The document provides information on sizing solid state motor starters for various applications. It discusses the data required for sizing including motor, load, and environmental parameters. Methods are described for calculating torque scaling factors, acceleration times, and voltage drop considerations. Charts are shown outlining typical starter sizing calculations with 10 speed segments to determine minimum current limits and total start time.

1. SOLCON
HRVS-DN Sizing & Calculations
ΔM
=J
dw/dt
Time
Voltage Ramp-up Time
Un
U start
30 sec2

2. SOLCON
HRVS-DN Sizing & Calculations
Data Required for correct Starter Sizing
• Application data (Pump , Fan , Compressor , Conveyer)
• Single start – Multi start
• Motor data
• Load data
• Network requirements
• Environmental conditions

3. SOLCON
HRVS-DN Sizing & Calculations
Motor Data
• Rated Power (KW)
• Rated Voltage (V)
• Rated Speed (RPM)
• Rated Current (A)
• Rotor Inertia J or GD2
/4 (Kgm2
)
• Motor Starting Curves (Torque & Current vs. Speed)

4. SOLCON
HRVS-DN Sizing & Calculations
Load Data
• Application
• Inertia J or GD2
/4 (Kgm2
)
• Gear Ratio
• Torque vs. Speed Curve
• Starting Conditions (Open/Closed Valve , dampers ect.)
• Rated Load Power (KW)

5. SOLCON
HRVS-DN Sizing & Calculations
Gear Ratio considerations
• Gear ratio = wM/wL ,
• Where wM = motor speed & wL= load speed
• Power , PM = PL
• MM x wM = ML x wL (for load torque scaling)
• Kinetic Energy , EKM = EKL
• 1/2JLMwM
2
= 1/2JLwL
2
• MLM= MLx wL/ wM
• JLM/JL= wL
2
/wM
2
• Important!!! – All values of Torque , Power & Inertia must
be reflected to motor shaft scale. (PU of motor values)

6. SOLCON
HRVS-DN Sizing & Calculations
Typical Motor Starting Curves
DOL Current
@ 100% V
DOL Current
@ 80% V
Motor Torque
@ 100% V
Motor Torque
@ 80% V
Load Torque

7. SOLCON
HRVS-DN Sizing & Calculations
Typical Pump Starting Curve
Note: Data are NOT
scaled to motor shaft
values!!!
Open valve curve
Closed valve curve

8. SOLCON
HRVS-DN Sizing & Calculations
Typical Pump Starting Curve
• Zero Speed - Friction Torque = 10-15% , Hydraulic Torque = 0
• Full Speed - Friction Torque = 0 , Hydraulic Torque = Full Rated
• With Closed Valves Starting Torque will be Low. (Such curve is
being given by manufacturer!)
• Note Full Rated Pump Torque Ratio to Motor Rated Torque.
• For Starting Calculations Pump (Load) Torque Must be scaled
to Motor’s Value (PU of motor torque)

9. SOLCON
HRVS-DN Sizing & Calculations
Pump Torque Scaling
(No Gear)
• PP ~ w3
• MP ~ w2
• Pump Torque (PU) = PP/ PM
• PU of Motor Scale.
• Starting Conditions : Open or Closed Valves

10. SOLCON
HRVS-DN Sizing & Calculations
Constant Torque Applications
• Torque is Constant at Any Speed
• Applications : Mixers , Extruders , Conveyers
• Main Problem : Motor Reduced Starting Torque

11. SOLCON
HRVS-DN Sizing & Calculations
Angular Motion Equations
MKS Units
• ΔM =J dw/dt , ΔM = Mm (w) – ML(w)
• Mm(w)= MDOL X (ICL/IDOL(w))2
• t start= JΣΔw/ΔM(w) , ΔM(w)> 0!!!
• w - is the speed in Rad/Sec , w = N(RPM)x2π/60
• J - is the moment of inertia in Kgm2
or GD2
/4
• ΔM(w) is the net acceleration torque (soft starter reduced)
• J = GD2
/4
• M - is the torque in NM

12. SOLCON
HRVS-DN Sizing & Calculations
Motor Torque Factor (MTF)
• Takes into account the torque reduction factor at full
DOL starting conditions
• Factor is calculated at 70% motor speed
• Can be calculated if starting curves are given at 100% &
80% (65%) voltage.
• MTF = (Mr/Mn)/(Ir/In)2
, Normally < 1
• Mnet = Mc x MTF
• Where :
-Mn – Motor Torque at rated voltage
-Mr – Motor Torque at reduced voltage
-In – Starting Current at rated voltage
-Ir – Starting Current at reduced voltage

