Modern semiconductor converters take high currents from power distribution network (PDN) conseque... more Modern semiconductor converters take high currents from power distribution network (PDN) consequently harmonic and interharmonic currents arise with high values and there are inconsiderable unallowable effects in PDN. We can sort softstarters as often used converters. Principal aim is reducing start up currents, the influence on PDN is not usually monitored and protective devices are not use as well.
We study the problem of the homogenization of the Dirichlet eigenvalue problems for m-Laplace ope... more We study the problem of the homogenization of the Dirichlet eigenvalue problems for m-Laplace operator in domains with flne-grained boundary.
2011 IEEE International Symposium on Electromagnetic Compatibility, 2011
This contribution introduces the education of EMC at the University of West Bohemia in Pilsen (UW... more This contribution introduces the education of EMC at the University of West Bohemia in Pilsen (UWB). The phenomenon of Electromagnetic compatibility (EMC) has been taken into account almost at all faculties of electrical engineering in the Czech Republic. However there often are only partial mentions of EMC in frame of individual electrical engineering subjects and the education is focused on
PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY Volume 134, Number 12, December 2006, Pages 3487... more PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY Volume 134, Number 12, December 2006, Pages 34873494 S 0002-9939(06)08001-4 Article electronically published on June 27, 2006 ... BASIS PROPERTIES OF EIGENFUNCTIONS OF THE p-LAPLACIAN
Power electronic converters produce not only characteristic harmonics, but also both non-characte... more Power electronic converters produce not only characteristic harmonics, but also both non-characteristic harmonics and interharmonics. This paper presents the physical background of both non-characteristic harmonics and interharmonics. Generation causes are explored and discussed in detail. Extensive series of simulation of different power converter topologies are provided and compared with experimental results and existing standards. This research offers missing background for standards covering low-frequency EMC.
This paper presents research motivated by industrial demand for energy storage system for city tr... more This paper presents research motivated by industrial demand for energy storage system for city transport vehicles. The kinetic energy is accumulated into the supercapacitor during vehicle braking. This energy can be used to accelerating in next time. It is important to save the energy in the vehicles, which accelerate very often.
We study the following bifurcation problem in any bounded domainΩinℝN:{Apu:=−∑i,j=1N∂∂xi[(∑m,k=1N... more We study the following bifurcation problem in any bounded domainΩinℝN:{Apu:=−∑i,j=1N∂∂xi[(∑m,k=1Namk(x)∂u∂xm∂u∂xk)p−22aij(x)∂u∂xj]= λg(x)|u|p−2u+f(x,u,λ),u∈W01,p(Ω).. We prove that the principal eigenvalueλ1of the eigenvalue problem{Apu=λg(x)|u|p−2u,u∈W01,p(Ω),is a bifurcation point of the problem mentioned above.
This paper presents research motivated by industrial demand for special traction drive topology d... more This paper presents research motivated by industrial demand for special traction drive topology devoted to minimization of traction transformer weight against topology with classical 50Hz traction transformer. The special traction drive topology for AC power systems consists of input high voltage trolley converter (single phase matrix converter) – middle frequency transformer – output converter -traction motor has been described. The main attention has been given to the control algorithm of the traction topology (inserting of NULL vector of matrix converter and Two-value control of secondary active rectifier).
This paper deals with the creation of mathematical model of switched reluctance motor. The basic ... more This paper deals with the creation of mathematical model of switched reluctance motor. The basic mathematical description of SRM is followed by several approximation methods, suitable for measured data processing (mainly function of the electromagnetic flux in dependence on the rotor current and position). The acquired results of mentioned methods are compared and are used for the choice of final
Zeitschrift für angewandte Mathematik und Physik, 2011
In this paper, we study critical points of the functional $$J_{\epsilon}(u):=\frac{\epsilon^2}{2}... more In this paper, we study critical points of the functional $$J_{\epsilon}(u):=\frac{\epsilon^2}{2} \int\limits_0^1|u_x|^2{\rm {d}}x+\int\limits_0^1F(u){\rm {d}}x, u \,\in W^{1,2}{(0,1)}, \quad \quad \quad(1)$$ where $${F : \mathbb {R}\rightarrow \mathbb {R}}$$ is assumed to be a double-well potential. This functional represents the total free energy in models of phase transition and allows for the study of interesting phenomena such as slow dynamics. In particular, we consider a non-classical choice for F modeled on $${F(u)=|1-u^2|^{\alpha}}$$ where 1 α F′′ at ±1 leads to the existence of multiple continua of critical points that are not present in the classical case $${F \in C^2}$$ . We prove that the interior points of these continua are local minima. The energy of these local minimizers is strictly greater than the global minimum of $${J_{\epsilon}}$$ . In particular, the existence of these continua leads to an alternative explanation for the slow dynamics observed in phase transition models.
Proceedings of the Royal Society of Edinburgh: Section A Mathematics, 2010
We study the problem of the homogenization of Dirichlet eigenvalue problems for the p-Laplace ope... more We study the problem of the homogenization of Dirichlet eigenvalue problems for the p-Laplace operator in a sequence of perforated domains with fine-grained boundary. Using the asymptotic expansion method, we derive the homogenized problem for the new equation with an additional term of capacity type. Moreover, we show that a sequence of eigenvalues for the problem in perforated domains converges to the corresponding critical levels of the homogenized problem.
