Co-simulation and hardware implementation of multi-port rectifier for power system and renewable energy applications

Abstract

In this article, a novel rectifier is designed for two three-phase sources with single-phase inverter and three-phase inverter. The proposed configuration results in back-to-back converter with the dual input source. The main objective is to reduce the semiconductor components in the rectifier. The rectifier design consists of six diodes and three split capacitors. A separate direct current link capacitor is eliminated due to the presence of split capacitors. The simulation model of rectifier and inverter is designed in Multisim, a PSpice-based power electronics simulator, and interfaced with LabVIEW, a graphical programming language for co-simulation. The co-simulation enables the user to utilize two simulation engines for better analysis. The hardware prototype is fabricated and tested for rectifier and inverter. The co-simulation and hardware results proved that proposed design is capable to use in back-to-back converter applications.

Keywords

Rectifier inverter back-to-back converter LabVIEW Multisim

Introduction

Back-to-back converters play an important role in the field of power system applications, renewable energy systems (Chen et al., 2009; Shuhui et al., 2012; Yaramasu et al., 2014), High Voltage Direct Current (HVDC) and industrial drive systems (Alireza et al., 2013; Monica et al., 2006). The configuration of back-to-back converters performs the operation of alternating current (AC) to direct current (DC), and vice versa. It consists of rectifier (AC to DC) as front end and inverter (DC to AC) at back end. In general, the applications of back-to-back converters are as follows:

To synchronize asynchronous or systems of various frequencies;

For stabilizing the weaker AC links;

To supply active power to the weaker systems.

Back-to-back converters (Nasiri et al., 2015; Senthilnathan and Annapoorani, 2016a) are connected through a common DC link capacitor, which enables the system to manipulate proper power balance and power flow (Zhang et al., 2015). In conventional configuration of back-to-back converters, the front end has single input. In order to supply high voltage or to integrate two supplies, it requires two rectifiers which consist of 12 diodes with two separate rectifier bridges (Jiacheng et al., 2011; Urtasun et al., 2013; Xiong et al., 2013). In order to reduce the usage of diodes, the rectifier with reduced number of diodes is designed (Tsutomu and Yasutaka, 2007). The multi-port rectifier provides the option of integrating multiple source with reduced number of diodes. Engineers have shown great interest in reducing the size, decreasing the overall weight and cost of the system by designing a topology that uses less number of power converter switches and provides more degrees of freedom for better control of the system. The article proposes a design which uses a six-diode topology to integrate two three-phase sources, thus reducing the number of power electronic switches by 30% and 50% from the conventional designs of 9- and 12-switch topologies, respectively (Jiacheng et al., 2011; Xiong et al., 2013).

The proposed multi-port rectifier (Mohammad et al., 2011) has the ability of connecting two independent sources. It consists of three legs in which two legs consist of three diodes in each. And another leg has three capacitors in split configuration (Ali et al., 2016; Heydari et al., 2012). The capacitor leg is common for rectifier and acts as DC link. The diodes in the middle will act as common for both sources. The total number of diodes is reduced to 50% while comparing to the conventional method of two separate rectifiers. At the joints of the capacitor legs, the third phase of each source is connected. The inverter is connected across the DC link to feed the power to the AC load (Bimbhra, 2011). The proposed model is tested with both single-phase inverter and three-phase inverter. The co-simulation of proposed model is done in LabVIEW and Multisim packages. LabVIEW (Senthilnathan and Annapoorani, 2016b) is a graphical programming language platform which is interfaced with Multisim, a PSpice-based power electronic simulator. The control pulse and output monitoring is done in LabVIEW. The developed model is analysed under various conditions like same voltage level, different voltage level and same and different voltage with phase delay. The hardware prototype is fabricated and tested.

Multi-port rectifier with single-phase inverter

The semiconductor device plays a vital role in the efficient conversion of the power. In order to reduce the number of semiconductor devices used in the conversion circuit, the proposed rectifier topology has capable of converting the dual three-phase voltage with six diodes and three split capacitors. This can be interlinked with an inverter to feed the stand-alone systems or grid-connected systems. The circuit configuration of proposed rectifier with single-phase inverter is shown in Figure 1. The circuit configuration with three-phase inverter and proposed rectifier is shown in Figure 2.

Figure 1.

Circuit configuration with rectifer and single-phase inverter.

Figure 2.

Circuit configuration with rectifer and three-phase inverter.

