Qualification of Photovoltaic Micromodules via Time-Domain Reflectometry Signature Testing for Energy-Harvesting Applications: A Novel Methodology

1. Introduction

Despite the maturity of qualification and inspection methodologies for conventional photovoltaic modules, PV micromodules remain outside the scope of current regulatory frameworks. Brazilian standards governing photovoltaic qualification, such as INMETRO Regulation No. 140, apply exclusively to devices with rated power above $5\mathrm{Wp}$. Consequently, there is a regulatory and scientific gap concerning performance, reliability, and environmental behaviour of low-power photovoltaic components, particularly in Internet of Things (IoT) applications [1,2,3,4]. This gap becomes critical given that micromodules are increasingly deployed as energy harvesting sources in environments characterised by severe power constraints, intermittent illumination, and stringent miniaturisation requirements. To address this scenario, this work proposes an innovative qualification methodology for crystalline silicon photovoltaic micromodules based on Time-Domain Reflectometry (TDR) as a high-resolution electrical characterisation tool [5,6,7]. The methodology consists of extracting the electrical signature of micromodules using the reflected parameter $S_{11}$ obtained from vector network analysers (VNAs), and employing this signature to detect structural alterations, internal defects, and degradation effects associated with natural or accelerated ageing mechanisms.

The proposed strategy relies on establishing reference electronic signatures for devices classified as healthy, enabling the construction of pass/fail electronic masks. These masks act as tolerance windows to monitor statistically significant variations in the TDR response of tested devices. It is assumed that any relevant structural, electrical, or material modification — arising from latent defects, microcracks, corrosion, delamination, or environmental stress — will induce detectable changes in the measured reflection signature. Furthermore, accelerated ageing tests including salt mist exposure, damp heat cycling and thermal cycling were conducted to induce multiple degradation mechanisms in the samples. These controlled stress experiments enable the evaluation of how the electronic signature evolves under environmental loading and allow correlating specific degradation modes to distinctive patterns observed in the TDR measurements. Finally, this work presents the TDR mask methodology as a precise, reliable, and innovative tool for the qualification of photovoltaic micromodules within laboratory environments.

2. Time-Domain Reflectometry Using VNA Scattering Parameters: Theory and Methodology

Time-Domain Reflectometry (TDR) is a measurement technique originally developed for detecting impedance discontinuities along transmission lines in telecommunications. When transferred to photovoltaic micromodules, TDR provides a purely structural electrical characterization, enabling early detection of damage and degradation mechanisms that manifest as impedance perturbations [8,9,10].

Although TDR is conceptually a time-domain method, modern implementations rely on frequency-domain data acquired by Vector Network Analyzers (VNAs) [11,12,13,14,15,16]. Therefore, the reflectometry waveform must be numerically reconstructed from the measured scattering parameter $S_{11}\left(f\right)$.

2.1. Acquisition of Frequency-Domain Data

A Vector Network Analyzer measures the complex scattering parameters $S_{ij}\left(f\right)$ of a device under test (DUT), relating incident $\left(a_i\right)$ and reflected $\left(b_i\right)$ waves at port i according to (1),

$$b_i=\sum _j{S}_{ij}\left(f\right)a_j$$

(1)

Where $S_{11}\left(f\right)$ quantifies the fraction of the injected energy reflected back to the source. The measurement is performed at discrete, uniformly spaced frequencies as (2),

$$f_k=f_0+k\Delta f,\Delta f=f_{k+1}-f_k.$$

(2)

Uniform spacing is a fundamental prerequisite for inverse Fourier transformation. When the DC term is not measured, it is extrapolated as (3),

$$S_{11}\left(0\right)\approx S_{11}\left(f_1\right)$$

(3)

2.2. Transformation to Time Domain

TDR reconstruction follows directly from the inverse Fourier transform [11], expressed in continuous form as (4),

$$s_{11}\left(t\right)={\mathcal{F}}^{-1}\left\{S_{11}\left(f\right)\right\}={\int }_{-\infty }^{+\infty }{S}_{11}\left(f\right)e^{j2\pi ft}df$$

(4)

Where $s_{11}\left(t\right)$ represents the reflection in the time domain.

In discrete form, due to sampling at N frequencies, the inverse discrete Fourier transform (IDFT) is used (5) and with the associated temporal grid as (6),

$$s_{11}\left[n\right]={\displaystyle \frac{1}{N}}\sum _{k=0}^{N-1}{S}_{11}\left[k\right]e^{j2\pi \frac{kn}{N}}$$

(5)

$$\begin{array}{cccc}\hfill F_s& =\Delta f·N_{\mathrm{FFT}};\Delta t\hfill & \hfill ={\displaystyle \frac{1}{F_s}};t_n& =n\Delta t\hfill \end{array}$$

(6)

Where $N_{\mathrm{FFT}}=2^m$ ensures efficient FFT computation.

