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-{
- "cells": [
- {
- "cell_type": "markdown",
- "id": "6abc5329-fdea-4f76-ad5f-f6e8ecc8cdac",
- "metadata": {},
- "source": [
- "Design and Simulation of a Grid Forming Inverter\n",
- "System definition\n",
- "This notebook presents the complete design and verification of an inverter working as grid forming"
- ]
- },
- {
- "cell_type": "code",
- "execution_count": null,
- "id": "bc402d67",
- "metadata": {
- "vscode": {
- "languageId": "plaintext"
- }
- },
- "outputs": [],
- "source": [
- "clear all\n",
- "% Set the Octave Engine to run the simulation\n",
- "SetSimulationEnvironment;\n",
- "% Input Data\n",
- "Rf = 0.1\n",
- "Lf = 0.01\n",
- "Rc = 0.01\n",
- "Cf = 0.001\n",
- "Rl = 10\n",
- "Ll = 0.1\n",
- "om = 2*pi*50\n",
- "Vref = sqrt(3)*220"
- ]
- },
- {
- "cell_type": "markdown",
- "id": "446033c6",
- "metadata": {},
- "source": [
- "Current Loop\n",
- "First thing we design the current loop compensating the pole of the inductance and fixing the\n",
- "bandwidth"
- ]
- },
- {
- "cell_type": "code",
- "execution_count": null,
- "id": "02055711",
- "metadata": {
- "vscode": {
- "languageId": "plaintext"
- }
- },
- "outputs": [],
- "source": [
- "ombc = 600*2*pi\n",
- "Kpc = ombc*Lf\n",
- "Kic = ombc*Rf"
- ]
- },
- {
- "cell_type": "markdown",
- "id": "d3944599",
- "metadata": {},
- "source": [
- "As result we have the following frequency responses\n",
- "Open loop current"
- ]
- },
- {
- "cell_type": "code",
- "execution_count": null,
- "id": "6a86cc64",
- "metadata": {
- "vscode": {
- "languageId": "plaintext"
- }
- },
- "outputs": [],
- "source": [
- "Gc = tf(1,[Lf Rf])\n",
- "bode(Gc)"
- ]
- },
- {
- "cell_type": "markdown",
- "id": "556532ab",
- "metadata": {},
- "source": [
- "Adding the controller to the open loop"
- ]
- },
- {
- "cell_type": "code",
- "execution_count": null,
- "id": "bd6ffa04",
- "metadata": {
- "vscode": {
- "languageId": "plaintext"
- }
- },
- "outputs": [],
- "source": [
- "Rcur = tf([Kpc Kic],[1 0])\n",
- "Gopenc = Rcur*Gc\n",
- "bode(Gopenc)"
- ]
- },
- {
- "cell_type": "markdown",
- "id": "9415b65d",
- "metadata": {},
- "source": [
- "Voltage Loop\n",
- "The design is performed by tuning the PI control and assuming that ESR does not play a role and\n",
- "that the current loop is too fast for the voltage loop"
- ]
- },
- {
- "cell_type": "code",
- "execution_count": null,
- "id": "ac110f53",
- "metadata": {
- "vscode": {
- "languageId": "plaintext"
- }
- },
- "outputs": [],
- "source": [
- "ombv = 100*2*pi\n",
- "fim = 60*pi/180\n",
- "Gv = tf(1,[Cf 0])\n",
- "[Go Fo]= bode(Gv,ombv)\n",
- "Fo = Fo*pi/180;\n",
- "Kpv = cos(-pi+fim-Fo)/Go\n",
- "Kiv = -sin(-pi+fim-Fo)*ombv/Go"
