A complete diagram of power system representing all the three phases becomes too complicated and cumbersome for a system of practical size, so much so that it may no longer convey the information it is intended to convey. It is much more practical to represent a power system by means of simple symbols for each component resulting in what is called a single line diagram.
Single Line Diagram of a Power System:
The single line diagram of a power system network shows the main connections and arrangements of the system components along with their data (such as output rating, voltage, resistance and reactance etc.). In case of transmission lines sometimes the conductor size and spacings are given.
It is not necessary to show all the components of the system on a single line diagram, e.g., circuit breakers need not be shown in a load flow study but are must for a protection study. In a single line diagram, the system components are usually drawn in the form of their symbols.
Generators and transformer connections—star; delta and neutral earthling are indicated by symbols drawn by the side of the representation of these elements. Circuit breakers are represented by rectangular blocks. Fig. 2.7 represents the single line diagram of a typical power system.
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The ratings of generator, motor and transformers are given in the diagram below:
Impedance Diagram Representation of a Power System:
A further simplification from the single line diagram, with its symbols for the various components, is to draw the diagram with impedances only.
The impedance diagram of the power system of Fig. 2.7 is shown in Fig. 2.8:
In impedance diagram, each component is represented by its equivalent circuit, e.g., the synchronous generator at the generating station by a voltage source in series with a resistance and reactance, the transformer by its equivalent circuit and the transmission line by nominal π-equivalent circuit. Loads are assumed to be passive (not involving rotating machines) and are represented by resistance and inductive reactance in series. Neutral earthling impedances do not appear in the diagram as balanced conditions are assumed.
The impedance diagram shown in Fig. 2.8 is known as positive sequence diagram since it is drawn for a balanced 3-phase system. Still another possibility would be to use three separate diagrams to represent the positive, negative and zero sequence networks separately. These three separate impedance diagrams are used in short circuit studies of unsymmetrical faults.
Reactance Diagram Representation of a Power System:
The impedance diagram can further be simplified by making certain assumptions and reduced to simplified reactance diagram. Reactance diagram is drawn by neglecting effective resistance of generator armature, transformer winding resistance, transmission line resistance, line charging and the magnetizing circuit of transformers.
Reactance diagram of power system of Fig. 2.7 is shown in Fig. 2.9:
Assumptions made for drawing reactance diagram give results quite accurate for many power system studies, such as short circuit studies etc., as winding resistances including the line resistances are quite small in comparison with leakage reactance and shunt path which includes line charging and transformer magnetizing circuit provide a very high parallel impedance with fault.
In general it is to be noted that if the resistance is less than one-third of the reactance, and resistance is ignored, the error introduced will not be more than 5%. If, however, the resistance is of the order of one-half that of reactance and resistance is ignored errors up to 12% may be introduced. By “errors” it is meant that calculations will result in values higher than is actually the case being obtained and in some cases, lead to the purchase of protective gear with a higher rating than required.