Power system stability is a single problem, however, it is impractical to deal with it as such. Instability of the power system can take different forms and is influenced by a wide range of factors. Analysis of stability problems, including identifying essential factors that contribute to instability and devising methods of improving stable operation is greatly facilitated by classification of stability into appropriate categories. These are based on the following considerations:
Ø The physical nature of the resulting instability related to the main system parameter in which instability can be observed.
Ø The size of the disturbance considered indicates the most appropriate method of calculation and prediction of stability.
Ø The devices, processes, and the time span that must be taken into consideration in order to determine stability.
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. The mechanism by which interconnected synchronous machines maintain synchronism with one another is through restoring forces, which act whenever there are forces tending to accelerate or decelerate one or more machines with respect to other machines. Under steady-state conditions, there is equilibrium between the input mechanical torque and the output electrical torque of each machine, 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 machine 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, as discussed above, is highly nonlinear. Beyond a certain limit, an increase in angular separation is accompanied by a decrease in power transfer; this increases the angular separation further and leads to instability. 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.
It should be noted that loss of synchronism can occur between one machine and the rest of the system, or between groups of machines, possibly with synchronism maintained within each group after separating from each other.
The change in electrical torque of a synchronous machine following a perturbation can be resolved into two components:
1) SYNCHRONIZING TORQUE: component, in phase with a rotor angle perturbation.
2) DAMPING TORQUE: component, in phase with the speed deviation.
System stability depends on the existence of both components of torque for each of the synchronous machines. Lack of sufficient synchronizing torque results in aperiodic or non-oscillatory 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 categories:
Severe system upsets generally result in large excursions of frequency, power flows, voltage, and other system variables, thereby invoking the actions of processes, controls, and protections that are not modeled in conventional transient stability or voltage stability studies. These processes may be very slow, such as boiler dynamics, or only triggered for extreme system conditions, such as volts/hertz protection tripping generators. In large interconnected power systems, this type of situation is most commonly associated with islanding. Stability in this case is a question of whether or not each island will reach an acceptable state of operating equilibrium with minimal loss of load. It is determined by the overall response of the island as evidenced by its mean frequency, rather than relative motion of machines. Generally, frequency stability problems are associated with inadequacies in equipment responses, poor coordination of control and protection equipment, or insufficient generation reserve.
Over the course of frequency instability, the characteristic times of the processes and devices that are activated by the large shifts in frequency and other system variables will range from a matter of seconds, corresponding to the responses of devices such as generator controls and protections, to several minutes, corresponding to the responses of devices such as prime mover energy supply systems and load voltage regulators.
Although frequency stability is impacted by fast as well as slow dynamics, the overall time frame of interest extends to several minutes. Therefore, it is categorized as a long-term phenomenon in Fig. 7.1.
Progressive drop in bus voltages can also be associated with rotor angles going out of step. For example, the gradual loss of synchronism of machines as rotor angles between two groups of machines approach or exceed 180 degree would result in very low voltages at intermediate points in the network close to the electrical center. In contrast, the type of sustained fall of voltage that is related to voltage instability occurs where rotor angle stability is not an issue.
The main factor contributing to voltage instability is usually the voltage drop that occurs when active and reactive power flow through inductive reactance associated with the transmission network; this limits the capability of transmission network for power transfer. The power transfer limit is further limited when some of the generators hit their reactive power capability limits. The driving forces for voltage instability are the loads; in response to a disturbance, power consumed by the loads tends to be restored by the action of distribution voltage regulators, tap changing transformers, and thermostats.
Restored loads increase the stress on the high voltage network causing more voltage reduction. A rundown situation causing voltage instability occurs when load dynamics attempts to restore power consumption beyond the capability of the transmission system and the connected.
While the most common form of voltage instability is the progressive drop in bus voltages, the possibility of overvoltage instability also exists and has been experienced at least on one. It can occur when EHV transmission lines are loaded significantly below surge impedance loading and under excitation limiters prevent generators and/or synchronous condensers from absorbing the excess reactive power. Under such conditions, transformer taps changers, in their attempt to control load voltage, may cause voltage instability.
Voltage stability problems may also be experienced at the terminals of HVDC links. They are usually associated with HVDC links connected to weak AC systems. The HVDC link control strategies have a very significant influence on such problems.
