## 1 Introduction  
Transportation takes up a lot of space on the overall energy spending of the population. The future transmission capacity of the grid might be limited because of the increasing electricity demand, therefore electric mobility of the future would aim to be less demanding for the grid [1]. Due to the optimization of the space utilization of rooftop photovoltaic systems and charging stations, photovoltaic (PV) electric vehicle (EV) charging stations [2, 3] and photovoltaic electric bicycle charging stations [4, 5] have received widespread attention [6]. Since photovoltaic charging stations require sufficient sunshine time and parking space, they are generally far from buildings [7]. Therefore, the photovoltaic charging station is often at the end of the low-voltage power grid of the building, and the grid impedance has a great influence on the stable operation of the photovoltaic charging station [8]. To improve the performance of new forms of EV charging such as by solar energy, it would be interesting to evaluate and quantify the power quality of charging stations.  
The common stability analysis methods of grid-connected inverters are the state space method [9] and the impedance analysis method [10]. When applying the state space method for stability analysis, all parameters of the inverter and the grid must be acquired to establish the state space model [11].  
Due to the curse of dimensionality problem [12], the state space method is very complicated for the analysis process of a large-scale grid-connected inverter-grid system.  
Therefore, the impedance analysis method is proposed [13]. This method considers the inverter and grid system as two independent subsystems and establishes an impedance model separately or directly measures the impedance by the frequency sweeping method. Then, through the Nyquist criterion, whether the inverter-grid system is stable or not can be judged. In this article, the passivity impedance-based stability criterion [14] and the impedance analysis method are combined to analyze the undesired resonance or harmonic phenomenon, which is called resonance instability [15; 16].  
In Section 2, the power quality of a photovoltaic (PV) charging station for e-bikes at the campus of the University of Twente (UT) [17] is measured and analyzed. This grid-connected PV charging station has been developed in house by UT using commercially available components (275 W\({}_{\text{P}}\) of Canadian Solar(r) PV modules and 2.0 kW inverter SOLAX Power(r) X1 Series) and was installed by the end of 2017.  
The resonance instability due to the grid impedance is found in the experimental results. The phenomenon of resonance instability, its principles, and its stability criteria are discussed. In Section 3, two common single-phase photovoltaic inverter control methods are presented as models. The modeling considers the influence of the phase-locked loop (PLL) on the inverter impedance. In Section 4, the model that is presented in Section 3 is validated through simulation. In the simulation, the phenomenon of resonance instability in the experiment is reproduced. In Section 5, the influences of various parameters on the stability of the inverter in each frequency band are analyzed and discussed. In addition, the improvement methods are presented and validated through simulation. The paper ends with conclusions in Section 6.