bility is a condition of equilibriu

bility is a condition of equilibrium between opposing forces. De- pending on the network topology, system operating condition and the form of disturbance, different sets of opposing forces may experience sustained imbalance leading to different forms of instability. In this section, we provide a systematic basis for classification of power system stability.


A. Need for Classification
Power system stability is essentially a single problem; however, the various forms of instabilities that a power system may undergo cannot be properly understood and effectively dealt with by treating it as such. Because of high dimension- ality and complexity of stability problems, it helps to make simplifying assumptions to analyze specific types of problems using an appropriate degree of detail of system representation and appropriate analytical techniques. Analysis of stability, including identifying key factors that contribute to instability and devising methods of improving stable operation, is greatly facilitated by classification of stability into appropriate cate- gories [8]. Classification, therefore, is essential for meaningful practical analysis and resolution of power system stability problems. As discussed in Section V-C-I, such classification is entirely justified theoretically by the concept of partial stability [9]–[11].


B. Categories of Stability
The classification of power system stability proposed here is based on the following considerations [8]:
• The physical nature of the resulting mode of instability as indicated by the main system variable in which instability can be observed.
• The size of the disturbance considered, which influences the method of calculation and prediction of stability.
• The devices, processes, and the time span that must be taken into consideration in order to assess stability.
Fig. 1 gives the overall picture of the power system stability problem, identifying its categories and subcategories. The fol- lowing are descriptions of the corresponding forms of stability phenomena.


B.1 Rotor Angle Stability:
Rotor angle stability refers to the ability of synchronous ma- chines of an interconnected power system to remain in synchro- nism after being subjected to a disturbance. It depends on the ability to maintain/restore equilibrium between electromagnetic torque and mechanical torque of each synchronous machine in the system. Instability that may result occurs in the form of in- creasing angular swings of some generators leading to their loss of synchronism with other generators.
The rotor angle stability problem involves the study of the electromechanical oscillations inherent in power systems. A fundamental factor in this problem is the manner in which the power outputs of synchronous machines vary as their rotor angles change. Under steady-state conditions, there is

equilibrium between the input mechanical torque and the output electromagnetic torque of each generator, and the speed remains constant. If the system is perturbed, this equilibrium is upset, resulting in acceleration or deceleration of the rotors of the machines according to the laws of motion of a rotating body. If one generator temporarily runs faster than another, the angular position of its rotor relative to that of the slower ma- chine will advance. The resulting angular difference transfers part of the load from the slow machine to the fast machine, depending on the power-angle relationship. This tends to reduce the speed difference and hence the angular separation. The power-angle relationship is highly nonlinear. Beyond a certain limit, an increase in angular separation is accompanied by a decrease in power transfer such that the angular separation is increased further. Instability results if the system cannot absorb the kinetic energy corresponding to these rotor speed differences. For any given situation, the stability of the system depends on whether or not the deviations in angular positions of the rotors result in sufficient restoring torques [8]. Loss of synchronism can occur between one machine and the rest of the system, or between groups of machines, with synchronism maintained within each group after separating from each other. The change in electromagnetic torque of a synchronous machine following a perturbation can be resolved into two
components:
• Synchronizing torque component, in phase with rotor angle deviation.
• Damping torque component, in phase with the speed de- viation.
System stability depends on the existence of both components of torque for each of the synchronous machines. Lack of suffi- cient synchronizing torque results in aperiodic or nonoscillatory instability, whereas lack of damping torque results in oscillatory instability.
For convenience in analysis and for gaining useful insight into the nature of stability problems, it is useful to characterize rotor angle stability in terms of the following two subcategories:
• Small-disturbance (or small-signal) rotor angle stability is concerned with the ability of the power system to main- tain synchronism under small disturbances. The distur- bances are considered to be sufficiently small that lin- earization of system equations is permissible for purposes of analysis [8], [12], [13].
- Small-disturbance stability depends on the initial op- erating state of the system. Instability that may result can be of two forms: i) increase in rotor angle through a nonoscillatory or aperiodic mode due to lack of syn- chronizing torque, or ii) rotor oscillations of increasing amplitude due to lack of sufficient damping torque.
- In today’s power systems, small-disturbance rotor angle stability problem is usually associated with insufficient damping of oscillations. The aperiodic instability problem has been largely eliminated by use of continuously acting generator voltage regulators; however, this problem can still occur when generators operate with constant excitation when subjected to the actions of excitation limiters (field current limiters).





Fig. 1. Classification of power system stability.




