A simplified method for fault detection and identification of mismatch modules and strings in a grid-tied solar photovoltaic system

1 Introduction

The generation of power in a photovoltaic (PV) system depends on the condition of the PV arrays and wiring connections, environmental conditions of site such as temperature and availability of solar radiation, and failures or faults that may occur during its operation [1]. The PV systems can be classified as PV array faults, faults in power converters and faults in interconnections of utility grid based on the location of faults. The identification of faults in PV arrays is difficult and have catastrophic effects in the entire system as explained in [2], [3], [4]. The PV array faults such as open-circuit faults, Line-Line (LL) faults, Line-Ground (LG) faults, arc faults and mismatch faults causes significant power loss in the PV system. The installations of PV systems worldwide follow the protection standards as stated in U.S. National Electric Code (NEC) or International Electro-Technical Commission (IEC) to use Over-Current Protection Device (OCPD) and Ground Fault Protection Device (GFPD) for detection and clearing of short-circuit faults like LL and LG faults respectively. But due to the operation of Maximum Power Point Tracking (MPPT), blocking diodes in the PV system and environmental conditions, conventional OCPD and GFPD often fail to detect LL fault in particular for most of the cases. Hence, the researchers have discussed various protection challenges in solar PV systems and also developed a fault detection method for LL faults only as in [5], [6], [7]. Further Outlier detection rules as mentioned in [8], [9] are developed based on measurement of instantaneous string current to identify the faults in PV system. The fault detection methods also developed based on the digital twin approach [10], and based on the magnitudes and changing pattern of first and last module voltages in each string [11]. Further, A. F. Murtaza et al. [12] used the measured incoming and outgoing current data from each string to identify the PV faults. However, all these methods require more number of sensors, controllers and additional hardware setups. Hence, the overall cost and complexity of the system increased.

The fault identification method given in [13] uses machine learning techniques like graph-based semi-supervised learning to classify the faulty operating conditions. Akram, M. N., and Lotfifard, S. [14] developed a Probabilistic Neural Network (PNN) method to detect the faults in PV system. The PNN method uses manufacturer’s datasheet values to build a correlation among the ideality factor and series resistance with temperature respectively which helped in the identification of faults. The detection methods in [8], [13] require voluminous data of the PV array, and the specific design of PV plant installation, which are quite non-feasible, and have limited applications in case of large PV systems. Further the authors have proposed a method using comparison between the values of measured and AC output power through model prediction in order to identify the faults in PV system [15], [16]. Hu, Y. et al. [17] proposed a method to optimize the placement of voltage sensor to identify faults. It was found that integrating sensors with the available power converters in the PV market were a very tough task. Hariharan, R. et al. [18] proposed a method using two variables such as array losses and gamma, which calculate the difference in power losses of the PV array and instantaneous ratios of power by irradiation in order to detect LL faults and also for PSC (partial shaded condition). For the calculations of the aforementioned variables, the PV system was observed for the values of current, voltage and insolations. Further the authors used a change in MPP values and dissimilarity in voltage and power ratios respectively to detect faults [19], [20]. Yi, Z. and Etemadi, A. H. [21] employed a technique called Multi-resolution Signal Decomposition (MSD) and fuzzy inference system to detect whether a fault has happened or not in the PV system. Chen, L. et al. [22] employed an Auto Regressive (AR) model to measure time correlation in the output signals of PV system to describe the faulty signal. Kumar, B. P. et al. [23] proposed a method to identify faults based on the observed current and voltage data points of PV array using Wavelet Packet Transforms (WPTs) technique. The WPT technique requires expensive software/hardware platforms and also it is difficult to integrate with the existing systems.

