An Advanced Active Rectifier based on the SingleStar Bridge Cells Modular Multilevel Cascade Converter for More-Electric-Aircrafts Applications Rosa A. Mastromauro, Sante Pugliese, Silvio Stasi Department of Electrical and Information Engineering Politecnico di Bari Via Orabona, 4, 70125 Bari, Italy
[email protected],
[email protected],
[email protected]
Abstract— An increasing interest is currently verified in DC power distribution systems for the More-Electric-Aircrafts (MEA). DC power distribution enables a more efficient use of the generated power and aids in paralleling and load sharing. Transformer Rectifier Units (TRU) and Autotransformer Rectifier Units (ATRU), commonly employed to date, are heavy to be deployed in a MEA because the power to be handled is much higher than in a conventional aircraft. This is particularly applicable in case variable frequency generators are used since it is not possible to synchronize their outputs directly. In this paper an advanced active rectifier is proposed for MEA applications. It is based on a Single-Star Bridge Cells Modular Multilevel Cascade Converter (SSBC MMCC) combined with Dual Active Bridge (DAB) DC/DC converters in order to create a DC Multibus. The performances of the system are analyzed considering different load configurations and variable frequency operation. Results confirm the validity of the proposed solution and the robustness of the control system in different operating conditions. Keywords-component; More-Electric-Aircrafts, Single-Star Bridge Cells Modular Multilevel Cascade Converter, Dual Active Bridge Converter
I.
INTRODUCTION
The requirement for electrical power onboard aircrafts is forecasted to rise dramatically in the future because of the following reasons: 1) additional electrical loads due to an increased use of electrical actuators and landing gear; 2) increased cabin loads for better in-flight entertainment; 3) information services and passenger comfort electrically operated (Environmental Conditioning Systems (ECS)); 4) anti-icing of the wings; 5) flight controls and other electrical loads [1]. To meet these requirements, a major reorganization of the aircraft electrical generation and power distribution systems is being undertaken coupling with the MEA concept. In a MEA, the jet engine is optimized to produce the thrust and the electric power. An electric machine is used for starting the engine and for generating electric power. Most of the loads are electrical, including the de-icing and ECSs. The fuel, hydraulic and oil pumps are all driven by electric motors. The
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more advanced MEA are currently the A380 and B787 where the generator output frequency is allowed to vary from 360 to 800 Hz (variable frequency operation), instead of 400 Hz (constant frequency operation), thus the engine speed is allowed to vary over a speed range of about 2:1. The wide variation of the frequency can have effect on frequencysensitive aircraft loads (such as AC electric motors) and on power converters employed in the MEA, involving the need of a complete replacement of the power electronics equipment. The variable frequency (VF) voltage is converted to 270 V DC and then converted to VF AC to control the ECS compressor motors and fans, electrically driven hydraulic pumps, nitrogen generating systems (NGSs) and so on. If the main AC/DC converter was an active rectifier, it could also be used for starting the engines electrically. Recent developments in power electronics have advanced active rectifier technologies which could replace the traditional TRU [2]. Furthermore, the active rectifier could facilitate the substitution of the synchronous machines by induction machines since the active rectifier can regulate the voltage at the AC bus of the aircraft. This implies lower weight and smaller volume of the machine, pursuing the main goal in the field of MEA. A simplified representation of the desired MEA power conversion system and loads is shown in Fig.1.
Figure 1. Typical MEA power conversion system and loads.
One of the main constraints for the power converters applied to aircrafts is the low ratio between the switching frequency and the fundamental frequency (400 Hz), coupled to the need of filter size minimization [3]. An advanced active rectifier unit, facilitating the DC power distribution system in a MEA, is proposed in this paper. It is based on a Modular Multilevel Cascade Converter (MMCC) [4] ensuring high power quality performances with reduced switching frequency. In particular, the Single-Star Bridge Cells (SSBC) MMCC topology results particularly proper for the present application since it provides a virtual switching frequency equal to twice the real switching frequency multiplied by the number of Bridge cells for each phase. A flexible DC Multibus can be obtained coupling the SSBC MMCC with DC/DC converters. The system redundancy is guaranteed since a single load can be supplied by a sole DC bus, by more buses simultaneously or sequentially [5]. Among DC/DC converters, the Dual Active Bridge (DAB) converter [6] ensures the desired output voltage (270V) avoiding the occurrence of undesired circulating currents in case of loads sharing among DC buses. The rest of the paper is structured as follows. Firstly, a short review about the power quality issues for MEA converters is presented in Section II; the proposed overall AC/DC power conversion stage and its control system is discussed in Section III. Selected results related to different operating conditions are shown in Section IV. The paper is concluded with some remarks in Section V. II.