To obtain a real-valued waveform, the Hermitian spectrum is formed by concatenating the measured positive-frequency branch (7) with the complex-conjugate mirrored negative branch (8), yielding the composite spectrum (9),

$$\begin{array}{cc}\hfill & \{S_{11}^{\left(w\right)}\left(f_0\right),\dots ,S_{11}^{\left(w\right)}\left(f_{N-1}\right)\},\hfill \end{array}$$

(7)

$$\begin{array}{cc}\hfill & \{\overline{S_{11}^{\left(w\right)}\left(f_{N-2}\right)},\dots ,\overline{S_{11}^{\left(w\right)}\left(f_1\right)}\},\hfill \end{array}$$

(8)

$$\begin{array}{cc}\hfill & \mathcal{S}=[S_{11}^{\left(w\right)}\left(f_0\right),\dots ,S_{11}^{\left(w\right)}\left(f_{N-1}\right),\overline{S_{11}^{\left(w\right)}\left(f_{N-2}\right)},\dots ,\overline{S_{11}^{\left(w\right)}\left(f_1\right)}]\hfill \end{array}$$

(9)

Spectral leakage—ringing due to finite acquisition bandwidth—is mitigated by windowing by (10),

$$S_{11}^{\left(w\right)}\left(f_k\right)=w\left[k\right]S_{11}\left(f_k\right),$$

(10)

Where $w\left[k\right]$ may be rectangular, Hann, Hamming, Blackman or Kaiser [16]. In this work, rectangular windowing is adopted so as not to broaden features in the reconstructed impedance profile.

2.3. Impedance Reconstruction and Interpretation

Reflectometry traces are expressed in terms of the instantaneous reflection coefficient as show in (11), from which the distributed impedance profile is obtained through (12). In practice, the real component is used (13) is used as the basis for comparison,

$$\mathsf{\Gamma }\left(t\right)=\mathrm{IFFT}\left\{\mathcal{S}\right\}$$

(11)

$$Z\left(t\right)=Z_0{\displaystyle \frac{1+\mathsf{\Gamma }\left(t\right)}{1-\mathsf{\Gamma }\left(t\right)}}{Z}_0=50\mathsf{\Omega }.$$

(12)

$$Z_{\mathrm{real}}\left(t\right)=\Re \left\{Z\left(t\right)\right\}$$

(13)

Multiple reflections and localized impedance shifts correspond to temporal peaks and valleys, each mapped to a physical feature of the micromodule (busbar, cell fragments, interconnects).

Finite-width excitation pulses used by VNAs broaden reflections, where spatial resolution obeys (14),

$$\Delta d\approx {\displaystyle \frac{v_p\tau }{2}}$$

(14)

With $v_p$ being the propagation velocity and $\tau$ the effective pulse width. Thus, shorter effective pulses (higher $f_{\max }$) resolve finer defects.

2.4. Statistical Definition of the Qualification Mask

To reduce high-frequency oscillations, Savitzky–Golay smoothing is applied (15),

$$Z_{\mathrm{smooth}}\left(t\right)=\mathrm{SGFilt}\left(Z_{\mathrm{real}}\left(t\right)\right)$$

(15)

For a set of M control samples, the mean signature is computed as (16),

$$\overline{Z}\left(t\right)={\displaystyle \frac{1}{M}}\sum _{i=1}^M{Z}_i\left(t\right)$$

(16)

And variability is quantified by the pointwise percentage error (17),

$${\epsilon }_j\left(t\right)=100\left|{\displaystyle \frac{Z_j\left(t\right)-\overline{Z}\left(t\right)}{\overline{Z}\left(t\right)}}\right|\%$$

(17)

Based on this distribution, a pass/fail mask is constructed by applying tolerance bounds as (18),

$$Z_{\mathrm{mask}}^{(\pm p)}\left(t\right)=\left[(1-p)\overline{Z}\left(t\right),(1+p)\overline{Z}\left(t\right)\right],p=5\%.$$

(18)

Each tested micromodule is evaluated by the fraction of points violating the mask (19),

$$P_{\mathrm{outside}}=100·{\displaystyle \frac{{\sum }_t\mathrm{outside\_mask}\left(t\right)}{N}},$$

(19)

Yielding the qualification rule as (20) and (21),

$$\begin{array}{cc}\hfill & P_{\mathrm{outside}}<1\%\Rightarrow \mathrm{Approved}\hfill \end{array}$$

(20)

$$\begin{array}{cc}\hfill & P_{\mathrm{outside}}\ge 1\%\Rightarrow \mathrm{Rejected}\hfill \end{array}$$

(21)

This integrated TDR methodology transforms conventional VNA reflection measurements into a spatial impedance fingerprint, enabling systematic comparison across samples. Deviations from a reference signature—quantified through statistical masking—serve as a rapid metric of degradation, supporting qualification of micromodule integrity.