Roy, S. [24] developed a new technique like Spread Spectrum Time Domain Reflectory (SSTDR) based on variation in impedance during faults to detect LG faults. It has a problem like the assessment of results had done on a baseline which depends on the number of strings present in the PV system and also the location of fault from the device. Pillai, D. S. et al. [25] developed a method to detect the faults using the existing P&O MPPT tracking operation. This method does not require any sensors during the detection process. The developed method considers the effects of varying temperatures and irradiances. However it excludes the effects of blocking diodes used in PV system during the faults. The comparative assessment of various existing fault detection approaches in PV systems is given in [26]. The fault detection methods existing so far developed using various parameters and techniques are able to detect mainly LL fault and PSC only. After a detailed literature survey, the authors have identified the following one or more problems in fault detection algorithms: (i) Problem in segregating the faults and partial shading conditions, (ii) Lack of compatibility with the existing MPPT methods, (iii) Necessity of added hardware and/or sensors, (iv) Ample data requirement, (v) Energy loss due to the fault detection with insufficient data about number of faulty modules and strings.

Hence, to address the above mentioned problems, the proposed method has developed with the following contributions: (i) PV array fault detection for dynamic change in irradiation, (ii) Identifying and segregating the faults between the LL and partial shading conditions, (iii) Status of PV array with type of fault such as LL or PSC, (iv) Number of mismatch modules (or Short circuited bypass diodes), (v) Number of mismatch strings (or Open circuited blocking diodes), (vi)Avoided additional requirement of sensors and hardware requirement, (vii) Compatible with existing MPPT methods.

This paper presents a new detection method which works in two phases. In the first phase, it detects the type of fault using three variables, namely gamma (γ) for LL fault detection and relative change in irradiation (G_r) and array losses (Lar) for PSC. In the second phase, it finds the number of mismatch modules and mismatch strings after L-L fault is detected in the PV system.

The organization of the paper as follows: Section 3 discusses the analysis of faults with and without blocking diodes in grid-connected PV system. Section 4 elaborates the analysis of the proposed method with methodology to find the faults and partial shade conditions and also with the methodology to find the number of mismatch modules and strings. Section 5 illustrates the algorithm and flowchart of the proposed method. Section 6 depicts the discussion about the experimental and simulations results with comparative assessment. Finally, the briefings of the investigations are given in Section 7.

2 Mathematical modeling of PV cell

The mathematical model used for a PV cell design in MATLAB/simulink is developed using equations as given in [27]. The specifications of the PV module used in MATLAB/simulink are given in Table 1.

3 Fault analysis in grid connected PV system

3.1 Analysis of faults with and without blocking diodes

The faults in PV system occur at various locations such as PV array, power converter and utility grid. The PV array faults such as LL faults occur between string one and string two of the PV system as shown in Figure 1(a).

Figure 1:

(a). Grid-connected PV System without blocking diodes under fault. (b). I-V Characteristic curve without blocking diodes under fault.

Figure 1(b) shows the Current versus Voltage (I-V) characteristic curve of the PV system without blocking diodes and its string current at prefault and postfault conditions along with the fault current (I_F). It is observed from Figure 1(a) and Figure 1(b) that a L-L fault reverses the flow of current through the faulty string. The faulty string generates a I_F between the points F₁ and F₂, while the other healthy string generates a back or reverse current (I_REV) that flows into the faulty string.

From Figure 1(b), it is observed that the I_F at the instant of fault is almost twice the short-circuit current of the string at prefault condition and hence it can be easily detected by the OCPDs used in the PV system. The grid-connected PV system with blocking diodes under fault condition is shown in Figure 2(a). The I-V characteristic curve of the PV system with blocking diodes and string current at prefault and postfault conditions along with the I_F is as shown in Figure 2(b). The faulty string generates a I_F between the points F₁ and F₂, while the back or I_REV generated by the other healthy string is blocked by the blocking diode from flowing into the faulty string.

Figure 2:

(a). Grid-connected PV System with blocking diodes under fault. (b). I-V Characteristic curve with blocking diodes under fault.

The instant I_F is almost equal to the short-circuit current of the string at prefault state as shown in Figure 2(b), because the I_REV is blocked with the blocking diodes. Hence, the I_F does not meet the threshold current of OCPDs and thus the fault remains undetected in the PV system. Moreover, the MPPT operation of the power converter often changes the operating point to a new position on the I-V characteristic curve such that the I_F magnitude decreases over the time. If the L-L fault occurs under low irradiation conditions such as during sunrise or sunset, the I_F through the affected strings is found to be not large enough to meet the threshold limit of the OCPDs, and thus the fault remains undetected.