Modern semiconductor converters take high currents from power distribution network (PDN) conseque... more Modern semiconductor converters take high currents from power distribution network (PDN) consequently harmonic and interharmonic currents arise with high values and there are inconsiderable unallowable effects in PDN. We can sort softstarters as often used converters. Principal aim is reducing start up currents, the influence on PDN is not usually monitored and protective devices are not use as well.
We study the problem of the homogenization of the Dirichlet eigenvalue problems for m-Laplace ope... more We study the problem of the homogenization of the Dirichlet eigenvalue problems for m-Laplace operator in domains with flne-grained boundary.
2011 IEEE International Symposium on Electromagnetic Compatibility, 2011
This contribution introduces the education of EMC at the University of West Bohemia in Pilsen (UW... more This contribution introduces the education of EMC at the University of West Bohemia in Pilsen (UWB). The phenomenon of Electromagnetic compatibility (EMC) has been taken into account almost at all faculties of electrical engineering in the Czech Republic. However there often are only partial mentions of EMC in frame of individual electrical engineering subjects and the education is focused on
PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY Volume 134, Number 12, December 2006, Pages 3487... more PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY Volume 134, Number 12, December 2006, Pages 34873494 S 0002-9939(06)08001-4 Article electronically published on June 27, 2006 ... BASIS PROPERTIES OF EIGENFUNCTIONS OF THE p-LAPLACIAN
Power electronic converters produce not only characteristic harmonics, but also both non-characte... more Power electronic converters produce not only characteristic harmonics, but also both non-characteristic harmonics and interharmonics. This paper presents the physical background of both non-characteristic harmonics and interharmonics. Generation causes are explored and discussed in detail. Extensive series of simulation of different power converter topologies are provided and compared with experimental results and existing standards. This research offers missing background for standards covering low-frequency EMC.
This paper presents research motivated by industrial demand for energy storage system for city tr... more This paper presents research motivated by industrial demand for energy storage system for city transport vehicles. The kinetic energy is accumulated into the supercapacitor during vehicle braking. This energy can be used to accelerating in next time. It is important to save the energy in the vehicles, which accelerate very often.
We study the following bifurcation problem in any bounded domainΩinℝN:{Apu:=−∑i,j=1N∂∂xi[(∑m,k=1N... more We study the following bifurcation problem in any bounded domainΩinℝN:{Apu:=−∑i,j=1N∂∂xi[(∑m,k=1Namk(x)∂u∂xm∂u∂xk)p−22aij(x)∂u∂xj]= λg(x)|u|p−2u+f(x,u,λ),u∈W01,p(Ω).. We prove that the principal eigenvalueλ1of the eigenvalue problem{Apu=λg(x)|u|p−2u,u∈W01,p(Ω),is a bifurcation point of the problem mentioned above.
This paper presents research motivated by industrial demand for special traction drive topology d... more This paper presents research motivated by industrial demand for special traction drive topology devoted to minimization of traction transformer weight against topology with classical 50Hz traction transformer. The special traction drive topology for AC power systems consists of input high voltage trolley converter (single phase matrix converter) – middle frequency transformer – output converter -traction motor has been described. The main attention has been given to the control algorithm of the traction topology (inserting of NULL vector of matrix converter and Two-value control of secondary active rectifier).
This paper deals with the creation of mathematical model of switched reluctance motor. The basic ... more This paper deals with the creation of mathematical model of switched reluctance motor. The basic mathematical description of SRM is followed by several approximation methods, suitable for measured data processing (mainly function of the electromagnetic flux in dependence on the rotor current and position). The acquired results of mentioned methods are compared and are used for the choice of final
Zeitschrift für angewandte Mathematik und Physik, 2011
In this paper, we study critical points of the functional $$J_{\epsilon}(u):=\frac{\epsilon^2}{2}... more In this paper, we study critical points of the functional $$J_{\epsilon}(u):=\frac{\epsilon^2}{2} \int\limits_0^1|u_x|^2{\rm {d}}x+\int\limits_0^1F(u){\rm {d}}x, u \,\in W^{1,2}{(0,1)}, \quad \quad \quad(1)$$ where $${F : \mathbb {R}\rightarrow \mathbb {R}}$$ is assumed to be a double-well potential. This functional represents the total free energy in models of phase transition and allows for the study of interesting phenomena such as slow dynamics. In particular, we consider a non-classical choice for F modeled on $${F(u)=|1-u^2|^{\alpha}}$$ where 1 α F′′ at ±1 leads to the existence of multiple continua of critical points that are not present in the classical case $${F \in C^2}$$ . We prove that the interior points of these continua are local minima. The energy of these local minimizers is strictly greater than the global minimum of $${J_{\epsilon}}$$ . In particular, the existence of these continua leads to an alternative explanation for the slow dynamics observed in phase transition models.
Proceedings of the Royal Society of Edinburgh: Section A Mathematics, 2010
We study the problem of the homogenization of Dirichlet eigenvalue problems for the p-Laplace ope... more We study the problem of the homogenization of Dirichlet eigenvalue problems for the p-Laplace operator in a sequence of perforated domains with fine-grained boundary. Using the asymptotic expansion method, we derive the homogenized problem for the new equation with an additional term of capacity type. Moreover, we show that a sequence of eigenvalues for the problem in perforated domains converges to the corresponding critical levels of the homogenized problem.
Uploads
Papers by Pavel Drabek