AbstractâIn this paper, grid-connected interleaved voltage source inverters for PMSG wind power generation system with coupled inductors is introduced.
1.5MVA Grid-Connected Interleaved Inverters using Coupled Inductors for Wind Power Generation System Dongsul Shin∗† , Jong-Pil Lee† Kyoung-Jun Lee∗† , Tae-Jin Kim† , Dong-Wook Yoo† , Fang Zheng Peng‡ , Baoming Ge‡ , Honnyong Cha§ ∗ Department
of Electrical Engineering, Pusan National University, Busan, South Korea Conversion & Control Research Center HVDC Research Division, Korea Electrotechnology Research Institute, Changwon, South Korea ‡ Department of Electrical and Computer Engineering, Michigan State University, East Lansing, MI 48824, USA § School of Energy Engineering, Kyungpook National University, Deagu, South Korea † Power
Abstract—In this paper, grid-connected interleaved voltage source inverters for PMSG wind power generation system with coupled inductors is introduced. In parallel operation, the undesirable circulating current flows between inverters. There are some differences in circulating currents according to source configuration. It is mathematically analyzed and simulated for the verification of analysis. In case of interleaved inverters, the uncontrollable circulating current in switching frequency level flows between inverter modules regardless of source configuration such as common or separated if filter inductance which is placed between inverters is significantly low. In order to suppress high frequency circulating current, the coupled inductors are employed in each phase. A case of 1.5MVA grid-connected interleaved inverters using coupled inductors prototype for the PMSG wind power generation Back To Back converters in parallel are introduced and experimentally verified the proposed topology.
I. I NTRODUCTION Wind energy has nowadays become the fastest developing renewable energy. Its individual wind generators capacity increases rapidly with multi-mega-watt-scale, which definitely anticipates the large capacity of generator-connected rectifiers and grid-connected inverters. However, the presently obtainable maximum apparent power capacity of modern power semiconductor is limited due to their maximum blocking voltage and maximum on-state current [1]–[3]. Therefore, the series connection for high voltage and the parallel connection for large current are important technology in the high power wind power system. For the multi-mega-watt-scale generator, it is preferable to increase the terminal voltage rather than the current due to higher efficiency. In order to interface with the high voltage generator, the widely developed open winding with the series rectifiers is a good solution [4]–[8]. It is not only suitable for This research was financially supported by the Ministry of TRADE INDUSTRY & Energy (MOTIE) Korea Institute for Advancement of Technology (KIAT) and Honam institute for Regional Program Evaluation
978-1-4799-0336-8/13/$31.00 ©2013 IEEE
high voltage applications with low voltage devices, but also the multilevel voltage with suitable PWM method which improves the quality of machine winding terminal voltage and reduce the current harmonics. However, the zero-sequence circulating current of the conventional scheme will cause many negative effects on the generator, and a common mode inductor is inevitably employed to suppress the zero-sequence current. For the grid-connected inverter, the parallel connection could effectively provide large current in achieving high capacity [9]–[12]. Also parallel operation of multiple inverters has been identified as means to reduce both relative and net harmonic distortion of an inverter, due to the cancellation of several lower order harmonic currents. In addition, modularity and redundancy are some of the key points, paralleling may lead to other benefits such as ease of maintenance through operation of identical units, scalable designs, increased reliability through redundancy, etc, without over-sizing the single inverter. However, the one drawback is circulating current generated between inverter modules. In order to avoid the circulating currents, most applications use an isolation approach such as transformers. With the isolation methods, the overall system is expensive and bulky. However, it is impossible to prevent the circulating current with isolation approach in interleaved case or other switching technique. The other papers proposed the inter-phase reactor, inter-cell transformer and commonmode coke to suppress the circulating currents which are the additional magnetic components in some applications. In this paper, in order to reduce the high frequency circulating currents in case of interleaved PWM, filter inductors of each same phase are coupled for grid-connected application. The circulating currents are described in case of the common and separated source. The current ripples of coupled inductor are reduced with coupling effect. The output current ripples of coupled inductors are reduced by interleaved method. With only coupled inductor without additional magnetic compo-
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(a)
(b)
Fig. 1. Voltage source configuration in parallel operation of three-phase voltage source inverters. (a) Single common voltage source. (b) Two separated voltage sources.
