Chapter 3 Iec 60909

Calculation Methodology This calculation is based on IEC 60909-0 (2001, c2002), "Short-circuit currents in three-phase a.c. systems - Part 0: Calculation of currents" and uses the impedance method (as opposed to the per-unit method). In this method, it is assumed that all short circuits are of negligible impedance (i.e. no arc impedance is allowed for). There are six general steps in the calculation:  Step 1: Construct the system model and collect the relevant equipment parameters  Step 2: Calculate the short circuit impedances for all of the relevant equipment  Step 3: Refer all impedances to the reference voltage  Step 4: Determine the Thévenin equivalent circuit at the fault location  Step 5: Calculate balanced three-phase short circuit currents  Step 6: Calculate single-phase to earth short circuit currents Step 1: Construct the System Model and Collect Equipment Parameters The first step is to construct a model of the system single line diagram, and then collect the relevant equipment parameters. The model of the single line diagram should show all of the major system buses, generation or network connection, transformers, fault limiters (e.g. reactors), large cable interconnections and large rotating loads (e.g. synchronous and asynchronous motors). The relevant equipment parameters to be collected are as follows:  Network feeders: fault capacity of the network (VA), X/R ratio of the network  Synchronous generators and motors: per-unit sub-transient reactance, rated generator capacity (VA), rated power factor (pu)  Transformers: transformer impedance voltage (%), rated transformer capacity (VA), rated current (A), total copper loss (W)

 

Cables: length of cable (m), resistance and reactance of cable ( ) Asynchronous motors: full load current (A), locked rotor current (A), rated power (W), full load power factor (pu), starting power factor (pu) Fault limiting reactors: reactor impedance voltage (%), rated current (A)

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Step 2: Calculate Equipment Short Circuit Impedances Using the collected parameters, each of the equipment item impedances can be calculated for later use in the motor starting calculations. Network Feeders Given the approximate fault level of the network feeder at the connection point (or point of common coupling), the impedance, resistance and reactance of the network feeder is calculated as follows: is reactance of the network feeder (Ω) is the nominal voltage at the connection point (Vac) is the fault level of the network feeder (VA) is a voltage factor which accounts for the maximum system voltage (1.05 for voltages 1kV)

is X/R ratio of the network feeder (pu) Where

is impedance of the network feeder (Ω)

is resistance of the network feeder (Ω)

Synchronous Generators and Motors The sub-transient reactance and resistance of a synchronous generator or motor (with voltage regulation) can be estimated by the following: is the per-unit sub-transient reactance of the generator (pu) is the nominal generator voltage (Vac) is the nominal system voltage (Vac) is the rated generator capacity (VA)

is the X/R ratio, typically 20 for Where (Ω)

is the sub-transient reactance of the generator

is the resistance of the generator (Ω) is a voltage correction factor - see IEC 60909-0 Clause 3.6.1 for more details (pu)

14.29 for

100MVA,

100MVA, and 6.67 for all generators

with nominal voltage 1kV is a voltage factor which accounts for the maximum system voltage (1.05 for voltages 1kV) is the power factor of the generator (pu)

For the negative sequence impedance, the quadrature axis sub-transient reactance place of the direct axis sub-transient reactance

can be applied in the above equation in

.

The zero-sequence impedances need to be derived from manufacturer data, though the voltage correction factor applies for solid neutral earthing systems (refer to IEC 60909-0 Clause 3.6.1).

also

Transformers The positive sequence impedance, resistance and reactance of two-winding distribution transformers can be calculated as follows: is the reactance of the transformer (Ω) is the impedance voltage of the transformer (pu) is the rated capacity of the transformer (VA) is the nominal voltage of the transformer at the high or low voltage side (Vac)

Where is the positive sequence impedance of the transformer (Ω)

is the rated current of the transformer at the high or low voltage side (I) is the total copper loss in the transformer windings (W)

is the resistance of the transformer (Ω) For the calculation of impedances for three-winding transformers, refer to IEC 60909-0 Clause 3.3.2. For network transformers (those that connect two separate networks at different voltages), an impedance correction factor must be applied (see IEC 609090 Clause 3.3.3). The negative sequence impedance is equal to positive sequence impedance calculated above. The zero sequence impedance needs to be derived from manufacturer data, but also depends on the winding connections and fault path available for zero-sequence current flow (e.g. different neutral earthing systems will affect zero-sequence impedance).

