# New Control Scheme for Solar Power Systems under Varying Solar Radiation and Partial Shading Conditions

^{1}

^{2}

^{3}

^{*}

## Abstract

**:**

## 1. Introduction

^{2}and the solar power generation (SPG) system output power is low [1]. The SPG system output energy is dependent on climatic elements (e.g., solar radiation and ambient temperature). Therefore, the maximum power point tracking (MPPT) controller can greatly improve the efficiency of the SPG system [2,3].

_{spv}

^{−1}) threshold control (CTC) implemented in the MPPT control scheme, combined with the P&O algorithm. The experimental comparison is of the proposed algorithm and the P&O algorithm under varying solar radiation and partial shading conditions. Moreover, the proposed algorithm efficiency is higher than the P&O algorithm, which could operate at the MPP and avoid being trapped in the LPPP under PSCs.

## 2. Perturbation and Observation Algorithm

_{spv}-V

_{spv}characteristic curve slope (dP

_{spv}/dV

_{spv}). If the P&O algorithm actuating point is on the left-half plane (LHP) for the SPV module P

_{spv}-V

_{spv}characteristic curve, it means that the slope is positive. On the contrary, if the P&O algorithm actuating point is on the right-half plane (RHP) for the SPV module P

_{spv}-V

_{spv}characteristic curve, it indicates that the slope is negative. This P&O algorithm depends on the slope and further perturbs the duty cycle to track the MPP. However, this algorithm’s actuating point oscillates near the MPP, causing low system efficiency. In addition, the SPV module under partial shading implies that this algorithm’s actuating point could converge to the SPV module’s local maximum power point (LMPP), resulting in power loss [24].

## 3. Proposed Algorithm

_{spv}-V

_{spv}characteristic curves of the SPV module, which has been informed. When solar radiation G and temperature T change, so do the SPV module output voltage V

_{spv}and the current I

_{spv}(2). The important parameter, R

_{spv}, of Equation (2) changes based on G and T. Thus, R

_{spv}can reflect G and T changes and R

_{spv}of the SPV module is an important reference factor for the CTC.

_{spv}-V

_{spv}characteristic curves of the T of 25 degrees and the G of 200, 400, 600, 800 and 1000 W/m

^{2}. Figure 1b shows the SPV module I

_{spv}-V

_{spv}characteristic curves of the G of 1000 W/m

^{2}and the T of 0, 25, 50 and 75 °C.

_{spv}-V

_{spv}characteristic curves) converted the relationship between I

_{spv}and R

_{spv}

^{−1}through Microsoft Excel and presented it with trend lines. Hence, four trend lines were drawn (as in Figure 2) to illustrate the relationship between I

_{spv}and R

_{spv}

^{−1}as follows: line A for the T of 0 °C and the G of 0–1000 W/m

^{2}, line B for the T of 25 °C and the G of 0–1000 W/m

^{2}, line C for the T of 50 °C and the G of 0–1000 W/m

^{2}and line D for the T of 75 °C and the G of 0–1000 W/m

^{2}. The mathematical model of the four trend lines could be approximated by the following quadratic equation, simplified as Equation (3).

_{spv}is obtained by Equation (3) as follows:

_{spv}

^{−1}and I

_{spv}range from line A to line D, as shown in Figure 2. In this study, R

_{spv}

^{−1}= P

_{spv}/V

_{spv}

^{2}, according to Equation (4), to calculate I

_{spv}

_{,line}(e.g., I

_{spv}

_{,lineA}, I

_{spv}

_{,lineB}, I

_{spv}

_{,lineC}and I

_{spv}

_{,lineD}). As shown in Figure 2, when R

_{spv}

^{−1}= 0.2 S, I

_{spv}

_{,lineA}, I

_{spv}

_{,lineB}, I

_{spv}

_{,lineC}and I

_{spv}

_{,lineD}are different. Although the four trend lines have the same R

_{spv}

^{−1}, a different T and G draw different trend lines and the calculated I

_{spv}

_{,line}will be significantly different.

