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3. SYSTEM STABILITY
3.1 Introduction
The problem of stability in a network concerns energy balance and the ability to generate sufficient restoring forces to counter system disturbances.
Minor disturbances to the system result in a mutual interchange of power between the machines in the system acting to keep them in step with each other and to maintain a single universal frequency. A state of equilibrium is retained between the total mechanical power/energy-input and the electrical power/energy-output by natural adjustment of system voltage levels and the common system frequency. There are three regimes of stability:
(a) Steady state stability describes the ability of the system to remain in synchronism during minor disturbances or slowly developing system changes such as a gradual increase in load as the 24-hour maximum demand is approached.
(b) Transient stability is concerned with system behavior following an abrupt change in loading conditions as could occur as a result of a fault, the sudden loss of generation or an interconnecting line, or the sudden connection of additional load. The duration of the transient period is in the order of a second. System behavior in this interval is crucial in the design of power systems.
(c) Dynamic stability is a term used to describe the behavior of the system in the interval between transient behavior and the steady state region.
For example dynamic stability studies could include the behavior of turbine governors, steam/fuel flows, load shedding and the recovery of motor loads, etc.
The response of induction motors to system disturbances and motor starting is also thought of as a stability problem. It does not relate specifically to the ability of the system to remain in synchronism.
This description is divided into two parts: the first deals with the analytical nature of synchronous machine behavior and the different types of stability; the second deals with the more practical aspects of data collection and interpretation of transient stability study results with case studies to illustrate the main points and issues. The complexity of such analysis demands the use of computing techniques and considerable data collection.
3.2 Analytical Aspects
3.2.1 Vector Diagrams and Load Angle
Fig. 6a shows the synchronous generator most simply represented on a per phase basis by an internally generated voltage (E) and an internal reactance (X). The internal voltage arises from the induction in the stator by the rotating magnetic flux of the rotor. The magnitude of this voltage is determined by the excitation of the field winding. The reactance is the synchronous reactance of the machine for steady state representation and the transient and subtransient reactance for the representation of rapid changes in operating conditions. The terminals of the generator (i.e. beyond E and X) are assumed to be connected to an 'infinite' busbar which has the properties of constant voltage and frequency with infinite inertia such that it can absorb any output supplied by the generator. In practice, such an infinite busbar is never obtained. However, in a highly interconnected system with several generators the system voltage and frequency are relatively insensitive to changes in the operating conditions of one machine. The generator is synchronized to the infinite busbar and the bus voltage (U) is unaffected by any changes in the generator parameters (E) and (X). The vector diagrams associated with this generator arrangement supplying current (I) with a lagging power factor (cos f) are shown in Figs 1.6b to 1.6e for low electrical output, high electrical output, high excitation operation and low excitation operation, respectively. The electrical power output is UI cos f per phase. The angle theta between the voltage vectors E and U is the load angle of the machine.
The load angle has a physical significance determined by the electrical and mechanical characteristics of the generator and its prime mover.
Above: Fig. 6 Vector diagrams and load angle.(a) Equivalent circuit (generator)
(b) Low electrical output (c) High electrical output (d) High excitation
operation (e) Low excitation operation (f) Zero PF lag (g) Zero PF lead
A stroboscope tuned to the supply frequency of the infinite busbar would show the machine rotor to appear stationary. A change in electrical loading conditions such as that from Figs 6b to 6c would be seen as a shift of the rotor to a new position. For a generator the load angle corresponds to a shift in relative rotor position in the direction in which the prime mover is driving the machine. The increased electrical output of the generator from Figs. 1.6b to 1.6c is more correctly seen as a consequence of an increased mechanical output of the prime mover. Initially this acts to accelerate the rotor and thus to increase the load angle. A new state of equilibrium is then reached where electrical power output matches prime mover input to the generator.
Figures 6d and 6e show the effect of changing the field excitation of the generator rotor at constant electrical power output and also with no change in electrical power output from the Fig. 6b condition _ that is UI cos f is unchanged. An increase in (E)in Fig. 6d results in a larger current (I) but a more lagging power factor. Similarly, in Fig. 6e the reduction in (E) results in a change in power factor towards the leading quadrant. The principal effect of a variation in generator internal voltage is therefore to change the power factor of the machine with the larger values of (E) resulting in lagging power factors and the smaller values for (E) tending towards leading power factors.
A secondary effect, which is important in stability studies, is also the change in load angle. The increased value of (E) shown in Fig. 6d (high excitation operation) has a smaller load angle compared to Fig. 6e (low excitation operation) for the same electrical power. Figures 6f and 6g show approximately zero lag and lead power factor operation where there is no electrical power output and the load angle is zero.
