ=12isb−isc.The stator voltage depends on the switches state (Sa, Sb, Sc) and the DC voltage Vdc; applying the Concordia transformation, we obtain the following:(15)vsα=23Vdc⋅Sa−12Sb+Sc,vsβ=12VdcSb−Sc.


## 3.2.2. Fuzzy Switching Table

The switching table used in conventional DTC and the hysteresis controllers are replaced by a fuzzy switching table; the latter is built using a FLC; the inputs of this fuzzy controller are the error of the stator fluxεφs, electromagnetic torque error εTem, and flux position θs (Figure 8).Figure 8
Fuzzy logic switching table.Generally, the control by fuzzy logic is done in three steps: fuzzification, the establishment of rules binding the outputs to the inputs called fuzzy inference, and defuzzification.


## 3.2.3. Fuzzification

The purpose of fuzzification is to convert physical input variables into fuzzy variables, by defining membership functions for different input variables; the fuzzy system performance is described using a fuzzy rule base. Approximate reasoning will be done by associating the input variable with fuzzy rules using a fuzzy inference engine.The first input of FLC is stator flux error; its universe of discourse is composed of three fuzzy variables: positive (P), zero (Z), and negative (N). The (Z) variable is represented by a triangular membership function, while (P) and (N) variables are represented by two trapezoidal membership functions (Figure 9(a)).Figure 9
Membership functions of (a) flux error, (b) torque error, and (c) flux position.
(a)(b)(c)The torque error is composed of five fuzzy variables: positive small (PS), positive large (PL), zero (Z), negative large (NL), and negative small (NS). The membership function of torque error is represented by two symmetric trapezoidal and three triangular (Figure 9(b)).The last input of FLC is the stator flux angle; its universe of discourse is divided into 12 fuzzy sets. This input is represented by twelve membership functions triangular of 60° wide and an overlap of 30° with neighborhood fuzzy sets which each fuzzy set works for an angle of 30° (Figure9(c)).Figure9 gives the membership functions for the input variables of the switching table. The output variable is illustrated in Figure 10, which is represented in our case by the switching state of the voltage inverter and defined by three output groups (Sa, Sb, Sc); the discourse universe of each output is divided into two fuzzy sets (0 and 1).Figure 10
Membership functions of output variables.


## 3.2.4. Fuzzy Control Rule

The optimal switching state is given by fuzzy rules, which are established using expert knowledge and intuition to govern the behavior of FLC. The control algorithm has 180 rules; the method adopted is the Max–Min inference (Mamdani method).(16)αi=minμAiεφ,μBiεTem,μCiθ,μ′ViV=maxαi,μViV,where μAiεφ, μBiεTem, and μCiθ represent the membership values of torque error, flux error, and stator flux angle and αi is the weighting factor for its rules.The fuzzy rules which determine the output variables of controller depending on input variables are presented in Table1.Table 1
Fuzzy control rules.
εφsεTemθ1θ2θ3θ4θ5θ6θ7θ8θ9θ10θ11θ12PLPV2V3V3V4V4V5V5V6V6V1V1V2PSV2V2V3V3V4V4V5V5V6V6V1V1ZV0V7V0V7V0V7V0V7V0V7V0V7NSV1V1V2V2V3V3V4V4V5V5V6V6NLV6V1V1V2V2V3V3V4V4V5V5V6PLZV2V3V3V4V4V5V5V6V6V1V1V2PSV2V3V3V4V4V5V5V6V6V1V1V2ZV7V0V7V0V7V0V7V0V7V0V7V0NSV7V0V7V0V7V0V7V0V7V0V7V0NLV6V1V1V2V2V3V3V4V4V5V5V6PLNV3V4V4V5V5V6V6V1V1V2V2V3PSV4V4V5V5V6V6V1V1V2V2V3V3ZV7V0V7V0V7V0V7V0V7V0V7V0NSV5V5V6V6V1V1V2V2V3V3V4V4NLV5V6V6V1V1V2V2V3V3V4V4V5


## 3.2.5. Defuzzification

This step converts the fuzzy values back into a numerical value at the output, which is one zero voltage (V0 or V7) and six nonzero voltage vectors. For this step, the max method is used and expressed by Equation (17). From this method, the fuzzy output value which has the maximum possibility distribution is used as a control output.(17)μ′VoutV=maxi=1180maxμ′VoutV,where μ′Vout is a membership degree of the output variable.


## 3.3. Rotation Speed Controller by Fuzzy Logic

To overcome the troubles of classical speed controller, such as static error, sensitivity, and overshoot, we propose a FLC with as input the error and the derivation of speed error. The two fuzzy controller inputs are the speed error and its variation [40].The speed error notede is defined as follows:(18)ek=Ωrefk−Ωk.The variation of the speed error notedΔe is defined as follows:(19)dek=ek−ek−1.The controller output corresponds to the torque notedΔu. The three magnitudes, e, Δe, and Δu, are normalized as follows:(20)E=K1·e,ΔE=K2·ΔE,Δu=K3·Δu,where K1, K2, and K3 are scale or standardization factors and play a decisive role in the static and dynamic performance of the control.Figure11 illustrates the schema of the fuzzy speed controller. The control rules must be expressed in terms of the input and output variables using the decision table; the decision rules are described as if E is A and ΔE is B, then Δu is C. The internal structure of the fuzzy speed controller is shown in Figure 12.Figure 11
Structure of fuzzy logic controller.Figure 12
Internal structure of fuzzy speed controller.


