reading / British practice / Vol D - 1990 (ocr) ELECTRICAL SYSTEM & EQUIPMENT

The impedance values of system components used in fault level studies are biased by applying a negative tolerance during initial stages of design. This allows

expected true values. Once plant is manufactured, impedance values are measured and these measured

,alues without tolerance are entered as program data. A list of data which can be processed in load flow

analysis has been given earlier.

data required for fault level studies is given below:

Circuit data

Zero sequence resistance

Zero sequence reactance

Generator data

Armature resistance

Direct axis synchronous reactance Zero sequence resistance

Zero sequence reactance Direct axis transient reactance

Direct axis subtransient reactance

Direct axis transient open-circuit (or short-circuit) ti me constant

Direct axis subtransient open-circuit (or short-circuit) ti me constant

Program run control data

System base (MVA)

Fault time

System frequency

3.3 Stability analysis

3.3.1Introduction

General

Stability analysis is used to prove that a power system is able to withstand the effects of credible faults. This means that when faulty equipment has been disconnected from the power system, frequency and voltage will return to near their pre-fault values on the remaining healthy part of the system within a few seconds, and generators, motors and static plant will continue to operate normally (i.e., as prior to the fault).

The capability of a power system to withstand the effects of a fault depends on:

(a)The severity of the fault, i.e., its type, voltage and duration.

(b)The configuration of the system itself.

(C)The robustness (in an electrical sense) of plant within the system.

Items (b) and (c) can be illustrated by considering a basic AC power system consisting of two generators,

two transmission circuits and two busbars/demand supply points loaded as in Fig 2.84.

200Mw

00.0

FIG. 2.84 Basic AC power system for stability analysis

The results of a load flow calculation on the above system are given in Fig 2.85, and a full list of the load flow analysis results on Fig 2.86. The generator at Bus 2 has to provide 321 MVAr to maintain Bus 2 voltage at 0.99 per-unit. At Bus 1, generator 1 provides the remainder of the system load plus system power losses, in total 608 MW. It also provides 161 MVAr to maintain Bus 1 voltage at 1.02 per-unit. Each line has a loss of 4 MW and 41 MVAr. Bus 2 voltage angle is 11.5 ° behind Bus 1.

Suppose one of the transmission circuits is switched out. The system will settle to a new operating state. This is shown in Fig 2.87 and a full list of the load flow analysis results on data sheet Fig 2.88. The system demand remains the same but the results show that the generation requirements have changed significantly. The generator at Bus 2 now has to provide 397 MVAr to maintain Bus 2 voltage at 0.99 per-unit. At Bus 1, generator 1 provides 617 MW and 176 MVAr. The line loss is 17 MW and 173 MVAr. Bus 2 voltage angle is 23.9 ° behind Bus 1. A consumer taking supplies from Bus 1 or Bus 2 would be unaware of the location of the generators supplying his power, or what transmission circuits are in service. He would not know whether he was being supplied from the system shown in Fig 2.85 or from the system shown in Fig 2.87 because, in both cases, his supply voltage and frequency are the same. However, it has already been shown that there are important differences between the two networks.

in Fig 2.85, when a transmission line is switched out, the power transfer between Bus 1 and Bus 2 is maintained by the second transmission line. There is an increase in VAr generation on both generators; this is required to maintain the voltage levels at Bus I and Bus 2 at 1.02 per-unit and 0.99 per-unit, respectively, with the increased transmission circuit VAr loss.

A small increase in watt generation is also required to supply the increased transmission circuit real power loss. The busbar phase angles move further apart but the consumer sees no change.

In Fig 2.87, there is only one transmission circuit between Bus 1 and Bus 2. If this is switched out, there is no interconnection between the two buses. At Bus 1, prior to switching out the transmission circuit, generation exceeds demand. Provided governor and automatic voltage regulator action is effective in reducing generator I output to match consumer demand at Bus

, 200 MW + 100 MVAr, and maintain voltage and frequency at pre-switching values, consumers' supplies will be unaffected. At Bus 2, only if the generator can produce 1000 MW and 300 MVAr is it possible to continue to supply full consumer demand.

For this reason, the system shown in Fig 2.87 is less secure than the system shown in Fig 2.85. This weakness manifests itself in another way. If both systems are subjected to the same disturbance or fault, we find that the stronger system shown in Fig 2.85 has better post-fault recovery characteristics. This is illustrated in Fig 2.89 and Fig 2.90, which show voltage recovery following a three phase fault at Bus I cleared in 0.12 s. Figure 2.89 shows voltage recovery with two transmission circuits in service and Fig 2.90 with one. Note that in the period of time from 0.3 to 0.6 s, the period following fault clearance, voltages in Fig 2.89 are significantly higher than those in Fig 2.90. Figure 2.91 shows the rotor angles of the generators with two transmission circuits in service and Fig 2.92 with one. The oscillations in Fig 2.91 are smaller in magnitude than those in Fig 2.92. Both characteristics point to the system shown in Fig 2.85 as being better able to withstand faults and other system disturbances.

