Magnetic Integration of an LCL Filter for the Single-Phase Grid-Connected Inverter Donghua Pan, Xinbo Ruan, Xuehua Wang, Chenlei Bao and Weiwei Li State Key Laboratory of Advanced Electromagnetic Engineering and Technology Huazhong University of Science and Technology Wuhan, P. R. China
[email protected] and
[email protected] is chosen consequently. The basic principle of the decoupled magnetic integration scheme is introduced in [17]. By utilizing an ungapped leg as the common low reluctance path and arranging the windings properly, the fluxes generated by different windings cancel out mostly in the common leg. As a result, the common leg with remainder flux can be dramatically reduced. Since there is no flux coupling between different windings of individual magnetic components, decoupled integrated magnetic components are fully compatible with their discrete counterparts. Based on this idea, Ref. [12] combines the two inductors of an interleaved quasi-square-wave DC/DC converter into a single core structure. Ref. [13], [14] integrate the two transformers of an asymmetrical half bridge converter to obtain high power density and high efficiency. Ref. [15], [16] apply this idea to the integration of inductor and transformer.
Abstract—The LCL filter is widely used in grid-connected inverters due to its outstanding performance of attenuating the switching frequency current harmonics. An LCL filter has two individual inductors. Numbers of magnetic cores are required, and large volume has to be reserved for these two inductors. In order to reduce the core volume, magnetic integration of these two inductors is introduced in this paper. Since the attenuating ability of the LCL filter would be weakened by the coupling between the two inductors, decoupled magnetic integration is chosen consequently. Though the reluctance of the common core can hardly be zero, the decoupled magnetic integration scheme is still attractive. A 6-kW prototype is built in the lab, and the experimental results validate the effectiveness of the proposed magnetic integration scheme.
I. INTRODUCTION Nowadays, distributed power generation systems (DPGSs) based on renewable energy sources, such as wind energy and solar energy etc, are attracting more and more attentions. It is regarded as a hopeful alternative to resolve the world-wide critical problems, such as energy crisis and environmental pollution [1]. As the interface between the renewable energy sources and the power grid, the grid-connected inverter plays an important role in DPGSs. Since the inverter is often controlled by pulse width modulation (PWM), a filter is necessary to attenuate the switching frequency harmonics. As we all know, L filter and LCL filter are widely used. Comparatively, the latter is competitive for its high attenuating ability [2]−[6]. It means that the total inductance of an LCL filter is lower than that of an L filter to meet the same harmonic limits specified in the standards (e.g., IEEE std.1547-2003 [7]).
This paper proposes a magnetic integration scheme for the two inductors of an LCL filter. Correspondingly, the core volume is reduced distinctly. This paper is organized as follows. In section Ⅱ, the characteristic of an LCL filter with coupled inductors is analyzed. It reveals that both direct and inverse coupling would weaken the attenuating ability of the LCL filter. As a consequence, the decoupled magnetic integration is chosen and derived in section Ⅲ. The design procedure of the proposed integrated inductors is presented in section Ⅳ. In order to verify the effectiveness of the proposed magnetic integration scheme, a 6-kW experimental prototype is built and tested. Specifically, experimental waveforms are presented in section Ⅴ. Finally, section Ⅵ concludes this paper.
However, two discrete inductors seem still bulky. In order to reduce the core volume, magnetic integration of these two inductors is introduced in this paper. The existing magnetic integration schemes, namely coupled magnetic integration [8]−[11] and decoupled magnetic integration [12]−[16], are both investigated. Since the attenuating ability of the LCL filter would be weakened by the coupling between the two inductors, decoupled magnetic integration
II. LCL FILTER WITH COUPLED INDUCTORS Fig. 1 shows the topology of an LCL-type single-phase grid-connected inverter. The LCL filter is composed of L1, C, and L2, where L1 is the inverter-side inductor, C is the filter capacitor, and L2 is the grid-side inductor. The equivalent series resistors of L1, C, and L2 are relatively small and can be ignored here. As shown in the figure, vAB is the output
This work was supported by the National Natural Science Foundation of China under Award 50837003 and Award 51007027, and the National Basic Research Program of China under Award 2009CB219706.