As in the case of rotor angle stability, it is useful to classify voltage stability into the following subcategories:
Ø The physical nature of the resulting instability related to the main system parameter in which instability can be observed.
Ø The size of the disturbance considered indicates the most appropriate method of calculation and prediction of stability.
Ø The devices, processes, and the time span that must be taken into consideration in order to determine stability.
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Figure 7.1 Possible classification
of power system stability into various categories and
subcategories. |
1) ROTOR ANGLE STABILITY:
Rotor angle stability is concerned with the ability of interconnected synchronous machines of a power system to remain in synchronism under normal operating conditions and 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 increasing 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. The mechanism by which interconnected synchronous machines maintain synchronism with one another is through restoring forces, which act whenever there are forces tending to accelerate or decelerate one or more machines with respect to other machines. Under steady-state conditions, there is equilibrium between the input mechanical torque and the output electrical torque of each machine, 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 machine 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, as discussed above, is highly nonlinear. Beyond a certain limit, an increase in angular separation is accompanied by a decrease in power transfer; this increases the angular separation further and leads to instability. 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.
It should be noted that loss of synchronism can occur between one machine and the rest of the system, or between groups of machines, possibly with synchronism maintained within each group after separating from each other.
The change in electrical torque of a synchronous machine following a perturbation can be resolved into two components:
1) SYNCHRONIZING TORQUE: component, in phase with a rotor angle perturbation.
2) DAMPING TORQUE: component, in phase with the speed deviation.
System stability depends on the existence of both components of torque for each of the synchronous machines. Lack of sufficient synchronizing torque results in aperiodic or non-oscillatory 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 categories:
1) SMALL SIGNAL (OR STEADY STATE) STABILITY:
is concerned with the ability of the power system to maintain synchronism under small disturbances. The disturbances are considered to be sufficiently small that linearization of system equations is permissible for purposes of analysis. Such disturbances are continually encountered in normal system operation, such as small changes in load.
Small signal stability depends on the initial operating state of the system. Instability that may result can be of two forms:
(i) Increase in rotor angle through a non-oscillatory or aperiodic mode due to lack of synchronizing torque, or
(ii) Rotor oscillations of increasing amplitude due to lack of sufficient damping torque.
In today’s practical power systems, small signal stability is largely a problem of insufficient damping of oscillations. The time frame of interest in small-signal stability studies is on the order of 10 to 20 s following a disturbance. The stability of the following types of oscillations is of concern:
Ø LOCAL MODES: or machine system modes, associated with the swinging of units at a generating station with respect to the rest of the power system. The term ‘‘local’’ is used because the oscillations are localized at one station or a small part of the power system.
Ø INTERAREA MODES: associated with the swinging of many machines in one part of the system against machines in other parts. They are caused by two or more groups of closely coupled machines that are interconnected by weak ties.
Ø CONTROL MODES: associated with generating units and other controls. Poorly tuned exciters, speed governors, HVDC converters, and static VAR compensators are the usual causes of instability of these modes.
Ø TORSIONAL MODES: associated with the turbine-generator shaft system rotational components. Instability of torsional modes may be caused by interaction with excitation controls, speed governors, HVDC controls, and series-capacitor-compensated lines.
Small signal stability depends on the initial operating state of the system. Instability that may result can be of two forms:
(i) Increase in rotor angle through a non-oscillatory or aperiodic mode due to lack of synchronizing torque, or
(ii) Rotor oscillations of increasing amplitude due to lack of sufficient damping torque.
In today’s practical power systems, small signal stability is largely a problem of insufficient damping of oscillations. The time frame of interest in small-signal stability studies is on the order of 10 to 20 s following a disturbance. The stability of the following types of oscillations is of concern:
Ø LOCAL MODES: or machine system modes, associated with the swinging of units at a generating station with respect to the rest of the power system. The term ‘‘local’’ is used because the oscillations are localized at one station or a small part of the power system.
Ø INTERAREA MODES: associated with the swinging of many machines in one part of the system against machines in other parts. They are caused by two or more groups of closely coupled machines that are interconnected by weak ties.
Ø CONTROL MODES: associated with generating units and other controls. Poorly tuned exciters, speed governors, HVDC converters, and static VAR compensators are the usual causes of instability of these modes.