Multi-port rectifier

A novel rectifier design is the most flexible solution for those organizations; with its unique design and small size, this project is cost-effective as well. By reducing the number of switches from 12 to 9 then from 9 to 6, it is not only a compact design but also becomes more efficient than its predecessors. Figure 1 shows the six-diode converter having six diodes $(D_{1} - D_{6})$ , three in each leg. The capacitor leg acts as the DC link between the rectifier and the inverter. The capacitor leg has three capacitors. The diodes $D_{1}$ and $D_{2}$ are for source 1, and diodes $D_{3}$ and $D_{4}$ are common for both sources 1 and 2. The diodes $D_{5}$ and $D_{6}$ are for source 2. The current flowing through the first leg diodes $D_{1}$ , $D_{3}$ and $D_{5}$ is $i_{1}$ . The current flowing through the second leg diodes $D_{2}$ , $D_{4}$ and $D_{6}$ is $i_{2}$ . The total current $i_{d c}$ is flowing through the DC link. The conduction path for rectifier is tabulated in Table 1.

Table 1.

Conduction path of six-diode rectifier.

Conduction angle	Positive phase	Negative phase	Conduction path
Conduction angle	Positive phase	Negative phase	$V_{a b c 1}$	$V_{a b c 2}$
$0 ° - 30 °$	$V_{c}$	$V_{b}$	$C_{1}, D_{4}$	$C_{2}, D_{6}$
$30 ° - 90 °$	$V_{a}$	$V_{b}$	$D_{1}, D_{4}$	$D_{3}, D_{6}$
$90 ° - 150 °$	$V_{a}$	$V_{c}$	$D_{1}, C_{2}$	$D_{3}, C_{3}$
$150 ° - 210 °$	$V_{b}$	$V_{c}$	$D_{2}, C_{2}$	$D_{4}, C_{3}$
$210 ° - 270 °$	$V_{b}$	$V_{a}$	$D_{2}, D_{3}$	$D_{4}, D_{5}$
$270 ° - 330 °$	$V_{c}$	$V_{a}$	$C_{1}, D_{3}$	$C_{2}, D_{5}$
$330 ° - 30 °$	$V_{c}$	$V_{b}$	$C_{1}, D_{4}$	$C_{2}, D_{6}$

The sources $V_{a b c 1}$ and $V_{a b c 2}$ are the input AC voltages for the rectifier. The analysis was done based on the various conditions like same amplitude, different amplitude and same and different amplitude with phase difference. The source voltage equations (1) to (4) are given as

V_{a 1} = V_{a 1} = V_{m} c o s (ω_{o} t)

(1)

V_{b 1} = V_{b 1} = V_{m} c o s (ω_{o} t - \frac{2 π}{3})

(2)

V_{c 1} = V_{c 1} = V_{m} c o s (ω_{o} t - \frac{4 π}{3})

(3)

V_{m} = V_{R M S} \sqrt{2}

(4)

where $V_{m}$ is the maximum amplitude of phase voltage and $V_{R M S}$ is the root mean square of phase voltage.

The maximum source current $I_{m}$ is

I_{m} = I_{m 1} = I_{m 2}

(5)

where $I_{m 1}$ and $I_{m 2}$ are the maximum current of two sources.

The DC voltage $(V_{D C})$ from the rectifier is derived using the equations (6) to (8)

V_{D C} = 2 (\frac{3}{π} \int_{\frac{π}{3}}^{\frac{π}{2}} \sqrt{3} V_{m} s i n (ω t + \frac{π}{6}) d ω t)

(6)

V_{D C} = 2 (\frac{3 \sqrt{6}}{π} V_{R M S} \int_{\frac{2 π}{3}}^{\frac{π}{3}} s i n (ω t) d ω t)

(7)

V_{D C} = 2 (\frac{3 \sqrt{6}}{π} V_{R M S})

(8)

The rectifier current $i_{d c}$ is given by

i_{d c} = i_{1} + i_{2}

(9)

where $i_{1}$ is the current in first diode leg of rectifier and $i_{2}$ is the current in second diode leg of rectifier.

Rating of diode is considered by the equation

V_{D C} (I_{m 1} + I_{m 2}) * 6 = T o t a l

(10)

Capacitor design

In rectifier design, three capacitors $(C_{1}, C_{2} and C_{3})$ are connected in series in the ratio of $1 : 0.5 : 1$ . This combination of capacitors acts as a third leg for rectifier.

