# Modified Grid-Connected CSI for Hybrid PV/Wind Power Generation System

Authors: D. Amorndechaphon; S. Premrudeepreechacharn; K. Higuchi; X. Roboam
Journal: International Journal of Photoenergy
 (2012)

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## Abstract

The principle of a power conditioning unit for hybrid PV/wind power generation system is proposed. The proposed power conditioner is based on the current source inverter (CSI) topology. All energy sources are connected in parallel with a DC-bus through the modified wave-shaping circuits. To achieve the unity power factor at the utility grid, the DC-link current can be controlled via the wave-shaping circuits with the sinusoidal PWM scheme. In this work, the carrier-based PWM scheme is also proposed to minimize the utility current THD. The power rating of the proposed system can be increased by connecting more PV/wind modules through their wave-shaping circuits in parallel with the other modules. The details of the operating principles, the system configurations, and the design considerations are described. The effectiveness of the proposed CSI is demonstrated by simulation results.


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## Body

## 1. Introduction

The steadily increasing energy consumption for the conventional energy sources like a fossil-energy-based fuel has created much interest in the alternative energy sources. Many renewable energy sources are now developed and being widely used. These energy sources can be integrated to form a hybrid system which is an excellent option for distributed energy product. In general, the hybrid systems have better potential to provide higher quality and more reliable power than the single source systems. Recently, the solar and wind energy are the most commonly used renewable energy sources in a hybrid system due to the high efficiency and reliability to supply the continuous power to the load or the utility grid. The typical hybrid power generation system is shown in Figure1(a). This system includes the energy sources, DC-DC converters, a DC-AC inverter, and the utility grid. All energy sources are connected in parallel to a common DC-AC inverter through their individual DC-DC converters.Hybrid PV/wind generation system—(a) general structure of typical hybrid system and (b) hybrid system based on VSI topology.
(a)
(b)Several configurations of hybrid PV/wind power generation systems, applying the various static converter topologies, have been proposed in the literatures [1, 2]. Previous approaches of the hybrid PV/wind power converters were mainly based on voltage source inverter (VSI) topology. One of the commonly used VSI for hybrid PV/wind is shown in Figure 1(b). In this topology, all energy sources are connected to a common DC-bus through the individual DC-DC boost converters. The DC-DC converters are responsible for tracking the maximum power of the wind and PV sources under all operating conditions. The outputs of both DC-DC converters are then connected to a single-phase DC-AC inverter. The DC-link voltage will be regulated by the DC-AC inverter with the current-regulated PWM control to achieve the unity power factor at the utility grid. Nowadays VSI has received a lot of attention but the high switching losses of the switching devices in both conversion stages are still a major drawback of this topology. To overcome this problem, several power converters based on the current source inverter (CSI) topology have been developed [3–8]. Compared with the VSI topology, CSI topology has the ability to boost the output voltage without an additional boost converter [4, 9]. Therefore, CSI is strongly suggested for the grid-connected systems which the magnitude of the DC input voltage is lower than the peak of utility voltage. In addition, CSI generally features simple converter structure and reliable short-circuit protection. Furthermore, the application of CSI for hybrid PV/wind grid-connected system has not been reported in the previous publications.In this paper, a modified grid-connected CSI for hybrid renewable energy systems consisting of PV and wind is proposed. The details of the operation principle and the system configuration are also discussed. The simulation setup has been carried out to verify the system performance of the proposed ideas under the different scenarios.


## 2. Operating Principles

### 2.1. Overview Concept of the Proposed System with DC-Link Current Sharing Technique

In this section, the overview of the proposed hybrid PV/wind power generation system as shown in Figure2 can be introduced. The proposed system consists of two constant current sources ipv and iwind, two current wave-shaping circuits (can be named as DC-DC chopper), an unfolding circuit, and a low-pass filter. Two constant current sources are connected in parallel to a common DC-bus through their own current wave-shaping circuits. Both wave shaping circuits, operating in the same switching frequency, are used to perform the PWM output currents i1 and i2 at a DC-bus. In order to supply active power to the utility grid, the DC-link current idc is controlled to be in phase with the utility voltage vac. Therefore, the unity power factor can be achieved. The unfolding circuit is used to produce a unipolar pulse-width modulation (PWM) current iinv by setting the direction of a PWM current idc at a DC link. At the last stage, low-pass filter is connected to eliminate the high-frequency harmonic components in a unipolar PWM current iinv before injected to the utility grid.Conceptual expression of the proposed current sharing technique—(a) simplified block diagram and (b) current waveforms for showing the part shared by each energy source.
(a)
(b)In Figure2(b), the waveforms of i1, i2, idc, and iinv in the block diagram in Figure 2(a) are shown. According to Kirchhoff’s current law (KCL), it can be seen that the PWM current at a DC-bus idc is the sum of output currents from the two wave-shaping circuits i1 and i2, respectively. Hence, the instantaneous DC-link current idc can be determined by idc=i1+i2. In addition, the magnitude of idc can be found by summing the magnitude of i1 and i2 (Idc=Ipv+Iwind), respectively. As a result, the magnitude of idc can be independently controlled by two constant current sources ipv and iwind, respectively.