Ø TORSIONAL MODES: associated with the turbine-generator shaft system rotational components. Instability of torsional modes may be caused by interaction with excitation controls, speed governors, HVDC controls, and series-capacitor-compensated lines.
2) LARGE DISTURBANCE ROTOR ANGLE STABILITY OR TRANSIENT STABILITY:
As it is commonly referred to, is concerned with the ability of the power system to maintain synchronism when subjected to a severe transient disturbance. The resulting system response involves 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 disturbance. Usually, the disturbance alters the system such that the post-disturbance steady state operation will be different from that prior to the disturbance. Instability is in the form of aperiodic drift due to insufficient synchronizing torque, and is referred to as first swing stability. In large power systems, transient instability may not always occur as first swing instability associated with a single mode; it could be as a result of increased peak deviation caused by superposition of several modes of oscillation causing large excursions of rotor angle beyond the first swing.
The time frame of interest in transient stability studies is usually limited to 3 to 5 sec following the disturbance. It may extend to 10 sec for very large systems with dominant inter-area swings.
Power systems experience a wide variety of disturbances. It is impractical and uneconomical to design the systems to be stable for every possible contingency. The design contingencies are selected on the basis that they have a reasonably high probability of occurrence.
As identified in Fig. 7.1, small signal stability as well as transient stability is categorized as short term phenomena.
Transient stability depends on both the initial operating state of the system and the severity of the disturbance. Usually, the disturbance alters the system such that the post-disturbance steady state operation will be different from that prior to the disturbance. Instability is in the form of aperiodic drift due to insufficient synchronizing torque, and is referred to as first swing stability. In large power systems, transient instability may not always occur as first swing instability associated with a single mode; it could be as a result of increased peak deviation caused by superposition of several modes of oscillation causing large excursions of rotor angle beyond the first swing.
The time frame of interest in transient stability studies is usually limited to 3 to 5 sec following the disturbance. It may extend to 10 sec for very large systems with dominant inter-area swings.
Power systems experience a wide variety of disturbances. It is impractical and uneconomical to design the systems to be stable for every possible contingency. The design contingencies are selected on the basis that they have a reasonably high probability of occurrence.
As identified in Fig. 7.1, small signal stability as well as transient stability is categorized as short term phenomena.
2) FREQUENCY STABILITY:
Frequency stability is concerned with the ability of a power system to maintain steady frequency within a nominal range following a severe system upset resulting in a significant imbalance between generation and load. It depends on the ability to restore balance between system generation and load, with minimum loss of load.Severe system upsets generally result in large excursions of frequency, power flows, voltage, and other system variables, thereby invoking the actions of processes, controls, and protections that are not modeled in conventional transient stability or voltage stability studies. These processes may be very slow, such as boiler dynamics, or only triggered for extreme system conditions, such as volts/hertz protection tripping generators. In large interconnected power systems, this type of situation is most commonly associated with islanding. Stability in this case is a question of whether or not each island will reach an acceptable state of operating equilibrium with minimal loss of load. It is determined by the overall response of the island as evidenced by its mean frequency, rather than relative motion of machines. Generally, frequency stability problems are associated with inadequacies in equipment responses, poor coordination of control and protection equipment, or insufficient generation reserve.
Over the course of frequency instability, the characteristic times of the processes and devices that are activated by the large shifts in frequency and other system variables will range from a matter of seconds, corresponding to the responses of devices such as generator controls and protections, to several minutes, corresponding to the responses of devices such as prime mover energy supply systems and load voltage regulators.
Although frequency stability is impacted by fast as well as slow dynamics, the overall time frame of interest extends to several minutes. Therefore, it is categorized as a long-term phenomenon in Fig. 7.1.
3) VOLTAGE STABILITY:
Voltage stability is concerned with the ability of a power system to maintain steady voltages at all buses in the system under normal operating conditions, and after being subjected to a disturbance. Instability that may result occurs in the form of a progressive fall or rise of voltage of some buses. The possible outcome of voltage instability is loss of load in the area where voltages reach unacceptably low values, or a loss of integrity of the power system.Progressive drop in bus voltages can also be associated with rotor angles going out of step. For example, the gradual loss of synchronism of machines as rotor angles between two groups of machines approach or exceed 180 degree would result in very low voltages at intermediate points in the network close to the electrical center. In contrast, the type of sustained fall of voltage that is related to voltage instability occurs where rotor angle stability is not an issue.
