## 1 Introduction  
Due to the technological breakthrough and the successive cost reduction, the use of photovoltaic (PV) systems in the grid is continuously increasing, resulting in a series of power quality issues, including harmonic pollution, voltage fluctuation, power imbalance, etc. [1, 2]. As PV systems are connected to the grid through dc-ac inverters, which are non-linear power electronic (PE) devices, they are characterized by inherent harmonic current emission. Their generated harmonic currents are injected into the grid and interact with the grid impedance, resulting in supply voltage distortion. This not only brings additional power losses and the potential harmonic resonance of the grid but also causes the malfunction or deteriorated performance of other harmonic sensitive electric equipment, such as breakers, energy meters and motors [3, 4]. To avoid the potential power quality disturbances resulting from the large-scale penetration of PV systems, international standards, such as IEEE Std. 1547 and IEC 61727, have been applied to limit the harmonic emission level of PV systems [5, 6]. Additionally, grid operators define their maximum allowable harmonic limits for the point of common coupling (PCC) in standards such as IEEE Std. 519 and EN 50160, which indirectly limit the overall harmonic emission level of grid-tied PV systems [7, 8]. The conventional rooftop PV system consists of PV panels, a dc-dc converter (optional), a dc-ac inverter, EMI filter and the controllers as shown in Figure 1. It is also observed from Figure 1 that the dc voltage and current outputs of PV panels are reshaped to grid-synchronized ac waveforms through the high-frequency pulse width modulation (PWM)of the dc-ac inverter, resulting in the harmonic emissions across multiple frequency bands. Previous findings have shown that the harmonic emission characteristics of PV systems are not only determined by device circuit topology and control strategy [9; 10] but also affected by the nonideal grid supply conditions referring to a combination of varying network impedance, voltage magnitude deviation and background voltage harmonics [11; 12]. For example, the harmonic performance is compared between full-bridge inverter topology and neutral point clamped topology through simulations [9]. A proportional-resonant-integral (PRI) controller with adaptive harmonic compensation capability is applied to a single-phase full-bridge inverter for the purpose of harmonic suppression [10]. The impact of background voltage harmonics on the harmonic emission characteristics of residential PV systems is evaluated in [11; 12] by performing compressive laboratory tests, where the tested PV systems do exhibit increased harmonic emissions under distorted supply voltage, as opposed to ideal supply condition. Figure 2 is the individual voltage harmonic magnitudes and phase angles recorded at the point of connection (PoC) of a residential house, indicating that the practical grid rarely operates under the ideal condition (i.e., sinusoidal supply voltage with close-to-zero source impedance). However, the existing standards on the grid integration of PV systems only consider the test conditions under ideal supply conditions, implying that a PV system that passes the harmonic emission requirements may still violate the limits under distorted supply voltage with source impedance. For example, Figure 3 illustrates the total demand distortion (TDD) of two rooftop PV systems operating at a combination of different powers and supply conditions. It is observed that both the two PV systems have amplified harmonic emissions when they are operating under distorted supply voltages (i.e., WF2 and WF3) with flicker source impedance (ZS2). Additionally, PV-A can no longer meet the harmonic emission limits in IEEE Std. 519, when its supply condition turns from the ideally sinusoidal supply voltage to distorted supply voltages.