3.2.2 The Power/Load Angle Characteristic
Fig. 6b represents the vector diagram for a low electrical power output:
P5UI cos f (per phase)
also for the vector triangles it’s true that:
E sin ?5IX cos f
substitute for I:
....
The electrical power output is therefore directly proportional to the generator internal voltage (E) and the system voltage (U) but inversely proportional to the machine reactance (X). With (U), (E)and (X) held constant, the power output is only a function of the load angle theta. Fig. 7 shows a family of curves for power output versus load angle representing this. As a prime mover power increases a load angle of 90 degr is eventually reached.
Beyond this point further increases in mechanical input power cause the electrical power output to decrease. The surplus input power acts to further accelerate the machine and it’s said to become unstable. The almost inevitable consequence is that synchronism with the remainder of the sys tem is lost.
Fast-acting modern automatic voltage regulators (AVRs) can now actually enable a machine to operate at a load angle greater than 90 degr. If the AVR can increase (E) faster than the load angle (?):
...then stability can be maintained up to a theoretical maximum of about 130 degr.
Above: Fig. 7 Power/load angle relationship.
This loss of synchronism is serious because the synchronous machine may enter phases of alternatively acting as a generator and then as a motor.
Power surges in and out of the machine, which could be several times the machine rating, would place huge electrical and mechanical stresses on the machine. Generator overcurrent relay protection will eventually detect out of-synchronism conditions and isolate the generator from the system. Before this happens other parts of the network may also trip out due to the power surging and the whole system may collapse. The object of system stability studies is therefore to ensure appropriate design and operational measures are taken in order to retain synchronism for all likely modes of system operation, disturbances and outages.
3.2.3 The Synchronous Motor
Operation of the synchronous motor may be envisaged in a similar way to the synchronous generator described in Section 3.2.2. In this case, how ever, the power flow is into the machine and, relative to the generator, the motor load angle is negative. An increase in load angle is in the opposite direction to shaft rotation and results in greater electrical power consumption. A leading power factor corresponds to high excitation and a lagging power factor low excitation.
3.2.4 Practical Machines
In reality practical machine characteristics depart from the behavior of the simple representations described above. However, in most cases the effects are small and they don’t invalidate the main principles. The principal differences are due to saturation, saliency and stator resistance.
Saturation describes the non-linear behavior of magnetic fluxes in iron and air paths produced by currents in the machine stator and rotor windings.
Saturation effects vary with machine loading.
Saliency describes the effect of the differing sizes of air gap around the circumference of the rotor. This is important with salient pole rotors and the effect varies the apparent internal reactance of the machine depending upon the relative position of rotor and stator. Saliency tends to make the machine 'stiffer'. That is, for a given load the load angle is smaller with a salient pole machine than would be the case with a cylindrical rotor machine. Salient pole machines are in this respect inherently more stable.
The effect of stator resistance is to produce some internal power dissipation in the machine itself. Obviously the electrical power output is less than the mechanical power input and the difference is greatest at high stator currents.
3.3 Steady State Stability
3.3.1 Pull Out Power
Steady state stability deals with the ability of a system to perform satisfactorily under constant load or gradual load-changing conditions. In the single machine case shown in Fig. 7 the maximum electrical power output from the generator occurs when the load angle is 90 degr.
The value of peak power or 'pull out power' is given as:
PMAX 5 EU/X
… with (U) fixed by the infinite bus and (X) a fixed parameter for a given machine, the pull out power is a direct function of (E). Fig. 7 shows a family of generator power/load angle curves for different values of (E). For a generator operating at an output power P1, the ability to accommodate an increase in loading is seen to be greater for operation at high values of (E) _ increased field excitation. From Section 3.2 and Figs. 1.6d and 1.6e, operation at high values of (E) corresponds with supplying a lagging power factor and low values of (E) with a leading power factor. A generator operating at a leading power factor is therefore generally closer to its steady state stability limit than one operating at a lagging power factor.
The value of (X), used in the expression for pull out power for an ideal machine, would be the synchronous reactance. In a practical machine the saturation of the iron paths modifies the assumption of a constant value of synchronous reactance for all loading conditions. The effect of saturation is to give a higher pull out power in practice than would be expected from a calculation using synchronous reactance. Additionally, in practical machines saliency and stator resistance, as explained in Section 3.2.4, would modify the expression for pull out power. Saliency tends to increase pull out power and reduces to slightly below 90 degr. the load angle at which pull out power occurs. Stator resistance slightly reduces both the value of pull out power and the load angle at which it occurs.
