Hsiao-dong Chiang
Cornell University, Electrical and Computer Engineering, Faculty Member
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This authoritative treatment covers theory, optimal estimation and a range of practical applications. The first book on the subject, and written by leading researchers, this clear and rigorous work presents a comprehensive theory for both... more
This authoritative treatment covers theory, optimal estimation and a range of practical applications. The first book on the subject, and written by leading researchers, this clear and rigorous work presents a comprehensive theory for both the stability boundary and the stability regions of a range of nonlinear dynamical systems including continuous, discrete, complex, two-time-scale and non-hyperbolic systems, illustrated with numerical examples. The authors also propose new concepts of quasi-stability region and of relevant stability regions and their complete characterisations. Optimal schemes for estimating stability regions of general nonlinear dynamical systems are also covered, and finally the authors describe and explain how the theory is applied in applications including direct methods for power system transient stability analysis, nonlinear optimisation for finding a set of high-quality optimal solutions, stabilisation of nonlinear systems, ecosystem dynamics, and immunisation problems.
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This paper presents analytical results on local optimal solutions; in particular, it establishes a close relationship between a local optimal power flow solution and a Type-one unstable equilibrium manifold (UEM) of the associated... more
This paper presents analytical results on local optimal solutions; in particular, it establishes a close relationship between a local optimal power flow solution and a Type-one unstable equilibrium manifold (UEM) of the associated nonlinear dynamical system. This paper also shows three possible situations where a Type-one UEM can link with two nearby stable equilibrium manifolds. If the Type-one UEM links with two nearby regular stable equilibrium manifolds (i.e., two feasible components), then there is a one-to-one correspondence between the constraint violations at the Type-one UEM and the constraint boundary points of one local optimal power flow solution located in one of the two feasible components. In addition, constraints violated by a Type-one UEM can be used to comprehensively explain why the feasible region is divided into multiple feasible components.
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In this paper, a new method is proposed for the optimal allocation of Phasor Measurement Units (PMUs) in power system state estimation. They play an important role to provide more accurate measurements with state estimation. This paper... more
In this paper, a new method is proposed for the optimal allocation of Phasor Measurement Units (PMUs) in power system state estimation. They play an important role to provide more accurate measurements with state estimation. This paper focuses on the improvement of the estimates accuracy with them. In practice, it is of main concern how to optimize the allocation for a set of power system conditions. The proposed method makes use of Evolutionary Particle Swarm Optimization (EPSO) to determine the optimal allocation of PMUs. In practice, the optimal allocation is dependent upon the power system conditions. To overcome the problem, this paper introduces Monte Carlo Simulation (MCS) in consideration of the nodal correlation. Specifically, Moment Matching Method is used to evaluate the optimal allocation efficiently. The effectiveness of the proposed method is demonstrated in the IEEE 30-node power system.
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The subject of optimal power flow (OPF) convexity has attracted great interest in the research community. In this brief, it will be shown that a new type of bifurcation can occur in OPF model to alter the convexity property; in... more
The subject of optimal power flow (OPF) convexity has attracted great interest in the research community. In this brief, it will be shown that a new type of bifurcation can occur in OPF model to alter the convexity property; in particular, a pseudo-bifurcation of OPF feasible region non-convexity can occur when some upper or lower bounds of the inequality constraints are tightened or relaxed. Hence, caution must be taken to state whether a feasible region of an AC OPF model is convex/non-convex without specifying the set of inequality constraints. Numerical studies on several IEEE test systems are conducted to illustrate the impact of this type of pseudo-bifurcation on the feasible region. The applicability of a class of convex relaxation methods is examined via the convex/non-convex feasible region. A guideline derived from our numerical studies is provided to give conditions under which the convex relaxation method is applicable.
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This chapter contains sections titled: Introduction Stability Boundary of Network-Reduction Models Network-Preserving Model One Dynamic Property of the Controlling UEP Concluding Remarks
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This paper presents a simulation method that can assess the impact of energy storage system(ESS) on the unit commitment(UC) problem with volatile wind power.In order to achieve the higher system flexibility and reduce the impact of... more
This paper presents a simulation method that can assess the impact of energy storage system(ESS) on the unit commitment(UC) problem with volatile wind power.In order to achieve the higher system flexibility and reduce the impact of volatility of wind power,ESS is incorporated into the UC problem with wind power.The UC problem with wind power and ESS is formulated as the mixed-integer convex program,which is optimized by branch and bound combined with interior point method.During the branch and bound process,best first search and depth first search are combined to expedite the computation.Numerical simulations on a ten-unit system show that the introduction of ESS is effective to reduce the impact of volatility of wind power on the UC problem.
