A Total-Cross-Tied-Based Dynamic Photovoltaic Array Reconfiguration for Water Pumping System

Most Photo-voltaic (PV) applications require a shadow-free area for the installation of the PV panels. However, shading is inevitable in a few applications like building-integrated PV pumping systems (BIPVPS). Partial shading occurs due to soiling, clouds, shades of nearby trees, buildings, current, and telephone poles. During this partial shading condition, the PV array output power decreases, reducing the efficiency of the BIPVPS. In this paper, a novel dynamic array reconfiguration technique is proposed to enhance the power output from the PV array. The proposed system uses a boost converter with an incremental conductance algorithm for operating enhanced power at the maximum. Sinusoidal Pulse Width Modulation (SPWM) technique based on $V/f$ control operates the induction motor. Thus, the proposed algorithm and maximum power point technique (MPPT) enhance the power output from the PV array and track the global power. The PI and $V/f$ control regulate the dc-link voltage and speed of the Induction motor. Simulations and experimental studies are performed to show the effectiveness of the proposed algorithm. The proposed system results in additional 234 W PV power extraction compared to the conventional system. Thus, making the proposed BIPVPS efficient.


I. INTRODUCTION
Photovoltaic (PV) based energy generation technologies have been at the forefront among renewables for power generation. Building-integrated photovoltaic pumping systems (BIPVPS) have gained increasing interest as a PV technology application over the last few decades [1]. Unlike conventional water pumps, correctly designed and sized PV water pumps can provide long-term savings.
A wide range of research has been done on PV water pumping systems [2]. It includes improving photovoltaic arrays efficiency, electric motor and pumps interaction against the irradiance variation, designing the motors for specific water pumping applications, and various maximum power point techniques (MPPT) [3]. Further, research also involves cost reduction, productivity gain, and life expansion of PV water pumping systems. However, there is scope to examine the The associate editor coordinating the review of this manuscript and approving it for publication was Chi-Seng Lam . PV water pumping system performance under partial shading conditions (PSC). It has a significant effect on the BIPVPS because of the poles and shading of the nearest buildings.
Partial shading conditions reduce the output power from the PV array [4]. In literature to revamp this issue primarily uses a bypass diode. Although these diodes protect the PV panel from the hot spot effect, they result in multiple peaks [5]. These multiple peaks make the conventional MPPT converge at the local maximum. Several artificial intelligence and bio-inspired algorithms are applied to overcome the ineffectiveness to track the maximum global power under partial shading conditions [6]. However, the global maximum power point techniques (GMPPT) cannot effectively utilize the PV array to enhance the maximum power.
The second category includes different PV array topologies. They reduce the mismatch losses during PSC [7]. The PV water pumping system commonly uses the series-parallel arrangement [8], [9]. However, Total-Cross-Tied (TCT) topology has better performance during most of the shading conditions [10]. So, this paper uses TCT topology for the proposed system. Distributed MPPT (DMPPT) also improves the PV array performance during PSC but requires more converters, thus making the PV water pumping system expensive [11].
Finally, reconfiguration provides a feasible solution to mitigate this problem. For a higher size PV array, static reconfiguration is economical as it does not require irradiance sensors and switches [12]. On the other hand, the BIPVPS system requires a lower-size PV array, making dynamic photovoltaic array reconfiguration (DPVAR) attractive for this application. The inherent advantage of the DPVAR is that it is applied to any shading condition [13]. Moreover, dynamic reconfiguration (DR) enhances the power to the maximum possible extent compared to all the mitigation approaches [14].
Over the past few years various PV water pumping systems are developed [15]- [23]. The different motors used for this application are elaborated in the literature [2]. The Induction motor is a wise choice for this application due to enormous advantages [8], [22], [23]. The induction motor design methodology was investigated extensively for improving the efficiency of the system [25], [26]. Although the design of the motor improves the efficiency, the effective utilization of PV array during partial shading has a significant effect on the overall efficiency of the PV water pumping system [26]. Therefore, in the proposed method to improve the overall system efficiency, emphasis is made on extracting and enhancing the maximum power from the PV array using an conventional induction motor.
Induction motor-based pumping is classified as singlestage and two-stage. The single-stage topology of the solar PV array system does not require a boost converter. However, both the benefits of MPPT and dc-link voltage control are achieved through the inverter. In two-stage, the primary stage comprises a boost converter, and the second stage is an inverter used for motor control [8]. However, most of the studies above assume uniform shading over the PV array and have done minimal research on partial shading conditions [23], [24], [28].
In [23], the effects of partial shading on series-parallel topology for PV water pumping system is elaborated. It is observed that the global peak location on the left side of the P-V curve during partial shading significantly affects the DC-DC converter operation. The maximum PV array voltage will be less during these cases. So the boost converter should operate at a higher duty ratio to meet the required dc-link voltage. A higher duty ratio will lead to higher switching stress and lower efficiency. A single-ended primary inductor converter (SEPIC) based on multi-input single-output (SEPIC-MISO) is used for photovoltaic water pumping system in [31] to reduce the stress on the circuit components and to improve the system's reliability. In paper [32], reconfiguration for PV water pumping system is developed, where the algorithm verifies all the combinations of irradiances to generate the maximum output power. Further, in [33], a cuckoo search algorithm is used for tracking global peak under partial shad-ing conditions. However, it does not enhance the output power from the PV array under partial shading conditions. This paper proposed a novel dynamic array reconfiguration method to solve the above-mentioned problems. In the proposed method, the peak always occurs on the right side of the P − V curve, maintaining the peak voltage almost constant similar to uniform shading conditions, thus reducing the burden on the DC-DC converter. The proposed method used a TCT PV array for reconfiguration. The MPPT algorithm extracts the maximum energy from the PV array using a boost converter. The PI controller regulates the dc-link voltage. The inverter controller controls the motor speed according to PV irradiance operating at the MPP.