Above: Fig. 8 Typical generator operation chart.
Arc of maximum MVA Arc of maximum excitation Prime mover power limit Theoretical stability limit
3.3.2 Generator Operating Chart
An example of the effect of maximum stable power output of a generator is given in the generator operating chart of Fig. 8. This is basically derived as an extension of the vector diagrams of Fig. 6, where the value of internal voltage (E) and load angle (theta) is plotted for any loading condition of MW or MVAr. In the operating chart, the circles represent constant values of (E) and load angle is shown for an assumed operating point. The operating points for which the load angle is 90 degr are shown as the theoretical stability limit. Operation in the area beyond the theoretical stability limit corresponds with load angles in excess of 90 degr. and is not permissible. The theoretical stability limit is one of the boundaries within which the operating point must lie. Other boundaries are formed by:
1. the maximum allowable stator current, shown on the chart as an arc of maximum MVA loading;
2. the maximum allowable field excitation current shown on the chart as an arc at the corresponding maximum internal voltage (E);
3. a vertical line of maximum power may exist and this represents the power limit of the prime mover.
Whichever of the above limitations applies first describes the boundaries of the different areas of operation of the generator.
In a practical situation, operation at any point along the theoretical stability limit line would be most undesirable. At a load angle of 90 degr. , the generator cannot respond to a demand for more power output without becoming unstable. A practical stability limit is usually constructed on the operating chart such that, for operation at any point on this line, an increased power output of up to a certain percentage of rated power can always be accommodated without stability being lost. The practical stability limit in Fig. 8 is shown for a power increase of 10% of rated power output. The dotted line beyond the theoretical stability limit with a load angle theta. 90 degr shows the stabilizing effect of the AVR.
3.3.3 Automatic Voltage Regulators
The AVR generally operates to maintain a constant generator terminal volt age for all conditions of electrical output. This is achieved in practice by varying the excitation of the machine, and thus (E), in response to any terminal voltage variations. In the simple system of one generator supplying an infinite busbar, the terminal voltage is held constant by the infinite bus. In this case changes in excitation produce changes in the reactive power MVAr loading of the machine. In more practical systems, the generator terminal voltage is at least to some degree affected by the output of the machine. An increase in electrical load would reduce the terminal voltage and the corrective action of the AVR would boost the internal voltage (E).
Referring to the generator operating chart of Fig. 8, an increase in power output from the initial point A would result in a new operating point B on the circle of constant internal voltage (E) in the absence of any manual or automatic adjustment of (E). Such an increase in power output takes the operating point nearer to the stability limit. If, at the same time as the power increase, there is a corresponding increase in (E) due to AVR action the new operating point would be at C. The operation of the AVR is therefore to hold the operating point well away from the stability limit and the AVR can be regarded as acting to preserve steady state stability.
3.3.4 Steady State Stability in Industrial Plants
From Section 3.3.3 it can be seen that the steady state stability limits for generators are approached when they supply capacitive loads. Since industrial plants normally operate at lagging power factors the problem of steady state stability is unlikely to occur. Where power factor compensation is used or where synchronous motors are involved the possibility of a leading power factor condition is relevant and must be examined. Consider the Channel Tunnel 21 kV distribution scheme shown in Fig. 9. This consists of long 50 km lengths of 21 kV cross-linked polyethylene (XLPE) cable stretching under the Channel between England and France. Standby generation has been designed to feed essential services in the very unlikely case of simultaneous loss of both UK and French National Grid supplies. The 3 MVAr reactor shown on the single-line diagram is used to compensate for the capacitive effect of the 21 kV cable system. The failed Grid supplies are first isolated from the sys tem. The generators are then run up and initially loaded into the reactor before switching in the cable network. The Channel Tunnel essential loads (ventilation, drainage pumping, lighting, control and communications plant) are then energized by remote control from the Channel Tunnel control centre.
3.4 Transient Stability
3.4.1 A Physical Explanation and Analogy
Above: Fig. 9 Channel Tunnel 21 kV simplified distribution network with
standby generation.
Transient stability describes the ability of all the elements in the network to remain in synchronism following an abrupt change in operating conditions.
The most onerous abrupt change is usually the three phase fault, but sudden applications of electrical system load or mechanical drive power to the generator and network switching can all produce system instability.