POWER QUALITY ISSUES FOR MEA CONVERTERS
Recognizing the negative impacts of harmonic currents on airborne electrical power generation and distribution systems, the international standard ISO-1540 [7] was the first to introduce limits for input harmonic current distortion of airborne user equipment. Following this trend, the RTCA standard DO-160G [8] added a new section (Section 16) defining limits for current harmonic emissions from loads. Similar requirements have also been discussed among the military system integrators and traduced in the standard MILSTD-704F [9]. Among the three standards, just the ISO-1540 refers explicitly to the Total Harmonic Distortion (THD) index and, it may be considered that, a special allowance was applied in the past permitting higher harmonic distortion produced by 12-pulse TRU (the current THD limit was 12% for the 12-pulse rectifiers and 8% for all other loads). Actually some aircraft manufacturing enterprises, such as Boeing and Airbus, put forward demands for a harmonic distortion rate around 3%, but controlling effectively the input current harmonics remains a challenge since it is difficult to meet the requirements simultaneously without affecting the other performances, such as the converter voltage transfer ratio, the input power factor and robustness against unbalanced and/or distorted input voltage. An important drawback related to TRU is the limited power quality performances. However TRU and ATRU were spread out in the past since significant changes in voltage level could be achieved only through transformers. Today power electronics can be used to make these changes in voltage level
irrespective of frequency; the use of modular multilevel topologies allows a great improvement of the power quality performances as in the proposed application. III.
PROPOSED AC/DC POWER CONVERSION STAGE
An advanced AC/DC power conversion stage based on a MMCC is here presented. The performances of a MMCC depends on the number of voltage levels denoted as M, where M is defined on the basis of the power conversion cells number (H) used for each phase: (1) Among the MMCC, the SSBC MMCC represents a topology particularly proper for battery energy storage systems based on one-converter-to-one-battery modules [1012]. In the present paper the SSBC MMCC creates a DC Multibus as shown in Fig.2. The Bridge Cell (BC) is a singlephase H-Bridge power conversion module. Each phase of the SSBC MMCC is treated separately. M = 2H + 1
The SSBC is coupled to H DAB converters in order to obtain in output the desired DC voltage level: 270 V. The outputs of the DAB converters can supply loads separately or can share a common load of higher power creating a flexible DC distribution system into the MEA. A. The SSBC MMCC and Its Control System In the proposed case-study one leg of the SSBC MMCC is composed by four single-phase H-bridge cells connected in cascade and controlled as shown in Fig.3 (H=4). It results: M=9 (in case the DC-links voltages are assumed all equal). For each power cell a unipolar phase-shifted Pulse Width Modulation (PWM) is adopted. The modulating signal is provided by the control system while the phase shift angle between the carriers of two adjacent cells is: φcr =
360° ( M − 1)
(2)
Hence, in the considered case-study, it results: φcr =45°. MEA AC Grid 235 V
I1 VDC_2*=270 V
I2
Cin
DC Load
I4 VDC_2*
DC/AC H-Bridge Converter
Cin
the vphase cluster
VDC_1*
the wphase cluster
DC/AC H-Bridge Converter
DAB Converter
VDC_2*
Lg
VDC_1*
DAB Converter
VDC_2*
I3
DC/AC H-Bridge Converter
DAB Converter
Cin
VDC_1*
DC/AC H-Bridge Converter
DAB Converter
Cin
VDC_1*
Figure 2. MEA active rectifier unit based on a SSBC MMCC and DAB converters working at the reference voltage VDC_2*=270 V.