The capacitor design equations are

C_{1} = C_{3} = 2 (\frac{I}{2 f * V_{P}})

(11)

C_{2} = \frac{I}{2 f * V_{P}}

(12)

where f is the frequency, $V_{P}$ is peak voltage and I is the current.

Single-phase inverter

The single-phase inverter is coupled with the rectifier across the DC link. The capacitor leg is common for both rectifier and DC link. The inverter comprises four IGBTs, and Pulse Width Modulation (PWM) is used to give the gate pulses for the Insulated-Gate Bipolar Transistor (IGBTs). The diagram of the inverter is shown in Figure 1. Same pulse is given for $S_{1}$ and $S_{4}$ and same for $S_{2}$ and $S_{3}$ . A phase difference of 180° between the two pulses is given so that when $S_{1}$ and $S_{4}$ are ON, $S_{2}$ and $S_{3}$ are OFF. This ensures that the flow of output voltage forms the negative and positive cycles of the output as AC voltage. The advantage of PWM is that there is less power loss in switching devices. When the switch is off, there is almost no current through the switch, and when the switch is on, the power is being transferred to the load with almost no voltage drop. The output of the inverter is connected to the load through an L-C filter.

The load voltage $(V_{o})$ and current $(I_{o})$ of full-bridge inverter is given by

V_{o} = \sum_{n = 1, 3, 5 \dots}^{\infty} \frac{4 V_{D C}}{n π} s i n ω t

(13)

I_{o} = \sum_{n = 1, 3, 5 \dots}^{\infty} \frac{4 V_{D C}}{n π Z_{n}} s i n (n ω t - \emptyset_{n})

(14)

Three-phase inverter

The three-phase inverter is coupled with the rectifier across the DC link. The capacitor leg is common for both rectifier and DC link. The inverter comprises six IGBTs, and PWM is used to give the gate pulses for the IGBTs. The diagram of the inverter is shown in Figure 2. The three-phase voltage $V_{A N}$ , $V_{B N}$ and $V_{C N}$ is given by

V_{A N} = \sum_{n = 1, 3, 5 \dots}^{\infty} \frac{2 V_{D C}}{n π} s i n ω t

(15)

V_{B N} = \sum_{n = 1, 3, 5 \dots}^{\infty} \frac{2 V_{D C}}{n π} s i n (ω t - \frac{2 π}{3})

(16)

V_{C N} = \sum_{n = 1, 3, 5 \dots}^{\infty} \frac{2 V_{D C}}{n π} s i n (ω t + \frac{2 π}{3})

(17)

The fundamental load power is given by

P_{o 1} = I_{o 1}^{2} R = I_{o 1} V_{o 1} C o s \emptyset_{1}

(18)

where $I_{o 1}$ is rms value of fundamental component of load current and $V_{o 1}$ is rms value of fundamental component of output voltage.

The inverter power $P_{i n v}$ is given by

P_{i n v} = V_{D C} * I_{i n v}

(19)

An L-C filter consists of inductor L in series with the load and a capacitor across the load. The L-C filter has ability to attenuate low-order harmonics in the output voltage waveform. The resonant frequency $f_{o}$ of L-C filter is given by

f_{o} = \frac{1}{2} \frac{1}{\sqrt{L C}}

(20)

The current ripple $(δ i_{p p})$ of AC waveform is given by

δ i_{p p} = \frac{D * T_{s} (V_{D C} - V_{O})}{L}

(21)

The inductor (L) and switching period $(T_{s})$ is given by

L = \frac{V_{D C}}{4 F_{s w} * δ i_{p p}}

(22)

T_{s} = \frac{1}{F_{s w}}

(23)

where L is filter inductor, C is filter capacitor, D is duty cycle and $F_{s w}$ is switching frequency.

Co-simulation of LabVIEW and Multisim

Plant model was designed by using LabVIEW and Multisim. The power electronics circuit design such as rectifier and inverter was modelled in Multisim. Multisim is a PSpice-based software for simulation and testing of the power electronics models. The control part for the Multisim is implemented through LabVIEW. The control and simulation modules have the facility to simulate the external model. The external model is the Multisim model with the power electronics circuit and interfaced with the LabVIEW co-simulation input/output terminals. The co-simulation terminals have the flexibility to select the input/output parameters either it is voltage or current. Before interconnecting the Multisim and LabVIEW control parts, the control and simulation loop has to be created. Within the simulation loop, the external model should be uploaded with the co-simulation terminals. The control and simulation loop synchronizes the Multisim model and LabVIEW with the Runge-Kutta 45 Ordinary Differential Equation (ODE) solver and interactive simulation option in Multisim for data synchronization. The block diagram for co-simulation of LabVIEW and Multisim is shown in Figure 3.

