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, generat
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:
ult capacity of the network (VA), X/R ratio of the network
Synchronous generators and motors: per-unit sub-transient reactance, rated generator capacity (VA), Transformers: transformer impedance voltage (%), rated transformer capaci
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)
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
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:
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| 53 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
em 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
ult capacity of the network (VA), X/R ratio of the network
transient reactance, rated generator capacity (VA), Transformers: transformer impedance voltage (%), rated transformer capacity (VA), rated current (A),
)
Asynchronous motors: full load current (A), locked rotor current (A), rated power (W), full load power
Using the collected parameters, each of the equipment item impedances can be calculated for later use in the
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:
Where is impedance of the network feeder ( is resistance of the network feeder (
is reactance of the network feeder (
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 maxi
>1kV)
is X/R ratio of the network feeder (pu) 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:
Where is the sub-transient reactance of the generator ( is the resistance of the generator (
is a voltage correction factor
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)
of the network feeder (Ω) is resistance of the network feeder (Ω)
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, 1.1 for voltages
is X/R ratio of the network feeder (pu) Synchronous Generators and Motors
transient reactance and resistance of a synchronous generator or motor (with voltage regulation) can be
transient reactance of the generator (Ω) is the resistance of the generator (Ω)
is a voltage correction factor - see IEC 60909-0 Clause 3.6.1 for more details (pu) transient reactance of the generator (pu)
is the nominal generator voltage (Vac) ltage (Vac) is the rated generator capacity (VA)
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| 54
mum system voltage (1.05 for voltages <1kV, 1.1 for voltages
transient reactance and resistance of a synchronous generator or motor (with voltage regulation) can be
0 Clause 3.6.1 for more details (pu)
is the X/R ra o, typically 20 for 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 above equation in place of the direct axis sub
The zero-sequence impedances need to be derived from manufacturer data; though the voltage correction factor also applies for solid neutral earthing systems (refer to IEC 60909
Transformers
The positive sequence impedance, resistance and reactance o calculated as follows:
Where is the positive sequence impedance of the transformer ( is the resistance of the transformer (
is the reactance of the transformer (
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 sid 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 X/R ra o, typically 20 for 100MVA, 14.29 for 100MVA, and 6.67 for all generators with
is a voltage factor which accounts for the maximum system voltage (1.05 for voltages <
is the power factor of the generator (pu)
For the negative sequence impedance, the quadrature axis sub-transient reactance above equation in place of the direct axis sub-transient reactance .
uence impedances need to be derived from manufacturer data; though the voltage correction factor also applies for solid neutral earthing systems (refer to IEC 60909-0 Clause 3.6.1).
The positive sequence impedance, resistance and reactance of two-winding distribution transformers can be
is the positive sequence impedance of the transformer (Ω) is the resistance of the transformer (Ω)
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) 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)
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| 55 100MVA, and 6.67 for all generators with
is a voltage factor which accounts for the maximum system voltage (1.05 for voltages <1kV, 1.1 for voltages
can be applied in the
uence impedances need to be derived from manufacturer data; though the voltage correction factor 0 Clause 3.6.1).
winding distribution transformers can be
e (Vac)
For the calculation of impedances for three
network transformers (those that connect two separate networks at different voltages), an impedance correction factor must be applied (see IEC 60909
The negative sequence impedance is equal to positive sequence impedance calculated above. The zer
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
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:
Where is the resistance of the cable { is the reactance of the cable { is the quoted resistance of the cable { is the quoted reactance of the cable { is the length of the cable {m)
The negative sequence impedance is equal to positive sequence impedance calculated above. T
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:
For the calculation of impedances for three-winding transformers, refer to IEC 60909
transformers (those that connect two separate networks at different voltages), an impedance correction factor must be applied (see IEC 60909-0 Clause 3.3.3).
The negative sequence impedance is equal to positive sequence impedance calculated above. The zer
impedance needs to be derived from manufacturer data, but also depends on the winding connections and fault sequence current flow (e.g. different neutral earthing systems will affect zero
e 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 resistance of the cable {Ω) 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)
The negative sequence impedance is equal to positive sequence impedance calculated above. T
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
magnetic cables:
An asynchronous motor's impedance, resistance and reactance is calculated as follows:
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| 56 winding transformers, refer to IEC 60909-0 Clause 3.3.2. For
transformers (those that connect two separate networks at different voltages), an impedance correction
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
sequence current flow (e.g. different neutral earthing systems will affect zero-sequence
e impedances are usually quoted by manufacturers in terms of Ohms per km. These need to be converted to
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
An asynchronous motor's impedance, resistance and reactance is calculated as follows:
Where is impedance of the motor ( is resistance of the motor ( is reactance of the motor (
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)
is the motor full load power fact 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):
Where is impedance of the reactor ( is reactance of the reactor(Ω
is the impedance voltage of the reactor (pu) is the nominal voltage of the reactor (Vac) is the rated current of the reactor (A)
Positive, negative and zero sequence impedances are all equal (assuming geometric symmetr is impedance of the motor (Ω)
is resistance of the motor (Ω) 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)
is the motor full load power factor (pu) 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.
lt limiting reactors is as follows (note that the resistance is neglected):
is impedance of the reactor (Ω) Ω)
is the impedance voltage of the reactor (pu) is the nominal voltage of the reactor (Vac) is the rated current of the reactor (A)
Positive, negative and zero sequence impedances are all equal (assuming geometric symmetr
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The negative sequence impedance is equal to positive sequence impedance calculated above. The zero sequence
lt limiting reactors is as follows (note that the resistance is neglected):
Positive, negative and zero sequence impedances are all equal (assuming geometric symmetry).
