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where A is the peak voltage and the voltages on L1, L2 and L3 are measured relative to the neutral.

Balanced loads

Generally, in electric power systems the loads are distributed as evenly as practical between the phases. It is usual practice to discuss a balanced system first and then describe the effects of unbalanced systems as deviations from the elementary case.

To keep the calculations simple we shall normalise A and R to 1 for the remainder of these calculations

Star connected systems with neutral

Constant power transfer

An important property of three-phase power is that the power available to a resistive load, $P = V I = \frac{V^2}R$ , is constant at all times.

since we have eliminated x we can see that the total power does not vary with time. This is essential for keeping large generators and motors running smoothly.

No neutral current

Star connected systems without neutral

Since we have shown that the neutral current is zero we can see that removing the neutral core will have no effect on the circuit, provided the system is balanced. In reality such connections are generally used only when the load on the three phases is part of the same piece of equipment (for example a three-phase motor), as otherwise switching loads and slight imbalances would cause large voltage fluctuations.

Three-Phase

Most alternating-current (AC) generation and transmission, and a good part of use, take place through three-phase circuits. If you want to understand electric power, you must know something about three-phase. It is rather simple if you go at it the right way, though it has a reputation for difficulty.

Phase is a frequently-used term around AC. The word comes from Greek fasis, "appearance," from fanein, "to appear." It originally referred to the eternally regular changing appearance of the moon through each month, and then was applied to the periodic changes of some quantity, such as the voltage in an AC circuit. Electrical phase is measured in degrees, with 360° corresponding to a complete cycle. A sinusoidal voltage is proportional to the cosine or sine of the phase.

Three-phase, abbreviated 3φ, refers to three voltages or currents that that differ by a third of a cycle, or 120 electrical degrees, from each other. They go through their maxima in a regular order, called the phase sequence. The three phases could be supplied over six wires, with two wires reserved for the exclusive use of each phase. However, they are generally supplied over only three wires, and the phase or line voltages are the voltages between the three possible pairs of wires. The phase or line currents are the currents in each wire. Voltages and currents are usually expressed as rms or effective values, as in single-phase analysis.

When you connect a load to the three wires, it should be done in such a way that it does not destroy the symmetry. This means that you need three equal loads connected across the three pairs of wires. This looks like an equilateral triangle, or delta, and is called a delta load. Another symmetrical connection would result if you connected one side of each load together, and then the three other ends to the three wires. This looks like a Y, and is called a wye load. These are the only possibilities for a symmetrical load. The center of the Y connection is, in a way, equidistant from each of the three line voltages, and will remain at a constant potential. It is called the neutral, and may be furnished along with the three phase voltages. The benefits of three-phase are realized best for such a symmetrical connection, which is called balanced. If the load is not balanced, the problem is a complicated one one whose solution gives little insight, just numbers. Such problems are best left to computer circuit analysis. Three-phase systems that are roughly balanced (the practical case) can be analyzed profitably by a method called symmetrical components. Here, let us consider only balanced three-phase circuits, which are the most important anyway.

The key to understanding three-phase is to understand the phasor diagram for the voltages or currents. In the diagram at the right, a, b and c represent the three lines, and o represents the neutral. The red phasors are the line or delta voltages, the voltages between the wires. The blue phasors are the wye voltages, the voltages to neutral. They correspond to the two different ways a symmetrical load can be connected. The vectors can be imagined rotating anticlockwise with time with angular velocity ω = 2πf, their projections on the horizontal axis representing the voltages as functions of time. Note how the subscripts on the V's give the points between which the voltage is measured, and the sign of the voltage. V_ab is the voltage at point a relative to point b, for example. The same phasor diagram holds for the currents. In this case, the line currents are the blue vectors, and the red vectors are the currents through a delta load. The blue and red vectors differ in phase by 30°, and in magnitude by a factor of √3, as is marked in the diagram.

Suppose we want to take two phase wires and neutral to make a three-wire household service supplying 120 V between each hot wire and ground. The neutral will become the grounded conductor, the two phases the hot conductors. Then, the wye voltage is 120, so the delta voltage will be √3 x 120 = 208 V. This is the three-phase line voltage necessary in this case. Note that the two 120 V sources are not opposite in phase, and will not give 240 V between them. On the other hand, suppose we do want a 240 V service. Then this must be the line voltage, and the voltages to neutral will be 139 V, not 120 V. A 120 V three-phase service will give only 69 V from line to neutral. Note that √3 appears everywhere, and that the differences in phase explain the unexpected results.

