updated with Multi-terminal HVDC

ScriptsData/Admittance Scan/dcAdmittancescanPRBS.m

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+%% This function estimates the admittance as transfer functions between Idc vs Vdc
+%using transfer function estimation function available in control system
+%tool box.
+function sys=dcAdmittancescanPRBS(Vdc,f,data,o)
+    arguments
+     Vdc  {mustBeGreaterThanOrEqual(Vdc,0)} % Should be the amplitude of D axis disturbance in PU
+     f {mustBeVector} % Disturbance frequency vector in Hz
+     data {mustBeNonempty}  % Should be a output structure containing the simulation data    
+     o {mustBeNumeric} % Should be a numeric value defining the order of the model
+    end
+    w =2*pi*f;
+    if(Vdc>1e-6)
+        GDCfrd = frestimate(data.dataDC,w,'rad/s'); % Transfer function YDC
+        figure;
+        opt = tfestOptions('InitializeMethod','n4sid','Display','off','SearchMethod','lsqnonlin');
+        sysDC = tfest(GDCfrd,o,opt);% Filtered transfer function YDD
+        plotAdmittanceDC(sysDC,f) %Plots the Bode plots for D-axis admittance
+    end
+end

ScriptsData/Admittance Scan/plotAdmittanceDC.m

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+function plotAdmittanceDC(sysDC,f)
+h1=bodeplot(sysDC,{f(1)*2*pi,f(end)*2*pi}); % Bode plot
+setoptions(h1,'FreqUnits','Hz','grid','on','PhaseWrapping','off');
+legend('Y_DC','Location','best');
+title('DC Admittances');
+figure;
+subplot(2,1,1)
+nichols(sysDC)
+ngrid
+title('Admittance Nichols Chart'); % Nichols Chart for YDD
+subplot(2,1,2)
+pzplot(sysDC)
+title('Poles and Zeros'); % Eigen plot for YDD
+end

ScriptsData/HVDC/MTHVDCparameters.m

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+%% Simulation Parameters
+% This file sets the parameters for all the blocks and variables used in the simulation model
+%% Renewable plant parameters
+BatteryStoragePVPlantGFMParameters;% PV and Battery plant parameters
+WindFarmGFMControlParameters;% Wind plant parameters
+% windTurbine.turbineRadius=90; % Turbine radius in m
+% base.kV=4.16e3;
+% base.mVA=50e6;                                                  %Base MVA
+% base.z=(base.kV)^2/base.mVA; 
+%% Configure Mppt parameters
+% sweepTurbine;
+% plotPowerCurves;
+% mpptPower=maxPower*0.98;
+% mpptWindSpeed=windSpeedv;
+% mpptOmega=maxPowerRPM;
+%% HVDC Station Parameters
+HVDC.L=3.1e-5;
+HVDC.C=0.085;
+HVDC.Vdc=250e3;
+HVDC.Vdcbase=10e3;
+HVDC.Imaxpu=1.2;
+windTransformer.hv1=HVDC.Vdc/(1.3*sqrt(2));
+base.kV1=windTransformer.hv1;
+grid.sensorTime=2*Ts;
+Grid.governor_droop=1e-3;
+Grid.H=0.1;%0.1;
+Grid.MVA=80e6;%100e6;
+%%%
+%%
+%% Admittance Scan parameters
+scan.end=2;% time to end frequency scan
+scan.start=1.0;% time to start frequency scan
+scan.samplingfrequency=5e3;% Sampling frequency of frequency scan
+scan.Vd=0.02;% Disturbance voltage magnitude in PU
+scan.Vq=0.0;% Disturbance voltage magnitude in PU
+scan.f=[1:1e4]/(2*pi); % Range of disturbance frequency in Hz
+modelorder=4; % Model order to obtain a reduced ordered admittance model of the system
+Tsim=scan.end+0.2;
+%% Event timings
+time.renewablevariation=11;% time to change renewable power
+time.fault=11;% time to to create ac onshore fault
+time.load=11;% time to change load power
+time.dcfault=11;% time to create dc fault