Fig. 3. Equivalent circuit of coupled inductor.
The difference between each output voltage of inverter is derived by subtracting (1) and (2)
Fig. 2. Coupled Inductor.
nents, the volume and weight of the filter is reduced. A case of 1.5MVA grid-connected parallel interleaved inverter using coupled inductors prototype as the PMSG wind power generation converter is introduced to experimentally verify the proposed topology.
dix1 dix2 (Lx1 + M ) − (Lx2 + M ) dt dt (3) Assuming Lx1 =Lx2 =Lx , and ignoring the voltage drop on the winding resistance, (3) becomes vx1 − vx2 = r(ix1 − ix2 ) +
vx1 − vx2 = (Lx + M )
II. M ODELING OF C OUPLED I NDUCTOR A model of coupled inductor is derived for the design. From Fig. 1(a) and 1(b), each inverter’s output voltage equation is expressed as vx1 = rix1 + Lx1
dix1 dix2 −M + vx dt dt
(1)
dix1 dix2 −M + vx (2) dt dt where vx1 and vx2 are output voltages of inverter 1 and 2 respectively, ix1 and ix2 are output currents of inverter 1 and 2 respectively, vx is common output voltage of inverter 1 and 2, r, L, and M is the winding resistance, self inductance, and mutual inductance of coupled inductor, subscript x denotes the phase a, b, and c.
d (ix − ix2 ) dt 1
(4)
It represents the voltage which generates the circulating current. The coupled inductor in Fig. 1(a) and 1(b) can be redrawn as Fig. 2, where i0x1 and i0x2 are the balanced currents transferred to the load or the grid from inverter 1 and 2, respectively. Output currents ixl and ix2 of two inverters are
vx2 = rix2 + Lx2
ix1 = i0x1 + icx
(5)
ix2 = i0x2 − icx
(6)
From (5) and (6), the circulating current icx is obtained with an assumption of i0x1 =i0x2
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icx =
ix1 − ix2 2
(7)
The obtained icx is the switching frequency components of circulating current. From (4) and (7), the circulating current can be expressed with inverter voltage difference, vx 1 − vx 2 dicx = dt (8) 2(Lx + M )
TABLE I PARAMETERS OF I NVERTERS IN S MULATION Parameters Rated power Grid voltage (line to line) Grid frequency (fundamental) DC-link voltage Self inductance Coupling coefficient Mutual inductance Leakage inductance Filter capacitance (delta connection) Grid-side inductance Switching frequency Sampling frequency Proportional gain Integral gain
The inverter’s output voltage difference (vx1 − vx2 ) and its duration (dt) are causes of circulating current and it is clearly shown by (8). Thus, its minimization depends on the self inductance and mutual inductance of coupled inductor. The (1) and (2) are rearranged for equivalent circuit of coupled inductor. d(ix1 + ix2 ) dix1 −M + vx (9) dt dt d(ix1 + ix2 ) dix + vx (10) vx2 = rix2 + (Lx2 + M ) 2 − M dt dt The resultant equivalent circuit of coupled inductor is shown in Fig. 3 vx1 = rix1 + (Lx1 + M )
III. A NALYSIS OF C IRCULATING C URRENT The DC and low frequency components of circulating current are not considered because it can be eliminated by a closed-loop control. The components of switching frequency level are analyzed to help the design of coupled inductor. The zero-sequence components of circulating current only exist in common source configuration. Therefore, in order to verify the difference of circulating current according to source configuration, the mathematical analysis and simulation for circulating current is progressed in this section. In Fig. 1(a), the zero-sequence components of output currents in two inverters are ia + ib1 + ic1 (11) i01 = 1 3 ia + ib2 + ic2 i02 = 2 (12) 3 The zero-sequence component of circulating current in inverter 1 can be obtained from (5)
(va1 − va2 ) + (vb1 − vb2 ) + (vc1 − vc2 ) (18) 3 From (3) and (18), the difference of zero-sequence voltages are rearranged v01 − v02 =
