89 WM 170-2. November 1989. Wheeling Rates Based on Marginal-Cost Theory. Hyde M. Merrill, Senior Member, IEEE and. Bruce W. Erickson, Member, IEEE.
recent discussions in the PES Dynamic Security Assessment Working Group. The new contingency measures eliminate all branch contributions where (a) the apparent power flow Skl is not larger than a fixed percentage (100 a) of the thermal limit for the branch, (b) the branch contribution to the contingency measure is not the ratio of the branch flow to the thermal limit raised to some power (Sk/IRk,)m but rather 1, (c) the branch contribution may be (SklIRkl - y)- where 'y c ct eliminated by setting the branch weight (Wk,) to zero. The four contingency measures tested in this paper are now reviewed. The Type 1 contingency measure is similar to those previously developed in [1-51 and exhibit the flaws described above. The Type 11 contingency measure is zero for all noncritical contingencies, has no misclassification or false alarm problems, and ranks contingencies based on their largest thermal limit violation. It should be used when operating conditions are known exactly. The Type Ill contingency measure has very small or zero contingency measure for noncritical contingencies, has no perceptible misclassification or false alarm problems, and appears to rank contingencies by their worst thermal limit violation. Contingencies that are not critical and are not close to being critical given a particular operating condition have zero Type Ill contingency measure value but noncritical contingencies that are close to being critical have a small contingency measure less than one. Critical contingencies have a contingency measure above a prespecified threshold. The Type Ill contingency measure is very useful for selecting contingencies where the precise operating conditions are unknown. A Type IV contingency measure sets branch weights to zero on all branches that do not experience thermal overloads for a set of contingencies. The Type IV contingency measure is useful in selecting single contingencies that when taken in combination could produce critical multiple contingencies. A production grade computer package has been developed that can compute any of these four contingency measures. The line outage contingencies to be ranked in this production grade package developed in this research are first evaluated using a matrix compensation method in a Multiple Contingency Load Flow program. The contingency measures for each contingency are then computed and ranked in a BOUNSM program. Some additional computation is required to compute the load flow solution using matrix compensation methods and then compute the contingency measure rather than computing the contingency measure directly using matrix compensation methods. However, the capabilities of having zero false alarms and misclassifications, ranking contingencies based on the product of their probability of occurrence and their maximum branch thermal limit violation, and the ability to identify subsets of contingencies that would produce critical multiple contingencies far outweighs the small additional computation required. Discussers: J. A. Momoh and A. Chuko
89 WM 187-6 November 1989
Transient Stability Hierarchical Control in Multimachine Power Systems Ahmed Rubaai, Student Member, IEEE and F. Eugenio Villaseca, Member, IEEE Electrical Engineering Department Cleveland State University This study addresses the optimal transient stability control problem a hierarchical structure for multiple machine power systems. The two-level control structure results from the decomposition of the overall problem into parallel subproblems. This allows the retention of the local closed-loop controls associated with each subsystem, which together constitute level 1. The central coordinating controller forms level 2. The coordination of the local feedback controls by the central controller, accounts for nonlinearities and interconnections, and yields the global optimization of the system transient performance. The steam input powers to the turbines are used as the system control variables. The transient phenomenon is initiated by a three-phase fault on the system. The initial conditions at the time of fault removal are assumed known. The equilibrium condition for the post-fault configuration is assumed to be determined by any of the computational techniques proposed in the literature. The performance measures of each subsystem in level 1 has a quadratic form, and includes three terms. The first one penalizes the deviation of each of the subsystem states from their post fault equilibrium conditions. The second weighs the control effort, and the third penalizes the error between the level 2 predicted state and the corresponding level 1 trajectories actual state trajectories. The proposed technique was tested on a 4-machine 1 0-bus system appearing in the literature, for fault clearing times greater than the critical, assuring unstable conditions. The well damped optimal state and control trajectories illustrate the successful solution of the problem. Testing of this technique on utility size systems is currently under consideration. This effort is not expected to pose any problems given that the prototype program is modular. That is, the modifications required to handle the systems of different sizes and characteristics can easily be implemented without need to reformulate the entire procedure. Discusser: J. G. Sverak in
References [1] R. Fischl, T. Halpin and A. Guvenis, "The Application of Decision Theory to Contingency Selection," CAS 29, No. 11, November 1982, pp. 712-723. [2] G. C. Ejebe and B. F. Wollenberg, "Automatic Contingency Selection," IEEE Trans PAS, Vol. 98, No. 1, January/February 1979, pp. 97-109. [31 G. Irisarri and D. Levner, "Automatic Contingency Selection for On-Line Security Analysis-Real-Time Tests," IEEE Trans PAS, Vol. 100, No. 2, February 1981, pp. 608-617. [41 T. A. Mikolinnas and B. F. Wollenberg, "An Advanced Contingency Selection Algorithm," IEEE Trans PAS, Vol. 100, No. 2, February 1981, pp. 608-617. [51 G. D. Irisari and A. M. Sasson, "An Automatic Contingency Selection Method for On-Line Security Analysis," IEEE Trans PAS, Vol. 100, No. 4, April 1981, pp. 1838-1844. [61 L. Fink, "Security: It's Meaning and Objectives," NSF Workshop on Power System Security Assessment," Ames, Iowa, April 2729, 1988.
89 WM 170-2 November 1989
Wheeling Rates Based
on
Marginal-Cost Theory
Hyde M. Merrill, Senior Member, IEEE and Bruce W. Erickson, Member, IEEE Power Technologies, Inc. Schenectady, NY Knowledge of marginal cost of wheeling electric power is vital in the debate on how wheeling should be priced. This paper presents the first extensive computations of marginal costs of wheeling, and of rates based on these marginal costs. Sensitivities to losses, constraints, load levels, amount of power wheeled, revenue reconciliation, etc., are examined in the context of two case studies. Marginal Cost Theory The short-run marginal costs of wheeling are the incremental costs of the last MWh of energy wheeled. Since wheeling is physically
IEEE Power
Engineering Review,
November 1989 IEEE Power Engineering Review, November 1989
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