Electrical Power System Analysis

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Graphs are very useful in the several fields like engineering, physical and social, etc. Many applications of several electrical components such as machines and power system component characteristics are representing in a simple way in graph form and for analysis of electrical circuits also it plays very important role. For small circuit analysis based on nodal and meshed equation methods by using Kirchhoff’s law and Ohm’s law are sufficient. But for complex networks these methods are difficult and take more time for solving the equations. In this chapter brief discussions on graph theory and the applications of graph theory in power system networks are going to be presented in detail.

The various operation aspects of an electrical power system, the symmetrical steady state operation is the most important mode of operation. A knowledge of this mode of operation is essential to ensure supply of real and reactive powers demanded by various loads, with the frequency and the various bus voltages maintained within specified tolerances and with optimum economy. Study of this mode of operation is carried out to arrive at the most satisfactory layout at the planning stage and to maintain quality and economy of power supply while the systems is in operation

Per unit system leads to great simplification of three-phase network involving transformers. An impedance diagram drawn on a per unit basis does not require ideal transformers to be included in it. The per unit value of any quantity is defined as the ratio of that actual quantity to its base value. The ratio in per cent is 100 times the per unit. The per unit method has the advantage over the per cent method because the product of two quantities is expressed in per unit itself, but the product of two quantities expressed in per cent must be divided by 100 to obtain the result in per cent.

The analysis of balanced three phase system (i.e., voltages are equal in magnitude and displaced by 120° from each other) with balanced loads is relatively simple affair. But when the system is unbalanced, (i.e., unbalance may be done to unbalanced loads or with unbalanced termination like short circuit fault) we have to resort to the application of Kirchhoff’s laws which is very difficult. Analysis of such circuits is made simpler by a method known as “symmetrical components” first presented by Dr. C.L. Fortescue in 1918. It is a mathematical tool for solving problems on any unbalanced polyphase system.

In chapter 1, we discussed about graph theory and determination of network matrices by singular transformation and non-singular transformation. In this techniques, there are some disadvantages. The main drawback is, the network having large say some hundred number of buses and branches, these methods will take more time for determining the network matrices. The other method is direct inspection method is fast but if there is any mutual coupling between the elements this is not useful.

Under abnormal conditions in a power system such as a fault, an insulator flash over or lightning stroke to the transmission tower etc., high currents flow in the system depending on the nature and location of the fault. These currents are sensed through relays which take about half a cycle or so and with proper coordination of relays, faulty sections are isolated quickly by actuation of the proper circuit breaker in another 3 to 4 cycles.

Most of the faults that occur on the power system are unsymmetrical faults. The faults due to open of one or more conductors through breaks or the action of fuses is called series faults. And the other faults are shunt faults that may consist of short circuits occur as LG, LL, LLG may or may not contain impedance.

A power system consists of a number of synchronous machines operating in synchronism under all conditions. When the system is subjected to some form of disturbance, there is a tendency for the system to develop restoring force to bring it to a normal or stable condition. The ability of a system to reach a normal or stable condition after being disturbed is called stability.

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