/// <summary>
/// Convert from abc to dq
/// Theta is radian
/// </summary>
/// <param name="a">fa</param>
/// <param name="b">fb</param>
/// <param name="c">fc</param>
/// <param name="theta">Angle (radian) from 0a to 0d (counter clockwise)</param>
/// <returns></returns>
public static Fdq abc_dq(double a, double b, double c, double theta)
{
Fdq fdq = new Fdq();
fdq.d = 2.0 / 3 * (Math.Cos(theta) * a + Math.Cos(theta - 2 * Math.PI / 3) * b + Math.Cos(theta + 2 * Math.PI / 3) * c);
fdq.q = -2.0 / 3 * (Math.Sin(theta) * a + Math.Sin(theta - 2 * Math.PI / 3) * b + Math.Sin(theta + 2 * Math.PI / 3) * c);
return(fdq);
}
public static Fabc dq_abc(Fdq fdq, double theta)
{
return(dq_abc(fdq.d, fdq.q, theta));
}
private VoltageLimitEllipse buildVoltageLimitEllipse(double speed, int count = 50, double Imax = 55, double Umax = 140)
{
var vle = new VoltageLimitEllipse
{
speed = speed,
Imax = Imax,
Umax = Umax,
curve = new List <Fdq>(),
torques = new List <double>(),
};
double maxt = 0;
bool minfound = false;
int index = 0;
for (int j = 0; j < count + 1; j++)
{
double id = -Imax * j / count;
double iq;
double t = 0;
bool bb = Brent.TryFindRoot(iq_ =>
{
var d = calculatePointdata(id, iq_, speed);
double u = Math.Sqrt(d.ud * d.ud + d.uq * d.uq);
t = d.torque;
return(u - Umax);
}, 0, Imax, 1e-5, 100, out iq);
if (bb)
{
var idq = new Fdq {
d = id, q = iq
};
if (maxt < t)
{
maxt = t;
vle.maxtorque_point = index;
}
if (!minfound)
{
vle.minid_point = index;
minfound = true;
}
vle.curve.Add(idq);
vle.torques.Add(t);
index++;
}
}
if (vle.curve[0].d < 0)
{
Fdq idq1 = vle.curve[0];
Fdq idq2 = vle.curve[1];
Fdq idq0 = new Fdq
{
d = idq1.d + (Imax / count) * (idq1.q / idq2.q) / (1 - idq1.q / idq2.q),
q = 0,
};
vle.curve.Insert(0, idq0);
vle.torques.Insert(0, 0);
vle.maxtorque_point++;
}
return(vle);
}
private EfficiencyMap buildEfficiencyMap(int torque_count, int speed_count, double Imax, double Umax, double max_speed)
{
MaxtorqueCapabilityCurve mtcc = buildMaxtorqueCapabilityCurve(speed_count, Imax, Umax, max_speed);
VoltageLimitCurve vlc = buildVoltageLimitCurve(speed_count, Imax, Umax, max_speed);
var em = new EfficiencyMap()
{
// input
Imax = Imax,
Umax = Umax,
MaxSpeed = max_speed,
// axis
speed_points = new double[speed_count + 1],
torque_points = new double[torque_count + 1],
// value
power = new double[speed_count + 1, torque_count + 1],
windingloss = new double[speed_count + 1, torque_count + 1],
rotor_coreloss = new double[speed_count + 1, torque_count + 1],
stator_coreloss = new double[speed_count + 1, torque_count + 1],
coreloss = new double[speed_count + 1, torque_count + 1],
totalloss = new double[speed_count + 1, torque_count + 1],
efficiency = new double[speed_count + 1, torque_count + 1],
voltage = new double[speed_count + 1, torque_count + 1],
current = new double[speed_count + 1, torque_count + 1],
beta = new double[speed_count + 1, torque_count + 1],
Ld = new double[speed_count + 1, torque_count + 1],
Lq = new double[speed_count + 1, torque_count + 1],
};
em.power.Fill2D(double.NaN);
em.windingloss.Fill2D(double.NaN);
em.rotor_coreloss.Fill2D(double.NaN);
em.stator_coreloss.Fill2D(double.NaN);
em.coreloss.Fill2D(double.NaN);
em.totalloss.Fill2D(double.NaN);
em.efficiency.Fill2D(double.NaN);
em.voltage.Fill2D(double.NaN);
em.current.Fill2D(double.NaN);
em.beta.Fill2D(double.NaN);
em.Ld.Fill2D(double.NaN);
em.Lq.Fill2D(double.NaN);
var mtpa = buildTableMaxtorquePerAmple();
double max_t = mtpa.GetMaxTorqueWithCurrentMagnitude(Imax);
LinearSpline torqueCapabilityLimit = LinearSpline.Interpolate(mtcc.speeds, mtcc.maxtorques);
for (int i = 0; i < speed_count + 1; i++)
{
for (int j = 0; j < torque_count + 1; j++)
{
// speed
double speed = max_speed * i / speed_count;
em.speed_points[i] = speed;
// torque
double t = max_t * j / torque_count;
em.torque_points[j] = t;
double max_possible_torque = torqueCapabilityLimit.Interpolate(speed);
if (t > max_possible_torque)
{
continue;
}
// speed limit 1
double speed1 = vlc.GetMaxSpeedForTorque(t);
