## 2 Analysis of PV PCC Harmonics
The effects of spectral leakage and fence of DFT algorithm can be mitigated by IpFFT methods. Windowed interpolation Fourier transform algorithm based on Hamming window was employed in this study. The Hamming data window is as follows:  
\[w(n)=0.54-0.46\cdot\cos\left(\frac{2\pi n}{N-1}\right),\ (0\leq n\leq N-1) \tag{1}\]  
The window is adopted to the signal data in time domain. DFT or FFT algorithm is employed to the windowed signals to obtain the signal spectra. More accurate amplitudes, frequencies and phases of signal spectra can be calculated by the IpFFT interpolation formula. The interpolation formula of Hamming IpFFT algorithm in frequency domain is presented as:  
\[\left\{ \begin{array}{l}\gamma=\frac{|X(l+1)\ |-|X(l)|}{|X(l+1)|+|X(l)|}\\ \delta=1.21874943\gamma+0.13349531\gamma^{3}+0.05301420\gamma^{5}+0.03656014 \gamma^{7}\\ A_{l}=\left(|X(l)|+|X(l+1)|\right)\times\left(2.26557103+1.22719978\delta^{2} \right.\\ \left.+0.37607775\delta^{4}+0.09767389\delta^{6}\right)\\ f_{l}=l+\delta+0.5\\ \varphi_{l}=\angle X(l)+\delta\pi\end{array} \right. \tag{2}\]  
where \(X(l)\) and \(X(l+1)\) are the highest and second highest spectral lines of one spectral peak of windowed signal spectrum, respectively; \(\gamma\) is the interpolation factor; \(\delta\) is the frequency deviation; and \(A_{l}\),\(f_{l}\) and \(\varphi_{l}\) are the estimations of the amplitude, frequency and phase of a harmonic, and their units are V, Hz and (\({}^{\circ}\)), respectively. Figure 4: PCC waveforms of a PV plant: (**a**) the voltage waveforms at PV PCC; and (**b**) the current waveforms at PV PCC. The harmonic analysis results of phase A voltage and current of PV PCC signals by IpFFT algorithm are shown in Figure 5.  
Figure 5: Spectra of phase A voltage and current at PV PCC: (**a**) spectra of phase A voltage while PCC harmonics occur; (**b**) spectra of phase A current while PCC harmonics occur; (**c**) spectra of phase A voltage while PCC harmonics disappear; and (**d**) spectra of phase A current while PCC harmonics disappear. As illustrated in Figure 5c,d, the spectra of PCC voltage and current waveforms recorded by DL850 ScopeCorder did not contain any significant background harmonics although the PV inverters were still working. When the production in the PV plant increased, as shown in Figure 5a,b, PCC harmonics occurred; the frequencies of the two significant harmonic components are 202.90 Hz and 302.90 Hz. These components are inter-harmonics with frequencies near 4 th and 6 th harmonic frequencies. The frequencies of the two inter-harmonics are denoted as \(f_{4}\) and \(f_{6}\), respectively, and the fundamental frequency is denoted as \(f_{1}\). The difference (denoted as \(f_{6}\)-\(f_{4}\)-\(2f_{1}\)) of these harmonic frequencies and double fundamental frequencies during 40 s is presented in Figure 6.  
The curve illustrated in Figure 6 reveals that the algebraic difference of the three frequencies is within the range of (\(-\)0.01 Hz, 0.01 Hz), and evenly distributed. It is considered that the frequency difference between the two inter-harmonics is twice the fundamental frequency (\(2f_{1}\)). The same frequency difference relationship exists between the two inter-harmonic components in the B-phase and C-phase signals. Such frequency difference relationship was satisfied as long as the PV PCC harmonics occurred. The waveforms recorded at other times led to the same results of the PCC harmonics in the PV plant. In addition, there is a special relationship between the phase sequences of PCC harmonics. The phase sequences of the fundamental and inter-harmonics were calculated for 40 s, as presented in Figure 7.  
Figure 6: Frequency difference of harmonics at PV PCC. Figure 7: \(Cont.\)  
The phase sequences of the fundamental and two inter-harmonics are denoted as \(\varphi_{f1}\), \(\varphi_{f4}\) and \(\varphi_{f6}\), where the yellow curves are phase A vs. phase B, the green curves are phase B vs. phase C, and the red curves are phase C vs. phase A.