Page 317 - Handbook of Electrical Engineering

FAULT CALCULATIONS AND STABILITY STUDIES 303

11.11.1.2 Steady state stability of an interconnected power system

As an example, consider two offshore platforms, each with its own generators and loads, operating
in synchronism through an interconnecting power cable of reactance X (as shown in Figure 11.14.
Assume the resistance of the interconnecting cable is zero.
In this situation it is desirable to keep both platform voltages close to their rated values, i.e.
1.0pu ± 0.05. A particular operating condition requires one of the generators on platform B to be
out of service for maintenance but the load still needs to be supplied.
This is achieved by operating an extra generator on platform A and transferring the surplus
power from A to B through the interconnecting cable X.
The value of X depends upon the route length and the maximum amount of power that is ever
likely to be continuously transferred under normal conditions (for example, it may be decided to size
the cable to handle the rated power output of one generator on one of the platforms).
The equation for the power transferred would be:

V s · V R
P = sin δ c
X
Where V s is the sending end voltage on Platform A
V R is the receiving end voltage on Platform B
δ c is the load angle across the cable reactance X.

A typical situation could be that the cable reactance X would be 0.2 pu, and 1.0 pu of its power
capability is being transferred. With V S and V R each about 1.0 pu then the load angle would be about
11.5 degrees. This represents a ‘tight’ coupling between the two platforms since the load angle is small
and considerable margin exists before the 90 degree limit of steady state stability is exceeded.
In order to even approach 90 degrees, considerable current would have to flow in the cable
(four to five times full-load power in this example). Therefore, a ‘tightly’ coupled system is unlikely
to become unstable in the steady state for normal and near-normal situations.
Problems can arise when a long cable or overhead line is rated for a relatively small amount
of power transfer, because its impedance will be relatively large. In this situation, the load angle will
be large and a small disturbance could bring about instability. Such a system may be described as
being ‘loosely’ coupled.

11.11.2 Transient Stability

This is a more complex subject since it is closely related to the dynamic behaviour of the generators,
prime-movers, motors, loads and the control systems used with these machines. The static elements
in an interconnected power system also have considerable effect on the transient responses of the
machines in the system.

In an interconnected power system there will be two or more synchronous machines (or groups
of machines). These machines will be coupled through their own internal reactances and through