## 1 Introduction
[22] studied the PV inverter's capability to provide harmonic current compensation for nonlinear loads and proposed an algorithm to determine the capability curves of a multifunctional inverter during the harmonic current compensation process. [PERSON] et al. [23] presented a hybrid approach considering both distribution network reconfiguration and the reactive power of a PV inverter. The PV inverter control of different power factors was discussed. The combination of PV inverter control and network reconfiguration can reduce active power loss by more than 37%. [PERSON] et al. [24] provided a voltage management strategy by the coordination of battery energy storage systems and smart PV inverters. To comprehensively improve stability and economy of the distribution network operation, the aforementioned PV and FID are simultaneously used. Due to the high R/X ratio of distribution networks [25], both active power and reactive power will influence the voltage profile and power quality. The optimization of active power and reactive power is required. It is difficult to obtain satisfied performance when adjustment is carried out with a single device. Thus, synergetic optimization is proposed. Active power control can be achieved by FID and PV. However, the curtailment of PV active power results in low a PV consumption rate and additional economical loss. To take the PV consumption rate into consideration, minimizing the ratio of PV abandonment is set as another optimization objective, except for power quality. The reactive power control can also be realized by FID and PV. However, the earlier reactive power optimization of PV mainly focuses on capacity constraint and power factor constraint. The specific analysis of PV reactive power output mode needs further study. In addition, different port numbers of FID and different solving algorithms of the optimal model can also impact the operation, which requires more analysis. In this paper, a synergetic optimization operation method of PV and FID is proposed. Multiple scenarios are taken into consideration including different reactive power output modes of PV, different port numbers of FID, and different algorithms for the solution. The main contributions of this paper can be summarized as follows:  
1. A synergetic optimization operation method of PV and FID is constructed. Three objectives of voltage deviation, network loss, and ratio of PV abandonment are selected. To flexibly control active power and reactive power, multiple reactive power output schemes of PV and multiple port numbers of FID are considered as constraints. The proposed method enhances power flow controlling, which provides better operation performance. 2. Five reactive power output modes of PV are analyzed and simulated. Three reactive power output schemes of power factor controlling, direct reactive power output, and night static var generator (SVG) scheme are considered. According to the adoption of different output schemes in different periods (day and night), five modes are built, simulated, compared, and discussed. By adopting a direct reactive power output scheme during daytime and the SVG scheme at night, PV is fully utilized in both active power consumption and reactive power compensation, which also improves the flexibility and stability of the system. 3. Multiple operation and optimization situations are analyzed and compared to verify the effectiveness of the proposed method. FIDs with different port numbers are taken into account. Three algorithms for solving the optimization model are compared. Cases with increasing permeability are simulated. Simulations show that the combination of FID with four ports, PV with operation mode 5, and the solving algorithm of NSGA-II gives the best result, which is the most suitable for optimization operation. The remainder of this paper is organized as follows: Section 2 introduces the modeling of PV and FID. Multiple reactive power output modes of a PV inverter are considered. Section 3 develops a synergetic optimization operation model of PV and FID.