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Guide for electrical design engineers
Power Quality Krzysztof Piatek AGH-University of Science & Technology
Voltage drop calculation: permissible level of voltage fluctuations for a motor 400 V
Supply system line Lz
Tr
Z PPC UN ZL
PPC
400 V line L1
Zr
Power Quality
M
U PPC
Power Quality http://www.leonardo-energy.org
Problem An industrial customer plans to connect a new induction motor to the power supply system as shown in the diagram.
Supply system
Power supply system parameters: - feeder line Lz impedance (at 0.4 kV level):
ZLz =1.55 + j1.66 mΩ
- supply line L impedance:
ZL = 25 + j 60 mΩ, ZL = 65 mΩ
line Lz
Transformer data: - rated power
SN =1MVA
- short-cir cuit voltage
u% =5%
- reactance to resistance ratio
X R =5
Tr PPC
400 V
Motor data: - rated voltage:
UN = 400 V
- rated power:
PN =75 kW
- starting power factor:
PFr = 0.3
- starting overload coefficient:
kr =7 kVA/kW
line L1
M
Using the permissible level of voltage fluctuations as a criterion, determine whether the motor should be installed. For the planned number of 20 starts per hour the voltage change: Kmax = 3%
Solution First, calculate the motor impedance during start then, employing Kirchhoff voltage law, find the voltage drop during start. The voltage drop value relative to the rated voltage at PCC is the sought coefficient; it has to be compared with the coefficients given for 20 starts per hour. The apparent power during start Sr = kr PN = 7⋅75 = 525 kVA The motor impedance during start Zr =
UN2 (cos ϕr + j sin ϕr ) Sr
where ϕrozr is the phase shift angle during start, and cosϕr = PFr is the starting power factor. Thus we obtain Zr =
0.4 2 (0.3 + j 0.954 ) = 91.43 + j 290.74 mΩ 525
The voltage drop at PCC is calculated from the voltage divider in the figure. The voltage at PCC is UPPC = UN
Z r + ZL Zr + ZL + ZPPC
2
Voltage drop calculation: permissible level of voltage fluctuations for a motor http://www.leonardo-energy.org
i.e. the relative voltage drop is
400 V
ZΣ U ku = PPC = UN Z Σ + ZPPC where
Z Σ = Zr + ZL =116.43 + j 350.74 mΩ
Z PPC
The power system impedance at PCC equals the sum of the feeder line Lz and the transformer Tr impedances
UN
ZPPC = Z Tr + ZLz The transformer impedance
ZL
Z Tr = Z Tr (cos ϕ Tr + j sin ϕ Tr ) where
u% UN2 0.4 2 = 0.05⋅ = 8 mΩ 100 SN 1 whereas the angle ϕ Tr can be determined from the X/R ratio X tan ϕ Tr = = 5, ϕ Tr = 78.69 R Inserting the calculated values to the transformer impedance formula, we obtain
U PPC
Z Tr =
Zr
Z Tr = 8 (0.196 + j 0.98 ) =1.57 + j 7.84 mΩ Summing up with the feeder line Lz impedance, we obtain ZPPC = 3.12 + j 9.5 mΩ Inserting the calculated impedances to the voltage divider formula, we obtain ku =
The relative voltage change coefficient is defined as ΔU K u = PPC UN where ΔUPPC is the voltage drop at PCC during starting. It can be determined directly as ΔUPPC = UN − kuUN = 400 (1− 0.9736 ) =10.56 V and, finally:
10.56 = 0.026 , K u = 2.6% 400 Since this coefficient does not exceed the limit value of 3% the motor can be directly connected to the network. Ku =
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