If the load consists of general impedances Z, the situation is described by current and voltage phasors connected by V = IZ, both in magnitude and phase. The diagrams are similar in shape, and rotated by the phase angle between voltage and current in each impedance. Remember that the line voltages are the red vectors, while the line currents are the blue vectors. Z relates either the line voltages and delta currents, or the wye voltages and the line currents, depending on the connection. Z does not relate the line current and line voltage, which are different in phase by 30° even for unity power factor (pure resistance load).

This comes out more clearly when we consider the power P delivered to the load. For a resistive delta load, P = 3 V_lineI_delta = √3 V_lineI_line, since I_delta = √3 I_line. For a wye load, P = 3 V_wyeI_line = √3 V_lineI_line. This is, of course, the same expression. For other than unity power factor, this must be multiplied by cos θ, which is the angle of Z, not the phase difference between the line voltage and line current. This means, most emphatically, that our usual rule for finding the power from phasors does not apply to three-phase!

If you write out the three phase currents as explicit functions of time, I_maxcos ωt, I_maxcos (ωt - 120°) and I_maxcos (ωt + 120°), square them, multiply by the resistance R, and add, the result is the constant (3/2)I_max²R = 3 I²R. The power is applied steadily as in DC circuits, not in pulses as in single-phase AC circuits. This is a great advantage, giving three-phase machines 48% greater capacity than identical single-phase machines.

In Germany and Switzerland, where three-phase power was originated and developed, it is known as Drehstrom, "rotating current" for this property of constant power. Ordinary AC is called Wechselstrom, or "change current." Nikola Tesla, the discoverer of polyphase currents and inventor of the induction motor, employed two-phase current, where the phase difference is 90°. This also can be used to create a rotating magnetic field, and is more efficient than single-phase, but is not quite as advantageous as three-phase. Two-phase power was once rather common in the United States, where Tesla was important in the introduction of AC, but has now gone completely out of use.

Two-phase can be supplied over three wires, but there is no true neutral, since the phases are not symmetrical. However, it is always easy to double the number of phases in a transformer secondary by making two secondary windings and connecting them in opposing phases. Four-phase does have a neutral, like three-phase, but requires four wires. In fact, three-phase is more economical than any other number of phases. For applications like rectifiers and synchronous converters where DC is produced, it is most efficient to use six-phase AC input, which is easily produced from three-phase in a transformer.

If you are transmitting a certain amount of power single-phase, adding one more conductor operated at the same line voltage and current and using three-phase will increase the power transmitted by 72% with only a 50% increase in the amount of copper and losses. The advantage is obvious. Under certain conditions, transmitting a certain amount of power by three-phase only requires 75% of the copper of single-phase transmission. This is not the major advantage of three-phase, but it does play a factor.

Three wires are usually seen in high-voltage transmission lines, whether on towers or poles, with pin or suspension insulators. Some high-voltage lines are now DC, since solid state devices make it easier to convert to and from AC. The DC lines are free of the problems created by phase, as well as eliminating the skin effect that reduces the effective area of the conductors. It is not nearly as easy to manage long-distance electrical transmission as might be thought.

Unbalanced systems

Practical systems rarely have perfectly balanced loads, currents, voltages or impedances in all three phases. The analysis of unbalanced cases is greatly simplified by the use of the techniques of symmetrical components. An unbalanced system is analyzed as the superposition of three balanced systems, each with the positive, negative or zero sequence of balanced voltages.

Revolving magnetic field

Any polyphase system, by virtue of the time displacement of the currents in the phases, makes it possible to easily generate a magnetic field that revolves at the line frequency. Such a revolving magnetic field makes polyphase induction motors possible. Indeed, where induction motors must run on single-phase power (such as is usually distributed in homes), the motor must contain some measure to produce a revolving field, otherwise the motor cannot generate any stand-still torque and will not start. The field produced by a single-phase winding can provide energy to a motor already rotating, but without auxiliary functions the motor will not accelerate from a stop when energized.

Conversion to other phase systems

Provided two voltage waveforms have at least some relative displacement on the time axis, other than a multiple of a half-cycle, any other polyphase set of voltages can be obtained by an array of passive transformers. Such arrays will evenly balance the polyphase load between the phases of the source system. For example, balanced two-phase power can be obtained from a three-phase network by using two specially constructed transformers, with taps at 50% and 86.6% of the primary voltage. This Scott T connection produces a true two-phase system with 90° time difference between the phases. Another example is the generation of higher-phase-order systems for large rectifier systems, to produce a smoother DC output and to reduce the harmonic currents in the supply.