Denoting as VMEA the rms value of the MEA AC grid and assuming VMEA=235 V, it results that VAC _ H =
VMEA H
V
2VAC _ H
=
m
Pmax 1 (V DC _1 ΔU ± ΔU 2 ) f sw 2
single cell configuration S1
S3
A
p cell 1
B
Cell 2
S2
S4
(4) p cell 2
represents the DC voltage reference value for each cell, where m is the modulation index. Choosing m=0.83, it results VDC_1*=100 V that is the minimum DC-link value to ensure the controllability of the converter in parallel operation with the grid. On the AC side an inductive filter is used to reduce the current harmonic distortion. Lg is designed limiting to 3% the maximum voltage drop and verifying that the power quality performance on the AC side are in compliance with the aircraft standards. A proper design of the capacitances Cin of each DC-link is fundamental to get the desired DC voltage. Since Cin may be chosen on the basis of the admissible voltage ripple, it can be calculated as: Cin =
Cell 1
(3)
is the rms value of the first-order component of the AC voltage applied to each H-bridge cell, hence * DC _ 1
MEA AC Grid Lg
(5)
*
where Pmax is the maximum value of the instantaneous power, VDC_1* is the reference voltage on each DC-link of the SSBC MMCC, ΔU is the admissible voltage ripple and fsw is the switching frequency. The control system has to guarantee synchronization with the MEA AC grid, hence a Phase-Locked-Loop (PLL) circuit is adopted to catch the reference sinusoidal waveform of unitary amplitude, used for the generation of the current reference (Fig.3). A single voltage controller is used for all the cells, it controls directly the DC voltage of every cell and indirectly the power exchanged with the main AC providing in output Ig*, which denotes the amplitude of the reference current for each cell. Differently the current control is operated for each cell separately. With reference to Fig. 3, the voltage vph* denotes the output of the current control of each cell while vph denotes the voltage reference of the PWM modulator establishing the switching function pcell1,..., pcell4. Describing more in details, the voltage loop operates as in the following: the SSBC MMCC DC real voltages (VDC_1,1, VDC_1,2, VDC_1,3, VDC_1,4), available at each DC-link, are summed and the average value is calculated; then the average value is firstly filtered in order to cut-off the second order harmonic, typical of the single-phase H-Bridge, and later this value is compared with the voltage reference VDC_1*. The voltage control is based on a PI regulator, a feedforward action is added to improve the dynamic performances of the system (Fig.4). The sinusoidal current reference i*g,ph is obtained multiplying the unitary sinusoidal signal provided by the PLL by Ig* (output of the voltage control). The current loop is based on a P+Resonant controller [13] as shown in Fig.5. The output vph* is the average voltage which may be generated by the overall power stage in order to annul the current error.
Cell 3
VDC_1,1 VDC_1,2 VDC_1,3 VDC_1,4 vg PLL p ph
p cell 3
PWM
Cell 4
v ph
Vdc adjustment
ωph
v*ph
θph
I g*
P+Resonant controller
VDC_avg * VDC _1
Vdc Control
ig _ meas
single cell control p cell 4
Figure 3. u-phase of the 9-levels SSBC MMCC and its control system.
The voltage reference vph* is shared among the different units. A correcting action is introduced by means of an offset to take into account the gap between the real voltage of each cell (VDC_1,1, VDC_1,2, VDC_1,3, VDC_1,4) and the average value VDC_avg. Hence vph denotes the PWM modulating signal obtained as overall output of the multiloop control system. B. The DAB Converter and Its Control System In the proposed case-study, four DAB converters are connected to the four DC-links of each phase of the SSBC MMCC. In Fig.6 it is presented the DAB circuit configuration consisting of two H-Bridges connected by a High Frequency Transformer (HFT) on their AC sides. The input voltage VDC_1,i denotes the voltage provided by the SSBC MMCC at the i-th DC bus (primary side), the output voltage VDC_2,i denotes the voltage obtained at the i-th DC bus secondary side. For the considered case study VDC_2 *=270 V, for all the DC buses. Different kinds of modulation strategy can be applied for the present topology, however in the present application a constant duty cycle d=0.5 is adopted. VDC _1,1 VDC _1,2 VDC _1,3
VDC ,avg
i *feed − forward
VDC _1,4
* VDC _1
I g*
Figure 4. u-phase voltage control of the SSBC MMCC. ig* , ph v*ph
ig , ph
×
÷
VDC _1,1 VDC _1,2 VDC _1,3
VDC _1,4
×
VDC ,avg VDC _1, j
v ph
×
Figure 5. Current control and DC voltage adjustment of the single power conversion cell of the SSBC MMCC.
