A Comprehensive Review of Solving Selective Harmonic Elimination Problem With Algebraic Algorithms

Selective harmonic elimination pulsewidth modulation (SHEPWM) is an effective way to eliminate low-order harmonics in high-power applications. However, one of the biggest challenges of SHEPWM is to solve the selective harmonic elimination (SHE) equations, which are composed of some nonlinear transce...

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Veröffentlicht in:	IEEE transactions on power electronics Jg. 39; H. 1; S. 850 - 868
Hauptverfasser:	Wang, Chenxu, Zhang, Qi, Yu, Wensheng, Yang, Kehu
Format:	Journal Article
Sprache:	Englisch
Veröffentlicht:	New York IEEE 01.01.2024 The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Schlagworte:	Algebra Algebraic algorithms Algorithms Biological system modeling Classification algorithms dc–ac conversion Exact solutions Harmonic analysis Harmonics high-power applications Identities inverters Mathematical models Polynomials Power system harmonics Pulse duration Pulse width modulation renewable energy system selective harmonic elimination (SHE) Voltage
ISSN:	0885-8993, 1941-0107
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Abstract	Selective harmonic elimination pulsewidth modulation (SHEPWM) is an effective way to eliminate low-order harmonics in high-power applications. However, one of the biggest challenges of SHEPWM is to solve the selective harmonic elimination (SHE) equations, which are composed of some nonlinear transcendental equations. Over the past few decades, algebraic algorithms have shown a considerable ability to solve SHE equations, specifically for obtaining all exact solutions. Much research has been published about algebraic algorithms, struggling to solve more switching angles, solving different mathematic models of SHEPWM, and so on. This article comprehensively reviews existing algebraic algorithms, including elementary symmetric polynomials, power sums, Newton's identities, resultant elimination method, Wu's method, Gröbner-basis-based method, Chudnovsky algorithm, polynomial homotopy continuation algorithm, and real-time implementation by algebraic algorithms. The principle operation of these methods is summarized, and their performance is analyzed in terms of execution time, solving ability, and applicability for different mathematical models.
AbstractList	Selective harmonic elimination pulsewidth modulation (SHEPWM) is an effective way to eliminate low-order harmonics in high-power applications. However, one of the biggest challenges of SHEPWM is to solve the selective harmonic elimination (SHE) equations, which are composed of some nonlinear transcendental equations. Over the past few decades, algebraic algorithms have shown a considerable ability to solve SHE equations, specifically for obtaining all exact solutions. Much research has been published about algebraic algorithms, struggling to solve more switching angles, solving different mathematic models of SHEPWM, and so on. This article comprehensively reviews existing algebraic algorithms, including elementary symmetric polynomials, power sums, Newton's identities, resultant elimination method, Wu's method, Gröbner-basis-based method, Chudnovsky algorithm, polynomial homotopy continuation algorithm, and real-time implementation by algebraic algorithms. The principle operation of these methods is summarized, and their performance is analyzed in terms of execution time, solving ability, and applicability for different mathematical models.
Author	Yang, Kehu Zhang, Qi Yu, Wensheng Wang, Chenxu
Author_xml	– sequence: 1 givenname: Chenxu orcidid: 0000-0001-5622-7480 surname: Wang fullname: Wang, Chenxu email: eechenxu@163.com organization: School of Mechanical and Electrical Engineering, China University of Mining and Technology (Beijing), Beijing, China – sequence: 2 givenname: Qi orcidid: 0000-0001-9094-9989 surname: Zhang fullname: Zhang, Qi email: qzg@energy.aau.dk organization: AAU Energy, Aalborg University, Aalborg, Denmark – sequence: 3 givenname: Wensheng orcidid: 0000-0002-3832-2748 surname: Yu fullname: Yu, Wensheng email: wsyu@bupt.edu.cn organization: School of Electronics Engineering, Beijing University of Posts and Telecommunications, Beijing, China – sequence: 4 givenname: Kehu orcidid: 0000-0001-9163-2713 surname: Yang fullname: Yang, Kehu email: ykh@cumtb.edu.cn organization: School of Artificial Intelligence, China University of Mining and Technology (Beijing), Beijing, China
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Snippet	Selective harmonic elimination pulsewidth modulation (SHEPWM) is an effective way to eliminate low-order harmonics in high-power applications. However, one of...
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SubjectTerms	Algebra Algebraic algorithms Algorithms Biological system modeling Classification algorithms dc–ac conversion Exact solutions Harmonic analysis Harmonics high-power applications Identities inverters Mathematical models Polynomials Power system harmonics Pulse duration Pulse width modulation renewable energy system selective harmonic elimination (SHE) Voltage
Title	A Comprehensive Review of Solving Selective Harmonic Elimination Problem With Algebraic Algorithms
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