Calculation Methodology
Step 1: Construct System Model and Collect Equipment Parameters
The first step is to construct a simplified model of the system single line diagram, and th
equipment parameters. The model of the single line diagram need only show the buses of interest in the motor starting calculation, e.g. the upstream source bus, the motor bus and possibly any intermediate or downstream buses that may be affected. All running loads are shown as lumped loads except for the motor to be started as it is assumed that the system is in a steady
The relevant equipment parameters to be collected are as follows:
Network feeders: fault capacity of the network (VA), X/R ratio of the network
Generators: per-unit transient reactance, rated generator capacity (VA)
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 (
Standing loads: rated load capacity (VA), average load power factor (pu)
Motor: full load current (A), locked rotor current (A), rated power (W), full load power factor (pu), starting power factor (pu)
Step 2: Calculate Equipment 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 fee
the impedance, resistance and reactance of the network feeder is calculated as follows:
Calculation Methodology
This calculation is based on standard impedance formulae and Ohm's law. To the author's knowledge, there are no international standards that govern voltage drop calculations during motor start.
It should be noted that the proposed method is not 100% accurate because it is a static calculation. In reality, the levels are fluctuating during a transient condition, and therefore so are the load currents drawn by the standing loads. This makes it essentially a load flow problem and a more precise solution would solve the load flow problem iteratively, for example using the Newton-Rhapson or Gauss-Siedel algorithms. Notwithstanding, the proposed method is suitably accurate for a first pass solution.
The calculation has the following six general steps:
Step 1: Construct the system model and assemble the relevant equipment parameters Step 2: Calculate the relevant impedances for each equipment item in the model Step 3: Refer all impedances to a reference voltage
Step 4: Construct the equivalent circuit for the voltage levels of interest Step 5: Calculate the ini al steady-state source emf before motor starting Step 6: Calculate the system voltages during motor start
Step 1: Construct System Model and Collect Equipment Parameters
The first step is to construct a simplified model of the system single line diagram, and thequipment parameters. The model of the single line diagram need only show the buses of interest in the motor starting calculation, e.g. the upstream source bus, the motor bus and possibly any intermediate or downstream
y be affected. All running loads are shown as lumped loads except for the motor to be started as it is assumed that the system is in a steady-state before motor start.
The relevant equipment parameters to be collected are as follows:
t capacity of the network (VA), X/R ratio of the network unit transient reactance, rated generator capacity (VA)
Transformers: transformer impedance voltage (%), rated transformer capacity (VA), rated current (A), es: length of cable (m), resistance and reactance of cable ( )
Standing loads: rated load capacity (VA), average load power factor (pu)
Motor: full load current (A), locked rotor current (A), rated power (W), full load power factor (pu), starting
Step 2: Calculate Equipment 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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| 38 m's law. To the author's knowledge, there are no international standards that govern voltage drop calculations during motor start.
It should be noted that the proposed method is not 100% accurate because it is a static calculation. In reality, the levels are fluctuating during a transient condition, and therefore so are the load currents drawn by the standing loads. This makes it essentially a load flow problem and a more precise solution would solve the load
Siedel algorithms. Notwithstanding,
ment parameters Step 2: Calculate the relevant impedances for each equipment item in the model
state source emf before motor starting
Step 1: Construct System Model and Collect Equipment Parameters
The first step is to construct a simplified model of the system single line diagram, and then collect the relevant equipment parameters. The model of the single line diagram need only show the buses of interest in the motor starting calculation, e.g. the upstream source bus, the motor bus and possibly any intermediate or downstream
y be affected. All running loads are shown as lumped loads except for the motor to be started as it is
t capacity of the network (VA), X/R ratio of the network
Transformers: transformer impedance voltage (%), rated transformer capacity (VA), rated current (A), )
Motor: full load current (A), locked rotor current (A), rated power (W), full load power factor (pu), starting
Using the collected parameters, each of the equipment item impedances can be calculated for later use in the
der 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 maximum system voltage (1.0
>1kV)
is X/R ratio of the network feeder (pu) Synchronous Generators
The transient resistance and reactance of a synchronous generator can be estimated by the following:
Where is the transient reactance of the is the resistance of the generator ( is impedance 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)
The transient resistance and reactance of a synchronous generator can be estimated by the following:
is the transient reactance of the generator (Ω) is the resistance of the generator (Ω)
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| 39
5 for voltages <1kV, 1.1 for voltages
The transient resistance and reactance of a synchronous generator can be estimated by the following:
is a voltage correction factor (pu)
is the per-unit 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 ra o, typically 20 for nominal voltage 1kV
is a voltage factor which accounts for the maximum system voltage (1.05 for voltages <1kV, 1.1 for voltages
>1kV)
is the power factor of the generator (pu) Transformers
The impedance, resistance and reactance of two
Where is the 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 a voltage correction factor (pu)
unit transient reactance of the generator (pu)
is the nominal generator voltage (Vac) is the nominal system voltage (Vac) is the rated generator capacity (VA)
s 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 <1kV, 1.1 for voltages
he generator (pu)
The impedance, resistance and reactance of two-winding transformers can be calculated as follows:
is the 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)
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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
winding transformers can be calculated as follows:
e (Vac)
is the total copper loss in the transformer windings (W) Cables
Cable impedances are usually quoted by manufacturers in terms of Ohms per km. These need to be converted 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)
Standing Loads
Standing loads are lumped loads comprising all loads that are operating on to be started. Standing loads for each bus need to be calculated.
The impedance, resistance and reactance of the standing load is calculated by:
Where is the impedance of the standing load { is the resistance of the standing load { is the reactance of the standing load { is the standing load nominal voltage (Vac) is the standing load apparent power (VA)
is the total copper loss in the transformer windings (W)
Cable impedances are usually quoted by manufacturers in terms of Ohms per km. These need to be converted 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)
Standing loads are lumped loads comprising all loads that are operating on a particular bus, excluding the motor to be started. Standing loads for each bus need to be calculated.
The impedance, resistance and reactance of the standing load is calculated by:
is the impedance of the standing load {Ω) of the standing load {Ω) is the reactance of the standing load {Ω) is the standing load nominal voltage (Vac) is the standing load apparent power (VA)
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| 41 Cable impedances are usually quoted by manufacturers in terms of Ohms per km. These need to be converted to
a particular bus, excluding the motor
is the average load power factor (pu) Motors
The motor's transient impedance, resistance and reacta
Where is transient impedance of the motor ( is transient resistance of the motor ( is transient 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 factor (pu) is the motor starting power factor (pu)