A Cascade Multilevel Inverter Using a Single DC Source

Transcription

1 A ascade Multileel Inerter Using a ingle D ource Zhong Du,LeonM.Tolbert,JohnN.hiasson, and Burak Özpineci emiconductor Power Electronics enter Electrical and omputer Engineering North arolina tate Uniersity Raleigh, N 766 zdu@ncsu.edu EE Department The Uniersity of Tennessee Knoxille, TN 7996 tolbert@utk.edu, chiasson@utk.edu Power Electronics and Electric Machinery Research enter Oak Ridge National Laboratory, NTR 6 herahala Bouleard Knoxille, TN 79 tolbertlm@ornl.go, ozpinecib@ornl.go Abstract A method is presented showing that a cascade multileel inerter can be implemented using only a single D power source and capacitors. A standard cascade multileel inerter requires D sources for leels. Without requiring transformers, the scheme proposed here allows the use of a single D power source (e.g., a battery or a fuel cell stack) with the remaining D sources being capacitors. It is shown that one can simultaneously maintain the D oltage leel of the capacitors and choose a fundamental frequency switching pattern to produce a nearly sinusoidal output. Index Terms Multileel Inerter, Fuel ell I. INTRODUTION A cascade multileel inerter is a power electronic deice built to synthesize a desired A oltage from seeral leels of D oltages. uch inerters hae been the subject of research in the last seeral years [][][][][5], where the D leels were considered to be identical in that all of them were either batteries, solar cells, etc. In [6], a multileel conerter was presented in which the two separate D sources were the secondaries of two transformers coupled to the utility A power. In contrast, in this paper, only one source is used without the use of transformers. The interest here is interfacing a single D power source with a cascade multileel inerter where the other D sources are capacitors. urrently, each phase of a cascade multileel inerter requires D sources for leels in applications that inole real power transfer. In this work, a scheme is proposed that allows the use of a single D power source (e.g., battery or fuel cell stack) with the remaining D sources being capacitors. It is shown that one can simultaneously maintain the D oltage leel of the capacitors and choose a fundamental frequency switching pattern to produce a nearly sinusoidal output. II. MULTILEEL INERTER ARITETURE To operate a cascade multileel inerter using a single D source, it is proposed to use capacitors as the D sources for all but the first source. onsider a simple cascade multileel inerter with two bridges as shown in Fig.. Fig.. n i D Power ource c = inglephase structure of a multileel cascaded bridges inerter. The D source for the first bridge ( ) is a D power source with an output oltage of, while the D source /6/$. 6 IEEE. 6

2 for the second bridge ( ) is a capacitor oltage to be held at. The output oltage of the first bridge is denoted by and the output of the second bridge is denoted by so that the output of this two D source cascade multileel inerter is ( ) = ( ) ( ) By opening and closing the switches of appropriately, the output oltage can be made equal to or while the output oltage of can be made equal to or by opening and closing its switches appropriately. Therefore, the output oltage of the inerter can hae the alues, which is seen leels and is illustrated in Fig. (a). Table I shows how a waeform can be generated using the topology of Fig.. / / / / / / / / (a) (b) Fig.. (a) Output waeform of an 7leel cascade multileel inerter. (b) and (c) bridge oltages and which achiee the same output oltage waeform =. TABLE I. OUTPUT OLTAGE FOR A 7LEEL INERTER = (c) Fig. (b) shows how the waeform of Fig. (a) is generated if, for, = and = is chosen. imilarly, Fig. (c) shows how the waeform of Fig. (a) is generated if, for, = and = is chosen. The fact that the output oltage leel can be achieed in two different ways is exploited to keep the capacitor oltage regulated. pecifically, one measures the capacitor oltage and the inerter current. Then, if and one sets = and = and the capacitor is being charged. Table II summarizes this case along with the discharge case. TABLE II. ONTROLLER FOR APAITOR OLTAGE LEEL ystem tate = By choosing the nominal alue of the capacitor oltage to be one half that of the D power source, the nominal alues of the leels are equally spaced. oweer, this is not required. The criteria required for this capacitor regulating scheme is that () the desired capacitor oltage is less than the D power source oltage, () the capacitance alue is chosen large enough so that the ariation of its oltage around its nominal alue is small, and () the capacitor charging cycle is greater than the capacitor discharge cycle. III. WITING ANGLE If the nominal capacitor oltage is chosen as, then one can compute the switching angles and as in [7]. Following the deelopment in [7] (see also [8]), the Fourier series expansion of the (staircase) output oltage waeform of the multileel inerter as shown in Fig. (a) is ( ) = () X ³ cos( )cos( )cos( ) sin( ) = 5 Ideally, gien a desired fundamental oltage, one wants to determine the switching angles and so that () becomes ( ) = sin( ). In practice, one is left with trying to do this approximately. For threephase systems, the triplen harmonics in each phase need not be canceled as they automatically cancel in the linetoline oltages. In this case where there are D sources, the desire is to cancel the 5 and 7 order harmonics as they tend to dominate the total harmonic distortion. The mathematical statement of these conditions is then ³ cos( )cos( )cos( ) = cos(5 )cos(5 )cos(5 )= () cos(7 )cos(7 )cos(7 )= This is a system of three transcendental equations in the three unknowns and. There are many ways one can sole for the angles (see, for example, [9], [], and []). ere the approach in [7] and [] is used. 7

