Real-time computer control of a multilevel converter using the mathematical theory of resultants
Introduction
A multilevel converter is a power electronic system that synthesizes a desired voltage output from several levels of dc voltages as inputs. For this reason, multilevel inverters can easily provide the high power required of a large electric traction drive. For example, in a parallel-configured HEV, a cascaded H-bridges inverter can be used to drive the traction motor from a set of batteries, ultracapacitors, or fuel cells. In a distributed energy system consisting of fuel cells, wind turbines, solar cells, etc. the multilevel converter provides a mechanism to feed these sources into an existing three phase power grid. The use of a cascade inverter also allows the converter to operate even with the failure of one level of the inverter structure [10], [11], [12].
A multilevel inverter is more efficient than a two-level pulse width modulation (PWM) inverter. This is because the individual devices in a multilevel converter have a much lower dV/dt per switching, and they switch at the much lower fundamental frequency rather than at 2–20 kHz frequency in a PWM-controlled inverters. As a result, the switching losses are on the order of ten times less in a multilevel inverter. Three, four, and five level rectifier–inverter drive systems that have used some form of multilevel PWM as a means to control the switching of the rectifier and inverter sections have been investigated in the literature [4], [6], [8], [9], [14].
However, a key issue in designing an effective multilevel inverter is to ensure that the voltage total harmonic distortion (THD) is small enough. To do so requires both an (mathematical) algorithm to determine when the switching should be done so as to not produce harmonics and a fast real-time computing system to implement the strategy. The present work addresses both of these issues.
Section snippets
Cascaded H-bridges
Cascade multilevel inverter consists of a series of H-bridge (single-phase full-bridge) inverter units. The general function of this multilevel inverter is to synthesize a desired voltage from several separate dc sources (SDCSs), which may be obtained from batteries, fuel cells, or ultracapacitors in a HEV. Fig. 1 shows a single-phase structure of a cascade inverter with SDCSs [5]. Each SDCS is connected to a single-phase full-bridge inverter. Each inverter level can generate three different
Switching algorithm for the multilevel converter
The Fourier series expansion of the (stepped) output voltage waveform of the multilevel inverter as shown in Fig. 2 is [10], [11], [12]where s is the number of dc sources. Ideally, given a desired fundamental voltage V1, one wants to determine the switching angles θ1,…,θn so that (1) becomes . In practice, one is left with trying to do this approximately. Two predominate methods in choosing the switching angles θ1,…,θn are (1)
Experimental work
A prototype three-phase 11-level wye-connected cascaded inverter has been built using 100 V, 70 A MOSFETs as the switching devices [13]. The gate driver boards and block diagram are shown in Fig. 5, Fig. 6 below. A battery bank of 15 SDCSs of 48 V dc (not shown) each feed the inverter (five SDCSs per phase). In the experimental study here, this prototype system was configured to be a seven-level (three SDCSs per phase) converter with each level being 12 V. The ribbon cable shown in the figure
Conclusions and further work
A full solution to the problem of eliminating the fifth and seventh harmonics in a seven level multilevel inverter has been given. Specifically, resultant theory was used to completely characterize for each m when a solution existed and when it did not (in contrast to numerical techniques such as Newton–Raphson). Further, it was shown that for a range of values of m, there were two sets of solutions and these values were also completely characterized. For each value of m, the solution set that
Acknowledgements
Dr. Tolbert would like to thank the National Science Foundation for partially supporting this work through contract NSF ECS-0093884, and both Drs. Chiasson and Tolbert would like to thank Oak Ridge National Laboratory for partially supporting this work through the UT/Battelle contract number 4000007596. The University of Tennessee is gratefully acknowledged for providing funding for the equipment in this project through its SARIF program. Finally, the authors would like to also thank Opal-RT
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