Performance analysis of a residential photovoltaic string under partial shading

As one of the most prominent renewable energy resources, Photovoltaic (PV) generation has been growing dramatically over the last years and its applications are classified into residential, commercial, and power plant class, based on its power capacity. Especially, a typical residential PV system has been configured with serially connected PV modules. For serially connected PV modules, shading is a critical factor to reduce the whole string PV output power. This paper presents study on performance analysis of a residential PV string under partial shading. This analysis contains how many maximum power points (MPPs) occur and how much power would be lost while a PV string is under partial shading with different shading positions and different shading intensities. PSIM simulation tool is used to verify the performance analysis. As a result, the number of MPPs is directly related with the number of shading intensities, regardless of the shading position. In this paper, it was verified that 8 maximum power points were generated for 8 solar intensities regardless of the location of the shadows under extreme conditions. These results can be utilized for fault diagnosis in the PV string.


INTRODUCTION
Renewable energy is energy that has been derived from earth's natural resources that are not finite or exhaustible, such as wind and sunlight. Renewable energy is an alternative to the traditional energy that relies on fossil fuels, and it tends to be much less harmful to the environment [1]- [3]. Photovoltaic (PV) generation is one of the most popular power generation sources among renewable energy sources, and worldwide growth of PV is extremely dynamic [4], [5]. By the end of 2019, a cumulative amount of 629 GW of solar power was installed throughout the world [6]. PV generates electric power by using PV modules to convert energy from the sunlight into a flow of electrons by the photovoltaic effect [7].
PV markets are classified into three segments: residential [8], [9], commercial [10], [11], and PV power plant [12]- [14]. Especially, residential PV application ranges. Most residential PV typically feature a capacity of about less than 10 kW, while commercial PV often reaches to 100 kW and PV power plant over 100 kW [15]. Especially, PV modules for typical 3 kW residential PV application in Korea are connected in series to match with PV inverter input voltage specification with single string [16]- [18]. For serially connected PV string, shading is a critical factor to reduce the whole string PV output power [19]- [23]. Up to now, the partial shading problems are analyzed partly based on a few string conditions [24]- [26]. This paper presents study on performance analysis of a residential PV string under partial shading. The relation between number of MPPs and the amount of reduced power in PV string configuration by the shading effect is to be dealt with in general. In order words, this analysis contains how many MPPs occur and how much power would be lost while a PV string is under partial shading with different shading positions and different shading intensities.
In this paper, typical specification of a PV string system is introduced first for various case studies. Then, analysis of both power loss analysis and number of MPPs are presented under partial shading. Finally, PSIM simulation results are provided in order to verify the performance.

THE PROPOSED SYSTEM DESIGN
In this study, an analysis is performed when a shadow occurs in a single PV string system, which is a typical residential PV system configuration. In order to model a typical 3 kW class PV residential system as shown in Figure 1(a), a 360 W commercial PV module specification is selected for a component of PV string. In addition, it is assumed that eight PV modules are connected in series to make a typical residential PV string power as 2,880 W as shown in Figures 1(b) and 1(c). Quantitative specification for PV module and PV string are presented in Table 1. The study is based on comprehensive shading effects by shading positions and shading intensities as shown in Tables 2 and 3.  Firstly, after setting the shading intensity to 500 W/m 2 , the effect was compared and analyzed while changing the location of the shadow, as shown in Table 2. From A1 to A8, the shadow position was changed while the number of shadows was fixed at one. From A9 to A15, when a shadow occurred on two modules, the shadow was fixed on PV module #1, and the position of the remaining shadow module was changed from PV module #2 to #8. From A16 to A21, the shadow was fixed on both PV #1 and #2, and the remaining one was changed from PV #3 to PV #8. From A22 to A26, the shadow was placed on both PV #1 and #3, and the other one was changed from PV #4 to #8. Under the above conditions, according to the location where the shadow of the same intensity occurs in the PV string connected in series, the number of PV maximum power points (MPPs) and the generation loss are analyzed. Lastly, in order to analyze the effect of different shadow intensities generated from the residential solar string, the shadow intensity for cases B1 to B7 was set to have a difference of 100 W/m 2 from 900 to 300 W/m 2 . Then, the effect of when the shadows were sequentially generated from PV #1 to module #7 was comparatively analyzed.

RESULTS AND DISCUSSION
In this section, we analyze the power generation loss and the number of maximum power points by analyzing the voltage-current and voltage-power characteristic curves according to the location and intensity of the shadow in the solar string. If solar irradiance, temperature, power generation amount, solar output voltage and output current. Are measured in the field, it is possible to diagnose failures such as shadows in residential PV string and defective solar modules based on the data presented in this paper. Figures 2(a) to 2(d) shows the voltage-current characteristic curve when the shadow of the same intensity changes depending on the position in the PV string, under case A1 to A26. Figure 3 shows the voltage-power characteristic curve under the same conditions. Table 4 shows power loss analysis results by different shading positions for a PV string, including number of MPP, main information of local maximum power point (LMPP). The efficiency in Table 4 is defined as the ratio of output in LMPP to output in standard test condition (STC) 1,000 W/m 2 and 25 °.

