{ "cells": [ { "cell_type": "markdown", "id": "ef584adf-8286-4bfa-9482-ed1a2dbda382", "metadata": {}, "source": [ "# Leistungsmessung\n", "\n", "Wir kennen nun bereits die Prinzipien zur Spannungs- und Strommessung. Der elektrische Stromnfluss dient dazu, Systeme anzutreiben, die **elektrische Leistung (in der Einheit Watt, W)** benötigen, wie z.B. einen Elektromotor. \n", "Um die Leistung in einem Schaltkreis zu bestimmen, müssen wir gleichzeitig die Spannung $U$ und Stromstärke $I$ messen. Das Grundprinzip der Leistungsmessung ist in {numref}`leistungsmessung_motor_stromrichtig` dargestellt. Diese beiden Messgrößen werden anschließend miteinander multipliziert. \n", "\n", ":::{figure-md} leistungsmessung_motor_stromrichtig\n", "\"leistungsmessung_motor_stromrichtig\"\n", "\n", "Schaltung zur Messung elektrischer Leistungen.\n", ":::\n", "\n", "## Leistungsmessung bei Gleichstrom\n", "\n", "Bei Gleichstrom gilt folgendes: \n", "\n", "$$P = U \\cdot I$$\n", "\n", "Es gibt verschiedene Messgeräte, die bereits intern eine Spannungs- und Stromstärkemessung integriert haben. Manche Geräte haben nur einen Ein- und Ausgang und man muss sich über die Beschaltung keine Gedanken machen, da es nur eine Möglichkeit gibt. Andere Messgeräte bieten die Flexibilität selber entscheiden zu können, wo Volt- und Amperemeter in der Schaltung angeschlossen werden können. Hierbei gibt es zwei Möglichkeiten:\n", "\n", "* **Stromrichtige** Leistungsmessung: Die Spannungsmessung erfolt an der Quelle und die Strommessung direkt am Verbraucher. \n", "* **Spannungsrichtige** Leistungsmessung: Die Spannungsmessung wird an dem Verbraucher angelegt und somit *richtig* gemessen. \n", "\n", "Bei der Messung zwischen diesen beiden Varianten wird es zu relevanten Unterschieden kommen, die das Messergebnis und die Abweichung beeinflussen.\n", "\n", "### Stromrichtige Leistungsmessung\n", "\n", "In {numref}`stromrichtig_innen` ist die *stromrichtige* Beschaltung der Leistungsmessung gezeigt, wobei die Innenwiderstände der einzelnen Messgeräte, $R_V$ und $R_A$ angegeben sind. Der Verbraucher hat den Widerstand $R_L$ (Last-Widerstand). Rechts daneben ist ein Ersatzschaltbild der stromrichtigen Leistungsmessung skizziert. Die Stromstärke wird direkt (*richtig*) am Motor, an der Last, gemessen. \n", "\n", ":::{figure-md} stromrichtig_innen\n", "\"stromrichtig_innen\"\n", "\n", "Stromrichtige Schaltung zur Messung elektrischer Leistungen.\n", ":::\n", "\n", "Die Messeingänge liefern die Messgräßen $U$ und $I$, woraus wir die Leistung ermitteln:\n", "\n", "$$P = U \\cdot I = (U_{R_A} + U_{R_L}) \\cdot I = R_A \\cdot I^2 + U_{R_L} = P_{R_A} + P_{R_L}$$\n", "\n", "In dieser Anschaltung wird nicht nur der Spannungsabfall an der Last, sondern fälschlicherweise auch am Strommessgerät. Dadurch wird ebenfalls der Leistungsverbrauch am Innenwiderstand $R_A$ des Strommessgeräts gemessen. \n", "Hierbei handelt es sich allerdings um eine systematisch Abweichung, die korrigiert werden kann. Im Datenblatt des Strommesseingangs wird der Innenwiderstand abgelesen oder extern ermittelt. Die systematisch Messabweichung ergibt sich zu\n", "\n", "$$A = R_A \\cdot I^2$$\n", "\n", "und muss daher nur noch mit dem Quadrat der