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24
Modeling and simulation of power electronic converters
 Proc. IEEE
, 2001
"... This paper reviews some of the major approaches to modeling and simulation in power electronics, and provides references that can serve as a starting point for the extensive literature on the subject. The major focus of the paper is on averaged models of various kinds, but sampleddata models are ..."
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Cited by 15 (1 self)
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This paper reviews some of the major approaches to modeling and simulation in power electronics, and provides references that can serve as a starting point for the extensive literature on the subject. The major focus of the paper is on averaged models of various kinds, but sampleddata models are also introduced. The importance of hierarchical modeling and simulation is emphasized. Keywords—Averaged models, boost converter, circuit averaging, dynamic phasors, hierarchical methods, modeling, power electronics, power factor correction, sampleddata models, simulation, statespace averaging, switched models. I.
Switched Networks and Complementarity
, 2002
"... A modeling framework is proposed for circuits that are subject both to externally induced switches (time events) and to state events. The framework applies to switched networks with linear and piecewise linear elements, including diodes. We show that the linear complementarity formulation, which al ..."
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Cited by 14 (9 self)
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A modeling framework is proposed for circuits that are subject both to externally induced switches (time events) and to state events. The framework applies to switched networks with linear and piecewise linear elements, including diodes. We show that the linear complementarity formulation, which already has proved effective for piecewise linear networks, can be extended in a natural way to cover also switching circuits. To achieve this, we use a generalization of the linear complementarity problem known as the cone complementarity problem. We show that the proposed framework is sound in the sense that existence and uniqueness of solutions is guaranteed under a passivity assumption. We establish an equivalence between passivity and representability in portHamiltonian form. We prove that only firstorder impulses occur and characterize all situations that give rise to a state jump; moreover, we provide rules that determine the jump. Finally, we show that within our framework energy cannot increase as a result of a jump, and we derive a stability result from this.
Stability of ideal thyristor and diode switching circuits
 IEEE Trans. Circuits and Systems, Part
, 1995
"... AbstrQctThis paper analyzes the stability of a general RLC circuit with ideal thyristors or diodes and periodic sources. Applications include high power thyristor controlled reactor and bridge rectifier circuits. The periodic steady states of the circuit are analyzed using a Poincar6 map and transv ..."
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Cited by 8 (2 self)
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AbstrQctThis paper analyzes the stability of a general RLC circuit with ideal thyristors or diodes and periodic sources. Applications include high power thyristor controlled reactor and bridge rectifier circuits. The periodic steady states of the circuit are analyzed using a Poincar6 map and transversal&y conditions are given to guarantee the smoothness of the Pgincar6 map. A simple and exact formula for the Jacobian of the Poincar6 map is proved. Account is taken of the varying state space dimension as diodes switch on and off. When the transversality conditions fail, switching times can jump or bifurcate. Examples show that these switching time bifurcations can cause instability of thy&or circuits and mode changes of diode circuits. The simplification of the Jacobian formula is used to explain why the switching time bifurcations occur and are not predicted by the eigenvalues of the Jacobian. Periodic orbits of ideal diode circuits are proved to be stable using Jacobian and incremental energy methods. A source of damping in switching circuits is identified. A I.
PETS  A Simulation Tool for Power Electronics
 IEEE WORKSHOP ON COMPUTERS IN POWER ELECTRONICS
, 1996
"... . . . Transient Simulator), a program for timedomain analysis of power electronic circuits. Methods implemented in PETS include standard techniques such as the modi ed nodal approach to forming system equations, and numerical integration with automatic timestep control, together with new technique ..."
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Cited by 6 (3 self)
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. . . Transient Simulator), a program for timedomain analysis of power electronic circuits. Methods implemented in PETS include standard techniques such as the modi ed nodal approach to forming system equations, and numerical integration with automatic timestep control, together with new techniques including a state determination algorithm, and representation of elements to maintain a constant system matrix. The simulator supports arbitrarily complex piecewiselinear models and smooth nonlinear models using a delay approximation. The methods implemented in PETS are illustrated using two examples: a quadratic buck converter, and a closedloop powerfactor corrector.
Quadratic Stability of a Class of Switched Nonlinear Systems
 IEEE Transactions on Automatic Control
, 2004
"... Abstract. This paper is concerned with the quadratic stabilization for a class of switched nonlinear singular systems. For this class of switched systems, when each individual subsystem fails to be minimumphase, the quadratic stabilization problem is solved via designing switching law. This extend ..."
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Cited by 5 (1 self)
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Abstract. This paper is concerned with the quadratic stabilization for a class of switched nonlinear singular systems. For this class of switched systems, when each individual subsystem fails to be minimumphase, the quadratic stabilization problem is solved via designing switching law. This extends available results for nonswitched nonlinear singular systems. Key Words. Switched nonlinear singular systems, single Lyapunov functions, zero dynamics, quadratic stabilization. 1.
Models of nonsmooth switches in electrical systems
, 2005
"... Idealized modelling of diodes, relays and switches in the framework of linear complementarity is introduced. Within the charge approach, the classical electromechanical analogy is extended to passively and actively switching components in electrical circuits. The associated branch relations are expr ..."
