# Design of a Portable Low-Cost I-V Curve Tracer for On-Line and In Situ Inspection of PV Modules

^{1}

^{2}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Principle of Operation

_{PH}is the photo-generated current, R

_{S}is the series resistance accounting for the voltage drop across the transport resistance of the solar cell, R

_{SH}is the shunt resistance representing the effect of leakage current in the p-n interface [24], n is the ideality factor of the diode, V

_{T}is the thermal voltage and I

_{0}is the saturation current. The I-V curve can be traced, connecting a variable load to the terminals of the PV generator, as schematized in Figure 1a. The operating point is given as the intersection between the I-V curve and the load curve (I = V/R), as graphically depicted in Figure 1b. Assuming that R is controlled by means of an external variable (V

_{EXT}), it is possible to trace the I-V characteristic from the short circuit current to the open circuit voltage by varying the value of R, ideally from 0 to infinity.

_{1}is PNP and Q

_{2}is NPN, Figure 2a), a resistive load R and a bias resistor R

_{BIAS}. The external variable V

_{EXT}, as shown in Figure 2b, used to control the load, is an analogue voltage applied to the base-collector of Q

_{1}.

_{1}and Q

_{2}are identical and working in the forward active region, V

_{EB}

_{1}can be considered equal to V

_{BE}

_{2}. Therefore, the external voltage V

_{EXT}is virtually applied across the load resistor R. Additionally, since the forward current gain of Q

_{2}is close to unity, I

_{E}

_{2}can be considered equal to I

_{PV}. From Equation (3), it can be inferred that the PV current is linearly controlled by V

_{EXT}.

_{EXT}is initially set to 0 to measure the open circuit voltage. Afterward, V

_{EXT}is increased in increments until the PV current gets saturated at its short circuit value (I

_{SC}). From Equation (3), it can be deduced that the sensitivity of the I-V curve tracer, expressed as $\partial {I}_{PV}/\partial {V}_{EXT}$, does depend on R. The typical I-V curve of a PV generator, presented in Figure 1b, exhibits two distinct regions, one characterized by a steep increase in the current with minimal voltage variation (the vertical branch from the open circuit point to the MPP) and one presenting a gradual increase in the current with large voltage variation (the horizontal branch from the MPP to the short circuit condition). Consequently, I-V curve tracing could result in an uneven distribution of the points along the characteristics, mainly concentrated in the vertical branch, and only a few points would be captured in the horizontal one.

_{EXT}

_{1}and V

_{EXT}

_{2}). Since Leg 2 provides a smaller current resolution compared to Leg 1 because $\u2206{I}_{2}=\u2206{I}_{1}/10$, Leg 1 can be exploited to capture the points in the vertical region of the I-V curve, whereas Leg 2 can be used to capture the points in the horizontal one. Moreover, since the power generated by the PV generator during the I-V tracing is fully dissipated in the circuit, the additional leg allows us to split the power dissipated by the transistors, thus mitigating the thermal stress. Additionally, the BJT are replaced with Darlington transistors to provide higher impedance and higher forward current gain.

_{SC}, the Darlington transistors enter the saturation region. For this reason, the proposed circuit is not able to impose the short circuit condition, because the minimum measured voltage across the PV generator is ${V}_{PV,min}=R{I}_{SC}+{V}_{CE,sat}$. To tackle this issue, the variable load proposed in Figure 2 is provided with an additional leg made of a power MOSFET with small ON resistance (in the range of few mΩ), thus providing a voltage, i.e., ${V}_{PV,min}={R}_{ON}{I}_{SC}$, closer to the short circuit condition.

#### 2.2. Device Implementation

#### 2.2.1. Disconnecting Circuit

_{DISC}and a bypass diode D

_{BYPASS}. The principle of operation is illustrated in Figure 4.

