# 7.4 Predictive Current Control of the Matrix Converter

## 7.4.1 Model of the Matrix Converter for Predictive Control

### 7.4.1.1 Matrix Converter Model

For predictive control the model of the MC is extremely simple: it considers only (7.2) and (7.5), which relate the instantaneous values of input and output currents and voltages. Based on the restriction presented by (7.1), the MC has 27 different switching states to be considered for prediction of the variables.

### 7.4.1.2 Load Model

In this case the objective is to obtain an equation to predict the value of the load current in the next sampling interval, for each of the 27 different switching states of the MC. The equation for the resistive–inductive–active load presented in Figure 7.1 is

7.22

where *L* and *R* are the inductance and resistance of the load and **e** is the electromotive force (emf). This load model is quite general, because it covers a wide variety of applications such as passive inductive load, motors, and grid-connected converters.

Considering the approximation for the derivative of the output current

7.23

where *T*_{s} is the sampling period, the equation for predicting the load current is obtained from substituting (7.22) into(7.23), which gives

7.24

where **i**_{o}(*k* + 1) is the predicted value of the current for sampling interval *k*