## 4. Simulation Results

To evaluate the performance and the robustness of the studied system, different tests are carried out using MATLAB/Simulink software. Eight PV panels (CSUN 235-60P shown in Table2) are connected in series to get power enough to run the motor of 1.5 kW (its parameters are given in Table 3). The sizing of the PVWPS components is summarized in Table 4.Table 2
Characteristics of the Csun235-60p PV Panel.
Photovoltaic panel CSUN235-60PMaximum power (Pmax)235 WOpen-circuit voltage (Voc)36.8 VShort-circuit current (Isc)8.59 AMaximum power voltage (Pmax, Vmpp)29.5 VMaximum power current (Pmax, Impp)7.97 AStandard test condition (STC)1000 W/m2, 25°C, AM 1.5Number of cells60Temperature coefficient of open-circuit voltage (Voc,Kv)-0.37%/°CTemperature coefficient of short-circuit current (Isc,Ki)0.07%/°CTable 3
Parameters of Induction Motor.
ParametersValuesStator resistance4.58ΩRotor resistance3.805ΩStator inductance0.274 HRotor inductance0.274 HMutual inductance0.258 HInertia moment0.031 kg m2Nominal power1.5 kWViscous friction0.00114 N.m.s/radPole pairs’ number2Table 4
Design of Parameters of the System.
ComponentExpressionUsed valueV∗dcVdc=22/3VLL.400 VCdcCdc=6αVLLIt/Vdc∗2−Vdc12.2000μFαα=Vdc−Vmp/Vdc.0.26LpvLpv=DVmp/ΔI.fs.3 mH


### 4.1. Sudden Change in Solar Radiation

Solar radiation is varied from 1000 W/m2 to 500 W/m2 at 3 s (Figure 13(a)) to examine the dynamic and steady-state performance of the proposed PV water pumping system.Figure 13
Results of sudden change in solar radiation: (a) irradiation profile, (b) photovoltaic power, (c) electric speed, (d) water flow, (e) FFT analysis of stator current using VSS P&O, (f) FFT analysis of stator current using VSS INC, and (g) flux response.
(a)(b)(c)(d)(e)(f)(g)Figure13(b) shows the response of VSS P&O and VSS INC algorithms. It can be seen that response time is reduced, and oscillations are minimized compared to VSS P&O. Figure 13(c) illustrates the evolution of electric speed using both MPPT algorithms. The simulation results show that in rapid changing in atmospheric conditions, PWPS based on VSS INC algorithm shows better response as compared to VSS P&O algorithm in terms of tracking speed.Moreover, the pumped water volume obtained shown in Figure13(d) is clearly higher using VSS INC. Figure 13(g) shows the developed flux responses of IM with a zoom-in view using VSS P&O and VSS INC; this latter presents low flux ripple under different values of solar radiation. To illustrate the impact of the MPPT algorithms on the quality of the signal, a FFT (fast Fourier transform) analysis of the stator current waveforms is done. Figures 13(e) and 13(f) show the frequency spectrum. It can be seen that VSS INC provides a lower total harmonic distortion (THD) in comparison with the VSS P&O.


### 4.2. Test under Daily Profile

In this section, a simulation test is carried out using the real data of solar radiation from Fez, Morocco for June 2016. The evolution of solar radiance is shown in Figure14(a).Figure 14
Results of daily profile: (a) irradiation profile, (b) photovoltaic power, (c) electric speed, (d) water flow, (e) FFT analysis of stator current using VSS P&O, (f) FFT analysis of stator current using VSS INC, and (g) flux response.
(a)(b)(c)(d)(e)(f)(g)Figure14(b) shows the PV power using the VSS P&O and VSS INC; it is clear that using this latter, the PV power increases rapidly than VSS P&O.Figures14(c) and 14(d) show the corresponding speed responses and the pumped water volume, respectively. The simulation results show that for a daily profile, the proposed system based on VSS INC method shows better response in terms of tracking speed and the pumped volume is clearly higher. Figures 14(e) and 14(f) show the frequency spectrum. It can be seen that the total harmonic distortion (THD) is equal to 4.85% using VSS INC. Contrary to VSS P&O method, the total harmonic distortion is equal to 9.59% that means that the quality of motor current is improved using VSS INC algorithm. Figure 14(g) shows the developed flux responses of IM. The simulation results illustrate that the response of the stator flux magnitude of VSS INC method represents low oscillations compared with VSS P&O and improved by 81.73%, 75.86%, and 70.96% under 500 W/m2, 1000 W/m2, and daily profile, respectively.The system performances of both techniques are compared in terms of the response time, flux ripples, THD current, and daily pumped water and represented in Table5. From the presented data and Figure 15, PVWPS-based VSS INC provides high performances than VSS P&O with increasing pumped water flow, maintaining a fast response time and reducing flux ripple and THD current.Table 5
Comparison between the proposed PVWPS and the PV system based on VSS P&O.
Irradiation (W/m2)PerformanceVSS P&OVSS INCImprovements (%)Response timeRipple flux (Wb)THD current (%)Response timeRipple flux (Wb)THD current (%)Response timeRipple fluxTHD current5000.37 s0.0237.440.20s0.00424.1845.9481.7343.8110000.35 s0.0290.25 s0.00728.5775.86Daily profile5.1 h0.0319.594.6 h0.0094.859.8070.9649.42Figure 15
Water volume comparison.


