Estimating the domain of attraction for power systems via a group of damping-reflected energy functions

Moon, Young-Hyun; Choi, Byoung-Kon; Roh, Tae Hoon

doi:10.1016/s0005-1098(99)00162-4

Cited by 31 publications

(22 citation statements)

References 7 publications

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“…As pointed out before, it is possible to prove that • there does not exist a scalar function such that satisfies the integrability conditions imposed by Poincare's Lemma (17). Hence, the construction proposed in Section V-B is not feasible.…”

Section: -Machine Casementioning

confidence: 97%

“…The well-known robustness problems, both against parameter uncertainties and unmodeled dynamics, of these nonlinearity cancellation schemes has motivated the more recent works on passivity-based techniques [19], [33]. Most results along these lines are based on the application of damping injection (also called ) controllers (see [7], [14], and [17].) See also [20] for an alternative passivation approach.…”

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confidence: 99%

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Transient stabilization of multimachine power systems with nontrivial transfer conductances

Ortega

Galaz

Astolfi

et al. 2005

IEEE Trans. Automat. Contr.

182

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Abstract-In this paper, we provide a solution to the long-standing problem of transient stabilization of multimachine power systems with nonnegligible transfer conductances.More specifically, we consider the full 3 -dimensional model of the -generator system with lossy transmission lines and loads and prove the existence of a nonlinear static state feedback law for the generator excitation field that ensures asymptotic stability of the operating point with a well-defined estimate of the domain of attraction provided by a bona fide Lyapunov function. To design the control law we apply the recently introduced interconnection and damping assignment passivity-based control methodology that endows the closed-loop system with a port-controlled Hamiltonian structure with desired total energy function. The latter consists of terms akin to kinetic and potential energies, thus has a clear physical interpretation. Our derivations underscore the deleterious effects of resistive elements which, as is well known, hamper the assignment of simple "gradient" energy functions and compel us to include nonstandard cross terms. A key step in the construction is the modification of the energy transfer between the electrical and the mechanical parts of the system which is obtained via the introduction of state-modulated interconnections that play the role of multipliers in classical passivity theory.

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Section: -Machine Casementioning

confidence: 97%

mentioning

confidence: 99%

Transient stabilization of multimachine power systems with nontrivial transfer conductances

Ortega

Galaz

Astolfi

et al. 2005

IEEE Trans. Automat. Contr.

182

View full text Add to dashboard Cite

show abstract

“…Moreover, high order equivalent circuits do not assure better modelling of the machine because the determination of circuit parameters is a formidable task even for small two-axis circuits. Recent developments in energy-shaping control designs and rigorous stability analyses of PSS schemes of synchronous generators are being performed using low-order two-axis equivalent circuits [7][8][9][10][11]. The actual performance of these control schemes along with their tuning guidelines are also applied and investigated using low-order two-axis models, wherein addition to the simplifications already mentioned, effects such as changes in generator speed and stator transformer emfs are assumed to be small.…”

Section: Testing Of the Energy-shaping Pss Schemementioning

confidence: 99%

“…To overcome this problem, Lyapunov-based methodologies has been explored in recent years. For three-or four-order flux decay models, energy-like Lyapunov functions have been reported [7][8][9][10]. The idea is to inject damping to the synchronous generator by decreasing the (negative) time-derivative of the Lyapunov function.…”

Section: Introductionmentioning

confidence: 99%

Performance evaluation of energy‐shaping approach controllers for synchronous generators using a finite‐element model

Escarela‐Perez

Espinosa-Pérez

Álvarez‐Ramírez

2004

Intl J Robust & Nonlinear

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SUMMARYUsually, power system stabilizer (PSS) design is usually made using low-order two-axis models. Remarkable robust characteristics and systematic construction can be obtained with the recent developments on energy-shaping approaches to the design of excitation control. However, the properties and performance of the resulting control designs are also evaluated using low-order equivalent-circuit models because large (i.e. industrial scale) synchronous machines are not readily available to designers and researches. This may lead to doubts about the controller behaviour under true operating conditions. The aim of this paper is to develop a finite-element model, derived from fundamental Maxwell equations, to simulate the dynamics of synchronous generators. Subsequently, the finite-element model is used to show that energy-shaping control designs, obtained with low-order models, keep their performance characteristics when applied to the actual machine. In this way, in order to circumvent the lack of the real machine, a very detailed finite-element model is developed to represent turbine generators connected to large power systems. The numerical model incorporates simulation of rotor motion, iron magnetic nonlinearity and eddy currents in the solid rotors of turbine generators.

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“…The use of energy function for control application has been given in [8]. The work based on damping injection controllers, also known as L g V controllers, is found in [9], [10], [11], [12]. In [13], [14] a dynamic damping injection controller is presented.…”

Section: Introductionmentioning

confidence: 99%

Nonlinear control synthesis for asymptotic stabilization of the swing equation using a controllable series capacitor via Immersion and Invariance

Manjarekar

Banavar

Ortega

2008

2008 47th IEEE Conference on Decision and Control

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A nonlinear control law is proposed to asymptotically stabilize a single machine infinite bus (SMIB) system based on Immersion and Invariance (I&I) control strategy. The actuator used is a controllable series capacitor (CSC). The SMIB system is described using the nonlinear second order swing equation model, and the CSC is modeled using a first order system. The control objective here is to approximate the complete third order system with a second order dynamics, for which we have an asymptotically stabilizing control law.

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Estimating the domain of attraction for power systems via a group of damping-reflected energy functions

Cited by 31 publications

References 7 publications

Transient stabilization of multimachine power systems with nontrivial transfer conductances

Transient stabilization of multimachine power systems with nontrivial transfer conductances

Performance evaluation of energy‐shaping approach controllers for synchronous generators using a finite‐element model

Nonlinear control synthesis for asymptotic stabilization of the swing equation using a controllable series capacitor via Immersion and Invariance

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