# A New Generalized Step-Down Single-Stage AC/AC Power Converter

^{1}

^{2}

^{3}

^{4}

^{*}

## Abstract

**:**

## 1. Introduction

- It cannot perform generalized/multi frequency power conversion;
- The output voltage waveform suffers from high total harmonic distortion (THD) problem;
- It adds lower-order harmonic and inter-harmonic contents to the output power for the inductive load.

- A new single-stage line-frequency switching AC/AC power converter is proposed;
- The proposed converter can be used to convert any frequency without changing the hardware circuit;
- The proposed topology does not require any high-frequency switching pulse width modulation technique.

## 2. Theoretical Background

_{ch}= f

_{i}± 2nf

_{0}

_{i}and f

_{0}are the input and output voltage frequency, respectively, and n = 1, 2, 3… For a six pulse bridge converter, the harmonic frequencies can be calculated as:

_{ch}= (6P ± 1) f

_{i}± 2nf

_{0}

_{h}= qf

_{i}± 2nf

_{0}

_{0}equals or very close to qf

_{i}.

## 3. Proposed AC/AC Power Converter

#### 3.1. Generalized Configuration of Proposed AC/AC Power Converter

_{o,}and even frequency conversion, m

_{e}.

_{o}can be calculated as:

_{wo}= m

_{o}+ 1

_{e}can be calculated as:

_{we}= m

_{e}

_{o}can be calculated as:

_{Do}= 2(m

_{o}+ 1)

_{e}can be calculated as:

_{De}= 2m

_{e}

_{o}can be calculated as:

_{So}= m

_{o}+ 1

_{e}), the required number of switches is equal to the number of even frequency conversions (m

_{e}).

_{Se}= m

_{e}

#### 3.2. Operating Principle of the Proposed Topology

_{out}= V

_{m}/2

_{out}= −V

_{m}/2

_{out}= V

_{m}/2

_{out}= −V

_{m}/2

_{out}= −V

_{m}

_{out}= V

_{m}

_{out}= −V

_{m}

_{out}= V

_{m}

_{out}= 0.5*V

_{m}*sinα; 0 ≤ α ≤ π

_{out}= −V

_{m}*sinα; π ≤ α ≤ 2π

_{out}= 0.5*V

_{m}*sinα; 2π ≤ α ≤ 3π

_{out}= 0.5*V

_{m}*sinα; 3π ≤ α ≤ 4π

_{out}= −V

_{m}*sinα; 4π ≤ α ≤ 5π

_{out}= 0.5*V

_{m}*sinα; 5π ≤ α ≤ 6π

_{out}= 0.5*V

_{m}*sinα; 0 ≤ α ≤ π

_{out}= −V

_{m}*sinα; π ≤ α ≤ 2π

_{out}= V

_{m}*sinα; 2π ≤ α ≤ 3π

_{out}= −0.5*V

_{m}*sinα; 3π ≤ α ≤ 4π

_{out}= −0.5*V

_{m}*sinα; 4π ≤ α ≤ 5π

_{out}= V

_{m}*sinα; 5π ≤ α ≤ 6π

_{out}= −V

_{m}*sinα; 6π ≤ α ≤ 7π

_{out}= 0.5*V

_{m}*sinα; 7π ≤ α ≤ 8π

## 4. Performance Analysis of the Proposed AC/AC Power Converter

_{1}and T

_{2}pass the winding-1 and winding-2 voltage, and switch T

_{3}and T

_{4}pass the winding-3 and winding-4 voltage. Therefore, the possible voltage stress for switches T

_{1}and T

_{2}is 110 V, and the possible voltage stress for switches T

_{3}and T

_{4}is 220 V.