A. CONTRIBUTIONS & ORGANIZATION OF THE PAPER
The main contributions of this paper are as follows: 1 Most of the research on PV water pumping system focus on uniform shading conditions applied on series-parallel topology. However, this paper uses TCT topology for improving the performance of BIPVPS under partial shading conditions. 2 This paper proposes a novel dynamic reconfiguration (DR) for TCT topology using irradiance sensors for power enhancement to improve the water discharge at any shading conditions. 3 The proposed algorithm avoids the necessity of complex optimization algorithms for tracking MPP even under partial shading conditions.
The rest of this paper organizes as follows: Section II describes the modelling and design analysis. Section III presents the control scheme. Section IV analyzes the simulation and experimental results. Finally, Section V ends with a conclusion.
The following nomenclature is used in the rest of the paper.  Fig. 1 shows the block diagram of the proposed system. The sizing of the system starts with a correct estimation of load (water requirement). The motor design depends on the load requirement. Later, the TCT PV array is modelled for the required motor rating. The proposed algorithm requires switches, sensors, and controllers for its operation. The following section elaborates the design of all these components:

A. DESIGN OF MOTOR AND PUMP
The design of the system starts with the motor rating. Based on the load requirement, the motor is designed as follows [28]: where H is the total head, Q is the flow discharge and ρ is the specific gravity of water. η p , η d represents the efficiency of the pump and motor drive, respectively. A motor rating of 745 W is considered for simulation. Based on the motor rating, the pump constant is determined using affinity laws as follows [28]: where T L and ω represents the load torque and speed of the motor in (N-m) and (rad/sec), respectively.

B. DESIGN OF PV ARRAY
For the induction motor 745 W an 900 W p PV array is chosen. A 100 W p panel is considered for (3 × 3) PV array. The TCT array current is determined as follows [29]: where where i, j represents the row and column of an array. I ij (shaded) and I ij(standard) represents the module current, during shaded and standard irradiance (1000 W /m 2 ). G ij represents the irradiance received by the ij module and G STC represents standard irradiance. The PV array voltage is determined as follows [29]: where m indicates the total number of rows, i indicates the row number, V i is the voltage of the i th row and V pv represents the array voltage. Table 1 represents the specifications of the PV module.