Other Equipment
Static converters feeding rotating loads may need to be considered, and should be treated similarly to asynchronous motors.
Line capacitances, parallel admittances and non
3.10. Effects from series capacitors can also be neglected if voltage
Step 3: Referring Impedances
Where there are multiple voltage levels, the equipment impedances calculated earlier need to be converted to 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:
Where is the transformer winding ratio
is the transformer nominal secondary voltage at the principal tap (Vac) is the transformer nominal primary voltage (Vac)
is the specified tap setting (%)
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:
Where is the impedance referred to the primary (HV) side ( is the impedance at the secondary (LV) side (
is the transformer winding ratio (pu)
Conversely, by re-arranging the equation above, impedances ca
Static converters feeding rotating loads may need to be considered, and should be treated similarly to
Line capacitances, parallel admittances and non-rotating loads are generally neglected as per IEC 60909 3.10. Effects from series capacitors can also be neglected if voltage-limiting devices are connected in parallel.
Where there are multiple voltage levels, the equipment impedances calculated earlier need to be converted to reference voltage (typically the voltage at the fault location) in order for them to be used in a single equivalent
The winding ratio of a transformer can be calculated as follows:
is the transformer winding ratio
ominal secondary voltage at the principal tap (Vac) is the transformer nominal primary voltage (Vac)
is the specified tap setting (%)
Using the winding ratio, impedances (as well as resistances and reactances) can be referred to the primary (HV) the transformer by the following relation:
is the impedance referred to the primary (HV) side (Ω) is the impedance at the secondary (LV) side (Ω)
is the transformer winding ratio (pu)
arranging the equation above, impedances can be referred to the LV side:
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| 58 Static converters feeding rotating loads may need to be considered, and should be treated similarly to
rotating loads are generally neglected as per IEC 60909-0 Clause limiting devices are connected in parallel.
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
Using the winding ratio, impedances (as well as resistances and reactances) can be referred to the primary (HV)
n be referred to the LV side:
Step 4: Determine Thévenin Equivalent Circuit at the Fault Location
Thévenin equivalent circuit
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
voltage source ( ) and an equivalent short circuit impedance ( This can be done using the standard formulae for
of complex arithmeticmust be used throughout.
If unbalanced short circuits (e.g. single phase to earth fault) will be analyzed, then a separate Thévenin equivalent circuit should be constructed for each of the positive, negative and zero sequence netwo
finding ( , and ).
Step 5: Calculate Balanced Three
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.
stages of the short circle cycle can be computed:
Initial Short Circuit Current
The initial symmetrical short circuit current is calculated from IEC 60909
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, 1.1 for voltages
>1kV)
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 rce and a set of complex impedances representing the power system equipment and load impedances
The next step is to simplify the circuit into a Thévenin equivalent circuit, which is a circuit containing only a ) 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 must be used throughout.
If unbalanced short circuits (e.g. single phase to earth fault) will be analyzed, then a separate Thévenin equivalent circuit should be constructed for each of the positive, negative and zero sequence netwo
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 phase short circuit at the fault location. Using this impedance, the following currents at different stages of the short circle cycle can be computed:
The initial symmetrical short circuit current is calculated from IEC 60909-0 Equation 29, as follows:
e initial symmetrical short circuit current (A)
is the voltage factor that accounts for the maximum system voltage (1.05 for voltages <1kV, 1.1 for voltages
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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 rce and a set of complex impedances representing the power system equipment and load impedances
, which is a circuit containing only a
, keeping in mind that the rules
If unbalanced short circuits (e.g. single phase to earth fault) will be analyzed, then a separate Thévenin equivalent circuit should be constructed for each of the positive, negative and zero sequence networks (i.e.
The positive sequence impedance calculated in Step 4 represents the equivalent source impedance seen by a Using this impedance, the following currents at different
0 Equation 29, as follows:
is the voltage factor that accounts for the maximum system voltage (1.05 for voltages <1kV, 1.1 for voltages
is the nominal system voltage at the fault location (V) is the equivalent positive sequen
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
components of the equivalent positive sequence impedance location, i.e.
The peak short circuit current is then calculated as follows:
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). Th
typically used for breaker sizing. IEC 60909
meshed networks can be conservatively estimated as follows:
Where is the symmetrical breaking current (A) is the initial symmetrical short circuit current (A)
More detailed calculations can be made for increased accuracy (e.g. IEC 60909 left to the reader to explore.
DC Short Circuit Component
The dc component of a short circuit can be calculated according to IEC 60909 is the nominal system voltage at the fault location (V)
is the equivalent positive sequence short circuit impedance (Ω)
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
components of the equivalent positive sequence impedance , we can calculate the X/R ratio at the fault
The peak short circuit current is then calculated as follows:
is the peak short circuit current (A)
is the initial symmetrical short circuit current (A)
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:
is the symmetrical breaking current (A) is the initial symmetrical short circuit current (A)
More detailed calculations can be made for increased accuracy (e.g. IEC 60909-0 equations 75 to 77), but this is
The dc component of a short circuit can be calculated according to IEC 60909-0 Equation 64:
Page 0 Section 4.3 offers three methods for calculating peak short circuit currents, but for the sake of | 60
simplicity, we will only focus on the X/R ratio at the fault location method. Using the real (R) and reactive (X) , we can calculate the X/R ratio at the fault
The symmetrical breaking current is the short circuit current at the point of circuit breaker opening (usually is is the current that the circuit breaker must be rated to interrupt and is
0 Equation 74 suggests that the symmetrical breaking current for
0 equations 75 to 77), but this is
0 Equation 64:
Where is the dc component of the short circuit current (A)
Where is the dc component of the short circuit current (A)