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4. SHORT CIRCUIT ANALYSIS
4.1 Purpose
A short circuit analysis allows the engineer to determine the make and break fault levels in the system for both symmetrical and asymmetrical, low or high impedance faults. This in turn allows the correct determination of system component ratings; For example the fault rating capability of circuit breakers. A full analysis will allow investigation of protection requirements and any changes to the system that might be necessary in order to reduce fault levels.
4.2 Sample Study
4.2.1 Network Single-Line Diagram
The system described in Section 2 for the load flow case is now analyzed under fault conditions. Figures 1.1 and 1.2 detail the system single-line diagram, busbar and branch data.
4.2.2 Input Data
The main input data file created for the load flow case using positive sequence impedances is again required for the short circuit analysis. A second data file containing generator parameters is also now needed if not already available from the load flow case. Induction and synchronous motor contributions to the faults may also be considered in most commercially available computer system analysis programs and the creation of a motor data file is necessary for this purpose. In this example a 5 MVA, 0.85 power factor induction motor load is assumed to form part of the total 25 MW load at busbar C.
Zero sequence data is required for the simulation of faults involving ground or earth. The zero sequence data file is not necessary if only three phase symmetrical faults are being investigated. Guidance concerning the derivation of zero sequence impedances is given in Section 28. Sample zero sequence, generator and motor files for the network are given in Fig. 22.
Line zero sequence impedances are assumed to be three times the positive sequence impedance values. Transformer zero sequence impedances are taken as equal to positive sequence values in this example for the vector groups used. The generator earthing resistance appears in positive, negative and zero sequence impedance circuits for earth faults and is therefore represented as 333.46 ohms or 9.61 pu (100 MVA base, 6 kV).
4.2.3 Solutions
A summary short circuit report from a software program covering this example is given in Fig. 23. Three phase (3-PH), single phase to earth or line to earth (L-G), phase to phase (L-L) and two phase to earth (L-L-G) fault cur rents at each busbar are given together with busbar voltage and fault MVA.
More detailed short circuit busbar reports are also available from most pro grams and an example of such a report is given in Fig. 24 for busbar 5c.
The fault infeed contributions from the different branches, including the induction motor contribution, into the busbar are shown.
Above: Fig. 22 Fault analysis sample study. Zero sequence, generator and motor files (system single-line diagram as per Fig. 1).
(a) Zero-sequence data file (p.u., 100 MVA base) (b) Machine (generator) data file.
Above: Fig. 23 Fault analysis sample study. Summary short circuit report.
Above: Fig. 24 Fault analysis sample study. Detailed report for busbar 5c.
As in the load flow case the results can also be drawn up in a pictorial manner by placing the fault level results against each busbar on the associated single-line diagram. The effect of changes to the network can be seen simply by altering the input data. This is particularly useful when carrying out relay protection grading for the more complex networks. A variety of operational and outage conditions can make backup IDMT grading particularly difficult. The computer takes the drudgery out of the analysis. An example of computer aided protection grading is given in Section 10.
4.2.4 Asymmetrical Fault Levels
An interesting aspect of fault level analysis is that the three phase solid sym metrical type of fault does not always lead to the highest fault level currents.
For highly interconnected transmission systems the ratio of the zero phase sequence impedance (Z0) and positive phase sequence impedance (Z1) may be less than unity (i.e. (Z0)/(Z1)),1.)
The Zambian Copperbelt Power Company 66 kV transmission system stretches for about 150 km close to the border between Zambia and Zaire.
The major power generation infeed is from the hydroelectric power station at Kariba Dam some 450 km to the south via 330 kV overhead lines and 330/220 kV stepdown autotransformers located at 'Central' and 'Luano' substations. Consider the case of reinforcement works at the 66 kV 'Depot Road', which requires the use of additional 66 kV circuit breakers. Bulk oil breakers from the early 1950s were found in the stores with a fault rating of approximately 500 MVA. A fault analysis on the system showed that the three phase fault level on the 66 kV busbars at ' Depot Road' substation to be some 460 MVA while the two phase to earth fault level could be as high as 620 MVA. For a single phase to earth fault the fault current is given by:
IF 5 3E Z1 1Z2 1Z0
… where E is the source phase to neutral e.m.f. and Z1, Z2 and Z0 are the positive, negative and zero sequence impedances from source to fault. This indicates that the sequence networks for this type of fault are connected in series.