C. DESIGN OF IRRADIANCE SENSORS AND SWITCHES FOR DR ALGORITHM
Sensors and switches play a crucial role in DR. The number of switches and sensors depends on the number of modules, number of rows, and columns in TCT configuration. The switches requirement are given by the following equation [29]: where S SPST represents the number of single pole single throw switches, m and n represent the number of rows and columns in a TCT PV array. The number of sensors required is given as follows: where I s , N represents the number of irradiance sensors and the PV modules, respectively.

D. DESIGN OF CONVERTERS
The design of the inductance and capacitance of the boost converter plays a vital role in deciding the system's performance. The inductance (L) and capacitance (C PV ) are derived from the following equations [23], [30]: where, V dc , V PV , I PV , P PV and f s represents dc-link and array voltage, PV array current, power and switching frequency. For V dc = 400 V, the duty cycle for the boost converter is D = 0.0625. The switching frequency of the converter and V dc /V dc is chosen as 10 kHz and 0.0001, respectively. The inductance and capacitance values are determined as 9.76 mH, 64 µF and are chosen as 10 mH, 65 µF, respectively. The design of dc-link voltage depends on the pulse width modulation technique used for the inverter. The relation between dc-link voltage and the line voltage of motor for the sinusoidal pulse width modulation (SPWM) technique is as follows [25]: where v LL is the line voltage of the motor. For 230 V line voltage V dc is calculated as 375 V. It is chosen as 400 V for simulation. The dc-link capacitance (C dc ) is determined as follows [8]: where, V * dc refers to the reference dc bus voltage, while V dc 1 is acceptable to the lowermost voltage during transients and is chosen as 375 V, α is overloading factor (1.2), V and I are the motor phase voltage and current, t is transient duration.
The C dc is estimated as 1025 µF and is chosen as 1050 µF. The overall design considerations are tabulated in Table 2.

III. PROPOSED SYSTEM CONTROL
The proposed control strategy initially uses sensors and switches to enhance the power output in the TCT PV array. The MPPT algorithm helps to operate the load at maximum power. The PI controller regulates the dc-link voltage, and V /f control is used to drive the induction motor. Fig. 2 shows the flowchart of the proposed dynamic reconfiguration algorithm. During partial shading, various modules in the TCT array receive different irradiances. These different irradiances result in varying currents in rows of the TCT PV array. Due to the difference in row currents, the TCT array exhibits multiple peaks [29]. Since in TCT, the panels in one row are connected in parallel and several such rows are connected in series, the lowest current among the rows will be the output current. This lowest current minimizes the output power of the TCT PV array. So the proposed algorithm aims at equalizing the current in rows to enhance output power from the TCT PV array.
The proposed DR triggers the switches based on the proposed algorithm. The algorithm uses the irradiance sensor data of each module to alter the connections. Let G and P indicate the irradiances and their corresponding position of modules in a PV array (m × n). Let Z corresponds to the row-wise summation of the G matrix.
The algorithm computes the set value based on the irradiances as given below where i, j represents corresponding module positions and m, n represents number of rows and columns. For simplifying the irradiance equalization process, the algorithm initially sorts the elements of G and the corresponding P matrix in column-wise order. Based on the sorted G matrix, the Z matrix is determined. The algorithm determines whether each element in Z is equal to the set value. If all the elements in Z are not equal to the set value, then the algorithm determines the rows of G in which the elements need to exchange. The switch matrix control is based on row selection. The algorithm determines the row index corresponding to the minimum and maximum element in Z and stores it in Min_pos and Max_pos. Some of the G matrix elements corresponding to Min_pos and Max_pos rows need to be swapped to make all the values in the Z matrix near to the set value.
Let u, and v indicate the position of irradiances in rows of G matrix corresponding to Max_pos and Min_pos. The elements to be swapped in the G matrix are selected so that the difference between those elements in Min_pos and Max_pos rows is nearer to the difference between a maximum element in Z and the set value.
If all the Z matrix elements are not equal to the set value, then the algorithm will be repeated. If the elements swapped in the previous iteration are again getting swapped in the present iteration, the algorithm terminates. Finally, based on the module positions, the corresponding switches are triggered to generate enhanced power during the partial shading conditions. The output of PV power has enhanced; however, it is necessary to operate the load at maximum power. A conventional incremental conductance algorithm is used for MPPT operation.
Once the MPPT is reached, the inverter dc-link voltage should be maintained constant for the effective operation of the motor. The PI controller regulates the dc-link voltage as follows: where V * dc represents the reference value and V dc represents the output of the boost converter. The output of the proportional-integral (PI) controller generates a speed, as represented in the below equation [8].  The reference speed for V /f is obtained from the pump affinity and the output of the PI controller, as shown in Fig. 3. The integration of ω generates θ, which is used to obtain the sinusoidal voltages as shown in Fig. 4. By controlling the frequency, the modulation index changes. The sinusoidal   voltages are compared with a high-frequency triangular wave to generate pulses for the inverter to control the speed of the motor.
Therefore, the study forms a complete framework for the successful operation of the PV-fed motor under partial shading conditions.

