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1
Content available The measurement test for the identification of current - flux linkage characteristics in synchronous reluctance motors
Burlikowski W., Kohlbrenner Ł.
Measurement Automation Monitoring
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2016
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Vol. 62, No. 1
33--36
EN
In the paper a new measurement procedure of identification of synchronous reluctance motors parameters is presented. It is based on extension of traditional current decay test, used both in case of induction and synchronous motors [1, 3]. The main aim of the method is to enable to obtain the current-flux linkage characteristic necessary in case of Hamiltonian model of the machine (eq. 1). In case of 3-phase machine without neutral wire, being the most popular in practical applications [3], the method is based on measurement of currents in two independent phases (Fig. 4, eq. 5). The result of its application in a form of trajectories presenting traces of the chosen flux linkage in a current space is shown in Fig. 8b.
2
Content available remote Error analysis in mathematical model of electromechanical actuator using Hamiltonian equations
Burlikowski W., Kowalik Z.
Czasopismo Techniczne. Elektrotechnika
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2015
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Y. 112, iss. 1-E
119--128
EN
This paper presents a methodology of error analysis in a mathematical model of an electromechanical actuator using Hamiltonian equations in the description of energy conversion. As the basic quantity in numerical algorithms, the coenergy of magnetic field Ecm is employed. The reason for the application of coenergy as a state function is the explicitness of its value for a given set of state variables, resulting from neglecting eddy currents and hysteresis phenomenon in the model.
PL
W artykule przedstawiono metodykę analizy błędu w modelu matematycznym przetwornika elektromechanicznego wykorzystującym równania Hamiltona w opisie przemiany elektromechanicznej. Jako podstawowej wielkości w algorytmie obliczeniowym użyto koenergii pola magnetycznego Ecm. Wykorzystano w tym celu jednoznaczność określenia wartości koenergii dla danej wartości zmiennych stanu, wynikającą z pominięcia w modelu prądów wirowych oraz zjawiska histerezy.
3
Content available remote Analiza błędu w modelu matematycznym przetwornika elektromechanicznego wykorzystującym równania Hamiltona
Burlikowski W., Kowalik Z.
Maszyny Elektryczne : zeszyty problemowe
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2014
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Nr 4(104)
131--136
PL
W artykule przedstawiono metodykę analizy błędu w modelu matematycznym przetwornika elektromechanicznego, wykorzystującym równania Hamiltona w opisie przemiany elektromechanicznej. Jako podstawową wielkość w algorytmie obliczeniowym użyto koenergię pola magnetycznego Ecm. Wykorzystano w tym celu jednoznaczność określenia wartości koenergii dla danej wartości zmiennych stanu, wynikającą z pominięcia w modelu prądów wirowych oraz zjawiska histerezy.
EN
The paper presents a methodology of error analysis in mathematical model of an electromechanical actuator using Hamiltonian equations in the description of energy conversion. As the basic quantity in numerical algorithm the coenergy of magnetic field Ecm is employed. The reason for application of coenergy as a state function is the explicitness of its value for a given set of state variables, resulting from neglecting Eddy currents and hysteresis phenomenon in the model.
4
Content available Reluctance motor mathematical model in natural reference frame using Hamiltonian equations - simulational analysis
Burlikowski W.
Maszyny Elektryczne : zeszyty problemowe
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2011
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Nr 5(93)
19-24
EN
In the paper a novel mathematical model of electromechanical actuator is presented. It is based on application of Hamiltonian equations in the description of electromechanical energy conversion. It results in employment of flux linkages as state variables in the state space equations. A 3-phase wye connected stator winding without a neutral wire is considered in detail as the most important connection schema in practical applications. The procedure can be generalised to any number of phases and arbitrary connection schema. Topology- based approach is used in the model implementation. Eddy currents and hysteresis phenomenon are neglected in formulation of the model to enable application of Hamiltonian description. Simulation analysis is performed using data from FEM model of reluctance cageless motor.
5
Content available Hamiltonian model of electromechanical actuator in natural reference frame.: Part II: Equations and simulations
Burlikowski W.
Archives of Electrical Engineering
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2011
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Vol. 60, nr 3
331-348
EN
In the paper a novel mathematical model of electromechanical actuator is presented. It is based on application of Hamiltonian equations in the description of electro-mechanical energy conversion. It results in employment of flux linkages as state variables in the state space equations. For simplicity only a 3-phase wye connected stator winding without a neutral wire is considered in detail. The procedure can be generalised to any number of phases. Topology-based approach is used in the model implementation. Procedures for evaluation of all quantities (currents, energy/coenergy, electro-magnetic torque) present in model equations are described. Eddy currents and hysteresis phenolmenon are neglected in formulation of the model to enable application of state-space description.
6
Content available Hamiltonian model of electromechanical actuator in natural reference frame.: Part I: Topology-based approximation algorithm
Burlikowski W.
Archives of Electrical Engineering
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2011
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Vol. 60, nr 3
317-330
EN
In the paper a novel mathematical model of electromechanical actuator is presented. It is based on application of Hamiltonian equations in the description of electromechanical energy conversion. It results in employment of flux linkages as state variables in the state space equations. For simplicity only a 3-phase wye connected stator winding without a neutral wire is considered in detail. The procedure can be generalised to any number of phases. Topology-based approach is used in the model implementation. Procedures for evaluation of all quantities (currents, energy/coenergy, electromagnetic torque) present in model equations are described. Eddy currents and hysteresis phenolmenon are neglected in formulation of the model to enable application of state-space description.
7
Content available remote A general statement of dual first-order sufficient optimality conditions for the generalized problem of Bolza
Galewska E.
Demonstratio Mathematica
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2003
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Vol. 36, nr 3
711--720
EN
In this paper we provide first-order sufficient optimality conditions for the generalized problem of Bolza when all arcs take values in a separable Hilbert space. Our approach consists in the explicit construction of a quadratic function that satisfies the dual Hamilton-Jacobi inequality. The essential role in the generalized conditions plays the existence of a certain function for which a certain inequality holds.
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