## 4 Predictive Current Control Strategy
### Cost Function Selection  
#### 4.3.1 The Optimization of the MPCC  
**Minimization of the switching frequency**. As with power converters, one of the primary measures of control effectiveness is the switching frequency. In many applications, it is important to control or limit the commutations number of the power switches [22]. To consider directly the reduction in the number of exchanges in the cost function, a simple method is to include a term that covers the number of switches that change when the switching state \(S(k)\) is applied relative to the switching state \(S(k-1)\) of the previous application. The resulting cost function is expressed as \(g=(i_{a}^{*}-i_{a}^{p})+(i_{\beta}^{*}-i_{\beta}^{p})+\lambda_{n}\cdot n\). Taking the three-phase inverter as an example, the switching state vector \(S=(S_{a},S_{b},S_{c})\), the switching state of each inverter arm [23] is defined. Then the number of switches changes from time \(k-1\) to time \(k\) is:  
\[n=|S_{a}(k)-S_{a}(k-1)|+|S_{b}(k)-S_{b}(k-1)|+|S_{c}(k)-S_{c}(k-1)| \tag{26}\]  
**The optimization of the MPCC**. In order to ensure the control accuracy of the system, the calculation speed of each sampling period must be improved, and the calculation amount in each period should be reduced.  
In this paper, we introduce a method that can reduce the computational cost by simplifying the optimal switching state selection method, while ensuring that the performance of the T-type three-level grid-connected system will not be affected in any way. From the [PERSON]'s voltage formula, we can obtain Equation (28):  
\[v(k)=L\frac{di}{dt}+Ri(k)+e(k) \tag{27}\]  
\[v(k)=\frac{L}{T_{s}}i^{p}(k+1)+(R-\frac{L}{T_{s}})i(k)+e(k) \tag{28}\]  
If the predicted current reference value \(i_{a\beta}^{*}(k+1)\) at \(t_{k+1}\) is, instead of the actual sampling current prediction value, \(i_{a\beta}^{p}(k+1)\) at the time, the \(i_{a\beta}^{*}(k+1)\) corresponding voltage vector \(v_{a\beta}^{*}(k+1)\) is directly tracked by using the current \(i_{a\beta}(k+1)\), i.e.:  
\[v^{*}(k+1)=\frac{L}{T_{s}}i^{*}(k+1)+(R-\frac{L}{T_{s}})i(k)+e(k) \tag{29}\]  
If the voltage vector \(v_{a\beta}(k)\) at the \(t_{k+1}\) time corresponding to the switching state is consistent with the predicted voltage value \(v_{a\beta}^{*}(k+1)\) of the next cycle, it is indicated that the current sampling \(i_{a\beta}(k+1)\) at the same time is consistent with the reference current value \(i_{a\beta}^{*}(k+1)\). Therefore, as long as the switching state closest to the predicted voltage value \(v_{a\beta}^{*}(k+1)\) is selected among  
Figure 7: T-type inverter predictive current control method.  
the voltage vectors corresponding to the 27 switching states to drive the switch at the next moment, the grid-connected current can be tracked. That is, as Equation (30) shows:  
\[\left\{\begin{array}{l}g_{i}=\|v_{a}^{*}(k+1)-v_{ja}\left(k+1\right)|+\left|v_{ \beta}^{*}(k+1)-v_{j\beta}(k+1)\right|+\lambda_{dc}\Big{|}v_{c1}^{p}(k+1)-v_{ c2}^{p}(k+1)\Big{|}+\lambda_{n}n_{c}\\ S_{opt}:\min\{g_{i}\}\end{array}\right. \tag{30}\]  
In that formula, \(i=1,2,\ldots,27\), \(v_{ja}(k+1)v_{j\beta}(k+1)\) represent, respectively, the real part and the imaginary part of the voltage vector in the \(\alpha\beta\) coordinate system.