gemessenen Stromstärke multipliziert werden. \n", "Anhand dieser Gleichung für die Messabweichung erkennt man, dass **je kleiner der Innenwiderstand $R_A$, desto kleiner die Messabweichung**. \n", "\n", "\n", "### Spannungsrichtige Leistungsmessung\n", "\n", "In {numref}`spannungsrichtig_innen` ist die *spannungsrichtige* Beschaltung der Leistungsmessung gezeigt, wobei die Innenwiderstände der einzelnen Messgeräte, $R_V$ und $R_A$ angegeben sind. Der Verbraucher hat den Widerstand $R_L$ (Last-Widerstand). Rechts daneben ist ein Ersatzschaltbild der spannungsrichtigen Leistungsmessung skizziert. Die Spannung wird nun direkt (*richtig*) am Motor, an der Last, gemessen. \n", "\n", ":::{figure-md} spannungsrichtig_innen\n", "\"spannungsrichtig_innen\"\n", "\n", "Spannungsrichtige Schaltung zur Messung elektrischer Leistungen.\n", ":::\n", "\n", "In dieser Anschaltung wird nun ein zu hoher Strom gemessen, nämlich der, der durch den Motor fließt und der Stromverlust aufgrund des Innenwiderstands des Spannungsmessgeräts:\n", "\n", "$$P = U \\cdot I = U \\cdot \\left( \\frac{U}{R_V} + \\frac{U}{R_L} \\right) = \\frac{U^2}{R_V} + \\frac{U^2}{R_L} = P_{R_V} + P_{R_L}$$\n", "\n", "Die Leistungsmessung gibt einen zu hohen Wert aus, der aufgrund des Leistungsverbrauchs des Spannungsmessgeräts anfällt. Auch hierbei handelt es sich um eine systematische Messabweichung, die mit der Kenntnis des Innenwiderstand $R_V$ korrigiert werden kann:\n", "\n", "$$A = \\frac{U^2}{R_V}$$\n", "\n", "Sollte die Korrektur nicht vorgenommen werden, so **steigt die Messabweichung indirekt proportional mit $R_V$**, bei gleichbleibender Spannung. \n", "\n", ":::{admonition} Aufgabe\n", ":class: tip\n", "Wie groß ist die Messabweichung für eine stromrichtige, bzw. spannungsrichtige Anschaltung einer Leistungsmessung an einem Lastwiderstand von $R_L = 10\\,\\Omega$, der mit einer Gleichspannung von $U = 22\\,\\mathrm{V}$ und einem Nennstrom von $I = 5\\,\\mathrm{A}$ betrieben wird? Die Innenwiderstände für Spannungs- bzw. Strommesseingang betragen $R_V = 2\\,\\mathrm{M\\Omega}$ und $R_A = 1\\,\\Omega$. Was ändert sich, wenn wir einen schlechteren Strommesseingang mit $R_A = 10\\,\\Omega$ verwenden? Die Ausgabe des folgenden Code-blocks liefert euch die Ergebnisse.\n", ":::" ] }, { "cell_type": "code", "execution_count": 1, "id": "d934bda7-e9f3-497a-8040-22397986acf2", "metadata": { "tags": [ "hide-input" ] }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Die Leistungsaufnahme am Gleichstrommotor beträgt demnach P = 110 W.\n", "\n", "-------- Messabweichung bei gutem Strommesseingang (R_A = 1 Ohm): ------------\n", "Stromrichtige Anschaltung: \t P_A= 25 W\n", "Spannungsrichtige Anschaltung: \t P_A= 0.000242 W\n", "\n", "-------- Messabweichung bei schlechtem Strommesseingang (R_A = 10 Ohm): ------------\n", "Stromrichtige Anschaltung: \t P_A= 250 W\n", "Spannungsrichtige Anschaltung: \t P_A= 0.000242 W\n" ] } ], "source": [ "U = 22 #V Gleichspannung\n", "I = 5 #A Nennstrom\n", "R_L = 10 #Ohm, Innenwiderstand Gleichstrommotor\n", "#print('Ein Gleichstrommotor mit Innenwiderstand R_L =',R_L,'Ohm wird mit', U, 'V Gleichspannung und', I, 'A Nennenstrom betrieben.')