- ]
- },
- {
- "cell_type": "code",
- "execution_count": null,
- "id": "4dead95b",
- "metadata": {
- "vscode": {
- "languageId": "plaintext"
- }
- },
- "outputs": [],
- "source": [
- "Rv = tf([Kpv Kiv],[1 0])\n",
- "Gopenv = Rv*Gv\n",
- "margin(Gopenv)"
- ]
- },
- {
- "cell_type": "code",
- "execution_count": null,
- "id": "9d1a0433",
- "metadata": {
- "vscode": {
- "languageId": "plaintext"
- }
- },
- "outputs": [],
- "source": [
- "% Set the Octave Engine to run the simulation\n",
- "SetSimulationEnvironment;\n",
- "tini = 0;\n",
- "tfinal = 0.1;\n",
- "dt = 0.0001;\n",
- "nflows = 44;\n",
- "nnode = 23;\n",
- "maxn = 20;\n",
- "toll = 0.0001;\n",
- "% Creating an hybrid diagram containing a power network and control\n",
- "hy = HybridSystem(nnode,nflows,tini,tfinal,dt,maxn,toll);\n",
- "% POWER NETWORK TOPOLOGY - Inverter+Filter+Load\n",
- "% Voltage Source\n",
- "c1{1} = Signal2Source(1,0,24);\n",
- "c1{2} = Signal2Source(2,0,25);\n",
- "c1{3} = Signal2Source(3,0,26);\n",
- "% Resistor\n",
- "c1{4} = Resistance(1,4,Rf);\n",
- "c1{5} = Resistance(2,5,Rf);\n",
- "c1{6} = Resistance(3,6,Rf);\n",
- "% Inductor\n",
- "c1{7} = Inductor(4,7,Lf);\n",
- "c1{8} = Inductor(5,8,Lf);\n",
- "c1{9} = Inductor(6,9,Lf);\n",
- "% Current Sensors\n",
- "c1{10} = CurrentSensor(7,10,29);\n",
- "c1{11} = CurrentSensor(8,11,30);\n",
- "c1{12} = CurrentSensor(9,12,31);\n",
- "% Capacitor Resistances\n",
- "c1{13} = Resistance(10,20,Rc);\n",
- "c1{14} = Resistance(11,21,Rc);\n",
- "c1{15} = Resistance(12,22,Rc);\n",
- "% Capacitor Filter\n",
- "c1{16} = Capacitor(20,23,Cf);\n",
- "c1{17} = Capacitor(21,23,Cf);\n",
- "c1{18} = Capacitor(22,23,Cf);\n",
- "% Line/Load Resistance\n",
- "c1{19} = Resistance(10,13,Rl);\n",
- "c1{20} = Resistance(11,14,Rl);\n",
- "c1{21} = Resistance(12,15,Rl);\n",
- "% Line/Load Inductor\n",
- "c1{22} = Inductor(13,16,Ll);\n",
- "c1{23} = Inductor(14,17,Ll);\n",
- "c1{24} = Inductor(15,18,Ll);\n",
- "% Current sensors on line\n",
- "c1{25} = CurrentSensor(16,19,34);\n",
- "c1{26} = CurrentSensor(17,19,35);\n",
- "c1{27} = CurrentSensor(18,19,36);\n",
- "% Voltage sensors across capacitors\n",
- "c1{28} = VoltageSensor(10,23,39);\n",
- "c1{29} = VoltageSensor(11,23,40);\n",
- "c1{30} = VoltageSensor(12,23,41);\n",
- "% Adding all the components to the network diagram\n",
- "hy.AddListComponents2Network(c1);\n",
- "CONTROL SYSTEM\n",
- "% Voltage Control\n",
- "b1{1} = Constant(1,Vref);\n",
- "b1{2} = Constant(2,0);\n",
- "b1{3} = Sum(1,42,3,1,-1);\n",
- "b1{4} = Sum(2,43,4,1,-1);\n",
- "b1{5} = PI(3,5,Kpv,Kiv,0);\n",
- "b1{6} = PI(4,6,Kpv,Kiv,0);\n",
- "% Feedforward and decoupling voltage loop\n",
- "b1{7} = Sum(5,8,9,1,1);\n",
- "b1{8} = Sum(6,7,10,1,-1);\n",