This instability can usually be thought of as an energy balance problem within the system. The analogy of the loaded spring is a useful aid to help visualize the situation. The general energy equation is as follows:
Mechanical energy + Electrical energy + Kinetic energy (energy of motion) + Losses
Under steady state conditions when changes are slow, the system kinetic energy remains unchanged. However, if the disturbance to the machine is sudden (fault or load change) the machine cannot supply the energy from its prime mover or absorb energy from the electrical supply instantaneously. As explained in more detail in Section 3.4.6, the most common cause of instability in a generator system is a fault close to the terminals, which suddenly prevents the energy of the machine from being supplied to the system.
The excess or deficit of energy must go to or come from the machine's kinetic energy and the speed changes. As an example, if a motor is suddenly asked to supply more mechanical load, it will supply it from the kinetic energy of its rotor and slow down. The slowing down process will go too far (overshoot) and will be followed by an increase in speed so that the new load condition is approached in an oscillatory manner just like the loaded spring (see Fig. 10).
If a spring of stiffness S is gradually loaded with a mass M it will extend by a distance delta_x until the stiffness force S delta_x5M g, the weight of the mass. The kinetic energy of the system won’t be disturbed. The spring is analogous to the machine and the extension of the spring delta_x is analogous to the machine load angle theta. Loading the spring beyond its elastic limit is analogous to steady state instability of a loaded machine. A machine cannot be unstable by itself, it can only be unstable with respect to some reference (another machine or infinite busbar to which it’s connected) with which it can exchange a restoring force and energy. In the analogy the spring can only be loaded against a restraining mass (its attachment): an unattached spring cannot be extended.
Consider the spring analogy case with the spring being suddenly loaded by a mass M to represent the transient condition. The kinetic energy of the system is now disturbed and the weight will stretch the spring beyond its normal extension:
Above: Fig. 10 Loaded spring machine stability analogy. Loaded; Unloaded
Above: Fig. 11 Loaded spring machine stability analogy _ overshoot.
Above: Fig. 13 Transient stability to faults _ power/load angle curve
under fault conditions.
3.4.6 Transient Stability for Close-up Faults on Generator Terminals
The worst case fault conditions for the generator are with a three phase fault applied close to its terminals. The terminal voltage reduces to zero and the electrical power output must also reduce to zero. The whole of the pre-fault mechanical driving power is then expended in accelerating the generator rotor because no power can be transferred across this close-up fault. The maximum permissible fault duration to avoid instability under these conditions is a useful guide to the correct protection settings and selection of circuit breaker characteristics used in the vicinity of generators. The maximum permissible fault duration is referred to in technical literature as the critical switching time.
The maximum (critical) fault duration is relatively insensitive to machine rating and any variation from one machine to another would largely be due to differences in inertia constant H. The two examples for critical fault duration given below are for identical machines with different inertia constants and give the order of fault durations for typical machines.
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Drive Source Inertia Constant (H) Maximum Fault Duration
1. Hydro or low speed diesel 1.0 MJ/MVA Approximately 0.14 seconds
2. Steam turbine 10 MJ/MVA Approximately 0.50 seconds
( Figures are for generators with 25% transient reactance, no AVR action and feeding into an infinite busbar.)
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3.4.7 Auto-Reclosing and Single Pole Switching
Section 3.4.6 shows that if the fault is of a transient nature it’s advantageous (from a stability point of view) to put the system back into service rap idly by use of auto-reclosing circuit breakers once the fault has cleared. If the fault persists the generator will be subjected to a second fault impact upon reclosing the circuit breaker and a stable situation may be rendered unstable. Great care is therefore necessary when considering auto-reclosing.
Applicable cases for overhead lines might be those where historical records show that the majority of faults are of a transient nature due to lightning or perhaps high impedance earth faults due to bush fires.
Over 90% of overhead line faults are single phase to earth faults. As an aid to stability auto-reclose single pole circuit breaker switching is often employed. A typical transmission system strategy is to employ single shot auto-reclose facilities only for single phase to earth faults. If the fault persists then three phase switching takes over to disconnect the circuit. Typical delay times between circuit breaker auto-reclose shots are of the order of 0.4 to 0.5 seconds allowing for a 0.3 second arc deionization time. The single pole auto-reclose technique is well established for transmission line voltages below 220 kV and stability is aided because during the fault clearance process power can be transferred across the healthy phases. It should be noted, however, that fault arc deionization takes longer with single pole switching because the fault is fed capacitively from the healthy phases. In addition the system cannot be run for more than a few seconds with one open circuit phase or serious overheating of the rotating plant may take place.
Distribution systems employ three phase auto-reclose breakers and sectionalizers to isolate the fault if it persists.
