Static bifurcations in electric power networks: Loss of steady-state stability and voltage collapse

Kwatny, Harry G.; Pasrija, A.; Bahar, Leon Y.

doi:10.1109/tcs.1986.1085856

Cited by 247 publications

(82 citation statements)

References 25 publications

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“…This allows us to introduce a set of new variables (relative angles) and reduce the number of differential equations in the first subsystem in (3) by one [3].…”

Section: Daes As Models Of Power Systemsmentioning

confidence: 99%

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Singular Hopf Bifurcations in DAE Models of Power Systems

Marszałek¹,

Trzaska²

2011

EPE

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We investigate an important relationship that exists between the Hopf bifurcation in the singularly perturbed nonlinear power systems and the singularity induced bifurcations (SIBs) in the corresponding differenttial-algebraic equations (DAEs). In a generic case, the SIB phenomenon in a system of DAEs signals Hopf bifurcation in the singularly perturbed systems of ODEs. The analysis is based on the linear matrix pencil theory and polynomials with parameter dependent coefficients. A few numerical examples are included.

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“…This allows us to introduce a set of new variables (relative angles) and reduce the number of differential equations in the first subsystem in (3) by one [3].…”

Section: Daes As Models Of Power Systemsmentioning

confidence: 99%

“…In an effort to better understand dynamical properties of power systems, their stability features and the impact of various parameters, the DAEs approach seems to be very important as was shown in a number of recent papers (see for example [1][2][3][4][5][6][7][8][9][10]). …”

Section: Introductionmentioning

confidence: 99%

Singular Hopf Bifurcations in DAE Models of Power Systems

Marszałek¹,

Trzaska²

2011

EPE

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“…2(b) and (c), any transition cannot be defined in the present formalism. This shows a loss of causality [25], [26] of the DAE (2) and possibly indicates a modeling breakdown. 1 Here, to use the above modeling, it is 1 It has been unclear whether the lose of model causality directly implies the system instability or not.…”

Section: B Modeling Of Transition Relationmentioning

confidence: 99%

Predicting Voltage Instability of Power System via Hybrid System Reachability Analysis

Susuki¹,

Hikihara²

2007

2007 American Control Conference

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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 machine-load 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.

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“…Throughout the past most of the work that was conducted would have linked the voltage collapse to a static bifurcation done by Kwatny et al [2], Schlutere et al [3], and Thomas and Tiranunchit [4]. While, the dynamic bifurcation was linked by Abed and Varaiya [5], Abed et al [6], Rajagopalan et al [7], Dobson et al [8], and Nayfeh et al [9].…”

Section: Introductionmentioning

confidence: 99%

Control of Instable Chaotic Small Power System

Shariff¹,

Harb²

2015

JPEE

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In this paper, we aim to control an instable chaotic oscillation in power system that is considered to be small system by using a linear state feedback controller. First we will analyze the stability of the mentioned power system by means of modern nonlinear theory (Bifurcation and Chaos). Our model is based on a three bus power system that consists of multi generators containing both dynamic and static loads. They are considered to be in the form of an induction motor in parallel with a capacitor, as well as a combination of constant power along with load impedance, PQ. We consider the load reactive power as the control parameter. At this stage, after changing the control parameter, the study showed that the system is experiencing a subcritical Hopf bifurcation point. This leads to a chaos within the system period doubling path. We then discuss the system controllability and present that the all chaotic oscillations fade away through the linear controller that we impose on the system.

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Static bifurcations in electric power networks: Loss of steady-state stability and voltage collapse

Cited by 247 publications

References 25 publications

Singular Hopf Bifurcations in DAE Models of Power Systems

Singular Hopf Bifurcations in DAE Models of Power Systems

Predicting Voltage Instability of Power System via Hybrid System Reachability Analysis

Control of Instable Chaotic Small Power System

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