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IMS_Start_Polyphase.mo
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IMS_Start_Polyphase.mo
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within Modelica.Magnetic.FundamentalWave.Examples.BasicMachines.InductionMachines.ComparisonPolyphase;
model IMS_Start_Polyphase
"Starting of polyphase induction machine with slip rings"
import Modelica.Constants.pi;
extends Modelica.Icons.Example;
constant Integer m3=3 "Number of stator phases of three-phase system";
parameter Integer m=5 "Number of stator phases" annotation(Evaluate=true);
parameter Integer mr=5 "Number of rotor phases" annotation(Evaluate=true);
parameter SI.Voltage VsNominal=100
"Nominal RMS voltage per phase";
parameter SI.Frequency fNominal=aimsData3.fsNominal "Nominal frequency";
parameter SI.Time tOn=0.1 "Start time of machine";
parameter SI.Resistance RStart=0.16/aimsData3.turnsRatio^2
"Starting resistance";
parameter SI.Time tRheostat=1.0
"Time of shortening the rheostat";
parameter SI.Torque T_Load=161.4 "Nominal load torque";
parameter SI.AngularVelocity w_Load(displayUnit="rev/min")=
Modelica.Units.Conversions.from_rpm(1440.45)
"Nominal load speed";
parameter SI.Inertia J_Load=0.29 "Load inertia";
Modelica.Electrical.Machines.Utilities.TerminalBox terminalBoxM(m=m,
terminalConnection="Y") annotation (Placement(transformation(extent={{20,46},
{40,66}})));
Modelica.Electrical.Machines.Utilities.TerminalBox terminalBox3(
terminalConnection="Y", m=m3) annotation (Placement(transformation(
extent={{20,-54},{40,-34}})));
Magnetic.FundamentalWave.BasicMachines.InductionMachines.IM_SlipRing aimsM(
Jr=aimsData3.Jr,
Js=aimsData3.Js,
p=aimsData3.p,
fsNominal=aimsData3.fsNominal,
TsRef=aimsData3.TsRef,
alpha20s(displayUnit="1/K") = aimsData3.alpha20s,
ratioCommonStatorLeakage=aimsData3.ratioCommonStatorLeakage,
frictionParameters=aimsDataM.frictionParameters,
statorCoreParameters=aimsDataM.statorCoreParameters,
strayLoadParameters=aimsDataM.strayLoadParameters,
phiMechanical(fixed=true),
wMechanical(fixed=true),
ratioCommonRotorLeakage=aimsData3.ratioCommonRotorLeakage,
TrRef=aimsData3.TrRef,
alpha20r(displayUnit="1/K") = aimsData3.alpha20r,
useTurnsRatio=aimsData3.useTurnsRatio,
VsNominal=aimsData3.VsNominal,
VrLockedRotor=aimsData3.VrLockedRotor,
rotorCoreParameters=aimsDataM.rotorCoreParameters,
TurnsRatio=aimsData3.turnsRatio,
mr=mr,
m=m,
Rs=aimsData3.Rs*m/3,
Lssigma=aimsData3.Lssigma*m/3,
Lszero=aimsData3.Lszero*m/3,
Lm=aimsData3.Lm*m/3,
Lrsigma=aimsData3.Lrsigma*mr/3,
Lrzero=aimsData3.Lrzero*mr/3,
Rr=aimsData3.Rr*mr/3,
TsOperational=293.15,
effectiveStatorTurns=aimsData3.effectiveStatorTurns,
TrOperational=293.15)
annotation (Placement(transformation(extent={{20,30},{40,50}})));
Magnetic.FundamentalWave.BasicMachines.InductionMachines.IM_SlipRing aims3(
p=aimsData3.p,
fsNominal=aimsData3.fsNominal,
Rs=aimsData3.Rs,
TsRef=aimsData3.TsRef,
alpha20s(displayUnit="1/K") = aimsData3.alpha20s,
ratioCommonStatorLeakage=aimsData3.ratioCommonStatorLeakage,
Lszero=aimsData3.Lszero,
Lssigma=aimsData3.Lssigma,
Jr=aimsData3.Jr,
Js=aimsData3.Js,
frictionParameters=aimsData3.frictionParameters,
phiMechanical(fixed=true),
