Due to the components at twice the fundamental frequency of output voltage in the instantaneous output power of a two-stage single-phase inverter (TSI), the second harmonic current (SHC) is generated in the front-end dc-dc converter (FDC). To reduce the SHC, optimizing the control strategy of the FDC is an effective and costless approach. From the view of visual impedance, this paper conducts an intensive study on the SHC reduction strategies. Origin of the SHC is illustrated first. Then, the equivalent circuit models of the FDC under different control strategies are proposed to analyse the SHC propagation characteristic. The derived model can offer a better insight into how the inductor SHC is affected by the control parameters. According to the derived models, a synthesis of different control strategies is presented and the relevant parameters are listed for control design to achieve better suppression effect. The benefits and limitations of these control strategies are also discussed. Based on the proposed equivalent circuit models, several optimization methods are proposed to enhance the effect. A 1500 VA TSI prototype is built and simulated on MATLAB/Simulink, verifying the effectiveness of the proposed optimization methods. This paper is aimed to provide a guideline for the control design and control optimization of the TSIs.
Two-stage single-phase inverters (TSIs) have been widely used in renewable systems [
Due to the components at twice the fundamental frequency of output voltage in the instantaneous output power, the SHC is generated in the input current of the TSI. The SHC will increase the current stress and affect the lifetime of power switches. Moreover, the SHC causes extra power loss and lessen the soft-switching range of power switches, reducing the overall system efficiency [
For an open-loop system, the magnitude of the SHC in the FDC is fully dependent on the passive energy-storage elements. Thus, the PCM is often to enlarge the energy storage elements in the converter (capacitor and/or inductor), such as connecting a large parallel capacitor to the input and/or the output terminals of the FDC [
As these disadvantages of the PCMs aforementioned, ACMs are more often used for their low cost and non-invasiveness. According to the different implementation approaches, the ACMs can be classified into two main categories. One way is the current-ripple injection method, where a bidirectional active filter is often used to compensate the required SHC of the dc-ac inverter [
In order to analyse these methods from a unified perspective, equivalent circuit models of the FDC under different control strategies are proposed in this paper. The derived model can offer a better insight into how the inductor SHC is affected by the control parameters. According to the derived models, a synthesis of different control strategies is presented and the key parameters relevant to SHC are listed to reveal the benefits and limitations of these control strategies. Based on the proposed equivalent circuit models, several optimization methods are also proposed to enhance the effect. A 1500 VA TSI prototype is built and simulated on MATLAB/Simulink, verifying the effectiveness of the proposed optimization methods. This paper is aimed to provide a guideline for the control design and control optimization of the TSIs.
To study the composition of the input SHC, neglecting the switching harmonics, the downstream inverter is equivalent to a dc current source
In most applications, FI-SHCRS is sufficient to reduce the input SHC into an acceptable level and along with its easy implementation, is more commonly used. But for better suppression effect in particular applications, input SHC control strategy is needed.
FI-SHCRS is the most common used method to suppress the input SHC of the two-stage inverters. For the FDC, control loops are often used to realize voltage regulation and short current limitation. Here, Buck converter is adopted as the FDC to analyse the influences of different control loop parameters on the SHC propagation. For a better insight into where the magnitude of the SHC lies, the equivalent circuit models under different control strategies are derived.
According to Manson’s rule, the inductor second harmonic currents of the three control strategies can be derived respectively as
From
The concept of visual impedance has been widely used in grid-connected inverters [
For the open-loop Buck converter, the equivalent circuit model can be derived according to
For the voltage single-loop Buck converter, the equivalent control block diagram can be acquired by moving the voltage-loop feedback node as shown in
From this perspective, the voltage loop can be equivalent to a visual impedance Zvs(s) in parallel with the filter inductor, where 1/Zvs(s) can be expressed by
To verify the correctness of the model,
Substituting
It can be found that
For the voltage current dual-loop Buck converter, the equivalent transform 1 can be achieved by moving the voltage and current loop feedback nodes as
From this perspective, the outer voltage loop is equivalent to a visual impedance
To verify the correctness of the model,
Substituting
It can be found that
Substituting
It can be found that
Accordingly, the resonance frequency can be calculated by
In general,
Therefore,
– | – | – | – | – | / | |
– | – | – | / | / | + | |
– | – | – | – | – | + | |
/ | / | / | + | / | + | |
/ | / | / | / | + | + | |
/ | / | / | + | + | + | |
– | – | – | –/+ | –/+ | + |
In conclusion, the impedance of the inductor branch
The visual impedance is useful for the analysis of the inductor SHC but may be helpless for the analysis of the input SHC.
Actually, if the dc components and the harmonic components at the switching frequency are neglected, a Buck converter is equivalent to the circuit model as shown in
As a matter of fact, the equivalent inductor
The existing SHC reduction control strategies are reviewed and an insight into the existing inductor SHC reduction strategies from the visual impedance is provided.
In [
In [
In [
Actually, for a voltage current dual-loop Buck converter, these control strategies can be summarized as shown in
In [
In [
In order to achieve a better effect in the input SHC reduction, the input SHC is directly extracted for control [
In order to verify the analysis above, a 1500 VA TSI prototype is built and simulated on MATLAB/Simulink. The FDC is a push-pull forward converter, and the downstream inverter is a single-phase full-bridge inverter. The main parameters of the built TSI are listed in
Parameter | Symbol | Value | Parameter | Symbol | Value |
---|---|---|---|---|---|
Input voltage | 28 | Filter capacitance | 400 | ||
Output voltage | 115 | Filter inductance | 670 | ||
DC bus voltage | 180 | Modulation ratio | m_{f} | 1/2.4 | |
Output frequency | 400 | Voltage sensor gain | 0.055 | ||
Output power | 1.5 | Current sensor gain | 0.5 | ||
Switching frequency | 80 | Transformer turn ratio | n | 10 |
The reverse propagation gains of SHC are drawn as shown in
Due to the components at twice the output voltage frequency in the instantaneous output power of a two-stage single-phase inverter, the second harmonic current (SHC) is generated in the front-end dc-dc converter. To reduce the SHC, optimizing the control strategy of the front-end dc-dc converter is an effective and costless approach. According to the input pulsating instantaneous power analysis, the origin of the input SHC is divided into two parts:
For a better comprehension of FI-SHCRS, equivalent circuit models are proposed from the view of visual impedance. The derived models can offer a better insight into where the magnitude of the inductor SHC lies when the front-end dc-dc converter is under different control strategies. Meanwhile, important parameters, which can be used to reduce the inductor SHC, are analysed and summarized. Knowledge about the effects of these parameters on the SHC propagation can serve as a guideline for the design and optimization of the front-end dc-dc converters.
With the derived circuit models, different inductor SHC reduction schemes are reviewed and several optimization strategies are proposed. The limitation of FI-SHCRS is also revealed and I-SHCRS is indicated to be a better control strategy in the input SHC reduction.