ScriptsData/HVDC/offshoreWind.m

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+% Copyright 2023 The MathWorks, Inc.
+%% Simulation Parameters
+T=5e-5;                % Step size [s]
+Ts=5e-5;               % Control time step [s]
+Tsim=10;               % Simulation time span
+tevent=5;              % Time [s] at which events are triggered
+time.fault=Tsim+1;     % Fault instant [s]
+time.load=Tsim+1;      % load change instant [s]
+time.wind=Tsim+1;      % Wind velocity instant [s]
+time.island=Tsim+1;    % Islanded instant [s]
+time.lineTrip=Tsim+1;  % Line trip instant [s]
+islanded=0;            % Flag on islanding 
+%% Wind Transformer
+windTransformer.lv=4.16e3;  % Wind transformer lv side L-L voltage in V
+windTransformer.hv=230e3;   % Wind transformer hv side L-L voltage in V
+windTransformer.va=2.5e9;   % Wind transformer VA rating
+windTransformer.windingResistance=0.002;     % Winding resistance in pu
+windTransformer.windingLekageReactance=0.04; % Winding lekage reactance in pu
+windTransformer.zeroSequenceReactance=0.1;   % Winding zero sequence reactance in pu 
+%% Grid Parameters
+grid.voltage=230e3; % Actual supply L-L voltage used for simulating the system,
+grid.frequency=60;  % Supply frequency in Hz
+grid.rs=0.01;       % Grid source resistance in ohms 0.01;
+grid.ls=0.3e-3;     % Grid source inductance in Henry 3e-3;
+%%Grid Parameters
+grid.voltage=0.98*230e3;  % Supply L-L voltage           
+grid.governorDroop=0.1/(2*pi*grid.frequency); % Grid generator governor droop in (pu)
+grid.damping=0.2;         % Grid generator damping ratio 
+grid.mva=100e6;           % Grid generator VA base
+grid.H=0.4;               % Grid generator inertia in (sec)
+grid.pRef=0.5;            % Grid generator real power reference 
+grid.sensorTime=8e-5;     % Speed sensor tim delay in (sec)
+%% Parameters of Wind Turbine
+load('wind_turbine_Cp.mat')                 % Loading wind turbine power coefficient table
+load('wind_MPPT.mat')                       % Loading MPPT characteristics -power/omega vs wind speed                                                        
+load('wind_derating.mat')                   % Loading derating table - wind speed vs pitch angle
+% Rotor hub parameters
+windTurbine.turbineRadius               = 83;                        % (m) Turbine radius
+windTurbine.inertia                     = 3.2e8;                     % Inertia in kgm^2
+windTurbine.airDensity                  = 1.225;                     % (kg/m^3) Air density
+windTurbine.vWindThreshold              = 0.01;                      % (m/s) Threshold wind velocity to avoid divison by zero in Tip Speed Ratio calculation
+windTurbine.wThreshold                  = 0.01;                      % (rad/s) Threshold wind turbine velocity for numerical convergence
+windTurbine.cpBraking                   = -0.001;                    % Power coefficient for aerodynamic braking
+windTurbine.turbineRatedPower           = 6.5;                       % Power turbine rated power
+% Turbine state machine parameters
+windTurbine.vWindCutInLower             = 4;                            % (m/s) Cut in lower wind speed
+windTurbine.vWindCutOut                 = 23;                           % (m/s) Cut out wind speed
+windTurbine.vWindCutInUpper             = 0.9*windTurbine.vWindCutOut;  % (m/s) Cut in upper wind speed
