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71
Hybrid systems: Generalized solutions and robust stability
 In IFAC Symposium on Nonliear Control Systems
, 2004
"... Abstract: Robust asymptotic stability for hybrid systems is considered. For this purpose, a generalized solution concept is developed. The first step is to characterize a hybrid time domain that permits an efficient description of the convergence of a sequence of solutions. Graph convergence is used ..."
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Cited by 46 (11 self)
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Abstract: Robust asymptotic stability for hybrid systems is considered. For this purpose, a generalized solution concept is developed. The first step is to characterize a hybrid time domain that permits an efficient description of the convergence of a sequence of solutions. Graph convergence is used. Then a generalized solution definition is given that leads to continuity with respect to initial conditions and perturbations of the system data. This property enables new results on necessary conditions for asymptotic stability in hybrid systems.
system modeling for inverse problems
 IEEE Trans. Circuits Syst. I: Reg. Papers
, 2004
"... Abstract—Large disturbances in power systems often initiate complex interactions between continuous dynamics and discrete events. The paper develops a hybrid automaton that describes such behavior. Hybrid systems can be modeled in a systematic way by a set of differentialalgebraic equations, modifi ..."
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Cited by 23 (13 self)
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Abstract—Large disturbances in power systems often initiate complex interactions between continuous dynamics and discrete events. The paper develops a hybrid automaton that describes such behavior. Hybrid systems can be modeled in a systematic way by a set of differentialalgebraic equations, modified to incorporate impulse (state reset) action and constraint switching. This differentialalgebraic impulsiveswitched (DAIS) model is a realization of the hybrid automaton. The paper presents a practical objectoriented approach to implementing the DAIS model. Each component of a system is modeled autonomously. Connections between components are established by simple algebraic equations. The systematic nature of the DAIS model enables efficient computation of trajectory sensitivities, which in turn facilitate algorithms for solving inverse problems. The paper outlines a number of inverse problems, including parameter uncertainty, parameter estimation, grazing bifurcations, boundary value problems, and dynamic embedded optimization. Index Terms—Boundary value problems, dynamic embedded optimization, dynamic modeling, hybrid systems, inverse problems, power system dynamics. I.
Control Lyapunov Functions: A Control Strategy for Damping of Power Oscillations in Large Power Systems
, 2000
"... Keywords: Controllable Series Devices (CSDs), Unified Power Flow Controller (UPFC), Quadrature Boosting Transformer (QBT), Controllable Series Capacitor (CSC), Lyapunov function, Control Lyapunov Function (CLF), Single Machine Equivalent (SIME), Variable Structure Control (VSC). ..."
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Cited by 17 (1 self)
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Keywords: Controllable Series Devices (CSDs), Unified Power Flow Controller (UPFC), Quadrature Boosting Transformer (QBT), Controllable Series Capacitor (CSC), Lyapunov function, Control Lyapunov Function (CLF), Single Machine Equivalent (SIME), Variable Structure Control (VSC).
Shooting methods for locating grazing phenomena in hybrid systems
 International Journal of Bifurcation and Chaos
, 2006
"... Hybrid systems are typified by strong coupling between continuous dynamics and discrete events. For such piecewise smooth systems, event triggering generally has a significant influence over subsequent system behaviour. Therefore it is important to identify situations where a small change in paramet ..."
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Cited by 14 (7 self)
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Hybrid systems are typified by strong coupling between continuous dynamics and discrete events. For such piecewise smooth systems, event triggering generally has a significant influence over subsequent system behaviour. Therefore it is important to identify situations where a small change in parameter values alters the event triggering pattern. The bounding case, which separates regions of (generally) quite different dynamic behaviour, is referred to as grazing. At a grazing point, the system trajectory makes tangential contact with an event triggering hypersurface. The paper formulates conditions governing grazing points. Both transient and periodic behaviour are considered. The resulting boundary value problems are solved using shooting methods that are applicable for general nonlinear hybrid (piecewise smooth) dynamical systems. The grazing point formulation underlies the development of a continuation process for exploring parametric dependence. It also provides the basis for an optimization technique that finds the smallest parameter change necessary to induce grazing. Examples are drawn from power electronics, power systems and robotics, all of which involve intrinsic interactions between continuous dynamics and discrete events. 1
Stability of limit cycles in hybrid systems
 In: Proc. of the 34th Hawaii International Conf. on System Sciences
, 2001
"... Limit cycles are common in hybrid systems. However the nonsmooth dynamics of such systems makes stability analysis difficult. This paper uses recent extensions of trajectory sensitivity analysis to obtain the characteristic multipliers of nonsmooth limit cycles. The stability of a limit cycle is det ..."
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Cited by 11 (1 self)
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Limit cycles are common in hybrid systems. However the nonsmooth dynamics of such systems makes stability analysis difficult. This paper uses recent extensions of trajectory sensitivity analysis to obtain the characteristic multipliers of nonsmooth limit cycles. The stability of a limit cycle is determined by its characteristic multipliers. The concepts are illustrated using a coupled tank system with on/offvalve switching.
Stability analysis of the continuousconductionmode buck converter via Filippov’s method
 IEEE Transactions on Circuits and Systems–I: Regular Papers
, 2008
"... Abstract—To study the stability of a nominal cyclic steady state in power electronic converters, it is necessary to obtain a linearization around the periodic orbit. In many past studies, this was achieved by explicitly deriving the Poincaré map that describes the evolution of the state from one cl ..."
