/// <summary>
/// Multidimensional scaling/PCoA: transform distances to points in a coordinate system.
/// </summary>
/// <param name="input">A matrix of pairwise distances. Zero indicates identical objects.</param>
/// <returns>A matrix, the columns of which are coordinates in the nth dimension.
/// The rows are in the same order as the input.</returns>
public static ILArray <double> Scale(ILArray <double> input)
{
int n = input.Length;
ILArray <double> p = ILMath.eye <double>(n, n) - ILMath.repmat(1.0 / n, n, n);
ILArray <double> a = -.5 * ILMath.multiplyElem(input, input);
ILArray <double> b = ILMath.multiply(p, a, p);
ILArray <complex> V = ILMath.empty <complex>();
ILArray <complex> E = ILMath.eig((b + b.T) / 2, V);
ILArray <int> i = ILMath.empty <int>();
ILArray <double> e = ILMath.sort(ILMath.diag(ILMath.real(E)), i);
e = ILMath.flipud(e);
i = ILMath.toint32(ILMath.flipud(ILMath.todouble(i)));
ILArray <int> keep = ILMath.empty <int>();
for (int j = 0; j < e.Length; j++)
{
if (e[j] > 0.000000001)
{
keep.SetValue(j, keep.Length);
}
}
ILArray <double> Y;
if (ILMath.isempty(keep))
{
Y = ILMath.zeros(n, 1);
}
else
{
Y = ILMath.zeros <double>(V.S[0], keep.Length);
for (int j = 0; j < keep.Length; j++)
{
Y[ILMath.full, j] = ILMath.todouble(-V[ILMath.full, i[keep[j]]]);
}
Y = ILMath.multiply(Y, ILMath.diag(ILMath.sqrt(e[keep])));
}
ILArray <int> maxind = ILMath.empty <int>();
ILMath.max(ILMath.abs(Y), maxind, 0);
int d = Y.S[1];
ILArray <int> indices = maxind + ILMath.toint32(ILMath.array <int>(SteppedRange(0, n, (d - 1) * n)));
ILArray <double> colsign = ILMath.sign(Y[indices]);
for (int j = 0; j < Y.S[1]; j++)
{
Y[ILMath.full, j] = Y[ILMath.full, j] * colsign[j];
}
return(Y);
}
//% The main file for running the wind farm controll and wake simulation.
// It is not completely done yet. Further updates will come
// Currently there are only 4 turbines, for test purposes. But is should be
// easily updated to a larger number of turbines.
// Similarly there is a lot of room for speed optimizations, even though it
// now runs slowly with only 4 turbines
// 19/07-13 MS
public static double[][] Simulation(WakeFarmControlConfig config)
{
var parm = new WindTurbineParameters();
ILMatFile env;
ILMatFile wt;
ILArray <int> idx;
ILArray <double> ee;
double Ki;
double Kp;
int PC_MaxPit;
int PC_MinPit;
double VS_CtInSp;
double VS_RtGnSp;
double VS_Rgn2K;
double omega0;
double beta0;
double power0;
ILArray <double> x;
ILArray <double> u0;
ILArray <double> u;
ILArray <double> Mg_old;
ILArray <double> P_ref;
ILArray <double> Pa;
ILArray <double> Power;
ILArray <double> Ct;
ILArray <double> P_ref_new;
ILArray <double> v_nac;
double alpha;
double Mg_max_rate;
ILArray <double> e;
ILArray <double> Mg;
ILArray <double> beta;
ILArray <double> Cp;
ILArray <double> Omega;
ILArray <double> out_;
if (config.NTurbines == 0)
{
return(null);
}
// Wind farm properties
//turbine properties
env = wt = new ILMatFile(config.NREL5MW_MatFile); //Load parameters from the NREL 5MW turbine
parm.N = config.NTurbines; // number of turbines in farm
parm.rho = (double)env.GetArray <double>("env_rho"); //air density
parm.radius = ((double)(wt.GetArray <double>("wt_rotor_radius"))) * ILMath.ones(1, config.NTurbines); // rotor radius (NREL5MW)