The power flowing between the two H-Bridges can be defined as: PDAB =
VDC _ 1, iVDC _ 2, i 2nLf sw
α (1 − α )
(6)
where L is the total inductance (including the equivalent inductance of the HFT), fsw is the switching frequency, n is the transformer turns ratio and α is the phase shift angle between the two converters voltages (at the primary and secondary side of the HFT). Hence, the phase shift angle can be controlled in order to control indirectly the exchanged power magnitude and the power flow direction. The dynamic behavior of the converter can by described using a simplified model as: dVDC _ 2,i dt
=−
1 1 VDC _ 2,i + Rload Cout Cout
⎛ VDC _ 1,i ⎞ ⎜⎜ 2nLf α (1 − α ) ⎟⎟ sw ⎝ ⎠
(7)
where Cout is the capacitance at the secondary side and Rload is the load resistance. Linearizing the converter model in order to use linear control techniques, the controller can be designed as in [14]:
(
)
* Vaux = − K1VDC _ 2,i + K 2 ∫ VDC _ 2 − VDC _ 2, i dt
(8)
where Vaux is the auxiliary input of the system defined as: Vaux = VDC _ 1, nα (1 − α )
(9)
K1 and K2 are the controller gains tuned in order to satisfy the desired damping (ξ) and natural frequency (ωn) specifications related to the closed-loop transfer function of the DAB: ⎛ 1 K1 = ⎜⎜ 2ξωn − Cout Rload ⎝
⎞ ⎟⎟ 2nCout Lf sw ⎠
(10) (11)
K 2 = 2nCout Lf swωn2
In the proposed application the block diagram of the DAB control algorithm is shown in Fig. 7.
VDC _ 2,i
VDC _1,i
IV.
The operation of the proposed rectifier unit based on one 9levels SSBC MMCC and four DAB converters has been investigated in different scenarios: 1) steady-state operation at the rated frequency f=400 Hz in case of a single load (shared among all the buses; 2) load variations, 3) frequency variations in the range 360-800 Hz. In Table I there are reported the power stage parameters used for the simulation of the system shown in Fig.2. In Table II there are summarized the overall control system parameters. The rated power of each cell of the SSBC MMCC is 6 kW. The control parameters of the DAB converters (K1 and K2) have been tuned in order to ensure an overshoot around 2% and a system bandwidth ωn=2π30 rad/s. The converters have been tested through PLECS toolbox, used for simulation of electrical circuits within the Simulink environment. The models have been developed on the basis of of the SEMiX202GB066HDs trench IGBT modules datasheet. A. Steady-state operation Load sharing allows continuous operation mode even in case of faults on one of the DC buses. Indeed, in case of failure, it is possible to supply part of the load by means of the remaining buses. The first test has been performed in case of a 24 kW single load shared among all the DC buses. The fundamental frequency of the system is f=400 Hz (rated frequency). The equivalent virtual switching frequency is 2·H·fsw= 80 kHz. The voltage reference for each DC-link of the SSBC MMCC is VDC_1*=100 V, as explained in Section II. The voltage reference for the DAB converters is: VDC_2*=270V. In Fig. 8 the 9-levels voltage of the MMCC SSBC is shown and compared to the MEA AC grid voltage; in the same figure there is depicted the AC current whose THD is equal to 3.5% in compliance with the aircraft standards. In Fig. 9 there are represented respectively the DAB converters output voltages and currents. It is verified that the buses share perfectly the load providing a quarter of the required power. TABLE I.
K1 K2 * VDC _2
Vaux s
1− 1− 4
Vaux
Vin
α
2
Figure 7. Control of the DAB converter.
VDC _ 2,i
POWER STAGE PARAMETERS
Parameters Switching frequency fsw HFT turns ratio n AC grid side inductance Lg Cout TABLE II.
Figure 6. DAB converter.