The main factor contributing to voltage instability is usually the voltage drop that occurs when active and reactive power flow through inductive reactance associated with the transmission network; this limits the capability of transmission network for power transfer. The power transfer limit is further limited when some of the generators hit their reactive power capability limits. The driving forces for voltage instability are the loads; in response to a disturbance, power consumed by the loads tends to be restored by the action of distribution voltage regulators, tap changing transformers, and thermostats.
Restored loads increase the stress on the high voltage network causing more voltage reduction. A rundown situation causing voltage instability occurs when load dynamics attempts to restore power consumption beyond the capability of the transmission system and the connected.
While the most common form of voltage instability is the progressive drop in bus voltages, the possibility of overvoltage instability also exists and has been experienced at least on one. It can occur when EHV transmission lines are loaded significantly below surge impedance loading and under excitation limiters prevent generators and/or synchronous condensers from absorbing the excess reactive power. Under such conditions, transformer taps changers, in their attempt to control load voltage, may cause voltage instability.
Voltage stability problems may also be experienced at the terminals of HVDC links. They are usually associated with HVDC links connected to weak AC systems. The HVDC link control strategies have a very significant influence on such problems.
As in the case of rotor angle stability, it is useful to classify voltage stability into the following subcategories:
1. LARGE DISTURBANCE VOLTAGE STABILITY:
Is concerned with a system’s ability to control voltages following large disturbances such as system faults, loss of generation, or circuit contingencies.
This ability is determined by the system-load characteristics and the interactions of both continuous and discrete controls and protections. Determination of large disturbance stability requires the examination of the nonlinear dynamic performance of a system over a period of time sufficient to capture the interactions of such devices as under-load transformer tap changers and generator field-current limiters. The study period of interest may extend from a few seconds to tens of minutes. Therefore, long term dynamic simulations are required for analysis.
This ability is determined by the system-load characteristics and the interactions of both continuous and discrete controls and protections. Determination of large disturbance stability requires the examination of the nonlinear dynamic performance of a system over a period of time sufficient to capture the interactions of such devices as under-load transformer tap changers and generator field-current limiters. The study period of interest may extend from a few seconds to tens of minutes. Therefore, long term dynamic simulations are required for analysis.
2. SMALL DISTURBANCE VOLTAGE STABILITY:
Is concerned with a system’s ability to control voltages following small perturbations such as incremental changes in system load. This form of stability is determined by the characteristics of loads, continuous controls, and discrete controls at a given instant of time. This concept is useful in determining, at any instant, how the system voltage will respond to small system changes. The basic processes contributing to small disturbance voltage instability are essentially of a steady state nature. Therefore, static analysis can be effectively used to determine stability margins, identify factors influencing stability, and examine a wide range of system conditions and a large number of post contingency scenarios. A criterion for small disturbance voltage stability is that, at a given operating condition for ever y bus in the system, the bus voltage magnitude increases as the reactive power injection at the same bus is increased. A system is voltage unstable if, for at least one bus in the system, the bus voltage magnitude (V) decreases as the reactive power injection (Q) at the same bus is increased. In other words, a system is voltage stable if V- Q sensitivity is positive for ever y bus and unstable if V-Q sensitivity is negative for at least one bus.
The time frame of interest for voltage stability problems may vary from a few seconds to tens of minutes. Therefore, voltage stability may be either a short term or a long-term phenomenon.
Voltage instability does not always occur in its pure form. Often, the rotor angle instability and voltage instability go hand in hand. One may lead to the other, and the distinction may not be clear. However, distinguishing between angle stability and voltage stability is important in understanding the underlying causes of the problems in order to develop appropriate design and operating procedures.
The time frame of interest for voltage stability problems may vary from a few seconds to tens of minutes. Therefore, voltage stability may be either a short term or a long-term phenomenon.
Voltage instability does not always occur in its pure form. Often, the rotor angle instability and voltage instability go hand in hand. One may lead to the other, and the distinction may not be clear. However, distinguishing between angle stability and voltage stability is important in understanding the underlying causes of the problems in order to develop appropriate design and operating procedures.
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