\n", "print('Die Leistungsaufnahme am Gleichstrommotor beträgt demnach P =', U*I, 'W.')\n", "R_V = 2e6 #Ohm, Innenwiderstand Spannungsmesseingang\n", "R_A = 1 #Ohm, Innenwiderstand Strommesseingang\n", "#print('Zur Leistungsbestimmung benutzen wir einen Spannungsmesseingang mit einem Innenwiderstand von R_V=',R_V/1e6,'MOhm und einen Strommesseingang mit einem Innenwiderstand von R_A=',R_A,'Ohm.')\n", "\n", "\n", "print('\\n-------- Messabweichung bei gutem Strommesseingang (R_A =',R_A,'Ohm): ------------')\n", "\n", "# Stromrichtige Anschaltung:\n", "A_stromrichtig = R_A * I**2\n", "\n", "# Spannungsrichtige Anschaltung:\n", "A_spannungsrichtig = U**2 / R_V\n", "\n", "print('Stromrichtige Anschaltung: \\t P_A=', A_stromrichtig, 'W')\n", "print('Spannungsrichtige Anschaltung: \\t P_A=', A_spannungsrichtig, 'W')\n", "\n", "\n", "R_A = 10 #Ohm, Innenwiderstand Strommesseingang\n", "print('\\n-------- Messabweichung bei schlechtem Strommesseingang (R_A =',R_A,'Ohm): ------------')\n", "\n", "# Stromrichtige Anschaltung:\n", "A_stromrichtig = R_A * I**2\n", "\n", "# Spannungsrichtige Anschaltung:\n", "A_spannungsrichtig = U**2 / R_V\n", "\n", "print('Stromrichtige Anschaltung: \\t P_A=', A_stromrichtig, 'W')\n", "print('Spannungsrichtige Anschaltung: \\t P_A=', A_spannungsrichtig, 'W')" ] }, { "cell_type": "markdown", "id": "c23d9f89-df61-4e2f-b90f-4c0ab2b68904", "metadata": {}, "source": [ "Nach dem Lösen der Aufgabe sollte euch aufgefallen sein, dass bei einem schlechteren Strommmesseingang sogar mehr Leistung bei der Strommessung verbraucht wird als an dem Motor selber. Die spannungsrichtige Anschaltung liefert hierbei einen deutlichen Vorteil und ist standardmäßig in den vielen Messgeräten bereits genau so eingebaut. Werden die Messströme $I$ jedoch recht klein, so kann die stromrichtige Anschaltung zu ggf. genaueren Messungen und geringerem Leistungsverbrauch führen.\n", "\n", "### Energieverbrauch\n", "\n", "Eine weitere häufig benutzt Messgröße ist die **elektrische Energie E (in der Einheit Ws)**. Diese gibt an, wie hoch der Verbraucht über eine bestimmte Zeitspanne ist und ist somit ein Maß für die aufgewandte elektrische Arbeit:\n", "\n", "$$E = U \\cdot I \\cdot t$$\n", "\n", "Besteht eine Zeitabhängigkeit bei $U$ und $I$, so muss man zusätzlich über die Zeit integrieren:\n", "\n", "$$E = \\int P(t) dt = \\int U(t)\\cdot I(t) dt$$\n", "\n", "$U(t)$ und $I(t)$, hier großgeschrieben, sind immer noch Gleichgrößen, die sich zwar mit der Zeit ändern, jedoch keine Wechselgrößen sind. D.h. Kenngrößen wie Gleichrichtwert oder Effektivwert existieren nicht." ] }, { "cell_type": "markdown", "id": "53dd297e-8298-4328-b48e-3321e9b0f1e5", "metadata": {}, "source": [ "## Leistungsmessung bei Wechselstrom\n", "\n", "Im Kapitel [Messsignal und Kenngrößen](3_Kenngroessen.ipynb) haben wir uns die Kenngrößen von Wechselgrößen angesehen. Bei der Leistungsmessung von Wechselstromsystemen kommen fast ausschließlich Sinussignale *ohne Gleichanteil* vor. Die Wechselgrößen $u(t)$ und $i(t)$ durch einen Verbraucher können wir also wiefolgt annehmen:\n", "\n", "$$u(t) = \\hat u \\cdot \\sin(\\omega t)$$\n", "\n", "und \n", "\n", "$$i(t) = \\hat i \\cdot \\sin(\\omega t + \\phi)$$" ] }, { "cell_type": "code", "execution_count": 