Fault Level Calculation Using The MVA Method

Abstract: There are a lot of methods that can be used for short-circuit current calculation. One method was previously discussed here and is based on the guidelines presented in IEC 60909. This article deals with an alternative method for the short-circuit current calculation so-called the MVA method. This method is simple, quick, and easy to remember. It is also sufficiently accurate for engineers in practice for basic estimation of fault levels at any point in an electrical network.

Keywords: short-circuit current, the MVA method, calculation methods

Introduction

The determination of the level of short-circuit current at any point of an electrical network can be of interest because of several reasons, e.g.:

• design of electrical equipment (from the point of view of thermal and dynamic effects of short-circuit currents),
• control of circuit breakers switching capability,
• design of grounding systems and the associated determination of allowable touch-voltage, step-voltage and transferred voltage (for example in the low-voltage grid during earth-fault in the high-voltage grid),
• design and operation of protection devices,
• power system stability verification,
• control of voltage ratios during short-circuit and during the start-up of large asynchronous motors,
• calculation of induced voltage in telecommunication lines caused by high-voltage or extra-high-voltage networks,
• control of propagation and impact of upper harmonics in power system,
• assessment of overvoltage occurrence during line-to-ground faults.

In most practical applications, it is not necessary to know the exact time course of short-circuit currents. A simplified calculation is often sufficient. There are several methods for the calculation of short-circuit currents. These can be divided into numerical and numeric-graphical methods. Some of them are listed below:

Numerical-Graphical Methods

Short-Circuit Curves Method

This method can be used when the task is limited only to finding the short-circuit current at the short-circuit location. This method is popular because of its simplicity and relative accuracy. The method consists of the application of special curves that give the value of the a.c. component of the short-circuit current in any moment of the short-circuit fault,

Nomogram Method

This is a simple graphical method that consists of subtracting the necessary parameters of the electrical system elements (impedances) from the graphs that were pre-printed on the sheets, separately for each voltage level. The disadvantage of nomograms is their limited use only for radial networks and the fact that the method accuracy is directly dependent on the accuracy of reading from the graphs drawn.

Numerical Methods

Ohmic Method

Also known as the Impedance Method. The disadvantage of this method is it is cumbersome if the system under investigation contains several voltage levels,

Per-unit Method

This method is no better in terms of manual calculations than the previous method since it involves a number of relationships and bonds associated with reference values, which can often cause errors in the calculation procedure,

Superposition Method

This method is used very often but requires knowledge of steady-state conditions before the short-circuit occurrence, which reduces its applicability for general and fast calculations.

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The MVA method

The MVA method is an alternative to the earlier mentioned methods. It is based on a mathematical modification of the ohmic method. The first step of calculation procedure is to convert classic single-line diagram of the power network to an equivalent MVA diagram. The next steps are based on the simplification of an equivalent MVA diagram to one final value of MVA at the fault point (this represents short-circuit MVA at the fault point).

This method has the following simplifications:

• magnetizing currents and losses in the transformer core are neglected,
• power lines capacitance is neglected,
• all transformers have set nominal tap (0),
• internal voltage of all sources is equal to 1 (in per unit).

Advantages of this method are the following:

• no need to convert impedance from one voltage level to another,
• no need to select common MVA base,
• no need to consider transformer ratios,
• contains simple formulas for calculation (in comparison with other methods),
• information about pre-fault steady-state is not required,
• fast and easy to remember,
• sufficiently accurate,
• easy to determine the contribution from each branch to fault point,
• can be used for calculation of symmetrical and unsymmetrical faults, voltage drop during motor start-up, or steady-state.

Let’s consider following a simple 22kV electrical network according to Figure 1 (taken from [3]  and modified). Let us assume that the industrial power network is connected through the power line V1 and supplied from the 22 kV external distribution network. For sake of simplicity, we consider only one synchronous generator, TG, and one synchronous motor, SM1 in the industrial power network. The task is to find out the value of initial symmetrical three-phase short-circuit current at 6.6 kV busbar. 

As mentioned earlier, the first step is the calculation of the MVA level of each component and converting the single line diagram to its equivalent MVA diagram.

Calculation of MVA level of each element of the electrical network

22kV External distribution network

22kV Power Line (V1)

For overhead power lines, the short-circuit MVA can be calculated directly from the impedance in form Zv=R+jX, therefore we can write

22/6.6kV Transformer (T1)

An advantage of this method is that the short-circuit voltage of the transformer (percentage value of reactance) is given directly in relationship with the nominal apparent power of the transformer. The same is valid for motors and generators as well.

6.6kV Generator (TG)

6.6kV Motor (SM1)

The equivalent MVA diagram is shown in figure 2.

Now we can reduce the equivalent MVA diagram. For elements connected in series the equivalent value of initial symmetrical short-circuit power is equal to the sum of inverted MVA values of elements.

For example, the equivalent MVA at branch A (consisting of network feeder, transformer T1 and power line V1) is

For elements connected in parallel, the final value of initial symmetrical short-circuit power is equal to the sum of MVA values of elements.

The electrical network equivalent MVA can be obtained from the sum of three parallel branches A, B, and C.

The graphical representation of industrial power network reduction is shown in figure 3.

Finally, the initial symmetrical short-circuit current at the fault point can be calculated from the equivalent network MVA.

Comparison to IEC 60909

In order to validate the accuracy of the MVA Method, we will calculate the initial symmetrical short-circuit current at the fault point using the calculation method based on IEC 60909. For simplicity, resistance will be neglected.

22kV External Distribution Network

22kV Power Line (V1)

22/6.6kV Transformer (T1)

6.6kV Generator (TG)

6.6kV Motor (SM1)

The equivalent short-circuit impedance at the fault point is calculated to be

Calculating the short-circuit MVA,

Finally, the initial symmetrical short-circuit current at the fault point can be calculated from the equivalent network MVA.

Bonus

If the value of initial symmetrical short-circuit current  is known, the peak short-circuit current can be determined using

A comparison of the results between the two methods is shown in the following table. The results based on IEC 60909 calculation method will be used as a reference.

It can be seen that the MVA method gives results with sufficient accuracy.

Conclusion

The methods calculation short-circuit currents vary in complexity and the amount of effort put into. The MVA method is known to be simple, quick, and easy, and is sufficiently accurate for engineers in practice for basic estimation of fault levels at any point in an electrical network.

References

[1] Jaffari, H.: Fault Current Calculation. Power System Review: Module 6. Northeast Public Power Association, 2013.

[2] Lee Wai, M., Pang, J.M.: Electrical Fault Level Calculations Using the MVA Method. Dostupné na internete: < http://www.jmpangseah.com>

[3] Kakilli, A.: System Analysis with the MVA Method for Symmetrical Three-Phase Faults. TEM Journal, vol2 no1, 2013.

[4] Máslo, K., Novák, J., Doležal, J.: Analysis of short-circuit currents. In Symposium Elektroenergetika. Stará Lesná, Slovakia, 2001.

[5] Pauza, J.: Short-circuits in electrical networks. SNTL Prague, Czech Republic, 1970.

[6] Máslo, K. et al.: Control and stability of power system. ČEPS and Energy managers’ association. Prague, Czech Republic, 2013. ISBN 978-80-260-4461-1

[7] STN IEC 60909 – 0: Short-circuit currents in three-phase a.c. systems. Part 0: Calculation of currents. Valid from 1.10.2016.