wMechanical(fixed=true),
statorCoreParameters=aimsData3.statorCoreParameters,
strayLoadParameters=aimsData3.strayLoadParameters,
Lm=aimsData3.Lm,
Lrsigma=aimsData3.Lrsigma,
ratioCommonRotorLeakage=aimsData3.ratioCommonRotorLeakage,
Lrzero=aimsData3.Lrzero,
Rr=aimsData3.Rr,
TrRef=aimsData3.TrRef,
alpha20r(displayUnit="1/K") = aimsData3.alpha20r,
useTurnsRatio=aimsData3.useTurnsRatio,
VsNominal=aimsData3.VsNominal,
VrLockedRotor=aimsData3.VrLockedRotor,
rotorCoreParameters=aimsData3.rotorCoreParameters,
m=m3,
TurnsRatio=aimsData3.turnsRatio,
TsOperational=566.3,
effectiveStatorTurns=aimsData3.effectiveStatorTurns,
TrOperational=566.3)
annotation (Placement(transformation(extent={{20,-70},{40,-50}})));
Modelica.Electrical.Machines.Utilities.SwitchedRheostat rheostatM(
tStart=tRheostat,
m=mr,
RStart=RStart*mr/m3)
annotation (Placement(transformation(extent={{-10,30},{10,50}})));
Modelica.Electrical.Machines.Utilities.SwitchedRheostat rheostat3(
RStart=RStart,
tStart=tRheostat,
m=m3) annotation (Placement(transformation(extent={{-10,-70},{10,-50}})));
Modelica.Mechanics.Rotational.Components.Inertia loadInertiaM(J=J_Load)
annotation (Placement(transformation(extent={{50,30},{70,50}})));
Modelica.Mechanics.Rotational.Components.Inertia loadInertia3(J=J_Load)
annotation (Placement(transformation(extent={{50,-70},{70,-50}})));
Modelica.Mechanics.Rotational.Sources.QuadraticSpeedDependentTorque
quadraticLoadTorqueM(
tau_nominal=-T_Load,
TorqueDirection=false,
useSupport=false,
w_nominal=w_Load) annotation (Placement(transformation(extent={{100,
30},{80,50}})));
Modelica.Mechanics.Rotational.Sources.QuadraticSpeedDependentTorque
quadraticLoadTorque3(
tau_nominal=-T_Load,
TorqueDirection=false,
useSupport=false,
w_nominal=w_Load) annotation (Placement(transformation(extent={{100,-70},
{80,-50}})));
parameter
Modelica.Electrical.Machines.Utilities.ParameterRecords.IM_SlipRingData aimsData3
"Induction machine data of a three-phase machine"
annotation (Placement(transformation(extent={{-100,-100},{-80,-80}})));
Modelica.Electrical.Analog.Basic.Ground groundM annotation (Placement(
transformation(origin={-90,50}, extent={{-10,-10},{10,10}})));
Modelica.Electrical.Polyphase.Basic.Star starM(final m=m)
annotation (Placement(transformation(extent={{-70,62},{-90,82}})));
Modelica.Electrical.Polyphase.Sources.SineVoltage sineVoltageM(
final m=m,
f=fill(fNominal, m),
V=fill(sqrt(2.0)*VsNominal, m),
phase=-Modelica.Electrical.Polyphase.Functions.symmetricOrientation(m))
annotation (Placement(transformation(origin={-50,72}, extent={{10,-10},{-10,
10}})));
Modelica.Electrical.Polyphase.Ideal.IdealClosingSwitch idealCloserM(
final m=m,
Ron=fill(1e-5*m/3, m),
Goff=fill(1e-5*m3/m, m)) annotation (Placement(transformation(origin={-20,
72}, extent={{-10,10},{10,-10}})));
Modelica.Blocks.Sources.BooleanStep booleanStepM[m](each startTime=tOn, each
startValue=false) annotation (Placement(transformation(extent={{-10,-10},
{10,10}}, origin={-40,40})));
Modelica.Electrical.Polyphase.Sensors.CurrentQuasiRMSSensor
currentRMSsensorM(m=m) annotation (Placement(transformation(
origin={10,72},
extent={{-10,10},{10,-10}})));
Modelica.Electrical.Analog.Basic.Ground ground3 annotation (Placement(