di02 di01 (Lx1 + M ) − (Lx2 + M ) dt dt (19) Assuming Lx1 =Lx2 =Lx , and ignoring the voltage drop on the winding resistance, (19) becomes v01 − v02 = r(i01 − i02 ) +
di01 (Lx + M ) (20) dt Each phase have the zero sequence voltage and current for three-phase system. The remained part of the output voltage difference between two inverters vdiff,remain in common source, when the difference of zero-sequence voltages are removed, will be the same as the case of separated source because there no zero-sequence current. It can be expressed as v01 − v02 = 2
ica + icb + icc (13) 3 Also, the zero-sequence component of circulating current in inverter 2 is obtained from (6) ica + icb + icc 3
(14)
From (13) and (14), i01 = −i02
vdiff,remain = vx1 − vx2 − (v01 − v02 ) d = (Lx + M ) (ix1 − ix2 − 2i01 ) dt icx ,remain = icx − i01
(21) (22)
The remained part of the current difference between two inverters idiff,remain in common source, when the zero-sequence current are removed, is twice icx ,remain , namely,
(15)
In order to investigate the zero-sequence circulating current, the zero-sequence output voltages of inverter 1 and 2 are obtained. The zero-sequence component of output voltages in two inverters are va + vb1 + vc1 (16) v01 = 1 3 va + vb2 + vc2 v02 = 2 (17) 3
Values 1.5 [MVA] 690 [V] 60 [Hz] 1100 [V] 1 [mH] 0.85 0.85 [mH] 150 [µH] 160 [µF] 100 [µH] 2 [kHz] 2 [kHz] 0.3 12
The difference between zero-sequence voltages of two inverters is the cause of zero-sequence components in circulating current. By Subtracting (17) from (16), it will be
i01 =
−i02 =
Symbols Prated Vgrid fg VDC Ls k M Lk Cf,p Lg,p fsw fs KP KI
idiff,remain = ix1 − ix2 − 2i01 = 2icx − 2i01
(23)
The difference of inverters’ voltage and current, the difference of zero-sequence voltages, circulating current and remained parts have been expressed. As a results, in separated source configuration, there’s no difference between zero-sequence voltages of inverters. For this reason, the zero-sequence circulating current does not exist.
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Fig. 4. The difference of inverters’ voltage and circulating current in Aphase with common source configuration. Upper : Voltage difference. Lower : Circulating current.
Fig. 5. The difference of inverters’ voltage and circulating current in Aphase with separated source configuration. Upper : Voltage difference. Lower : Circulating current.
The above-motioned approaches is verified by simulation. The parameters of 1.5MVA interleaved two inverters used in simulation are listed in Table I. Fig. 4 present the simulated voltage differences between inverters and circulating current in common voltage source. Fig. 5 present the simulated voltage difference between inverters and circulating current in separated voltage source. Those are obtained in simulation with defined equations (4) and (7). The difference between two cases is the difference of zero-sequence voltages as shown in Fig. 6. In common source configuration, when the difference of zero-sequence voltage is removed from the inverters’ voltage difference and zero-sequence current is removed from the circulating current, the remained parts are the same as the separated source configuration as shown in Fig. 7. Generally, the circulating current in separated source configuration is neglected. However, it should be considered if inverter-side filter inductance between inverters is significantly low. Fig. 8 shows the simulation results both non-interleaved and inter-
Fig. 6. The difference of zero-sequence voltage in inverters in A-phase. Upper : Common voltage source. Lower : Separated voltage source.