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A new uniform methodology to study the fast subsystem stability of general two-time scale nonlinear systems is developed. It consists of a direct method that provides estimates of the stability region of the fast subsystem that are... more
A new uniform methodology to study the fast subsystem stability of general two-time scale nonlinear systems is developed. It consists of a direct method that provides estimates of the stability region of the fast subsystem that are uniform with respect to the slow variables, which are treated as uncertainties. The methodology is illustrated on small power systems leading to much improved results in estimating the stability region, critical clearing times as compared to traditional methods. As a by-product, it gives the required theoretical support to justify and to correct the heuristic approaches used in power system stability analysis literature.
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Several recent major power system blackouts are characterised by a progressive decline in voltage magnitude at the system buses. These events are termed 'voltage collapses'. The mechanisms of voltage collapse are not... more
Several recent major power system blackouts are characterised by a progressive decline in voltage magnitude at the system buses. These events are termed 'voltage collapses'. The mechanisms of voltage collapse are not well defined and the dynamics of the process are not well ...
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The literature dealing with bifurcation and chaos in electric power systems is surveyed. A brief discussion of relevant mathematical concepts and results is included in order to make the presentation self-contained and readily accessible.... more
The literature dealing with bifurcation and chaos in electric power systems is surveyed. A brief discussion of relevant mathematical concepts and results is included in order to make the presentation self-contained and readily accessible. The objective is to determine the extent and significance of power system behavior that can be understood by dynamic models exhibiting bifurcation and chaotic motion. Bifurcation denotes a qualitative change in system behavior. The study is divided into three parts dealing with static bifurcations, Hopf bifurcations, and chaos. Static bifurcation occurs when two or more equilibrium points coincide. Hopf bifurcation occurs when a periodic oscillation emerges from a stable equilibrium. These are both examples of local bifurcation - they are determined by the system behavior in a neighborhood of the equilibrium. Chaos emerges from a global bifurcation - a non-local change in the phase portrait of tile system. The following conclusions are reached. Even the simplest models of power systems exhibit both local and global bifurcations. Local bifurcations occur because power flow equations have multiple solutions. In models that only incorporate real power flow, the capacity of transmission systems is so large that local bifurcations although present are unlikely to be practically significant. However, in modelsmore » where voltage is determined by reactive power flows, local bifurcations can dramatically shrink the stability region. These bifurcations may explain ``voltage collapse``. The simplest models also exhibit chaotic behavior. However, for analytical convenience, chaos has mostly been investigated in systems with unrealistic parameter values.« less
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Research Interests: Mechanical Engineering, Mathematics, Applied Mathematics, Computer Science, Stability, and 10 moreTrajectory, Nonlinear Systems, Dynamical Systems Theory, Nonlinear system, Nonlinear Dynamical Systems, Numerical Stability, Asymptotic Stability, Electrical And Electronic Engineering, Equilibrium point, and equilibrium points
... Ian Dobson, Hsiao-Dong Chiang, James S. Thorp, Lazhar Fekih-Ahmed School of Electrical Engineering Cornell University Ithaca, NY, 14853 ... Dobson and Chiang [l] suggested that voltage collapse be identified with the system dynamics... more
... Ian Dobson, Hsiao-Dong Chiang, James S. Thorp, Lazhar Fekih-Ahmed School of Electrical Engineering Cornell University Ithaca, NY, 14853 ... Dobson and Chiang [l] suggested that voltage collapse be identified with the system dynamics at a saddle-node bifurca-tion of a ...
Research Interests: Engineering, Power Systems, Power System, Stability, Differential Equations, and 12 moreElectric Power Systems, Trajectory, Reactive Power, Bifurcation, Electric Power System, Voltage, Induction Motor, Catastrophe Theory, Power System Modeling, Load Flow, Voltage Collapse, and Saddle-node bifurcation
A comprehensive theory for the stability boundaries and the stability regions of a general class of nonlinear discrete dynamical systems is developed in this article. This general class of systems is modeled by diffeomorphisms and admits... more
A comprehensive theory for the stability boundaries and the stability regions of a general class of nonlinear discrete dynamical systems is developed in this article. This general class of systems is modeled by diffeomorphisms and admits as limit sets only fixed points and periodic orbits. Topological and dynamical characterizations of stability boundaries are developed. Necessary and sufficient conditions for fixed points and periodic orbits to lie on the stability boundary are derived. Numerical examples, including applications to associative neural networks illustrating the theoretical developments, are presented.
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ABSTRACT This paper presents the foundations of the controlling unstable equilibrium point (CUEP) theory for stability assessment of two-time-scale power system models. A conceptual two-time-scale algorithm to calculate the CUEP is... more
ABSTRACT This paper presents the foundations of the controlling unstable equilibrium point (CUEP) theory for stability assessment of two-time-scale power system models. A conceptual two-time-scale algorithm to calculate the CUEP is provided. Taking into account the time scale features of power systems in the CUEP theory has several advantages from both a numerical and analytical point of view. Numerically, the two-time scale algorithm to calculate the CUEP is faster and more robust when compared to the traditional BCU algorithm. Analytically, we gain more insight into power system dynamics and obtain less conservative estimates of stability region and critical clearing time.