RESULTS
Value 10 kHz 3 27 µH 0.45 mF
CONTROL SYSTEM PARAMETERS
Parameters Sampling frequency fs VDC_1 PI controller Kp Ti P+Resonant current controller Kp_RES Ki_RES Voltage adjustment PI kp ki DABs controller K1 K2
Value 20 kHz 40 0.02 1 2000 2 50 0.0588 18.0639
500
V
SSBC MMCC
V
MEA AC GRID
I
g
400
voltage [V]/ current [A]
300
200
100 0
-100
-200 -300
-400 0.18
0.182
0.184
0.186
0.188
0.19
0.192
0.194
0.196
0.198
0.2
components are in compliance with the same standard limits. The harmonics over the limits are marked in bold. It should be noticed that, for these tests, also the switching frequency has been varied (around 10 kHz) in order to guarantee an integer ratio R between the switching frequency and the fundamental frequency. It is verified that the lowest harmonic sideband is centered at 2·H·fsw and that the very few harmonics over the limits are always located at 2R±1. Some selected results related to the 9-levels voltage waveform of the MMCC SSBC, the MEA AC grid voltage and the AC current, in case the fundamental frequency is equal to 600 Hz and 800 Hz, are shown respectively in Fig. 12-13.
time [s] 105
Figure 8. MEA AC voltage, 9-levels voltage of the SSBC MMCC, AC current in case f=400 Hz. *
V
270.05
DC 2,1
23 22 21 0.1
100 0.11
0.12
0.13
0.14
103
0.15
2
0.12
0.13
0.14
0.11
0.14
0.15
99.8
99.9
102
99.7 99.8
99.6 3
I [A]
time [s]
0.13
time [s]
0.15
88.95
0.12
99.9
100
voltage [V]
I [A] 0.11
23 22 21 0.1
101 0.11
0.12
0.13
0.14
99.7 0.3
0.32
0.34
0.36
0.38
99.5 0.7
0.4
0.72
0.74
0.76
0.78
0.8
0.15
time [s] 88.9
100
0.14
0.15
0.11
0.12
0.13
0.14
V
Figure 9. DAB converters output voltages and currents in case all the DC buses are connected in parallel supplying a single load of 24 kW.
B. Load variations Load variations at one or more buses involves imbalance of the power absorbed by the cells of the SSBC MMCC. With the aim to test the robustness of the control system, the performances of the system have been analyzed in case of load variations. Just some selected results are reported in Fig.10-11. The DC buses operate with one load of 12 kW shared by the DC bus 1 and the DC bus 2 and another load, of the same power, supplied together by the DC bus 3 and the DC bus 4. A load reduction of 10% is applied at the first load (DC bus 1 and DC bus 2) at t1=0.3 s. At t2=0.7 s a load increment of 10% is applied at the second load (DC bus 3 and DC bus 4). High performances are obtained due to the proper action of the DC voltage adjustment, related to every power conversion cell of the SSBC MMCC. The DC-links voltages of the SSBC MMCC converter, in the described perturbed conditions, are shown in Fig.10. It is possible to observe that the transient behavior is extinguished in less than 0.06 s. The DAB converters output voltages and currents are shown in Fig.11, it is verified that the DAB converters control guarantees correct operation also in case of power variations respect to the rated conditions: the tuning of the parameters K1 and K2 allows to limit the voltage overshoot up 4%. This result is coupled to a very fast dynamics. C. Frequency variations The performances of the system have been investigated in case of fundamental frequency variations in the range 360-800 Hz. In Table III there listed the u-phase ig current harmonic components, classified as in standard RTCA DO-160G [8]. For all the considered frequencies, almost the totality of the
V
DC 1,1
0.15
time [s]
99 0.2
V
DC 1,2
0.3
V
DC 1,3
V
DC 1,4
0.4
*
DC 1
0.5
0.6
0.7
0.8
0.9
1
time [s]
Figure 10. SSBC MMCC DC-links voltages in case of 10% load reduction applied at the first load (bus 1 and bus 2) and in case of 10% load increase applied at the second load (bus 3 and bus 4) at different times. current [A]
0.13
time [s]
290 V
DC 2
*
V
DC 2,1
280
50 40 30 20 0.2
I I I 0.4
0.6
0.8
1
LOAD 1 1 2
time [s]
270 260 250 0.2
0.4
0.6
0.8
45
55
40
50 45
35
1
40
time [s] 30
35
290 V
DC 2
*
25
V
30
DC 2,3
280
20
270
25
15 0.25
260 250 0.2
0.4
0.6
0.8
1
current [A]
0.12
voltage [V]
0.11
voltage [V]
88.85 0.1
23 22 21 0.1
time [s]
0.3
0.35
0.4
20 0.65
0.7
0.75
0.8 I
LOAD 2
40
I
3
20 0.2
I 0.4
0.6
0.8
1
4
time [s]
Figure 11. DAB convertes output voltages and currents in case of 10% load reduction applied at the first load (bus 1 and bus 2) and in case of 10% load increase applied at the second load (bus 3 and bus 4) at different times. 500
V
V
SSBC MMCC
MEA AC GRID
I
g
400
300
voltage [V], current [A]
4
overall load current [A]
269.9 0.1
23 22 21 0.1
100.2 100.1
time [s]
269.95
100.3
100.2
100.1
270
I [A]
voltage [V]
DC 2
1
V
I [A]
270.1
100.3
104
200
100
0
-100
-200
-300
-400 0.18
0.182
0.184
0.186
0.188
0.19
0.192
time [s]
Figure 12. MEA AC voltage, 9-levels voltage of the SSBC MMCC, AC current in case f=600 Hz.
