Current-injected photovoltaic array for concentrated space solar power station

In this article, the power generation of a concentrated space solar power station (SSPS) is enhanced by current-injected total-cross-tied (TCT-CI) photovoltaic (PV) array. First, a mathematical model of the TCT-CI–connected PV array is established. Second, PV arrays with several common topologies and TCT-CI topology are simulated and analyzed using MATLAB/Simulink. At last, comparative experiments are conducted for TCT and TCT-CI–connected PV arrays under the condition of non-uniform light intensity distribution. The results of the above indicate the following: 1) TCT-CI–connected PV arrays reduce the difficulty of MPPT in concentrated SSPS, 2) TCT-CI–connected PV arrays increase the power generated in concentrated SSPS, and 3) TCT-CI–connected PV arrays are applicable for concentrated SSPS.

intensity distribution can cause mismatch losses, reduce power generation, cause hot spot problems, and even cause damage to the PV array (Alanazi et al., 2022). Uneven light intensity distribution reduces the performance of PV arrays, which affects the power generation of SSPS. Now, we have to find a method suitable for SSPS to improve the performance of photovoltaic arrays under non-uniform light intensity distribution.
To reduce the impact of non-uniform light intensity distribution on PV arrays, many methods have been proposed.
The first method uses a different PV array topology. Instead of the traditional series-parallel (SP) configuration, new structures such as BL, HC, and TCT are adopted. In Jazayeri et al. (2014), under the SP, BL, and TCT configurations, PSCs were simulated using MATLAB/Simulink. In ElyaqoutiIzbaimBouhouch (2021), the electrical behavior of S, parallel (P), SP, TCT, BL, and HC connected PV arrays under different PSCs. The aforementioned literature shows that TCT PV array performs the best among several common configurations under non-uniform irradiation.
The second method is PV array reconfiguration (PVAR), which is based on the TCT topology (Qi, 2022). This method can be divided into two types, namely, static PVAR (SPVAR) and dynamic PVAR (DPVAR) (Krishna and Moger, 2018;Storey et al., 2014). DPVAR changes the electrical connection between PV modules to adapt to non-uniform light intensity distribution (Bularka and Gontean, 2017;Wang et al., 2012;Matam and Barry, 2018), whereas SPVAR changes the physical position of PV panels to create a uniform light intensity distribution (RaniIlango and Nagamani, 2013;Sahu and Nayak, 2016).
SPVAR requires rearranging the positions of the PV panels, which consumes a large number of transmission wires. DPVAR does not change the physical positions of the PV panels but relies on the switch matrix to change the electrical connection relationship until the optimal connection mode is found (NahidanNiroomand and Dehkordi, 2021).
In the concentrated SSPS, the physical position of the PV modules is fixed. Therefore, SPVAR cannot be applied here. Because DPVAR makes the system more expensive and complex (Belhachat and Larbes, 2021), this method is also unsuitable for concentrated SSPS.
In order to maximize the power generated, the maximum power point tracking (MPPT) method is required. The non-uniform light intensity distribution causes multiple peaks in the power-voltage (PV) curve of the PV array (Ahmad et al., 2017;Awan et al., 2022). Conventional MPPT algorithms, such as P&O (Salameh and Taylor, 1990;SantosAntunes et al., 2006) and conductance increment method (INC) (ElgendyZahawi and Atkinson, 2013;Liu et al., 2008), can usually only find the first peak close to the starting point of the PV curve. When light intensity distribution is nonuniform, it is possible that the first peak is the local MPP but not global MPP (GMPP) (Titri et al., 2017). To make the MPPT algorithm more accurate, smarter but complex MPPT control algorithms have been proposed, such as the gray wolf algorithm improved by the Levy flight (WangCai and Zeng, 2021), ant colony algorithm (ACO) (Chao and Rizal, 2021), hybrid global MPPT searching method (Rizzo and Giacomo, 2021), and genetic algorithm (GA) (Mohammad et al., 2015). Although the GMPP can be tracked using the aforementioned algorithm, this increases the difficulty and time of MPPT.
To increase the output power of PV arrays in concentrated SSPS and reduce the difficulty of MPPT, the current injection TCT (TCT-CI) topology has been applied in this study. In the TCT-CI-connected PV array, each row is parallel with a controllable current source. Without considering the effect of light intensity from the PV module output voltage, each PV module can be operated at its GMPP.
In this article, Section 2 performs mathematical modeling on the PV cell and TCT-CI-connected PV array. Section 3 describes the evaluation method of PV array performance. Section 4 discusses and compares simulation results of the TCT-CI-connected PV array and other PV array configurations. In Section 5, comparative experiments are conducted for TCT and TCT-CI-connected PV arrays. Finally, Section 6 summarizes this whole article.