_{DISC}is ON, guaranteeing that the PV module under test is electrically connected to the string. In this phase, M

_{DISC}acts as an almost ideal short circuit, because its ON resistance is in the order of few mΩ and both D

_{BYP}and the variable load are inactive, guaranteeing that I

_{PV}is equal to the string current I

_{S}. At the start of the measurement, the control unit turns OFF M

_{DISC}to electrically isolate the PV module, thus forcing the activation of D

_{BYPASS}(Figure 4b). The bypass diode prevents the interruption of the I

_{S}by creating an unimpeded path around the isolated PV module. During this period, the string keeps producing power, which is only reduced by the bypassed module’s contribution. Since the measurement takes less than 1 s, the operating point of the string, usually handled by the inverter, is immediately recovered.

#### 2.2.2. Control Unit

- The START command is sent to the MCU from the remote controller.
- The MCU electrically disconnects the PV module under test by deactivating the disconnecting MOSFET (M
_{DISC}). - A preliminary measurement of V
_{OC}(V_{EXT}_{1}and V_{EXT}_{2}are set to 0 and M_{SC}is deactivated) and I_{SC}(V_{EXT}_{1}= V_{EXT}_{2}= 0 and M_{SC}is activated). - The MCU controller computes the current and voltage resolution as follows:$${\u2206I}_{PV}=\frac{{\u2206I}_{SC}}{N/2}\phantom{\rule{0ex}{0ex}}{\u2206V}_{PV}=\frac{{\u2206V}_{OC}}{N/2}$$
_{PV}corresponds to the minimum current distance between two consecutive operating points captured in the vertical branch of the I-V curve, and ∆V_{PV}corresponds to the minimum voltage distance between two consecutive operating points captured in the horizontal branch of the I-V curve. Equation 4 assumes a square-shaped I-V characteristic. - The MCU calculates the required voltage steps:$${\u2206V}_{EXT1}={\u2206I}_{PV}{R}_{1}\phantom{\rule{0ex}{0ex}}\u2206{V}_{EXT2}=\u2206{V}_{PV}$$
- The complete flowchart of the I-V sweeping is systematically described in Algorithm 1. The first data point inserted into the buffer, k = 0, is the V
_{OC}previously acquired. The MCU measures the second data point (k = 1) incrementing V_{EXT}_{1}and imposing V_{EXT}_{2}= 0, assuming that it lies on the vertical branch of the I-V curve. The next task is the identification of the I-V branch. The MCU calculates the slope at the actual operating points as follows:$$slope=\frac{{I}_{k-1}-{I}_{k}}{{V}_{k}-{V}_{k-1}}$$_{k}_{−1}; I_{k}_{−1}) is the data point acquired at the k − 1st iteration, whereas (V_{k}; I_{k}) is the data point acquired at the k-th iteration. The slope is compared to a threshold value, corresponding to the knee of the I-V curve, calculated as in [25]:$$knee=\frac{{I}_{SC}}{{V}_{OC}}$$

_{EXT}

_{1}(see line 15 in Algorithm 1). The measured data point is stored in the buffer if the distance in current from the previous acquired data is equal or greater than $\u2206{I}_{PV}$. By contrast, if slope < knee, the operating point lies on the horizontal branch and the MCU increments V

_{EXT}

_{2}(see line 13 in Algorithm 1). The measured data point is stored in the buffer if the distance in current from the previous acquired data is equal or greater than $\u2206{V}_{PV}$. If not, the point is discarded, and the measurement is repeated.

- 7.
- Once the measurement is completed, the MCU turns ON M
_{DISC}to restore the normal operation of the PV module under test. - 8.
- The data points are sent to the remote controller over the wireless link.

_{EXT}

_{1}and V

_{EXT}

_{2}, by means of a 12-bit double-channel digital to analogue converter (DAC) and measures the data points (voltage and current) through two independent 12-bit analogue to digital converter (ADC) channels working at 500 kS/s.