3. Preparation of Micromodule Samples

3.1. Identification of Photovoltaic Micromodules

Commercial samples of photovoltaic (PV) micromodules specifically designed for energy-harvesting applications were manufactured and distributed into two distinct families (A and B). The physical dimensions of the devices are shown in Figure 1, while Table 1 summarize the total sample population considered in the experiments. Both families are composed of bifacial Passivated Emitter and Rear Cell (PERC) technology, commonly employed in compact photovoltaic micromodules. Micromodules intended for energy-harvesting applications differ structurally from conventional photovoltaic modules. These differences include the absence of bypass diodes, the adoption of a single-busbar configuration, the lack of MC4 connectors, and the use of reduced-size fragmented solar cells. Despite these differences, the lamination process of the micromodules follows the same principles applied to traditional PV modules and consists of tempered glass, EVA encapsulant layers, and a polymeric backsheet.

3.2. Sample Selection and Control Strategy

Validation of the qualification methodology based on TDR electronic signatures requires the definition of a reference sample set. For each family (A and B), three healthy samples were selected, which exhibited electrical and optoelectronic conformity with the parameters specified by the manufacturer. These samples constitute the control group and are used to construct the TDR mask.

For each family, the remaining modules were classified as test samples and subjected to accelerated degradation tests, including salt mist [17,18,19], thermal cycling [20,21,22,23,24], and damp heat [25,26,27,28]. The applied tests were additionally categorized by severity levels from 1 to 4. The objective is to induce representative failure mechanisms consistent with real-world PV module degradation. The TDR signatures of the degraded samples are later compared with the mask constructed from healthy units, enabling the assessment of method sensitivity and discrimination capability.

3.3. Sample Coding Scheme

To ensure traceability and standardization, a coding system based on the elements described in (22) was adopted,

$$\mathrm{ID}=\left(\mathrm{Family}\right)-\left(\mathrm{Type}\right)-\left(\mathrm{Test}\right)-\left(\mathrm{Level}\right)$$

(22)

Where $\mathrm{Family}\in \{A,B\}$, $\mathrm{Type}\in \{C,M\}$, with C = Control and M = Test, $\mathrm{Test}\in \{\mathrm{NS},\mathrm{CT},\mathrm{CU}\}$ and $\mathrm{Level}\in \{1,2,3,4\}$. After the aging tests, all samples—degraded or not—were reanalyzed using the pre-established TDR mask. The goal is to investigate whether the electronic signature exhibits systematic variations capable of indicating the onset or progression of electrical or structural degradation in the micromodule.

3.4. Degradation Testing of PV Micromodules

To assess the robustness and reliability of the PV micromodules, the full sample population—except those classified as control—was subjected to accelerated degradation tests in environmental chambers Thermotron, Vötsch, and ABMTM salt mist chamber. The applied stress protocols included: (i) salt mist [17,18,19]; (ii) thermal cycling [20,21,29]; and (iii) damp heat [25,27,28], each implemented across distinct severity levels. The objective of these tests is to induce, in a controlled manner, representative degradation mechanisms typically observed in field conditions, particularly relevant to the tropicalization of electronic products, thereby enabling subsequent comparison between healthy and degraded samples. It is emphasized that, throughout the entire testing period, the samples remained unpowered, ensuring that the observed failures were exclusively attributable to the applied environmental stresses.

3.5. Accelerated Stress Test Arrangement

Figure 2 illustrates the experimental infrastructure employed for the accelerated degradation tests applied to the PV micromodules and Table 2 summarizes the methodologies applied and their corresponding severity levels.

Electroluminescence imaging inspection techniques were used to quantify the structural degradation of the samples [30,31,32]. Approximately 50% of the population exhibited measurable degradation with direct impact on energy generation performance. These degraded samples will form the validation basis for the TDR mask method, enabling evaluation of its ability to reliably distinguish degraded micromodules from those considered healthy.

4. Qualification of PV Micromodules via TDR Masking

The proposed qualification method is based on the detection of structural and electrical degradation in photovoltaic (PV) micromodules using the electronic signature obtained through Time-Domain Reflectometry (TDR). The method is grounded on the hypothesis that each micromodule exhibits a unique electromagnetic behavior determined by its internal geometry, materials, and manufacturing process. Therefore, variations introduced by defects or degradation mechanisms modify the electronic signature measured in the time domain.