APointData data = null;
if (t == 0)
{
data = calculatePointdata(0, 0, speed);
}
// zone 1
else if (speed <= speed1)
{
Fdq idq = mtpa.GetCurrentForTorque(t);
if (double.IsNaN(idq.d) || double.IsNaN(idq.q))
{
data = null;
}
else
{
data = calculatePointdata(idq.d, idq.q, speed);
}
}
else
{
Fdq idq = getCurrentForZone2(t, speed, Imax, Umax);
if (double.IsNaN(idq.d) || double.IsNaN(idq.q))
{
data = null;
}
else
{
data = calculatePointdata(idq.d, idq.q, speed);
}
}
if (data != null)
{
em.rotor_coreloss[i, j] = data.rotorloss;
em.stator_coreloss[i, j] = data.statorloss;
em.coreloss[i, j] = data.rotorloss + data.statorloss;
em.windingloss[i, j] = data.copperloss;
em.totalloss[i, j] = data.copperloss + data.rotorloss + data.statorloss;
em.power[i, j] = data.power;
em.efficiency[i, j] = 100 * data.power / (data.power + em.totalloss[i, j]);
em.voltage[i, j] = data.voltage;
em.current[i, j] = data.current;
em.beta[i, j] = data.beta;
em.Ld[i, j] = double.IsNaN(data.Ld) || data.Ld < 0 ? -0.0001 : data.Ld * 1000; //to mH
em.Lq[i, j] = double.IsNaN(data.Ld) || data.Ld < 0 ? -0.0001 : data.Lq * 1000; //to mH
}
}
}
return(em);
}
private MaxtorqueCapabilityCurve buildMaxtorqueCapabilityCurve(int count = 50, double Imax = 55, double Umax = 140, double max_speed = 6000)
{
var mtpa = buildTableMaxtorquePerAmple();
MaxtorqueCapabilityCurve mtcc = new MaxtorqueCapabilityCurve()
{
Imax = Imax,
Umax = Umax,
MaxSpeed = max_speed,
};
// Look for beta to get max torque
double max_t = mtpa.GetMaxTorqueWithCurrentMagnitude(Imax);
Fdq idq = mtpa.GetCurrentForTorque(max_t);
// Create PointPairList
// look for speed1
var speed1 = Brent.FindRoot(s =>
{
var data_ = calculatePointdata(idq.d, idq.q, s);
var u_ = Math.Sqrt(data_.ud * data_.ud + data_.uq * data_.uq);
return(u_ - Umax);
}, 100, max_speed, 1e-3);
// speed by speed
int count1 = (int)(speed1 / max_speed * count) + 1;
int count2 = count - count1;
for (int i = 1; i < count1 + 1; i++)
{
double speed = speed1 * i / count1;
var data = calculatePointdata(idq.d, idq.q, speed);
mtcc.speeds.Add(speed);
mtcc.maxtorques.Add(data.torque);
mtcc.currents.Add(idq);
mtcc.voltages.Add(new Fdq()
{
d = data.ud, q = data.uq
});
mtcc.power.Add(data.power);
mtcc.effs.Add(data.efficiency);
}
double t = max_t;
for (int i = 1; i < count2 + 1; i++)
{
double speed = speed1 + (max_speed - speed1) * i / count2;
// find beta which make U=Umax
//double beta = 0;
//bool success = Brent.TryFindRoot(b =>
//{
// var data_ = calculatePointdata(Imax * Math.Cos(b * Math.PI / 180), Imax * Math.Sin(b * Math.PI / 180), speed);
// var u_ = Math.Sqrt(data_.ud * data_.ud + data_.uq * data_.uq);
// return u_ - Umax;
//}, 100, 180, 1e-5, 100, out beta);
// Here:
// Find Id,Iq that bring max torque at speed
// it is intersect of circle Imax and ellipse Umax/w if Imax < ellipse center (-psiM/Ld)
// or ellipse center itself if Imax > ellipse center
Fdq idq2 = default(Fdq);
bool found = false;
var vle = buildVoltageLimitEllipse(speed, 1000, Imax, Umax);
var maxtorque_point = vle.curve[vle.maxtorque_point];
var minid_point = vle.curve[vle.minid_point];
if (maxtorque_point.Magnitude <= Imax)
{
idq2 = new Fdq {
d = maxtorque_point.d, q = maxtorque_point.q
};
found = true;
}
else if (minid_point.Magnitude > Imax) //Imax out of ellipse
{
found = false;
}
else
{
var range = Enumerable.Range(0, vle.maxtorque_point);
LinearSpline spline = LinearSpline.Interpolate(range.Select(k => vle.curve[k].Magnitude), range.Select(k => vle.curve[k].d));
double id = spline.Interpolate(Imax);
double iq = Math.Sqrt(Imax * Imax - id * id);
idq2 = new Fdq {
d = id, q = iq
};
found = true;
}
if (found)
{
//double id = idq2.d;//Imax * Math.Cos(beta * Math.PI / 180);
//double iq = idq2.q;//Imax * Math.Sin(beta * Math.PI / 180);
var data = calculatePointdata(idq2.d, idq2.q, speed);
mtcc.speeds.Add(speed);
mtcc.maxtorques.Add(data.torque);
mtcc.currents.Add(idq2);
mtcc.voltages.Add(new Fdq()
{
d = data.ud, q = data.uq
});
mtcc.power.Add(data.power);
mtcc.effs.Add(data.efficiency);
}
}
return(mtcc);
}