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Abstract -Considerable progress has been made in recent years in the application of direct methods to power system transient stability analysis. The methods are derived largely based on heuristics and simulations. In this paper, a... more
Abstract -Considerable progress has been made in recent years in the application of direct methods to power system transient stability analysis. The methods are derived largely based on heuristics and simulations. In this paper, a theoretical foundation for the direct methods is ...
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Nonlinear dynamical systems exhibiting complex structure in their limit sets, such as chaotic and closed orbits, do not admit energy functions. The theory of generalized energy functions, which may assume positive derivative in some... more
Nonlinear dynamical systems exhibiting complex structure in their limit sets, such as chaotic and closed orbits, do not admit energy functions. The theory of generalized energy functions, which may assume positive derivative in some bounded sets, appears as an alternative to study the asymptotic behavior of solutions of these systems. In this article, a generalized energy function and a complete characterization of the stability boundary and stability region are developed for a class of third-order dynamical systems. This class of systems appears in electrical power system models and has a class of quasi-gradient systems and second-order systems as particular cases. These systems may admit complex structure in their limit sets and do not admit an energy function that is general for the class. Numerical examples illustrate how generalized energy functions provide estimates of stability regions.
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With the increasing penetration of renewable generation, the problem of transient stability has changed and new unstable scenarios have emerged. Consequently, the foundations of direct methods for stability assessment must be revisited.... more
With the increasing penetration of renewable generation, the problem of transient stability has changed and new unstable scenarios have emerged. Consequently, the foundations of direct methods for stability assessment must be revisited. Unstable modes triggered by disconnection of renewable generators are commonly related to violation of operating limits and not to the problem of synchronism among synchronous generators. In this paper, the concept of constrained stability region is used to study transient stability of a power system with a wind generator subject to the low-voltage ride-through (LVRT) curve constraint. The constrained stability region is studied by means of an associated auxiliary system that has its unconstrained stability region equal to the constrained stability region of the original system.
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The knowledge of the steady-state security region is essential for secure operation of the integrated energy system (IES). The two-time-scale feature of the IES is explored to facilitate construction of its exact steady-state security... more
The knowledge of the steady-state security region is essential for secure operation of the integrated energy system (IES). The two-time-scale feature of the IES is explored to facilitate construction of its exact steady-state security region. Conditions allowing decomposition of the IES into fast and slow subsystems are established. A complete characterization of the IES steady-state security region via the stable equilibrium manifold of the fast subsystem and the slow subsystem is derived and theoretically proven. This characterization can significantly facilitate construction of the IES steady-state security region (SSR) and is derived under the AC power flow model and gas flow model without any model approximation and simplification. Numerical studies are conducted to validate the derived characterization of the SSR and to illustrate the advantages of the proposed characterization in terms of robustness and reduced computational burden. Numerical studies show that exploring the fast and slow subsystems can lead to fast computation of feasible solutions with a 20-fold speed up in calculation time, as compared with the direct integration of the original IES system. Hence, the proposed two-time-scale method appears to be fast and yet accurate.
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Research Interests: Electrical Engineering, Mathematics, Power System, Power Transmission, Reactive Power, and 12 moreBifurcation, Oscillations, Electric Power System, Phase Space, Power Factor, Differential equation, Power flow, Bifurcation diagram, Hopf Bifurcation, Equilibrium point, Saddle-node bifurcation, and Period-doubling bifurcation
Abstract --In this paper we provide a theoretical foundation for the Potential Energy Boundq Surface (PEBS) method for power system transient stability analysis. First, we present a theory of stability boundaries for two classes of... more
Abstract --In this paper we provide a theoretical foundation for the Potential Energy Boundq Surface (PEBS) method for power system transient stability analysis. First, we present a theory of stability boundaries for two classes of dynamical systems: generalized gradient systems and ...
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ABSTRACT This paper presents the foundations of controlling unstable equilibrium point (CUEP) theory for stability assessment of two-time-scale power system models. A conceptual two-time-scale CUEP method is developed. The two-time scale... more
ABSTRACT This paper presents the foundations of controlling unstable equilibrium point (CUEP) theory for stability assessment of two-time-scale power system models. A conceptual two-time-scale CUEP method is developed. The two-time scale CUEP method is faster and more robust as compared to the traditional CUEP method. Furthermore, more insight into power system dynamics and less conservative estimates of the stability region and critical clearing time are obtained.