Figure 3.

Block diagram for co-simulation of LabVIEW and Multisim.

Simulation results and discussion

The simulation of the proposed model is verified by co-simulation of LabVIEW and Multisim. The power electronics model is designed in Multisim, a PSpice-based simulator. The co-simulation terminals of the voltage, current and PWM input are connected to the Multisim circuit. The control and monitoring of the performance of the circuit are through LabVIEW. This type of simulation made the circuit user-friendly to test at various test modes. The rectifier is fed by the two sources and gives the output along the DC link which is formed by the three capacitors, $C_{1}$ , $C_{2}$ and $C_{3}$ . The DC link voltage is given as input to the inverter. The inverter converts the DC voltage to AC voltage and supplies the load through an L-C filter. The output voltage and current waveforms are also shown as Output AC Voltage and Output AC Current. The line voltage is 50 V for both the sources and is of 50 Hz.

Analysis of rectifier with single-phase inverter

Analysis of rectifier under same voltage (110 V)

The performance of the rectifier is tested under the same voltage level in both sources. The source voltage is considered as 110 V, 50 Hz. Figure 4 shows the resultant waveforms.

Figure 4.

Performance of rectifier under same voltage (110 V).

Analysis of rectifier under same voltage (55 V)

The performance of the rectifier is tested under the same voltage level in both sources. The source voltage is considered as 55 V, 50 Hz. The dual three-phase input voltage of 55 V, 50 Hz, capacitor voltage $C_{1}$ and $C_{3}$ , rectified voltage $(V_{D C})$ and current $(I_{d c})$ . The PWM for inverter, inverter voltage and current is shown in Figure 5.

Figure 5.

Performance of rectifier under same voltage (55 V).

Analysis of rectifier under different voltage (110 and 55 V)

The performance of the rectifier is tested under the different voltage level. The source voltage is considered as 110 V, 50 Hz and 55 V, 50 Hz. The upper side voltage is 110 V and the lower side voltage is 55 V. Figure 6 shows the resultant waveforms. The rectifier is tested under the different voltage condition like upper side 110 V, 50 Hz and lower side 55 V, 50 Hz. The performance of the rectifier is same even under variable voltage conditions.

Figure 6.

Performance of rectifier under different voltage (110 and 55 V).

Analysis of rectifier under same voltage with 30° phase difference (55 V)

The performance of the rectifier is tested under the same voltage level in both sources with 30° phase difference. The source voltage is considered as 55 V, 50 Hz. Figure 7 shows the resultant waveforms. The rectifier is tested under same voltage, but the phase difference of the sources is 30⁰. The operation of rectifier even at phase difference also shows better results.

Figure 7.

Performance of rectifier under same voltage with 30° phase difference (55 V).

Analysis of rectifier under different voltage with 30° phase difference (110 and 55 V)

The performance of the rectifier is tested under the different voltage level with 30° phase shift. The source voltage is considered as 110 V, 50 Hz and 55 V, 50 Hz. The upper side voltage is 110 V and the lower side voltage is 55 V. Figure 8 shows the resultant waveforms.

Figure 8.

Performance of rectifier under diferent voltage with 30° phase difference (55 V).

Analysis of rectifier with three-phase inverter

Analysis of rectifier under same voltage (110 V)

The performance of the rectifier is tested under the same voltage level in both sources. Three-phase inverter is connected across the DC link, and the performance is analysed. The source voltage is considered as 110 V, 50 Hz. Figure 9 shows the resultant waveforms.

Figure 9.

Performance of rectifier under same voltage (110 V).

Analysis of rectifier under different voltage (110 and 55 V)

The performance of the rectifier is tested under the different voltage level with three-phase inverter. The source voltage is considered as 110 V, 50 Hz and 55 V, 50 Hz. The upper side voltage is 110 V and the lower side voltage is 55 V. Figure 10 shows the resultant waveforms. The rectifier is tested under the different voltage condition like upper side 110 V, 50 Hz and lower side 55 V, 50 Hz. The performance of the rectifier is same even under variable voltage conditions.

Figure 10.

Performance of rectifier under different voltage (110 and 55 V) with three-phase inverter.