2, "id": "cad9cab9-c08f-45d3-9908-95829d35363f", "metadata": { "tags": [ "hide-input" ] }, "outputs": [ { "data": { "text/html": [ " \n", " " ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "image/png": "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\n", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "#Benötigte Libraries:\n", "import numpy as np\n", "import pandas as pd\n", "import matplotlib.pyplot as plt\n", "import plotly.offline as py\n", "py.init_notebook_mode(connected=True)\n", "import plotly.graph_objs as go\n", "import plotly.tools as tls\n", "import seaborn as sns\n", "import time\n", "import warnings\n", "warnings.filterwarnings('ignore')\n", "\n", "# MatplotLib Settings:\n", "plt.style.use('default') # Matplotlib Style wählen\n", "#plt.xkcd()\n", "plt.rcParams['font.size'] = 10; # Schriftgröße\n", "\n", "A = 1.0 # Amplitude\n", "f = 10 # Frequenz in Hz\n", "phi = 0. # Phase in radian\n", "T = 1/f # Perdiodendauer\n", "t = np.linspace(0,2*T,100) # Zeitwerte der Sinusfunktion in sec\n", "\n", "fig = plt.figure(figsize=(7,3))\n", "ax = fig.add_axes([0.1, 0.1, 0.8, 0.8])\n", "ax.plot(t,A * np.sin(2*np.pi*f*t + phi), 'tab:blue',label = r'$u(t) = \\hat u \\cdot \\sin(\\omega t)$')\n", "ax.plot(t,A * np.sin(2*np.pi*f*t + 1.), 'tab:red', label = r'$i(t) = \\hat i \\cdot \\sin(\\omega t + \\phi)$')\n", "plt.annotate(r'', xy=(0.87*T, 0.25*A), xytext=(1.05*T, 0.25*A), arrowprops=dict(arrowstyle='->'))\n", "plt.annotate(r'$+ \\phi$', xy=(0.25*T, 0.25*A), xytext=(0.94*T, 0.35*A))\n", "ax.set_xlabel('Zeit')\n", "ax.set_ylabel('Spannung (V) bzw. Strom (A) ')\n", "ax.set_xlim(0,2*T)\n", "ax.set_xticks([0, T, 2*T])\n", "ax.set_xticklabels(['0','T','2T'])\n", "ax.set_yticks([-A, 0, A])\n", "ax.set_yticklabels([r'$-\\hat u, \\hat i$','0','$\\hat u, \\hat i$'])\n", "#ax.set_title(r'u(t) =%5.1f $\\cdot$ sin(%5.1f Hz $\\cdot t$ + $\\phi$)' %(A, 2*np.pi*f))\n", "ax.grid()\n", "ax.legend()\n", "plt.show()" ] }, { "cell_type": "markdown", "id": "17c30989-b327-425b-9729-199757b0bb70", "metadata": {}, "source": [ "Die Phasenverschiebung des Stroms um $\\phi$ ist je nach elektronischer Komponente unterschiedlich:\n", "\n", "* bei einem rein **ohmschen Verbraucher**, wie z.B. einem Widerstand oder Heizmatte, ist $\\phi = 0$\n", "* bei einer **idealen Spule (Induktivität)** ist $\\phi = -90^\\circ$\n", "* bei einem **idealen Kondensator (Kapazität)** ist $\\phi = +90^\\circ$\n", "\n", "Ein negatives Vorzeichen bedeutet, dass sich das Stromsignal auf der Zeitachse nach rechts verschiebt. Im Bild oben handelt es sich um einen nicht idealen Kondensator mit weniger als $\\phi = +90^\\circ$ Phasenverschiebung. Dies kommt in Schaltungen vor, die auch andere Komponenten besitzen. Die Gesamtcharakteristik ist jedoch kapazitiv. \n", "\n", "### Wirkleistung\n", "\n", "Um die **Leistung $P$** zu bestimmen, wir in einem Verbraucher wirkt, müssen wir die Momentanleistungen über eine Perdiode $T$ mitteln. Die **Momentanleistung** ergibt sich aus der Multiplikation der zu dem Zeitpunkt angenommen Strom- bzw. Spannungswerte, also folgt für die gemittelte Leistung:\n", "\n", "$$\n", "\\begin{align}\n", "P &= \\frac{1}{T} \\int_0^T \\hat u \\cdot \\sin(\\omega t) \\cdot \\hat i \\cdot \\sin(\\omega t + \\phi) dt \\\\\n", "&= \\frac{1}{2T} \\hat u \\hat i \\int_0^T \\left[ \\cos(-\\phi) - \\cos(2\\omega t + \\phi) \\right] \\\\\n", "&= \\frac{\\hat u}{\\sqrt{2}} \\cdot \\frac{\\hat i}{\\sqrt{2}}\\cdot \\cos(\\phi) \\\\\n", "&= u_\\mathrm{eff} \\cdot i_\\mathrm{eff} \\cdot \\cos(\\phi)\n", "\\end{align}\n", "$$\n", "\n", ":::{admonition} Aufgabe\n", ":class: tip\n", "Beweise die obige Formel für die Leistung $P$. Verwende für den ersten Schritt das Additionstheorem\n", "\n", "$$\\sin x \\sin y = \\frac{1}{2}\\left[ \\cos(x-y) - \\cos(x+y) \\right]$$\n", "\n", "Was gilt für das Integral der 2. Cosinus-Funktion über eine Periode $T$?\n", ":::" ] }, { "cell_type": "markdown", "id": "eb44a2aa-ef7a-4fc3-890c-83f305c2735c", "metadata": {}, "source": [ "Die Leistung kann also direkt aus den Effektivwerten der Wechselgrößen bestimmt werden, sofern die Phasenverschiebung $\\phi$ bekannt ist. \n", "\n", ":::{warning} \n", "Achtung, die Formel gilt nur bei Sinusschwingungen!\n", ":::\n", "\n", "Diese Leistung nennt man auch **Wirkleistung** im Verbraucher, und $\\cos(\\phi)$ nennt man auch **Leistungsfaktor oder Wirkfaktor, Wirkleistungsfaktor**.\n", "\n", "### Messung der Wirkleistung\n", "\n", "Um im Labor die Wirkleistung zu messen, müssen wir die beiden Effektivwerte für Spannung und Strom bestimmen, sowie die Phasenbeziehung zwischen den beiden Wechselgrößen, und zwar bei genau des Messfrequenz $f$. Hierfür gibt es verschiedene Varianten:\n", "\n", "* es werden Zeitserien für die beiden Wechselgrößen mit einem Oszilloskop aufgenommen\n", "* es können theoretische Betrachtungen über das innere des Verbrauchers gemacht werden (wenn es denn seitens des Herstellers überhaupt möglich ist). Dies benötigt aber ein gewisses elektrotechnisches Know-How\n", "* viele Verbraucher werden mit 230V Wechselspannung betrieben und der Leistungsfaktor ist seitens des Herstellers hierfür direkt angegeben. In Deutschland haben wir eine Netzfrequenz von 50Hz, wofür der Leistungsfaktor dann gilt. Typischerweise liegt der Wert zwischen 0.85-0,95.\n", "\n", "### Stromrichtige und spannungsrichtige Anschaltung\n", "\n", "Die Betrachtungen, die wir weiter oben für die Leistungsmessung mit Gleichstrom, gemacht haben, gelten unverändert auch für Leistungsmessungen im Wechselstromssystem. Auch hier gibt es stromrichtige und spannungsrichtige Anschaltungen. \n", "\n", "### Blindleistung\n", "\n", "Zusätzlich zur Wirkleistung gibt es noch die **Blindleistung**. Befinden sich beispielsweise Induktivitäten im Verbraucher, so wir diesen ein periodischer Strom zugeführt, der das magnetische Feld in der Spule erzeugt. Beim Zusammenbruch des magnetischen Feldes wird dieser Strom zurück gespeist. Das gleich gilt auch für Kapazitäten und elektrische Felder. Das heißt es existieren **Blindströme**, die im Leitungsnetz zwischen Quelle und Verbraucher hin und her pendeln. Die korrespondierende **Blindleistung** werden jedoch nicht in Arbeit umgesetzt und *wirken* daher nicht im Verbraucher, wie es bei der *Wirkleistung* der Fall ist. Es handelt sich jedoch um *echte* Leistungen, weshalb sie das Leitungsnetz entsprechend *belasten* und beim Design von Schaltungen berücksichtigt werden müssen. \n", "\n", "Die Blindleistung wird mi t $Q$ angeben und berechnet sich ähnlich wie die Wirkleistung. nur wird der Cosinus durch einen Sinus ausgetauscht:\n", "\n", "$$Q = u_\\mathrm{eff} \\cdot i_\\mathrm{eff} \\cdot \\sin(\\phi)$$\n", "\n", "$Q$ wird oftmals in der **Einheit Var (var)** angegeben.