Algorithm 1. Flowchart of the I-V sweeping. | |

Pseudo-code of the Algorithm | |

1 | k = 1 |

2 | V_{EXT}_{1} = 0 |

3 | V_{EXT}_{2} = 0 |

4 | V [0] = V_{OC} |

5 | I [0] = 0 |

6 | WHILE k < N |

7 | IF k == 1 |

8 | V_{EXT}_{1}+ = ∆V_{EXT}_{1} |

9 | V_{EXT}_{2} = 0 |

10 | ELSE |

11 | COMPUTE $slope=\frac{I\left[k-1\right]-I\left[k\right]}{V\left[k\right]-V[k-1]}$ |

12 | IF slope < knee |

13 | V_{EXT}_{2}+ = ∆V_{EXT}_{2} |

14 | ELSE |

15 | V_{EXT}_{1}+ = ∆V_{EXT}_{1} |

16 | END IF-ELSE |

17 | END IF-ELSE |

18 | SEND V_{EXT}_{1} AND V_{EXT}_{2} TO DAC |

19 | RECEIVE V_{NEW} AND I_{NEW} FROM ADC |

20 | COMPUTE $\u2206{I}_{DIFF}={I\left[k-1\right]-I}_{NEW}$ |

21 | COMPUTE $\u2206{V}_{DIFF}={V}_{NEW}-V\left[k-1\right]$ |

22 | IF $\u2206{I}_{DIFF}\ge \u2206{I}_{PV}$ OR $\u2206{V}_{DIFF}\ge \u2206{V}_{PV}$ |

23 | V[k] = V_{NEW} |

24 | I[k] = I_{NEW} |

25 | k++ |

26 | END IF |

27 | END WHILE |

#### 2.2.3. Wireless Communication Module

#### 2.3. Experimental Setup

^{2}, 500 W/m

^{2}and 300 W/m

^{2}. Since the PV efficiency is significantly affected by the level of irradiance [27,28], these values are selected to provide a comprehensive understanding of the modules’ performance under high, medium and low illumination conditions, respectively. The set of PV panels comprises two free-standing bifacial N-type mono-Si PV modules, two flexible mono-Si PV modules of different power ratings, one flexible a-Si thin film PV module and one rigid poly-Si PV module, as labelled in Figure 6a. The ratings of the modules are reported in Table 1.

## 3. Results

#### 3.1. Prototype Design

_{OC}and I

_{SC}up to 40 V and 10 A, respectively, the proposed circuit solution can easily be extended to larger systems, such as PV strings, by replacing transistors with higher power ratings and selecting current and voltage sensors with the appropriate measurement range.

#### 3.2. Measured I-V Curves

^{2}, 500 W/m

^{2}and 700 W/m

^{2}. For each curve, three main electric parameters are extracted (V

_{OC}, I

_{SC}and P

_{MAX}), and the PV temperature as well as the environmental parameters are reported in Table 4. G

_{f}indicates the irradiance received on the front side of the PV modules, whereas G

_{b}represents the irradiance received on the back side of the bifacial PV modules.

_{OC}decreases whilst the level of irradiance decreases, except for the black curve. It is well known that the V

_{OC}has a strong negative dependence on the temperature and only a fair positive dependence on the solar irradiation. Consequently, the black curve shows a higher V

_{OC}compared to the red one due to the lower PV temperature (28 °C and 35 °C, respectively, as reported in Table 4).

_{0}= 0.3 mA) and shunt resistance (R

_{SH}= 30 Ω) indicate a reduction in the charge carriers’ extraction at the contacts of the silicon cells, as well as a significant amount of leakage current through the shunted paths across the PV cells.

## 4. Discussion

_{SC}. The utilization of a 70 MHz clock-speed MCU, along with two independent 12-bit ADC, enables the simultaneous acquisition of PV current and voltage. The data are digitally filtered during the acquisition thanks to a real-time moving average filter comprising 16 consecutive points, thus enhancing the signal-to-noise ratio (SNR) and avoiding post-processing delays. Consequently, our I-V tracer measures the I-V curve in less than 1 s, with high precision. The accuracy of the measurement, measured in terms of mean relative error and standard deviation, underscores the reliability of our I-V tracer. The prototype exhibits a maximum mean error of approximately 3% in mono-Si technology, demonstrating a remarkable alignment between the measured and theoretical data.