transformation(origin={-90,-52}, extent={{-10,-10},{10,10}})));
Modelica.Electrical.Polyphase.Basic.Star star3(final m=m3)
annotation (Placement(transformation(extent={{-70,-40},{-90,-20}})));
Modelica.Electrical.Polyphase.Sources.SineVoltage sineVoltage3(
final m=m3,
V=fill(sqrt(2.0)*VsNominal, m3),
phase=-Modelica.Electrical.Polyphase.Functions.symmetricOrientation(m3),
f=fill(fNominal, m3)) annotation (Placement(transformation(origin={-50,-30},
extent={{10,-10},{-10,10}})));
Modelica.Electrical.Polyphase.Ideal.IdealClosingSwitch idealCloser3(
final m=m3,
Ron=fill(1e-5, m3),
Goff=fill(1e-5, m3)) annotation (Placement(transformation(origin={-20,-30},
extent={{-10,10},{10,-10}})));
Modelica.Blocks.Sources.BooleanStep booleanStep3[m3](each startTime=tOn,
each startValue=false) annotation (Placement(transformation(extent={{-10,
-10},{10,10}}, origin={-40,-60})));
Modelica.Electrical.Machines.Sensors.CurrentQuasiRMSSensor
currentRMSsensor3(m=3) annotation (Placement(transformation(
origin={10,-30},
extent={{-10,10},{10,-10}})));
Modelica.Blocks.Math.Gain gain(k=(m/m3))
annotation (Placement(transformation(extent={{40,80},{60,100}})));
Modelica.Blocks.Math.Feedback feedback
annotation (Placement(transformation(extent={{80,10},{100,-10}})));
parameter
Electrical.Machines.Utilities.ParameterRecords.IM_SlipRingData aimsDataM(
m=m,
Rs=0.03*m/3,
Lszero=3*(1 - sqrt(1 - 0.0667))/(2*pi*fNominal)*m/3,
Lssigma=3*(1 - sqrt(1 - 0.0667))/(2*pi*fNominal)*m/3,
statorCoreParameters(m=m),
Lm=3*sqrt(1 - 0.0667)/(2*pi*fNominal),
Lrsigma=3*(1 - sqrt(1 - 0.0667))/(2*pi*fNominal)/aimsDataM.turnsRatio^2,
Lrzero=3*(1 - sqrt(1 - 0.0667))/(2*pi*fNominal)/aimsDataM.turnsRatio^2,
Rr=0.04/aimsDataM.turnsRatio^2,
rotorCoreParameters(m=m)) "Induction machine data of an m-phase machine"
annotation (Placement(transformation(extent={{-100,0},{-80,20}})));
initial equation
aims3.is[1:2] = zeros(2);
aims3.ir[1:3] = zeros(3);
aimsM.is[1:2] = zeros(2);
aimsM.ir[1:mr - 2] = zeros(mr - 2);
equation
connect(loadInertia3.flange_b, quadraticLoadTorque3.flange) annotation (
Line(points={{70,-60},{76,-60},{80,-60}}));
connect(aims3.flange, loadInertia3.flange_a) annotation (Line(points={{
40,-60},{40,-60},{50,-60}}));
connect(terminalBox3.plug_sn, aims3.plug_sn)
annotation (Line(points={{24,-50},{24,-50}}, color={0,0,255}));
connect(terminalBox3.plug_sp, aims3.plug_sp)
annotation (Line(points={{36,-50},{36,-50}}, color={0,0,255}));
connect(rheostat3.plug_p, aims3.plug_rp) annotation (Line(points={{10,-54},
{10,-54},{20,-54}}, color={0,0,255}));
connect(rheostat3.plug_n, aims3.plug_rn) annotation (Line(points={{10,-66},
{10,-66},{20,-66}}, color={0,0,255}));
connect(loadInertiaM.flange_b, quadraticLoadTorqueM.flange)
annotation (Line(points={{70,40},{70,40},{80,40}}));
connect(aimsM.flange, loadInertiaM.flange_a)
annotation (Line(points={{40,40},{40,40},{50,40}}));
connect(terminalBoxM.plug_sp, aimsM.plug_sp)
annotation (Line(points={{36,50},{36,50}}, color={0,0,255}));
connect(terminalBoxM.plug_sn, aimsM.plug_sn)
annotation (Line(points={{24,50},{24,50}}, color={0,0,255}));
connect(rheostatM.plug_p, aimsM.plug_rp) annotation (Line(
points={{10,46},{20,46}},
