Bifurcation analysis of a three node power system with detailed models

Rajesh, Kasala; Padiyar, К.R.

doi:10.1016/s0142-0615(99)00002-2

Cited by 63 publications

(38 citation statements)

References 4 publications

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“…For detailed meanings of variables and parameters see [21]. We System (22) has been also studied by several studies, such as [2], [6], [14], [21], [25]. They have linked voltage collapse to saddle-node bifurcation, and have numerically shown that Hopf bifurcation, cyclic-fold, and periodic-doubling bifurcations, and chaotic dynamics does occur in the power system (22) by using the numerical bifurcation software package.…”

Section: Application To a 3-bus Power Systemmentioning

confidence: 99%

“…In this section, we give the amplitude, frequency and stability of limit cycle near the Hopf bifurcation for the model (22) by using the method and criterion described in Section II. And the new analytic formulas for bifurcation curves of the model (22) are presented by the analytic method. Some new saddle-node bifurcation with the new method at low voltages are found.…”

Section: Application To a 3-bus Power Systemmentioning

confidence: 99%

“…1) The Case of a Constant Power Load: First, we consider the case of a constant power load, i.e., q 2 = q 3 = 0, in (22). We use the reactive power Q 1 of the bus load, with q 1 being equal to unity, as a control parameter, and fix all of the system parameters.…”

Section: A Equilibrium Solutions and Their Bifurcationmentioning

confidence: 99%

“…Letting q1 = q3 = 0 in system (22), denoting q2Q1 Q2 as the control parameter and fixing all of the system parameter, we calculate the equilibrium point curve and their bifurcation for the four cases as same as the constant power PQ load. The resulting bifurcation diagram and the bifurcation points for the bifurcation curves are shown in Fig.…”

Section: A Equilibrium Solutions and Their Bifurcationmentioning

confidence: 99%

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Computation of limit cycle via higher order harmonic balance approximation and its application to a 3-bus power system

Jing

Wang

Chen

2002

IEEE Trans. Circuits Syst. I

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This brief reviews and elaborates a frequency domain approximate method of estimating amplitude, frequency, and stability of the limit cycle near Hopf bifurcations. A new iterative method and new criterion for ascertaining stability are presented. The method and criterion are applied to a 3-bus dynamic power system model to give the amplitude, frequency and stability at its Hopf bifurcations. New analytic formulas for bifurcation curves are derived by using analytic method, some new saddle-node bifurcation at low voltage levels are found on the formulas. The influence of rotor inertia on the Hopf bifurcation is also studied.Index Terms-Amplitude and frequency of limit cycle, higher order harmonic balance, Hopf bifurcation, saddle-node bifurcation, stability.

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Section: Application To a 3-bus Power Systemmentioning

confidence: 99%

Section: Application To a 3-bus Power Systemmentioning

confidence: 99%

Section: A Equilibrium Solutions and Their Bifurcationmentioning

confidence: 99%

Section: A Equilibrium Solutions and Their Bifurcationmentioning

confidence: 99%

See 2 more Smart Citations

Computation of limit cycle via higher order harmonic balance approximation and its application to a 3-bus power system

Jing

Wang

Chen

2002

IEEE Trans. Circuits Syst. I

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“…Kartvelishvili and Andronov applied static bifurcation theory to a three-bus system and proved the existence of static bifurcation [6]. Venikov and Tamura's research shows that when the load is increased to a certain level, the Jacobi matrix will become singular, which is the typical saddle-node bifurcation (SNB) [7,8]. Based on the Center Manifold theory, I.Dobson and H.D.Chiang interpreted the theory of SNB's tendency to lead to voltage collapse [9].…”

Section: Introductionmentioning

confidence: 99%

Research on Voltage Stability of Photovoltaic PCC Based on the Hopf Bifurcation Theory

Li¹,

Tengyu²,

Teng

et al. 2015

2015 Sixth International Conference on Intelligent Systems Design and Engineering Applications (ISDEA)

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Due to the large number of distributed generation and nonlinear components in the Photovoltaic (PV) System, Voltage condition at the point of common coupling (PCC) faces severe challenges. Evaluation of the PCC voltage stability has become critical to the steady operation of the PV system. PV system is a typical nonlinear nonautonomous system, and bifurcation theory, as one the effective ways to solve the nonlinear dynamic system, was adopted to conduct a research on voltage stability or collapse on the PCC. In the paper, a PV system equivalent circuit model was proposed. In order to find the main parameters that contribute most to the voltage instability on the PCC, a mathematical analysis was conducted based on the equivalent circuit. Then, with irradiance intensity chosen as the bifurcation parameter, the Hopf bifurcation simulation was conducted. A MATLAB m-file was developed to study the voltage stability analysis. A MATCONT bifurcation software has been used to conduct the bifurcation analysis.

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Sliding mode control with mismatched disturbance observer for chaotic oscillation in a seven‐dimensional power system model

Wang

Liu

2020

Int Trans Electr Energ Syst

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In this article, a sliding mode control scheme with mismatched disturbance observer to achieve chaos control in power system is presented. A novel design method of mismatched disturbance observer is proposed for a second‐order system with mismatched disturbance, it is proved that the designed observer can theoretically observe disturbances with arbitrary accuracy by adjusting the parameters of disturbance observer artificially, and the designed controller realizes uniformly ultimately bounded asymptotic system stability. The designed disturbance observer and controller exhibit two main features. The first is the form of the observer is simpler than the existing observer. The other is the designed observer and controller do not contain system functions, which makes them can be applied to the control of complex systems. Furthermore, the proposed control scheme is adopted to design mismatched disturbance observers and controllers for suppressing chaotic oscillation in a seven‐dimensional power system model and simulation results are presented to demonstrate its validity.

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Bifurcation analysis of a three node power system with detailed models

Cited by 63 publications

References 4 publications

Computation of limit cycle via higher order harmonic balance approximation and its application to a 3-bus power system

Computation of limit cycle via higher order harmonic balance approximation and its application to a 3-bus power system

Research on Voltage Stability of Photovoltaic PCC Based on the Hopf Bifurcation Theory

Sliding mode control with mismatched disturbance observer for chaotic oscillation in a seven‐dimensional power system model

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