#### Fundamental current tracking

In order to achieve a higher power factor, the fundamental tracking error of the incoming current must be resolved. This paper briefly introduces several fundamental current tracking control methods commonly used in L-filter grid-connected inverters

1. Proportional-integral (PI) regulator

The form of the PI regulator is as follows:

Among them, k_{p} is the proportional gain, T_{i} is the time integral constant. This type of regulator can achieve no static error tracking of the DC quantity, but it cannot achieve no static error for the 50Hz fundamental wave signal. Therefore, in a single-phase system or a three-phase stationary coordinate system, it is difficult for this type of regulator to achieve zero steady-state error. Although the fundamental gain can be greatly improved by adjusting the PI parameters to weaken the steady-state error, it is limited by stability when there is a digital control delay in the system.

In the three-phase synchronous rotation dq coordinate system, the PI regulator can realize the static-free control of the fundamental wave signal, which is widely used.

2. Proportional-resonant (PR) regulator

The ideal PR regulator is as follows:

Among them, ω_{0} is the fundamental angular frequency; k_{r} is the spectral gain of the ideal PR regulator. Considering that the grid frequency will change slightly around ω_{0} and the undamped resonance control cannot be achieved in actual implementation, the practical form of the PR regulator is as follows:

Among them, k_{r}/ω_{r} is the gain of the resonance part of the PR regulator at the fundamental frequency, and selecting an appropriate ω_{r} makes the resonance controller have better robustness when the grid frequency changes slightly (eg gain reduction not more than 3dB at maximum grid frequency deviation). This PR regulator has very high gain at the fundamental frequency, so even in a single-phase grid-connected inverter or a three-phase grid-connected inverter in a static coordinate system, the grid-connected current can track the reference current with approximately no static error. Figure 1 shows the Bode plot of the PR regulator when kr and ω_{r}, where k_{p}=15.

3. Deadbeat (DB) controller

Deadbeat control is actually a predictive control. In the digital controller, the inverter output voltage required for the next switching cycle is deduced through the state equation of the system and the feedback signal, and then the output voltage is used as the PWM modulation wave. In theory, DB control has a very high bandwidth, but in practice its dynamic response is often difficult to complete within one switching cycle. The steady-state and dynamic performance of inverters controlled by PI, PR and DB are very close. The main difference is that the inverter can achieve better performance when the grid voltage drops when DB control is used. However, it should be pointed out that, since the DB control depends on the mathematical model of the controlled object, the design of the DB control needs to fully consider factors such as the parameter disturbance of the actual inverter.