Off grid control of three-phase inverter - PR control

Three phase inverter control technology ——PR control

1 PR Introduction of control technology

    Inverter control is often used PI control technology , and PI Control can only be achieved for constant values Tracking without static error . Therefore, it is necessary to rotate the three-phase voltage in the control 、 The current rotates to dq Control in a coordinate system ,dq At this time, the voltage and current are constant in the coordinate system , Good for PI Control tracking . First, let's see why PI The control can only track the constant value without static error .

    Take the controlled object as the first-order inertia link $\frac{1}{Ts+1}$ , use PI Control to control , The transfer function is ：$k_i+\frac{k_p}{s}$ , Design below Simulink The simulation system is shown in the figure below ：

   It can be found by adjusting PI Parameters , It can realize better tracking of step signal . Use Liner Analysis Tool Draw its closed loop Bode Tude ：

   It can be seen that when the input signal frequency is small , The system can realize the zero of amplitude and phase , But when the frequency of the input signal increases to a high frequency signal , Output signal amplitude and generation attenuation , Phase shift . The actual situation is tested as follows ：

   In the above process , It can be seen that when the input signal is DC component , The system can basically realize tracking without static error , When the output signal is AC component , The system output will produce an offset between amplitude and phase , And the higher the frequency , The greater the deviation between amplitude and phase . namely PI The control cannot realize the lossless tracking of AC signals , So you need to use PR The controller controls the AC signal .

2 PR Control the basic idea

    In order to realize no static error tracking of AC signal , Use PR The controller controls the system ;PR The controller is ： The proportion + Resonance controller . Tradition PR The controller expression is ：$k_p+\frac{2\ast k_{r}s}{s^2+{{\omega }_0}^2}$, In order to improve its control accuracy, there are expressions such as quasi resonant control , Different PR The controller is expressed for Achieve good frequency selection characteristics , That is to realize input signal tracking in various complex situations . Only the principle is explained here , A relatively simple PR For example, controller , It's about 10Hz The sinusoidal signal forms the following control system ：

  

   By adjusting the parameters , At this time, the output signal can track the input ：

   The basic control of three-phase inverter can be realized by using this control idea

3 inverter PR control

   The expression of inverter in two-phase static coordinate system is ：

$$\{\begin{array}{c}\left[\begin{array}{c}\frac{d{i}_{\alpha }}{dt}\\ \frac{d{i}_{\beta }}{dt}\\ \frac{d{i}_0}{dt}\end{array}\right]=\frac{1}{L}\left[\begin{array}{c}{U}_{\alpha }\\ U_{\beta }\\ U_0\end{array}\right]-\frac{R}{L}\left[\begin{array}{c}{i}_{\alpha }\\ i_{\beta }\\ i_0\end{array}\right]-\frac{1}{L}\left[\begin{array}{c}{U}_{C\alpha }\\ U_{C\beta }\\ U_{C0}\end{array}\right]\\ \left[\begin{array}{c}\frac{d{U}_{C\alpha }}{dt}\\ \frac{d{U}_{C\beta }}{dt}\\ \frac{d{U}_{C0}}{dt}\end{array}\right]=\frac{1}{C}\left[\begin{array}{c}{i}_{\alpha }\\ i_{\beta }\\ i_0\end{array}\right]-\frac{1}{C}\left[\begin{array}{c}{i}_{g\alpha }\\ i_{g\beta }\\ i_{g0}\end{array}\right]\end{array}$$

   According to the above equation, Laplace transform can be obtained ：
$$\{\begin{array}{c}{U}_{c\alpha }=\frac{1}{sC}(i_{\alpha }-i_{g\alpha })\\ \\ i_{\alpha }=\frac{1}{sL+R}(U_{\alpha }-U_{c\alpha })\end{array}$$
   At this time, the mathematical model of the inverter is shown in the figure below ：

   In order to realize inverter PR control , The design is shown in the control block diagram below ：

   You can easily find ,PR The control can realize good tracking of sinusoidal signal in two-phase static coordinate system , Therefore, there is no need for additional structural control , be relative to PI Control optimizes the control mode .

   build PR The control model is shown in the figure ：

4 Experimental simulation test

   Comparison between given voltage and output voltage ：

Model links , I need to take it myself ： Model links