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The harmonics of line to line voltage in two-stage matrix converter (TSMC) with fixed carrier frequency had discrete and high values and produced powerful electromagnetic interference (EMI). In this paper, chaotic carrier frequency modulation technique (CCFMT) was applied in TSMC for the first time to spread sideband range and suppress harmonic peak value. Although this technique could suppress EMI, it would increase the probability of narrow pulses. In order to improve reliability, the rectifier in the two-stage matrix converter uses PWM modulation with zero vector to extend the zero current commutation time, solves the narrow pulse problem, and simplifies the commutation process. At last, an experiment platform was designed and experimental results showed that harmonics of line to line voltage was efficiently suppressed.

TSMC is a kind of direct AC/AC converters, which consists of rectifier and inverter with no filter capacitors. Apart from the advantages of matrix converter, TSMC also possesses some outstanding features, for instance, zero current commutation of rectifier, simple clamping circuit, and less switches at particular condition. Therefore, TSMC has become one of the most promising areas in many fields [

However, due to the fixed carrier frequency, the harmonics which appear at integer multiples of the carrier frequency of TSMC line to line voltage possess discrete and high values and produce powerful EMI. In order to meet the demands of electromagnetic compatibility (EMC), output filter should be adopted, which not only increases the volume and weight but also produces additional harmonics [

In response to these shortcomings, we propose a new CCFMT which can improve commutation reliability. It can solve the narrow pulse problem and simplify the commutation process. In addition, we demonstrate the effectiveness and superiority of the proposed CCFMT to suppress EMI of TSMC on TSMC experiment platform [

Figure

Topology of TSMC.

In this paper, we adopt chaotic carrier frequency. The carrier frequency

When the carrier frequency changes according to chaotic principle, the switching moment will be uncertain. It brings about irregularly distributed narrow pulses due to decreasing commutation time as the carrier period shortens. Although some enlarged carrier periods can remove the corresponding narrow pulses, CCFMT will increase the narrow pulses generally. The rectifier zero vector action time (ZVAT) is large at the transition of sectors. Thus if rectifier zero vector is employed, we can extend the commutation time, remove the influence of narrow pulses, and improve commutation reliability. Based on that, we propose a new CCFMT to improve the commutation reliability of TSMC [

Suppose the normalized form of expected three-phase input current is as follows:_{α}, d_{β}, and d_{0} are action time duty radios of

Space vectors of input current.

The definitions of i_{1} and i_{2} are as follows:

Waveforms of rectifier and inverter.

In (

To make full use of the two line voltages, the same duty ratio of inverter should be adopted in two action times, which ensures the phase angle could stay same in one carrier period. Equation (

Modulation diagram of rectifier and inverter: (a) sector 1 and (b) sector 2.

The TSMC conventional modulation contains three constant frequencies, namely,

The phase voltage of the output A-phase is expressed as follows:

In the formula,

Since the modulation function of phase B lags the phase A by 2

Thus, the Fourier series of the line voltage

The amplitude of the

According to (

Output line voltage spectrum simulation diagram.

From the perspective of time domain analysis, the PWM pulse is formed by the pulse connection of different switching moments of a certain width [

According to the principle of conservation of harmonic energy, the wider the frequency bands of a single harmonic extension, the lower the amplitude. It can be seen from (

According to the constant carrier frequency modulation, the output voltage frequency at the maximum frequency offset frequency Δ

The TSMC modulates the sinusoidal input and output current through the cooperative operation of the rectification stage and the inverter stage. The change of the current is determined by the applied pulse, so the modulated current has ripples of up and down jitter. The magnitude of the ripple is related to the pulse width of the action, and the pulse width is determined by the product of the duty cycle of each switch and the switching period. The duty cycle is related to the modulation wave and is independent of the carrier frequency. In constant carrier frequency modulation, the pulse width changes over and over again. In CCFMT, the pulse width changes in a chaotic manner, thus causing a chaotic change in current modulation time. In a carrier cycle, as the carrier period becomes larger, the current change time also increases, and the range of variation also increases. As the carrier cycle becomes smaller, the range of current variation also becomes smaller. The CCFMT changes the carrier frequency up and down around the center frequency, resulting in an increase in current ripple. The larger the range of carrier frequency variation, the larger the maximum frequency offset Δ

During one carrier cycle, the TSMC rectification stage is modulated by two line voltages, and the inverter stage is demodulated separately during the two line voltages. The pulse width of the rectification stage is affected by the change of the carrier frequency than the pulse width of the inverter stage, so the input current ripple is also affected by the CCFMT and larger than the output current ripple.

In Figure

Figure

Relation between minimum commutation time and

To verify the effectiveness of CCFMT, the TSMC experiment platform is built in Figure

Experimental platform of TSMC.

(a) Waves of input phase voltage and input current (CFMT). (b) Waves of output line voltage and output current, and frequency spectrum of output line voltage (CFMT). (c) Waves of input phase voltage and input current (CCFMT). (d) Waves of output line voltage and output current, and frequency spectrum of output line voltage (CCFMT).

In order to evaluate the effect of △

HSF of output voltages from fixed CFMT and CCFMT with different △

△ | 0 | 2 | 3 | 4 | 5 |
---|---|---|---|---|---|

HSF | 0.85 | 0.7 | 0.68 | 0.66 | 0.64 |

This paper first proposed the application of CCFMT to TSMC. The proposed new CCFMT can effectively improve the reliability of commutation, solve the narrow pulse problem, and simplify the commutation process. By changing the carrier frequency, extending the harmonic spectrum, and reducing the peak value of the output voltage harmonics, EMI is effectively suppressed. In addition, the effectiveness of CCFMT was proved by experiments. However, CCFMT will increase the input current ripple and still need improvement in future research.

The data used to support the findings of this study are available from the corresponding author upon request.

The authors declare that there are no conflicts of interest regarding the publication of this article.

The work was supported by the Qingdao Postdoctoral Fund (No. 2015118) and Key Research, the Development Plan of Shandong Province (No. 2017GGX50114 and No. 2018GGX105007), and the Scientific Research Development Plan of Shandong Higher Education Institutions (No. J18KA316).

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