IV. RESULTS AND ANALYSIS A. SIMULATION RESULT ANALYSIS
During standard test conditions (STC), the TCT array generates a power of 900 W p , as shown in Fig. 5.
Two shading patterns are considered to show the efficiency of the proposed SPWPS. In TCT1S, irradiance levels seen by each module is as follows: The row current corresponding to TCT1S pattern is given as follows:   After reconfiguration according to the proposed algorithm, the module position changes. After reconfiguration, all the row currents are equal, which enables a single peak P − V curve, as shown in Fig. 5. Fig. 6 & 7 shows the source and load side performance during STC. Fig. 8 shows the source side performance under TCT1S. The maximum PV array power is 472 W for TCT1S. Based on the available input PV power, the motor rotates at a speed and torque of 1104 rpm and 3.7 N-m, respectively. The dc-link voltage and motor speed for TCT1S is shown in Fig. 9.
After reconfiguration, since the I PV increases and the mismatch losses decreases, the overall PV array power increase, as shown in Fig. 10. The PV power after reconfiguration is 523 W. The input power increases by 10.8 % compared to TCT1S. The dc-link voltage remains at 400 V. The ratio of V /f remains constant in TCT1S and TCT1R, as shown in Table 3. Since the PV power enhances, the power delivered to the motor increases, which aids in increasing the motor speed.      Fig. 11 shows the corresponding dc-link voltage, speed and motor power for TCT1R. Fig. 12 & 13 show the comparison of PV current, power during TCT1S and TCT1R. The PV current and power were enhanced after reconfiguration. Therefore under this shading condition, the system performances enhanced with the same available source. During this case, three different row currents appear; as a result, three distant peaks occur in the P − V curve. After reconfiguration, the difference between the row currents is small. Therefore, it appears as a single peak, as shown in The row current equations after reconfiguration reveal that the mismatch losses will reduce, which will enhance the PV power. The P PV during TCT2S shading is 318 W, as shown in Fig. 14. Although the global power is 463 W, the BIPVPS with conventional MPPT tracks 318 W. Since the local peak exists on the right side of the P − V curve, which is shown in Fig. 5. Therefore, the speed of the motor is 938 rpm, which is relatively low compared to the other cases, as shown in Fig. 15.     After reconfiguration, the PV array power is 552 W, as shown in Fig. 16. Thus the PV power has been enhanced to 73.58% compared to the TCT2S. The PV array current and power before and after reconfiguration are shown in Fig. 18 & 19, respectively. The speed is enhanced to 23.7%, compared to the TCT2S. The performance comparison of the proposed system under different shading conditions, shown in Table 3.   During TCT2R, the reference frequency value is 39 Hz, and the modulation index is 0.78, demonstrating that the ratio of V /f is maintained constant. Moreover, the dc-link voltage is settled to a reference value of 400 V during all the shading and reconfiguration conditions which resemble the effectiveness of PI controller operation. The PI controller is tuned using a closed-loop PI auto tuner using Matlab. In both the shading cases, the proposed algorithm enhances the output power whether the maximum power is either nearer or far away from the open-circuit voltage. After reconfiguration, the The working of the DR algorithm is visualized by the switching logic of the switches (S 9 -S 16 ) as shown in Fig. 21 & 22 respectively. During the initial shading pattern at t = 0 s, the switches S 10 and S 12 are switched on, which indicates that module-3 will remain in the same position (second row) as TCT configuration. The switches S 13 and S 15 are turned on, which alter the position of module-4 to the first row as its initial position is the second row in TCT configuration. Similarly, module-2 switches S 6 and S 8 are turned on to change the position of the module to the second row.