parm.rated = 5e6 * ILMath.ones(1, config.NTurbines); //rated power (NREL5MW)
parm.ratedSpeed = (double)wt.GetArray <double>("wt_rotor_ratedspeed"); //rated rotor speed
idx = ILMath.empty <int>();
ILMath.max(wt.GetArray <double>("wt_cp_table")[ILMath.full], idx); //Find index for max Cp;
parm.Cp = ILMath.ones(1, config.NTurbines) * wt.GetArray <double>("wt_cp_table").GetValue(idx.ToArray()); //Set power coefficent to maximum value in the cp table
parm.Ct = ILMath.ones(1, config.NTurbines) * wt.GetArray <double>("wt_ct_table").GetValue(idx.ToArray()); //Set power coefficent to maximum value in the ct table
// NOTE: controller parameters should be imported from the wt....struct in
//Pitch control
ee = 0; //blade pitch integrator
Ki = 0.008068634 * 360 / 2 / ILMath.pi; // integral gain (NREL5MW)
Kp = 0.01882681 * 360 / 2 / ILMath.pi; // proportional gain (NREL5MW)
PC_MaxPit = 90;
PC_MinPit = 0;
//region control NREL
VS_CtInSp = 70.16224;
VS_RtGnSp = 121.6805;
VS_Rgn2K = 2.332287;
// load initial wind data
var wind = new ILMatFile(config.Wind_MatFile);
//% Set initial conditions
omega0 = 1.267; //Rotation speed
beta0 = 0; //Pitch
var timeLine = (int)config.TimeLine();
power0 = parm.rated.GetValue(0); //Power production
x = (omega0 * ILMath.ones(parm.N, 1)).Concat((wind.GetArray <double>("wind").GetValue(0, 1) * ILMath.ones(parm.N, 1)), 1);
u0 = (beta0 * ILMath.ones(parm.N, 1)).Concat((power0 * ILMath.ones(parm.N, 1)), 1);
u = u0.C;
Mg_old = u[ILMath.full, 1];
P_ref = ILMath.zeros(parm.N, (int)config.TimeLine()); //Initialize matrix to save the power production history for each turbine
Pa = P_ref.C; //Initialize available power matrix
Power = P_ref.C;
Ct = parm.Ct.C; //Initialize Ct - is this correct?
Ct[timeLine - 1, ILMath.full] = Ct[0, ILMath.full];
P_ref_new = power0 * ILMath.ones(config.NTurbines, 1);
v_nac = ILMath.zeros(Ct.Size[1], timeLine);
Mg = ILMath.zeros(u.Size[0], timeLine);
beta = ILMath.zeros(u.Size[0], timeLine);
Omega = ILMath.zeros(Ct.Size[1], timeLine);
Cp = ILMath.zeros(timeLine, parm.Cp.Size[1]);
var turbineModel = new TurbineDrivetrainModel();
//% Simulate wind farm operation
//var timeLine = (int) config.TimeLine();
for (var i = 2; i <= timeLine; i++) //At each sample time(DT) from Tstart to Tend
{
//Calculate the wake using the current Ct values
{
ILArray <double> out_v_nac;
WakeCalculation.Calculate((Ct[i - 1 - 1, ILMath.full]), i, wind, out out_v_nac);
v_nac[ILMath.full, i - 1] = out_v_nac;
}
x[ILMath.full, 1] = v_nac[ILMath.full, i - 1];
//Farm control
//Calculate the power distribution references for each turbine
if (config.EnablePowerDistribution)
{
ILArray <double> out_Pa;
PowerDistributionControl.DistributePower(v_nac[ILMath.full, i - 1], config.Pdemand, Power[ILMath.full, i - 1 - 1], parm, out P_ref_new, out out_Pa);
Pa[ILMath.full, i - 1] = out_Pa;
}
//Hold the demand for some seconds
if (ILMath.mod(i, ILMath.round(config.PRefSampleTime / config.DT)) == 2) //???
{
P_ref[ILMath.full, i - 1] = P_ref_new;
}
else
{
if (config.PowerRefInterpolation)
{
alpha = 0.01;
P_ref[ILMath.full, i - 1] = (1 - alpha) * P_ref[ILMath.full, i - 1 - 1] + (alpha) * P_ref_new;
}
else
{
P_ref[ILMath.full, i - 1] = P_ref_new;
}
}
//Calculate control for each individual turbine - should be moved to the
//turbine (drivetrain) model.