[3]
500
VSSBC MMCC
VMEA AC GRID
Ig
400
voltage [V], current [A]
300
200
[4]
100
0
[5]
-100
-200
-300
[6]
-400 0.18
0.181
0.182
0.183
0.184
0.185
0.186
0.187
0.188
0.189
0.19
time [s]
[7]
Figure 13. MEA AC voltage, 9-levels voltage of the SSBC MMCC, AC current in case f=800 Hz.
[8]
V.
CONCLUSIONS
An advanced active rectifier for a MEA has been proposed in this paper. It is based on a SSBC MMCC consisting of four single-phase H-Bridge cells for each phase. The system is coupled to four DAB converters providing output voltage equal to 270 V in compliance with the aircraft standards. The proposed topology exhibits high power quality performances since the power conversion stage operation is characterized by a virtual switching frequency of 80 kHz in case of rated conditions (f=400 Hz). High performances are guaranteed also in case of load variations and frequency variations in the range 360-800 Hz.
[9]
REFERENCES
[13]
TABLE III.
EVEN
ODD NON TRIPLEN HARMONICS
[2]
K. Rajashekara, "Power Electronics for More-Electric-Aircraft", Chapter 12 in "Power Electronics for Renewable Energy Systems, Transportation and Industrial Applications", IEEE/Wiley, 2014. J. Chang, A. Wang, "New VF power system architecture and evaluation for future aircraft", IEEE Transactions on Aerospace and Electronic Systems, vol.42, no.2, April 2006, pp. 527–539.
ODD TRIPLEN HARMONICS
[1]
Figure 3.
[10]
[11]
[12]
[14]
R. A. Mastromauro, S. Stasi, F. Gervasio, M. Liserre, "A ground power unit based on paralleled interleaved inverters for a More-ElectricAircraft," 2014 International Symposium on Power Electronics, Electrical Drives, Automation and Motion (SPEEDAM), 18-20 June 2014, pp.216-221. H. Akagi,"Classification, Terminology, and Application of the Modular Multilevel Cascade Converter (MMCC)," IEEE Transactions on Power Electronics, vol.26, no.11, pp.3119-3130, Nov. 2011. D. Ricchiuto, R. A. Mastromauro, M. Liserre, I. Trintis, S. MunkNielsen, "Overview of multi-DC-bus solutions for DC microgrids" , 2013 4th IEEE International Symposium on Power Electronics for Distributed Generation Systems (PEDG), 8-11 July 2013, pp.1-8. S. Inoue, H. Akagi, "A Bidirectional DC-DC Converter for an Energy Storage System with Galvanic Isolation", IEEE Transactions on Power Electronics, vol. 22, pp. 2299-2306, Nov. 2007. ISO 1540:2006, "Aerospace -- Characteristics of aircraft electrical systems". RTCA DO-160G, Environmental Conditions and Test Procedures for Airbone Equipment, Radio Technical Commission for Aeronautics, December 2010. MIL-STD-704F, Aircraft Electric Power Characteristics, Department of Defense Interface Standard, issue F, 12 March 2004. I. Trints, S. Munk-Nielsen, R. Teodorescu, "Cascaded H-bridge with bidirectional boost converters for energy storage", 