3.4.8 Hunting of Synchronous Machines
The load angle of a stable machine oscillates about a point of equilibrium if momentarily displaced. The machine has a characteristic natural frequency associated with this period of oscillation which is influenced by its loading and inertia constant. In order to avoid large angle swings, the possibility of mechanical damage to the shaft and couplings and loss of synchronism, the natural frequency should not coincide with the frequency of pulsating loads or prime mover torque. Hunting of this type may be detected from pulsating electrical measurements seen on machine meters and excessive throbbing machine noise. Damping windings on the machine and the power system load itself assist in reduction of hunting effects. In both these cases damping arises from induced currents in the damper windings caused by rotor oscillation. The damping torques decrease with increasing resistance in the paths of the induced currents. Machines operating at the ends of long, high-resistance supply lines or having high resistance damper windings can be particularly susceptible to hunting.
The possibility of hunting can be seen from the equations in Section 3.4.1 if the mechanical torque takes the form Tm sin st. The second-order differential equation of motion has oscillatory solutions exhibiting a natural frequency theta_0.
A resonance condition will arise if the mechanical driving torque frequency, s, approaches the machine natural frequency omega_0.
3.5 Dynamic Stability
Although a system may not lose synchronism in the transient interval following a disturbance, the ability to adapt in the longer term to a significantly new set of operating conditions is the subject of dynamic stability studies. In the transient period of perhaps a second or two following a disturbance, many of the slower reacting power system components can be assumed constant. Their effect on the preservation or otherwise of transient stability is negligible. In the seconds and minutes following a disturbance such slow reacting components may become dominant. Thus a thorough study of system stability from the end of the transient period to steady state must consider such effects as turbine governor response, steam flows and reserves, boiler responses and the possibility of delayed tripping of interconnectors which may have become overloaded, or load loss by frequency-sensitive load-shedding relays. In addition, during the dynamic period, motor loads shed at the start of the disturbance may be automatically restarted.
Dynamic stability studies are more normally carried out for large interconnected systems to assist with the development of strategies for system control following various types of disturbance. With smaller industrial reticulation the preservation of stability in the transient period is generally regarded as the most important case for investigation.
The adaptation of the network in the dynamic interval is left largely up to the natural properties of the system and by automatic or operator control.
The control system can, for example restore the correct frequency by adjustments to turbine governor gear and improve voltage profiles by capacitor bank switching or alteration of synchronous motor excitation.
3.6 Effect of Induction Motors
3.6.1 Motor Connection to the System
The stability of an induction motor generally refers to its ability to recover to a former operating condition following a partial or complete loss of supply.
Induction motors always run asynchronously and stability studies involve a consideration of the load characteristics before and after a system disturbance. For a fault close to the induction motor the motor terminal voltage is considerably reduced. Unable to supply sufficient energy and torque to the driven load the motor slows down:
1. For a given terminal voltage the current drawn is a function only of speed.
As the speed drops the current increases rapidly to several times normal full load value and the power factor drops from, say, 0.9 lag to 0.3 lag or less.
2. The torque of the motor is approximately proportional to the square of the terminal voltage.
Because of these characteristics substation induction motor loads are often characterized as:
1. 'Essential' loads _ Those supplying boiler feed pumps, lubricating systems, fire pumps, etc., which must be kept running throughout a disturbance. The ability of these motors to recover and reaccelerate in the post disturbance period depends upon the nature of the load and system volt age profile. Square law loads such as centrifugal pumps will recover with greater ease than constant torque loads such as reciprocating compressors.
2. 'Non-essential' loads _ Motors that can be shed by undervoltage relays if the disturbance is sufficiently severe to depress the voltage below, say, 66%. These loads may be reconnected automatically after a delay.
The system designer must, however, consider the possibility of voltage collapse upon reconnection as the starting of motors places a severe burden on generation reactive power supply capability.
3.6.2 Motor Starting
In itself motor starting constitutes a system disturbance. Induction motors draw 5 to 6 times full load current on starting until approximately 85_90% of full speed has been attained. The starting torque is only about 1.5 to 2 times full load torque and does not therefore constitute a severe energy disturbance. The motor VAr demand is, however, very large because of the poor starting power factor.
The system voltage can be severely depressed before, for example, on-site generator AVR action comes into play. Checks should be made to ensure that direct-on-line (DOL) starting of a large motor or group of motors does not exceed the VAr capability of local generation in industrial distribution systems.
The depressed voltage should not be allowed to fall below 80% otherwise failure to start may occur and other connected motors on the system may stall.
If studies show large motor starting difficulties then DOL starting may have to be replaced with current limiting, or soft start solid state motor starting methods. The star/delta starter is not recommended without consideration of the switching surge when moving from star to delta induction motor winding connections.