Analysis of rectifier under different voltage with 30° phase difference (110 and 55 V)

The performance of the rectifier is tested under the different voltage level with 30° phase shift with three-phase inverter. The source voltage is considered as 110 V, 50 Hz and 55 V, 50 Hz. The upper side voltage is 110 V and the lower side voltage is 55 V. Figure 11 shows the resultant waveforms.

Figure 11.

Performance of rectifier under diferent voltage with 30° phase difference (110 and 55 V).

Hardware results and discussion

The Hardware prototype is modelled with ultra-fast recovery rectifier diode U15A30 for the rectifier and IGBT NGTB15N60EG for the inverter. The capacitor ratings are $C_{1} = C_{3} = 440 μ F$ and $C_{2} = 220 μ F$ . The prototype is tested under a same voltage of 50 V, 50 Hz. The experimental setup with rectifier and inverter prototype is shown in Figure 12.

Figure 12.

Experimental setup.

The dual three-phase supply connected through the isolation transformer is fed into the rectifier prototype. The waveforms are captured using Tektronix TPS2024B four-channel Digital Storage Oscilloscope (DSO). Figure 13(a) shows the voltage of two phases of dual inputs. The channels 1 and 2 represent the two phases of source voltage $V_{a b c 1}$ . The channels 3 and 4 represent the two phases of source voltage $V_{a b c 2}$ . The source voltage is with supply frequency of 50 Hz. Figure 13(b) represents the source voltage and current. The channels 1 and 2 represent the two phases of source voltage. The channels 3 and 4 represent the two phases of source current. Figure 13(c) represents the DC link voltage and voltage across capacitor. The channel 1 shows the DC link voltage. The channels 2, 3 and 4 show the voltage across the capacitors $C_{1}$ , $C_{2}$ and $C_{3}$ . The capacitor is common for rectifier and DC link. The rectifier is coupled with single-phase inverter. Figure 14(a) represents the DC link voltage in channel 1 and DC link current in channel 2. The gate pulse is generated using the controller for frequency 50 Hz. The pulse generated is integrated with the IGBT using the driver circuit. The Texas Instruments SM72295 gate driver is used for integrating the controller and IGBT. In Figure 14(b), the gate pulse for IGBT $S_{1}$ to $S_{4}$ is shown. Channels 1 and 3 show the gate pulses for $S_{1}$ and $S_{3}$ . Channels 2 and 4 show the gate pulses for $S_{2}$ and $S_{4}$ .

Figure 13.

Hardware prototype results: (a) source voltage $V_{a b c 1}$ and $V_{a b c 2}$ , (b) source voltage and current and (c) $V_{D C}$ and capacitor voltage.

Figure 14.

Hardware prototype results: (a) DC link voltage $i_{1}$ and DC Link current $I_{D C}$ , (b) PWM for inverter at 50 Hz and (c) inverter output voltage and current.

The proposed rectifier with dual three-phase supply with six diodes and three capacitors. The capacitors are common for both rectifier and DC link. The single-phase inverter connected across the DC link is able to supply the single-phase load. Figure 14(c) shows the output voltage and current. The channel 1 shows the output voltage waveform, and channel 2 shows the output current. The proposed rectifier with three-phase inverter is tested for 50 Hz. The output voltage and current of the three-phase inverter are shown in Figure 15. The DC link voltage is shown in Figure 14(a). The corresponding three-phase inverter is obtained. Figure 15(a) shows the three-phase inverter output voltage. The corresponding output current for the three-phase inverter is shown in Figure 15(b). Figure 15(c) shows the per-phase voltage and current in Fluke Power Quality Analyser. The Total Harmonic Distortion (THD) is analysed for both voltage and current. The voltage THD obtained is 5% as shown in Figure 16(a). The current THD obtained is 5.4% as shown in Figure 16(b).

Figure 15.

Hardware prototype results: (a) three-phase inverter output voltage at 50 Hz, (b) three-phase inverter output current and (c) per-phase voltage and current obtained in Fluke Power Quality Analyser.

Figure 16.

Hardware prototype results: (a) THD of output voltage and (b) THD of output current.

The proposed rectifier is analysed with simulation and experimental hardware prototype. The results show that the rectifier is capable of converting the dual three-phase AC supply to DC. The rectifier is tested with both single-phase inverter and three-phase inverter.