### 2.2. Circuit Configuration and Control Strategy

Figure3(a) shows the circuit topology of the proposed grid-connected CSI for hybrid PV/wind power generation. The circuit diagram differs from that of a VSI in Figure 1(b) by the absence of a DC-link capacitor C3. The proposed circuit is composed of two wave-shaping circuits, a thyristor-based H-bridge inverter, and CL low-pass filter. Input renewable energy sources, PV and wind, are connected to a common DC-bus through their own wave-shaping circuits. The proposed system control scheme is also illustrated in Figure 3(b).Proposed grid-connected CSI for hybrid PV/wind power generation—(a) power converter scheme and (b) system control scheme.
(a)
(b)On the DC-side of the inverter, the DC chokesLpv and Lwind are required to provide the smooth and continuous DC currents ipv and iwind, respectively. Chopper switches Spv and Swind can be controlled to shape the constant input DC current ipv and iwind to be the PWM currents i1 and i2, respectively, at a DC-bus. To achieve the unity power factor at the utility grid, the utility current iac is required to be sinusoidal and in phase with the utility voltage vac. Thus the voltage vac will be rectified to establish a full-wave rectified sinusoidal signal vm, where K1 is an absolute gain. In the same time, the maximum power point tracker (MPPT) can be used for tracking the maximum power of PV and wind by multiplying the reference signal vm with the MPPT reference of each energy source irpv and irw to produce the modulating signal vm,pv and vm,wind, respectively. In PV array, an MPPT algorithm is used to determine the optimal operating point irpv. The optimal current irpv is calculated and tracked from measured valued of PV voltage vpv and PV current ipv. Similarly, for the wind turbine, the extracted power of the wind turbine Pcal and wind speed ωm are measured. The optimal point irw can be provided by the MPPT controller. In both energy sources, Kpv and Kwind are the constant gain of the MPPT controller of PV and wind, respectively.To obtain the control signal of chopper switchesvS,pv and vS,wind, the modulating signals vm,pv and vm,wind are compared with a triangular-shaped carrier waveform vcr of the switching frequency fsw. The instantaneous DC-link current idc can be obtained by the summation of i1 and i2. The H-bridge inverter operates in synchronism with the utility grid and is controlled to provide a unipolar PWM current iinv. The zero-crossing circuit is used to generate the control signal of H-bridge inverter vT1,vT2,vT3,andvT4. Switches T1 and T4 are turned on in the positive half-cycle of the grid voltage vac, whereas T2 and T3 are turned on in the negative half cycle. It can be observed that the inverter current iinv is obtained by unfolding the DC-link current idc. At the last stage, Cf and Lf form the low-pass filter which attenuates the high frequency components in the inverter output current iinv.The principle of the PWM scheme for the proposed CSI is illustrated in Figure4. For the proposed modulation scheme, two modulating waves vm,pv and vm,wind are required. Both modulating waves are of the same frequency and synchronize with the utility grid but the magnitudes Vm,pv and vm,wind are different. The modulating waves vm,pv and vm,wind are compared with a common triangular carrier wave vcr, generating two gating signals vS,pv and vS,wind for chopper switches Spv and Swind, respectively. It should be noted that the fundamental-frequency component of the inverter current iinv can be expressed as iinv1 as shown in Figure 4.Figure 4
Steady-state waveforms of the proposed grid-connected CSI for hybrid PV/wind system.


### 2.3. Inverter Mode of Operation

In order to understand the operation details of the proposed grid-connected CSI in Figure3(a), the equivalent circuit is illustrated in Figure 5. This circuit can be subdivided into two configurations, the input DC-side and the output AC-side, respectively.Figure 5
Simplified equivalent circuit of the proposed system.For a simplify analysis in each interval of the circuit, the following conditions are assumed.(I)
The input voltage sourcesvpv and vwind and DC chokes Lpv and Lwind can be considered and modeled as the constant current sources Ipv and Iwind, respectively.(II)
The output voltage at the DC-side can be assumed to be a constant DC voltage sourceVdc.(III)
The input current at the AC-side can be assumed to be a constant DC current sourceIdc.(IV)
All semiconductor switches in the DC-side and the AC-side are operated at the switching frequency (fsw) and the grid frequency (fline), respectively.


#### 2.3.1. DC-Side Operation

For the one switching period, the operation of the converter in the DC-side can be divided into two stages. The equivalent circuit for each stage is shown in Figure6 and its key waveforms are depicted in Figure 4. Assuming that the modulating signals for energy sources can be defined as vm,pv=vm,wind=vm. The operation processes of the DC-side are specified as follows.DC-side operation—(a)vm<vcr and (b) vm>vcr.
(a)
(b)Stage 1 (vm<vcr).
Whenvm<vcr, chopper switches Spv and Swind are on, chopper diodes Dpv and Dwind are off, the input DC currents Ipv and Iwind flow through Spv and Swind, respectively. The current Ipv and Iwind cannot flow through the diodes Dpv and Dwind, leading to i1=i2=0. According to KCL, the DC-link current idc can be considered as consisting of the sum of diode currents i1 and i2. That is,
(1)idc(t)=0.Stage 2 (vm>vcr).
Whenvm>vcr, chopper switches Spv and Swind are off, chopper diodes Dpv and Dwind are on, the input DC currents Ipv and Iwind flow to the load through Dpv and Dwind, respectively, resulting in i1=Ipv and i2=Iwind. Similar to the first stage, the DC-link current idc is obtained as
(2)idc(t)=Ipv+Iwind.The DC-link currentidc for all stages can be rewritten in term of the switching states as follows:
(3)idc(t)=Ipv[1-dpv]+Iwind[1-dwind],
where dpv and dwind are the switching states of the chopper switches Spv and Swind, respectively. The switching states dpv=1 and dwind=1 if vm<vcr (in stage 1); otherwise 0 (in stage 2).