color={0,0,255}));
connect(rheostatM.plug_n, aimsM.plug_rn) annotation (Line(
points={{10,34},{20,34}},
color={0,0,255}));
connect(starM.pin_n, groundM.p) annotation (Line(points={{-90,72},{-90,
72},{-90,60}}, color={0,0,255}));
connect(sineVoltageM.plug_n, starM.plug_p) annotation (Line(points={{-60,
72},{-60,72},{-70,72}}, color={0,0,255}));
connect(sineVoltageM.plug_p, idealCloserM.plug_p) annotation (Line(
points={{-40,72},{-30,72}},
color={0,0,255}));
connect(idealCloserM.plug_n, currentRMSsensorM.plug_p) annotation (Line(
points={{-10,72},{0,72}},
color={0,0,255}));
connect(booleanStepM.y, idealCloserM.control) annotation (Line(
points={{-29,40},{-20,40},{-20,60}},
color={255,0,255}));
connect(star3.pin_n, ground3.p)
annotation (Line(points={{-90,-30},{-90,-42}}, color={0,0,255}));
connect(sineVoltage3.plug_n, star3.plug_p) annotation (Line(points={{-60,
-30},{-60,-30},{-70,-30}}, color={0,0,255}));
connect(sineVoltage3.plug_p, idealCloser3.plug_p) annotation (Line(
points={{-40,-30},{-30,-30}},
color={0,0,255}));
connect(idealCloser3.plug_n, currentRMSsensor3.plug_p) annotation (Line(
points={{-10,-30},{0,-30}},
color={0,0,255}));
connect(booleanStep3.y, idealCloser3.control) annotation (Line(
points={{-29,-60},{-20,-60},{-20,-42}},
color={255,0,255}));
connect(currentRMSsensorM.I, gain.u) annotation (Line(
points={{10,83},{10,90},{38,90}},
color={0,0,127}));
connect(currentRMSsensor3.plug_n, terminalBox3.plugSupply) annotation (
Line(
points={{20,-30},{30,-30},{30,-48}},
color={0,0,255}));
connect(currentRMSsensorM.plug_n, terminalBoxM.plugSupply) annotation (
Line(
points={{20,72},{30,72},{30,52}},
color={0,0,255}));
connect(currentRMSsensor3.I, feedback.u1) annotation (Line(
points={{10,-19},{10,0},{82,0}},
color={0,0,127}));
connect(feedback.u2, gain.y) annotation (Line(
points={{90,8},{90,16},{100,16},{100,90},{61,90}},
color={0,0,127}));
annotation (
experiment(
StopTime=1.5,
Interval=1E-4,
Tolerance=1e-06),
Documentation(info="<html>
<p>
At start time <code>tOn</code> voltages are supplied to the
<a href=\"modelica://Modelica.Magnetic.FundamentalWave.BasicMachines.InductionMachines.IM_SlipRing\">induction machines with sliprings</a>.
The two machine start from standstill, accelerating inertias against load torque quadratic dependent on speed,
using a starting resistance. At time tRheostat external rotor resistance is shortened, finally reaching nominal speed. Two equivalent machines with different numbers of phases are compared and their equal behavior is demonstrated.</p>
<p>
Simulate for 1.5 seconds and plot (versus time):
</p>
<ul>
<li><code>aimcM|M3.tauElectrical</code>: machine torque</li>
<li><code>aimsM|M3.wMechanical</code>: machine speed</li>
<li><code>feedback.y</code>: zero since difference of three-phase current phasor and scaled polyphase current phasor are equal</li>
</ul>
</html>"),
Diagram(coordinateSystem(preserveAspectRatio=false, extent={{-100,
-100},{100,100}}),
graphics={ Text(
extent={{40,68},{100,60}},
textString="%m-phase machine",
textStyle={TextStyle.Bold}),Text(
extent={{40,-32},{100,-40}},
textString="Three-phase machine",
textStyle={TextStyle.Bold})}));
end IMS_Start_Polyphase;