Keith McKenzie

Control of a multilevel converter using resultant theory

In this work, a method is given to compute the switching angles in a multilevel converter to produce the required fundamental voltage while at the same time cancel out specified higher order harmonics. Specifically, a complete analysis is given for a seven-level converter (three dc sources), where it is shown that for a range of the modulation index m/sub I/, the switching angles can be chosen to produce the desired fundamental V/sub 1/=m/sub I/(s4V/sub dc///spl pi/) while making the fifth and seventh harmonics identically zero.

A unified approach to solving the harmonic elimination equations in multilevel converters

A method is presented to compute the switching angles in a multilevel converter so as to produce the required fundamental voltage while at the same time not generate higher order harmonics. Using a staircase fundamental switching scheme, previous work has shown that this is possible only for specific ranges of the modulation index. Here it is shown that, by considering all possible switching schemes, one can extend the lower range of modulation indices for which such switching angles exist. A unified approach is presented to solve the harmonic elimination equations for all of the various switching schemes. In particular, it is shown that all such schemes require solving the same set of equations where each scheme is distinguished by the location of the roots of the harmonic elimination equations. In contrast to iterative numerical techniques, the approach here produces all possible solutions.

Eliminating harmonics in a multilevel converter using resultant theory

A method is given to determine conditions for which the switching angles in a multilevel converter can be chosen to produce the required fundamental voltage while at the same time cancel out higher order harmonics. A complete analysis is given for a 7- level converter where it is shown that for a range of the modulation index m/sub I/, the switching angles can be chosen to produce the desired fundamental V/sub 1/=m/sub I/(s4V/sub dc///spl pi/) while making the 5/sup th/ and 7/sup th/ harmonics identically zero.

A complete solution to the harmonic elimination problem

The problem of eliminating harmonics in a switching converter is considered. That is, given a desired fundamental output voltage, the problem is to find the switching times (angles) that produce the fundamental while not generating specifically chosen harmonics. In contrast to the well known work of Patel and Hoft and others, here all possible solutions to the problem are found. This is done by first converting the transcendental equations that specify the harmonic elimination problem into an equivalent set of polynomial equations. Then, using the mathematical theory of resultants, all solutions to this equivalent problem can be found. In particular, it is shown that there are new solutions that have not been previously reported in the literature. The complete solutions for both unipolar and bipolar switching patterns to eliminate the fifth and seventh harmonics are given. Finally, the unipolar case is again considered where the fifth, seventh, 11th, and 13th harmonics are eliminated along with corroborative experimental results.

Elimination of harmonics in a multilevel converter with nonequal DC sources

The problem of eliminating harmonics in a multilevel converter in which the separate DC sources vary is considered. That is, given a desired fundamental output voltage, the problem is to find the switching times (angles) that produce the fundamental while not generating specifically chosen harmonics. Assuming that the separate DC sources can be measured, a procedure is given to find all sets of switching angles for which the fundamental is produced while the 5th and 7th are eliminated. This is done by first converting the transcendental equations that specify the elimination of the harmonics into an equivalent set of polynomial equations. Then, using the mathematical theory of resultants, all solutions to this equivalent problem can be found. Experimental results are presented to validate the theory.

A new approach to solving the harmonic elimination equations for a multilevel converter

A method is presented to compute the switching angles in a multilevel converter so as to produce the required fundamental voltage while at the same time not generate higher order harmonics. Previous work has shown that the transcendental equations characterizing the harmonic content can be converted to polynomial equations which are then solved using the method of resultants from elimination theory. A difficulty with this approach is that when there are several DC sources, the degrees of the polynomials are quite large making the computational burden of their resultant polynomials (as required by elimination theory) quite high. Here, it is shown that the theory of symmetric polynomials can be exploited to reduce the degree of the polynomial equations that must be solved which in turn greatly reduces the computational burden. In contrast to results reported in the literature that use iterative numerical techniques to solve these equations, the approach here produces all possible solutions.

The Use of Power Sums to Solve the Harmonic Elimination Equations for Multilevel Converters

Abstract A method is presented to compute the switching angles in a multilevel converter so as to produce the required fundamental voltage while at the same time not generate higher order harmonics. Previous work has shown that the transcendental equations characterizing the harmonic content can be converted to polynomial equations which are then solved using the method of resultants from elimination theory. However, when there are several DC sources, the degree of the polynomials are quite large making the computational burden of their resultant polynomials via elimination theory quite high. Here, it is shown that by reformulating the problem in terms ofpower sums, the degree of the polynomial equations that must be solved are reduced significantly which in turn reduces the computational burden. In contrast to numerical techniques, the approach here produces all possible solutions.

Elimination of harmonics in a multilevel converter using the theory of symmetric polynomials and resultants

A method is presented to compute the switching angles in a multilevel converter so as to produce the required fundamental voltage while at the same time not generate higher order harmonics. Previous work has shown that the transcendental equations characterizing the harmonic content can be converted to polynomial equations which are then solved using the method of resultants from elimination theory. A difficulty with this approach is that when there are several DC sources, the degrees of the polynomials are quite large making the computational burden of their resultant polynomials (as required by elimination theory) quite high. In this paper, it is shown that the theory of symmetric polynomials can be exploited to reduce the degree of the polynomial equations that must be solved which in turn greatly reduces the computational burden. In contrast to results reported in the literature that use iterative numerical techniques to solve these equations, the approach here produces all possible solutions.

Real-time computer control of a multilevel converter using the mathematical theory of resultants

The mathematical theory of resultants is used to compute the switching angles in a multilevel converter so that it produces the required fundamental voltage while at the same time cancels out unwanted order harmonics. Experimental results are given for the three dc source case. It is shown that for a range of the modulation index the switching angles can be chosen to produce the desired fundamental while at the same time the fifth and seventh harmonics are identically zero.

Control of cascaded multilevel converters with unequal voltage sources for HEVs

One promising technology to interface battery packs in electric and hybrid electric vehicles is the multilevel converter. In the work presented here, it is shown how the switching times (angles) in a multilevel inverter can be chosen to achieve a required fundamental voltage and not generate specific higher order harmonics. The method gives a complete solution to the problem in that all possible solutions are found.