4 Analysis of the proposed method

4.1 Methodology to find LL fault and partial shade conditions

The Grid-connected PV system with various types of faults is as shown in Figure 3. To understand the effects of L-L faults and PSC in a Grid-connected PV system, it is designed with the specifications of the individual PV module as given in Table 1 and simulated in MATLAB/simulink.

Figure 3:

Grid-connected PV System with various types of faults.

The Power versus Voltage (P-V) and I-V characteristic curves at prefault and postfault conditions at Standard Testing Conditions (STC) as Temperature (T) of 25 °C and irradiance (G_O) of 1000 W/m² are shown in Figure 4. It is observed that the postfault power of the PV system at the Maximum Power Point (MPP) is less than that of the prefault power which is found to be equal to 91.6 W. To measure the instantaneous change in the power due to fault, a variable Gamma (γ) is used which is defined as ratio of the instantaneous power of the PV system to the instantaneous irradiation falling on the PV system with a unit of m².

(1)Gamma(γ)=PPVG=VPV×IPVG

Figure 4:

P-V and I-V characteristic curves at prefault and postfault conditions.

Based on the P-V characteristic curve in Figure 4 and using Equation (1), the threshold value for the change in gamma (γ) is taken as 0.09 m². The least power loss occurs from a PV system when atleast one of the modules in PV system is partially shaded. Therefore to understand the effects of partial shading, only one module of the designed Grid-connected PV system has been shaded as shown in Figure 3. The corresponding P-V and I-V simulation characteristic curves of the PV system with one module partial shade condition with three different irradiations are as shown in Figure 5.

Figure 5:

P-V and I-V curves of the PV system under various partial shaded conditions (PSC).

The least power drop in a PV system caused during LL fault with one module mismatch has been excluded the effect of PSC. Based on the P-V and I-V curves of the PV system as shown Figure 5, the value of gamma and the change in value of gamma is calculated for each PSC from the prefault to postfault condition as given in Table 2.

(2)Change in Gamma (Δγ)=Prefault value of gamma–Postfault value of gamma

Table 2:

Gamma and change in gamma for various PSCs.

PSC	Gamma (γ)	Change in gamma
I	0.249 m2	0.054 m2
II	0.183 m2	0.12 m2
III	0.207 m2	0.096 m2

For low irradiation condition of below 400 W/m² as given Table 2, the PV system power loss is almost same as that of one module-mismatch.

Therefore, it is important to find a way to detect whether the power loss is due to PSC or LL fault. To detect the partial shading condition, two variables are used namely, approximate array losses (Lar) and G_r.

Approximate array loss (Lar) is derived as the difference between the estimated power and actual power of the PV array and it has a unit of Watt.

(3)Estimated Power(Pestimated)=Maximum Power×Instantane ous IrradiationIrradiation at STC=Pm×GGO

(4)Actual Power(Pactual)=PPV=VPV×IPV

(5)Approximate array losses(Lar)=Pestimated–Pactual=Pm×GGO−(VPV×IPV)

G_r is derived as the ratio of the difference in irradiation at STC and instantaneous irradiation to the irradiation at STC and it is unit less, which is expressed as:

(6)Relative change in irradiation(Gr)=Irradiation at STC−Instantaneous IrradiationIrradiation at STC=GO−GGO

Based on the P-V and I-V characteristic of the PV system from Figure 5, the value of approximate array loss (Lar) and G_r are calculated for different cases as given in Table 3. In each case, the maximum power from the P-V curve is taken as actual power of the PV system.

Table 3:

Lar and G_r for various PSCs.

