Research on a Compound Control Strategy of Three-Phase Inverter for Unbalanced Loads

: To solve the problem of unbalanced output voltage of inverter under three-phase unbalanced load. In this paper, the main circuit topology using three-phase three-wire inverter topology. Established the mathematical model in several different coordinate system of the three-phase inverter. A compound control method is proposed by combining voltage current dual loop control method and repetitive control method, The control method is realized in three - phase 400 Hz inverter , and can meet the demand of unbalanced load to inverter, the reliability of the inverter circuit is improved. At the end of this paper, Matlab simulation analysis and experimental results are given, it is proved that the composite control method designed in this paper has a strong ability of unbalanced load.


Introduction
With today's power electronics technology continues to advance and rapid development in the petroleum, ship, communications switches and other fields, inverter power supply has a very wide range of applications [1].
More and more applications require three-phase inverters with very strong unbalanced load supply capability.
Normally under unbalanced load conditions, three phase inverter power supply can produce unbalanced output voltage [2][3]. Thus, the three-phase inverter power supply cannot be very good normal work. Therefore, it is of great significance to improve the analysis and research of unbalanced load capacity of three-phase inverter power supply.
At present, measures for correcting output voltage asymmetry of three phase inverter under unbalanced load, the main circuit mainly includes the following topological forms: three-phase split-capacitor inversion topology [4], three-phase four-leg inverter topology [5], combined three-phase inverter topology, insertion Δ / Y transformer topology [6][7]. But the four topologies have their flaws, The three phase splitting capacitance inverter topology requires a large number of DC filter capacitance, and there is a problem of the capacitor pressure, and the utilization of DC voltage will be very low [8]. The three-phase four-bridge arm contravariant topology, under the condition of adding a bridge arm, to some extent to achieve the effect of suppressing the output voltage imbalance, but also makes the control more complex, difficult to design parameters. The combined three-phase inverter topology is mainly composed of three single-phase inverters which are independent of each other. So the number of switches will be more use, increasing the difficulty of control [9]. Insert Δ/Y transformer topology structure and control methods are relatively simple. However, the weight, volume and cost of the inverter will be increased, and it is not suitable for use in high power applications [10].
The symmetrical output voltage of three phase inverter under unbalanced load is discussed in this paper, method is proposed, mainly combined with the repeated control and double-loop control of these two control methods. The improvement of the control method is realized, and the unbalanced load capacity of the inverter is obviously improved [11]. Simulation studies show that, the inverter operates normally under various loads and can output very symmetrical voltages.

Mathematical model of three-phase inverter
As shown in Figure 1, the three phase three-wire inverter topology is composed of capacitance C, three-phase filter inductance L and three-phase inverter bridge, r is equivalent impedance and loss. The output voltage of the inverter is U AB , U BC , U CA , the capacitance voltage is ab , bc , ca ,the inductor current isi A , i B , i C , the load current is ′ , ′ , ′ .
Formula 1 and Formula 2 are transformed by CLARK as follows: The CLARK transform can be used to derive the mathematical model of the three-phase inverter in the stationary coordinate system, then type 3 and 4 through the Park transformation, available: The mathematical model of the three-phase inverter in the dq rotating coordinate system is obtained. The following vector diagram can be obtained by converting the three-phase still abc coordinate system into two phase-rotating dq coordinate systems.
The inverter's three-phase output voltage is converted to two-phase rotation dq coordinate system:

Inverter control system design
When the three-phase inverter is operating in a non-linear load and unbalanced load，the output voltage has periodic disturbances, and use of repetitive control methods to suppress this disturbance. And in order to improve the dynamic response of the system, a compound control algorithm with repetitive control and voltage and current double loop control is adopted.

Repetitive controller design
Repetitive control in inverters has a wide range of applications. The main control method of the system is based on the principle of system internal mode, it is to add an "internal model" that can better describe the characteristics of the system under the control system. Therefore, the control accuracy can be improved by solving the tracking of the controlled signal.
So the core of the repetitive control system is the internal model, the performance of repetitive control lies in the establishment of internal model. Figure 7(a) is a block diagram of an ideal structure, which is equivalent to an integral of a step size with certain cycles, so that a given signal is tracked. If the repeat control system is stable，the constraint is ∥ 1 − P ∥ ∞ < 1. However, it is difficult for the system to satisfy this constraint during the operation of the ideal internal mode. Therefore, internal model structure should be improved. As shown in Figure 7(b), in the feedback loop, the auxiliary compensator 1 − − is replaced by Q(z) to ensure the stability of the system. 7 (a). the ideal structure block diagram + + Q(z) Fig. 7 (b). Improved internal model block diagram The N is the fundamental period sampling number, and the Q(z) is a low-pass filter constant, or a function, to enhance system stability, this paper takes 0.95 and z −N as the periodic delay link, the E(z) is the input and output error, the (z) is the internal model output.
In the improved internal model structure, the auxiliary compensator S(z) and the periodic delay link − . The complete repeat controller is constructed, as shown in figure 8. In the formula, Kr is the compensator gain to adjust the output amplitude, generally 0 < Kr < 1, the main function is to compensate filter phase, S'(z) for low pass filter, To eliminate the high resonance peak of P(z).  and distortion is small. Fig. 9 (a). Voltage simulation waveforms of compound control in one phase no-load operation