When three-phase is needed but only single-phase is readily available from the utility company a phase converter can be used to generate three-phase power from the single phase supply. The US Phase Converter Standards Organization conducts independent three phase tests on the various phase converter technologies and publishes the results.

If the frequency (HZ) of the three-phase power supplied does not match the frequency needed to run the machines or equipment a Frequency converter can be used

Three-phase Y and Δ configurations

Initially we explored the idea of three-phase power systems by connecting three voltage sources together in what is commonly known as the "Y" (or "star") configuration. This configuration of voltage sources is characterized by a common connection point joining one side of each source:

If we draw a circuit showing each voltage source to be a coil of wire (alternator or transformer winding) and do some slight rearranging, the "Y" configuration becomes more obvious:

The three conductors leading away from the voltage sources (windings) toward a load are typically called lines, while the windings themselves are typically called phases. In a Y-connected system, there may or may not be a neutral wire attached at the junction point in the middle, although it certainly helps alleviate potential problems should one element of a three-phase load fail open, as discussed earlier:

When we measure voltage and current in three-phase systems, we need to be specific as to where we're measuring. Line voltage refers to the amount of voltage measured between any two line conductors in a balanced three-phase system. With the above circuit, the line voltage is roughly 208 volts. Phase voltage refers to the voltage measured across any one component (source winding or load impedance) in a balanced three-phase source or load. For the circuit shown above, the phase voltage is 120 volts. The terms line current and phase current follow the same logic: the former referring to current through any one line conductor, and the latter to current through any one component.

Y-connected sources and loads always have line voltages greater than phase voltages, and line currents equal to phase currents. If the Y-connected source or load is balanced, the line voltage will be equal to the phase voltage times the square root of 3:

However, the "Y" configuration is not the only valid one for connecting three-phase voltage source or load elements together. Another configuration is known as the "Delta," for its geometric resemblance to the Greek letter of the same name (Δ). Take close notice of the polarity for each winding in the drawing below:

At first glance it seems as though three voltage sources like this would create a short-circuit, electrons flowing around the triangle with nothing but the internal impedance of the windings to hold them back. Due to the phase angles of these three voltage sources, however, this is not the case.

One quick check of this is to use Kirchhoff's Voltage Law to see if the three voltages around the loop add up to zero. If they do, then there will be no voltage available to push current around and around that loop, and consequently there will be no circulating current. Starting with the top winding and progressing counter-clockwise, our KVL expression looks something like this:

Indeed, if we add these three vector quantities together, they do add up to zero. Another way to verify the fact that these three voltage sources can be connected together in a loop without resulting in circulating currents is to open up the loop at one junction point and calculate voltage across the break:

Starting with the right winding (120 V ∠ 120^o) and progressing counter-clockwise, our KVL equation looks like this:

Sure enough, there will be zero voltage across the break, telling us that no current will circulate within the triangular loop of windings when that connection is made complete.

Having established that a Δ-connected three-phase voltage source will not burn itself to a crisp due to circulating currents, we turn to its practical use as a source of power in three-phase circuits. Because each pair of line conductors is connected directly across a single winding in a Δ circuit, the line voltage will be equal to the phase voltage. Conversely, because each line conductor attaches at a node between two windings, the line current will be the vector sum of the two joining phase currents. Not surprisingly, the resulting equations for a Δ configuration are as follows:

With each load resistance receiving 120 volts from its respective phase winding at the source, the current in each phase of this circuit will be 83.33 amps:

So, the each line current in this three-phase power system is equal to 144.34 amps, substantially more than the line currents in the Y-connected system we looked at earlier. One might wonder if we've lost all the advantages of three-phase power here, given the fact that we have such greater conductor currents, necessitating thicker, more costly wire. The answer is no. Although this circuit would require three number 1 gage copper conductors (at 1000 feet of distance between source and load this equates to a little over 750 pounds of copper for the whole system), it is still less than the 1000+ pounds of copper required for a single-phase system delivering the same power (30 kW) at the same voltage (120 volts conductor-to-conductor).

One distinct advantage of a Δ-connected system is its lack of a neutral wire. With a Y-connected system, a neutral wire was needed in case one of the phase loads were to fail open (or be turned off), in order to keep the phase voltages at the load from changing. This is not necessary (or even possible!) in a Δ-connected circuit. With each load phase element directly connected across a respective source phase winding, the phase voltage will be constant regardless of open failures in the load elements.