#### 2.3.2. AC-Side Operation

In Figure7, the equivalent circuit in the AC-side is shown. The AC utility voltage can be expressed by vac=Vac·sin(ωt), where Vac is the peak of utility voltage. The operation of this side consists of two stages during the switching cycle. The operation can be described as follows.AC-side operation—(a)vac>0 and (b) vac<0.
(a)
(b)Stage 1 (vac>0).
Whenvac>0, the inverter switches T1 and T4 are on, T2 and T3 are off, the input DC current Idc flows to the grid through T1 and T4, respectively. Then the AC utility current iac equals to Idc.Stage 2 (vac<0).
The inverter switchesT1 and T4 are off, T2 and T3 are on, when vac<0. The DC current Idc flows to the grid through T2 and T3, respectively, resulting in the utility current iac to be equal to -Idc.Therefore, the utility currentiac can be defined as
(4)iac(t)={idc(t);sin(ωt)≥0-idc(t);sin(ωt)<0.It should be noted that the low-pass filter is not considered in this analysis. Hence, the PWM output currentiinv is equal to the utility current iac (iinv=iac).


### 2.4. PWM Current Analysis

From the PWM scheme in Section2.2, the analysis of harmonic components in the proposed CSI can be performed. The mathematical expression of the PWM currents i1 and i2 can generally be expressed as follows [3]:
(5)i1(t)=mpvIpv2·|sin(ωt)|+∑k=1∞Ipvπk·sin[kπmpv|sin(ωt)|]·cos(kωst).i2(t)=mwindIwind2·|sin(ωt)|+∑k=1∞Iwindπk·sin[kπmwind|sin(ωt)|]·cos(kωst),
where k= the number of kth harmonic component; ω≪ωs; ω=2πfline and ωs=2πfsw; mpv=Vm,pv/Vcr and mwind=Vm,wind/Vcr; mpv and mwind are the modulation index of PV and wind sources, respectively; Vm,pv and Vm,wind are the peaks of modulating signals for PV and wind sources vm,pv and vm,wind, respectively; Vcr is the peak of the triangular carrier waveform vcr. Equations (5) are valid to 0≤mpv≤1 and 0≤mwind≤1, respectively.The DC-link currentidc can be found from
(6)idc(t)=i1(t)+i2(t).
Thus,
(7)idc(t)=12(mpvIpv+mwindIwind)·|sin(ωt)|+∑k=1∞Ipvπk·sin[kπmpv|sin(ωt)|]·cos(kωst)+∑k=1∞Iwindπk·sin[kπmwind|sin(ωt)|]·cos(kωst).According to (4) the inverter output current iinv can be obtained by the operating of the unfolding circuit. Hence, the inverter output current iinv can be expressed in terms of its harmonic components as
(8)iinv(t)=12(mpvIpv+mwindIwind)·sin(ωt)+∑k=1∞Ipvπk·sin[kπmpvsin(ωt)]·cos(kωst)+∑k=1∞Iwindπk·sin[kπmwindsin(ωt)]·cos(kωst).Under the conditions ofIpv=Iwind and mpv≠mwind, the waveform of the inverter output current iinv and its harmonic contents in (8) can be shown in Figure 8. It can be observed that the waveform of the inverter current iinv is close to a unipolar PWM waveform. We can consider at the conditions of Ipv=Iwind=I and mpv=mwind=m, the current iinv simplified as follows:
(9)iinv(t)=mI·sin(ωt)+∑k=1∞2Iπk·sin[kπmsin(ωt)]·cos(kωst).
From this result, the PWM inverter current iinv can be shown in Figure 9(a). This waveform is similar to a unipolar PWM waveform. Figure 9(b) shows the harmonic spectrum of the inverter current iinv. It can be seen that the current has harmonics at the multiples of the switching frequency, that is, at fsw, 2fsw, and so on. The harmonics of significant magnitudes also appear in the side bands of the switching frequency and its multiples.PWM output current waveformiinv and harmonic content of the proposed circuit operating at mpv≠mwind, Ipv=Iwind, fline=50 Hz and fsw=1 kHz.
(a)
(b)PWM output current waveformiinv and harmonic content of the proposed circuit operating at mpv=mwind, Ipv=Iwind, fline=50 Hz, and fsw=1 kHz.
(a)
(b)