PSC	Approximate array loss (Lar)	Relative change in irradiation (Gr)
I	38.69 W	0.05
II	89.55 W	0.1
III	50.46 W	0.15

1. G_r, Relative change in irradiation; Lar, Approximate array loss; PSCs, partial shaded conditions

From Table 3, it is observed that the approximate array loss (Lar) in PSC II is almost same as that of LL fault with one module mismatch but the G_r is found to be almost zero. Thus, the two variables together are used to identify whether the power loss in a PV system is due to the partial shading or not. The constant parameters used to find LL fault and partial shade conditions are derived from the above equations as given in Table 4. Based on the PV system condition and type of faults, the statuses of the faults are denoted as mentioned in Table 5.

Table 4:

Constant parameters used to find LL fault and partial shade conditions.

Parameters	Formula used	Value
ε1	Least value of Gr	0.05
ε2	80% of least value of Lar	30.95 W
ε3	−(Threshold value for the change in gamma (γ) in one module mismatch under LL fault)	−0.09 m2

Table 5:

Status of PV System fault.

PV system condition	Status of PV system fault
Normal operating condition (STC)	0
Line-line fault	1
Partial shaded condition (PSC)	2

4.3 Effect of mismatched modules and strings in PV Array under LL fault

It is observed that the drop in the value of voltage during LL fault is almost equal to the product of the number of mismatched modules and the open-circuit voltage of one PV module. Similarly the drop in current on the onset of fault is found to be equal to the product of the number of mismatched strings and the short-circuit current of one PV module. To analyse the above mentioned condition, a PV array of 5 × 4 is designed using the specification of PV module mentioned in Table 1 and simulated for different cases of mismatched modules and strings in the following two ways.

1. String-mismatch is kept constant while varying modules mismatches and the I-V Characteristic curves obtained for each case as depicted in Figure 6.

2. Module-mismatch is kept constant while varying strings mismatches and the I-V Characteristic curves obtained for each case as depicted in Figure 7.

Figure 6:

I-V Characteristic curves of the PV System with varying module-mismatches while keeping string-mismatch constant at (a) One string-mismatch, (b) Two string-mismatches, (c) Three string-mismatches and (d) Four string-mismatches.

Figure 7:

I-V Characteristic curves of the PV System with varying string-mismatches while keeping module-mismatch constant at (a) One module-mismatch, (b) Two module-mismatches, (c) Three module-mismatches, (d) Four module-mismatches and (e) Five module-mismatches.

Based on the obtained I-V characteristic curves for all cases, the drops in voltage and current are calculated in order to find the number of mismatch modules and number of mismatch strings using the following formulae.

(7)Voltage drop(Vk)=Open-circuit voltage of the PV system(VocSYS)–Instantaneous PV system voltage(VPV)

(8)Number of mismatch modules(n)=Voltage Drop(Vk)Open-circuit voltage of one module(Vocm)

(9)Error in the value of number of mismatch modules(e1)=n–round of n

(10)Current drop(Ik)=Short-circuit current of the PV system(IscSYS)– Instantaneous PV system current(IPV)

(11)Number of mismatch strings(m)=Current Drop(Ik)Short-circuit current of one module(ISCm)

(12)Error in the value of number of mismatch strings(e2)=m–round of m

The obtained results from the calculations given in Table 6 help in deriving the range of approximate error values of e₁ and e₂ for finding the number of mismatch modules and number of mismatch strings in the grid-connected PV system. The calculated errors e₁ and e₂ have not considered the effect of MPPT tracker operation in its calculations. Thus, the designed PV system is simulated with MPPT tracker using P&O method in MATLAB/Simulink. It is observed that the effect of MPPT operation, changes the error e₁ to ± 0.5 while the error e₂ remains almost same as given in Table 4. Based on the calculations as given in Table 6 and simulations results as given Figure 6 and Figure 7, the corrected range of error values εr₁ and εr₂ are derived for finding the number of mismatch modules and strings in the grid-connected PV system as given in Table 7.

Table 6:

Calculated values obtained from the I-V characteristics of Figure 6 and Figure 7.