_{spv}-V

_{spv}characteristic curves, converted the relationship between R

_{spv}

^{−1}and the G through Microsoft Excel and presented it with trend lines. The four trend lines were drawn (as in Figure 3) to show the relationship between the R

_{spv}

^{−1}and the G as follows: line A.1 for the T of 0 °C and the G of 0–1000 W/m

^{2}, line B.1 for the T of 25 °C and the G of 0–1000 W/m

^{2}, line C.1 for the T of 50 °C and the G of 0–1000 W/m

^{2}and line D.1 for the T of 75 °C and the G of 0–1000 W/m

^{2}. The mathematical model of the four trend lines could be approximated by the following quadratic equation, simplified as Equation (5):

^{−11}, e = 2612.8 and f = 2 × 10

^{−12}; line B.1 was drawn with d = 662.46, e = 3148.2 and f = −0.2585; line C.1 was drawn with d = −232.85, e = 3541.1 and f = −5.7651 and line D.1 was drawn with d = 6 × 10

^{−11}, e = 3575.5 and f = −5 × 10

^{−13}.

_{spv}

^{−1}and I

_{spv}fall on line A in Figure 2, they correspond with line A.1 in Figure 3 and then the G can be calculated by Equation (5). Furthermore, if the values of R

_{spv}

^{−1}and I

_{spv}fall on line B or C or D in Figure 2, they correspond with line B.1 or C.1 or D.1 in Figure 3, respectively, and then the G can be calculated by Equation (5).

_{spv}> 1.06·I

_{pv,lineB}, it falls in the interval of line A; (3) if I

_{spv}≦ 0.94·I

_{spv}

_{,lineA}or I

_{spv}> 1.005·I

_{spv}

_{,lineC}, it falls in the interval of line B; (4) assuming I

_{spv}≦ 0.995·I

_{spv}

_{,lineB}or I

_{spv}> 1.018·I

_{spv}

_{,lineD}, it falls in the interval of line C; (5) assuming I

_{spv}≦ 0.982·I

_{spv}

_{,lineC}, it falls in the interval of line D.

^{2}) [25]. In this control scheme judgment, G does not change, which reduces unnecessary vibrations of the actuating point. Therefore, in this study, the CTC threshold value was set to 27 W/m

^{2}. Once the G change was detected to be more than 27 W/m

^{2}, the proposed algorithm tracked the new MPP.

^{2}, P

_{spv}= 12 W and a duty cycle of 0.7, then when time = 0.2 s, the G of 600 W/m

^{2}drops to 500 W/m

^{2}. Thus, the G variation value is more than 27 W/m

^{2}. Therefore, the proposed algorithm starts to track the new MPP. The P

_{spv}of 10 W and duty cycle of 0.6 are shown in Figure 4b,c. Figure 4a displays that when time = 0.4 s, the G of 500 W/m

^{2}drops down to 490 W/m

^{2}. Thus, the G variation value is less than 27 W/m

^{2}. Therefore, the proposed algorithm to calculate the duty cycle is fixed, preventing perturbations that cause power loss. The P

_{spv}of 9.8 W and the duty cycle of 0.6 are shown in Figure 4b,c. Figure 4a illustrates that when time = 0.6 s, the G increases from 490 W/m

^{2}to 500 W/m

^{2}. Thus, the G variation value is less than 27 W/m

^{2}and that the duty cycle is also fixed. The P

_{spv}of 10 W and duty cycle of 0.6 are shown in Figure 4b,c.

_{spv}of the SPV module is an important factor for MPPT. This proposed algorithm not only detects the SPV Module P

_{spv}-V

_{spv}characteristic curves but also utilizes the CTC based on R

_{spv}to track the MPP. Furthermore, the proposed algorithm is suitable for poor climates (e.g., rain, cloud and shadow).

_{spv}(n) = V

_{spv}(n) − V

_{spv}(n − 1); dP

_{spv}(n) = P

_{spv}(n) − P

_{spv}(n − 1); the present SPV module output current is I

_{spv}; the present solar radiation is G; dG = |G(n) − G(n − 1)|; a, b and c are the parameters of Equations (3) and (4) and d, e and f are the parameters of Equation (5).

_{1}), a diode (D) and a capacitor (C

_{out}of 220 μF). It includes feedback circuits of an optical coupler and a current transducer. Further, it detects the V

_{spv}and I

_{spv}and transmits the signals to the microcontroller unit (MCU). The MCU (Microchip Technology, model number 18F452) outputs the PWM signal (PWM frequency of 30 kHz) and then drives the gate driver to control S

_{1}and reach the MPP.

