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Power electronic control in electrical systems 83
A transmission system cannot be operated too close to the steady-state stability
limit, because there must be a margin to allow for disturbances. In determining an
appropriate margin, the concepts of transient and dynamic stability are useful.
Dynamic stability is concerned with the ability to recover normal operation following
a specified minor disturbance. Transient stability is concerned with the ability to
recover normal operation following a specified major disturbance.
2. Voltage profile. It is obvious that the correct voltage level must be maintained
within narrow limits at all levels in the network. Undervoltage degrades the perform-
ance of loads and causes overcurrent. Overvoltage is dangerous because of the risks
of flashover, insulation breakdown, and saturation of transformers. Most voltage
variations are caused by load changes, and particularly by the reactive components
of current flowing in the reactive components of the networkimpedances. If gen-
erators are close by, excitation levels can be used to keep the voltage constant; but
over long links the voltage variations are harder to control and may require reactive
compensation equipment.
Different techniques are used for controlling the voltage according to the under-
lying rate of change of voltage. Cyclic, diurnal load variation is gradual enough to be
compensated by excitation control or the timely switching in and out of capacitors
and reactors. But sudden overvoltages ± such as those resulting from disconnection of
loads, line switching operations, faults, and lightning ± require immediate suppression
by means of surge arrestors or sparkgaps. Between these extremes there are many
possibilities for controlled reactive compensation equipment operating over time
scales ranging from a few milliseconds to a few hours.
Table 3.1 is a matrix of methods for stability and voltage control, including a range
of reactive power compensators. Some of the compensator devices can serve several
functions, which makes the subject somewhat complicated. Table 3.2 lists some of the
main advantages and disadvantages of the different compensators.
3.2 Uncompensated lines
3.2.1 Voltage and current equations of a long, lossless
transmission line
Figure 3.1 shows one phase of a transmission line or cable with distributed induct-
ance l H/m and capacitance c F/m. The voltage and current phasors V(x)and I(x)
both obey the transmission line equation
2
d V 2 p
V where (r jol)(g joc) (3:1)
dx 2
and x is distance along the line. r is the resistance per unit length [ohm/m] in series
with l and g is the `shunt' conductance per unit length [S/m] in parallel with c. o is the
p
radian frequency 2pf .If r and g are both small, then jb where b o (lc) is the
p
wavenumber. The propagation velocity u 1/ (lc) is rather lower than the speed of
5
light (3 10 km/s) and b 2pf /u 2p/l where l u/f is the wavelength. For exam-
5
ple, at 50Hz l 3 10 /50 6000 km and b 1:047 10 3 rad/km 6:0 /100 km.