We have seen that disturbances, when they occur, affect a power system by changing its voltage levels and voltage angles. Power flows between the synchronous generators, and this usually restores a system to a steady operating state. In a strong stable system, a steady operating state is restored quickly, the synchronous machines initially oscillate about their new stable positions within the power system and their oscillations are rapidly damped out.

A weak power system, although initially stable, may be made unstable by a large disturbance. Here, the initial power transfers between the synchronous generators are insufficient to restore a steady operating state. The generators are no longer cohesive in an electrical sense; voltages vary widely and may change rapidly from small to high values.

System transients and disturbances

The fastest significant disturbances on power systems are caused by switching operations. Travelling voltage waves result: these are reflected from circuit terminations or circuit impedance changes, for example, where a line is connected to a transformer. These super-

imposed waves may lead to overvoltages. The time for such disturbances is a few milliseconds. Due to their short duration, they do not affect power system stability, except when they cause short-circuits.

Short-circuit disturbances usually last up to about 0.15 s and are limited by protection detection and operating time, and by circuit-breaker fault clearance ti me. They result from a variety of causes, such as, the overvoltages described above, human error (e.g., not removing earths from equipment after maintenance), pollution of line insulator surfaces, or mechanical causes (e.g., accidental damage to a buried cable during site excavation). One, two or three phases may be affected and voltage is depressed to some degree throughout the electrical power system. At generator terminals, this reduction in voltage causes an imbalance between power output and input. This is because mechanical power input remains constant until changed by governor action, while the electrical power output (V3 VI cos) changes as V changes and approaches zero as V nears zero. The reduction in voltage also causes a reduction in the transmission capacity of lines because the maximum power transmitted is proportional to the voltage. Further, induction motors may be unable to draw sufficient electrical power input to match their mechanical power output, and slow down. The fault current will probably be high and may cause thermal and mechanical damage to plant.

Often related to short-circuit disturbances, but longer in timescale, are disturbances involving mechanical oscillations of synchronous machine rotors. They occur as a result of system faults, being severe when the faulted equipment is not disconnected quickly, and also occur when system switching causes a major redistribution of power flows. If these disturbances are not contained, i.e., the mechanical oscillations are allowed to increase, a major power system breakdown will occur. The power system is referred to as 'unstable'. Generators will poleslip, voltage will fluctuate from zero to high levels, and distance protection operates to disconnect transmission lines. Induction motors within power station electrical systems may be unable to sustain their mechanical loads, leading to substantial loss of generation output.

Minimising power system instability

Obviously a power system designer seeks to minimise the possibility of power system instability. For this, he requires primarily:

•Generators able to provide and absorb substantial synchronising power, i.e., having low transient reactance.

•Generators with high inertia.

•Power transmission and distribution networks matched to demand requirements.

•Fast acting protection and switching to disconnect faulty plant.

•Fast acting generator automatic voltage regulators.

•Fast acting generator governors and valving.

•Automatic switching to restore transmission lines after transient faults.

•Automatic load disconnection schemes to back-up the above.

Power flows in large systems

Basic theory tells us power will only flow along a transmission line when there is a voltage difference between the ends of the line. On AC systems, voltage is measured in both magnitude and phase angle.

On the British supergrid and other large power systems the resistance of transmission lines is much

less than the reactance. Transformer resistance is also much less than reactance. This means that the difference

in phase angle between line ends, not the difference between voltage moduli, is dominant in determining the watt flow on a transmission line. This is illustrated

in Fig 2.93.

Similarly, the difference in absolute value of voltage between line ends, not the difference between phase angles, is dominant in determining the VAr flow on a

transmission line.

Suppose a transmission circuit has a nominal X:R ratio of 10:1, and the voltage at the sending end of the circuit (V,) is equal in magnitude to the voltage at the receiving end of the circuit (V,), and V, leads V, by an angle 45° .

Then the voltage difference between the circuit ends IS V s V r , and the circuit current I, will lag behind the voltage difference by an angle determined by the X:R ratio of the circuit; here, the angle is tan - I 10 =

Power system performance analysis

84.3 ° . This is shown in Fig 2.93 (a), note the relative positions of vectors V s , I and V i..

Now let the angle 6 be increased by 50%, but the magnitude of V, and V r remain unchanged. This is shown in Fig 2.93 (b). V, - V r increases by nearly 50% and, in consequence, the circuit current I increases by nearly 50%. [ maintains its position between V, and V r ; at the sending end I lags behind V 5 , i.e., power is being exported at a lagging power factor, and at the receiving end of the circuit I is leading V r , i.e., power is being imported at a leading power factor.

Now let V, on Fig 2.93 (a) be increased by 5% and (5 remain unchanged (Fig 2.93 (c)). The position of vector V s - V. is now changed and consequently I changes its position too. V, and V both now lead I and it can be seen that increasing V s has changed the VAr flow on the circuit with only a corresponding minor change in watt flow.