### 2.5. Carrier-Based PWM Scheme

In order to reduce the harmonic distortion in the inverter output currentiinv, a carrier-based PWM scheme can be proposed. In general, this scheme can be classified into two categories: phase-shifted and level-shifted modulations. In this paper, a phase-shifted modulation is only studied and applied to the proposed hybrid PV/wind power systems. Normally, the hybrid PV/wind system may be connected in parallel more than two energy sources. The n energy sources require n triangular carrier signals. For the phase-shifted multicarrier modulation, the carrier waves for each module vcr,pv and vcr,wind are of same amplitude and frequency, but there is a phase shift ϕcr between any the adjacent carrier waves, given by
(10)ϕcr=360∘n.For the proposed hybrid PV/wind system as shown in the Figure3(a), there are two energy sources for system. The modulating signals vm,pv and vm,wind have the same frequency but the amplitude is different depending on the MPPT signals of each module. According to (10), the phase shift ϕcr between each carrier wave vcr,pv and vcr,wind is 180°. The gate signals vS,pv and vS,wind are generated by comparing the modulating wave vm,pv and vm,wind with the carrier waves vcr,pv and vcr,wind, respectively. The principle of the proposed phase-shifted modulation for the hybrid PV/wind system can be shown in Figure 10. The inverter operates under the conditions of Ipv=Iwind=I and mpv=mwind=m. The inverter PWM current iinv can be expressed in terms of Fourier series as [3]
(11)iinv(t)=mI·sin(ωt)+∑evenk2Iπk·sin[kπmsin(ωt)]·cos(kωst).
The inverter output current waveform iinv based on phase-shifted multicarrier modulation is shown in Figure 11(a), and its spectrum is also illustrated in Figure 11(b). The operating conditions are Ipv=Iwind=I, mpv=mwind=m,fline=50 Hz, and fsw=1 kHz. The inverter current has harmonics and sidebands at the multiple of the twice switching frequency, that is, 2fsw, 4fsw, and so on. It is clear that the current waveform is formed by five current steps: 2I, I, 0, -I, and -2I, resulting in a further reduction in THD.Figure 10
The steady-state waveforms of the proposed phase-shifted PWM multicarrier modulation.PWM output current waveformiinv and harmonic content of the proposed circuit with phase-shifted modulation operating at Ipv=Iwind, mpv=mwind, fline=50 Hz, and fsw=1 kHz.
(a)
(b)


## 2.1. Overview Concept of the Proposed System with DC-Link Current Sharing Technique

In this section, the overview of the proposed hybrid PV/wind power generation system as shown in Figure2 can be introduced. The proposed system consists of two constant current sources ipv and iwind, two current wave-shaping circuits (can be named as DC-DC chopper), an unfolding circuit, and a low-pass filter. Two constant current sources are connected in parallel to a common DC-bus through their own current wave-shaping circuits. Both wave shaping circuits, operating in the same switching frequency, are used to perform the PWM output currents i1 and i2 at a DC-bus. In order to supply active power to the utility grid, the DC-link current idc is controlled to be in phase with the utility voltage vac. Therefore, the unity power factor can be achieved. The unfolding circuit is used to produce a unipolar pulse-width modulation (PWM) current iinv by setting the direction of a PWM current idc at a DC link. At the last stage, low-pass filter is connected to eliminate the high-frequency harmonic components in a unipolar PWM current iinv before injected to the utility grid.Conceptual expression of the proposed current sharing technique—(a) simplified block diagram and (b) current waveforms for showing the part shared by each energy source.
(a)
(b)In Figure2(b), the waveforms of i1, i2, idc, and iinv in the block diagram in Figure 2(a) are shown. According to Kirchhoff’s current law (KCL), it can be seen that the PWM current at a DC-bus idc is the sum of output currents from the two wave-shaping circuits i1 and i2, respectively. Hence, the instantaneous DC-link current idc can be determined by idc=i1+i2. In addition, the magnitude of idc can be found by summing the magnitude of i1 and i2 (Idc=Ipv+Iwind), respectively. As a result, the magnitude of idc can be independently controlled by two constant current sources ipv and iwind, respectively.


## 2.2. Circuit Configuration and Control Strategy

Figure3(a) shows the circuit topology of the proposed grid-connected CSI for hybrid PV/wind power generation. The circuit diagram differs from that of a VSI in Figure 1(b) by the absence of a DC-link capacitor C3. The proposed circuit is composed of two wave-shaping circuits, a thyristor-based H-bridge inverter, and CL low-pass filter. Input renewable energy sources, PV and wind, are connected to a common DC-bus through their own wave-shaping circuits. The proposed system control scheme is also illustrated in Figure 3(b).Proposed grid-connected CSI for hybrid PV/wind power generation—(a) power converter scheme and (b) system control scheme.
(a)
(b)On the DC-side of the inverter, the DC chokesLpv and Lwind are required to provide the smooth and continuous DC currents ipv and iwind, respectively. Chopper switches Spv and Swind can be controlled to shape the constant input DC current ipv and iwind to be the PWM currents i1 and i2, respectively, at a DC-bus. To achieve the unity power factor at the utility grid, the utility current iac is required to be sinusoidal and in phase with the utility voltage vac. Thus the voltage vac will be rectified to establish a full-wave rectified sinusoidal signal vm, where K1 is an absolute gain. In the same time, the maximum power point tracker (MPPT) can be used for tracking the maximum power of PV and wind by multiplying the reference signal vm with the MPPT reference of each energy source irpv and irw to produce the modulating signal vm,pv and vm,wind, respectively. In PV array, an MPPT algorithm is used to determine the optimal operating point irpv. The optimal current irpv is calculated and tracked from measured valued of PV voltage vpv and PV current ipv. Similarly, for the wind turbine, the extracted power of the wind turbine Pcal and wind speed ωm are measured. The optimal point irw can be provided by the MPPT controller. In both energy sources, Kpv and Kwind are the constant gain of the MPPT controller of PV and wind, respectively.To obtain the control signal of chopper switchesvS,pv and vS,wind, the modulating signals vm,pv and vm,wind are compared with a triangular-shaped carrier waveform vcr of the switching frequency fsw. The instantaneous DC-link current idc can be obtained by the summation of i1 and i2. The H-bridge inverter operates in synchronism with the utility grid and is controlled to provide a unipolar PWM current iinv. The zero-crossing circuit is used to generate the control signal of H-bridge inverter vT1,vT2,vT3,andvT4. Switches T1 and T4 are turned on in the positive half-cycle of the grid voltage vac, whereas T2 and T3 are turned on in the negative half cycle. It can be observed that the inverter current iinv is obtained by unfolding the DC-link current idc. At the last stage, Cf and Lf form the low-pass filter which attenuates the high frequency components in the inverter output current iinv.The principle of the PWM scheme for the proposed CSI is illustrated in Figure4. For the proposed modulation scheme, two modulating waves vm,pv and vm,wind are required. Both modulating waves are of the same frequency and synchronize with the utility grid but the magnitudes Vm,pv and vm,wind are different. The modulating waves vm,pv and vm,wind are compared with a common triangular carrier wave vcr, generating two gating signals vS,pv and vS,wind for chopper switches Spv and Swind, respectively. It should be noted that the fundamental-frequency component of the inverter current iinv can be expressed as iinv1 as shown in Figure 4.Figure 4
Steady-state waveforms of the proposed grid-connected CSI for hybrid PV/wind system.