Fig. 7. The remained components by removing zero-sequence components. Upper : The remained voltage. Lower : The remained circulating current.
leaved cases in separated source and non-coupled case. The upper simulation result shows normally operated inverters’ currents with non-interleaving. The lower simulation result shows impossibility to operate inverter with interleaving in spite of separation of source. Therefore, although the voltage sources are separated, the coupled inductor is necessary in case of low filter inductance. IV. E FFECT OF C OUPLED I NDUCTOR A. Suppression of Circulating Current The circulating currents are emerged because of mismatch of system parameters such as filter inductance and difference of switching times [10], [11], [13]. In addition, the differences of carrier waves and reference waves are included and also, dead time. The zero-sequence current flows as circulating current when DC-link capacitors of each inverter are shared. Even though DC-link capacitors are separated, high frequency circulating current should be considered for operating interleaved inverters without any problem. In order to suppress high frequency zero-sequence circulating currents, the high
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Fig. 8. The comparison of non-interleaved and interleaved case with low inductance using non-coupled inductor. Upper : The inverter currents of Aphase in non-interleaved case. Lower : The inverter currents of A-phase in interleaved case.
Fig. 10. The proposed coupled inductor with water cooling
possible to operate interleaved inverters using couple inductor without air-gap because the coupled inductor is operated like as transformer. B. Reduction of current ripple in coupled inductor
Fig. 9. The reduction of current ripple in coupled inductors
impedance has to be developed in circulating current path. In case of the non-coupled inductor in two inverter with L filter, the circulating current is expressed as dicc,nci =
VDC dt Lf
(24)
where VDC is DC-link voltage, Lf is filter inductance of inverters. However, in case of inversely coupled inductor, dicc,ci
VDC = dt Ls (1 + k)
(25)
where, Ls is self inductance of coupled inductor, k is coupling coefficient. As shown in (25), more impedance is developed by coupling effect in coupled case. The circulating current is determined by self inductance and coupling coefficient of coupled inductor. For achieving above-mentioned goals to suppress the high frequency circulating current, high self inductance and high coupling coefficient are required. In order to make high self inductance and high coupling coefficient, mutual flux path without air-gap should be formed. It is
Generally, when DC-DC converters are connected in parallel, the interleaving method is employed to reduce the output current ripples of inductors [14]–[17]. The ripple reduction of output current due to interleaving effect is represented as 1 − 2D for D < 0.5, (26a) diLo 1−D = diLo.single phase 2D − 1 for D > 0.5 (26b) D If the leakage inductance Lk of coupled inductor and filter inductance (non-coupled) Lnc is identical, the output current ripples of coupled inductor and combined current ripple of filter inductor currents are the same when interleaving method is applied [18]. dio =
VDC VDC (1 − 2D)DTs = (1 − 2D)DTs Lk Lnc
(27)
where, VDC is DC-link voltage, D is duty cycle and Ts is switching period. In this condition, the current ripples of coupled inductor and non-coupled inductor are comparable. The reduction of current ripples of coupled inductor is determined by duty cycle D and coupling coefficient k as shown in Fig. 9 and (28). D 1− D 0k for D < 0.5, (28a) diLinv.cp 1+k = 0 D diLnc 1− Dk for D > 0.5 (28b) 1+k
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Fig. 11. The description of the Proposed PMSG Wind Power Generation System
TABLE II T HE PARAMETERS OF EXPERIMENTED SYSTEM Parameters Rated power Grid voltage (line to line) Grid frequency (fundamental) DC-link voltage Self inductance Coupling coefficient Mutual inductance Leakage inductance Filter capacitance (delta connection) Grid-side inductance Switching frequency Sampling frequency
Symbols Prated Vgrid fg VDC Ls k M Lk Cf,p Lg,p fsw fs
Values 1.5 [MW] 690 [V] 60 [Hz] 1100 [V] 1.2 [mH] 0.875 1.05 [mH] 150 [µH] 160 [µF] 100 [µH] 2 [kHz] 2 [kHz] Fig. 12. The 1.5MVA prototype PMSG wind power generation system