978-1-4673-0803-8/12/$31.00 ©2012 IEEE
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(a)
(b)
Figure 3. LCL filter with coupled inductors. (a) Direct coupling. (b) Inverse coupling.
Figure 1. An LCL-type single-phase grid-connected inverter.
(a)
(b)
Figure 4. Equivalent circuit of LCL filter with coupled inductors. (a) Direct coupling. (b) Inverse coupling.
where M is the mutual inductance. If the coupling coefficient is defined as k, then M can be expressed as M = k L1 L2 . (4) From (3), the resonant frequencies can be obtained as ⎧ 1 L1 + L2 + 2 M ( Direct Coupling ) ⎪ 2 ⎪⎪ 2π ( L1 L2 − M ) C f r′ = ⎨ . (5) L1 + L2 − 2M ⎪ 1 ( Inverse Coupling ) ⎪ 2π ( L1 L2 − M 2 ) C ⎪⎩
Figure 2. Characteristic of the LCL filter with different coupling methods.
voltage of the inverter bridge, vC is the filter capacitor voltage, vg is the grid voltage, iL1 is inverter-side inductor current, iC is the filter capacitor current, and iL2 is the injected grid current. The transfer function from vAB to iL2 is i (s) 1 = GLCL ( s ) = L 2 (1) v AB ( s ) s 3 L1 L2 C + s ( L1 + L2 ) and its magnitude versus frequency plot is shown as the solid line in Fig. 2 (the parameters of the LCL filter will be given in TABLE I of section Ⅳ). It has a resonant peak, and the corresponding frequency is 1 L1 + L2 fr = . (2) 2π L1 L2 C
The dashdotted line and the dashed line in Fig. 2 denote direct coupling and inverse coupling respectively. As we can see, mutual inductor weakens the attenuating ability of the LCL filter evidently. The slope is only −20 dB/dec above 30 kHz, which leads poor harmonic attenuation. In addition, the inverse coupling scheme has an anti-resonant peak above its resonant frequency. It is produced by the mutual inductor M and the filter capacitor C.
Above fr, the magnitude plot has a slope of −60 dB/dec, which exhibits high harmonic attenuation. If we adopt the integration schemes as shown in Fig. 3 (a) and (b), the corresponding transfer function from vAB to iL2 can be easily deduced from their equivalent circuits as shown in Fig. 4 (a) and (b), which is ⎧ 1 − s 2 MC ⎪ 3 2 ⎪ s ( L1 L2 − M ) C + s ( L1 + L2 + 2 M ) ⎪ ( Direct Coupling ) ⎪ ′ (s) = ⎨ GLCL (3) 1 + s 2 MC ⎪ ⎪ s 3 ( L L − M 2 ) C + s ( L + L − 2M ) 1 2 1 2 ⎪ ⎪ ( Inverse Coupling ) ⎩
Conclusion can be easily drawn from Fig. 2. No matter direct coupling scheme or inverse coupling scheme is used, the attenuating ability of the LCL filter is weakened. Trade-off should be done to get a satisfactory result, or the core volume may be even larger than that of two discrete inductors. III. PROPOSED MAGNETIC INTEGRATION SCHEME To avoid the side effect introduced by coupled magnetic integration, decoupled magnetic integration is employed here. With the corresponding parameters listed in TABLE I of section Ⅳ, the simulation waveforms of iL1, iL2 and iC under rated condition are presented in Fig. 5, where IL1m, IL2m and ICm are the peak values of iL1, iL2 and iC, ∆IL1m is the maximum peak-to-peak current ripple of iL1, IL2 and ICf are 574
iL1:[20 A/div]
IL1m=40.77 A ∆IL1m=8.52 A
iL2:[20 A/div]
IL2=27.42 A IL2m=38.83 A
0
(a)
0
(b)
Figure 6. Core structures of the discrete inductors. (a) L1. (b) L2.
iC:[5 A/div]
iL1
ICf =0.70 A, ICm=5.13 A
N1
0 Φc
Time:[5 ms/div] Figure 5. Simulation waveforms of an LCL-type single-phase grid-connected inverter.