Mathematical modeling
PV arrays are connected by many PV cells. Commonly used PV cell models are single-diode models (Hasan and Parida, 2016).
As shown in Figure 1, the relationship between I pv and V pv (Mehta et al., 2019;Sai Krishna and Moger, 2019) is defined as where I ph is the light generated current; I 0 is the diode's reverse saturation current; q is the electric charge on an electron, which is  equal to 1.602176487*10 −19 ; n is the ideality factor; K is the Boltzmann's constant, which is equal to 1.3806504*10 −23 ; T is temperature in Kelvin, R s is series resistance, and R sh is shunt resistance. I sc is the short-circuit current at the standard test condition (STC).
I ph is proportional to solar irradiation(G) and temperature (T), which is defined as where K isc is the temperature coefficient of I sc ; G 0 is the light intensity under STC; T STC is temperature under STC.
Parameters of the PV model used in Section 3/Simulink are shown in Table 1 and the PV curves are shown in Figure 2.
According to the I pv and V pv relationship, under constant temperature, I pv is approximately proportional to the light intensity G and V pv is approximately logarithmic to G. In concentrated SSPS, when PV modules are deployed, the same row of PV modules in the TCT-CI connected PV array are on the same horizontal line of the solar receiver. The light intensity distribution and temperature of PV modules in the same row is approximately the same, therefore the output voltages of PV modules in the same row are assumed to be the same.
When the temperature is constant, I pv and V pv are functions of G. In an m × n PV array (Figure 3), the light intensity on the module ij is G ij , and then I pv and V pv at the GMPP of the module are expressed as follows: In the TCT-CI topology, the output current in row k at GMPP is and the output voltage in row k at GMPP is V r k V G ky y is any integer between 1 and n .
When the photoelectric effect of the PV modules in row k is weaker than that in other rows, the relative I r k is smaller. The parallel controlled current source operates in row k and injects current into it, such that its output current is equal to that in the other rows. Under the action of controllable current sources, the output current of the array (I o ) is and the output voltage FIGURE 3 PV arrays with TCT-CI topology.

FIGURE 5
Flux density distribution of the hemisphere receiver with rotating parabolic concentrators (Liu et al., 2007).

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Research frontiersin.org 04 The output current of the controllable current source in row k (I CI k ) is The total output power of m controllable current sources is The output power of the array is In practical applications, max[I r 1 , I r 2 , . . . , I r m ] is obtained by measuring the currents of the bypass diodes and the output current of the array when the current injection section is not started.
According to Eqs 8-10, when the PV array has a TCT-CI topology, the working current of each row is the current at the GMPP, and there is no mismatch loss.

Evaluation of the PV array
When the irradiation is not uniform, the performance of the PV array can be evaluated from GMPP, mismatch power loss (MPL), power loss (PL), filling factor (FF), and efficiency (η).

Mismatch power loss
The larger the MPL, the greater is the influence of the output power of the PV array with non-uniform irradiation.

Power loss
PL represents the difference between the global maximum power of the PV array under STC (1,000 W/m 2 , AM1.5, 25°C) and that under non-uniform light intensity distribution. PL can be determined as PL Power at MPP uni − Power at GMPP non−uni .
Because the irradiation on the PV array in concentrated SSPS is not uniform, MPL is used in this study to measure the effectiveness of various configurations.

Filling factor
The product of I sc and V oc is the limit of the output power of the PV module. The ratio of the product of I sc and V oc to the global maximum power (P m ) is defined as the filling factor (FF).
The larger the FF, the higher is the output power and efficiency of the photovoltaic module. FF affects the output efficiency of the PV module.

