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23
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
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.
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.
Predicting voltage instability of power system via hybrid system reachability analysis
 in Proceedings of the American Control Conference
, 2007
"... Abstract — Estimating voltage instability of power systems is important for reduction of large blackouts. This paper proposes to use reachability analysis of hybrid systems for predicting voltage instability of a power system. The reachability analysis is performed by computing backward reachable se ..."
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Cited by 4 (2 self)
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Abstract — Estimating voltage instability of power systems is important for reduction of large blackouts. This paper proposes to use reachability analysis of hybrid systems for predicting voltage instability of a power system. The reachability analysis is performed by computing backward reachable sets for unsafe sets of hybrid automata. The automata represent continuous voltage dynamics and discrete operations by relay devices. The unsafe sets of hybrid automata are also subsets of state space in which a system voltage shows unacceptable levels such as low or high values. With single machineload bus (SMLB) system with controlled route switching, we show that voltage instability in the SMLB system can be predicted using the reachability analysis. The obtained result implies that voltage instability leading to large blackouts is possibly detected before its occurrence in power systems. I.
Limitinduced stable limit cycles in power systems
 In Proceedings of the IEEE Saint Petesburg PowerTech
, 2005
"... Abstract — Heavily loaded power systems are susceptible to Hopf bifurcations, and consequent oscillatory instability. The onset of instability can be predicted by small disturbance (eigenvalue) analysis, but the ensuring behaviour may depend strongly on nonlinearities within the system. In particula ..."
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Cited by 2 (0 self)
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Abstract — Heavily loaded power systems are susceptible to Hopf bifurcations, and consequent oscillatory instability. The onset of instability can be predicted by small disturbance (eigenvalue) analysis, but the ensuring behaviour may depend strongly on nonlinearities within the system. In particular, physical limits place bounds on the divergent behaviour of states. This paper explores the situation where generator fieldvoltage limits capture behaviour, giving rise to a stable (though nonsmooth) limit cycle. It is shown that shooting methods can be adapted to solve for such nonsmooth limitinduced limit cycles. By continuing branches of limitinduced and smooth limit cycles, the paper established the coexistence of equilibria, smooth and nonsmooth limit cycles. Furthermore, it is shown that when branches of limitinduced and smooth limit cycles merge, the limit cycles are annihilated at a grazing bifurcation. Index Terms — Limit cycles, piecewise smooth dynamics, hybrid systems, shooting methods, Hopf bifurcations, continuation methods. I.
2003] “Timedelay modelling for multilayer power systems
 in Proceedings of the IEEE International Symposium on Circuits and Systems
"... Modelling of multilayer power system interactions will become increasingly important as market mechanisms and feedback controls become more tightly coupled into the physical system layer. Timedelays are an important aspect of that interlayer coupling. This paper integrates deterministic, nonli ..."
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Modelling of multilayer power system interactions will become increasingly important as market mechanisms and feedback controls become more tightly coupled into the physical system layer. Timedelays are an important aspect of that interlayer coupling. This paper integrates deterministic, nonlinear timedelays into a systematic hybrid (continuous/discrete) system model. The paper addresses issues arising in the implementation of implicit numerical integration techniques, and computation of trajectory sensitivities. Applications that have the form of inverse problems are motivated. 1.
Analysis of the State Estimation Performance in Transient Conditions
"... Abstract—An accurate and reliable performance of a state estimation under all network conditions is crucial for the monitoring of power systems and thus their secure operation. State estimation is based on a static representation of the power system, although the most critical operation conditions ..."
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Abstract—An accurate and reliable performance of a state estimation under all network conditions is crucial for the monitoring of power systems and thus their secure operation. State estimation is based on a static representation of the power system, although the most critical operation conditions occur when power system is in dynamic transition from one state to another. We propose how the performance of a state estimator can be monitored, evaluated during dynamic conditions and which factors affect it most. Based on that, we propose a method, which can be used to guide upgrading of a state estimation infrastructure to improve the state estimator performance during dynamic conditions. We demonstrate our suggestions on a test system. Index Terms—Measurements, power system dynamics, power system monitoring, power system planning, state estimation, trajectory sensitivities. I.
Modeling and Control of Discrete Event Systems Using Finite State Machines with Variables and Their Applications in Power Grids
"... Control theories for discrete event systems modeled as finite state machines have been well developed to address various fundamental control issues. However, finite state machine model has long suffered from the problem of state explosion that renders it unsuitable for some practical applications. I ..."
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Control theories for discrete event systems modeled as finite state machines have been well developed to address various fundamental control issues. However, finite state machine model has long suffered from the problem of state explosion that renders it unsuitable for some practical applications. In an attempt to mitigate the state explosion problem, we propose an efficient representation that appends finite sets of variables to finite state machines in modeling discrete event systems. We also present the control synthesis techniques for such finite state machines with variables (FSMwV). We first present our notion and means of control under this representation. We next present our algorithms for both offline and online synthesis of safety control policies. We then apply these results to the control of electric power grids.
Safety Control of PHEVs in Distribution Networks Using Finite State Machines with Variables
"... Abstract—Transportation electrification is viewed as one of the most viable ways of reducing CO2 emissions and gasoline dependency. However, how to manage the dramatically increasing Plugin Hybrid Electric Vehicles (PHEVs) and Electric Vehicles (EVs) for the safety of distribution networks is still ..."
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Abstract—Transportation electrification is viewed as one of the most viable ways of reducing CO2 emissions and gasoline dependency. However, how to manage the dramatically increasing Plugin Hybrid Electric Vehicles (PHEVs) and Electric Vehicles (EVs) for the safety of distribution networks is still a vital challenge. To mitigate the influence of PHEVs, we propose that a distribute network be modeled by a Finite State Machine with Variables (FSMwV) method and then controlled by a corresponding safety controller. The calculation results of four scenarios verify the effectiveness of managing PHEVs by the FSMwV method. To manage a distribution network within a wider area, a supervisory control approach is proposed to cooperate with smart distribution network technologies. Therefore, the distribution network could be effectively managed with the safety controller on the bottom layer and supervisory control on the upper layer. Index Terms—Discrete event systems, finite state machines, PHEV, supervisory control, smart distribution networks. P I.