MATLAB simulation of dead zone effect harmonics of AC/DC/AC power supply

At present, most of the control methods of various inverter power supplies and the analysis of SPWM signal modulation methods are based on the assumption that the power switching device is an ideal switching device, that is, the rise, fall and storage time of the switching device are not considered. But in fact, any switching device has a switching delay, especially the shutdown process. Therefore, in the voltage-type inverter, in order to prevent the upper and lower switches of the same bridge arm of the inverter bridge from being directly connected, a fixed delay time (i.e., dead time) must be inserted between the upper and lower tube control signals. The introduction of dead time will deteriorate the waveform quality of the inverter output, increase the harmonic components, and reduce the dynamic performance of the system. In addition, as the switching frequency increases, the various effects caused by the addition of dead time (referred to as dead time effect) increase.

1 Mathematical analysis of harmonics in SPWM system

In the SPWM system, in addition to the harmonics generated by the dead zone effect, the harmonics generated by the inherent reasons of the SPWM signal modulation method itself are called inherent harmonics. The output AC waveform during SPWM control (carrier frequency ratio is 2N, modulation parameter is M) can be expressed as (k=1,2,3,...) using Fourier series. Analyzing the waveform characteristics of the figure, it can be seen that the output is a unit amplitude waveform with odd quarter wave symmetry. Therefore, it can be proved that in formula (1), (θ1, θ2, etc. are the pulse triggering moments, that is, the intersection of the triangle wave and the sine wave), where N is an even number. Integrating each term of the above formula, it can be proved that when k is any odd number.

Among them, 0°<θ1<θ2<…<θN <π/2. Since the switching angle of the natural sampling method follows an iterative relationship, it cannot be expressed explicitly, so the regular sampling method is often used in actual application. Its main principles are as follows: At a fixed moment in each cycle of the triangular carrier (such as the peak point of the carrier), the sine wave is sampled to determine the on and off of the switching element, regardless of whether the sine wave and the triangular wave intersect at the sampling point. The components of each harmonic can be calculated from this formula.

2 MATLAB modeling of AC/DC/AC power supply and dead zone characteristics

MATLAB is an advanced mathematical analysis and calculation software that can be used for modeling and simulation of dynamic systems. The MATLAB language has been successfully and conveniently applied in the development of electric drive systems in its simulation research. It has the following characteristics: (a) user-friendly, high programming efficiency, simple language, rich connotations, easy to learn and use; (b) efficient and convenient matrix and array operations; (c) extremely convenient drawing functions; (d) with SIMULINK dynamic simulation tools and other functions such as Toolbox; (e) strong expansion capabilities.

3 Simulation Examples

First, it is drawn from the 50Hz power supply, and then it is transformed into a low voltage acceptable to the rectifier through a Y/Δ transformer. After rectification and filtering, it is sent to the IGBT inverter. The trigger signal of the inverter is sent by the PWM signal with dead zone. Then it is sent to the load after three-phase filtering. 4 Implementation of dead zone

Although there are many ready-made modules in Simulink, there is only an idealized PWM generator in the Toolbox. For the dead zone effect to be studied in this paper, it is necessary to expand and repackage it to establish a PWM generator module with dead zone.

In an ideal PWM module, the trigger pulses pulse1 and pulse2 of the upper and lower switches of the bridge arm are complementary. However, in an actual inverter, since the switch elements have a turn-off time, if the trigger signals are ideally complementary, the upper and lower bridge arms will inevitably be directly connected, causing a short circuit and directly destroying the entire power supply . Therefore, for the two signals pulse1 and pulse2, there must be a certain interval between the two trigger signals, which is the so-called dead zone.

First, find the transport delay module in the continuous directory of simulink. This module can delay a function, which is equivalent to shifting the entire function to the right on the time axis. Let pulse 1 be pulse1, and the delayed signal be pulse 1' or pulse1'. According to the logical relationship, the adjusted pulse signal is pulse 1" or pulse1": pulse1*pulse1'=pulse1"; compared with pulse1, the rising edge of the trigger signal of pulse1" is shifted to the right, while the falling edge remains unchanged.

5 Simulation Results

The output power signal is simulated when the carrier frequency is 3000Hz, the dead time is 0, and the modulation depth is 0.8.

The existence of dead zone has a great impact on the voltage waveform, not only greatly reducing the amplitude of the fundamental wave, but also increasing the content of harmonics. It is extremely harmful to the motor, not only reducing the machine efficiency, but also the harmonics generate stray torque, endangering the safe operation of the motor.

6 Conclusion

This paper mathematically analyzes the inherent harmonics generated by SPWM inversion and the additional harmonics generated by dead zone, and establishes a mathematical model for quantitative analysis. The AC/DC/AC power supply is simulated based on MATLAB, and the MATLAB programming of the dead zone time trigger model is realized . Based on the above work, the Fourier transform of the SPWM voltage waveform with dead zone is performed, and the influence of the dead zone on the voltage waveform is preliminarily studied.