Conclusion

The proposed multi-port rectifier with single-phase inverter is able to supply the power to the load with multiple source. The proposed rectifier design is capable of converting dual three-phase supply. The performance of the rectifier is tested under various conditions like same voltage amplitude and different voltage amplitude with and without phase shift. The performance analysis is done with co-simulation of designed circuit with LabVIEW and Multisim. LabVIEW is a graphical programming language, which has control and monitoring of signals. Multisim is a PSpice-based electronics simulator for accurate simulations. The usage of these two simulation engines makes the analysis better. The hardware prototype is fabricated and tested under laboratory conditions. From the results, it can be concluded that the proposed dual three-phase rectifier is capable of converting two different sources and can fed to the load with single-phase inverter and three-phase inverter.

Footnotes

Acknowledgements

The authors thank the Smart Grid Laboratory and Power Electronics Laboratory, School of Electrical Engineering, Vellore Institute of Technology (VIT) University, Chennai, India, for carrying out this project.

Declaration of conflicting interests

The author(s) declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

Funding

The author(s) received no financial support for the research, authorship, and/or publication of this article.

ORCID iDs

Karthikrajan Senthilnathan

K Iyswarya Annapoorani

References

Ajami

Alizadeh

Elmi

(2016) Design and control of a grid tied 6-switch converter for two independent low power wind energy resources based on PMSGs with MPPT capability. Renewable Energy 87: 532–543.

Alireza

Mahdi

Mustafa

et al . (2013) Single-phase dual-output inverters with three-switch legs. IEEE Transactions on Industrial Electronics 60: 1769–1779.

Bimbhra

(2011) Power Electronics. New Delhi, India: Khanna Publications.

Chen

Guerrero

Blaabjerg

(2009) A review of the state of the art of power electronics for wind turbines. IEEE Transactions on Power Electronics 24: 1859–1875.

Heydari

Varjani

Mohamadian

et al . (2012) Three-phase dual output six-switch inverter. IET Power Electronics 5: 1634–1650.

Jiacheng

Dewei

Bin

et al . (2011) A low-cost rectifier topology for variable-speed high-power PMSG wind turbines. IEEE Transactions Power Electronics 26: 2192–2200.

Mohammad

Ali

Mustafa

(2011) A novel three-phase to three-phase AC/AC converter using six IGBTs. In: EPECS II, Sharjah, UAE, 15–17 November.

Monica

Santiago

Juan

(2006) Control of permanent-magnet generators applied to variable-speed wind-energy systems connected to the grid. IEEE Transactions on Energy Conversion 21: 130–135.

Nasiri

Milimonfared

Fathi

(2015) A review of low-voltage ride through enhancement methods for permanent magnet synchronous generator based wind turbines. Renewable and Sustainable Energy Reviews 47: 399–415.

10.

Senthilnathan

Annapoorani

(2016a) A review on back-to-back converters in permanent magnet synchronous generator based wind energy conversion system. Indonesian Journal of Electrical Engineering and Computer Science 2: 583–591.

11.

Senthilnathan

Annapoorani

(2016b) Implementation of unified power quality conditioner (UPQC) based on current source converters for distribution grid and performance monitoring through LabVIEW simulation interface Toolkit server: A cyber physical model. IET Generation, Transmission and Distribution 10: 2622–2630.

12.

Shuhui

Timothy

Richard

(2012) Optimal and direct-current vector control of direct-driven PMSG wind turbines. IEEE Transactions Power Electronics 27: 2325–2337.

13.

Tsutomu

Yasutaka

(2007) A novel nine-switch inverter for independent control of two three-phase loads. In: International conference IEEE IAS annual meeting, New Orleans, LA, 23–27 September, pp. 2346–2350. New York: IEEE.

14.

Urtasun

Sanchis

Martín

et al . (2013) Modeling of small wind turbines based on PMSG with diode bridge for sensorless maximum power tracking. Renewable Energy 55: 138–149.

15.

Xiong

Peng

Poh

et al . (2013) A three-phase dual-input matrix converter for grid integration of two AC type energy resources. IEEE Transactions on Industrial Electronics 60: 20–30.

16.

Yaramasu

Rivera

et al . (2014) A new power conversion system for megawatt PMSG wind turbines using four-level converters and a simple control scheme based on two-step model predictive strategy – Part II: Simulation and experimental analysis. IEEE Emerging and Selected Topics on Power Electronics 2: 14–25.

17.

Zhang

Zhao

Qiao

et al . (2015) A discrete-time direct torque control for direct-drive PMSG-based wind energy conversion systems. IEEE Transactions on Industrial Applications 51: 3504–3514.