3.7 Data Requirements and Interpretation of Transient Stability Studies
3.7.1 Generator Representation
The simplest generator representation for transient stability studies involving minimum data collection in the mechanical sense is by its total inertia constant H MJ/MVA. In the electrical sense by a fixed internal voltage E (kV) behind the transient reactance x0 d pu or percent. The fixed internal voltage implies no AVR action during the studies and the computer assigns a value after solving the pre-disturbance system load flow. This is adequate for 'first swing type' stability assessments giving pessimistic results.
Where instability or near instability is found with the simple representation, or if it’s required to extend the study beyond the 'first swing' effects, a more detailed representation of the generator is necessary. AVR characteristics, saturation effects, saliency, stator resistance and machine damping are then included in the input data files. Such data collection can be time consuming and for older machines such data are not always available. A com promise is sometimes necessary whereby generators electrically remote from the disturbance, and relatively unaffected by it, can use the simple representation and those nearer can be modeled in more detail. For example, a primary substation infeed from a large grid network with high fault level to an industrial plant can usually be represented as a simple generator with large inertia constant and a transient reactance equal to the short circuit reactance.
If the grid system is of a similar size to the industrial plant then a more detailed representation is necessary since the stability of the grid machines can affect plant performance.
3.7.2 Load Representation
The detailed representation of all loads in the system for a transient stability study is impracticable. A compromise to limit data collection and reduce computing time costs is to represent in detail those loads most influenced by the disturbance and use a simple representation for those loads electrically remote from the disturbance. In particular where large induction motor performance is to be studied it’s important to correctly represent the torque/speed characteristic of the driven load. Simple load representation to voltage variations falls into one of the following categories:
1. Constant impedance (static loads)
2. Constant kVA (induction motors)
3. Constant current (controlled rectifiers)
In summary:
Induction motors (close to disturbance):
_ Use detailed representation including synchronous reactance, transient reactance, stator resistance, rotor open circuit time constant, deep bar factor, inertia constant and driven load characteristics (e.g. torque varies as speed).
Induction motors (remote from disturbance and represented as a static load):
_ Fully loaded motors can be represented as constant kVA load. Partially loaded motors can be represented as constant current loads. Unloaded motors can be represented as constant impedance loads.
Controlled rectifiers:
_ Treat as constant current loads.
Static loads:
_ Generalize as constant impedance unless specific characteristics are known.
Fig. 14 shows a flow chart indicating the stages in obtaining information for data files necessary for load flow, transient stability and dynamic stability studies.
3.7.3 Interpretation of Transient Stability Study Results
The following broad generalizations can be made in the interpretation of transient stability study results following the application and clearance of a three phase fault disturbance:
1. System faults will depress voltages and restrict power transfers. Usually, generators will speed up during the fault and the load angle will increase.
2. Generators closest to the fault will suffer the greatest reduction in load and will speed up faster than generators remote from the fault. Some generators may experience an increased load during the fault and will slow down.
3. For the same proportionate loss in load during the fault, generators with lower inertia constants will speed up more quickly. On-site generators may remain in step with each other but diverge from the apparently high inertia grid infeed.
4. Induction motor slips will increase during the fault.
5. After the fault, stability will be indicated by a tendency for the load angle swings to be arrested, for voltages and frequency to return to pre-fault values and for induction motor slips to return to normal load values.
6. If a grid infeed is lost as a result of the fault, an industrial load may be 'islanded'. If on-site generators remain in synchronism with each other but cannot match the on-site load requirements, a decline in frequency will occur. Load shedding will then be necessary to arrest the decline.
Above: Fig. 14 Information for stability studies. System data and configuration.
Practical examples of these principles are given in the case studies in Section 3.8. Faults may be classified according to their severity in terms of:
1. Type of fault (three phase, single phase to earth, etc.). A three phase fault is normally more severe than a single phase fault since the former blocks virtually all real power transfer. The single phase fault allows some power transfer over healthy phases.
2. Duration of fault. If the fault persists beyond a certain length of time the generators will inevitably swing out of synchronism. The maximum permissible fault duration therefore varies principally with the inertia constant of the generators, and the type and location of the fault.
Determination of maximum fault clearing time is often the main topic of a transient stability study. The limiting case will usually be a three phase fault close up to the generator busbars. Low inertia generators (H51.0 MJ/MVA) will require three phase fault clearance in typically 0.14 s to remain stable as described in Section 3.4.6. Note that with modern vacuum or SF6 circuit breakers fault clearance within three cycles (0.06 seconds at 50 Hz) or less is possible.