+windTurbine.vWindRated                  = 11;                           % (m/s) Rated wind speed
+% Extending power coefficient table in aerodynamic pitch brake region
+windTurbine.numTSR                      = size(cp,2);                % Estimating size of power coefficient table
+windTurbine.pitch                       = [pitch,90,95];             % (deg) Extending pitch angle vector to brake region
+windTurbine.cp                          = [cp;windTurbine.cpBraking*ones(2,windTurbine.numTSR)]; % Power coefficient table extension to braking region
+windTurbine.TSR                         = TSR;
+%% 
+% *Wind Inverter Parameters*
+windInverter.imaxPU=1.2;                                      % Max current limit of inverter in (pu).
+windInverter.vdc=windTransformer.lv*sqrt(2)*2/(1*sqrt(3))*1.25; % Calculation of required dc voltage of inverter
+windInverter.c=1e-2;                                            % Inverter dc bus capacitance
+windInverter.l=(2*0.5e-3);                                      % Inverter ac side filter inductance
+windInverter.cFilter=1.1e-3;                                    % Inverter ac side filter capacitance 
+%Define base for Wind controller design
+base.kV=4.16e3;                                                 %Base KV
+base.mVA=100e6;                                                  %Base MVA
+base.z=(base.kV)^2/base.mVA;                                    %Base impedance
+%% Wind Controller Parameters
+%Current controller Wind inverter
+windController.tSensor=2e-5; % Sensor time constant
+windController.kpic=1.5;       % Proportional gain
+windController.kiic=250;     % Integral gain
+windController.kd=0;         % Derivative gain
+% AC Voltage controller Wind inverter
+windController.mv=0.05;       % Volatge controller gain
+windController.vRef=1.0;      % Volatge controller reference
+%DC bus Voltage_controller
+windController.kpv=4;         % Proportional gain
+windController.kiv=0.5;       % Integral gain
+windController.kdv=0.0;       % Derivative gain
+windController.vdcBase=1e3;   % Dc side base voltage in (Volts)
+%GFM wind controller parameters
+windController.kpvgfm=0.05; %Voltage controller proportional gain
+windController.kivgfm=0.3;  %Voltage controller integral gain
+windController.kdvgfm=0;    %Voltage controller derevative gain
+%% GFM using Dc link voltage control by GSC (G-GFM)
+%Parameters of G-GFM Transfer function 
+gGFM.kt=10.5;      %GFM tracking cofficient
+gGFM.kj=0.05;      %GFM inertia cofficient
+gGFM.kd=100;         %GFM damping cofficient
+gGFMTf=tf([1 gGFM.kt],[gGFM.kj gGFM.kd]); % G-GFM Real power vs Frequency Transfer function
+%Converting the Transfer Function Parameters to descrete domain
+gGFMTfz=c2d(gGFMTf,Ts/10);
+%Reactive Power and Current Limiter Parameters 
+gGFM.qref=0.01;     %GFM reactive power reference
+gGFM.kq=0.3;        %GFM reactive power droop cofficient
+gGFM.vref=1.0;     %GFM voltage reference
+gGFM.fref=60;       %GFM frequency reference
+gGFM.Imax=0.4;      %Current limit
+gGFM.x_vir=3e-1;    %Virtual reactance
+gGFM.r_vir=5e-2;  %Virtual resistance
+%% GFM using Dc link voltage control by MSC (M-GFM)
+mGFM.d=0.7;        %GFM damping cofficient
+mGFM.h=0.1;        %GFM inertia cofficient
+mGFM.kp=0.07;        %GFM active power droop cofficient
+mGFM.kq=1.95;      %GFM reactive power droop cofficient