## 5. Harmonics Analysis of the Proposed AC/AC Power Converter

_{0}and a

_{n}are always zero, and b

_{n}exists. For the b

_{n}coefficient, all of the even terms are zero; only odd harmonic terms exist. The output wave-form of the conventional AC/AC converter is always half-wave symmetry. Hence, using the technique of the half-cycle pairs method [26], the Fourier series expression of the conventional 3:1 frequency conversion output voltage can be written as follows:

_{m}. However, in the proposed AC/AC converter, the amplitude of all of the half cycles is not the same. The amplitude of the second half cycle and the fifth half cycle is V

_{m}, but the first, third, fourth, and sixth half cycles are V

_{m}/2 as shown in Figure 3. Therefore, the Fourier series expression of the proposed AC/AC power converter (e.g., 3:1 conversion) can be rewritten as follows:

## 6. Hardware Implementation

## 7. Result Analysis and Comparison

_{s}= 120f/p

_{s}is the speed of the machine. The proposed series-connected diode SCR-controlled AC/AC power converter drive operates on the variable frequency drive principle; when the frequency is changed, the speed is changed as well. Figure 20 depicts the dynamic speed change response of the single phase induction motor using the conventional and proposed AC/AC power converters. There is a significant speed ripple in the dynamic response of conventional converter drive. The power quality problems are responsible for this phenomena. The rated and variable frequency operations were also noted in Figure 20. In the rated frequency operating region, there is no difference between the speeds of the conventional and proposed AC/AC power converters.

- The PWM/delta modulation technique uses a complex gate driving technique with high frequency switching. However, every modulation technique needs a line filtering method for harmonic removal. As a result, the modulation technique is very complex, in relative terms.
- The line filtering technique needs a massive number of passive components. The passive components, i.e., the inductor, reduce the power factor, and the tuning of the filtering parameter is difficult at the dominant harmonics.
- The proposed transformer based harmonic reduction technique can easily remove the lower order harmonic content, as well as reducing the overall THD without using any line filtering technique. The lower order harmonic content removal is highly desirable for motor drive applications, in order to reduce the speed ripple. Most of the industry uses a transformer-based AC/AC converter topology because it provides galvanic isolation for the converter as well as the motor load. As such, the proposed transformer-based harmonic reduction technique proves its excellency as an AC/AC converter in variable frequency drive applications.