Shading position effects
In cases A1 to A8 as shown in Figure 2(a), the shadow occurs in one module at 500 W/m 2 , but the location of the shadow is different for each module. One of the modules has a shadow intensity of 500 W/m 2 and the rest is 1,000 W/m 2 , indicating that the type of short-circuit current is divided into two. In Figure 2(b), two shadows occur with two kinds of intensity, and Figures 2(c) and 2(d) show that three shadows occur with two kinds of intensity. It can be seen that the same two short-circuit current type occurs. Figure 3 shows voltage-power characteristic curves for PV string under different shading positions. As shown in Figure 3(a), two different LMPPs are identified, and the larger value is called as global maximum power point (GMPP). From A1 to A8, GMPP is formed as 2,519 W at PV voltage 267 V. If the solar intensity is two types, it can be confirmed that the MPP is also two with the same PV voltage/current/power characteristic curves. In cases A9 to A15 as shown in Figure 3(b), shadows are generated on two modules at 500 W/m 2 , but the location of occurrence is different. Although the number of shaded PV modules increases compared to cases A1 to A8, the number of MPPs is also two because there are still two types of solar intensity. From A9 to A15, GMPP is formed as 2,159 W at PV voltage 229 V. In the same way, For the cases A16 to A26 as shown in Figures 3(c) and 3(d), the number of shaded PV modules increases to three, but the type of shadow intensity is constant as one 500 W/m 2 , so it can be seen that they have the same solar light characteristic curve and power generation characteristic, as shown in Figures 2 and 3. However, since the shadow intensity is applied differently for each module, it is important to look at the effect of shadows occurring in the PV string. This point will be explored in the next section.

Shading intensity effects
Multiple maximum power points are generated in the solar module through the bypass of the solar module in the condition where the shadow effect occurs. Analyzing the effect with a formula is as follows: If the shaded solar intensity is Irr_1, Irr_2, ..., Irr_n in descending order of magnitude, where Vpv,max, Irr_n is the voltage at the maximum power of a single PV module with shading intensity Irr_n, N is the number of series connected PV modules for PV string, Vpv,maxn is the voltage at the local maximum power of a PV string with shading intensity Irr_n, and Ipv,max,Irr_n is the current at the local maximum power of a PV string with shading intensity Irr_n. Ppv,max1, Ppv,max2, and Ppv,maxnP are the local maximum power point respectively under different shading intensities. Figure 4(a) to (f) shows the voltage-current characteristic curve when the intensity of the shadow in the solar string varies according to the position, Figure 5(a) to (f) shows the voltage-power characteristic curve. Table 5 shows the LMPPs and the tracking efficiency compared to the STC condition. In case B1, three types of solar intensity according to shadow are formed, and as shown in Figure 4(a), the resulting short-circuit current is divided into three types. Accordingly, as shown in Figure 5(a), three maximum power points were formed by three types of short-circuit current types. As shown in (6), the maximum power point voltage/current of the unit module in the solar radiation condition of 800 W/m 2 is connected in 8 series to form an LMPP. In the solar condition of 900 W/m 2 , the maximum power point voltage/current of the unit module is connected in 7 series to form LMPP, and Finally, the maximum power point voltage/current of the unit module in the solar radiation condition of 1,000 W/m 2 is 6 in series to form the LMPP. Among them, GMPP is formed with the largest value, and according to Table 5, among them, GMPP is 2,498 W, and the voltage at that time is 323 V.    In the same way, Figures 4(b) to 4(f) shows voltage-current characteristic curves for PV string under different shading intensities from cased B2 and B7, respectively. The number of maximum power points is determined according to the number of types of solar intensities from cases B2 to B7, as shown in Figures 5(b) to 5(f), respectively. GMPP is determined as the largest value among them in Table 5. Through the above analysis, it can be confirmed that the number of LMPPs is determined according to the number of types of solar intensity, and the largest value among them does not always exist at a constant position, and the position is determined as the largest value among LMPPs.

CONCLUSION
In this paper, a performance analysis on the effect of shadows in a residential solar system is presented. If the shadowed PV modules were generated with the same shadow intensity, it was confirmed that the number of LMPPs was the same regardless of the location of the shadow, and the related characteristic curves were also the same.
When the intensity of the shadow generated by each module of the solar string is different, the number of LMPPs was determined by the number of types of shadow intensity, and the largest value GMPP among them was not always presented at a certain shaded position. In this paper, it was verified that eight maximum power points were generated for eight solar intensities regardless of the location of the shadows under extreme conditions. Using the results of this paper as basic data, it is expected to be able to diagnose the cause of failures in PV string such as shadow effects or module defects.