The primary objectives of the method can be summarized as follows: (I) Establish a unique and reproducible electronic signature for each structural pattern of PV micromodules, (II) Detect and quantify degradation-induced anomalies by comparing healthy samples with samples subjected to reliability tests

4.1. Test Fixture for TDR Pulse Injection

To ensure reproducible conditions, optical isolation, and proper TDR pulse coupling into the micromodules, a dedicated measurement fixture was developed. This fixture ensures: minimization of coupling losses, a stable and repeatable reference plane, shielding from ambient light, and geometric repeatability across measurements. Figure 3 shows the manufactured fixture along with cross-sectional and top-view schematics.

4.2. Return-Loss Measurement Setup for PV Micromodules

The return-loss experiment was conducted using the classical configuration for RF characterization of passive devices. The test fixture was connected to a VNA (model ENA 5071C), with a $50\mathsf{\Omega }$ termination at the DUT far end to ensure symmetric and stable measurement conditions. A 85052D mechanical calibration kit, calibrated RF coaxial cable (SMA male–female), ESD wrist strap, and a linear sweep from 500 kHz to 20 GHz with 2001 points were used. Figure 4 shows the laboratory setup.

All 24 samples were measured to obtain $S_{11}$, which is the fundamental dataset for reconstructing the TDR electronic signatures.

4.3. Interpretation of the Electronic Signature

The time-domain electronic signature contains multiple reflections originating from both the DUT and the test fixture. Therefore, it is essential to identify and segment unwanted contributions to ensure that only internal discontinuities within the micromodule are analyzed. Figure 5 illustrates the separation between reflections from the measurement system and reflections inherent to the DUT. Due to spatial heterogeneity in dielectric permittivity among the measurement components, time–distance conversion is not employed as an absolute metric; instead, the analysis is carried out directly in the time domain.

4.4. Mask Construction and Percent Error Analysis

To validate the TDR method, a test mask was defined based on the mean electronic signature of the control samples. Figure 6 show the masks for Families A and B, along with the pointwise percentage error relative to the mean signature.

The mask incorporates an acceptable percentage deviation threshold, accounting for device stability, solder uniformity, electrical polarization symmetry, and intrinsic manufacturing variation. Limits of $\pm 5\%$ of the average value were adopted as a design rule.

4.5. Experimental Validation of the TDR Mask

With the mask established, automatic qualification was carried out comparing healthy micromodules with degraded micromodules from the reliability tests. Figure 7 and Figure 8 show the final results for Families A and B.

The method exhibited a tolerance of $\pm 1\%$, demonstrating robustness against fixture instability and small variations in electrical contact.

5. Discussion of the Results

After validating the qualification method based on the TDR mask, a detailed analysis of the rejected samples was carried out with the objective of identifying peak/trough divergences, temporal displacements, and alterations in the electronic signature responsible for the observed degradation. Figure 9 and Figure 10 consolidate the graphical comparison between the degraded samples and the reference patterns from Families A and B.

Table 3 summarizes the degradation effects caused by the accelerated reliability tests observed in each rejected sample.

In general, the samples that presented dead zones had suppression of the first valley as their main characteristic, while the samples that presented moisture penetration in the central busbar showed phase shift due to pulse propagation delay as their main characteristic. However, other defects such as electrode cracks due to microcracks, sparse dark blotches, and reduction in overall light intensity did not present distinct and clear results, behaving randomly in relation to their impact on the TDR electronic signature.

6. Conclusions

This work presented and experimentally validated a qualification methodology for photovoltaic micromodules based on high-resolution electronic signatures generated through Time-Domain Reflectometry (TDR). The method addresses the current absence of qualification standards for low-power photovoltaic devices by enabling rapid, illumination-independent detection of structural and electrical degradation.

Using VNA-based acquisition and Fourier reconstruction, combined with a dedicated coupling test fixture, the approach delivered repeatable TDR signatures from which statistical pass/fail masks were derived. Results showed that degraded micromodules systematically violated these masks, confirming the effectiveness and sensitivity of the method.

A key limitation, however, remains: while the TDR mask clearly indicates that degradation has occurred, it cannot distinguish the underlying failure mechanism. Identifying root causes—such as corrosion, moisture ingress, delamination, or metallization defects—still requires complementary diagnostic tools.

In summary, the proposed TDR-mask methodology provides a fast, robust path to qualify miniaturized photovoltaic devices, offering a reliable binary assessment (healthy vs. degraded) and representing a valuable step toward future standardization for energy-harvesting and IoT micromodules.