3. Location of a fault. This affects the extent of voltage depression at the generator terminals and thus the degree of electrical loading change experienced by the generator during the fault.
4. Extent of system lost by the fault. Successful system recovery, after a fault, is influenced by the extent of the system remaining in service. If a main transmission interconnector is lost, the generators may not be able to transmit total power and power imbalance can continue to accelerate rotors towards loss of synchronism. The loss of a faulted section may also lead to overloading of system parts remaining intact. A second loss of transmission due to, say, overload could have serious consequences to an already weakened system. In order to improve transient stability, fault durations should be kept as short as possible by using high speed circuit breakers and protection systems, particularly to clear faults close to the generators. The incidence of three phase faults can be reduced by the use of metal clad switchgear, isolated phase bus ducting, single core cables, etc. Impedance earthing further reduces the severity of single phase to earth faults. Appropriate system design can therefore reduce the extent of system outages by provision of more automatic sectionalizing points, segregation of generation blocks onto separate busbars, etc.
System transient reactances should be kept as low as possible in order to improve transient stability. Machines (and associated generator transformers) with low reactance values may be more expensive but may provide a practical solution in a critical case. Such a solution is in conflict with the need to reduce fault levels to within equipment capabilities and a compromise is therefore often necessary.
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HV system voltage to be controlled HV system voltage to be controlled Transformer for systems above about 60 kV Filters Compensating capacitor Reactor Thyristors Transformer for systems above about 60 kV Filters Compensating capacitor Saturable reactor
Above: Fig. 15 Static compensators.
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A resonant link can, in principle, solve this conflicting requirement by having a low reactance under normal load conditions and a high reactance to fault currents. Fig. 15 shows the functionally different and more widely used static compensation equipment containing saturable reactors or thyristor controlled reactors. These devices can supply leading or lagging VArs to a system and thereby maintain nearly constant voltages at the point of connection in the system. For this reason they also have value in improving power quality. The characteristics of such devices are shown in Fig. 16. This constant voltage effect may be considered to represent a sort of inertialess infinite busbar and therefore the transfer reactance is reduced increasing the stability margin of the system. The disadvantages of such systems are their initial cost, need for maintenance, volume of equipment to be accommodated and generation of harmonics necessitating the use of filters.
3.8 Case Studies
3.8.1 Introduction
Fig. 17 shows a power transmission and distribution system feeding an industrial plant with its own on-site generation and double busbar arrangement. Normally the busbar coupler is open and grid infeed is via the non priority busbar No. 2. On-site generation and a major 5,000 hp induction motor are connected to busbar No. 1. Other smaller motor loads are connected to busbars 3, 4 and 5.
Above: Fig. 16 Characteristics of static compensators.
The computer data files represent the grid infeed as a generator with transient reactance equal to the short circuit reactance x0 d and a very large inertia constant of 100 MJ/MVA. The large induction motors connected to busbars 1 and 5 are represented in detail in order that slip and current variations during a disturbance may be studied. These motor load torque/speed characteristics are assumed to follow a square law. The two groups of smaller 415 V motors connected to busbars 3 and 4 are not to be studied in detail and are represented as constant kVA loads. On-site generator No. 1 is represented simply by its transient reactance and inertia constant and site conditions are assumed to allow full rated output during all case studies.
The results of the computer analysis associated with this system for Case studies 1_4 have been re-plotted in Figs. 18 to 21 to allow easy comparison.
Above: Fig. 17 Power system for case studies.
Above: Fig. 18 Transient stability analysis _ Case study 1.
3.8.2 Case Study 1
The system is operating as in Fig. 17 with industrial plant on-site generator No. 2 not connected. Generator No. 1 is delivering full power at near unity power factor. A three phase fault is imagined to occur on the 6.6 kV feeder to busbar 3 at point (F). The protection and circuit breaker are such that a total fault duration of 0.35 seconds is obtained. Clearance of the fault disconnects busbar 3 and its associated stepdown transformer from busbar 1 and all other loads are assumed to remain connected.
Fig. 18 shows the behavior of the generator and the main motors. In Fig. 18a, the rotor angle of generator 1 is seen to increase during the fault period. Shortly after fault clearance, a return towards the original operating load angle position is seen. The generator terminal voltage is also seen to recover towards prefault value. The on-site generator No. 1 is therefore stable to this particular fault condition.
Fig. 18b shows the behavior of the 5,000 hp induction motor load under these fault conditions. During the fault the slip increases. However, shortly after fault clearance the terminal voltage recovers and the slip reduces towards the prefault value. Similar behavior for motors 2 and 3 is shown in Fig. 18c. The main motor loads therefore seem to be able to operate under the fault condition; the smaller motor loads have not been studied.