δ1 iL2
δ2
N2
the RMS values of iL2 and the fundamental-frequency component of iC. To limit the reactive power introduced by the filter capacitor, ICf is generally limited to less than 5% of IL2 [2]. In addition, to reduce the power device losses with proper inverter-side inductance, ∆IL1m is typically chosen as 20%~30% of IL2 [3]. As shown in the figure, ∆IL1m and ICf are about 31% and 2.6% of IL2 respectively. IL1m and IL2m are close to each other, and far larger than ICm.
Figure 7. Core structure of the integrated inductors.
amplitudes of ΦC, ΦI1 and ΦI2 respectively). With the simulation results shown in Fig. 5, we can get Φ cm I Cm = = 6.44% . (9) Φ I 1m + Φ I 2 m I L1m + I L 2 m It is obvious that, if the E-type cores and the common I-type core are operating in the same maximum flux density, the cross-section area of the common I-type core in integrated magnetics is just needed to be 6.44% of the sum of that of the I-type cores for L1 and L2 in discrete magnetics.
A straightforward consideration for inductors design of the LCL filter is to use an individual magnetic core for each inductor, as shown in Fig. 6, EI-type magnetic cores are utilized for both inductors. Due to the symmetry of the magnetic circuit, fluxes in the I-type cores for L1 and L2 can be obtained as Li Li Φ I 1 = 1 L1 , Φ I 2 = 2 L 2 (6) 2 N1 2N2 where N1 and N2 are the winding turns of L1 and L2 respectively.
In addition, if the condition L1/N1=L2/N2 is satisfied, we can get ΦI1m≈ΦI2m according to (6). That means, if the two parts of E-type cores are operating in the same maximum flux density, the cross-section areas of the E-type cores for L1 and L2 should be the same. IV. MAGNETICS DESIGN FOR INTEGRATED INDUCTORS
If the EI cores for both inductors are in the same width and thickness, L1 and L2 can be integrated with the core structure shown in Fig. 7, where the E-type cores and air gaps of L1 and L2 remain unchanged, the I-type core serving as a common path is arranged between the two parts of E-type cores. According to the flux paths shown in the figure, the fluxes generated by the windings of L1 and L2 go through the common path in the opposite directions. Thus, the flux in the common I-type core can be obtained as Φc = Φ I1 − Φ I 2 . (7) If the discrete inductors are designed to meet L1/N1=L2/N2, then substituting (6) into (7), yields Li L Φ c = 1 ( iL1 − iL 2 ) = 1 C . (8) 2 N1 2 N1 It indicates that the flux in the common I-type core is generated by the filter capacitor current. As discussed above, ICm is far smaller than IL1m and IL2m, thereby ΦCm is far smaller than ΦI1m and ΦI2m (ΦCm, ΦI1m and ΦI2m are the
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A 6-kW prototype is constructed in the lab to verify the proposed magnetic integration scheme. The parameters of the prototype are given in TABLE I. The single-phase grid-connected inverter is modulated by unipolar, sinetriangle, asymmetrical regular sampled PWM. For an inductor design, the required inductance may be obtained by using a variety of magnetic materials, including low-permeability powder cores or high-permeability ferrite cores. The former with higher saturation flux density would permit a smaller inductor compared to the latter for the same application [18]. However, from the point of magnetic integration, a low reluctance common path is required to decouple L1 and L2, based on this consideration, a highpermeability ferrite core is preferred in this work. Magnetic cores are selected according to the well-known area-product method [18]. Referring to the product catalog of NCD EE ferrite cores [19], L1 is implemented using two pairs of EE70/33/32, 32-turn windings are designed and
TABLE I. PARAMETERS OF THE PROTOTYPE Parameter
Symbol
Symbol
TABLE Ⅱ. CORE SIZES FOR THE LCL FILTER
Value
Parameter
Value
L1
360 μH
Input voltage
Vin
360 V
Inverter-side inductor
Grid voltage (rms value)
Vg
220 V
Grid-side inductor
L2
90 μH
Output power
Po
6 kW
Filter capacitor
C
10 μF
Fundamental frequency
fo
50 Hz
Switching frequency
fs
15 kHz
Figure 8. EI-type magnetic core.