## 2.3. Inverter Mode of Operation

In order to understand the operation details of the proposed grid-connected CSI in Figure3(a), the equivalent circuit is illustrated in Figure 5. This circuit can be subdivided into two configurations, the input DC-side and the output AC-side, respectively.Figure 5
Simplified equivalent circuit of the proposed system.For a simplify analysis in each interval of the circuit, the following conditions are assumed.(I)
The input voltage sourcesvpv and vwind and DC chokes Lpv and Lwind can be considered and modeled as the constant current sources Ipv and Iwind, respectively.(II)
The output voltage at the DC-side can be assumed to be a constant DC voltage sourceVdc.(III)
The input current at the AC-side can be assumed to be a constant DC current sourceIdc.(IV)
All semiconductor switches in the DC-side and the AC-side are operated at the switching frequency (fsw) and the grid frequency (fline), respectively.


### 2.3.1. DC-Side Operation

For the one switching period, the operation of the converter in the DC-side can be divided into two stages. The equivalent circuit for each stage is shown in Figure6 and its key waveforms are depicted in Figure 4. Assuming that the modulating signals for energy sources can be defined as vm,pv=vm,wind=vm. The operation processes of the DC-side are specified as follows.DC-side operation—(a)vm<vcr and (b) vm>vcr.
(a)
(b)Stage 1 (vm<vcr).
Whenvm<vcr, chopper switches Spv and Swind are on, chopper diodes Dpv and Dwind are off, the input DC currents Ipv and Iwind flow through Spv and Swind, respectively. The current Ipv and Iwind cannot flow through the diodes Dpv and Dwind, leading to i1=i2=0. According to KCL, the DC-link current idc can be considered as consisting of the sum of diode currents i1 and i2. That is,
(1)idc(t)=0.Stage 2 (vm>vcr).
Whenvm>vcr, chopper switches Spv and Swind are off, chopper diodes Dpv and Dwind are on, the input DC currents Ipv and Iwind flow to the load through Dpv and Dwind, respectively, resulting in i1=Ipv and i2=Iwind. Similar to the first stage, the DC-link current idc is obtained as
(2)idc(t)=Ipv+Iwind.The DC-link currentidc for all stages can be rewritten in term of the switching states as follows:
(3)idc(t)=Ipv[1-dpv]+Iwind[1-dwind],
where dpv and dwind are the switching states of the chopper switches Spv and Swind, respectively. The switching states dpv=1 and dwind=1 if vm<vcr (in stage 1); otherwise 0 (in stage 2).


### 2.3.2. AC-Side Operation

In Figure7, the equivalent circuit in the AC-side is shown. The AC utility voltage can be expressed by vac=Vac·sin(ωt), where Vac is the peak of utility voltage. The operation of this side consists of two stages during the switching cycle. The operation can be described as follows.AC-side operation—(a)vac>0 and (b) vac<0.
(a)
(b)Stage 1 (vac>0).
Whenvac>0, the inverter switches T1 and T4 are on, T2 and T3 are off, the input DC current Idc flows to the grid through T1 and T4, respectively. Then the AC utility current iac equals to Idc.Stage 2 (vac<0).
The inverter switchesT1 and T4 are off, T2 and T3 are on, when vac<0. The DC current Idc flows to the grid through T2 and T3, respectively, resulting in the utility current iac to be equal to -Idc.Therefore, the utility currentiac can be defined as
(4)iac(t)={idc(t);sin(ωt)≥0-idc(t);sin(ωt)<0.It should be noted that the low-pass filter is not considered in this analysis. Hence, the PWM output currentiinv is equal to the utility current iac (iinv=iac).