The situation in this configuration is therefore stable and only one busbar is lost as a result of the fault.
3.8.3 Case Study 2
In this study it’s assumed that a decision has been made to use surplus industrial plant gas to generate more electrical power and thus reduce grid infeed tariffs. A 2.5 MVA generator No. 2 is added to busbar 1. This machine has a relatively low inertia constant compared to the existing on site generator No. 1. No changes are proposed to the existing protection or circuit breaker arrangements. Both site generators are supplying full load.
Fig. 19 shows the consequences of an identical fault at (F) under these new system conditions. Fig. 19a shows generator 1 to continue to be stable. Fig. 19b shows generator 2 has become unstable. The duration of the fault has caused generator 2 to lose synchronism with generator 1 and the grid infeed. The ensuing power surging is not shown in Fig. 19 but can be assumed to jeopardize the operation of the whole of the power system.
Acting as a consultant engineer to the industrial plant owner what action do you recommend after having carried out this analysis?
Above: Fig. 19 Transient stability analysis _ Case study 2.
1. Do you have anything to say about protection operating times for busbar 5 feeder or generator 2 breaker?
2. The client, not wishing to spend more money than absolutely necessary, queries the accuracy of your analysis. Generator 2 is a new machine and good manufacturer's data is available including AVR characteristics, saliency, saturation, damping and stator resistance. Would you consider a further study under these conditions with more accurate generator modeling? This study demonstrates the need to review plant transient stability whenever major extensions or changes are contemplated. In this example a solution could be found by decreasing protection and circuit breaker operating times.
Alternatively, if generator 2 has not already been purchased a unit with a similar inertia constant to generator 1 (if practicable) could be chosen.
3.8.4 Case Study 3
The system is as for study 1 _ i.e. generator 2 is not connected. Generator 1 is supplying full load at unity power factor and the grid infeed the balance of site demand. It’s now imagined that the grid infeed is lost due to protection operation.
The site electrical load now considerably exceeds the on-site generation capacity and a decline in frequency is expected. The mechanical driving power to generator 1 is assumed to remain constant. Stability in the sense of loss of synchronism is not relevant here since the two power sources are isolated by the 132 kV transmission line and 132/6.6 kV transformer disconnection.
Fig. 20a shows the predicted decline in plant system frequency. As the grid supply engineer in charge of this connection, you have been called by the plant manager to explain what precautions could be taken to prevent plant shut down under similar outage conditions in the future. You have some knowledge of protection systems, although you are not an expert in this field. You propose an under-frequency relay associated with the bus-coupler circuit breaker separating busbars 1 and 2. From the transient stability studies shown in Fig. 20a, you recommend an under-frequency relay setting of approximately 49.4 Hz. The hoped for effect of bus-coupler opening is for recovery in system frequency.
The plant manager considers that too much load will be shed by utilizing the bus coupler in this way, although he is thinking more about plant down times than system stability. Again as grid engineer you acknowledge the point and indeed you are worried that such a large load shed could leave generator 1 underloaded. Unless some adjustment is made to the generator 1 driving power an overfrequency situation could arise. With more thought what similar action to plant protection could be taken? In this example, the crude bus coupler protection allows motor 1 to recover successfully. Motors 2 and 3 connected to busbar 5 will decelerate to a standstill due to loss of supply as will all motors connected to busbar 4.
3.8.5 Case Study 4
Above: Fig. 20 Transient stability analysis _ Case study 3.
The system of Fig. 17 is originally operating without the 5,000 hp motor 1 or the second on-site generator 2 connected.
The result of direct-on-line (DOL) starting of motor 1 is shown in Fig. 21. Since the fault level is relatively high (the system is said to be 'stiff' or 'strong'), the induction motor starts with only slight disturbance to operating conditions. Fig. 21a shows only minor changes to generator 1 load angle (note sensitivity of the scale). The deflection is in the direction of decreasing rotor angle and indicates that the motor starting has initially acted to slow down generator 1 relative to the grid generation. There is, however, no instability since the rotor angle is seen to recover towards its original position.
As consultant to the plant manager are you able to confirm successful DOL starting and run up of motor 1?
Would you wish to place any provisos on your answer?
With fast electronic protection, together with vacuum or SF6 circuit breakers, would you consider fault durations reduced from some 0.35 to 0.175 seconds to be more representative of modern practice?
Above: Fig. 21 Transient stability analysis _ Case study 4.