- Small-disturbance rotor angle stability problems may be either local or global in nature. Local problems involve a small part of the power system, and are usu- ally associated with rotor angle oscillations of a single power plant against the rest of the power system. Such oscillations are called local plant mode oscillations. Stability (damping) of these oscillations depends on the strength of the transmission system as seen by the power plant, generator excitation control systems and plant output [8].
- Global problems are caused by interactions among large groups of generators and have widespread effects. They involve oscillations of a group of generators in one area swinging against a group of generators in another area. Such oscillations are called interarea mode oscil- lations. Their characteristics are very complex and sig- nificantly differ from those of local plant mode oscilla- tions. Load characteristics, in particular, have a major effect on the stability of interarea modes [8].
- The time frame of interest in small-disturbance sta- bility studies is on the order of 10 to 20 seconds fol- lowing a disturbance.
• Large-disturbance rotor angle stability or transient sta- bility, as it is commonly referred to, is concerned with the ability of the power system to maintain synchronism when subjected to a severe disturbance, such as a short circuit on a transmission line. The resulting system response in- volves large excursions of generator rotor angles and is influenced by the nonlinear power-angle relationship.
- Transient stability depends on both the initial operating state of the system and the severity of the dis- turbance. Instability is usually in the form of aperiodic angular separation due to insufficient synchronizing torque, manifesting as first swing instability. However, in large power systems, transient instability may not always occur as first swing instability associated with

a single mode; it could be a result of superposition of a slow interarea swing mode and a local-plant swing mode causing a large excursion of rotor angle beyond the first swing [8]. It could also be a result of nonlinear effects affecting a single mode causing instability beyond the first swing.
- The time frame of interest in transient stability studies is usually 3 to 5 seconds following the disturbance. It may extend to 10–20 seconds for very large systems with dominant inter-area swings.
As identified in Fig. 1, small-disturbance rotor angle stability as well as transient stability are categorized as short term phenomena.
The term dynamic stability also appears in the literature as a class of rotor angle stability. However, it has been used to denote different phenomena by different authors. In the North American literature, it has been used mostly to denote small-dis- turbance stability in the presence of automatic controls (partic- ularly, the generation excitation controls) as distinct from the classical “steady-state stability” with no generator controls [7], [8]. In the European literature, it has been used to denote tran- sient stability. Since much confusion has resulted from the use of the term dynamic stability, we recommend against its usage, as did the previous IEEE and CIGRE Task Forces [6], [7].


B.2 Voltage Stability:
Voltage stability refers to the ability of a power system to main- tain steady voltages at all buses in the system after being sub- jected to a disturbance from a given initial operating condition. It depends on the ability to maintain/restore equilibrium be- tween load demand and load supply from the power system. In- stability that may result occurs in the form of a progressive fall or rise of voltages of some buses. A possible outcome of voltage instability is loss of load in an area, or tripping of transmis- sion lines and other elements by their protective systems leadi

Kết quả (Anh) 2:

