//P_ref is a vector of power refenreces for tehe wind turbine with dimension 1xN //v_nac is a vector of wind speed at each wind turbine with dimension 1xN //P_demand is a scale of the wind farm power demand. //parm is a struct of wind turbine parameters e.g. NREL5MW public static void DistributePower(ILArray <double> v_nac, double P_demand, ILArray <double> Power, WindTurbineParameters parm, out ILArray <double> P_ref, out ILArray <double> P_a) { double rho; ILArray <double> R; ILArray <double> rated; int N; ILArray <double> Cp; double P_avail; rho = parm.rho; //air density for each wind turbine(probably the same for all) R = parm.radius.C; //rotor radius for each wind turbine(NREL.r=63m) rated = parm.rated.C; //Rated power for each wind turbine(NREL.Prated=5MW) N = parm.N; //Number of turbines in windfarm Cp = parm.Cp.C; // Max cp of the turbines for each wind turbine(NREL.Cp.max=0.45) P_a = ILMath.zeros(N, 1); P_ref = ILMath.zeros(N, 1); // Compute available power at each turbine for (var i = 0; i <= N - 1; i++) { //P_a=A*pi*r*r*Cp*v*v*v P_a[i] = Math.Min(rated.GetValue(i), (ILMath.pi / 2) * rho * Math.Pow(R.GetValue(i), 2) * Math.Pow(v_nac.GetValue(i), 3) * Cp.GetValue(i)); } //Compute total available power P_avail = (double)ILMath.sum(P_a); //Distribute power according to availibility for (var i = 0; i <= N - 1; i++) { if (P_demand < P_avail) { P_ref[i] = Math.Max(0, Math.Min(rated.GetValue(i), P_demand * P_a.GetValue(i) / P_avail)); } else { P_ref[i] = P_a.GetValue(i); } } }
protected static ILArray <double> sum(ILArray <double> ilArray) { return(ILMath.sum(ilArray)); }
//% 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); }