# Three-phase photovoltaic grid-connected inverter control system

The control structure diagram of the three-phase photovoltaic grid-connected inverter system is shown in Figure 1. The control system mainly has three parts: current Pl regulator, voltage feedforward, and repetitive control unit.

In order to realize the decoupling of the three-phase current, it is necessary to transform the currents Ia, Ib, Ic in the three-phase static ABC coordinate system to the two-phase synchronous rotating d-q coordinate system. The relationship between the stationary ABC coordinate system and the synchronously rotating d-q coordinate system is shown in Figure 2.

In order to track the current to the grid voltage, the grid voltage needs to be phase-locked. Due to the limited processing capacity of the DSP used, in order to reduce the processing burden of the DSP, this book adopts a simple phase-locking method: capture the zero-crossing points of the line voltage Uab and Ubc through the hardware circuit, and determine the power grid through the relationship between the two zero-crossing points. The direction of rotation of the voltage is oriented when the Ua phase voltage reaches its peak value. In the next cycle, the angle θ between the d-axis and the A-axis increases with the grid angular velocity ω. This method avoids the calculation of division and arctangent, saves processor resources, and is proven to be feasible.

(1) PI regulator design
After 3s/2r conversion, the three-phase AC component becomes a two-phase DC component to facilitate the design and control of the PI regulator. The phase-locked loop orients the voltage space composite vector on the d-axis, and the flux linkage composite vector on the q-axis. In this way, the decoupling of power is realized, which can realize the independent adjustment of active and reactive power. The d-axis is the active component and the q-axis is the reactive component. The goal of control is to realize the tracking of the command current Id, Iq by the sampling current Id *and Iq* so that the current steady-state error is close to zero. Figure 3 shows the control block diagram of the d-axis.

in:
Gdi(s)=(KpS＋Ki)/S
Pdi(s)=1/(LS+R)
Since the switching frequency is much higher than the power grid’s whisker rate, the Kpwm link is equivalent to a proportional link K in order to facilitate the analysis and ignore the influence of the switching action on the system.
Then the open-loop transfer function of the system is:
Gd(s)=Gdi(s)*K*Pdi(s)
In the actual system, L=4.5mH, R=0.2Ω, K=0.77, Kpd=0.05, Kid=10, draw the Bode diagram of the d-axis open-loop transfer function as shown in Figure 4. It can be seen from the figure that the phase angle margin at the shear frequency is 60°, and the amplitude margin is also large enough. In the debugging process, the adjustable range of the proportional integral coefficient is very large, which shows that the control system has good stability. The design of the PI regulator of the q-axis is basically the same as that of the d-axis, as long as the command value is changed to Iq* that is, the q-axis current is not separately adjusted during the test adjustment process, and the parameters are the same as the d-axis. When the inverter is generating full power to the grid, set Iq*to zero.

(2) Design of repetitive control part
Due to the influence of non-linear factors such as the dead zone, the asymmetry of the drive circuit, and the periodic disturbance of the grid voltage, it is difficult to meet the requirements of the total distortion rate (THD) of the grid-connected current with a pure PI regulator. In order to reduce the influence of periodic disturbances, repetitive control is introduced. The principle of repetitive control has been introduced in the previous section of the single-phase inverter, so I won’t repeat it here.

(3) Design of voltage feedforward part
The power grid voltage measured by the experiment is not a standard sine wave, and the distortion of the surrounding power grid is different in different power usage occasions. In order to suppress the instantaneous disturbance of the power grid, this book introduces a voltage feedforward link in the control system. The voltage feedforward link uses the real-time sampled voltage signal after a certain phase compensation to multiply the DC bus voltage by a gain value, and then act on the output, so that the output approximately cancels the grid voltage. In this way, the photovoltaic system is similar to a passive tracking system. The PI regulator only needs to adjust the current command part without compensating for changes in the grid voltage. The voltage feedforward link can improve the dynamic process of grid connection and reduce the impact of grid current on the grid during the grid connection process. Disturbances to the DC bus voltage and grid voltage can all act quickly. The feedforward link always plays a role in the whole process of grid connection.

(4) Three-phase software phase-locked loop
In the three-level high-power grid-connected inverter, through the vector control based on the virtual flux linkage orientation, the control of the active and reactive power delivered to the grid can be realized. To this end, it is necessary to dynamically obtain the phase information of the grid voltage, and dynamically adjust the orientation angle of the virtual flux through the phase-locked loop.