Strings mismatch	Modules mismatch	Vk (V)	N	e1	Ik (A)	m	e2
1	1	21.509	1.005	0.005	4.050	1.250	0.250
	2	42.960	2.007	0.007	3.601	1.111	0.111
	3	64.358	3.007	0.007	3.474	1.072	0.072
	4	85.847	4.012	0.012	3.193	0.985	−0.015
	5	106.224	4.964	−0.036	3.236	0.999	−0.001
2	1	21.520	1.006	0.006	6.966	2.150	0.150
	2	42.901	2.005	0.005	6.722	2.075	0.075
	3	64.341	3.007	0.007	6.583	2.032	0.032
	4	85.747	4.007	0.007	6.500	2.006	0.006
	5	106.224	4.964	−0.036	6.472	1.998	−0.002
3	1	21.463	1.003	0.003	9.950	3.071	0.071
	2	42.888	2.004	0.004	9.787	3.021	0.021
	3	64.294	3.004	0.004	9.755	3.011	0.011
	4	85.733	4.006	0.006	9.558	2.950	−0.050
	5	106.224	4.964	−0.036	9.708	2.996	−0.004
4	1	21.418	1.001	0.001	12.936	3.993	−0.007
	2	42.833	2.002	0.002	12.942	3.995	−0.005
	3	64.250	3.002	0.002	12.943	3.995	−0.005
	4	85.668	4.003	0.003	12.943	3.995	−0.005
	5	106.224	4.964	−0.036	12.943	3.995	−0.005
1	1	21.509	1.005	0.005	4.050	1.250	0.250
2		21.520	1.006	0.006	6.966	2.150	0.150
3		21.463	1.003	0.003	9.950	3.071	0.071
4		21.415	1.001	0.001	12.941	3.994	−0.006
1	2	42.960	2.007	0.007	3.601	1.111	0.111
2		42.901	2.005	0.005	6.722	2.075	0.075
3		42.888	2.004	0.004	9.787	3.021	0.021
4		42.833	2.002	0.002	12.943	3.995	−0.005
1	3	64.358	3.007	0.007	3.474	1.072	0.072
2		64.341	3.007	0.007	6.583	2.032	0.032
3		64.294	3.004	0.004	9.755	3.011	0.011
4		64.252	3.002	0.002	12.937	3.993	−0.007
1	4	85.847	4.012	0.012	3.193	0.985	−0.015
2		85.747	4.007	0.007	6.500	2.006	0.006
3		85.733	4.006	0.006	9.558	2.950	−0.050
4		85.668	4.003	0.003	12.942	3.995	−0.005
1	5	106.224	4.964	−0.036	3.236	0.999	−0.001
2		106.224	4.964	−0.036	6.472	1.998	−0.002
3		106.224	4.964	−0.036	9.708	2.996	−0.004
4		106.224	4.964	−0.036	12.943	3.995	−0.005

Table 7:

Constant parameters used to find the number of mismatch modules and strings.

Parameters	Minimum value	Maximum value
εr1	−0.5	0.5
εr2	−0.05	0.25

5 Proposed fault detection method for grid connected PV system

Based on the analysis given in Section 4, a new fault detection method is developed to know the number of mismatch modules (or short-circuited bypass diodes) and mismatch strings (or open-circuited blocking diodes) along with the status of L-L fault and PSC. Hence, it can differentiate whether the power drop in PV system is due to PSC or LL fault. Further, the power loss can be estimated by knowing the number of mismatch modules and strings in PV system. The detailed step by step approach of the proposed fault detection method is given with an algorithm in Section 5.1 and it is illustrated with flow chart as given in Figure 8. The derived error values from the calculations as given in Table 4 and Table 5 are used in the proposed detection method. Further the fault status representation using the proposed detection method is given in Table 6.

Figure 8:

Flowchart for the proposed method to detect faults in PV system.