//Torque controller
for (var j = 1; j <= parm.N; j++)
{
if ((x.GetValue(j - 1, 0) * 97 >= VS_RtGnSp) || (u.GetValue(j - 1, 0) >= 1)) // We are in region 3 - power is constant
{
u.SetValue(P_ref.GetValue(j - 1, i - 1) / x.GetValue(j - 1, 0), j - 1, 1);
}
else if (x.GetValue(j - 1, 0) * 97 <= VS_CtInSp) //! We are in region 1 - torque is zero
{
u.SetValue(0.0, j - 1, 1);
}
else //! We are in region 2 - optimal torque is proportional to the square of the generator speed
{
u.SetValue(97 * VS_Rgn2K * x.GetValue(j - 1, 0) * x.GetValue(j - 1, 0) * Math.Pow(97, 2), j - 1, 1);
}
}
//Rate limit torque change
// u(:,2) - Mg_old;
Mg_max_rate = 1e6 * config.DT;
u[ILMath.full, 1] = ILMath.sign(u[ILMath.full, 1] - Mg_old) * ILMath.min(ILMath.abs(u[ILMath.full, 1] - Mg_old), Mg_max_rate) + Mg_old;
//Pitch controller
e = 97 * (omega0 * ILMath.ones(parm.N, 1) - x[ILMath.full, 0]);
ee = ee - config.DT * e;
ee = ILMath.min(ILMath.max(ee, PC_MinPit / Ki), PC_MaxPit / Ki);
u[ILMath.full, 0] = -Kp * config.DT * e + Ki * ee;
for (var j = 1; j <= parm.N; j++)
{
u.SetValue(Math.Min(Math.Max(u.GetValue(j - 1, 0), PC_MinPit), PC_MaxPit), j - 1, 0);
}
if (!config.EnableTurbineDynamics)
{
u = u0;
}
Mg[ILMath.full, i - 1] = u[ILMath.full, 1];
Mg_old = Mg[ILMath.full, i - 1];
beta[ILMath.full, i - 1] = u[ILMath.full, 0]; //Set pitch
//Turbine dynamics - can be simplified
if (config.EnableTurbineDynamics)
{
for (var j = 1; j <= parm.N; j++)
{
double out_x;
double out_Ct;
double out_Cp;
turbineModel.Model(x[j - 1, ILMath.full], u[j - 1, ILMath.full], wt, env, config.DT, out out_x, out out_Ct, out out_Cp);
x.SetValue(out_x, j - 1, 0);
Ct.SetValue(out_Ct, i - 1, j - 1);
Cp.SetValue(out_Cp, i - 1, j - 1);
}
}
else
{
Ct[i - 1, ILMath.full] = parm.Ct;
Cp[i - 1, ILMath.full] = parm.Cp;
x[ILMath.full, 0] = parm.ratedSpeed;//Rotational speed
}
Omega[ILMath.full, i - 1] = x[ILMath.full, 0];
Power[ILMath.full, i - 1] = Omega[ILMath.full, i - 1] * Mg[ILMath.full, i - 1];
}
//% Save output data
out_ = (config.DT * (ILMath.counter(0, 1, config.TimeLine())));
out_ = out_.Concat(v_nac.T, 1);
out_ = out_.Concat(Omega.T, 1);
out_ = out_.Concat(beta.T, 1);
out_ = out_.Concat(P_ref.T, 1);
out_ = out_.Concat(Ct, 1);
out_ = out_.Concat(Cp, 1);
out_ = out_.Concat(Pa.T, 1);
out_ = out_.Concat(Mg.T, 1);
out_ = out_.Concat(Power.T, 1);
//Ttotal power demand
var l = config.NTurbines * 3 + 1;
var r = l + config.NTurbines - 1;
out_ = out_.Concat(ILMath.sum(out_[ILMath.full, ILMath.r(l, r)], 1) / 1e6, 1); // P_ref sum
l = config.NTurbines * 6 + 1;
r = l + config.NTurbines - 1;
out_ = out_.Concat(ILMath.sum(out_[ILMath.full, ILMath.r(l, r)], 1) / 1e6, 1); // Pa sum. 'Power Demand'
out_ = out_.Concat(ILMath.sum(Power).T / 1e6, 1); // 'Actual Production'
//Ttotal power demand
out_ = out_.Concat(ILMath.sum(P_ref.T, 1), 1); // 'Demand'
out_ = out_.Concat(ILMath.sum(Pa.T, 1), 1); // 'Available'
out_ = out_.Concat(ILMath.sum(Mg * Omega).T, 1); // 'Actual'
//Total power produced
out_ = out_.Concat((Mg * Omega).T, 1);
var out_doubleArray = new double[out_.Size[0]][];
for (int i = 0; i <= out_doubleArray.GetLength(0) - 1; i++)
{
out_doubleArray[i] = new double[out_.Size[1]];
for (int j = 0; j <= out_doubleArray[i].GetLength(0) - 1; j++)
{
out_doubleArray[i][j] = out_.GetValue(i, j);
}
}
return(out_doubleArray);
}