## 4. Experimental Results

^{2}and T of 25 °C specifications are as follows: V

_{MPP}= 8.3 V, I

_{MPP}= 2.4 A and P

_{MPP}= 20 W. In this experiment, the SPV module output power was connected to the input of the boost converter and the boost converter output was connected to the load. The MCU was employed to perform the MPPT control. The MCU outputted the PWM signal to drive the boost converter power MOSFET, S

_{1}, which then reached the MPP.

^{2}dropped to 220 W/m

^{2}then increased to 500 W/m

^{2}with a T of 25 °C. Figure 8a shows that the proposed algorithm’s MPPT was activated. When time = t

_{0}, the SPV module R

_{spv}

^{−1}= 0.154 S, V

_{spv}= 8.5 V, I

_{spv}= 1.32 A and P

_{spv}= 11.22 W. According to Equation (4), the following were calculated: I

_{spv,line}

_{A}, I

_{spv,line}

_{B}, I

_{spv,line}

_{C}and I

_{spv,line}

_{D}, respectively. The I

_{spv,lineC}= 1.299 A and I

_{spv}> 1.005·I

_{spv, lineC}. Thus, the I

_{spv}fell on line B (Figure 2), which corresponded with line B.1 (Figure 3). Equation (5) was used to calculate the G = 500 W/m

^{2}. At time = t

_{1}, the SPV module R

_{spv}

^{−1}= 0.072 S, V

_{spv}= 8.5 V, I

_{spv}= 0.62 A and P

_{spv}= 5.3 W. According to Equation (4), the following were calculated: I

_{spv,line}

_{A}, I

_{spv,line}

_{B}, I

_{spv,line}

_{C}and I

_{spv,line}

_{D}, respectively. The I

_{spv,lineC}= 0.6 A and I

_{spv}> 1.005·I

_{spv,lineC}. Therefore, the I

_{spv}fell on line B (Figure 2), which corresponded with line B.1 (Figure 3). Equation (5) was used to calculate the G = 220 W/m

^{2}. At time = t

_{2}, the SPV module R

_{spv}

^{−1}= 0.154 S, V

_{spv}= 8.5 V, I

_{spv}= 1.32 A and P

_{spv}= 11.22 W. According to Equation (4), the following were calculated: I

_{spv,line}

_{A}, I

_{spv,line}

_{B}, I

_{spv,line}

_{C}and I

_{spv,line}

_{D}, respectively. The I

_{spv,lineC}= 1.299 A and I

_{spv}> 1.005·I

_{spv,lineC}. Thus, the I

_{spv}fell on line B (Figure 2, which corresponded with line B.1 (Figure 3). Equation (5) was used to calculate the G = 500 W/m

^{2}. The proposed algorithm could accurately calculate the G and adjust the duty cycle track to the MPP. When the G was constant, the duty cycle was fixed. Therefore, the proposed algorithm caught the MPP accurately.

_{0}and a G of 500 W/m

^{2}, at time = t

_{1}, the G of 500 W/m

^{2}dropped to 220 W/m

^{2}and at time = t

_{2}, the G of 220 W/m

^{2}rose to 500 W/m

^{2}. The experiment results verified that the proposed algorithm’s MPPT efficiency was better than the P&O algorithm (as in Table 1).

^{2}and 25 °C. Figure 9a shows that the proposed algorithm MPPT was activated. When the proposed algorithm at time = t

_{0}, the SPV module R

_{spv}

^{−1}= 0.166 S, V

_{spv}= 9 V, I

_{spv}= 1.5 A and P

_{spv}= 13.5 W. According to Equation (4), the following were calculated: I

_{spv,line}

_{A}, I

_{spv,line}

_{B}, I

_{spv,line}

_{C}and I

_{spv,line}

_{D}, respectively. The I

_{spv,lineC}= 1.41 A and I

_{spv}> 1.005·I

_{spv,lineC}. Therefore, I

_{spv}fell on line B (Figure 2), which corresponded with line B.1 (Figure 3). Equation (5) was used to calculate the G = 540 W/m

^{2}. At time = t

_{1}, the SPV module suffered 1/2 partial shading conditions P

_{spv}= 6 W. The proposed algorithm was provided by the P&O algorithm with a quick response and accurately calculated the G and adjusted the duty cycle track to the MPP. When the G was constant, the duty cycle was fixed. Therefore, the proposed algorithm stably caught the MPP. At time = t

