## Methodology
### The Power Dependency Evaluation of HAM by Laboratory Tests  
The analytical analysis performed in Section 2.2 indicates that there exist inherent correlations between harmonic distortion characteristics (and hence HAM) at different powers. To further investigate the power dependency of HAM for PV systems, a testbed is set up as in Figure 7, consisting of a fully programmable ac supply (capable of generating defined supply voltage harmonics), a controllable dc supply (capable of providing defined constant power to the PV inverter), single-phase residential PV systems, data acquisition system and a control PC. With the aid of the testbed, the harmonic sensitivity tests are performed on two single-phase PV systems with their basic information tabulated in Table 1. Specifically, the individual harmonic tests are performed for PV-A and PV-B operating at 100% \(P_{rated}\) down to 10% \(P_{rated}\) (with a step of 10% \(P_{rated}\)). For each test, only one individual voltage harmonic is superimposed on the fundamental sinusoidal supply voltage, with a combination of different harmonic magnitudes and phase angles. The considered individual voltage harmonics include even harmonics from 2 to 6, and odd harmonics from 3 to 19. Their harmonic magnitudes vary from a tenth of the individual harmonic limits (denoted as \(V_{h,limit}\)) given in [8] to 1.2 \(\times\)\(V_{h,limit}\) (for 0.8 \(\times\)\(V_{h,limit}\) PVI-C) with a step of \(V_{h,limit}\)/10, while the harmonic phases increase from 0\({}^{\circ}\) to 360\({}^{\circ}\) with a step of 30\({}^{\circ}\). During the individual harmonic tests, the rms value of the resultant supply voltage waveform is maintained at 1 pu (i.e., 230 V). All the test points are programmed as testing sequences in MATLAB, while the communication between the testbed and control PC is achieved by using SCPI commands via RS232 and GPIB remote interface.  
By applying the conventional HAM derivation approach in Section 2.1 to the measurements obtained from the harmonic sensitivity tests, the HAMs for the tested PV systems operating at different powers can be derived, with their magnitudes displayed in Figures 8 and 9. It is noticed that the dominant elements of the HAM matrix are those on the diagonal, implying the current harmonics of PVIs are mainly determined by the voltage harmonics at the same order. This is attributed to the waveform shaping capability  
Moreover, the distribution patterns of HAMs exhibit strong similarity at different powers, which is also proved by the analytical analysis in Section 2.2. Here, the Pearson correlation coefficient, \(\rho\), is used to quantify the correlation of HAMs at different powers, as illustrated in Figure 10. It turns out that a strong linear correlation (\(\rho>0.98\)) exists between HAMs at adjacent powers, implying the feasibility of HAM interconversion. Additionally, the linear correlation of HAMs at different powers deteriorates with the increasing power  
Figure 8: HAMs derived from the harmonic sensitivity tests for PV-A operating at 100%, 50%, 20% and 10% \(P_{ntal}\): (**a**) HAM for PV-A operating at 100% \(P_{ntal}\): (**b**) HAM for PV-A operating at 50% \(P_{ntal}\): (**c**) HAM for PV-A operating at 20% \(P_{ntal}\): (**d**) HAM for PV-A operating at 10% \(P_{ntal}\):  
Figure 9: HAMs derived from the harmonic sensitivity tests for PV-B operating at 100%, 50%, 20% and 10% \(P_{ntal}\): (**a**) HAM for PVI-B operating at 100% \(P_{ntal}\): (**b**) HAM for PV-B operating at 50% \(P_{ntal}\): (**c**) HAM for PV-B operating at 20% \(P_{ntal}\): (**d**) HAM for PV-B operating at 10% \(P_{ntal}\).  
difference. The above power-dependency features of PVs' HAMs are the basis for proposing the practical HAM derivation approach in the next section.