Selection of Output Voltage Compensators Gains in Two Cascaded Boost Converters with Input Filters by Means of the \({\mathfrak{D}}\)-Decomposition Technique
In this paper, the <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi mathvariant="fraktur">D</mi></semantics></math></inline-formula>-decomposition technique is investigated a...
| Main Authors: | , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
MDPI AG
2021-09-01
|
| Series: | Energies |
| Subjects: | |
| Online Access: | https://www.mdpi.com/1996-1073/14/18/5883 |
| _version_ | 1797519421590208512 |
|---|---|
| author | Karol Najdek Radosław Nalepa Robert Lis |
| author_facet | Karol Najdek Radosław Nalepa Robert Lis |
| author_sort | Karol Najdek |
| collection | DOAJ |
| description | In this paper, the <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi mathvariant="fraktur">D</mi></semantics></math></inline-formula>-decomposition technique is investigated as an intuitive method for finding the non-linear trajectories of PI-compensator gains. The trajectories reflect the desired dynamic properties at a system level specified by the gain and the phase margin (GMPM) in the frequency domain. They are presented as parametric curves in the proportional and the integral gains coordinates in form of <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mi>K</mi><mi mathvariant="normal">I</mi></msub><mo>=</mo><mi>f</mi><mrow><mo>(</mo><msub><mi>K</mi><mi mathvariant="normal">P</mi></msub><mo>)</mo></mrow></mrow></semantics></math></inline-formula> functions. The curves are inscribed into global stability boundaries (GSB). The corresponding Nyquist plots are included for comparison. The analysis is based on a system consisting of two serial-connected boost converters. Each converter has its input filter. The major parasitic components of the system are taken into account during the mathematical and simulation modelling. The control circuit time delays and non-linear semiconductors characteristics are also included. A complete set of practically useful system-level transfer functions in form of mathematical formulas is included. Selected aspects, such as the control-to-output voltage and the control-to-input current of one sub-system of the simulation model, have been verified experimentally. The presented results clearly indicate the need for interactions between the sub-systems of a system to be taken into account during controller gains selection. |
| first_indexed | 2024-03-10T07:42:33Z |
| format | Article |
| id | doaj.art-672d237481474e2c9aede01bb904e740 |
| institution | Directory Open Access Journal |
| issn | 1996-1073 |
| language | English |
| last_indexed | 2024-03-10T07:42:33Z |
| publishDate | 2021-09-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Energies |
| spelling | doaj.art-672d237481474e2c9aede01bb904e7402023-11-22T12:54:32ZengMDPI AGEnergies1996-10732021-09-011418588310.3390/en14185883Selection of Output Voltage Compensators Gains in Two Cascaded Boost Converters with Input Filters by Means of the \({\mathfrak{D}}\)-Decomposition TechniqueKarol Najdek0Radosław Nalepa1Robert Lis2Department of Electrical Power Engineering, Faculty of Electrical Engineering, Wrocław University of Science and Technology, 50370 Wrocław, PolandDepartment of Electrical Power Engineering, Faculty of Electrical Engineering, Wrocław University of Science and Technology, 50370 Wrocław, PolandDepartment of Electrical Power Engineering, Faculty of Electrical Engineering, Wrocław University of Science and Technology, 50370 Wrocław, PolandIn this paper, the <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi mathvariant="fraktur">D</mi></semantics></math></inline-formula>-decomposition technique is investigated as an intuitive method for finding the non-linear trajectories of PI-compensator gains. The trajectories reflect the desired dynamic properties at a system level specified by the gain and the phase margin (GMPM) in the frequency domain. They are presented as parametric curves in the proportional and the integral gains coordinates in form of <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mi>K</mi><mi mathvariant="normal">I</mi></msub><mo>=</mo><mi>f</mi><mrow><mo>(</mo><msub><mi>K</mi><mi mathvariant="normal">P</mi></msub><mo>)</mo></mrow></mrow></semantics></math></inline-formula> functions. The curves are inscribed into global stability boundaries (GSB). The corresponding Nyquist plots are included for comparison. The analysis is based on a system consisting of two serial-connected boost converters. Each converter has its input filter. The major parasitic components of the system are taken into account during the mathematical and simulation modelling. The control circuit time delays and non-linear semiconductors characteristics are also included. A complete set of practically useful system-level transfer functions in form of mathematical formulas is included. Selected aspects, such as the control-to-output voltage and the control-to-input current of one sub-system of the simulation model, have been verified experimentally. The presented results clearly indicate the need for interactions between the sub-systems of a system to be taken into account during controller gains selection.https://www.mdpi.com/1996-1073/14/18/5883\({\mathfrak{D}}\)-decomposition techniqueboost convertercascaded convertersPI voltage compensatorstability boundary |
| spellingShingle | Karol Najdek Radosław Nalepa Robert Lis Selection of Output Voltage Compensators Gains in Two Cascaded Boost Converters with Input Filters by Means of the \({\mathfrak{D}}\)-Decomposition Technique Energies \({\mathfrak{D}}\)-decomposition technique boost converter cascaded converters PI voltage compensator stability boundary |
| title | Selection of Output Voltage Compensators Gains in Two Cascaded Boost Converters with Input Filters by Means of the \({\mathfrak{D}}\)-Decomposition Technique |
| title_full | Selection of Output Voltage Compensators Gains in Two Cascaded Boost Converters with Input Filters by Means of the \({\mathfrak{D}}\)-Decomposition Technique |
| title_fullStr | Selection of Output Voltage Compensators Gains in Two Cascaded Boost Converters with Input Filters by Means of the \({\mathfrak{D}}\)-Decomposition Technique |
| title_full_unstemmed | Selection of Output Voltage Compensators Gains in Two Cascaded Boost Converters with Input Filters by Means of the \({\mathfrak{D}}\)-Decomposition Technique |
| title_short | Selection of Output Voltage Compensators Gains in Two Cascaded Boost Converters with Input Filters by Means of the \({\mathfrak{D}}\)-Decomposition Technique |
| title_sort | selection of output voltage compensators gains in two cascaded boost converters with input filters by means of the mathfrak d decomposition technique |
| topic | \({\mathfrak{D}}\)-decomposition technique boost converter cascaded converters PI voltage compensator stability boundary |
| url | https://www.mdpi.com/1996-1073/14/18/5883 |
| work_keys_str_mv | AT karolnajdek selectionofoutputvoltagecompensatorsgainsintwocascadedboostconverterswithinputfiltersbymeansofthemathfrakddecompositiontechnique AT radosławnalepa selectionofoutputvoltagecompensatorsgainsintwocascadedboostconverterswithinputfiltersbymeansofthemathfrakddecompositiontechnique AT robertlis selectionofoutputvoltagecompensatorsgainsintwocascadedboostconverterswithinputfiltersbymeansofthemathfrakddecompositiontechnique |