_{2}, the SPV module R

_{spv}

^{−1}= 0.166 S, V

_{spv}= 9 V, I

_{spv}= 1.5 A and P

_{spv}= 13.5 W. According to Equation (4), the following were calculated: I

_{spv,line}

_{A}, I

_{spv,line}

_{B}, I

_{spv,line}

_{C}and I

_{spv,line}

_{D}, respectively. The I

_{spv,lineC}= 1.41 A and I

_{spv}> 1.005·I

_{spv,lineC}, so I

_{spv}fell on line B (Figure 2), which corresponded with line B.1 (Figure 3). Equation (5) was used to calculate the G = 540 W/m

^{2}. Similarly, the proposed algorithm caught the MPP accurately.

_{0}and G of 540 W/m

^{2}, at time = t

_{1}, the SPV module suffered 1/2 partial shading conditions P

_{spv}= 4.7 W and at time = t

_{2}, a G of 540 W/m

^{2}. Similarly, the experiment results verified that the proposed algorithm’s MPPT efficiency was higher than the P&O algorithm (as in Table 1).

## 5. Conclusions

^{2}to 220 W/m

^{2}then to 500 W/m

^{2}) and partial shading conditions reached 99% of MPPT efficiency. Thus, the proposed algorithm was better than the P&O algorithm. Accordingly, the proposed algorithm was confirmed to be of a high performance under various solar radiation and partial shading conditions.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Acknowledgments

## Conflicts of Interest

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**Figure 1.**A single SPV module I

_{spv}-V

_{spv}characteristic curve graph (Everbright, model number Q025). (

**a**) T of 25 °C; G of 200, 400, 600, 800 and 1000 W/m

^{2}, respectively. (

**b**) G of 1000 W/m

^{2}; T of 0, 25, 50 and 75 °C, respectively.

**Figure 4.**Corresponding SPV module for (

**a**) solar radiation, G, (W/m

^{2}), (

**b**) SPV module output power, P

_{spv}, (W) and (

**c**) duty cycle waveforms.

**Figure 8.**

**Fig**

**ure**

**8.**V

_{GS}, V

_{spv}, I

_{spv}and P

_{spv}waveforms for a SPV module under a T of 25 °C and varying irradiance of 500 W/m

^{2}to 220 W/m

^{2}then to 500 W/m

^{2}: (

**a**) the proposed algorithm and (

**b**) the P&O algorithm. (V

_{GS}: 20 V/div; V

_{spv}: 10 V/div; I

_{spv}: 1 A/div; P

_{spv}: 10 W/div; Hor: 4 s/div).

**Figure 9.**V

_{GS}, V

_{spv}, I

_{spv}and P

_{spv}waveforms for a SPV module under a T of 25 °C and partial shading conditions: (

**a**) the proposed algorithm and (

**b**) the P&O algorithm. (V

_{GS}: 20 V/div; V

_{spv}: 10 V/div; I

_{spv}: 1 A/div; P

_{spv}: 10 W/div; Hor: 4 s/div).

**Table 1.**Comparison efficiency of the proposed and P&O algorithm under various solar radiation and partial shading conditions.

Algorithm | Various Solar Radiation | Partial Shading Conditions | |
---|---|---|---|

G of 500 W/m^{2}Drop to 220 W/m ^{2} | G of 220 W/m^{2}Rise to 500 W/m ^{2} | ||

Proposed | 99% | 99% | 99% |

P&O | 96% | 96% | 80% |

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**MDPI and ACS Style**

Jana, A.-S.; Liu, H.-D.; Lu, S.-D.; Lin, C.-H. New Control Scheme for Solar Power Systems under Varying Solar Radiation and Partial Shading Conditions. *Processes* **2021**, *9*, 1359.
https://doi.org/10.3390/pr9081359

**AMA Style**

Jana A-S, Liu H-D, Lu S-D, Lin C-H. New Control Scheme for Solar Power Systems under Varying Solar Radiation and Partial Shading Conditions. *Processes*. 2021; 9(8):1359.
https://doi.org/10.3390/pr9081359

**Chicago/Turabian Style**

Jana, Anindya-Sundar, Hwa-Dong Liu, Shiue-Der Lu, and Chang-Hua Lin. 2021. "New Control Scheme for Solar Power Systems under Varying Solar Radiation and Partial Shading Conditions" *Processes* 9, no. 8: 1359.
https://doi.org/10.3390/pr9081359