## Methodology  
### Conventional HAM Derivation Approach  
The mathematical expression of HAMM can be written as (1), representing the correlations between the voltage and current harmonics at the PoC of a PV system with constant operating power. \[ \begin{bmatrix}\overline{I}_{1}\\ \overline{I}_{2}\\ \overline{I}_{3}\\ \vdots\\ \overline{I}_{h}\end{bmatrix} = \begin{bmatrix}\overline{Y}_{1,1}&\overline{Y}_{ 1,2}&\overline{Y}_{1,3}&\cdots&\overline{Y}_{1,H}\\ \overline{Y}_{2,1}&\overline{Y}_{2,2}&\overline{Y}_{2,3}&\cdots&\overline{Y}_ {2,H}\\ \overline{Y}_{3,1}&\overline{Y}_{3,2}&\overline{Y}_{3,3}&\cdots&\overline{Y}_ {3,H}\\ \vdots&\vdots&\vdots&\ddots&\vdots\\ \overline{Y}_{h,1}&\overline{Y}_{h,2}&\overline{Y}_{h,3}&\cdots&\overline{Y}_ {h,H}\end{bmatrix} \times \begin{bmatrix}\overline{V}_{1}\\ \overline{V}_{2}\\ \overline{V}_{3}\\ \vdots\\ \overline{V}_{H}\end{bmatrix}  \tag{1}\]  
where \(\overline{I}_{h}\) and \(\overline{V}_{H}\) are the individual complex current and voltage harmonics at PoC; the HAM element \(\overline{Y}_{k,j}\) represents the influence of \(j\)th voltage harmonic on the \(k\)th current harmonic. Conventionally, the derivation of HAM requires performing the individual voltage harmonic sensitivity tests (or the so-called \"fingerprint tests\") on the considered device under a fully controllable voltage source, as in [21; 22]. Specifically, the device is first tested under ideally sinusoidal voltage with varying voltage magnitudes. This step is to investigate the impact of the fundamental voltage component on the harmonic current spectrum. Then, individual harmonic is superimposed on the ideal supply voltage with a stepwise adjustment of harmonic voltage magnitudes and phase angles, as illustrated in Figure 5. This step is to investigate the impact of individual voltage harmonic on the harmonic current spectrum. As the output current of the PV system is power-dependent, the PV system has to be kept at a constant operating power to avoid the impact of operating powers on the current harmonic spectrum. Accordingly, a PV panel emulator (in the form of a programmable dc source) has to be applied in order to regulate the operating power of the PV system, while a programmable ac voltage source has to be applied for the harmonic sensitivity tests. Figure 5: The variation in 3 rd current harmonic in response to the changing magnitude and phase angle of 3 rd voltage harmonic, which is superimposed on the ideally sinusoidal supply voltage of a single-phase PV system tested under laboratory conditions: (**a**) the stepwise change of 3 rd voltage harmonic magnitude and phase angle; (**b**) the variation in 3 rd current harmonic under different 3 rd voltage harmonic. The derivation process of HAM from the harmonic sensitivity tests is given below. It should be noted that (1) can be rewritten as (2), indicating that the \(h\)th current harmonic, \(\overline{I}_{h}\), is determined by both the fundamental voltage, \(\overline{V}_{1}\), and all the voltage harmonics \(\overline{V}_{H}\) (\(H\
eq 1\)). It is also noticed that \(\overline{Y}_{h,1}\) can be calculated from \(\overline{I}_{h}\) and \(\overline{V}_{1}\) when the PV system is tested under ideal supply voltage, as in (3). When the modelled device is tested under any individual supply voltage harmonic, \(\overline{V}_{H}\), (2) is simplified into (4), where \(\overline{Y}_{h,H}\), can be directly calculated from the measurements. \[ \begin{bmatrix}\overline{I}_{1}\\ \overline{I}_{2}\\ \overline{I}_{3}\\ \vdots\\ \overline{I}_{h}\end{bmatrix} = \begin{bmatrix}\overline{Y}_{1,1}\\ \overline{Y}_{2,1}\\ \overline{Y}_{3,1}\\ \vdots\\ \overline{Y}_{h,1}\end{bmatrix} \
abla_{1}+ \begin{bmatrix}\overline{Y}_{1,2} &\overline{Y}_{1,3}&\cdots&\overline{Y}_{1,H}\\ \overline{Y}_{2,2}&\overline{Y}_{2,3}&\cdots&\overline{Y}_{2,H}\\ \overline{Y}_{3,2}&\overline{Y}_{3,3}&\cdots&\overline{Y}_{3,H}\\ \vdots&\vdots&\ddots&\vdots\\ \overline{Y}_{h,2}&\overline{Y}_{h,3}&\cdots&\overline{Y}_{h,H}\end{bmatrix}  \times