In practice, the British supergrid voltage is maintained close to 400 kV or 275 kV throughout the network but, when power transfers are high, there will be considerable differences in voltage angles between busbars. A maximum difference of 40 ° between the extremes of the network would not be unusual.

3.3.2 Analytical and programming considerations

General

In mathematical terms, power system stability analysis is the progressive solution of sets of non-linear differential equations. The computation requirements are much greater than for load flow or fault analysis, hence efficient solution methods and data input/output routines are very desirable.

Consider the basic operation of a turbine-generator. In its steady state, the mechanical power input is balanced by its electrical power output plus losses, and the generator runs at constant synchronous speed. If a difference exists (say the mechanical input exceeds the electrical output plus losses), the surplus energy is used to change the kinetic energy of the turbine-generator rotor, and to overcome damping torque developed in the damper windings of the generator. (Damper windings are fitted to absorb cyclic disturbing torques.)

Unless the energy change is very slow, the equations used in the load flow solution can no longer be used. Let the voltage at the terminals of a generator be reduced due to, say, a short-circuit fault on the system. This means the stator currents will change. This current change is much greater than that brought about by a gradual change in voltage. It is computed using the generator transient and subtransient reactances, while the slower changes are computed using the generator synchronous reactance.

To compute these changes, assumptions are made that the generator can be represented by EMEs behind synchronous, transient and subtransient reactances. Transient and subtransient time constants are then used to link the reactance effects.

Various methods exist to solve the coupled non-linear differential equations. An approach often used, is to linearise the equations over a very small range and to compute the machine voltage angles in this way over a small time increment. This time increment, or step length, can be made as small as required, but obviously an unnecessarily small step length increases the number of calculations, increasing the cost of computation and the time taken. It is vital to predict post-fault rotor swings accurately. The success of this depends on the accuracy of the model used and the accuracy of the data entered into the program.

The speed of movement of individual generator rotors relative to each other is usually very small compared with their basic 50 Hz angular velocity. For this reason, static components of the power system (transmission lines, cable circuits and transformers) are modelled with constant 50 Hz characteristics. Some programs are, however, designed to accommodate changes in system frequency by recalculating component parameters, where they are frequency dependent.

Machine controllers (governors and AVRs)

There are many types of controller in use. It is not necessary to model controller actions in load flow and most fault level studies because controller action does not influence the solution.

For transient stability calculations, it is essential to model the behaviour of machine controllers accurately and include them in the simulation because these controllers have a strong influence in this case.

An IEEE committee [13] set up to standardise computer representation of excitation.- systems, produced

reports setting out general representations of the AVRs then in use. Two of these models are reproduced in Figs 2.94 (a) and (b). These models are usually available in transient stability programs and are used extensively. Figure 2.95 shows a simple rate and position limited integrator controller used to simulate automatic voltage regulators. It is used in several analysis programs developed by the CEGB.

A composite steam/hydro governor model is shown in Fig 2.96. This simple model is adequate only if the functions it represents are dominant in the timescale considered. Other more complex models are available which simulate boiler/turbine reheat cycles and the associated valving. The data requirements for these more complex models are given later.

The analyst will always wish to use a standard model for his analysis if he can. However, because modern controller design varies so much it is often difficult to match the characteristics of a particular controller to those of a standard model. To overcome this, generalised methods of modelling controllers have been developed, both inside and outside the CEGB. The controller under consideration is modelled in termr of its block diagram. It is then used with synchronous machines in transient stability studies. Facilities also exist in some programs to test the controller by itself in open loop simulation. The elements used to form a controller are of two types. The first type, operational elements, contain the integral operator S. and are phase lag, differential lag, lead-lag and quadratic lag. The second type, non-linear elements, include limiters, deadbands, saturation functions, switches, adders, junctions and user defined functions. Inputs to controllers can be taken from any point in the system under consideration but usually are in the form of electrical power, frequency, terminal voltage, a reference (set according to initial conditions) and a constant value. Output from the controller can be fed to any point in the system, but usually is set to mechanical power for a governor and to field voltage for an automatic voltage regulator.

Data requirements

The data which can be processed for load flow and fault level analysis have been listed earlier. Additional data which may be processed for transient stability analysis are given below. Some data are essential, e.g., generator inertia, motor inertia:

Circuit data

Any specified switching operation

Generator data Inertia

Damping factor Potier reactance

Saturation factor

Quadrature axis synchronous reactance

INPUT FILTE

AVR mode). IEEE Type 1

INPUT FILTER

V

E,

E.

STABILISER

, b) AVR model, IEEE Type 2

INPUT FILTER TIME CONSTANT

•FORWARD GAIN

FORWARD GAIN TIME CONSTANT

MAXIMUM REGULATOR VOLTAGE LIMIT MINIMUM REGULATOR VOLTAGE LIMIT

•EXCITER CONSTANT EXCITER TIME CONSTANT

EXCITER SATURATION FUNCTION

V.MACHINE TERMINAL VOLTAGE