Therefore, the reduction of circulating currents and current ripples is possible at the same time with coupled inductor. On the basis of section II and III, the coupled inductors are designed and implemented for 1.5MVA interleaved two inverters. Fig. 10 shows the coupling inductor in the proposed system with water cooling. This is smaller than conventional LCL filter(about 40%). V. T HE P ROPOSED PMSG W IND P OWER G ENERATION S YSTEM Fig. 11 presents the proposed scheme, where the PMSGs windings are connected to two PWM rectifiers in parallel and two separate DC-link voltage buses supply two gridconnected inverters that connect in parallel through the current balancer. The high frequency circulating current and unbalancing current will be minimized because of the coupled inductor. The output currents of each inverter are controlled with dq current controller in synchronous reference frame and the other harmonics controller is not applied. In order to confirm the effect of coupled inductor for circulating current, the controller for zero-sequence components of circulating currents which are controllable is not utilized. Space-Vector
Pulse-Width Modulation (SVPWM) is employed with 180phase shift for interleaving method. The four controllers are implemented on Texas Instruments floating point digital signal processor (DSP) TMS320F28335 for two rectifiers and two inverters. Each controller share the data through Controller Area Network (CAN) bus and each PWM controller in DSP TMS320F28335 is synchronized by fiber optic connection. The experimental test are conducted by 1.5MV prototype. VI. E XPERIMENTAL R ESULTS Fig. 12 shows the proposed 1.5MVA prototype Back To Back Converters. The leakage inductance of coupled inductor is 150uH. Coupling coefficient (k) should be above 0.85. The parameters used in experiments are summarized in Table II. The grid-connected interleaved two inverters are only tested for coupled inductor with the separated two voltage sources. Fig. 13 shows the non-coupled inductor’s inverter currents and grid current waveform with interleaving. Fig. 14 shows the magnified inverter currents. The currents of inverter 1 and 2 are crossing at every switching cycle due to interleaving. It makes high frequency circulating currents. Fig. 15 shows
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Fig. 13. Experimental Results with non-coupled inductor. Each inverter current and grid current in A-phase are measured
Fig. 14. Experimental Results with non-coupled inductor. Measured each inverter current in A-phase is magnified to investigate current difference.
coupled inductor’s inverter current and grid current waveforms with interleaving. Fig. 16 shows the magnified inverter currents and grid current. The ripples of inverter currents with coupled inductor are dramatically reduced under same grid current. Also the high frequency circulating currents are considerably removed by coupled inductor. VII. C ONCLUSION In this paper, wind power generation system with coupled inductors for interleaved three-phase voltage source gridconnected inverters is proposed. The high frequency circulating currents are suppressed by coupled inductor. As compared with non-coupled case, it is possible to operate paralleled inverters more stably in high current application. The current ripples of filter inductors are reduced with coupling effect. The output current ripples of coupled inductors are reduced by interleaving method. With no additional components and coupling the two filter inductors of each phase, the volume of the whole system is reduced. The experimental results show the good performances of proposed grid-connected interleaved inverters. R EFERENCES [1] Z. Chen, J. M. Guerrero, and F. Blaabjerg, “A review of the state of the art of power electronics for wind turbines,” IEEE Trans. Power Electron., vol. 24, no. 8, pp. 1859–1875, Aug. 2009. [2] H. Abu-Rub, J. Holtz, J. Rodriguez, and B. Ge, “Medium voltage multilevel converters - state of the art, challenges and requirements in industrial applications,” IEEE Trans. Ind. Electron., vol. 57, no. 8, pp. 2581–2596, Aug. 2010.
Fig. 15. Experimental Results with coupled inductor. Each inverter current and grid current in A-phase are measured
Fig. 16. Experimental Results with coupled inductor. Measured each inverter current in A-phase is magnified to investigate current difference.
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