## 8. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

## Nomenclature

SAG | Semi-autogenous grinding |

THD | Total harmonic distortion |

PDM | Pulse density modulation |

VFD | Variable frequency drive |

PWM | Pulse width modulation |

AM | Amplitude modulation. |

## References

- Surapaneni, R.K.; Yelaverthi, D.B.; Rathore, A.K. Cycloconverter-based double-ended microinverter topologies for solar photovoltaic ac module. IEEE J. Emerg. Sel. Top. Power Electron.
**2016**, 4, 1354–1361. [Google Scholar] [CrossRef] - Xu, D.; Zhong, S.; Xu, J. Bipolar Phase Shift Modulation Single-Stage Audio Amplifier Employing a Full Bridge Active Clamp for High Efficiency Low Distortion. IEEE Trans. Ind. Electron.
**2020**. [Google Scholar] [CrossRef] - Branko, L.; Branko, B. Power Electronics: Converters and Regulators; Springer: New York, NY, USA, 2015. [Google Scholar]
- Rashid, M.H. Power Electronics: Circuits, Devices, and Applications; Prentice Hall: Upper Saddle River, NJ, USA, 1993. [Google Scholar]
- Jacovides, L.J.; Matouka, M.F.; Shimer, D.W. A cycloconverter-synchronous motor drive for traction applications. IEEE Trans. Ind. Electron.
**1981**, IA-17, 407–418. [Google Scholar] [CrossRef] - Wu, B.; Pontt, J.; Rodríguez, J.; Bernet, S.; Kouro, S. Current-source converter and cycloconverter topologies for industrial medium-voltage drives. IEEE Trans. Ind. Electron.
**2008**, 55, 2786–2797. [Google Scholar] - Palavicino, P.C.; Valenzuela, M.A. Modeling and evaluation of cycloconverter-fed two-stator-winding SAG mill drive—Part I: Modeling options. IEEE Trans. Ind. Appl.
**2015**, 51, 2574–2581. [Google Scholar] - Palavicino, P.C.; Valenzuela, M.A. Modeling and evaluation of cycloconverter-fed two-stator-winding SAG mill drive—Part II: Starting evaluation. IEEE Trans. Ind. Appl.
**2015**, 51, 2582–2589. [Google Scholar] [CrossRef] - Greer, S.A. Selection criteria for SAG mill drive systems. IEEE Trans. Ind. Appl.
**1990**, 26, 901–908. [Google Scholar] [CrossRef] - Rodríguez, J.R.; Pontt, J.; Newman, P.; Musalem, R.; Delpino, H.A.M.; Moran, L.; Alzamora, G. Technical evaluation and practical experience of high-power grinding mill drives in mining applications. IEEE Trans. Ind. Appl.
**2005**, 41, 866–874. [Google Scholar] [CrossRef] - Pontt, J.; Rodriguez, J.; Rebolledo, J.; Martin, L.S.; Cid, E.; Figueroa, G. High-power LCI grinding mill drive under faulty conditions. In Proceedings of the 2005 Fourtieth IAS Annual Meeting. Conference Record of the 2005 Industry Applications Conference, Kowloon, Hong Kong, China, 2–6 October 2005; pp. 670–673. [Google Scholar]
- Kant, P.; Singh, B.; Chandra, A.; Al-haddad, K. Twenty pulse AC-DC converter fed 3-level inverter based vector controlled induction motor drive. In Proceedings of the 43rd Annual Conference IEEE Industry Applications Society Annual Meeting, Beijing, China, 29 October–1 November 2017; pp. 2225–2230. [Google Scholar]
- Singh, B.; Kant, P. A 54-pulse AC-DC converter fed 15-level inverter based vector controlled induction motor drive. In Proceedings of the 2017 IEEE Industry Applications Society Annual Meeting, Cincinnati, OH, USA, 1–5 October 2017; pp. 1–7. [Google Scholar]
- Liu, Y.; Heydt, G.T.; Chu, R.F. The power quality impact of cycloconverter control strategies. IEEE Trans. Power Deliv.
**2005**, 20, 1711–1718. [Google Scholar] [CrossRef] - Slonim, M.A.; Biringer, P.; Slonim, M.A.; Biringer, P.P. Harmonics of Cycloconverter Voltage Waveform (New Method of Analysis). IEEE Trans. Ind. Electron. Control Instrum.
**1980**, IECI-27, 53–56. [Google Scholar] [CrossRef] - Taufik, T.; Adamson, J.; Prabuwono, A.S. Pulse density modulated soft-switching single-phase cycloconverter. In Proceedings of the 2011 IEEE Applied Power Electronics Colloquium (IAPEC), Johor Bahru, Malaysia, 18–19 April 2011; pp. 189–194. [Google Scholar]
- Agarwal, V.; Agarwal, A. FPGA based delta modulated cyclo-converter. In Proceedings of the 2011 5th International Power Engineering and Optimization Conference, Shah Alam, Selangor, Malaysia, 6–7 June 2011; pp. 301–305. [Google Scholar]