## 5. Conclusions

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

## References

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**Figure 1.**Principle of operation of an I-V curve tracer. (

**a**) Variable load controlled by means of external parameter (V

_{EXT}); (

**b**) sweeping of the operating points (in red) along the characteristics given as the intersection between the I-V curve of the PV generator and the load curves (black dashed lines) obtained at different R

_{k}values. The open circuit and short circuit points (in light blue) are obtained for R = ∞ and R = 0, respectively.

**Figure 2.**Circuit diagram of the developed I-V curve tracer. (

**a**) Basic schematic of the variable load; (

**b**) two legs variable load with additional branch for the short circuit measurement.

**Figure 4.**Principle of working of the disconnecting circuit. The grey color indicates the inactive components and the branches where no current is flowing. (

**a**) Normal operation of the PV module embedded into the string, i.e., the disconnecting circuit is inactive; (

**b**) during the measurement phase, the disconnecting circuit is active.

**Figure 7.**Physical layout of the developed I-V curve tracer. (

**a**) The implemented prototype; (

**b**) IP67-rated enclosure and connectors to PV module and PV string.

**Figure 8.**I-V curves of the N-type mono-Si bifacial PV modules under three nominal irradiance levels, namely 700 W/m

^{2}in blue, 500 W/m

^{2}in red and 300 W/m

^{2}in black, measured with our custom-made I-V tracers. (

**a**) Module #1 with the front side exposed to the sun; (

**b**) module #2 with the back side exposed to the sun. The ladder-shape curves are caused by the wires partially shadowing the exposed surface.

**Figure 9.**I-V curves of the mono-Si modules under three nominal irradiance levels, namely 700 W/m

^{2}in blue, 500 W/m

^{2}in red and 300 W/m

^{2}in black, measured with our custom-made I-V tracers. (

**a**) Module #1 with rated power 20 Wp; (

**b**) module #2 with rated power 100 Wp.

**Figure 10.**I-V curves under three nominal irradiance levels, namely 700 W/m

^{2}in blue, 500 W/m

^{2}in red and 300 W/m

^{2}in black, measured with our custom-made I-V tracers (solid lines) compared to the theoretical I-V curve in the same operating conditions (dashed lines). (

**a**) a-Si thin film PV module; (

**b**) Poly-Si PV module.

N-Type Mono-Si | Mono-Si | a-Si Thin Film | Poly-Si | |||
---|---|---|---|---|---|---|