3 I. EXPERIMENTAL REULT A threephase wyeconnected cascaded multileel inerter using, 7 A MOFETs as the switching deices [] was used to carry out the experiments. A power supply was used as the D power source with = 5 anda8 mf capacitor was used as the second D source. The realtime controller was implemented on an FPGA chip with an 8 sec time step where the switching angles as a function of the modulation index were stored in a lookup table. The multileel conerter was connected to a three phase induction motor whose nameplate data is hp, 5 A, 75 rpm and 8 (RM linetoline µ at 6 z). With, [see equation ()], Fig. shows the inerter oltage waeforms of the three phases for = and =6z. (Note that the modulation index is where is the number of D sources, which in this experiment is =). Phase oltage oltage. time with m=. and f = 6 z Time in seconds a k /a max Fig FFT of the normalized line line oltage with m=. and f=6 5th 7th Frequency (z) FFT of the lineline oltage for = and =6z. Fig. 5 is the current in one of the phases of the induction machine, and its corresponding FFT is shown in Fig. 6. urrent urrent s. time with m=. and f = 6 z Time in seconds) Fig.. Threephase output waeforms of the seenleel multileel inerter. Fig. 5. Phase current waeform with = and =6z. Note that the second leel in Fig. is constant at 5 because this leel is due to only the power supply source with the capacitor oltage not being used. oweer, the first leel and the third leel both require using the capacitor oltage, and note that they are not constant. In particular, note that the first leel aries considerably, but the capacitor oltage controller pushes back in the right direction. The fact that the capacitor oltage aries so much is due to the low alue of capacitance used (8 mf). Also, oltage spikes are seen in Fig.. These occur at those times when both of the sources (power supply and capacitor) are being switched in or out simultaneously. This is due to the differences in dead time of the bridge switches as well as the timing of turning the switches on and off not being exactly the same between the two bridges. The FFT plot of a lineline oltage waeform is shown in Fig.. The 5th and 7th harmonics are not quite zero due to the arying capacitor oltage. a k /a max Fig Normalized Magnitude of Phase urrent s Frequency (m=.)... 5th 7th Frequency (z) FFT of the phase current for = and =6z. 8

4 . 5LEEL INERTER onsider now a 5leel inerter with three bridges as shown in Fig. 7. The corresponding waeform is shown in Fig. 8. n Fig / 5 / / 5 / 7 i D Power ource c = c = ardware architecture for a 5leel ( D sources) inerter Fig. 8. ardware architecture and output oltage waeform for a 5leel inerter. The D source for the first bridge ( ) is a D power source with an output oltage of, the D source for the second bridge ( ) is a capacitor oltage to be held at, and the D source for the third bridge ( ) is a second capacitor oltage held at. As in the 7leel inerter, the capacitor oltages are chosen in this way so that the difference between leels is the same. oweer, this is not essential. The output oltages of each of the bridges are denoted and, respectiely, so the output oltage of the 5leel inerter is gien by ( ) = ( ) ( ) ( ) The possible ways in which the oltage waeform of Fig. 8(b) canbeachieedaregienintableiii. TABLE III. OUTPUT OLTAGE FOR A 5LEEL IN ERTER I. ONLUION A cascade multileel inerter topology has been proposed that requires only a single D power source. ubject to specified constraints, it was shown that the oltage leel of the capacitors can be controlled while at the same time choosing the switching angles to achiee a specified modulation index and eliminate harmonics in the output waeform. REFERENE [] M. Klabunde, Y. Zhao, and T. A. Lipo, urrent control of a leel rectifier/inerter drie system, in onference Record 99 IEEE IA Annual Meeting, 99, pp [] W.Menzies,P.teimer,andJ.K.teinke, FieleelGTOinerters for large induction motor dries, IEEE Transactions on Industry Applications, ol., no., pp. 98 9, July 99. [] G. inha and T. A. Lipo, A four leel rectifierinerter system for drie applications, in onference Record IEEE IA Annual Meeting, October 996, pp [] J. K. teinke, ontrol strategy for a three phase A traction drie with three leel GTO PWM inerter, in IEEE Power Electronic pecialist onference (PE), 988, pp. 8. [5] J. Zhang, igh performance control of a three leel IGBT inerter fed A drie, in onf. Rec. IEEE IA Annual Meeting, 995, pp. 8. [6] M. Manjrekar, P. K. teimer, and T. Lipo, ybrid multileel power conersion system: A competitie solution for highpower applications, IEEE Transactions on Industry Applications, ol. 6, no., pp. 8 8, May/June. [7] J. hiasson, L. M. Tolbert, K. McKenzie, and Z. Du, ontrol of a multileel conerter using resultant theory, IEEE Transactions on ontrol ystem Technology, ol., no., pp. 5 5, May. [8] L. M. Tolbert, F. Z. Peng, and T. G. abetler, Multileel conerters for large electric dries, IEEE Transactions on Industry Applications, ol. 5, no., pp. 6, Jan./Feb [9] P. N. Enjeti, P. D. Ziogas, and J. F. Lindsay, Programmed PWM techniques to eliminate harmonics: A critical ealuation, IEEE Transactions Industry Applications, ol. 6, no., pp. 6, March/April 99. 9

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