+mGFM.Vd=1.0;       %GFM voltage reference
+mGFM.fref=60;      %GFM frequency reference
+mGFM.kpdc=0.3;     %DC bus voltage controller proportional gain
+mGFM.kidc=0.8;     %DC bus voltage controller integral gain 0.2
+mGFM.Imax=0.35;    %Current Limit
+mGFM.x_vir=0.3;    %Virtual reactance
+mGFM.r_vir=0.05;   %Virtual resistance
+
+%% Machine Parameters
+pmsm.pmax = 50.5e6;  % Maximum power                   [W]
+pmsm.ld   = 1.6e-4; % Stator d-axis inductance        [H]
+pmsm.lq   = 1.6e-4; % Stator q-axis inductance        [H]
+pmsm.rs   = 8.2e-5; % Stator resistance per phase     [Ohm]
+pmsm.psim = 9;      % Permanent magnet flux linkage   [Wb]
+pmsm.p    = 26;     % Number of pole pairs
+pmsm.alpha=6000;    % pmsm Current controller cofficient
+%% Transmission Line Parameters
+line.r=0.03;      % Resistance in Ohms per Km
+line.l=0.6;       % Inductance in mH per Km
+line.m=0.1;       % Mutual inductance in mH per Km
+line.cll=1.731e-2;% Capacitance line to line in micr0-farad per Km
+line.clg=6.751e-2;% Line to ground capacitance in micro-farad per Km
+line.mr=0;        % Line mutual resistance in ohms per km
+line.length1=100; % Line length in Km
+%% Feeder Parameters
+feeder.r=0.026;           % Feeder resistance in Ohms per Km
+feeder.l=2.1e-4;          % Feeder inductance in Henry per Km 
+feeder.length=0.5;        % Feeder length in Km
+%% Loads
+loads.P1=5e6;  %Load 1 real power
+loads.Q1=1e6;  %Load 1 reactive power
+loads.P2=1e6;  %Load 2 real power
+%% Grid Code Settings
+%(Following the IEEE 2800 standards)
+lvrt.time=[0.32,0.32,0.32,1.2,3,6,inf,inf,1800,1,1,0.015,0.003,0.001,0.0002]; % Trip time vs Volatge (PU)
+lvrt.voltage=[0,0.1,0.25,0.5,0.7,0.9,0.91,1.05,1.051,1.11,1.19,1.2,1.4,1.6,1.7];
+%Volatge vs Reactive Current Injection (Following the German Grid Code)
+lvrt.iq=[1,1,0.2,0,0];  % Reactive current vs Volatge (PU)
+lvrt.voltageiq=[0,.5,.9,.91,1];
+% Frequency Ride Through characteristics: Frequency (Hz) vs Tripping Time (sec) (Following the IEEE 2800 standards)
+frt.time=[0.1,299,inf,299,299,0.1,0.1];
+frt.frequency=([-0.2,-0.05,-0.02,0.021,0.03,0.031,0.2]+1)*grid.frequency;
+code.vh=1.1;          %Voltage upper limit
+code.vl=0.9;          %Voltage lower limit
+code.fh=61.2;         %Frequency upper limit
+code.fl=58.8;         %Frequency lower limit
+gridCode="IEEE 2800"; %Default grid code for tests
+%% PLL Parameteters
+pll.kp=100;  %Proportional PLL gain
+pll.ki=2000; %Integral PLL gain
+WindControl=1; %Choose Grid Model 1 for grid forming G-GFM and 2 for M-GFM control
+WindVSMControlDClink=Simulink.Variant(' WindControl == 1 ');
+WindVSMControlTurbineInertia =Simulink.Variant(' WindControl == 2 ');
+%% Standard Compliance Table
+TableIII=readtable('BatteryStoragePVPlantGFMTableComplianceIEEEStd.xlsx','VariableNamingRule', 'preserve');
+TableIII.('Satisfied'){1}= char(hex2dec('2713'));
+TableIII.('Satisfied'){2}= char(hex2dec('2713'));
+TableIII.('Satisfied'){3}= char(hex2dec('2713'));
+TableIII.('Satisfied'){4}= char(hex2dec('2713'));
+TableIII.('Satisfied'){5}= char(hex2dec('2713'));
+TableIII=table(TableIII,'VariableNames',{'Table: Compliance on Key Criteria mentioned in Standards'});
+%% Initilazation of model with GGFM control as default wind GFM Controller
+imGFM=0; %Set flag to 1 for initating the initilization process with MGFM control
+%%

