modelInductionMachine
Extends from Modelica.Electrical.Machines.Icons.TransientMachine.
Information
Model of an electric induction machine that includes the calculation of:
-> mechanical output (torque and speed)
-> electrical output (current and power)
It delivers positive torque and negative electrical power when operating below the synchronous speed (motor) and can switch into generating electricity (positive electrical power and negative torque) when operating above the synchronous speed (generator).
The calculations are based on simple electrical equations and an analytical approach by Pichai Aree (2017) that determinates stator current and torque depending on the slip.
The parameters rho0, rho1, rho3 and k are used for the calculation of the characteristic curves. They are determined from the general machine data at nominal operation and realistic assumptions about the ratio between starting torque, starting current, breakdown torque, breakdown slip and nominal current and torque. These assumptions are taken from DIN VDE 2650/2651. It shows good agreement for machines up to 100kW of mechanical power operating at a speed up to 3000rpm and with a rated voltage up to 500V.
The only data required is:
- number of polepairs or synchronous speed (p or n0)
- voltage and frequence of the electric power supply (U_1 and f_1)
- nominal current and speed (I_elNominal and n_nominal )
- power factor if available (default=0.8)
Additional Information:
- Electric power calculation as a generator from mechanical input
speed can be further approached by small changes to the speed.
- The electric losses are calculated from the slip depending rotor loss which corresponds to roughly 22% of the total losses according to Almeida (DOI: 10.1109/MIAS.2010.939427).
Parameters
| Type | Name | Default | Description |
|---|---|---|---|
| Machine specifications | |||
| Modelica.Units.SI.Frequency | n0 | f_1/p | Idling speed of the electric machine |
| Modelica.Units.SI.Frequency | n_nominal | 1530/60 | Rated rotor speed |
| Modelica.Units.SI.Frequency | f_1 | 50 | Frequency |
| Modelica.Units.SI.Voltage | U_1 | 400 | Rated voltage |
| Modelica.Units.SI.Current | I_elNominal | P_elNominal/(sqrt(3)*U_1*cosPhi) | Rated current |
| Modelica.Units.SI.Power | P_elNominal | 15000 | Nominal electrical power of electric machine |
| Real | p | 2 | Number of pole pairs |
| Real | cosPhi | 0.8 | Power factor of electric machine (default=0.8) |
| Real | gearRatio | 1 | Transmission ratio (engine speed / generator speed) |
| Calculations | |||
| Modelica.Units.SI.Current | I_1_start | if P_Mec_nominal <= 15000 then 7.2*I_elNominal else 8*I_elNominal | Motor start current (realistic factors used from DIN VDE 2650/2651) |
| Modelica.Units.SI.Power | P_Mec_nominal | P_elNominal*(1 + s_nominal/0.22) | Nominal mechanical power of electric machine |
| Modelica.Units.SI.Torque | M_nominal | P_Mec_nominal/(2*Modelica.Constants.pi*n_nominal) | Nominal torque of electric machine |
| Modelica.Units.SI.Torque | M_til | 2*M_nominal | Tilting torque of electric machine (realistic factor used from DIN VDE 2650/2651) |
| Modelica.Units.SI.Torque | M_start | if P_Mec_nominal <= 4000 then 1.6*M_nominal elseif P_Mec_nominal >= 22000 then 1*M_nominal else 1.25*M_nominal | Starting torque of electric machine (realistic factor used from DIN VDE 2650/2651) |
| Real | s_nominal | abs(1 - n_nominal*p/f_1) | Nominal slip of electric machine |
| Real | s_til | abs((s_nominal*(M_til/M_nominal) + s_nominal*sqrt(abs(((M_til/M_nominal)^2) - 1 + 2*s_nominal*((M_til/M_nominal) - 1))))/(1 - 2*s_nominal*((M_til/M_nominal) - 1))) | Tilting slip of electric machine |
| Calibration | |||
| Modelica.Units.SI.Inertia | J_Gen | 1 | Moment of inertia of the electric machine (default=0.5kg.m2) |
| Real | calFac | 1 | Calibration factor for electric power outuput (default=1) |
Components
| Type | Name | Default | Description |
|---|---|---|---|
| Modelica.Units.SI.Frequency | n | inertia.w/(2*Modelica.Constants.pi) | Speed of machine rotor [1/s] |
| Modelica.Units.SI.Current | I_1 | Electric current of machine stator | |
| Modelica.Units.SI.Power | P_E | Electrical power at the electric machine | |
| Modelica.Units.SI.Power | P_Mec | Mechanical power at the electric machine | |
| Modelica.Units.SI.Power | CalQ_Loss | Calculated heat flow from electric machine | |
| Modelica.Units.SI.Torque | M | Torque at electric machine | |
| Real | s | 1 - n*p/f_1 | Current slip of electric machine |
| Real | eta | Total efficiency of the electric machine (as motor) | |
| Real | calI_1 | 1/(1 + ((k - 1)/((s_nominal^2) - k))*((s^2) + rho1*abs(s) + rho0)) | |
| Boolean | OpMode | (n <= n0) | Operation mode (true=motor, false=generator) |
| Boolean | SwitchOnOff | isOn | Operation of electric machine (true=On, false=Off) |
| Modelica.Mechanics.Rotational.Components.Inertia | inertia | ||
| Modelica.Blocks.Sources.RealExpression | electricTorque | ||
| Modelica.Mechanics.Rotational.Sources.Torque | torque | ||
| Modelica.Mechanics.Rotational.Interfaces.Flange_a | flange_Machine | ||
| Modelica.Mechanics.Rotational.Components.IdealGear | transmission | ||
| Modelica.Blocks.Interfaces.BooleanInput | isOn | ||
| Modelica.Blocks.Interfaces.RealOutput | electricCurrent | ||
| Modelica.Blocks.Interfaces.RealOutput | electricPower | ||
| Modelica.Blocks.Interfaces.RealOutput | rotationalSpeed | ||
| Modelica.Blocks.Sources.RealExpression | current | ||
| Modelica.Blocks.Sources.RealExpression | power | ||
| Modelica.Blocks.Sources.RealExpression | speed |
Revisions
- January, 2019, by Julian Matthes:
First implementation (see issue 667).