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Cited by 11 (4 self)
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Abstract—To study the stability of a nominal cyclic steady state in power electronic converters, it is necessary to obtain a linearization around the periodic orbit. In many past studies, this was achieved by explicitly deriving the Poincaré map that describes the evolution of the state from one clock instant to the next and then locally linearizing the map at the fixed point. However, in many converters, the map cannot be derived in closed form, and therefore this approach cannot directly be applied. Alternatively, the orbital stability can be worked out by studying the evolution of perturbations about a nominal periodic orbit, and some studies along this line have also been reported. In this paper, we show that Filippov’s method—which has commonly been applied to mechanical switching systems—can be used fruitfully in power electronic circuits to achieve the same end by describing the behavior of the system during the switchings. By combining this and the Floquet theory, it is possible to describe the stability of power electronic converters. We demonstrate the method using the example of a voltagemodecontrolled buck converter operating in continuous conduction mode. We find that the stability of a converter is strongly dependent upon the socalled saltation matrix—the state transition matrix relating the state just after the switching to that just before. We show that the Filippov approach, especially the structure of the saltation matrix, offers some additional insights on issues related to the stability of the orbit, like the recent observation that coupling with spurious signals coming from the environment causes intermittent subharmonic windows. Based on this approach, we also propose a new controller that can significantly extend the parameter range for nominal period1 operation. Index Terms—Bifurcation, buck converter, differential inclusions, discontinuous systems, Filippov systems, power electronics. I.
Sensitivity, approximation and uncertainty in power system dynamic simulation
 IEEE TRANSACTIONS ON POWER SYSTEMS, SUBMITTED
, 2006
"... Parameters of power system models, in particular load models, are seldom known exactly. Yet dynamic security assessment relies upon simulation of those uncertain models. This paper proposes a computationally feasible approach to assessing the influence of uncertainty in simulations of power system d ..."
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Cited by 10 (4 self)
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Parameters of power system models, in particular load models, are seldom known exactly. Yet dynamic security assessment relies upon simulation of those uncertain models. This paper proposes a computationally feasible approach to assessing the influence of uncertainty in simulations of power system dynamic behaviour. It is shown that trajectory sensitivities can be used to generate accurate firstorder approximations of trajectories that arise from perturbed parameter sets. The computational cost of obtaining the sensitivities and perturbed trajectories is minimal. The mathematical structure of the trajectory approximations allows the effects of uncertainty to be quantified and visualized using worstcase analysis and probabilistic approaches.
Dynamic securityconstrained rescheduling of power systems using trajectory sensitivities
 IEEE Trans. Power System
"... Abstract—In the deregulated environment of power systems, the transmission networks are often operated close to their maximum capacity to achieve transfer of power. Besides, the operators must operate the system to satisfy its dynamic stability constraints under credible contingencies. This paper pr ..."
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Cited by 8 (1 self)
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Abstract—In the deregulated environment of power systems, the transmission networks are often operated close to their maximum capacity to achieve transfer of power. Besides, the operators must operate the system to satisfy its dynamic stability constraints under credible contingencies. This paper provides a method using trajectory sensitivity to reschedule power generation to ensure system stability for a set of credible contingencies while satisfying its economic goal. System modeling issue is not a limiting concern in this method, and hence the technique can be used as a preventive control scheme for system operators in real time. Index Terms—Optimal power flow, trajectory sensitivity, generation rescheduling, preventive control, dynamic security. I.
Voltage Stability Enhancement via Model Predictive Control of Load
 Proceedings of the Symposium on Bulk Power System Dynamics and Control VI, Cortina d’Ampezzo
, 2004
"... Abstract — Impending voltage collapse can often be avoided by appropriate control of loads. However the traditional form of load control (shedding) is unpopular due to the resulting consumer disruption. Advances in communications and computer systems allow more selective load control though. Individ ..."
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Cited by 8 (1 self)
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Abstract — Impending voltage collapse can often be avoided by appropriate control of loads. However the traditional form of load control (shedding) is unpopular due to the resulting consumer disruption. Advances in communications and computer systems allow more selective load control though. Individual loads that are sacrificeable in the shortterm can be switched with minimal consumer disruption. The paper considers the use of such nondisruptive load control for improving voltage stability. A control strategy that is based on model predictive control (MPC) is proposed. MPC utilizes an internal model to predict system dynamic behaviour over a finite horizon. Control decisions are based on optimizing that predicted response. MPC is a discretetime form of control, so inaccuracies in predicted behaviour are corrected at the next control interval. A standard 10 bus voltage collapse example is used to illustrate this control strategy.
Dynamic performance assessment: Grazing and related phenomena
 IEEE Transactions on Power Systems
, 2005
"... Abstract—Performance specifications place restrictions on the dynamic response of many systems, including power systems. Quantitative assessment of performance requires knowledge of the bounding conditions under which specifications are only just satisfied. In many cases, this limiting behavior can ..."
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Cited by 7 (4 self)
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Abstract—Performance specifications place restrictions on the dynamic response of many systems, including power systems. Quantitative assessment of performance requires knowledge of the bounding conditions under which specifications are only just satisfied. In many cases, this limiting behavior can be related to grazing phenomena, where the system trajectory makes tangential contact with a performance constraint. Other limiting behavior can be related to timedriven event triggering. In all cases, pivotal limiting conditions can be formulated as boundary value problems. Numerical shooting methods provide efficient solution of such problems. Dynamic performance assessment is illustrated in the paper using examples drawn from protection operation, transient voltage overshoot, and induction motor stalling. Index Terms—Boundary value problems, dynamic performance assessment, grazing phenomena, nonlinear nonsmooth system dynamics, shooting methods. I.