At t = 2.5 s, the switches S 9 and S 11 are turned on, which indicates module-3 will alter the position to the first row. The switches S 14 and S 16 are switched on to remain module-4 in the first row. Similarly, the switches of modules-1&2 correspondingly turned on to make the irradiance equalization in rows to enhance the output power. The algorithm is applicable to any size PV array. However, the system is more reliable for smaller size PV array. For simplicity the P-V characteristics before and after reconfiguration are emulated using PV simulator (Chroma 62050H-600S programmable DC power supply). The prototype for experimental verification is shown in Fig. 23. The PV module specifications used  are V oc = 98 V , I sc = 0.52 A, V mp = 83.3 V and I mp = 0.5 A. A 745 W three-phase induction motor 415 V, 1.9 A, 1405 rpm is used for implementation. The dc-link voltage is selected as 300 V. The pump characteristics are realized using a DC generator with a resistive load box.
A hall effect sensors are used for voltage and current measurement. The gating pulses for the converter are fed through a DSP processor. Fig. 24 shows the PV side performance during STC. The scaling factor for current and power is (k = 0.5), since two turns are used for the measurement of current. The indices V PV = 250 V, I PV = 1.5 A and P PV = 375 W indicates the effectiveness of MPPT operation. The V dc = 300 V demonstrates PI controller operation. Fig. 25 & 26 shows the PV side performance under TCT1S and TCT1R, respectively. It is observed that the V dc and P PV are 300 V and 196 W for TCT1S. After reconfiguration, the P PV power increases by 24 W. Since the PV power enhances, the speed of the induction motor also increases.      27 shows the MPPT performance during TCT2S and TCT2R. It is observed that the MPPT tracks the local maximum in the I −V curve during TCT2S, as shown in Fig. 27 (a).   As the MPPT tracks the local peak, the P PV is significantly less (i.e., 135 W), as shown in Fig. 28. However, after reconfiguration, the MPPT algorithm tracks the global peak, as shown in Fig. 27 (b). Therefore, the P PV is 225 W, as shown in Fig. 29, which allows the motor to run faster compared to the shading condition. Therefore, the proposed system can deliver more amount of water. Although the proposed system requires sensors and switches for reconfiguration, it is VOLUME 10, 2022 a one-time arrangement, which significantly enhances the output power of the PV array. The proposed method effectively utilizes the PV array source and improves the system reliability and efficiency.

V. CONCLUSION
This paper introduces a novel dynamic array reconfiguration to enhance the performance of BIPVPS under partial shading conditions. The proposed reconfiguration scheme using switches and sensors enhances the TCT array output power. During TCT2R condition, the PV power has been enhanced to 73.5% compared to TCT2S. As the PV power increases, it enhances the torque and speed of the induction motor. Further, during all the shading and reconfiguration conditions, the V /f remains constant, which helps in the smooth operation of the induction motor. During most shading conditions, the global peak with proposed reconfiguration appeared on the right side of the P-V curve eliminating the necessity of complex MPPT techniques. Thus the proposed system is simple and efficient.