## 2.3.1. DC-Side Operation

For the one switching period, the operation of the converter in the DC-side can be divided into two stages. The equivalent circuit for each stage is shown in Figure6 and its key waveforms are depicted in Figure 4. Assuming that the modulating signals for energy sources can be defined as vm,pv=vm,wind=vm. The operation processes of the DC-side are specified as follows.DC-side operation—(a)vm<vcr and (b) vm>vcr.
(a)
(b)Stage 1 (vm<vcr).
Whenvm<vcr, chopper switches Spv and Swind are on, chopper diodes Dpv and Dwind are off, the input DC currents Ipv and Iwind flow through Spv and Swind, respectively. The current Ipv and Iwind cannot flow through the diodes Dpv and Dwind, leading to i1=i2=0. According to KCL, the DC-link current idc can be considered as consisting of the sum of diode currents i1 and i2. That is,
(1)idc(t)=0.Stage 2 (vm>vcr).
Whenvm>vcr, chopper switches Spv and Swind are off, chopper diodes Dpv and Dwind are on, the input DC currents Ipv and Iwind flow to the load through Dpv and Dwind, respectively, resulting in i1=Ipv and i2=Iwind. Similar to the first stage, the DC-link current idc is obtained as
(2)idc(t)=Ipv+Iwind.The DC-link currentidc for all stages can be rewritten in term of the switching states as follows:
(3)idc(t)=Ipv[1-dpv]+Iwind[1-dwind],
where dpv and dwind are the switching states of the chopper switches Spv and Swind, respectively. The switching states dpv=1 and dwind=1 if vm<vcr (in stage 1); otherwise 0 (in stage 2).


## 2.3.2. AC-Side Operation

In Figure7, the equivalent circuit in the AC-side is shown. The AC utility voltage can be expressed by vac=Vac·sin(ωt), where Vac is the peak of utility voltage. The operation of this side consists of two stages during the switching cycle. The operation can be described as follows.AC-side operation—(a)vac>0 and (b) vac<0.
(a)
(b)Stage 1 (vac>0).
Whenvac>0, the inverter switches T1 and T4 are on, T2 and T3 are off, the input DC current Idc flows to the grid through T1 and T4, respectively. Then the AC utility current iac equals to Idc.Stage 2 (vac<0).
The inverter switchesT1 and T4 are off, T2 and T3 are on, when vac<0. The DC current Idc flows to the grid through T2 and T3, respectively, resulting in the utility current iac to be equal to -Idc.Therefore, the utility currentiac can be defined as
(4)iac(t)={idc(t);sin(ωt)≥0-idc(t);sin(ωt)<0.It should be noted that the low-pass filter is not considered in this analysis. Hence, the PWM output currentiinv is equal to the utility current iac (iinv=iac).


## 2.4. PWM Current Analysis

From the PWM scheme in Section2.2, the analysis of harmonic components in the proposed CSI can be performed. The mathematical expression of the PWM currents i1 and i2 can generally be expressed as follows [3]:
(5)i1(t)=mpvIpv2·|sin(ωt)|+∑k=1∞Ipvπk·sin[kπmpv|sin(ωt)|]·cos(kωst).i2(t)=mwindIwind2·|sin(ωt)|+∑k=1∞Iwindπk·sin[kπmwind|sin(ωt)|]·cos(kωst),
where k= the number of kth harmonic component; ω≪ωs; ω=2πfline and ωs=2πfsw; mpv=Vm,pv/Vcr and mwind=Vm,wind/Vcr; mpv and mwind are the modulation index of PV and wind sources, respectively; Vm,pv and Vm,wind are the peaks of modulating signals for PV and wind sources vm,pv and vm,wind, respectively; Vcr is the peak of the triangular carrier waveform vcr. Equations (5) are valid to 0≤mpv≤1 and 0≤mwind≤1, respectively.The DC-link currentidc can be found from
(6)idc(t)=i1(t)+i2(t).
Thus,
(7)idc(t)=12(mpvIpv+mwindIwind)·|sin(ωt)|+∑k=1∞Ipvπk·sin[kπmpv|sin(ωt)|]·cos(kωst)+∑k=1∞Iwindπk·sin[kπmwind|sin(ωt)|]·cos(kωst).According to (4) the inverter output current iinv can be obtained by the operating of the unfolding circuit. Hence, the inverter output current iinv can be expressed in terms of its harmonic components as
(8)iinv(t)=12(mpvIpv+mwindIwind)·sin(ωt)+∑k=1∞Ipvπk·sin[kπmpvsin(ωt)]·cos(kωst)+∑k=1∞Iwindπk·sin[kπmwindsin(ωt)]·cos(kωst).Under the conditions ofIpv=Iwind and mpv≠mwind, the waveform of the inverter output current iinv and its harmonic contents in (8) can be shown in Figure 8. It can be observed that the waveform of the inverter current iinv is close to a unipolar PWM waveform. We can consider at the conditions of Ipv=Iwind=I and mpv=mwind=m, the current iinv simplified as follows:
(9)iinv(t)=mI·sin(ωt)+∑k=1∞2Iπk·sin[kπmsin(ωt)]·cos(kωst).
From this result, the PWM inverter current iinv can be shown in Figure 9(a). This waveform is similar to a unipolar PWM waveform. Figure 9(b) shows the harmonic spectrum of the inverter current iinv. It can be seen that the current has harmonics at the multiples of the switching frequency, that is, at fsw, 2fsw, and so on. The harmonics of significant magnitudes also appear in the side bands of the switching frequency and its multiples.PWM output current waveformiinv and harmonic content of the proposed circuit operating at mpv≠mwind, Ipv=Iwind, fline=50 Hz and fsw=1 kHz.
(a)
(b)PWM output current waveformiinv and harmonic content of the proposed circuit operating at mpv=mwind, Ipv=Iwind, fline=50 Hz, and fsw=1 kHz.
(a)
(b)