6 Results and discussions

The small scale PV grid connected experimental set-up as shown in Figure 9 is used to validate the MATLAB/Simulink simulation results. For better validation of the proposed method, the PV modules with the specifications as given in Table 8 are used in the experimentation, which are close to the PV modules with the specifications as given in Table 1 used in MATLAB/Simulink simulations. The grid-tied inverter incorporates the Perturb & Observe (P&O) MPPT algorithm. The specifications of grid-tied inverter are given in Table 9. The PV array by 3 × 2 modules in series-parallel connections is used for experimentation and also for MATLAB/Simulink simulation. The specifications of each PV module and its corresponding accessories are shown in Table 8. The halogen lamps are used to create the artificial light source on PV modules. The light intensity on PV modules is controlled from 976.13 to 626.23 W/m² using the halogen regulator to create the partial shade conditions. The toggle switches are used to create the required faults by connecting lines between the strings and modules as performed in MATLAB/Simulink simulations. The faults are created at 12 h 04 min in experimentation by turn ON/OFF switches for all type faults considered in this work. The Data Acquisition Unit is used to record the necessary data from PV array.

Figure 9:

Experimental set-up of the PV system.

The proposed method to know the number of mismatch modules (or short-circuited bypass diodes) and mismatch strings (or open-circuited blocking diodes) along with the status of L-L fault and PSC are tested with MATLAB/Simulink simulations and also on small scale laboratory developed grid connected PV system for four different fault conditions in grid-connected PV system as given in Figure 3. Further, the discussions on corresponding simulation and experimental results have been discussed in Case 1 to Case 4. The comparative assessment of the proposed method is given in Table 10 to shows the advantages over the existing methods by finding the number of mismatch modules and mismatch strings in grid-connected PV system.

Figure 10:

LL fault with one module-mismatches and one string-mismatch.

• The value of γ keeps on changing gradually till it settles to a value at the prefault state. However, when fault occurs in the PV system, γ drops sharply from 0.303 to 0.151 m² in simulation and 0.220–0.08 m² in experimentation. Thus, the change in γ occurrence in simulation and experimentation at the moment of fault is found to be 0.152–0.14 m² respectively. This is more than the prescribed threshold value of 0.09 m². Then the change in γ after the instant of fault reduces to a value of 0.0918 m² with respect to the prefault value of 0.303 m² which is also greater than 0.09 m².

• There is a sudden drop in the PV system current and then it gradually restores to its previous value.

• There is a sudden drop in PV power at the instant of fault, then it gradually restores to a low power value of 211.5–172 W both in simulation and experimentation respectively.

Figure 11:

LL fault with two module-mismatches and one string-mismatch.

• The value of γ initially keeps on changing gradually till it settles to a value before the occurrence of fault. At the moment of fault, γ drops suddenly from 0.303 to 0.1 m² and 0.235–0.1 m² in both simulation and experimentation respectively. Therefore the net drop in gamma is 0.203–0.135 m² respectively which is much greater than 0.09 m². It is observed that the change in the value of γ is settle at a value which is also found to be greater than the threshold value for the change in γ i.e., 0.09 m².

• After the occurrence of fault, the PV system current shows a sudden drop at the instant of fault and afterwards it follows a low value of current around 3.3 and 3.2 A both in simulation and experimentation respectively.

Figure 12:

LL fault with one module-mismatch and two string-mismatches.

Figure 13:

Partial shaded condition.

7 Conclusions

The proposed method with a systematic approach had successfully detected and differentiated the faults and partially shaded conditions by providing the status with type of the fault. Further, it also found the number of mismatch modules (or short-circuited bypass diodes) and mismatches strings (or open-circuited blocking diodes) under various mismatches conditions in Grid-connected PV system for dynamic change in irradiation. It can be easily incorporated in existing PV systems with conventional algorithms for MPPT such as P&O method without additional sensors, significant data, and hardware equipment. The theoretical performance had been validated with MATLAB/simulink simulations and small scale grid-connected PV systems developed in the laboratory. The results demonstrate the importance of the proposed algorithm by finding the number of mismatch modules (or short-circuited bypass diodes) and mismatch strings in grid-connected PV system. The proposed concept with experimental validation helps us to extend our work in future to find out the location of the faults/mismatch modules and strings in the large scale PV system.