#1 | #2 | A | B | |||

P_{rated} [W_{p}] | 415 | 20 | 100 | 100 | 120 | |

V_{OC} [V] | 37.67 | 21.6 | 22.5 | 23.75 | 22.0 | |

I_{SC} [A] | 13.95 | 1.1 | 5.75 | 5.5 | 7.93 | |

V_{MPP} [V] | 31.81 | 18.5 | 18.9 | 19.8 | 17.5 | |

I_{MPP} [A] | 13.05 | 0.7 | 5.29 | 5 | 6.98 | |

Efficiency [%] | 21.3 | 19.2 | 19.2 | 23 | 17 | |

T coefficient P_{MAX} [%/°C] | −0.30 | −0.44 | −0.44 | −0.2 | −0.5 | |

Bifaciality factor | 0.8 | - | - | - | - |

Description | Model | ||
---|---|---|---|

MCU | 16-bit, 70 MHz clock speed | DSPIC33EP256GM604-I-PT | |

Current Sensor | Hall-sensor IC | LEM HY 15-P | |

Voltage Sensor | Resistive voltage divider | - | |

DAC | 12-bit double-channel | MCP4822-E/MS | |

NPN Darlington | Leg 1 | 90 V, 50 A | MJ11032G |

Leg 2 | 100 V, 20 A | MJH6284G | |

PNP Darlington | 60 V, 4 A | BD678 | |

R_{1} | 1 Ω, 100 W | Ohmite TEH100M1R00FE | |

R_{2} | 10 Ω, 100 W | Ohmite TEH100M10R0FE | |

M_{SC} | 80 V, 120 A | PSMN2R8-80BS | |

M_{DISC} | 80 V, 120 A | PSMN2R8-80BS | |

D_{BYP} | 100 V, 30 A | VS-30CPQ100PBF | |

BT | - | LAIRD TECNOLOGIES BT740-SC | |

Battery | 3.7 V, 2050 mAh, 7.59 Wh | - |

Price (EUR) | |
---|---|

Proposed I-V tracer | 355.00 |

Amprobe Solar-600 | 2048.05 |

RS ISM 490A | 1261.63 |

Seaward PV200 | 1720.80 |

DS-100C | 5298.22 |

G_{f} [W/m^{2}] | G_{b} [W/m^{2}] | T_{AMB} [°C] | T_{PV} [°C] | V_{OC} [V] | I_{SC} [A] | P_{MAX} [W] | ||
---|---|---|---|---|---|---|---|---|

N-type mono-Si | #1 | 710 | 120 | 26 | 38 | 36.35 | 9.76 | 283.5 |

502 | 101 | 24 | 35 | 35.69 | 7.09 | 204.2 | ||

303 | 80 | 21 | 28 | 36.01 | 4.18 | 121.76 | ||

#2 | 709 | 119 | 26 | 38 | 36.01 | 8.13 | 208.2 | |

502 | 101 | 24 | 35 | 35.15 | 5.80 | 126 | ||

320 | 82 | 21 | 28 | 35.60 | 3.48 | 60.2 | ||

Mono-Si | A | 711 | - | 26 | 39 | 19.94 | 0.24 | 2.95 |

502 | - | 24 | 38 | 19.42 | 0.17 | 1.65 | ||

299 | 21 | 31 | 18.49 | 0.10 | 0.59 | |||

B | 711 | - | 26 | 39 | 20.65 | 3.81 | 44.79 | |

510 | - | 24 | 37 | 20.29 | 2.71 | 30.09 | ||

312 | - | 21 | 31 | 19.94 | 1.65 | 20.59 | ||

a-Si thin film | 699 | - | 26 | 38 | 22.62 | 3.82 | 62.25 | |

510 | - | 24 | 35 | 22.45 | 2.82 | 45.58 | ||

305 | - | 21 | 28 | 22.17 | 1.63 | 27.75 | ||

Poly-Si | 700 | - | 26 | 39 | 21.04 | 5.99 | 88.94 | |

510 | - | 24 | 35 | 20.67 | 4.32 | 63.05 | ||

305 | - | 21 | 28 | 20.00 | 2.58 | 36.58 |

Bifacial N-Type Mono-Si | Mono-Si | a-Si Thin Film | Poly-Si | |||
---|---|---|---|---|---|---|

#1 | #2 | A | B | |||

Mean [%] | 0.94 | 1.69 | 2.13 | 3.04 | 1.28 | 0.38 |

Standard Deviation [%] | 5.14 × 10^{−15} | 0.16 | 0.25 | 0.41 | 0.15 | 0.045 |

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## Share and Cite

**MDPI and ACS Style**

De Riso, M.; Dhimish, M.; Guerriero, P.; Daliento, S.
Design of a Portable Low-Cost I-V Curve Tracer for On-Line and In Situ Inspection of PV Modules. *Micromachines* **2024**, *15*, 896.
https://doi.org/10.3390/mi15070896

**AMA Style**

De Riso M, Dhimish M, Guerriero P, Daliento S.
Design of a Portable Low-Cost I-V Curve Tracer for On-Line and In Situ Inspection of PV Modules. *Micromachines*. 2024; 15(7):896.
https://doi.org/10.3390/mi15070896

**Chicago/Turabian Style**

De Riso, Monica, Mahmoud Dhimish, Pierluigi Guerriero, and Santolo Daliento.
2024. "Design of a Portable Low-Cost I-V Curve Tracer for On-Line and In Situ Inspection of PV Modules" *Micromachines* 15, no. 7: 896.
https://doi.org/10.3390/mi15070896