Stabilizing Control in Emergencies Part 2. Control by Local Feedback

These nonlinear algebraic equations implicitly define a tranformation from the Conventional State Space of z into the Observation Decoupled State Space of w. This space will indeed be Observation Decoupled since xj, £ j, + ¡ and xj, + j for the connected (Cy^n) neighboring buses can all be measured or estimated within the local bus i. It's validity as a state space can also be rigorously proven. Substitution of the coordinates of the system wide equilibrium Xe¡ into (4), (5), as well as the use of the fact X0¡, + e¡, +oi, Xj Xq/, +¡ of topoiogical equivalence between the spaces of z and of w makes it clear that the origin of the Observation Decoupled State Space is an equilibrium point of the system. It still requires considerable mathematical apparatus to show that it it also the unique stable equilibrium point of the =

=

=

$0j

power system [43. A companion paper [1] utilizies these results for stabilizing control.

one

approach

to

not be considered nearly stable enough for opera¬ tion now. Really major savings in investment in EHV and HVDC line con¬ struction would then result after being partially offset by the cost of the control equipment. Another paper [7] analyzes all the rigorous mathematical aspects of this proposed operation. Case History Involving Emergency Control by Local Feedback in

systems which would

the Observation

Decoupled State Space [1]

Modified IEEE test System System: Emergency: 3-Phase short circuit on line 17-38 near bus 17. Line 17-38 and 300 MW of load at bus 17 lost at clearing. A segment (area 1) separating from the system. The Outcome: The Control: Local Feedback control in the Observation Decoupled State Space. The Tools: Braking resistor capacity of the generator at the bus Load Skipping Angles are generator rotor phases Number on curves identify buses [9] The The

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[.] Reference numbers from full papers. This research was supported by the Department of Energy under contract numbers DE-AC01-79-ET-29367 and ET-78-D-01-3090 and in part by the National Science Foundation under Grant #INT 76-17175.

May 1981, p. 2381

Stabilizing Control in Emergencies Part 2. Control by Local Feedback John Zaborszky, Krishna Prasad, and Keh-Wen Whang Department of Systems Science and Mathematics, Washington University, St. Louis, Missouri 63130 New methods are introduced for the stabilization of the power system during violent swings after major disturbances. These techniques utilize existing or attainable measurements, computer facilities, and devices such as short rating resistors, capacitors, or fast valving. Stabilizing ac¬ tion is based on a new Observation Decoupled State Space which is in¬ troduced in a companion paper [1]. Components of this state space associated with individual buses can be computed locally from local con¬ ventional measurements. The origin is always the stable system equilibrium-the target of the control. In this paper methods are introduc¬ ed to track this target by purely local feedback control. No telemetering is involved in either the state estimation or the control. Stability of the con¬ trol in a global domain is proven. Excellent performance is demonstrated by simulation of on a 118 bus system with a consistent, up to ten-fold, in¬ crease in the critical clearing times. Two modifications were made on the original IEEE 118 bus system [9] used in these experiments: 1. Buses connected by just a transformer or a very short line were con¬ solidated as an approximation since very short lines tend to distort the in¬ terpretation of the Observation Decoupled state vector. 2. The impedances of certain lines were increased to make this system (which is its original form is extremely stable) susceptible to stability crises. The systems created by the modifications are so vulnerable stability wise that they could not possibly be operated in today's state of art. In¬ troducing the proposed emergency control would make it possible to operate the system without strengthening it, thus causing major savings. Shown in Figures 1-2 is a case history which involves the islanding and ultimate breakup of one segment (area 1) of the modified system, but which is very smoothly and successfully handled by the proposed control. Figures 1 and 2 show a more than ten-fold increase in the critical clearing time. The system is violently unstable at only 3 cycles fault duration without stabilizing control. This shows that this system would not be fit to be operated in existing state of art, but it could function reliably using the proposed emergency control. Thus the proposed control would make it feasible to safely operate

PER MAY 1981

TIME

(SECONDS)

Fig.

1. 3 cycles fault duration. No control action except for Selective Protection. System islanding with one segment (area 1) separating.

TIHE

Fig. 2. 30 cycles fault duration. control.

(SECONDS)

Islanding prevented by the proposed

[¦] Reference numbers from full paper. This research was supported by the Department of Energy under contract numbers DE-AC01-79-ET-29367 and ET-78-D-01-3090 and in part by the National Science Foundation under Grant #INT 76-17175.

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