Trajectory sensitivity analysis of hybrid systems

Hiskens, Ian A.; Pai, M.A.

doi:10.1109/81.828574

Cited by 421 publications

(317 citation statements)

References 27 publications

(52 reference statements)

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“…Specifically, the sensitivity of the system dynamic response to the changes of each parameter will be evaluated [13]. For complex load models such as the CMPLDW, it is difficult to develop their mathematical state-space representations to evaluate the trajectory sensitivity [4].…”

Section: Background and Objectivementioning

confidence: 99%

Parameter Sensitivity and Dependency Analysis for the WECC Dynamic Composite Load Model

Zhang

Guo

Zhu

2017

Proceedings of the 50th Hawaii International Conference on System Sciences (2017)

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An accurate dynamic load model plays a crucial role in the analysis of power system transient stability. The WECC dynamic composite load model (CMPLDW) has been developed recently to better represent faultinduced delayed-voltage-recovery (FIDVR) events, which are of increasing concern to electric utilities. To facilitate the understanding of the CMPLDW, it is worth studying the effect of parameters that describe the model structure on its dynamic response. In this paper, we show that 1) some parameters have very minimal sensitivities under certain FIDVR events; 2) sensitivities of certain parameters are strongly dependent on the temporal profile of given fault, such as its minimum fault voltage or recovery time; and 3) some parameters share similar sensitivity patterns and thus the change of their values may complement each other. These observations are essential for further developing enhanced measurement-based dynamic load modeling approaches by tackling the parameter identifiability issues pointed out in the present work.

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Section: Background and Objectivementioning

confidence: 99%

Parameter Sensitivity and Dependency Analysis for the WECC Dynamic Composite Load Model

Zhang

Guo

Zhu

2017

Proceedings of the 50th Hawaii International Conference on System Sciences (2017)

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“…Thus, it has two special inherent properties: stability and low energy consumption [2][3][4][5][6][7]. However, these special properties lead to high sensitivity of the gait stability to the inner structural parameters and external disturbances; any tiny change in parameters will cause an obvious change in the gait [8,9].…”

mentioning

confidence: 99%

Analysis of period doubling bifurcation and chaos mirror of biped passive dynamic robot gait

Zhao

Zang

et al. 2012

Chin. Sci. Bull.

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With a reasonable parameter configuration, the passive dynamic walking model has a stable, efficient, natural periodic gait, which depends only on gravity and inertia when walking down a slight slope. In fact, there is a delicate balance in the energy conversion in the stable periodic gait, making the gait adjustable by changing the model parameters. Poincaré mapping is combined with Newton-Raphson iteration to obtain the numerical solution of the final state of the passive dynamic walking model. In addition, a simulation on the walking gait of the model is performed by increasing the slope step by step, thereby fixing the model's parameters synchronously. Then, the gait features obtained in the different slope stages are analyzed and discussed, the intrinsic laws are revealed in depth. The results indicate that the gait can present features of a single period, doubling period, the entrance of chaos, merging of sub-bands, and so on, because of the high sensitivity of the passive dynamic walking to the slope. From a global viewpoint, the gait becomes chaotic by way of period doubling bifurcation, with a self-similar Feigenbaum fractal structure in the process. At the entrance of chaos, the gait sequence comprises a Cantor set, and during the chaotic stage, sub-bands in the final-state diagram of the robot system present as a mirror of the period doubling bifurcation. period doubling bifurcation, chaos, fractals, passive dynamic walking, final-state diagram, Feigenbaum constant Citation:Zhao J, Wu X G, Zang X Z, et al. Analysis of period doubling bifurcation and chaos mirror of biped passive dynamic robot gait.

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“…However the computational burden is minimal when an implicit numerical integration technique such as trapezoidal integration is used to generate the trajectory. Further details can be found in [12,13,14].…”

Section: Trajectory Sensitivitiesmentioning

confidence: 99%

“…It is shown in [12] that at an event i → j, occurring at time τ , the trajectory sensitivities Φ generically jump according to…”

Section: Trajectory Sensitivitiesmentioning

confidence: 99%

Dynamic Embedded Optimization and Shooting Methods for Power System Performance Assessment

Hiskens

Park

Donde

Power Electronics and Power Systems

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Power system dynamic performance enhancement can often be formulated as a dynamic embedded optimization problem. The associated cost function quantifies performance and involves dynamically evolving state variables. The dynamic model is embedded within the constraints. Power systems form an important example of hybrid systems, with interactions between continuous dynamics and discrete events playing a fundamental role in behavior. However, it is shown that for a large class of problems, the cost function is smooth even though the underlying dynamic response is non-smooth. Complementing this design-oriented optimization framework, techniques for assessing power system performance and vulnerability can often be expressed as boundary value problems, and solved using shooting methods. It is shown that performance limitations are closely related to grazing phenomena. Techniques are presented for determining parameter values that induce limit cycles and grazing.179 I.A. Hiskens, J-W. Park and V. Donde, "Dynamic embedded optimization and shooting methods for power system performance assessment", in Applied Mathematics for Deregulated

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Trajectory sensitivity analysis of hybrid systems

Cited by 421 publications

References 27 publications

Parameter Sensitivity and Dependency Analysis for the WECC Dynamic Composite Load Model

Parameter Sensitivity and Dependency Analysis for the WECC Dynamic Composite Load Model

Analysis of period doubling bifurcation and chaos mirror of biped passive dynamic robot gait

Dynamic Embedded Optimization and Shooting Methods for Power System Performance Assessment

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