On the Formulation of Power Distribution Factors for Linear Load Flow ...

respectively, to zero). Although the masking is not completely eliminated, its effects are reduced. In summary, the new ranking algorithms does remarkably well and is superior to the old algorithm. The ranking agrees almost perfectly with the ranking produced by calculating PI from de load flows; the correla¬ tion between overloads and high rank is also quite good, the only difficulty being masking. The effects of masking can be greatly reduced through partitioning followed by multiple rankings. for transformers and circuits,

February 1981,

p. 745

Stability Enhancement by 120-Degree Phase Rotation

Transient

R. L. Cresap, C. W. Taylor, and M. J. Kreipe Bonneville Power Administration, Portland, Oregon

Transient stability enhancement by 120-degree phase rotation is de¬ scribed. The concept is to disconnect two generators or two groups of generators when loss of synchronism is imminent (large rotor angle dif¬ ference due to a fault or other disturbance). The systems are then reclosed with 120-degree phase rotation. Stability can be improved be¬ cause fast valving, excitation control, or governor control is allowed more time to become effective. The technique is analyzed for radial connection of a fossil-fired steam-turbine unit connected to a large system via long EHV lines and for two large systems with a relatively weak interconnection. For the radial system, the effect of the switching on transient shaft torques and on transient overvoltages is investigated. Also, comparison with alternate stability enhancement methods are made. Phase rotation for stability enhancement (or as augmentation of other stability controls) may be attractive in various applications.

-1 LINE WITH -

120° PHASE

Deceleration of the rotor begins after the advancing angle causes the electrical output to exceed the mechanical input. Because acceleration energy exceeds deceleration energy, the generator will lose synchronism or go out-of-step with the large system. Commonly, out-of-step detec¬ tion is used to insure opening of the circuit breaker prior to reaching an angle of about 120-degrees. This is to prevent excessively high circuit breaker recovery voltages. Without additional means of control, the plant would be lost. How¬ ever, by providing an additional switch or circuit breaker with a rotated phase connection, the possibility of a successful reclosure exists. To minimize the acceleration which occurs while the generator is isolated from the system, reclosure would be timed to occur at about dD. By allowing time for fast valving to become effective, a large amount of deceleration energy becomes available. Also, note that the rotated con¬ nection power-angle curve is higher. This is due to voltage regulator boosting which would occur during the fault and subsequent swing (ef¬ fect idealized on Figure 1). Because the net deceleration energy is larger than the acceleration energy, the reclosure with rotation would be successful. Fast valving may not always be necessary. In marginal cases (par¬ ticularly with a nonreheat turbine), the phase rotation switching could maintain stability by allowing more time for the normal governor con¬ trol and the excitation control to be effective. For extremely severe faults and very fast swings, fast valving with phase rotation may not maintain stability. It would be theoretically possible to rotate phases a second time (total of 240-degrees) to allow sufficient time for fast valving to be effective. Compared with other discrete stability enhancement measures, phase rotation has the advantage that no control action is taken unless insta¬ bility is actually imminent. Future developments in switchgear may in¬ crease the attractiveness of the phase rotation technique.

February 1981,

On the Formulation of Power Distribution Factors for Linear Load Flow Methods P. W.

ROTATION

Sauer, Member IEEE

Department of Electrical Engineering and The Coordinated Science Laboratory, University of Illinois

Pm WITHOUT

FAST VALVING

Urbana-Champaign, Urbana,

at

'

p. 764

Pm WITH

Illinois 61801

Abstract

FAST VALVING

Fast linear load flows used in contingency analysis, interchange studies and many optimization schemes often utilize power distribu¬ tion factors. The success of many of these methods has hinged greatly on the use of the Z matrix reference to swing or an arbitrary ground tie. This paper furnishes a mathematical basis for these heuristic methods. ANGLE-DEGREES

Current Distribution Factors with Constant Swing Bus

Voltage power system with one or more ground Figure 1. Equal area diagram for one machine infinite bus system with impedance ties to ground (reactive shunts, line charging etc.). For a phase ro ta tion. A t angle Ô A three-phase fault. A t angle b B -clear faulted giflen schedule of constant power bus loads and swing bus #j, a base line. At angle 8c.open remaining line due to out-of-step condition. At case A solution satisfies angle 5D. reelose with 120-degree phase rotation. At angle 5E.equal Consider

area

criteria met.

bus plus

Vi* v2A

be explained by equal area analysis. Consider re¬ generation with fast valving serving a large system over a pair of long lines. Suppose a slow-clearing three-phase fault occurs on one of the lines close to the sending end. Referring to the equal area diagram of Figure 1, the faulted line is cleared at 8B. During the fault

The concept

an n

Z\\ Z\2

¿2\ ^2 2

¿2n

'2

¿¦nn

'

can

mote steam-turbine

I

n

A

and

S¡A V¡A If

(2) 1,2, where Z¡¡ is the ijxh entry of the bus impedance matrix reference to ground, V,A is the /th bus voltage referenced to ground in the base case,

the rotor accelerates because of the imbalance between the mechanical and electrical torques. A small amount of additional acceleration occurs immediately following clearing because the electrical output with one line removed is initially less than the mechanical imput.

=

26

and l,A is the /th bus total injection current entering bus / through a branch not included in Z As a minimum these include the swing or slack bus (constant voltage) and load bus (constant power) currents The solution (1) is the result of an iterative scheme Additional base case quantities such as line currents or line power flows can be com pu ted from the case A voltage vector as, / A 'ii

vA

vA