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Cited by 4 (1 self)
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Idealized modelling of diodes, relays and switches in the framework of linear complementarity is introduced. Within the charge approach, the classical electromechanical analogy is extended to passively and actively switching components in electrical circuits. The associated branch relations are expressed in terms of setvalued functions, which allow to formulate the circuit’s dynamic behaviour as a dierential inclusion. This approach is demonstrated by the example of the DC–DC buck converter. A dierence scheme, known in mechanics as time stepping, is applied for numerical approximation of the evolution problem. The discretized inclusions are formulated as a linear complementarity problem in standard form, which implicitly takes care of all switching events by its solution. State reduction, which requires manipulation of the setvalued branch relations in order to obtain a minimal model, is performed on the example of the buck converter.
Modelling, Wellposedness and Stability of Switched Electrical Networks
"... A modeling framework is proposed for circuits that are subject to both time and state events. The framework applies to switched networks with linear and piecewise linear elements including diodes and switches. We show that the linear complementarity formulation, which already has proved effective ..."
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Cited by 4 (2 self)
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A modeling framework is proposed for circuits that are subject to both time and state events. The framework applies to switched networks with linear and piecewise linear elements including diodes and switches. We show that the linear complementarity formulation, which already has proved effective for piecewise linear networks, can be extended in a natural way to cover also switching circuits. We show that the proposed framework is sound in the sense that existence and uniqueness of solutions is guaranteed under a passivity assumption. We prove that only firstorder impulses occur and characterize all situations that give rise to a state jump; moreover, we provide rules that determine the jump. Finally, we derive a stability result. Hence, for a subclass of hybrid dynamical systems, the issues of wellposedness, regularity of trajectories, jump rules, consistent states and stability are resolved.
On Inconsistent Initial Conditions for Linear TimeInvariant DifferentialAlgebraic Equations
"... Abstract—Given an arbitrary initial value for the differentialalgebraic equation _ ()+ ( ) = (), an initial value can be selected from among all consistent initial values by means of the Laplace transform. We show that this choice is the only one that fulfills some simple, physically reasonable ..."
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Cited by 3 (1 self)
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Abstract—Given an arbitrary initial value for the differentialalgebraic equation _ ()+ ( ) = (), an initial value can be selected from among all consistent initial values by means of the Laplace transform. We show that this choice is the only one that fulfills some simple, physically reasonable assumptions on linear systems ’ behavior. Our derivation is elementary compared to previous justifications of the above Laplace transform based method. We also characterize by means of a system of linear equations involving, , derivatives of, and, which gives a new method to numerically calculate. Index Terms—Differentialalgebraic equations (DAEs). I. BACKGROUND For several reasons, differentialalgebraic equations (DAEs) of the form F (x(t); _x(t); t)=0 (1) are preferred models in many fields, even if an equivalent explicit equation _x(t) =f (x(t); t) could be obtained [4]. (Here, F:
Computer Simulation of ContinuousTime and Switched Circuits: Limitations of SPICEFamily Programs and Pending Issues
"... Abstract. The contribution deals with some open problems from the area of Transient and AC analyses of large continuoustime and switched circuits with the focus on switched capacitor circuits and switched DCDC converters. The discussed weak points of SPICElike and SPICEcompatible simulation prog ..."
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Cited by 2 (0 self)
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Abstract. The contribution deals with some open problems from the area of Transient and AC analyses of large continuoustime and switched circuits with the focus on switched capacitor circuits and switched DCDC converters. The discussed weak points of SPICElike and SPICEcompatible simulation programs consist in the absence of finding effectively the steadystate, in an inefficient integration algorithm for the transient analysis of switching phenomena, and in the absence of a direct AC analysis of switched circuits. The paper also describes some new approaches, which could be helpful in overcoming the above limitations.
Interval Algorithms For Finding The Minimal Root In A Set Of Multiextremal OneDimensional Functions
, 1999
"... . Two problems very often arising in applications are considered. The rst problem consists of nding the minimal root of an analytic onedimensional function over a given interval. It is supposed that the objective function can be multiextremal and nondierentiable. The second problem is a generaliza ..."
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Cited by 2 (0 self)
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. Two problems very often arising in applications are considered. The rst problem consists of nding the minimal root of an analytic onedimensional function over a given interval. It is supposed that the objective function can be multiextremal and nondierentiable. The second problem is a generalization of the rst one and deals with the search of the minimal root in a set of the functions. New algorithms based on Interval Analysis and BranchandBound Global Optimization approaches are proposed for solving both problems. Numerical experiments carried out on a wide set of test functions demonstrate a quite satisfactory performance of the new algorithms in comparison with interval analysis techniques traditionally used for nding roots of equations. Key words. Minimal Root, Interval Analysis, BranchandBound. AMS subject classications. 6504,6505,65G10,65H20,65K05,90C30 1. Introduction. There exist many applications where the problem of nding the roots of onedimensional funct...