Perhaps the greatest advantage of the Δ-connected source is its fault tolerance. It is possible for one of the windings in a Δ-connected three-phase source to fail open without affecting load voltage or current!

The only consequence of a source winding failing open for a Δ-connected source is increased phase current in the remaining windings. Compare this fault tolerance with a Y-connected system suffering an open source winding:

With a Δ-connected load, two of the resistances suffer reduced voltage while one remains at the original line voltage, 208. A Y-connected load suffers an even worse fate with the same winding failure in a Y-connected source:

In this case, two load resistances suffer reduced voltage while the third loses supply voltage completely! For this reason, Δ-connected sources are preferred for reliability. However, if dual voltages are needed (e.g. 120/208) or preferred for lower line currents, Y-connected systems are the configuration of choice.

Three-phase power systems

Split-phase power systems achieve their high conductor efficiency and low safety risk by splitting up the total voltage into lesser parts and powering multiple loads at those lesser voltages, while drawing currents at levels typical of a full-voltage system. This technique, by the way, works just as well for DC power systems as it does for single-phase AC systems. Such systems are usually referred to as three-wire systems rather than split-phase because "phase" is a concept restricted to AC.

But we know from our experience with vectors and complex numbers that AC voltages don't always add up as we think they would if they are out of phase with each other. This principle, applied to power systems, can be put to use to make power systems with even greater conductor efficiencies and lower shock hazard than with split-phase.

Suppose that we had two sources of AC voltage connected in series just like the split-phase system we saw before, except that each voltage source was 120^o out of phase with the other:

Since each voltage source is 120 volts, and each load resistor is connected directly in parallel with its respective source, the voltage across each load must be 120 volts as well. Given load currents of 83.33 amps, each load must still be dissipating 10 kilowatts of power. However, voltage between the two "hot" wires is not 240 volts (120 ∠ 0^o - 120 ∠ 180^o) because the phase difference between the two sources is not 180^o. Instead, the voltage is:

Nominally, we say that the voltage between "hot" conductors is 208 volts (rounding up), and thus the power system voltage is designated as 120/208.

If we calculate the current through the "neutral" conductor, we find that it is not zero, even with balanced load resistances. Kirchhoff's Current Law tells us that the currents entering and exiting the node between the two loads must be zero:

So, we find that the "neutral" wire is carrying a full 83.33 amps, just like each "hot" wire.

Note that we are still conveying 20 kW of total power to the two loads, with each load's "hot" wire carrying 83.33 amps as before. With the same amount of current through each "hot" wire, we must use the same gage copper conductors, so we haven't reduced system cost over the split-phase 120/240 system. However, we have realized a gain in safety, because the overall voltage between the two "hot" conductors is 32 volts lower than it was in the split-phase system (208 volts instead of 240 volts).

The fact that the neutral wire is carrying 83.33 amps of current raises an interesting possibility: since it's carrying current anyway, why not use that third wire as another "hot" conductor, powering another load resistor with a third 120 volt source having a phase angle of 240^o? That way, we could transmit more power (another 10 kW) without having to add any more conductors. Let's see how this might look:

A full mathematical analysis of all the voltages and currents in this circuit would necessitate the use of a network theorem, the easiest being the Superposition Theorem. I'll spare you the long, drawn-out calculations because you should be able to intuitively understand that the three voltage sources at three different phase angles will deliver 120 volts each to a balanced triad of load resistors. For proof of this, we can use SPICE to do the math for us:

Sure enough, we get 120 volts across each load resistor, with (approximately) 208 volts between any two "hot" conductors and conductor currents equal to 83.33 amps. At that current and voltage, each load will be dissipating 10 kW of power. Notice that this circuit has no "neutral" conductor to ensure stable voltage to all loads if one should open. What we have here is a situation similar to our split-phase power circuit with no "neutral" conductor: if one load should happen to fail open, the voltage drops across the remaining load(s) will change. To ensure load voltage stability in the even of another load opening, we need a neutral wire to connect the source node and load node together:

So long as the loads remain balanced (equal resistance, equal currents), the neutral wire will not have to carry any current at all. It is there just in case one or more load resistors should fail open (or be shut off through a disconnecting switch).

This circuit we've been analyzing with three voltage sources is called a polyphase circuit. The prefix "poly" simply means "more than one," as in "polytheism" (belief in more than one deity), polygon" (a geometrical shape made of multiple line segments: for example, pentagon and hexagon), and "polyatomic" (a substance composed of multiple types of atoms). Since the voltage sources are all at different phase angles (in this case, three different phase angles), this is a "polyphase" circuit. More specifically, it is a three-phase circuit, the kind used predominantly in large power distribution systems.