## 2.5. Carrier-Based PWM Scheme

In order to reduce the harmonic distortion in the inverter output currentiinv, a carrier-based PWM scheme can be proposed. In general, this scheme can be classified into two categories: phase-shifted and level-shifted modulations. In this paper, a phase-shifted modulation is only studied and applied to the proposed hybrid PV/wind power systems. Normally, the hybrid PV/wind system may be connected in parallel more than two energy sources. The n energy sources require n triangular carrier signals. For the phase-shifted multicarrier modulation, the carrier waves for each module vcr,pv and vcr,wind are of same amplitude and frequency, but there is a phase shift ϕcr between any the adjacent carrier waves, given by
(10)ϕcr=360∘n.For the proposed hybrid PV/wind system as shown in the Figure3(a), there are two energy sources for system. The modulating signals vm,pv and vm,wind have the same frequency but the amplitude is different depending on the MPPT signals of each module. According to (10), the phase shift ϕcr between each carrier wave vcr,pv and vcr,wind is 180°. The gate signals vS,pv and vS,wind are generated by comparing the modulating wave vm,pv and vm,wind with the carrier waves vcr,pv and vcr,wind, respectively. The principle of the proposed phase-shifted modulation for the hybrid PV/wind system can be shown in Figure 10. The inverter operates under the conditions of Ipv=Iwind=I and mpv=mwind=m. The inverter PWM current iinv can be expressed in terms of Fourier series as [3]
(11)iinv(t)=mI·sin(ωt)+∑evenk2Iπk·sin[kπmsin(ωt)]·cos(kωst).
The inverter output current waveform iinv based on phase-shifted multicarrier modulation is shown in Figure 11(a), and its spectrum is also illustrated in Figure 11(b). The operating conditions are Ipv=Iwind=I, mpv=mwind=m,fline=50 Hz, and fsw=1 kHz. The inverter current has harmonics and sidebands at the multiple of the twice switching frequency, that is, 2fsw, 4fsw, and so on. It is clear that the current waveform is formed by five current steps: 2I, I, 0, -I, and -2I, resulting in a further reduction in THD.Figure 10
The steady-state waveforms of the proposed phase-shifted PWM multicarrier modulation.PWM output current waveformiinv and harmonic content of the proposed circuit with phase-shifted modulation operating at Ipv=Iwind, mpv=mwind, fline=50 Hz, and fsw=1 kHz.
(a)
(b)


## 3. Design Consideration

### 3.1. Input DC Choke Design

Large inductorsLpv and Lwind are used in the DC-side of the inverter, which make the input voltage sources vpv and vwind appear as the constant DC current sources Ipv and Iwind. When the chopper switch is turned on, the inductor current rises and the energy is stored in the inductor. If switch is turned off, the energy stored in the inductor is transferred to the AC-side through the diode and the inductor current falls. To design the value of this inductor, the inductor stored energy must be considered. When the switch is turned on, the energy stored in the inductor is
(12)EL=12LI2=PdcTon,
where L= choke inductance, Pdc= average input power at DC-side, T= switching period, Ton=T/2= turn-on time, and I= average input current. The choke inductance can be expressed as
(13)L=PacηI2fsw,
where η= converter efficiency, Pac=η·Pdc= average output power at AC-side, and fsw= switching frequency.


### 3.2. Output Low-Pass Filter Design

In order to reduce the high-frequency harmonics in the PWM output currentiinv of the grid-connected inverter, a low-pass filter is needed. Passive low-pass filters are normally used as L, LC, CL, and LCL filters. In this paper, a simple CL low-pass filter is chosen. A detailed analysis is not considered in this paper. Following the design procedure of [10], the inductor Lf and capacitor Cf can be found through the following equations:
(14)Lf=VacPac2πfsw,Cf=0.332πfswLf,
where Vac is the amplitude of the grid voltage vac.


## 3.1. Input DC Choke Design

Large inductorsLpv and Lwind are used in the DC-side of the inverter, which make the input voltage sources vpv and vwind appear as the constant DC current sources Ipv and Iwind. When the chopper switch is turned on, the inductor current rises and the energy is stored in the inductor. If switch is turned off, the energy stored in the inductor is transferred to the AC-side through the diode and the inductor current falls. To design the value of this inductor, the inductor stored energy must be considered. When the switch is turned on, the energy stored in the inductor is
(12)EL=12LI2=PdcTon,
where L= choke inductance, Pdc= average input power at DC-side, T= switching period, Ton=T/2= turn-on time, and I= average input current. The choke inductance can be expressed as
(13)L=PacηI2fsw,
where η= converter efficiency, Pac=η·Pdc= average output power at AC-side, and fsw= switching frequency.


## 3.2. Output Low-Pass Filter Design

In order to reduce the high-frequency harmonics in the PWM output currentiinv of the grid-connected inverter, a low-pass filter is needed. Passive low-pass filters are normally used as L, LC, CL, and LCL filters. In this paper, a simple CL low-pass filter is chosen. A detailed analysis is not considered in this paper. Following the design procedure of [10], the inductor Lf and capacitor Cf can be found through the following equations:
(14)Lf=VacPac2πfsw,Cf=0.332πfswLf,
where Vac is the amplitude of the grid voltage vac.