\n", "\n", "### Scheinleistung\n", "\n", "Die Scheinleistung, $S$, ist die vektorielle Addition von Wirk- und Blindleistung:\n", "\n", "$$S = \\sqrt{P^2 + Q^2} = u_\\mathrm{eff} \\cdot i_\\mathrm{eff}$$\n", "\n", "$S$ wird oftmals in der **Einheit Voltampere (VA)** angegeben.\n", "\n", "### Energieverbrauch\n", "\n", "Der Energieverbrauch in einem Wechselstromsystem berechnet sich zu\n", "\n", "$$E = \\int P(t) dt = \\int u_\\mathrm{eff} \\cdot i_\\mathrm{eff} \\cdot \\cos(\\phi) dt$$" ] }, { "cell_type": "markdown", "id": "ee4f91b3-71e9-4f5d-914a-cba338b91fbb", "metadata": {}, "source": [ "## Leistungsmessung in Drehstromsystemen\n", "\n", "Wenn man einen Verbraucher hat, der einen etwas höheren Leistungsverbrauch hat, wie z.B. Kochherde, werden diese üblicherweise nicht mit dem 230V-Wechselstromnetz betrieben. Statt dessen nutzt man den sogenannten **Drehtstrom (oder auch Dreiphasenwechselstrom, oder Kraftstrom)**. Maschinen in der Industrie werden fast nur mit Drehstrom betrieben. \n", "\n", ":::{figure-md} drehstrom_netz\n", "\"drehstrom_netz\"\n", "\n", "Anschluss eines Verbrauchers, einer Last, an ein Drehtstromnetzwerk.\n", ":::\n", "\n", "In {numref}`drehstrom_netz` der Anschluss eines Verbrauchers an das Drehstromnetzwerk dagestellt. Über drei **Außenleiter $L_1, L_2, L_3$** wird der Verbraucher versorgt und der **Neutralleiter $N$** dient als gemeinsame Rückführung.\n", "\n", "Der Verlauf der *drei Phasen* mit jeweils 50Hz Netzfrequenz ist in folgendem Diagramm in Bezug auf den Neutralleiter dargestellt:" ] }, { "cell_type": "code", "execution_count": 3, "id": "b02e9e69-3aa0-4383-8a91-8f303c603d85", "metadata": { "tags": [ "hide-input" ] }, "outputs": [ { "data": { "text/html": [ " \n", " " ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "image/png": "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\n", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "#Benötigte Libraries:\n", "import numpy as np\n", "import pandas as pd\n", "import matplotlib.pyplot as plt\n", "import plotly.offline as py\n", "py.init_notebook_mode(connected=True)\n", "import plotly.graph_objs as go\n", "import plotly.tools as tls\n", "import seaborn as sns\n", "import time\n", "import warnings\n", "warnings.filterwarnings('ignore')\n", "\n", "# MatplotLib Settings:\n", "plt.style.use('default') # Matplotlib Style wählen\n", "#plt.xkcd()\n", "plt.rcParams['font.size'] = 10; # Schriftgröße\n", "\n", "A = 1.0 # Amplitude\n", "f = 50 # Frequenz in Hz\n", "phi = 0. # Phase in radian\n", "T = 1/f # Perdiodendauer\n", "t = np.linspace(0,2*T,100) # Zeitwerte der Sinusfunktion in sec\n", "\n", "fig = plt.figure(figsize=(7,3))\n", "ax = fig.add_axes([0.1, 0.1, 0.8, 0.8])\n", "ax.plot(t,A * np.sin(2*np.pi*f*t + phi), 'tab:blue',label = r'$u_{1N}(t) = \\hat u \\cdot \\sin(\\omega t)$')\n", "ax.plot(t,A * np.sin(2*np.pi*f*t - 2*np.pi/3), 'tab:red', label = r'$u_{2N}(t) = \\hat