# Software Design of String Three phase Inverter

The main difference between two-level and three-level in the design of string three-phase inverter software lies in the modulation part. Since the three-level introduces a midpoint, there is a problem of midpoint point control. First, the three-phase inverse is given. The mathematical model and decoupling model of the inverter. Secondly, according to the decoupled model, the controller is designed on the d and 9 axes respectively. The control idea is equivalent to the single-phase inverter. Then, we will introduce the realization of three-phase software phase lock. The modulation part is introduced in detail, and finally the entire control system is analyzed based on the simulation results.
(1) Mathematical model on ABC three-phase stationary coordinate system

In Figure 1, Uu, Uv, and Uw are the three-phase output voltage of the inverter respectively: iu, iv, and iw are the three-phase output current respectively; C1 is the DC bus capacitor: Lu, Lv, and Lw in the main circuit are respectively The inductance of each phase outgoing reactor: R is the sum of the inductance resistance and the equivalent resistance Rs of the power device loss. Assuming that the main power device in Figure 1 is an ideal switch, the mathematical description between the inverter and the grid in the three-phase static coordinate system is: :
{ L(diu)/(dt)=[(Udc)/（2）]×Su﹣ea＋Uno
{ L(div)/(dt)=[(Udc)/（2）]×Sv﹣eb＋Uno
{ L(diw)/(dt)=[(Udc)/（2）]×Sw﹣ec＋Uno (1)

In the formula, Su, Sv, Sw are the switching functions of the three bridge arms in the main circuit of the inverter. Considering that the three-phase non-neutral wiring method is generally used in the inverter, and when the three-phase grid voltage is balanced, according to Kirshoff’s current law, the sum of the three-phase current on the AC side is zero, that is:
ea＋eb＋ec=0 iu+iv+iw=0 (2)

Combining formula (1) and formula (2) can be obtained

Then bring it to formula (3) to get

(2) Mathematical model of inverter in synchronous rotating d-q coordinate system
From the above analysis, it can be seen that the mathematical model of the photovoltaic grid-connected inverter in the three-phase static coordinate system is that multiple variables are coupled with each other and change with time. This is very similar to the mathematical model of AC motor speed regulation, so it can be used for reference. The idea of ​​coordinate transformation realizes the simplification of the decoupling control strategy between variables. As shown in Figure 2, the mathematical model of the inverter in the three-phase coordinate system is transformed by the equivalent transformation of the two-phase static a-β coordinate system and the two-phase dynamic dq coordinate system to simplify the decoupling of multiple variables to facilitate The output power of the inverter can be individually controlled.

① Transformation of three-phase and two-phase stationary orthogonal coordinate system Here is the transformation matrix under the constraint of keeping the power constant

② Transformation of stationary two-phase and rotating orthogonal coordinate system.

③ Transformation from three-phase stationary to two-phase rotating coordinate system.

Simplify equation (7)（8） according to the power equivalent coordinate transformation, and transform the inverter from the three-phase coordinate system to the two-phase rotating coordinate system. The mathematical model is:

From equation （9), it can be seen that the variable of the photovoltaic inverter in the two-phase dynamic d-q coordinate system is obviously less than that in the three-phase static coordinate system, and the coupling is weakened, but there is still a small coupling between the currents. In order to achieve decoupling control of the d-q axis and reduce the impact of grid fluctuations on the current closed-loop system, the control strategy shown in Figure 3 can usually be used.

The formula of μd, μg is as follows:

By substituting formula (9) for human formula (10), we can get

From equation (11), it can be seen that this control strategy realizes the decoupling between d and q,