Power System Impedance Diagram – A one-line diagram of a power system shows the main connections and arrangements of components. Any particular component may or may not be shown depending on the information required in a system study, e.g. circuit breakers need not be shown in a load flow study but are a must for a protection study. Power system networks are represented by one-line diagrams using suitable symbols for generators, motors, transformers and loads. It is a convenient practical way of network representation rather than drawing the actual three-phase diagram which may indeed be quite cumbersome and confusing for a practical size power network. Generator and transformer connections—star, delta, and neutral grounding are indicated by symbols drawn by the side of the representation of these elements. Circuit breakers are represented as rectangular blocks. Figure 4.5 shows the one-line diagram of a simple power system. The reactance data of the elements are given below the diagram.
Generator No. 1 : 30 MVA, 10.5 kV, X” =1.6 ohms
Generator No. 2 : 15 MVA, 6.6 kV, X” = 1.2 ohms
Generator No. 3 : 25 MVA, 6.6 kV, X” = 0.56 ohms
Transformer T1 (3 phase) : 15 MVA, 33/11 kV, X= 15.2 ohms per phase on high tension side Transformer T2 (3 phase): 15 MVA, 33/6.2 kV, X= 16 ohms per phase on high tension side Transmission line: 20.5 ohms/phase
Load A: 15 MW, 11 kV, 0.9 lagging power factor
Load B: 40 MW, 6.6 kV, 0.85 lagging power factor
Note: Generators are specified in three-phase MVA, line-to-line voltage and per phase reactance (equivalent star). Transformers are specified in three-phase MVA, line-to-line transformation ratio, and per phase (equivalent star) impedance on one side. Loads are specified in three-phase MW, line-to-line voltage and power factor.
The Power System Impedance Diagramm on single-phase basis for use under balanced operating conditions can be easily drawn from the one-line diagram. For the system of Fig. 4.5 the Power System Impedance Diagram is drawn in Fig. 4.6. Single-phase transformer equivalents are shown as ideal transformers with transformer impedances indicated on the appropriatee side. Magnetizing reactances of the transformers have been neglected. This is a fairly good approximation for most power system studies. The generators are represented as voltage sources with series resistance and inductive reactance (synchronous machine model will be discussed in Sec. 4.6). The transmission line is represented by a π-model (to be discussed in Chapter 5). Loads are assumed to be passive (not involving rotating machines) and are represented by resistance and inductive reactance in series. Neutral grounding impedances do not appear in the diagram as balanced conditions are assumed.
Three voltage levels (6.6, 11 and 33 kV) are present in this system. The analysis would proceed by transforming all voltages and impedances to any selected voltage level, say that of the transmission line (33 kV). The voltages of generators are transformed in the ratio of transformation and all impedances by the square of ratio of transformation. This is a very cumbersome procedure for a large network with several voltage levels. The per unit method discussed below is the most convenient for power system analysis