## 4. Results and Discussion

To verify the proposed grid-connected CSI for hybrid PV/wind system with a simple current-sharing technique, the simulation setup has been designed and carried out with PSIM. It should be noted that the MPPT operating for PV and wind energy is not studied in this paper. The circuit parameters are shown in Table1. The PV and wind energy sources vpv and vwind and input DC chokes Lpv and Lwind are modeled by DC current sources Ipv and Iwind, respectively.Table 1
Simulation parameters.
Output-rated power
P
ac
=
1000 W
PV source current
I
pv
=
5 A
Wind source current
I
wind
=
5 A
Utility grid voltage
v
ac
=
220 Vrms
Utility grid frequency
f
line
=
50 Hz
Chopper switching frequency
f
sw
=
3 kHz
Input inductor for PV converter
L
pv
=
13 mH
Input inductor for wind converter
L
wind
=
13 mH
Low-pass filter inductor
L
f
=
4 mH
Low-pass filter capacitor
C
f
=
2 μFFigure12 confirms the principle of PWM strategy for the proposed CSI operating under the condition of mpv=0.9 and mwind=0.4. The gate signals for all switches in CSI vS,pv, vS,wind, vT1, vT2, vT3, and vT4 are also shown in Figure 12. Figures 13, 14 and 15 show the simulated waveform for the proposed CSI, operating under the different conditions, (a) mpv=mwind and Ipv=Iwind; (b) mpv=mwind and Ipv<Iwind; (c) mpv>mwind and Ipv<Iwind. The following can be observed.(a)
The two different currentsi1 and i2 can be combined to produce the current idc at a DC-bus.(b)
The amplitude ofidc can be determined by IDC=Ipv+Iwind. The magnitude of i1 and i2 can be independently controlled by the output power of each energy source.(c)
The unfolding circuit has two complementary switch pairs (T1, T4 and T2, T3) switching at line frequency 50 Hz. The unipolar PWM current iinv is performed by unfolding the DC-link current idc.(d)
The waveform of the grid currentiac is close to sinusoidal with low THD. The low amount of harmonic distortion is due to the elimination of high-order harmonic contents by the filtering effect of CL low-pass filter.PWM switching strategy (top to bottom)vm,pv, vm,wind, vcr, vS,pv, vS,wind, vT1, vT4, vT2, and vT3.
(a)
(b)
(c)
(d)
(e)Operation of the system under the conditions ofmpv=mwind, Ipv=Iwind, fline=50 Hz and fsw=3 kHz (top to bottom) i1, i2, idc, iinv, vac, and iac.
(a)
(b)
(c)
(d)Operation of the system under the conditions ofmpv=mwind, Ipv<Iwind, fline=50 Hz and fsw=3 kHz (top to bottom) i1, i2, idc, iinv, vac, and iac.
(a)
(b)
(c)
(d)Operation of the system under the conditions ofmpv>mwind, Ipv<Iwind, fline=50 Hz and fsw=3 kHz (top to bottom) i1, i2, idc, iinv, vac, and iac.
(a)
(b)
(c)
(d)Figure16 shows the simulated waveforms for the proposed CSI, operating at higher switching frequency. It can be observed that the proposed converter can produce a smooth AC current at the utility grid with low harmonic components. The waveforms of the proposed grid-connected CSI for hybrid PV/wind system with phase-shifted multicarrier modulation are shown in Figure 17. It can be noted that the inverter output current waveform iinv is formed with five current levels.Operation of the system under the conditions ofmpv>mwind, Ipv<Iwind, fline=50 Hz and fsw=20 kHz (top to bottom) i1, i2, idc, iinv, and iac.
(a)
(b)
(c)
(d)Simulated waveforms of the hybrid PV/wind system with phase-shifted PWM operating under the conditions ofmpv=mwind, Ipv=Iwind, fline=50 Hz and fsw=20 kHz (top to bottom) i1, i2, idc, iinv, vac, and iac.
(a)
(b)
(c)
(d)In higher power applications, the increasing of output power rating of a hybrid PV/wind power generation system is required. It can be achieved by connecting more PV/wind modules in parallel with the other modules through their own DC-DC chopper to a common DC-bus. The configuration of multimodules PV/wind system with all modules connected in parallel is shown in Figure18. The waveforms of the converter can be shown in Figure 19.Figure 18
Extension energy sources for increasing the output power of the proposed hybrid PV/wind system.Simulated waveforms of the multimodules hybrid PV/wind system with phase-shifted PWM operating under the conditions ofmpv1=mwind=mpv2, Ipv1=Iwind=Ipv2, fline=50 Hz andfsw=20 kHz (top to bottom) i1, i2, i3, idc, iinv, vac, and iac.
(a)
(b)
(c)
(d)


## 5. Conclusion

A grid-connected inverter for hybrid PV/wind power generation system was proposed. The proposed inverter was based on the current source inverter (CSI) topology. A number of issues were investigated, including the simple current sharing technique, the inverter configuration, operating principle, PWM strategy technique, PWM current analysis, and design consideration. The emphasis of this paper was on the new power converter scheme, where the operating analysis was discussed in details. The proficiency of the proposed inverter was accessed through the computer simulation under the different operation conditions. The performance of the proposed CSI was confirmed by the simulation results.



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*Source: 381016-2012-09-23.xml*