In this example Z0 is small because (i) the 66 kV overhead lines in the copperbelt area are very short; (ii) the 66/11 kV transformers are star-delta connected with the high voltage star point solidly earthed and (iii) the 330/ 220 kV and 220/66 kV transformers have a low zero sequence impedance.
The parallel effect of these low zero sequence impedances swamps the zero sequence impedance of the long overhead lines from the power source at Kariba making Z0 tend to a very small value.
Above: Fig. 25 Effect of network zero to positive sequence impedances
on system fault levels.
Because of this effect the old spare oil circuit breakers could not be used without further consideration of the financial aspects of purchasing new switchgear or fault limiting components. Fig. 25 shows a plot of fault current against the ratio of Z0 /Z1 for the different types of symmetrical and asymmetrical fault conditions and shows how the phase to earth and two phase to earth fault current levels maybe higher than the three phase sym metrical fault level if the zero sequence impedance is very low in relation to the positive sequence impedance.
4.2.5 Estimations for Further Studies
Above: Fig. 26 Simple radial network and system resistance, reactance and scalar impedance values.
(a) Simple radial network (load contribution to fault ignored) 3ø fault as shown on 11 kV busbar
(b) % Impedance and ohmic impedance network values
(c) Source to fault impedance values
Scaler vs vector impedance simplification gives -4% to resulting fault level
Reactance vs vector impedance simplification gives +1.3% to resulting fault level
Possibly the biggest single obstacle in fault calculations is obtaining reliable information on system constants. Equipment nameplate data and equipment test certificates are the best starting point followed by contacting the original manufacturers. However, checking the authenticity of information, particularly where old machines are concerned, can be quite fruitless. Some approximate constants are given in this guide as a guide and they may be used in the absence of specific information.
Longhand working of fault calculations is tedious. The principle employed is that of transforming the individual overhead line, generator, cable, transformer, etc., system impedances to a per unit or percentage impedance on a suitable MVA base. These impedances, irrespective of net work voltage, may then be added arithmetically in order to calculate the total impedance per phase from source to fault. Once this has been determined it’s only necessary to divide the value by the phase to neutral voltage to obtain the total three phase fault current. Consideration of even a small section of the system usually involves at least one delta_star conversion. Obviously hand calculation of earth fault currents involving sequence impedance net works is even more time consuming and hence the computer is the best option for all but the simplest system.
Sometimes it’s a knowledge of phase angle (e.g. in directional relay protection studies) that may be important. More usually, as is the case of circuit breaker ratings or stability of balance protection schemes, it’s the magnitude of the fault level which is of prime interest. Some assumptions may be made for hand calculations in order to simplify the work and avoid vector algebra with errors of approximately 610%. For example:
1. Treat all impedances as scalar quantities and manipulate arithmetically.
This will lead to an overestimation of source to fault impedance and hence an underestimation of fault current. This may be adequate when checking the minimum fault current available with suitable factors of safety for protection operation.
2. Ignore resistance and only take inductive reactance into account. This will lead to an underestimation of source to fault impedance and hence an overestimation of fault current. This may be satisfactory for circuit breaker rating and protection stability assessment where the results are pessimistic rather than optimistic.
3. Ignore the source impedance and assume a source with infinite MVA capability and zero impedance. This may be satisfactory for calculating fault levels well away from the source after several transformations. In this case the transformer reactance between source and fault will swamp the relatively low source impedance. Such an assumption would not be valid for an assessment of fault level near the source busbars.
4. Ignore small network impedances such as short lengths of cable between transformers and switchgear. This may be valid at high voltages but at low voltages of less than 1 kV the resistance of cables compared to the inductive reactance will be significant.
5. If exact earth resistivity measurements are unavailable use known data for the type of soils involved. Remember that the zero sequence impedance is proportional to the log of the square root of the resistivity and therefore wide variations in resistivity values won’t cause such large variations in zero sequence impedance approximations. For the calculation of new substation earth grids a soil resistivity survey should always be carried out.
Fig. 26 shows a simple radial network and system resistance, reactance
and scalar impedance values. The simplifications described above are taken
into account to derive the total vector impedance, the total reactance
and the total scalar impedance of the system components from source to
fault. The errors resulting from the use of reactance only or scalar impedance
compared to the more correct vector impedance are less than 10% in this
example.