ScriptsData/HVDC/plotHVDC.m

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+function plotHVDC(Data,Tsim)
+%UNTITLED2 Summary of this function goes here
+PS1 = getsamples(Data.PST1,find(Data.tout==0.2):find(Data.tout==Tsim))/1e6;
+PS2 = getsamples(Data.PST2,find(Data.tout==0.2):find(Data.tout==Tsim))/1e6;
+PS3 = getsamples(Data.PST3,find(Data.tout==0.2):find(Data.tout==Tsim))/1e6;
+PS4 = getsamples(Data.PST4,find(Data.tout==0.2):find(Data.tout==Tsim))/1e6;
+PS5 = getsamples(Data.PST5,find(Data.tout==0.2):find(Data.tout==Tsim))/1e6;
+PS6 = getsamples(Data.PST6,find(Data.tout==0.2):find(Data.tout==Tsim))/1e6;
+V1 = getsamples(Data.Vabc,find(Data.tout==0.2):find(Data.tout==Tsim));
+I1 = getsamples(Data.Iabc,find(Data.tout==0.2):find(Data.tout==Tsim));
+V = getsamples(Data.Vmag,find(Data.tout==0.2):find(Data.tout==Tsim));
+F = getsamples(Data.f,find(Data.tout==0.2):find(Data.tout==Tsim));
+aboveLinev = (V.Data>1.1 | V.Data<0.9);
+% Create 2 copies of v
+bottomLinev = V.Data;
+topLinev = V.Data;
+% Set the values you don't want to get drawn to nan
+bottomLinev(aboveLinev) = NaN;
+topLinev(~aboveLinev) = NaN;
+%%
+aboveLinef = (F.Data>61.2 | F.Data<58.8);
+% Create 2 copies of v
+bottomLinef = F.Data;
+topLinef = F.Data;
+% Set the values you don't want to get drawn to nan
+bottomLinef(aboveLinef) = NaN;
+topLinef(~aboveLinef) = NaN;
+c=figure;
+subplot(2,2,1)
+plot(PS1)
+hold on;
+plot(PS2);
+plot(PS3);
+xlim([0.5 Tsim])
+ylim([0 500])
+ylabel('MW');
+grid on;
+legend('P_{Station 1}','P_{Station 2}','P_{Station 3}',Location='best');
+title('Real Power From Onshore Stations')
+subplot(2,2,2)
+plot(PS4)
+hold on;
+plot(PS5);
+plot(PS6);
+xlim([0.5 Tsim])
+ylabel('MW');
+grid on;
+legend('P_{Station 4}','P_{Station 5}','P_{Station 6}',Location='best');
+title('Real Power From Offshore Stations')
+subplot(2,2,3)
+plot(V.Time,bottomLinev,V.time,topLinev);
+hold on;
+plot(Data.tout,1.1*ones(size(Data.tout)),'--g');
+plot(Data.tout,0.9*ones(size(Data.tout)),'--g');
+xlim([0.5 Tsim]);
+xlabel('Time (sec)');
+ylabel('PU');
+grid on;
+d=find(V.Data>1.1 | V.Data<0.9);
+if(length(d)>0)
+     lgd=legend('V_{mag}','V_{out of limit}','V_{limits}',Location='best'); 
+else
+    lgd=legend('V_{mag}','','V_{limits}',Location='best');
+end
+title('Volatge Magnitude at Onshore Station 1')
+subplot(2,2,4)
+plot(F.Time,bottomLinef,F.time,topLinef);
+hold on;
+plot(Data.tout,61.2*ones(size(Data.tout)),'--g');
+plot(Data.tout,58.8*ones(size(Data.tout)),'--g');
+xlim([0.5 Tsim]);
+xlabel('Time (sec)');
+ylabel('Hz');
+grid on;
+df=find(F.Data>61.2 | F.Data<58.8);
+if(length(df)>0)
+     lgd=legend('F','F_{out of limit}','F_{limits}',Location='best'); 
+else
+    lgd=legend('F','','F_{limits}',Location='best');
+end
+title('Onshore Frequency at POI')
+set(c,'position',[0,0,700,400]); 
+d=figure;
+subplot(2,1,1)
+plot(V1);
+xlim([0.5 Tsim])
+ylim([-2 2])
+ylabel('PU');
+grid on;
+title('Volatges at Onshore Station 1')
+subplot(2,1,2)
+plot(I1);
+xlim([0.5 Tsim])
+ylim([-2 2])
+ylabel('PU');
+grid on;
+title('Currents at Onshore Station 1')
+end