Photoelectric conversion efficiency (η)
When the photovoltaic module is exposed to light, the ratio of the output electric power to incident optical power is the photovoltaic conversion efficiency (η) of the photovoltaic module.
where P in is the incident optical power.

Simulation and analysis using MATLAB/Simulink
To prove the advantage of the TCT-CI-connected PV array in concentrated SSPS, this section simulates PV arrays with several common topologies and the TCT-CI topology (Figure 4). The PV array consists of 5 × 5 PV cells. The characteristic curves of the PV modules are shown in Figure 2.
The flux density distribution of the hemisphere receiver when the concentrator is a rotating paraboloid is shown in Figure 5. When the PV array is uniformly attached to the surface of the receiver, the light intensity distribution on the same row is approximately equal but different between the rows.
The six light intensity distributions used in the simulation are shown in Table 2, which are based on the light concentration characteristics of the abovementioned rotating parabolic concentrator. Cases 1, 2, and 3 had errors of 10%, and some others had errors of 20%. The PV array was evaluated in three

Estimation of power generation form TCT and TCT-CI-connected PV arrays 1TCT-connected PV arrays
In the PV array, if the output current of the array (I TCT out ) is greater than the short-circuit current of a row (I r i sc ), the parallel bypass diode will be turned on and the row will be short-circuited. When estimating the GMP of the TCT-connected PV array, we should pay attention to whether a row is short-circuited by the bypass diode.
According to Eqs 1, 2 and Figure 2, when the temperature is at the standard test condition (STC), the output current at the GMPP is almost proportional to the light intensity, and the output voltage almost does not change with the change in light intensity.
I m represents the current at the GMPP of the module under STC. I r i m is used to represent the current at the GMPP of row i under the existing irradiative condition. I r i sc is used to represent the short-circuit current of row i under the existing irradiative condition. In Case 1, I r 1 m and I r i sc are, Same as the above, get row currents in the other cases, and substitute the values in Table 1 into Eqs 15, 16 to obtain I r i m and I r i sc .
If I TCT out > I r i sc , row i will be short-circuited, and the PV modules in row i will not generate electricity.
In Case 1 and Case 2, the difference between the I r i m is not large, so no PV module will be short-circuited. The minimum of the row current values is chosen as I TCT out .
In Case 1, P TCT out I TCT out × 5V m 4046W.
In Case 2, In Case 3, a) If I TCT out I r 1 m , rows 2, 3,4, and 5 will be short-circuited, and in this situation, b) If I TCT out I r 2 m , rows 3, 4, and 5 will be short-circuited, and in this situation, c) If I TCT out I r 3 m , rows 4 and 5 will be short-circuited, and in this situation, P TCT out I TCT out × 4V m 2360W. Frontiers in Energy Research frontiersin.org 08 e) If I TCT out I r 5 m , no PV model will be short-circuited, and in this situation, P TCT out I TCT out × 4V m 2448W.
From a) to e), the value that makes P TCT out maximum is selected as I TCT out . So I TCT out I r 5 m , and no PV model will be short-circuited. Same as the above, P TCT from the other cases is obtained. Results are shown in Table 3.
When I r i m < I TCT out < I r i sc , the output voltage in row i is actually less than V m . When I TCT out < I r i m , the output voltage in row i is actually greater than V m and less than V oc . Therefore, this subsection has some errors in estimating the generation of PV arrays but can correctly calculate whether PV modules are short-circuited.

4.1.2TCT-CI-connected PV arrays
Because of the controlled current source of the TCT-CI-connected PV array, each PV module can operate at the GMPP.
According to Table 4, in Case 1, the global maximum power of TCT-CI-connected PV array is defined as P TCT CI 9.758I m + 10.476I m + 10.126I m + 9.718I m + 10.53 ( ) V m 50.608P m 4214.88W.
(31) Same as the above, P TCT CI from the other cases is obtained. Results are shown in Table 5.

