Power system analysis software: Transient stability; Fast transients; Reliability

Transient stability

After a disturbance, due usually to a network fault, the synchronous machine's electrical loading changes and the machines speed up (under very light loading conditions they can slow down). Each machine will react differently depending on its proximity to the fault, its initial loading and its time constants. This means that the angular positions of the rotors relative to each other change. If any angle exceeds a certain threshold (usually between 100° and 140°) the machine will no longer be able to maintain synchronism.

This almost always results in its removal from service.

Early work on transient stability had concentrated on the reaction of one synchronous machine coupled to a very large system through a transmission line. The large system can be assumed to be infinite with respect to the single machine and hence can be modeled as a pure voltage source. The synchronous machine is modeled by the three phase windings of the stator plus windings on the rotor representing the field winding and the eddy current paths. These are resolved into two axes, one in line with the direct axis of the rotor and the other in line with the quadrature axis situated 90° (electrical) from the direct axis. The field winding is on the direct axis. Equations can be developed which determine the voltage in any winding depending on the current flows in all the other windings. A full set of differential equations can be produced, which allows the response of the machine to various electrical disturbances to be found. The variables must include rotor angle and rotor speed. The great disadvantage with this type of analysis is that the rotor position is constantly changing as it rotates. As most of the equations involve trigonometrical functions relating to stator and rotor windings, the matrices must be constantly re-evaluated.

In the most severe cases of network faults the results, once the DC transients decay, are balanced. Further, on removal of the fault, the network is considered to be balanced.

There is thus much computational effort involved in obtaining detailed information for each of the three phases, which is of little value to the power system engineer. By contrast, this type of analysis is very important to machine designers. However, programs have been written for multi-machine systems using this method.

Initially, transient stability programs all ran in the time domain. A set of differential equations is developed to describe the dynamic behavior of the synchronous machines.

All the machine equations are written in the direct and quadrature axes. The network is represented in the real and imaginary axes, similar to that used by the load flow and fault analysis programs.

Modern programs also look at the response of the system, not only to major disturbances but also to the build-up of oscillations due to small disturbances (such as asynchronous resonance) and poorly set control systems. In calculating the system response for these disturbances, very long time domain solutions are not suitable, so frequency domain models of the system were developed.

Fast transients

Transient stability program considers the dynamic response of the power system in the range of 1-10 Hz. There is however also a need to calculate the system's response to faster transients from switching ranges to the propagation of steep voltage and current waves traveling down transmission lines as a result of a lightning strike. To model these effects a very detailed model is required, e.g. all the stray capacitances and inductances need to be incorporated into the model.

Many of these programs are difficult to use and take a long time to solve. For this reason only short time periods are usually studied.

Reliability

Reliability of equipment is of constant concern to the operators of power systems. In the past, reliability was ensured by providing reserve equipment, either connected in parallel with other similar devices or which could be easily connected in the event of a failure.

However, providing reserve equipment to cater for all eventualities has become very costly as systems expand. Reliability of a system is governed by the reliability of all the parts and their configuration. Much work has been done on the determination of the reliability of power systems but work is still being done to comprehensively model power system components and integrate them into system reliability models. Much of the early work was focused on generation facilities. The reasons for this was that, first, more information was available about the generation; second, the geographical size of the problem was smaller; and, third, the emphasis of power systems was placed in generation. With the onset of deregulation (in the USA), distribution and customer requirements are considered paramount.

At the generation and transmission levels, the loss of load expectation and frequency and duration evaluation are prime reliability indicators. The usual method for evaluating reliability indicators at the distribution level, such as the average interruption ratio per customer per year, is an analytical approach based on a failure-mode assessment.