u \\cdot \\sin(\\omega t - 120^\\circ)$')\n", "ax.plot(t,A * np.sin(2*np.pi*f*t - 4*np.pi/3), 'tab:orange', label = r'$u_{3N}(t) = \\hat u \\cdot \\sin(\\omega t - 240^\\circ)$')\n", "#plt.annotate(r'', xy=(0.87*T, 0.25*A), xytext=(1.05*T, 0.25*A), arrowprops=dict(arrowstyle='->'))\n", "#plt.annotate(r'$+ \\phi$', xy=(0.25*T, 0.25*A), xytext=(0.94*T, 0.35*A))\n", "ax.set_xlabel('Zeit (s)')\n", "ax.set_ylabel('Spannung (V)')\n", "ax.set_xlim(0,2*T)\n", "ax.set_xticks([0, T, 2*T])\n", "#ax.set_xticklabels(['0','T','2T'])\n", "ax.set_yticks([-A, 0, A])\n", "ax.set_yticklabels([r'$-\\hat u$','0','$\\hat u$'])\n", "#ax.set_title(r'u(t) =%5.1f $\\cdot$ sin(%5.1f Hz $\\cdot t$ + $\\phi$)' %(A, 2*np.pi*f))\n", "ax.grid()\n", "ax.legend()\n", "plt.show()" ] }, { "cell_type": "markdown", "id": "91575f8f-e6ff-4b49-94d1-469e294ced9d", "metadata": {}, "source": [ "Diese Spannungen werden auch häufig **Sternspannungen** genannt und liegen jeweils 120° außer Phase zueinander. Diese Phasenverschiebung hat einen historischen Hintergrund. Damals hat man klassische Drehstromgeneratoren aus drei, um 120° versetzte, Spulen realisiert. Durch einen rotierbaren Magneten wurde dann sinusförmig Spannungen induziert, mit halt 120° Phasenverschiebung. \n", "\n", "### Effektivwert\n", "\n", "In Deutschland und den meisten anderen europäischen Ländern beträgt der Effektivwert der Sternspannung 230V, also genau der gleiche Wert wie im klassichen 230V Haushaltsnetz. Allerdings ist die Strombelastbarkeit deutlich erhöht, indem Leitungen mit größeren Querschnitten verwendet werden. Die **Effektivwerte** zwischen zwei beliebigen Außenleitern betragen immer:\n", "\n", "$$u_{12} = u_{23} = u_{31} = 230\\,\\mathrm V \\cdot \\sqrt{3} \\approx 400\\,\\mathrm V$$\n", "\n", "Daher kommt auch der umgangssprachliche Begriff 400V-Drehstrom. \n", "\n", ":::{admonition} Aufgabe\n", ":class: tip\n", "Wenn 230V der Effektivwert unseres Haushaltsstroms sind, welche Amplitude $\\hat u$ hat dann die Sinusspannung?\n", ":::\n", "\n", "### Wirkleistung\n", "\n", "In {numref}`drehstrom_wirk` ist dargestellt, wie die Wirkleistung in einem Drehstromnetzwerk gemessen wird. \n", "\n", ":::{figure-md} drehstrom_wirk\n", "\"drehstrom_wirk\"\n", "\n", "Messung der Wirkleistung in einem Drehstromnetzwerk.\n", ":::\n", "\n", "Wie auch bei der klassichen Wirkleistungsmessung wird parallel Strom und Spannung gemessen, bzw. deren Effektivwerte natürlich. Aus den Effektivwerten wird dann jeweils die Wirkleistung in jedem Außenleiter bestimmt:\n", "\n", "$$P = u_\\mathrm{eff} \\cdot i_\\mathrm{eff} \\cdot \\cos(\\phi)$$\n", "\n", "Die Gesamtleistung ergibt sich aus der Summe der Einzelmessungen:\n", "\n", "$$P = P_1 + P_2 + P_3$$\n", "\n", "Auch hier gelten wieder die Regeln und abweichungen für strom- bzw. spannungsrichtige Anschaltung der Messinstrumente während der Leistungsmessung. " ] }, { "cell_type": "code", "execution_count": null, "id": "3fad57ff-ff93-4166-9339-67253a7732d5", "metadata": {}, "outputs": [], "source": [] } ], "metadata": { "kernelspec": { "display_name": "Python 3", "language": "python", "name": "python3" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.9.12" } }, "nbformat": 4, "nbformat_minor": 5 }