## 4.1. Sudden Change in Solar Radiation

Solar radiation is varied from 1000 W/m2 to 500 W/m2 at 3 s (Figure 13(a)) to examine the dynamic and steady-state performance of the proposed PV water pumping system.Figure 13
Results of sudden change in solar radiation: (a) irradiation profile, (b) photovoltaic power, (c) electric speed, (d) water flow, (e) FFT analysis of stator current using VSS P&O, (f) FFT analysis of stator current using VSS INC, and (g) flux response.
(a)(b)(c)(d)(e)(f)(g)Figure13(b) shows the response of VSS P&O and VSS INC algorithms. It can be seen that response time is reduced, and oscillations are minimized compared to VSS P&O. Figure 13(c) illustrates the evolution of electric speed using both MPPT algorithms. The simulation results show that in rapid changing in atmospheric conditions, PWPS based on VSS INC algorithm shows better response as compared to VSS P&O algorithm in terms of tracking speed.Moreover, the pumped water volume obtained shown in Figure13(d) is clearly higher using VSS INC. Figure 13(g) shows the developed flux responses of IM with a zoom-in view using VSS P&O and VSS INC; this latter presents low flux ripple under different values of solar radiation. To illustrate the impact of the MPPT algorithms on the quality of the signal, a FFT (fast Fourier transform) analysis of the stator current waveforms is done. Figures 13(e) and 13(f) show the frequency spectrum. It can be seen that VSS INC provides a lower total harmonic distortion (THD) in comparison with the VSS P&O.


## 4.2. Test under Daily Profile

In this section, a simulation test is carried out using the real data of solar radiation from Fez, Morocco for June 2016. The evolution of solar radiance is shown in Figure14(a).Figure 14
Results of daily profile: (a) irradiation profile, (b) photovoltaic power, (c) electric speed, (d) water flow, (e) FFT analysis of stator current using VSS P&O, (f) FFT analysis of stator current using VSS INC, and (g) flux response.
(a)(b)(c)(d)(e)(f)(g)Figure14(b) shows the PV power using the VSS P&O and VSS INC; it is clear that using this latter, the PV power increases rapidly than VSS P&O.Figures14(c) and 14(d) show the corresponding speed responses and the pumped water volume, respectively. The simulation results show that for a daily profile, the proposed system based on VSS INC method shows better response in terms of tracking speed and the pumped volume is clearly higher. Figures 14(e) and 14(f) show the frequency spectrum. It can be seen that the total harmonic distortion (THD) is equal to 4.85% using VSS INC. Contrary to VSS P&O method, the total harmonic distortion is equal to 9.59% that means that the quality of motor current is improved using VSS INC algorithm. Figure 14(g) shows the developed flux responses of IM. The simulation results illustrate that the response of the stator flux magnitude of VSS INC method represents low oscillations compared with VSS P&O and improved by 81.73%, 75.86%, and 70.96% under 500 W/m2, 1000 W/m2, and daily profile, respectively.The system performances of both techniques are compared in terms of the response time, flux ripples, THD current, and daily pumped water and represented in Table5. From the presented data and Figure 15, PVWPS-based VSS INC provides high performances than VSS P&O with increasing pumped water flow, maintaining a fast response time and reducing flux ripple and THD current.Table 5
Comparison between the proposed PVWPS and the PV system based on VSS P&O.
Irradiation (W/m2)PerformanceVSS P&OVSS INCImprovements (%)Response timeRipple flux (Wb)THD current (%)Response timeRipple flux (Wb)THD current (%)Response timeRipple fluxTHD current5000.37 s0.0237.440.20s0.00424.1845.9481.7343.8110000.35 s0.0290.25 s0.00728.5775.86Daily profile5.1 h0.0319.594.6 h0.0094.859.8070.9649.42Figure 15
Water volume comparison.


## 5. Conclusion

In this paper, a standalone photovoltaic water pumping system without battery storage is investigated. The proposed system consists of using a variable step size incremental conductance method to adjust the duty ratio and fuzzy logic control based on DTC to control the induction motor. The innovative aspect of this paper is to propose a PV water pumping system which combined a variable step size incremental conductance method and fuzzy logic controller based on DTC; this combination has never been discussed. The efficiency of the proposed system has been studied under different operating conditions. For more accuracy, the obtained results are compared to those using the variable step size perturb and observe method. The proposed PV water pumping system based on VSS INC presents a better performance in terms of the time of response pumped water; flux ripples and the stator currents are reduced around 4.84%.



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*Source: 3872529-2020-08-18.xml*