84 WM 071-7 August 1984, pp. 2199-2206 84 WM 051-9 August 1984, pp. 2207-2214 Critical Energy for Direct Transient Stability Assessment of a Multimachine Power System A. A. Fouad, Vijay Vittal, and Tae Kyoo Oh Iowa State University, Ames, IA In recent years, considerable progress has been made in the transient stability analysis of multimachine power systems by direct methods. Using transient energy functions, "first swing" transient stability of power systems has been investi¬ gated with a fair degree of success. This progress can be largely attributed to two factors: (i) development of functions that adequately describe the transient energy responsible for the separation of one or more generators from the rest of the system , and (ii) better estimate of the critical energy required for these generators to lose synchronism with the system. The latter issue, which is often referred to in the literature as the determination of the "region of stability", is of considera¬ ble practical significance, and is the subject dealt with in this paper. Previous investigators had shown the existence of a controlling unstable equilibrium point 0U (u.e.p.). The system transient energy evaluated at the controlling u.e.p. (0U) is called the critical energy and provides an estimate of the boundary of the region of stability. The controlling u.e.p. could be among a group of u.e.p.'s located in the direction in which the severely disturbed generators move. Hence, accu¬ rate determination of the controlling u.e.p. has a significant effect on direct transient stability assessment. A method for determining the controlling u.e.p. among several possible candidate ones is presented in this paper. For a given disturbance, the method accounts for two important aspects of the transient phenomena: i) the effect of the disturbance on the various generators, and ii) the energy absorbing capacity of the post-disturbance network. The proposed method utilizes the concept of the normalized potential energy margin AVPE.|n. The relative degree of stress to the various generators, associated with difference u.e.p.'s following a disturbance is reliably indicated by AVPE.|n. Therefore, the following crite¬ rion is proposed, "The post-disturbance trajectory approaches (if the distur¬ bance is large enough) the controlling u.e.p. This is the u.e.p. with lowest normalized potential energy margin at the instant the disturbance is removed. " Calculating AVPE.|n requires knowledge of 0U for all the candidate u.e.p.'s. Since computationally this can be an expensive and time-consuming task, a simplified method is proposed based on computing AVPE.|n for the candidate u.e.p.'s using an approximate value of 0U. The technique has been tested in complex situations on two medium-size power networks and in all cases has correctly identified the controlling u.e.p. The procedure for determining APE.|n based on the approximate u.e.p. simplifies the computational burden for large power networks and is of great practical significance. Discusser: Anjon Bose Reliability Modeling of Protective Systems P. M. Anderson, Fellow, IEEE Arizona State University, Tempe, AZ Electric power systems are comprised of a very large number of interconnected components that are designed for the sole purpose of generating and delivering electrical energy to consumers. Usually, the consumers are free to accept or reject the available electrical energy at will, suggesting a probabilistic rather than deterministic demand pattern. The system is operated by humans and by automatic control apparatus, both having some probability of failure to perform their function. Moreover, the system physical components are subject to failure in some random way, with each failure often requiring corrective action. Since the system is geo¬ graphically extensive, it is subject to a large number of natural and man-made hazards. Examples are lightning induced faults and physically damaged components that result from natural or man-made causes. For the purpose of this discussion we classify all of the above as disturbances. Some of these disturbances, such as short circuits, cause severe upsets in system operation and must be somehow removed or isolated. This is the role of the 'protective systems,' which are installed throughout the power system, to detect and remove hazardous disturbances, which we usually call faults. A protective system is designed to do one of the following 1 ) to protect the sound (unfaulted) portion of a power system from damage or undesired operation by removing a faulted component from service, or 2) to protect a component from permanent damage, due to an intolerable operating condition, by removing that com¬ ponent from service soon enough to preclude permanent failure or extensive damage. In either case, the protective system must have two essential parts; an intelligence unit and a switching unit. The intelligence unit measures system performance and com¬ pares a measured or computed quantity against a predeter¬ mined threshold quantity. If the measured or computed quantity exceeds the threshold quantity, the intelligence unit orders the switching unit to operate. As long as the measured or computed quantity is less than (or, in some cases, more than) the threshold quantity, the intelligence unit considers that portion of the system under observation to be essentially 'normal,' or at least not far enough from normal to warrant action by the switching unit(s) under its control. In order to perform analysis, a system configuration must be assumed. We shall examine three Control Configurations, with different degrees of redundancy. Control Configuration #1 assumes a single battery supply, a single breaker mecha¬ nism, and parallel redundant relays. Control Configuration #2 provides redundant current transformers (CT) and potential transformers (PT). Control Configuration #3 provides redun¬ dant circuit breaker trip coils, in addition to the redundancies of Configuration #2. These three Control Configurations are considered typical of industry practice. The actual configura¬ tion used depends on many factors, including the desire for increased operational reliability offered by redundancy. The three Control Configurations are applied to realistic substation arrangements: a single bus, a ring bus, and a breaker-and-a-half bus scheme. These control and bus ar¬ rangements are typical of systems used by the industry. Analysis of these systems is of interest in demonstrating a technique that can be applied to any practical system. Control Configuration 1 is characterized as having redun¬ dancy only in the relays. A logic diagram for this configuration is shown in the fig. 1. For this configuration we can write 58 IEEE Power Engineering Review, August 1984