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Friday, 9 January 2015

Single-Line diagram representation of a Power System

The complete circuit diagram for a 3-phase power system is rarely used to represent and convey the information about the system. 


"It is much more practical to represent a power system by means of simple symbols for each component resulting in the so called single-line diagram."

A balanced 3-phase system is studied on per phase basis. It is always solved as a single-phase circuit consisting of one of the three lines and a neutral return. The loop impedance of a single phase circuit is supposed to be concentrated in one conductor only with the impedance of the return conductor assumed to be zero. Hence the transmission line is represented by a single line and the main components such as generators, transformers, motors etc are indicated by standard symbols. Such as simplified diagram of an electric power system is called single-line diagram

Thus a 3-phase balanced system is effectively replaced by a single line or one line diagram.

Purpose of single-line diagram:

The purpose of single-line diagram is to provide the important information about the power system. The importance of different features of a system varies with the problem under consideration. Any particular component may or may not be shown in a single-line diagram depending on the information required in a system study. 

For instance, the line diagram for load flow studies may not include circuit breakers. On the other hand, in stability studies position of circuit breakers and relays are of extreme importance. In a short circuit studies, three separate diagrams to represent positive, negative and zero sequence networks are shown.

In single-line diagrams, the connection of generators and transformers (star /delta connection, neutral grounding etc) are indicated by symbols drawn by the side of the representation of these elements. Generators and transformers are specified in 3-phase MVA, line to line voltage and per phase reactance (or impedance in case of transformer). Loads are specified in 3-phase MW, line to line voltage and power factor.

Impedance and reactance diagram:

To compute the performance of a power system under load conditions or during short circuits, the single-line diagram must be converted into an impedance diagram. 

In an impedance diagram, the equivalent circuit of the transmission line is represented by 'nominal pi' model with the total resistance and inductive reactance of the line in series and the total capacitance to neutral divided between its parallel arms at the two ends. The generators are represented as voltage source with appropriate values of series resistance and reactance. 

Loads are assumed to be passive and are shown by resistance and inductive reactance in series. Since the magnetizing current of a transformer is usually very small when compared to its full load current, the magnetizing circuit is usually omitted in the equivalent circuit of a transformer.

The impedance diagram can be further simplified by making certain assumptions. The inductive reactance of a system is much larger than its resistance. Hence, in many power system studies the resistance of generator and transformer winding, resistance of transmission lines, line charging and magnetizing circuits of transformers are neglected. Loads which do not contain rotating machines have negligible effect on the total line current during a fault and are normally omitted. However, synchronous motor loads are always included in fault calculations as their generated emfs contribute to the short circuit current.         


To simplify the calculations, if all the static loads, all resistances, the magnetizing circuit of each transformer and the capacitance of the transmission line are omitted, the impedance diagram becomes the reactance diagram

These simplifications apply to fault calculations only and not to load flow studies. The impedance and reactance diagrams are also called as positive sequence diagrams since they show impedance to balanced currents in a symmetrical 3-phase system.