The problem of system collapse or blackout characterized by a local severe voltage depression is generally believed to be associated with inadequate VAR support at key busses. The authors discuss techniques for improving the system security with respect to this index. The effect of adding capacitors are examined. They also present a continuation technique that redistributes the system generation to the optimal operating condition with respect to the minimum singular value index. >

A posturing strategy against voltage instabilities in electric power systems

The relationship is presented between a detailed power system dynamic model and a standard load-flow model. The linearized dynamic model is examined to show how the load-flow Jacobian appears in the system dynamic-state Jacobian for evaluating steady-state stability. Two special cases are given for the situation when singularity of the load-flow Jacobian implies singularity of the system dynamic-state Jacobian. The standard load-flow Jacobian can provide information about the existence of a steady-state equilibrium point for a specified level of loading or interchange. There are two very special cases when the determinant of the standard load-flow Jacobian implies something about the steady-state stability of a dynamic model. Both of these cases involve very drastic assumptions about the synchronous machines and their control systems. The load level which produces a singular load-flow Jacobian should be considered an optimistic upper bound on maximum loadability. >

Power system steady-state stability and the load-flow Jacobian

This paper presents an analysis of static stability in electric power systems. The study is based on a model consisting of the classical swing equation characterization for generators and constant admittance, PV bus and/or PQ bus load representations which, in general, leads to a semi-explicit (or constrained) system of differential equations. A precise definition of static stability is given and basic concepts of static bifurcation theory are used to show that this definition does include conventional notions of steady-state stability and voltage collapse, but it provides a basis for rigorous analysis. Static bifurcations of the load flow equations are analyzed using the Liapunov-Schmidt reduction and Taylor series expansion of the resulting reduced bifurcation equation. These procedures have been implemented using symbolic computation (in MASYMA). It is shown that static bifurcations of the load flow equations are associated with either divergence-type instability or loss of causality. Causality issues are found to be an important factor in understanding voltage collapse and play a central role in organizing global power system dynamics when loads other than constant admittance are present.

http://www.pages.drexel.edu/~hgk22/papers/Kwatny%20Pasrija%20Bahar%20IEEE%20TCS%2086.pdf

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

It is shown that when the characteristic of the composite load of a typical utility system is taken into account, large disturbance voltage stability is assured by the existence of the stable equilibrium state of the post-disturbance system, as determined from the standard power flow model. When the load contains static components, stability limits extend considerably. The exact limit for such loads can also be determined from a power flow model, properly modified to reflect the static component of the load. In specific situations, where the bulk of the load is composed of fast response loads, a correct assessment of voltage stability would require comprehensive analyses, employing detailed dynamic models of all system components. The use of the conventional power flow model may lead to considerable error. >

Voltage stability conditions considering load characteristics

This paper provides a comprehensive list of books, reports, workshops and technical papers related to voltage stability and security

Bibliography on voltage stability

Power system voltage stability is characterized as being capable of maintaining load voltage magnitudes within specified operating limits under steady state conditions. In this paper, the first order delay model of a load admittance change is introduced. Then, using this model, a set of linearized dynamic equations is derived and stability conditions are obtained. An earlier result in the literature is shown to agree with that in this paper. The stability conditions are tested and verified in a 2-load, 2- power source system and a 13-node, 4-power source system.

/pdf/power-system-voltage-stability-2q1j6wvg2l.pdf

Power System Voltage Stability

A field control apparatus for a generator having a field winding comprises a terminal voltage control unit for controlling a field current of the generator in accordance with a difference between a terminal voltage signal of the generator and a reference voltage signal, which control unit has at least one of a line drop compensation function, an under-excitation limitation function, an over-excitation limitation function, a power factor regulation function, an armature winding over-current compensation function and a cross-current compensation function. The field control apparatus includes a detector as a common signal source for detecting active power and reactive power components at an output terminal of the generator and means responsive to the output of the detector for performing scalar operation in accordance with a function of the added compensation/control function described above. An output of the operating means is added to the differential signal as an added function signal to control the field current for excitation of the field winding.

Excitation control apparatus for a generator

Because load flow problems are expressed as sets of nonlinear simultaneous equations, they have no unique solutions. In this paper a region where a set of initial values converges to a stable load flow solution under specified conditions, is investigated theoretically when the Newton-Raphson method is applied to a set of nodal power equations expressed in either polar or rectangular coordinates. The results are tested in load flow calculations on a 28-node power system and the convergence characteristics for the two types of coordinates are compared.

/pdf/load-flow-convergence-in-the-vicinity-of-a-voltage-stability-27trus57hk.pdf

Load Flow Convergence in the Vicinity of a Voltage Stability Limit

In a control system for a hydroelectric power station system including upper and lower water reservoirs connected through a water channel, an intermediate water reservoir having a smaller storage capacity than those of the upper and lower reservoirs and provided on the water channel in cascade with the upper and lower reservoirs, and two power stations disposed between the upper and intermediate reservoirs and between the intermediate and lower reservoirs, respectively, the control system is arranged such that the water level of the intermediate reservoir is detected continuously and the detected value of the water level is used to correct the load instructions which are applied to the power stations for controlling outputs of the power stations whereby the water level of the intermediate reservoir is maintained substantially constant, while the power generation of the power stations is controlled so as to satisfactorily meet with the load instruction applied to the power system.

Akira Isono

Papers

Power System Voltage Stability

Excitation control apparatus for a generator

Load Flow Convergence in the Vicinity of a Voltage Stability Limit

Control system for hydroelectric power station system

Determination of power system voltage stability. Part I: Theory