Cables Cable impedances are usually quoted by manufacturers in terms of Ohms per km. These need to be converted to Ohms based on the length of the cables: is the reactance of the cable {Ω) is the quoted resistance of the cable {Ω / km) is the quoted reactance of the cable {Ω / km) is the length of the cable {m) Where is the resistance of the cable {Ω) The negative sequence impedance is equal to positive sequence impedance calculated above. The zero sequence impedance needs to be derived from manufacturer data. In the absence of manufacturer data, zero sequence impedances can be derived from positive sequence impedances via a multiplication factor (as suggested by SKM Systems Analysis Inc) for magnetic cables:

Asynchronous Motors An asynchronous motor's impedance, resistance and reactance is calculated as follows: is reactance of the motor (Ω) is ratio of the locked rotor to full load current is the motor locked rotor current (A) is the motor nominal voltage (Vac) is the motor rated power (W) Where

is impedance of the motor (Ω)

is the motor full load power factor (pu)

is resistance of the motor (Ω)

is the motor starting power factor (pu) The negative sequence impedance is equal to positive sequence impedance calculated above. The zero sequence impedance needs to be derived from manufacturer data. Fault Limiting Reactors The impedance of fault limiting reactors is as follows (note that the resistance is neglected): is the impedance voltage of the reactor (pu) is the nominal voltage of the reactor (Vac) Where

is impedance of the reactor (Ω)

is the rated current of the reactor (A)

is reactance of the reactor(Ω) Positive, negative and zero sequence impedances are all equal (assuming geometric symmetry). Static Converters Static converters and converter-fed drivers (i.e. feeding rotating loads) should be considered for balanced three-phase short circuits. Per IEC 60909-0 Clause 3.9, static converters contribute to the initial and peak short circuit currents only, and contribute 3 times the rated current of the converter. An R/X ratio of 0.1 should be used for the short circuit impedance. Other Equipment Line capacitances, parallel admittances and non-rotating loads are generally neglected as per IEC 60909-0 Clause 3.10. Effects from series capacitors can also be neglected if voltage-limiting devices are connected in parallel.

Step 3: Referring Impedances Where there are multiple voltage levels, the equipment impedances calculated earlier need to be converted to a reference voltage (typically the voltage at the fault location) in order for them to be used in a single equivalent circuit. The winding ratio of a transformer can be calculated as follows: is the transformer nominal primary voltage (Vac) is the specified tap setting (%) Where

is the transformer winding ratio

is the transformer nominal secondary voltage at the principal tap (Vac) Using the winding ratio, impedances (as well as resistances and reactances) can be referred to the primary (HV) side of the transformer by the following relation: is the impedance at the secondary (LV) side (Ω) is the transformer winding ratio (pu) Where is the impedance referred to the primary (HV) side (Ω) Conversely, by re-arranging the equation above, impedances can be referred to the LV side:

Step 4: Determine Thévenin Equivalent Circuit at the Fault Location

The system model must first be simplified into an equivalent circuit as seen from the fault location, showing a voltage source and a set of complex impedances representing the power system equipment and load impedances (connected in series or parallel). The next step is to simplify the circuit into a Thévenin equivalent circuit, which is a circuit containing only a voltage source ( ) and an equivalent short circuit impedance ( ). This can be done using the standard formulae for series and parallel impedances, keeping in mind that the rules of complex arithmeticmust be used throughout. If unbalanced short circuits (e.g. single phase to earth fault) will be analysed, then a separate Thévenin equivalent circuit should be constructed for each of the positive, negative and zero sequence networks (i.e. finding (

,

and

).

Step 5: Calculate Balanced Three-Phase Short Circuit Currents The positive sequence impedance calculated in Step 4 represents the equivalent source impedance seen by a balanced three-phase short circuit at the fault location. Using this impedance, the following currents at different stages of the short circuit cycle can be computed: Initial Short Circuit Current The initial symmetrical short circuit current is calculated from IEC 60909-0 Equation 29, as follows:

Where is the initial symmetrical short circuit current (A) is the voltage factor that accounts for the maximum system voltage (1.05 for voltages 1kV) is the nominal system voltage at the fault location (V) is the equivalent positive sequence short circuit impedance (Ω) Peak Short Circuit Current IEC 60909-0 Section 4.3 offers three methods for calculating peak short circuit currents, but for the sake of simplicity, we will only focus on the X/R ratio at the fault location method. Using the real (R) and reactive (X) components of the equivalent positive sequence impedance

, we can calculate the X/R ratio at the fault location, i.e.

The peak short circuit current is then calculated as follows: (for non-meshed networks) or (for meshed networks - see clause 4.3.12b) Where

is the peak short circuit current (A)

is the initial symmetrical short circuit current (A) is a constant factor, Symmetrical Breaking Current The symmetrical breaking current is the short circuit current at the point of circuit breaker opening (usually somewhere between 20ms to 300ms). This is the current that the circuit breaker must be rated to interrupt and is typically used for breaker sizing. IEC 60909-0 Equation 74 suggests that the symmetrical breaking current for meshed networks can be conservatively estimated as follows:

Where

is the symmetrical breaking current (A)

is the initial symmetrical short circuit current (A) For close to generator faults, the symmetrical breaking current will be higher. More detailed calculations can be made for increased accuracy in IEC 60909, but this is left to the reader to explore.

DC Short Circuit Component The dc component of a short circuit can be calculated according to IEC 60909-0 Equation 64:

Where

is the dc component of the short circuit current (A) is the initial symmetrical short circuit current (A)

is the nominal system frequency (Hz) is the time (s) is the X/R ratio - see more below The X/R ratio is calculated as follows:

Where (Ω)

and

are the reactance and resistance, respectively, of the equivalent source impedance at the fault location

is a factor to account for the equivalent frequency of the fault. Per IEC 60909-0 Section 4.4, the following factors should be used based on the product of frequency and time (