Let's survey the advantages of a three-phase power system over a single-phase system of equivalent load voltage and power capacity. A single-phase system with three loads connected directly in parallel would have a very high total current (83.33 times 3, or 250 amps:

This would necessitate 3/0 gage copper wire (very large!), at about 510 pounds per thousand feet, and with a considerable price tag attached. If the distance from source to load was 1000 feet, we would need over a half-ton of copper wire to do the job. On the other hand, we could build a split-phase system with two 15 kW, 120 volt loads:

Our current is half of what it was with the simple parallel circuit, which is a great improvement. We could get away with using number 2 gage copper wire at a total mass of about 600 pounds, figuring about 200 pounds per thousand feet with three runs of 1000 feet each between source and loads. However, we also have to consider the increased safety hazard of having 240 volts present in the system, even though each load only receives 120 volts. Overall, there is greater potential for dangerous electric shock to occur.

When we contrast these two examples against our three-phase system, the advantages are quite clear. First, the conductor currents are quite a bit less (83.33 amps versus 125 or 250 amps), permitting the use of much thinner and lighter wire. We can use number 4 gage wire at about 125 pounds per thousand feet, which will total 500 pounds (four runs of 1000 feet each) for our example circuit. This represents a significant cost savings over the split-phase system, with the additional benefit that the maximum voltage in the system is lower (208 versus 240).

One question remains to be answered: how in the world do we get three AC voltage sources whose phase angles are exactly 120^o apart? Obviously we can't center-tap a transformer or alternator winding like we did in the split-phase system, since that can only give us voltage waveforms that are either in phase or 180^o out of phase. Perhaps we could figure out some way to use capacitors and inductors to create phase shifts of 120^o, but then those phase shifts would depend on the phase angles of our load impedances as well (substituting a capacitive or inductive load for a resistive load would change everything!).

The best way to get the phase shifts we're looking for is to generate it at the source: construct the AC generator (alternator) providing the power in such a way that the rotating magnetic field passes by three sets of wire windings, each set spaced 120^o apart around the circumference of the machine:

Together, the six "pole" windings of a three-phase alternator are connected to comprise three winding pairs, each pair producing AC voltage with a phase angle 120^o shifted from either of the other two winding pairs. The interconnections between pairs of windings (as shown for the single-phase alternator: the jumper wire between windings 1a and 1b) have been omitted from the three-phase alternator drawing for simplicity.

In our example circuit, we showed the three voltage sources connected together in a "Y" configuration (sometimes called the "star" configuration), with one lead of each source tied to a common point (the node where we attached the "neutral" conductor). The common way to depict this connection scheme is to draw the windings in the shape of a "Y" like this:

The "Y" configuration is not the only option open to us, but it is probably the easiest to understand at first. More to come on this subject later in the chapter.

Technische Stromarten: Gleichstrom, Wechselstrom und Drehstrom

Gleichstrom

Im einfachsten Fall fließt ein zeitlich konstanter Strom. Einen solchen Strom nennt man Gleichstrom (engl. direct current).

Zu beachten ist die Technische Stromrichtung: Vereinbarungsgemäß wird eine Stromrichtung von Plus nach Minus angenommen. Diese Stromrichtung geht auch in alle physikalischen Gleichungen ein, die den Strom als solchen betreffen. Eine elektrische Spannungsdifferenz ist jedoch immer von Plus nach Minus positiv. Daher ist die technische Stromrichtung sinnvoll und wird üblicherweise verwendet, damit die Richtung von Strom und Spannung identisch ist. Die technische Stromrichtung ist nicht zu verwechseln mit der Flussrichtung der Elektronen (negative Ladungträger), die entgegen der technischen Stromrichtung fließen. Siehe auch Technische und physikalische Stromrichtung.

Physikalische Stromrichtung: Um den Mechanismus des Stromflusses zu verstehen und bestimmte elektrische Eigenschaften von Materialien herzuleiten, betrachtet man die wirkliche Bewegung der Ladungsträger. In Metallen bewegen sich in der Regel Elektronen, also negative Ladungsträger, die vom Minus-Pol zum Plus-Pol fließen, denn am Minus-Pol herrscht ein Überschuss an Elektronen, und/oder am Plus-Pol ein Mangel, der durch den elektrischen Strom ausgeglichen wird, sobald der Stromkreis geschlossen wird.

