The number of (equilibrium) steady-state solutions of models of power systems

1994 ◽  
Vol 41 (9) ◽  
pp. 584-600 ◽  
Author(s):  
S.X. Guo ◽  
F.M.A. Salam
Keyword(s):  
Steady State ◽  
Power Systems ◽  
Steady State Solutions

scholarly journals The Geometry of Power Systems Steady-State Equations– Part II: a Power Surface Study

2020 ◽  
pp. 47-53
Author(s):  
B. Ayuev ◽  
V. Davydov ◽  
P. Erokhin ◽  
V. Neuymin ◽  
A. Pazderin
Keyword(s):  
Steady State ◽  
Power Systems ◽  
Transmission Loss ◽  
Normal Vector ◽  
State Equations ◽  
Marginal State ◽  
Normal Vectors ◽  
System States ◽  
Steady State Solutions ◽  
System Power

Steady-state equations play an essential part in the theory of power systems and the practice of computations. These equations are directly or mediately used almost in all areas of the theory of power system states, constituting its basis. This two-part study deals with a geometrical interpretation of steady-state solutions in a power space. Part I has proposed considering the power system's steady states in terms of power surface. Part II is devoted to an analytical study of the power surface through its normal vectors. An interrelationship between the entries of the normal vector is obtained through incremental transmission loss coefficients. Analysis of the normal vector has revealed that in marginal states, its entry of the slack bus active power equals zero, and the incremental transmission loss coefficient of the slack bus equals one. Therefore, any attempts of the slack bus to maintain the system power balance in the marginal state are fully compensated by associated losses. In real-world power systems, a change in the slack bus location in the marginal state makes this steady state non-marginal. Only in the lossless power systems, the marginal states do not depend on a slack bus location.

scholarly journals The Geometry of Power Systems Steady-State Equations– Part I: Power Surface

2020 ◽  
pp. 37-46
Author(s):  
B. Ayuev ◽  
V. Davydov ◽  
P. Erokhin ◽  
V. Neuymin ◽  
A. Pazderin
Keyword(s):  
Steady State ◽  
Power Systems ◽  
Power System ◽  
Power Flow ◽  
Analytical Study ◽  
State Theory ◽  
Steady States ◽  
State Equations ◽  
Feasibility Region ◽  
Steady State Solutions

Steady-state equations play a fundamental role in the theory of power systems and computation practice. These equations are directly or mediately used almost in all areas of the power system state theory, constituting its basis. This two-part study deals with a geometrical interpretation of steady-state solutions in a power space. Part I considers steady states of the power system as a surface in the power space. A power flow feasibility region is shown to be widely used in power system theories. This region is a projection of this surface along the axis of a slack bus active power onto a subspace of other buses power. The findings have revealed that the obtained power flow feasibility regions, as well as marginal states of the power system, depend on a slack bus location. Part II is devoted to an analytical study of the power surface of power system steady states.

scholarly journals Series Compensation of Transmission Systems: A Literature Survey

Energies ◽  
2021 ◽  
Vol 14 (6) ◽  
pp. 1717
Author(s):  
Camilo Andrés Ordóñez ◽  
Antonio Gómez-Expósito ◽  
José María Maza-Ortega
Keyword(s):  
Steady State ◽  
Power Systems ◽  
Power System ◽  
Case Studies ◽  
Electronic Devices ◽  
Literature Survey ◽  
Power Electronic ◽  
Transmission Systems ◽  
Series Compensation ◽  
Near Future

This paper reviews the basics of series compensation in transmission systems through a literature survey. The benefits that this technology brings to enhance the steady state and dynamic operation of power systems are analyzed. The review outlines the evolution of the series compensation technologies, from mechanically operated switches to line- and self-commutated power electronic devices, covering control issues, different applications, practical realizations, and case studies. Finally, the paper closes with the major challenges that this technology will face in the near future to achieve a fully decarbonized power system.

Explicit steady state solutions for a particularM(x)/M/1 queueing system

1977 ◽  
Vol 24 (4) ◽  
pp. 651-659 ◽  
Author(s):  
George L. Jensen ◽  
Albert S. Paulson ◽  
Pasquale Sullo
Keyword(s):  
Steady State ◽  
Queueing System ◽  
Steady State Solutions

Nonlinear Vibrations of Viscoelastic Plane Truss Under Harmonic Excitation

2014 ◽  
Vol 14 (04) ◽  
pp. 1450009 ◽  
Author(s):  
Andrew Yee Tak Leung ◽  
Hong Xiang Yang ◽  
Ping Zhu
Keyword(s):  
Steady State ◽  
Fractional Derivatives ◽  
Harmonic Excitation ◽  
Homotopy Continuation ◽  
Response Curves ◽  
System A ◽  
Structural Responses ◽  
Voigt Model ◽  
Two Degree Of Freedom ◽  
Steady State Solutions

This paper is concerned with the steady state bifurcations of a harmonically excited two-member plane truss system. A two-degree-of-freedom Duffing system having nonlinear fractional derivatives is derived to govern the dynamic behaviors of the truss system. Viscoelastic properties are described by the fractional Kelvin–Voigt model based on the Caputo definition. The combined method of harmonic balance and polynomial homotopy continuation is adopted to obtain steady state solutions analytically. A parametric study is conducted with the help of amplitude-response curves. Despite its seeming simplicity, the mechanical system exhibits a wide variety of structural responses. The primary and sub-harmonic resonances and chaos are found in specific regions of system parameters. The dynamic snap-through phenomena are observed when the forcing amplitude exceeds some critical values. Moreover, it has been shown that, suppression of undesirable responses can be achieved via changing of viscosity of the system.

An airfoil theory of bifurcating laminar separation from thin obstacles

1990 ◽  
Vol 216 ◽  
pp. 255-284 ◽  
Author(s):  
C. J. Lee ◽  
H. K. Cheng
Keyword(s):  
Boundary Layer ◽  
Reynolds Number ◽  
Steady State ◽  
Steady State Solution ◽  
Equation System ◽  
Branch Points ◽  
Laminar Separation ◽  
Kutta Condition ◽  
Numerical Studies ◽  
Steady State Solutions

Global interaction of the boundary layer separating from an obstacle with resulting open/closed wakes is studied for a thin airfoil in a steady flow. Replacing the Kutta condition of the classical theory is the breakaway criterion of the laminar triple-deck interaction (Sychev 1972; Smith 1977), which, together with the assumption of a uniform wake/eddy pressure, leads to a nonlinear equation system for the breakaway location and wake shape. The solutions depend on a Reynolds numberReand an airfoil thickness ratio or incidence τ and, in the domain$Re^{\frac{1}{16}}\tau = O(1)$considered, the separation locations are found to be far removed from the classical Brillouin–Villat point for the breakaway from a smooth shape. Bifurcations of the steady-state solution are found among examples of symmetrical and asymmetrical flows, allowing open and closed wakes, as well as symmetry breaking in an otherwise symmetrical flow. Accordingly, the influence of thickness and incidence, as well as Reynolds number is critical in the vicinity of branch points and cut-off points where steady-state solutions can/must change branches/types. The study suggests a correspondence of this bifurcation feature with the lift hysteresis and other aerodynamic anomalies observed from wind-tunnel and numerical studies in subcritical and high-subcriticalReflows.

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