- Babaei, E.; Heris, A.A. PWM-based control strategy for forced commutated cycloconverters. In Proceedings of the 2009 IEEE Symposium on Industrial Electronics & Applications, Kuala Lumpur, Kuala Lumpur, Malaysia, 4–6 October 2009; pp. 669–674. [Google Scholar]
- Agarwal, A.; Agarwal, V. Design of Delta-Modulated Generalized Frequency Converter. IEEE Trans. Ind. Electron.
**2010**, 57, 3724–3729. [Google Scholar] [CrossRef] - Idris, Z.; Hamzah, M.K.; Hamzah, N.R. Modelling & Simulation of a new Single-phase to Single-phase Cycloconverter based on Single-phase Matrix Converter Topology with Sinusoidal Pulse Width Modulation Using MATLAB/Simulink. In Proceedings of the 2005 International Conference on Power Electronics and Drives Systems, Kuala Lumpur, Malaysia, 28 November–1 December 2005; pp. 1557–1562. [Google Scholar]
- Yan, Z.; Xu, S.; Han, X.; Sun, X.; Li, J. A novel de-re-couple modulation strategy for full-wave mode single-phase high-frequency link inverter. In Proceedings of the 2014 IEEE Transportation Electrification Conference & Expo Asia-Pacific (ITEC Asia-Pacific), Beijing, China, 31 August–3 September 2014; pp. 1–4. [Google Scholar]
- Meier, S.; Norrga, S.; Nee, H. Modulation strategies for a mutually commutated converter system in wind farms. In Proceedings of the 2007 European Conference on Power Electronics and Applications, Aalborg, Denmark, 2–5 September 2007; pp. 1–10. [Google Scholar]
- Nayanasiri, D.R.; Vilathgamuwa, D.M.; Maskell, D.L. Half-Wave Cycloconverter-Based Photovoltaic Microinverter Topology With Phase-Shift Power Modulation. IEEE Trans. Ind. Appl.
**2013**, 28, 2700–2710. [Google Scholar] [CrossRef] - Basic, D.; Ramsden, V.S.; Muttik, P.K. Selective compensation of cycloconverter harmonics and interharmonics by using a hybrid power filter system. In Proceedings of the 2000 IEEE 31st Annual Power Electronics Specialists Conference, Galway, Ireland, 23–23 June 2000; pp. 1137–1142. [Google Scholar]
- Olivares, C.; Astudillo, P.; Moran, L.; Dixon, J. Interaction between Passive Filter and High Power Cycloconverter Drive. In Proceedings of the 2009 IEEE Industry Applications Society Annual Meeting, Houston, TX, USA, 4–8 October 2009; pp. 1–5. [Google Scholar]
- Ashraf, N.; Hanif, A.; Farooq, U.; Asad, M.U.; Rafiq, F. Half cycle pairs method for harmonic analysis of cycloconverter voltage waveform. In Proceedings of the 2013 International Conference on Open Source Systems and Technologies, Lahore, Pakistan, 16–18 December 2013; pp. 97–102. [Google Scholar]
- Bessadet, I.; Tedjini, H. The Performances of Hybrid Filter in Elimination of AC-AC Converters Harmonics Pollution. In Proceedings of the 2018 6th International Renewable and Sustainable Energy Conference (IRSEC), Rabat, Morocco, 5–8 December 2018; pp. 1–6. [Google Scholar]
- Frangopol, G.; Dache, C.R. A Solution for Reducing Harmonic Regime and Reactive Power Absorbed by a Cycloconverter. In Proceedings of the 2019 6th International Symposium on Electrical and Electronics Engineering (ISEEE), Galati, Romania, 18–20 October 2019; pp. 1–6. [Google Scholar]
- Kornilov, A.; Reznikov, S.B. Hybrid Direct Frequency Cycloconverter with Power Factor Correction for Use in Single and Multi-Phase Electric Power Systems. In Proceedings of the 2019 IEEE International Symposium on Electromagnetic Compatibility, Signal and Power Integrity (EMC+SIPI), New Orleans, LA, USA, 22–26 July 2019; pp. 13–17. [Google Scholar]
- Antunes, H.M.A.; Pires, I.A.; Silva, S.M. Evaluation of Series and Parallel Hybrid Filters Applied to Hot Strip Mills with Cycloconverters. IEEE Trans. Ind. Appl.
**2019**, 55, 6643–6651. [Google Scholar] [CrossRef] - Thompkins, T.M.; Kim, D.; Stone, P.; Shin, Y. Rolling Mill Cycloconverter Condition Assessment by Harmonic Current via Time–Frequency Signature. IEEE Trans. Ind. Inform.
**2018**, 14, 4376–4384. [Google Scholar] [CrossRef]