- "b1{9} = Gain(43,8,2*pi*50*Cf);\n",
- "b1{10} = Gain(42,7,2*pi*50*Cf);\n",
- "b1{11} = Sum(9,37,11,1,1);\n",
- "b1{12} = Sum(10,38,12,1,1);\n",
- "% Current Control\n",
- "b1{13} = Sum(11,32,13,1,-1);\n",
- "b1{14} = Sum(12,33,14,1,-1);\n",
- "b1{15} = PI(13,15,Kpc,Kic,0);\n",
- "b1{16} = PI(14,17,Kpc,Kic,0);\n",
- "% Feedforward and decoupling current loop\n",
- "b1{17} = Sum(15,16,19,1,1);\n",
- "b1{18} = Sum(17,18,20,1,-1);\n",
- "b1{19} = Gain(33,16,2*pi*50*Lf);\n",
- "b1{20} = Gain(32,18,2*pi*50*Lf);\n",
- "b1{21} = Sum(19,42,21,1,1);\n",
- "b1{22} = Sum(20,43,22,1,1);\n",
- "% Park Output Voltage Reference\n",
- "b1{23} = InvPark(21,22,2,24,25,26,23);\n",
- "% Angle Reference\n",
- "b1{24} = Constant(27,2*pi*50);\n",
- "b1{25} = Integrator(27,23,0);\n",
- "% Measurement Current Filter\n",
- "b1{26} = Park(29,30,31,32,33,44,23);\n",
- "% Measurement Voltage Filter\n",
- "b1{27} = Park(39,40,41,42,43,44,23);\n",
- "% Measurement Current Load\n",
- "b1{28} = Park(34,35,36,37,38,44,23);\n",
- "% Adding all the components to the Control Schema\n",
- "hy.AddListComponents2Schema(b1);\n",
- "% Initialization\n",
- "hy.Init();\n",
- "p=1;\n",
- "% Simulation Loop\n",
- "while hy.Step()\n",
- "time(p) = hy.GetTime();\n",
- "% Park Voltage\n",
- "out(1,p) = hy.GetFlow(42);\n",
- "out(2,p) = hy.GetFlow(43);\n",
- "% Park Currents\n",
- "out(3,p) = hy.GetFlow(32);\n",
- "out(4,p) = hy.GetFlow(33);\n",
- "% Phase Voltages\n",
- "out(5,p) = hy.GetFlow(39);\n",
- "out(6,p) = hy.GetFlow(40);\n",
- "out(7,p) = hy.GetFlow(41);\n",
- "% Phase Currents\n",
- "out(8,p) = hy.GetFlow(34);\n",
- "out(9,p) = hy.GetFlow(35);\n",
- "out(10,p) = hy.GetFlow(36);\n",
- "p=p+1;\n",
- "end"
- ]
- },
- {
- "cell_type": "markdown",
- "id": "d03968d1",
- "metadata": {},
- "source": [
- "Park Voltages on the filter"
- ]
- },
- {
- "cell_type": "code",
- "execution_count": null,
- "id": "754899a0",
- "metadata": {
- "vscode": {
- "languageId": "plaintext"
- }
- },
- "outputs": [],
- "source": [
- "plot(time,out(1,:),time,out(2,:));"
- ]
- }
- ],
- "metadata": {
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- "display_name": "Octave",
- "language": "octave",
- "name": "octave"
- },
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- "help_links": [
- {
- "text": "GNU Octave",
- "url": "https://www.gnu.org/software/octave/support.html"
- },
- {
- "text": "Octave Kernel",
- "url": "https://github.com/Calysto/octave_kernel"
- },
- {
- "text": "MetaKernel Magics",
- "url": "https://metakernel.readthedocs.io/en/latest/source/README.html"
- }
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- "mimetype": "text/x-octave",
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