Symbol
Value
Symbol
Value
A1 B1 D1 E1 F1 G1 H1
70.5 mm 55.1 mm 22 mm 13 mm 43.8 mm 31.6 mm 11.3 mm
A2 B2 D2 E2 F2 G2 H2
70.5 mm 23.3 mm 22 mm 13 mm 12 mm 31.6 mm 11.3 mm
(a)
(b)
Figure 9. Ansoft Maxwell 3D model and simulation result. (a) 3D model. (b) Simulation result.
fabricated by copper foils with width and thickness of 40 mm and 0.2 mm respectively. Moving the air gaps in the EE-type core to the end of the window, we can get its equivalent EI-type magnetic core, as shown in Fig. 8. The core sizes are listed as A1~H1 in TABLE Ⅱ . Correspondingly, the core sizes for L2 can be obtained according to the principles of the proposed magnetic integration scheme. As discussed in section Ⅲ, the width and thickness of the EI cores for both inductors should be the same, namely A2=A1, G2=G1, and to achieve the same cross-section areas, D2=D1 is required, furthermore, E2=E1 is satisfied obviously. Additionally, N2=8 turns can be derived from L1/N1=L2/N2. To ensure the same window utilization and current density, the windings of L2 are fabricated by copper foils with width and thickness of 10 mm and 0.8 mm respectively. Considering isolation requirements, a margin of 1 mm should be reserved at both ends of the windings [18], thus, a height of 12 mm is necessary for the core window of L2, namely F2=12mm. Consequently, the overall core sizes for L2 are listed as A2~ H2 in TABLE Ⅱ, the core volumes of L1 and L2 can be calculated as Ve1 = 2 A1 ( B1 + H1 ) G1 − 4 E1 F1G1 = 2.24 × 105 mm3 (10) Ve 2 = 2 A2 ( B2 + H 2 ) G2 − 4 E2 F2 G2 = 1.34 × 105 mm 3 .
hardly be zero. Therefore, the mutual inductor cannot be avoided. Based on the Ansoft Maxwell 3D model shown in Fig. 9, the corresponding simulation result reveals that the coupling coefficient will increase with decreasing height of the common I-type core. Therefore, trade-off would be done between the core volume and the coupling coefficient. For simplicity, a height of 11 mm is chosen for initial study, thus, the reduced core volume is ΔVe = 2 A1 ( H1 + H 2 − H c ) G1 = 5.17 × 104 mm3 (12) compared to the total core volume of the discrete magnetics, the reduced core volume in percentage terms is ΔVe ΔVe % = × 100% = 14.4% . (13) Ve1 + Ve 2 It means that the core volume is reduced by 14.4% with the proposed magnetic integration scheme. Meanwhile, since the fluxes generated by iL1 and iL2 cancel out mostly, only very little remainder flux generated by iC flows in the common I-type core, with the selected height much larger than the minimum one given in (11), the corresponding flux density in the common I-type core is much lower than that in the I-type cores for L1 and L2 in discrete magnetics. Therefore, the loss in the common I-type core is reduced compared to that in discrete magnetics [20].