13. SOLCON
HRVS-DN Sizing & Calculations
Starting Calculations Chart -10 Segments
Project: Igel Saudi Application : Chiller
Motor Rated Voltage = 4000 [V] Motor Sn = 1732 [KVA]
Motor Rated Current = 250 [A]
Motor Rated Power = 1500 [KW]
Motor Rated Torque = 3980.89172 [NM]
Motor+Load Inertia= 12.96 [KG*m^2] Motor Inertia 10.12 Load Inertia 2.84
Motor Sync. Speed = 3600 [RPM]
Motor Torque Factor = 1 Note: Taken from motor curve acording to T/Tn and I/In at 0.7 Sync. Speed
[1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11] [12] [13] [14]
Speed Tmot[p.u] Tload[p.u] In [p.u] min C.L. Net Torque @ C.L. Acceleration @ C.L. TIME @ C.L.
2.7 2.8 2.9 2.7 2.8 2.9 2.7 2.8 4
0 1.000 0.040 5.900 1.18 674 737 803 52.04 56.89 61.92 0.72 0.66 0.61
0.1 1.000 0.020 5.800 0.82 783 848 916 60.42 65.44 70.65 0.62 0.58 0.53
0.2 1.000 0.040 5.700 1.14 734 801 871 56.63 61.83 67.22 0.67 0.61 0.56
0.3 1.050 0.080 5.650 1.56 636 708 783 49.08 54.64 60.40 0.77 0.69 0.62
0.4 1.100 0.160 5.600 2.14 381 458 537 29.40 35.32 41.47 1.28 1.07 0.91
0.5 1.140 0.200 5.500 2.30 297 380 466 22.95 29.32 35.92 1.64 1.29 1.05
0.6 1.180 0.250 5.400 2.49 179 268 360 13.82 20.66 27.74 2.73 1.82 1.36
0.7 1.300 0.300 5.300 2.55 149 250 355 11.48 19.30 27.40 3.28 1.95 1.38
0.8 2.000 0.350 5.180 2.17 770 933 1102 59.40 71.99 85.04 0.63 0.52 0.44
0.9 2.400 0.350 4.500 1.72 2046 2306 2575 157.88 177.91 198.66 0.24 0.21 0.19
minimum current limit setting > 2.55 total start time[sec] = 12.58 9.40 7.65
[1] - Relative Speed
[2] - Motor Torque at Rated Voltage
[3] - Load Torque
[4] - Motor Current at Rated Voltage
[5] - Minimum Current Limit required (at each segment and total) to overcom load. Current limit must be set to higher value.
[6],[7],[8] - Net torque (Motor Torque at specified Current Limit - Load Torque) available for acceleration
[9],[10],[11] - Acceleration (Rad / Sec^2) at Specified Current Limit
[12],[13],[14] - Time at each Segment and Total Time at Specified Current Limit

14. SOLCON
HRVS-DN Sizing & Calculations
Verifying Starting Calculations
• If Starting Time at 100% & 80% or 65% is given with data
• Insert to table as CL I DOL Value
• Insert to table as CL IDOL Value x 0.8 (or 0.65)
• Compare with Manufacturer calculated acceleration time

15. SOLCON
HRVS-DN Sizing & Calculations
General Sizing Criteria
• Starter FLC > Motor FLA !!! (around 15%)
• Starting Conditions of CL < 4XIn & tST < 30 Sec. – OK
• Starting Conditions of CL > 4XIn , < 4XIFLC & tST < 30 Sec –OK
• Starting Conditions of CL > 4XIFLC may require a higher size unit
• Starting Conditions of Low CL & tST >> 30 Sec.
• Needs to be Re-evaluated - Multi – Starting Applications

16. SOLCON
HRVS-DN Sizing & Calculations
Special Applications
• Ball Mills
• Crushers
• Conveyers
Inertia and Torque vary with angular position & speed
Starter Sizing - FLC > 1.8 – 2.0 Motor FLA

17. SOLCON
HRVS-DN Sizing & Calculations
Standard Applications W/O Data
• Sizing can be provided for :
• Standard Application (pump , fan)
• Motor rated current , starting & critical torque must be
known
• Low power rating (up to 400KW)

18. SOLCON
HRVS-DN Sizing & Calculations
Voltage Drop Considerations (Transformer)
• Voltage drop limit specified by customer
• Motor minimum CL to be calculated
• Transformer voltage drop: I = ICL
ΔV = IrTCOSφ + IxTSINφ
where r is the resistance of the transformer and x is the reactance.
Assuming : rT is very low , COSφ is very low also (about 0.17) so we
can omit the resistive voltage drop. The equation becomes
ΔV = IxTSINφ ,
SINφ = SIN (ARC COS(0.17) = 0.98.

19. SOLCON
HRVS-DN Sizing & Calculations
Generators Power Plants Supply Starting
• Generator KW rating must be > 1.6-1.8 x Motor KW rating
• Motor minimum CL to be calculated
• Generator impedance is XG
• Motor starting current (first instant) = 0.8 x IFLA
• Allow a reasonable acceleration time
• Generator AVR recovers the voltage once current increases
• Generator specified short time over current to withstand
motor CL and starting time – IGx tG > ICL x tST

20. SOLCON
HRVS-DN Sizing & Calculations
Network Supply Voltage Drop
• Given Data - Mains SCC (Short Circuit Capacity) (MVA)
• Mains Impedance XM= V2
/S (Ω) , S = SCC
• ΔVPh = ICL x XM (V/Ph)
• ΔV(PU) = (ΔVPhx √3)/V
• ΔV(%) = ΔV(PU) x 100