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Performance improvement of three-phase AFE rectifier during switching of loads with fractional feedback current control

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Abstract

This proposed work investigates the performance of dc voltage of a three-phase Active Front-End (AFE) Sinusoidal Pulse Width Modulated (SPWM) rectifier during load switching. To obtain desired performances, a transfer function is derived in synchronous reference frame (dq), from which the gain of the PI controllers are estimated and observed the performance accordingly. In this research, the load current is feed-forwarded with d-axis current by a suitable choice of gain factor, which results a fractional feedback d-axis current control and improves the transient behaviour simultaneously. This will unalter the other performance parameters of the system such as, UPF operation, less Total Harmonic Distortion (THD) of input current, dc voltage boost etc. All the simulation results exhibits satisfactory performance and validated with a prototype developed using STM32F303RE microcontroller accordingly.

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Abbreviations

\((V_{c_1})_{LL}\) :

Fundamental line-to-line converter voltage

\(m_a\) :

Amplitude modulation index

\(V_{dc}\) :

dc-link voltage

\(v_{s_{dq}}\) :

Source voltage in dq domain

\(i_{s_{dq}}\) :

Fundamental source current in dq domain

\(v_{c_{dq}}\) :

Fundamental converter voltage in dq domain

\(L_s\) :

Source inductance

\(r_s\) :

Parasitic resistance

\(X_s\) :

Source reactance

\(V_m\) :

Peak input voltage

\(R_L\) :

Load resistance

\(P_o\) :

Output Power

\(R_{eq}\) :

Equivalent load resistance

\(\omega \) :

Angular resonant frequency

\(S_{dq}\) :

dq - axis switching function

\(i_L\) :

Load current

\(C_d\) :

dc side filter capacitance

\(\omega _n\) :

Angular natural frequency

\(\zeta \) :

Dam** ratio

\(f_{sw}\) :

Switching frequency

\(T_s\) :

Sampling rate of controller

\(T_i\) :

Current loop time constant

\(k_{p_i}, k{i_i}\) :

PI controller current loop gains

\(k_{p_v}, k{i_v}\) :

PI controller voltage loop gains

\(B_{0_i}, B_{1_i}\) :

Discrete PI controller current loop gains

\(B_{0_v}, B_{1_v}\) :

Discrete PI controller voltage loop gains

\(f_i, f_v\) :

Frequency bandwitdh of current and voltage loop

\(\omega _{c_g}\) :

Gain cross-over frequency

\(\omega _{c_p}\) :

Phase cross-over frequency

\(\delta \) :

Angle between source and converter voltage

\(\Delta i_{s_d}\) :

Ripple inductor current

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Authors and Affiliations

  1. Department of Electrical Engineering, Narula Institute of Technology, Kolkata, India

    Arkendu Mitra

  2. Power Electronics Divison, Epoch Innova Pvt. Ltd., Howrah, India

    Sayan Das

  3. Department of Electrical Engineering, Swami Vivekananda University, Kolkata, India

    Sujoy Bhowmik

  4. Department of Applied Physics, University of Calcutta, Kolkata, India

    Sumana Chowdhuri

Authors
  1. Arkendu Mitra
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  2. Sayan Das
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  3. Sujoy Bhowmik
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  4. Sumana Chowdhuri
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Corresponding author

Correspondence to Arkendu Mitra.

Appendix

Appendix

The passive elements of the filter at ac side of the converter plays major role from its stability. The inductor provides a coupling between source voltage and converter voltage, whereas the transient behaviour of the converter is defined by the capacitor.

For boost operation of the converter, the ratio between output and input voltage can be established as

$$\begin{aligned} \dfrac{V_{dc}}{V_{s_d}} = \dfrac{1}{S_d} \end{aligned}$$

where, \(S_d = 0.5 m_a \cos \delta \). The ripple current through the inductor will be

\(\Delta \) \(i_{s_d} = \dfrac{(1-S_d)V_{s_d}}{L_s f_s}\)

For small value of \(\delta \), \(\cos \delta \approx 1\) and \(S_d \approx 0.5 m_a\). Considering Continuous Conduction Mode (CCM) of operation, the value of inductance should be maintained at

$$\begin{aligned} L_s \ge \frac{\left( 2 - m_a\right) (m_a V_{dc})^2}{16 P_o f_s} \end{aligned}$$

The ripple in the capacitor voltage in can be defined as

$$\begin{aligned} \Delta V_{dc} = \dfrac{\left( 1-S_d\right) P_o}{V_{dc} C_d f_s} \end{aligned}$$

To maintain ripple of the output voltage within 5% from the set point, the value of capacitor should be kept at

$$\begin{aligned} C_d \ge \frac{(2 - m_a) P_o}{0.1 V_{dc}^2 f_s} \end{aligned}$$

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Mitra, A., Das, S., Bhowmik, S. et al. Performance improvement of three-phase AFE rectifier during switching of loads with fractional feedback current control. Sādhanā 49, 203 (2024). https://doi.org/10.1007/s12046-024-02539-3

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