PV arrays' performance
The models were simulated using MATLAB/Simulink. The PV curves under the light intensity distribution are shown in Figure 6, and the MPL and filling factor are shown in Figure 7.
In Case 5 and Case 6, the output voltage at GMPP of the TCT-CI PV array is significantly greater than that of the others, indicating that some modules of the others are short-circuited by the bypass diode. This is consistent with the estimate in Section 4.1.
As shown in Figure 6, simulation results show that TCT-CI connected PV arrays have higher output power compared to other PV arrays. PV curves of TCT-CI connected PV arrays show a single peak. So conventional MPPT algorithms can be used here. PV curves of others PV arrays show multiple peaks. Conventional MPPT algorithms cannot track to GMPP, so more complex algorithm is required. Therefore, TCT-CI connected PV arrays reduce the difficulty of MPPT under non-uniform light intensity distribution. As shown by the polyline in Figure 7, the FF of TCT-CI connected PV arrays are slightly larger than that of others, and the MPL of TCT-CI connected PV arrays is 0.
In conclusion, TCT-CI-connected PV arrays have the following advantages under non-uniform illumination intensities:

FIGURE 9
Real shooting of experiment.

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frontiersin.org i. no mismatch loss, ii. maximum GMPP, iii. maximum photoelectric conversion efficiency, iv. maximum filling factor and best performance, and v. PV curve showing a single peak value, which reduces the difficulty of MPPT.

Experiment and analysis
To further verify that the TCT-CI-connected PV arrays are more suitable for concentrated SSPS, a comparative experiment between the TCT-CI and TCT-CI topologies was carried out. The experimental schematic is shown in Figure 8. The real shooting is shown in Figure 9. In the experiment, 30 photovoltaic models constituting 5*6 photovoltaic arrays were analyzed. Parameters of the PV module for this experiment at STC are shown in Table 6.
In Figure 8, the dashed line represents parallel controlled current sources. When the PV array is in the TCT topology, the controllable current source is not connected to the PV module. When the PV array is in the TCT-CI topology, the controllable current source is connected to the PV module as shown in Figure 8. During the experiment, the PV array was oriented toward the sun in such a way that sunlight was perpendicular to the PV module.
A pure resistive load was used in the experiment. In the TCT topology experiment, when the line loss was not considered, with the MPPT controller, the power consumed by the load (P load ) was the global maximum power (P m ) of the PV array. Therefore, P m can be calculated by directly measuring the voltage across the load.
In the TCT-CI topology experiment, the external power supply was used as a controllable current source. Because the energy of the  external power supply is an external input, to obtain the global maximum power (P m ) of the PV array, the power of the external power supply (P CI ) has to be subtracted from the power consumed by the load (P load ). Then, the expression of P m becomes P m P load − P CI .
In the experiment, some photovoltaic modules were covered with a shading cloth to create a non-uniform light intensity distribution. Five groups of experiments were conducted, and the numbers and positions of the shading cloths are shown in Figure 10.
Because the basic light intensity did not change significantly during the experiment, the experimental results were not normalized; P m of the PV arrays with TCT and TCT-CI topologies obtained in the experiment is shown in Table 7. It can be seen that under a non-uniform light intensity distribution, the global maximum power of the PV array with the TCT-CI topology is significantly larger than that with the TCT topology.

Conclusion
This study shows that the TCT-CI-connected PV array is suitable for concentrated SSPS. In the future, the following research has to be carried out: the existing TCT-CI-connected PV array uses a large number of controllable current sources, therefore the number of controllable current sources can be reduced in the next step.
This study analyzes and compares the performance of SP, BL, HC, TCT, and TCT-CI-connected PV arrays under non-uniform light intensity. Several PV arrays with different topologies were simulated by considering light intensity distribution in concentrated SSPS with rotating paraboloids as an example. Finally, comparative experiments on PV arrays with TCT and TCT-CI topologies were carried out. Both simulation and experimental results show that the PV array with TCT-CI topology has the best performance, and the difficulty of MPPT is reduced in non-uniform light intensity distribution.
In other words, PV arrays with TCT-CI topology are more suitable for concentrated SSPS, which can reduce the influence of non-uniform light intensity distribution on the performance of PV arrays.

Data availability statement
The original contributions presented in the study are included in the article/Supplementary Material; further inquiries can be directed to the corresponding author.