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Analysis of stability that, Identifying Key Factors That Contribute gồm to instability and devising methods of Improving stable operation, is greatly facilitated by the appropriate classification of stability that cate- gories Into [8]. Classification, therefore, is essential for meaningful analysis and resolution of practical power system stability that problems. As Discussed print Section VCI, is entirely justified theoretically such 'classification by the concept of partial stability that [9] - [11]. B. Categories of Stability The proposed classification of power system stability that is based on the drop down here Considerations [8]: • The physical nature of the mode of instability as quả indicated by the main system can be variable chứa Observed instability. • The size of the Considered disturbance, the method of calculation mà influences and prediction of stability that. • The devices, processes, and the time span taken Into Consideration mà Phải để Assess stability that. Fig. 1 Gives the overall picture of the power system stability that problem, categories and subcategories Identifying its. The fol- lowing are descriptions of the forms of stability that tương ứng phenomena. B.1 Rotor Angle Stability: Rotor angle stability that Refers to the ability of synchronous ma- chines of an interconnected power system to Remain print synchro- nism being subjected to a disturbance after . It depends on the ability to Maintain / restore equilibrium electromagnetic torque and mechanical giữa torque of each machine in the system synchronous. Instability có result in the form of in- Occurs creasing angular swings of some generators leading to loss of synchronism with other có generators. The rotor angle stability that problem involves the study of the inherent oscillations print Electromechanical power systems. A fundamental factor in this problem is the Manner chứa power outputs of synchronous machines vary as có rotor angles change. Under steady-state conditionsEND_SPAN, there is equilibrium giữa input and the output mechanical torque of each generator electromagnetic torque, and the speed Remains constant. If the system is perturbed, this equilibrium is upset, acceleration or deceleration quả print of the rotors of the machines theo laws of motion of a rotating body. If one generator coal Faster temporarily runs another, the angular position of the rotor relative to its mà ma- chine of the Slower will advance. The angular difference quả transfers part of the load from the slow to the fast machine machine, the power-angle phụ thuộc relationship. This tends to Reduce the speed difference and the angular separation Hence. The power relationship is highly nonlinear Angle. Beyond A Certain Limit, an angular separation is accompanied tăng printed by a printing Decrease power transfer angular separation is such 'rằng Further Increased. Instability results if the system can not absorb the kinetic energy to these rotor speed tương ứng Hiệu. For any given situation, the stability that depends on nếu of the system deviations or not the angular positions of the rotors print print result đủ hồi torques [8]. Loss of synchronism can occur giữa one machine and the rest of the system, or the between groups of machines, with each group synchronism maintained sau sau from each other phân cách cách. The change print electromagnetic torque of a synchronous machine can be resolved sau Into a perturbation of two components: • Synchronizing torque component, print phase with rotor angle deviation. • Damping torque component, printed with the speed de- viation phase. System stability that depends on the Existence of Both components of torque for each of the synchronous machines. Lack of suffi- cient torque synchronizing print results or nonoscillatory aperiodic instability, còn Lack of oscillatory instability damping torque print results. For convenience print analysis and for Gaining insight ích nature of stability that vào problems, it is ích to characterize rotor angle stability that print terms of những two subcategories: • Small-disturbance (or small-signal) rotor angle stability that is Concerned with the ability of the system to main- tain power under small disturbances synchronism. The distur- bances are Considered to be sufficiently small lin mà earization of system equations is permissible for Purposes of analysis [8], [12], [13]. - Small-disturbance stability that depends on the initial state of the op- erating system. Instability có result of two forms can be: i) tăng print through a rotor angle or aperiodic mode nonoscillatory Due to Lack of syn- chronizing torque, or ii) Increasing rotor oscillations of amplitude Due to Lack of đủ damping torque. - In today's power systems, small-disturbance rotor angle stability that problem is associated with Thường damping of oscillations đủ. The aperiodic instability problem largely eliminated by Đã use of Continuously generator voltage regulators acting; Tuy nhiên, this problem can still occur with constant excitation thực khi generators subjected to the actions of khi excitation limiters (field current limiters). Fig. 1. Classification of power system stability that. - Small-disturbance rotor angle stability that local problems hoặc lẽ print or global nature. Local problems to involve a small part of the power system, and are usu- ally associated with the rotor angle oscillations of a single power plant Against the rest of the power system. Such oscillations are local plant gọi mode oscillations. Stability (damping) of những oscillations depends on the strength of the transmission system as seen by the power plant, generator excitation control systems and plant output [8]. - Global problems are caused by large groups of generators Among interactions and have Widespread effects. They oscillations of a group to involve in one area of generators swinging với a group of generators print another area. Such oscillations are gọi interarea mode oscil- lations. Their are very complex and nificant đặc nificantly differs from local plant như mode oscilla- tions. Load đặc, print Particular, have a major effect on the stability that of interarea modes [8]. - The time frame of interest-disturbance small print sta- bility studies is on the order of 10 to 20 seconds fol- lowing a disturbance. • Large-disturbance rotor angle stability that or transient sta- bility, as it is commonly Referred to, is Concerned with the ability of the power system to Maintain synchronism khi subjected to a Severe disturbance, như a short circuit on a transmission line. The quả system in- volves large response of generator rotor angles Excursions and is influenced by the nonlinear power-angle relationship. - Transient stability that depends on the initial cả operating state of the system and the severity of the dis- turbance. Instability is in the form of aperiodic Thường angular separation Due to đủ synchronizing torque, manifesting as the first swing instability. Tuy nhiên, printing large power systems, transient instability unfortunately not always occur as the first swing instability associated with a single mode; it could be a result of superposition of a slow mode and a local interarea swing-swing mode plant Causing a large excursion of the rotor angle beyond the first swing [8]. It could be a result of nonlinear cũng effects Causing instability affecting a single mode beyond the first swing. - The time frame of interest is printed transient stability that studies Thường 3 to 5 seconds sau the disturbance. It unfortunately extend to 10-20 seconds for very large systems with dominant inter-area swings. As print Identified Fig. 1, small-disturbance rotor angle stability that as well as transient stability that are categorized as short term phenomena. The term dynamic stability that am also in the literature as a vẻ class of rotor angle stability that. Tuy nhiên, it used to denote khác Đã phenomena by khác authors. In the North American literature, mostly used it to denote Đã small-dis- turbance in the presence of automatic stability that controls (partic- ularly, the generation excitation controls) as distinct from the classical "steady-state stability that" with no generator controls [7], [8]. In the European literature, it used to denote Đã tran- sient stability that. Since much confusion has resulted from the use of the term dynamic stability that, chúng với recommend its usage, as did the previous IEEE and CIGRE Task Forces [6], [7]. B.2 Voltage Stability: Refers to the ability Voltage Stability of main- tain a steady power to system voltages at all buses in the system after being sub- jected to a disturbance from a given initial operating condition. It depends on the ability to Maintain / restore equilibrium be- tween demand load from the power supply and system load. In- có stability that result in the form of a Occurs progressive rise or fall of voltages of some buses. A possible The outcome of voltage instability is loss of load in an area, or tripping of transmis- sion lines and other elements by protective systems chúng leadi