**Figure 1.**Simulated output voltage waveform of the conventional: (

**a**) 3:1 (m = 3) and (

**b**) 15:1 (m = 15) frequency conversions of a 50 Hz input frequency.

**Figure 3.**Eight operating modes for the 3:1 (m = 3) and 4:1 (m = 4) frequency conversions of a 50 Hz fundamental frequency.

**Figure 4.**Active operating mode for the (

**a**) 3:1 (m = 3) and (

**b**) 4:1 (m = 4) frequency conversions of a 50 Hz fundamental frequency.

**Figure 5.**(

**a**) Winding voltage, (

**b**) Rectified voltage, (

**c**) Switching pulses, and (

**d**) Output voltage for 3:1 (m = 3) of a 50 Hz frequency conversion.

**Figure 6.**(

**a**) Winding voltage, (

**b**) Rectified voltage, (

**c**) Switching pulses, and (

**d**) Output voltage for 4:1 (m = 4) of a 50 Hz frequency conversion.

**Figure 7.**Simulated current waveform for (

**a**) 3:1 (m = 3) and (

**b**) 4:1 (m = 4) of a 50 Hz frequency conversion.

**Figure 8.**The harmonic spectrums of the: (

**a**) output voltage, (

**b**) output current for the proposed 3:1 (m = 3) and 4:1 (m = 4) conversions, harmonic spectrums of the (

**c**) output voltage, and (

**d**) output current.

**Figure 10.**Experimental gate drive signals (5V/div) for the (

**a**) 3:1 (m = 3) and (

**b**) 4:1 (m = 4) frequency conversions of a 50 Hz fundamental frequency.

**Figure 11.**Experimental output voltage and current waveform for the (

**a**) 3:1 (m = 3) and (

**b**) 4:1 (m = 4) frequency conversions of a 50 Hz fundamental frequency.

**Figure 12.**Experimental dynamic frequency change response of the output voltage of the proposed AC/AC converter.

**Figure 13.**Experimental frequency spectra of the output voltage for the (

**a**) 3:1 (m = 3) and (

**b**) 4:1 (m = 4) frequency conversions.

**Figure 14.**Simulated output (

**a**) voltage waveform and (

**b**) current waveform of the 3:1 (m = 3) frequency conversion for the motor load of the proposed topology.

**Figure 15.**Simulated output (

**a**) voltage waveform and (

**b**) current waveform of the 3:1 (m = 3) frequency conversion for the motor load of the conventional topology.

**Figure 16.**Simulated total harmonic distortion of: (

**a**) the conventional output voltage, (

**b**) the proposed output voltage, (

**c**) the conventional output current, and (

**d**) the proposed output current of the 3:1 (m = 3) frequency conversion for the motor load.

**Figure 17.**Simulated harmonic spectra of the (

**a**) conventional and (

**b**) proposed 3:1 (m = 3) AC/AC power converters for the resistive load.

**Figure 18.**Simulated harmonic spectra of the (

**a**) conventional and (

**b**) proposed 4:1 (m = 4) AC/AC power converters for the resistive load.

**Figure 19.**(

**a**) Simulated dynamic frequency change response and (

**b**) a comparison of the output voltage THDs between the conventional and proposed AC/AC converter.

**Figure 20.**Simulated dynamic speed change response of a single phase induction motor using the conventional and proposed AC/AC power converter.