2011-14th European Conference on Power Electronics and Applications (EPE 2011), Aug. 30- Sept.1 2011, pp.1-9. L. Maharjan, S. Inoue, H. Akagi, J. Asakura, J., "State-of-Charge (SOC)-Balancing Control of a Battery Energy Storage System Based on a Cascade PWM Converter", IEEE Transactions on Power Electronics, vol.24, no.6, pp.1628,1636, June 2009. H. Akagi, S. Inoue, T. Yoshii, "Control and Performance of a Transformerless Cascade PWM STATCOM With Star Configuration", IEEE Transactions on Industry Applications, vol.43, no.4, July-Aug. 2007, pp.1041-1049. R.A. Mastromauro; M.; Liserre, A. Dell'Aquila, "Study of the Effects of Inductor Nonlinear Behavior on the Performance of Current Controllers for Single-Phase PV Grid Converters," IEEE Transactions on Industrial Electronics, vol.55, no.5, pp.2043-2052, May 2008. D.D.M. Cardozo, J.C. Balda, D. Trowler, H.A., Mantooth, "Novel nonlinear control of Dual Active Bridge using simplified converter model," 2010 Twenty-Fifth Annual IEEE Applied Power Electronics Conference and Exposition (APEC), 21-25 Feb. 2010, pp.321-327.
ig CURRENT HARMONIC COMPONENTS FOR FREQUENCY VARYING FROM 360 TO 800 HZ
harmonic order RTCA DO-160G Limits 1 2 0.01* I1/2 = 0.539 4,6,8…40 0.0025*I1 = 0.269 3 0.15* I1/3 = 5.397 9 0.15* I1/9 = 1.800 15 0.15* I1/15 = 1.079 21 0.15* I1/21 = 0.770 27 0.15* I1/27 = 0.600 33 0.15* I1/33 = 0.490 39 0.15* I1/39 = 0.415 5 0.3* I1/5 = 6.476 7 0.3* I1/7 = 4.626 11 0.3* I1/11 = 2.940 13 0.3* I1/13 = 2.490 17 0.3* I1/17 = 1.900 19 0.3* I1/19 = 1.700 23 0.3* I1/23 = 1.400 25 0.3* I1/25 = 1.295 29 0.3* I1/29 = 1.116 31 0.3* I1/31 = 1.046 35 0.3* I1/35 = 0.925 37 0.3* I1/37 = 0.875 THD%
fsw=10440Hz f=360Hz 107.94 ≈0 ≈0 2.82206 1.25212 0.46364 0.57364 0.24362 0.233638 0.0681375 1.381 1.07267 1.14304 0.733021 0.154225 0.520929 0.565692 0.558728 0.281628 0.282268 0.195146 0.140607 3.73
fsw=10000Hz f=400Hz 107.94 ≈0 ≈0 2.730 1.240 0.386 0.380 0.286 0.106 0.190 1.370 1.200 0.100 0.590 0.287 0.346 0.316 0.328 0.100 0.090 0.070 0.124 3.53
fsw=10000Hz f=500Hz 107.94 ≈0 ≈0 3.109 1.207 0.600 0.572 0.251 0.005 1.65 1.461 0.947 1.338 0.971 0.208 0.740 0.171 0.166 0.254 0.171 0.026 0.185 4.19
fsw=10200Hz f=600Hz 107.94 ≈0 ≈0 3.0588 1.21663 0.190136 0.231109 0.09758 1.91993 0.0850553 1.28508 0.953208 1.11421 0.524189 0.28173 0.157137 0.191226 0.18482 0.057984 0.209702 1.7722 0.0726662 4.35
fsw=10500Hz f=700Hz 107.94 ≈0 ≈0 3.20012 1.03198 0.673958 0.130338 0.270902 0.122977 0.191232 1.45037 0.679997 1.30954 0.927213 0.410546 0.119749 0.108044 0.0939368 2.10147 1.92973 0.169901 0.288892 4.67
fsw=10400Hz f=800Hz 107.94 ≈0 ≈0 3.26552 1.31771 0.232749 0.0736313 2.22806 0.258028 0.111093 1.03804 0.668315 1.43835 0.730544 0.0871365 0.0968954 0.328238 2.47088 0.12985 0.13066 0.177873 0.154092 4.9
