Harmonic Control of Single-Phase Square Wave Inverter Circuit

Harmonic control of single-phase square wave inverter circuit

1. Basic methods of harmonic control in inverter circuits
Through the previous introduction, the square wave inverter circuit solves the problems of frequency modulation and voltage regulation.
There is no problem for applications such as induction heating. However, if the inverter circuit is applied to
applications such as motor speed regulation, the main problem is the high harmonic content; therefore, solving
the harmonic problem is the key to the application of inverter power supply
in speed regulation, UPS and other occasions. Commonly used harmonic control methods include: SPWM modulation method, current tracking method, specified detuning
method and other methods.
2. SPWM modulation technology and its application
1. Theoretical basis of sinusoidal pulse width modulation (SPWM) technology
There is an important conclusion in sampling control theory:
when narrow pulses of different shapes but equal areas are added to linear links, the output effect obtained is basically the same. As shown in the figure,
the voltage source u(t) with rectangular, triangular, half-sine narrow pulse and ideal unit pulse function as waveforms
is applied to R and L loads. When the load time constant is much longer than the excitation pulse duration
, the response i(t) is basically the same, and only differs in the rising section. Since the descending section with a
longer response duration reflects the low-frequency component, and the rising section with a short duration reflects the
high-frequency component of the response, the responses are basically the same in the low-frequency section according to Fourier analysis, and the difference exists
in the high-frequency section. When the excitation pulse is narrower (or the load inertia constant differs more from the pulse duration
), the proportion of the high-frequency section of the response is smaller, and the whole response is more similar.

The response of a linear system's periodic narrow pulse group can be equivalent to the corresponding superposition of each narrow pulse
. In this way, the response of a certain excitation function with time as the independent variable added to the inertial link can
be equivalent to the response obtained by adding a narrow pulse sequence with the same area as the time period to the same link
.
By using the area of ​​the corresponding time period of the equal-area sequence pulse equivalent to the sine half wave,
a series of pulse sequences with pulse widths varying with the instantaneous value of the sine wave are formed, namely, SPWM waves, as
shown in the figure. The output of the switching power converter is a pulse function. By applying a high-frequency SPWM wave to the load
and configuring a low-pass filter link, the required low-frequency sinusoidal response can be generated, namely,
the basic principles and methods of SPWM modulation technology.
2. Natural sampling method - the basic method of generating SPWM waves
According to the comparison between the triangle wave (or sawtooth wave, collectively referred to as the carrier) and the sine wave (modulation wave), the method of generating the SPWM pulse sequence is called the natural sampling method.
The value of the sine wave is different at different phase angles, and the pulse width obtained by intersecting with the triangle wave is also different;
when the frequency and amplitude of the sine wave change, the width of each pulse also changes accordingly. This function can be easily realized
using an analog circuit. The sine wave and the triangle wave are applied to the two inputs of the comparator, and its output is the SPWM wave. Therefore, this method is more commonly used in analog control methods, but it is generally not commonly used as a digital control due to the large amount of calculation.
Illustration of the natural sampling method:
uc is a triangle carrier with a period of Tc
us is a sine modulation wave with a period of Ts
When us> uc, the output is +Uo
When us< uc, the output is -Uo
Generally, there is: Ts>> Tc
usm≤ ucm

3. Regular sampling method (improvement of natural sampling method - suitable for digital control)
Principle of regular sampling method
Taking the instantaneous value of the modulation wave at the valley point of the carrier cycle as the amplitude of the modulation wave in the entire carrier cycle
, the method of comparing the modulation wave with the carrier to obtain the SPWM signal is called regular sampling method.
Characteristics of regular sampling method
(1) It is equivalent to replacing the sinusoidal modulation wave with a step wave based on the instantaneous value of the modulation wave at the valley point of the carrier cycle
to generate the SPWM wave;
(2) In digital control systems, the SPWM signal is generated by a computer, and the start and
end times of each pulse need to be calculated or looked up in real time. This method greatly reduces the calculation workload
, so it is widely used in digital control systems.
Schematic diagram of regular sampling method:
uc is a triangular carrier with a period of Tc
us is a sinusoidal modulation
wave with a period of Ts The instantaneous value of the modulation wave at the valley point of the carrier cycle
is the amplitude of the modulation wave in the entire carrier cycle us(t0)
When us>uc, output +Uo
When us