Applying the core structure shown in Fig. 7 to the integration of L1 and L2, while the two parts of E-type cores remain unchanged, the key issue lies in the selection of the height of the common I-type core. With the limit of maximum flux density, according to (9), the minimum height of the common I-type core can be obtained as H c min = 6.44% ( H1 + H 2 ) ≈ 2 mm . (11) While in practice, the reluctance of the common core can
V. EXPERIMENTAL VERIFICATION Based on the design procedure developed in section Ⅳ, L1 is implemented using two pairs of EE70/33/32. However, the required magnetic core for L2 is irregular, for simplicity, we take one pair of EE70/33/32 instead. The core structure and photograph of the integrated inductors are shown in Fig. 10, where the cores for L1 are placed on those for L2, and the 576
a
iL1
iL1:[30 A/div]
N1 b
iL2
iL2:[30 A/div]
N2 c (a)
(b)
Time:[5 ms/div]
Figure 10. Core structure and photograph of the integrated inductors. (a) Core structure. (b) Photograph.
(a)
iL1:[100 mA/div]
iL1:[30 A/div]
iL2:[100 mA/div] iL2:[30 A/div]
Harmonic limit: 116mA
Time:[5 ms/div]
0 (a)
30k
60k
Frequency (Hz)
90k
120k
(b) Figure 12. Experimental results with integrated inductors. (a) Experimental waveforms. (b) Harmonic spectra.
iL1:[50 mA/div]
Temperature (°C)
Harmonic limit: 116mA
iL2:[50 mA/div]
0
30k
60k
Frequency (Hz)
90k
120k
(b) Figure 11. Experimental results with discrete inductors. (a) Experimental waveforms. (b) Harmonic spectra.
ends of the former are serving as the common cores. The measured coupling coefficient between L1 and L2 is 0.045, and they are directly coupled.
Figure 13. Core temperature comparison under different load conditions.
According to IEEE std.1547-2003 [7], the upper limit for harmonics higher than 35th in the injected grid current is specified as 0.3% of its rated value, namely Ih_limit=0.3%IL2m =116mA. Fig. 11 shows the experimental results with discrete inductors. The key current harmonics in iL1 are placed around multiples of the double switching frequency [21].Because of the high attenuating ability of the LCL filter, the filter capacitor branch bypasses most of the high frequency current harmonics, and only a little of them injects into the grid. As shown in the figure, the most significant current harmonics in iL2 are placed around 30
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kHz with maximum amplitude of about 52 mA. Fig. 12 shows the experimental results with integrated inductors. As mentioned above, the coupling coefficient between L1 and L2 is relatively small, which has just a little effect on the attenuation ability of LCL filter. As shown in Fig. 12(b), the current harmonics around 30 kHz emerges in the injected grid current with an amplitude of about 100 mA, which is still lower than the harmonic limit. Experimental results verify that the proposed magnetic integration scheme is effective. Fig. 13 shows the core temperature comparisons under
different load conditions, where Ta, Tb and Tc represent the temperatures at three different test points shown in Fig. 10(a). As discussed in section Ⅳ, the flux density at point b is much lower than that at point a and c, which results in a lower core loss and temperature. Moreover, since iC is almost unchanged under different load conditions, so as the flux density at point b, Tb varies little consequently. All the experimental data are obtained at the room temperature of 29 °C without fan cooling.
[7] [8]
[9]
[10]
VI. CONCLUSION A magnetic integration scheme for the LCL filter is proposed in this paper. Compared with direct coupling and inverse coupling schemes, we can conclude that these two coupled magnetic integration schemes will weaken the attenuating ability of the LCL filter, whereas the decoupled magnetic integration scheme will not. With the proposed magnetic integration scheme, fluxes cancel out mostly in the common core, core volume can be reduced by 14.4%, and a lower core loss is obtained. Experimental results from a 6-kW single-phase grid-connected inverter validate that the proposed idea is effective. This idea can also be extended to the LCL-type three-phase grid-connected inverter.
[11]
[12]
[13]
[14]
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