Output Frequency (Hz) | Operating Mode | Active Secondary Winding | Switching State (ON = 1; OFF = 0) | Output Voltage (V) | |||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|

D1 | D2 | D3 | D4 | D5 | D6 | D7 | D8 | T1 | T2 | T3 | T4 | ||||

16.67 | 1 | 1 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | +V_{m}/2 |

8 | 2 and 4 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 1 | 0 | +V_{m} | |

1 | 1 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | +V_{m}/2 | |

2 | 1 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | −V_{m}/2 | |

7 | 2 and 4 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 1 | −V_{m} | |

2 | 1 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | −V_{m}/2 | |

12.5 | 1 | 1 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | +V_{m}/2 |

8 | 2 and 4 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 1 | 0 | +V_{m} | |

6 | 1 and 3 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | + V_{m} | |

3 | 2 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | +V_{m}/2 | |

4 | 2 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | −V_{m}/2 | |

5 | 1 and 3 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 1 | −V_{m} | |

7 | 2 and 4 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 1 | −V_{m} | |

2 | 1 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | −V_{m}/2 |

Title | Specifications |
---|---|

Input voltage (AC) | 220 V, 50 Hz |

Center tapped transformer | (28-14-0-14-28) V (1:4 winding) |

SCR | TYN612 |

Diode | 1N4007 |

Opto-coupler | Moc3021, 4n35 |

Microcontroller board | Arduino Uno (ATMega328p) |

Oscilloscope | Tektronix (2-channel) |

Harmonic Order | Conventional 3:1 (m = 3) | Proposed 3:1 (m = 3) | ||||
---|---|---|---|---|---|---|

Fundamental% of Output Voltage (V) (Resistive Load) | Fundamental% of Output Voltage (V) (Motor Load) | Fundamental% of Load Current (A) (Motor Load) | Fundamental% of Output Voltage (V) (Resistive Load) | Fundamental% of Output Voltage (V) (Motor Load) | Fundamental% of Load Current (A) (Motor Load) | |

1 | 100.00% | 100% | 100% | 100.00% | 100% | 100% |

3 | 40.39% | 38.24% | 58.35% | 0.00% | 1.84% | 3.22% |

5 | 50.38% | 42.64% | 61.48% | 50.44% | 47.13% | 54.06% |

7 | 20.34% | 14.40% | 16.94% | 20.46% | 18.42% | 17.97% |

9 | 0.00% | 1.69% | 0.77% | 0.00% | 1.05% | 0.83% |

11 | 7.14% | 3.27% | 3.67% | 7.10% | 5.26% | 4.11% |

13 | 5.12% | 1.29% | 1.17% | 5.15% | 4.12% | 2.66% |

15 | 0.00% | 0.69% | 0.29% | 0.00% | 1.20% | 0.54% |

17 | 2.83% | 0.91% | 1.31% | 2.80% | 1.61% | 1.08% |

19 | 2.34% | 0.68% | 0.30% | 2.35% | 1.93% | 1.01% |

21 | 0.00% | 0.17% | 0.66% | 0.00% | 1.04% | 0.31% |

23 | 1.51% | 0.58% | 0.86% | 1.48% | 0.94% | 0.61% |

25 | 1.35% | 0.88% | 0.16% | 1.35% | 1.29% | 0.56% |

THD | 68.42% | 60.40% | 91.39% | 55.32% | 51.76% | 58.16% |

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## Share and Cite

**MDPI and ACS Style**

Uddin, M.S.; Biswas, S.P.; Islam, M.R.; Anower, M.S.; Kouzani, A.Z.; Mahmud, M.A.P.
A New Generalized Step-Down Single-Stage AC/AC Power Converter. *Sustainability* **2020**, *12*, 9181.
https://doi.org/10.3390/su12219181

**AMA Style**

Uddin MS, Biswas SP, Islam MR, Anower MS, Kouzani AZ, Mahmud MAP.
A New Generalized Step-Down Single-Stage AC/AC Power Converter. *Sustainability*. 2020; 12(21):9181.
https://doi.org/10.3390/su12219181

**Chicago/Turabian Style**

Uddin, Md. Shihab, Shuvra Prokash Biswas, Md. Rabiul Islam, Md. Shamim Anower, Abbas Z. Kouzani, and M A Parvez Mahmud.
2020. "A New Generalized Step-Down Single-Stage AC/AC Power Converter" *Sustainability* 12, no. 21: 9181.
https://doi.org/10.3390/su12219181