Power System Stability

Dynamics in Power Systems

There are a lot of different dynamical phenomena with different characteristics in a power system. The phenomena could be local, in which case they only involve a minor part of the system or a single component. But they can also involve interactions between different parts of the system that might be geographically far from each other. In many cases these system-wide interactions are initiated by a local disturbance causing e.g. an earth fault with subsequent change in network topology. In this compendium interactions and phenomena that involve many power system components, e.g. generators and loads, or parts of the system are dealt with. These interactions have in common that they can cause system instabilities that can lead to black outs in large parts of the system, i.e. to interruptions of power supply for many consumers. Dynamics can also be initiated by actions of different controllers or by switchings of lines or other components by system operators. Such “disturbances” should be regarded as normal and should consequently not endanger the stability of the system.

Classification of Dynamics

 Dynamic phenomena in power systems are usually classified as 

1. Electro-magnetic transients (100 Hz – MHz) 

2. Electro-mechanical swings (rotor swings in synchronous machines) (0.1 – 3 Hz) 

3. Non-electric dynamics, e.g. mechanical phenomena and thermodynamics (up to tens of Hz) Approximate values of typical frequencies are given in brackets. One single initial event in the power system can give rise to dynamics in all the three groups above. A lightning stroke in a power line can induce so high over-voltages that the insulation fails, causing an earth fault. The earth fault can cause rotor swings in synchronous machines with high amplitudes. This can trigger protections to disconnect generators, so that an unbalance between produced and consumed power in the system arises. The frequency in the system drops and generators participating in the frequency control compensate this by increasing their power outputs. Thus the initial lightning stroke has initiated dynamics in all the three groups above. Another way to classify dynamic phenomena is given fig. This classification is based on the time scale of the phenomenon and the (mathematical) models used in analysis.

Dynamic phenomena in a power system. In the figure approximate time scales are given and types of mathematical models used. The different groups are called: 

A. Electro-magnetic transients. 

B. Synchronous machine dynamics.

C. Quasi steady state phenomena D. Steady state phenomena.                 

Modelling

It is of course almost impossible to develop models that can describe all dynamics in a power system and still being of practical use. Often one has to utilise a model that captures correctly the specific dynamic phenomenon or interaction that is the aim of the particular investigation. Depending on the purpose of the study the appropriate model of a given power system component could vary significantly. It is obvious that if the aim is to study relatively slow power oscillations between generators in the system, completely different models are required as compared with if one wants to analyse the influence of lightning impulses in the windings of the synchronous machine. Even if it were theoretically possible to develop a complete model of all the dynamics in the power system, it is questionable if such a model would be particularly useful. Firstly, such a model would require an enormous amount of parameter data to be uniquely specified. Secondly, the results obtained from such a model would be very hard to analyse and interpret. Critical review and understanding of obtained results is a necessary prerequisite for sound engineering. When making simulations and computations, which all are done with the help of computers nowadays in system sciences, it is important to have an expectation of what are reasonable outputs. Thus trivial errors due to wrong input data files, mistakes in modelling, etc. can be eliminated to a large extent. The human factor is of utmost importance in computer-based analysis and simulation. Models can in principle be erroneous in two different ways. Firstly, it can have the wrong structure. It can be too simple overlooking important interactions and processes or modelling them incorrectly. This is of course very serious and might give rise to detrimental consequences. But it is also very serious if wrong parameter data is used in a model of the correct structure. This latter shortcoming occurs not seldom in technical systems, which might look surprising at first sight. Since technical systems are man made, one should in principle have access to all design parameters defining the system. But it turns out that many parameters, e.g. the gain in the controller, could easily be changed after the system has been commissioned and such changes are not always reported to system analysts. It is obvious that the consequences could be very serious. In technical systems there are of course parameters that are “genuinely” unknown, e.g. the ground resistivity under a power line. In a large system like a power system, thousands of parameters are needed to define the system completely. It is a very difficult, but also very important, task to maintain and keep the data bases where all these parameter values are stored and updated. This is now a special activity usually referred to as data engineering. In this compendium models needed for the problems to be analysed are developed. Due to space limitations more detailed and elaborate derivation cannot be presented, but the reader is advised to consult other sources.