Voltage stability of radial power links

Abstract

SynopsisThe general phenomenon of voltage collapse or instability at the load end of transmission links is introduced with reference to previous work, and the induction motor is seen to be the critical constituent of system loads. The power/voltage and reactive-power/voltage characteristics of power-system loads are predicted and accurately represented by polynomial expressions which are used in the analysis of radial transmission links fed from infinite busbars. Graphs summarising the critical load voltages and the corresponding short-circuit levels for various transformer tap ratios are given and are general in application; these are based on the dV\dZ criterion for voltage stability. It is shown that, although tap changing to raise the load voltage increases the critical length of the link, it also reduces the margin between normal operating voltage and the voltage at the onset of instability. The effects of the injection of reactive power by static capacitors are discussed, together with the effect of the induction-motor content of the loads. The use of the dEJdV r criterion as advocated in the Russian literature is discussed.List of symbols E s = voltage at supply infinite busbar I sc = short-circuit current at load (3-phase symmetrical) N = off-nominal tap ratio P -power Q = reactive power 5 = apparent power s -slip V r = voltage at receiving end Z = impedance = Z ^/d S 12 = angle between phasors V x and V 2 6 = tan" 1 {XIR) a = 90 -0 OJ S = synchronous speed r refers to receiving end s refers to sending end IntroductionThe various papers which have previously discussed the process of voltage instability suggest that it can take more than one form. A process called voltage instability is discussed by Birch, 1 in which the instability, although caused by an insufficiency of reactive power at a load busbar, is synchronous in nature. In another report, 2 a voltage 'avalanche' process is described in a system during a period of light load in summer, when generating plant was at a minimum and short-circuit levels were low. A lack of reactive power caused a lowering of voltage, which resulted in load tap-changing transformers reducing transformation ratios, thus increasing further the line-voltage drops. As this process continued around the system, eventually voltage collapse was experienced.. This process was essentially nonsynchronous in form and occurred over a relatively long period of time. In a further description, 3 the process is not synchronous and depends upon the characteristics of the asynchronous load.The main factor in all these accounts is the inability of the network to meet a demand for reactive power, the actual process of instability being triggered by some form of disturbance resulting in changes in the reactive-power situation. Also, the local generation with respect to the load is relatively remote electrically, and the voltage changes do not create an adequate response from the generators. Owing to the slow nature of the voltage collapse (except as described in Reference 1), the process may...

CNN based power system transient stability margin and voltage stability index prediction

“…There are various methods of determining voltage stability load index (VSLI) in literature. Singularity of the Jacobian of power flow equations have been used as a test for onset of voltage collapse [9], [22].…”

Real Time System Operations 2006-2007

“…The first paper related to voltage instability apparently appeared in 1968 [32], [40]. Since then, numerous approaches for voltage stability assessment have been suggested.…”

Voltage security enhancement using energy based sensitivities

“…The time to reach the collapse point then used to rank the vulnerability of different system configurations to voltage collapse. Numerous authors have recognized that the Jacobian of the powefflow becomes singular at the point of voltage collapse [5], [8], [9], using this as the indicator that the collapse point has been reached. In [9] and [ 101 the smallest singular value of the Jacobian is proposed as a qualitative measure of proximity to voltage collapse.…”

“…However, voltage instability problems have been shown to occur in systems where voltage magnitudes never decline below acceptable levels [4]. Furthermore, near the point of collapse voltage variations can be extremely sensitive to changes in load [5], so knowledge of the voltage level only at the current operating point may not be sufficient to predict the onset of stability problems. The need to expand the optimal power flow problem to include voltage security is recognized in [3] and [6].…”