In elektrisch leitfähigen Flüssigkeiten sind gegebenenfalls positive und negative Ladungsträger oder reduzierbare und oxidierbare Stoffe vorhanden, die sich zu den jeweiligen Polen hinbewegen. An den Polen werden sie reduziert bzw. oxidiert, nehmen also an einem Pol Elektronen auf und geben Elektronen an dem anderen Pol ab und überbrücken dadurch die Übertragung von Elektronen im Stromkreis.

In einem Experiment mit einer wässrigen Lösung zur Feststellung der Stromrichtung wurde die physikalisch falsche, technische Stromrichtung ermittelt, da nur die positiven Ladungsträger sichtbar waren, die sich allerdings auf den Minus-Pol zubewegen.

Ein anderer Fall tritt bei p-dotierten Halbleitern auf: Hier verhalten sich fehlende Elektronen (so genannte Löcher oder Defektelektronen) wie positive Ladungsträger mit Masse. Da in der Löcherleitung die Elektronen die Löcher füllen wandern tatsächlich die Elektronen und hinterlassen an ihrem vorherigen Ort ein Loch. Daher wandern die Löcher in die entgegengesetzte Richtung der Elektronen.

Als Gleichspannungsquelle kommen galvanische Zellen (Batterien), entsprechende Dynamos (zum Teil mit nachgeschalteter Gleichrichtung), photovoltaische Zellen (Solaranlagen) oder Schaltnetzteile in Frage. In der Technik häufig anzutreffen ist auch eine Kombination von Transformator und Gleichrichter.

Fällt bei gleich bleibender Stromrichtung die Spannung (und damit, sofern ein Verbraucher angeschlossen ist, die Stromstärke) periodisch stark ab, so spricht man von einer pulsierenden Gleichspannung. Gleichrichter liefern beim Umwandeln von Wechselspannung in Gleichspannung meist pulsierende Gleichspannung, sofern die Spannung nicht durch Kondensatoren oder andere Maßnahmen geglättet wird.

Wechselstrom

Drehstrom - die wundersame Dreieinigkeit von drei verketteten Wechselströmen

Neben der Möglichkeit des Ferntransports von elektrischer Energie bietet Wechselstrom noch weitere Vorteile, wenn er als "Drehstrom" angewendet wird. Schon bei der ersten Fernübertragung elektrischer Energie, die 1891 anläßlich der Frankfurter Elektrizitätsausstellung stattfand, wurde davon Gebrauch gemacht. Auf der Drehstromtechnik basiert heute die gesamte Stromwirtschaft.

Bei Drehstrom handelt es sich um drei Wechselströme, die im selben Generator erzeugt werden. Die "Phasen" dieser Wechselströme - also das Auf und Ab der Sinuskurve bei jeder Drehung der Generatorachse um 360 Winkelgrade - sind um jeweils 120 Winkelgrade gegeneinander versetzt. So entsteht ein dreiphasiger Wechselstrom, dessen Sinuskurven sich gleichmäßig überlagern. Betrachtet man die miteinander verketteten Phasen des Drehstroms auf dem Diagramm rechts, wird man feststellen, daß sich die Ausschläge der Sinuskurven in den positiven oder negativen Bereich in jedem Augenblick zur Gesamtsumme null ergänzen.

Drehfeld für robuste Motoren

Der Drehstrom verdankt seinen Namen der Anwendung für den Betrieb von Elektromotoren. Er erzeugt nämlich in den Ständerwicklungen dieser Motoren ein magnetisches Drehfeld, das den Rotor mitnimmt und so die Drehbewegung des Motors erzeugt. Dadurch entfällt der verschleißträchtige Stromwender, der beim Gleichstrommotor auf mechanische Weise für die Stromversorgung und Umpolung des Magnetfeldes im Rotor sorgen muß. Drehstrommotoren brauchen nicht einmal Bürsten und Schleifringe. Ihre Rotoren können sich völlig kontaktfrei drehen, wenn sie den Strom für den Aufbau des Rotorfelds auf induktivem Wege aus dem Magnetfeld des Ständers beziehen ("Käfigläufer"). Deshalb sind Drehstrommotoren äußerst robust und leistungsfähig. Dasselbe gilt für Drehstromgeneratoren.

Stern-und Dreieck-Schaltung

Drehstrom benötigt insgesamt drei Leitungen. Das mag auf den ersten Blick überraschen, da schon für einphasigen Wechselstrom zwei Leitungen erforderlich sind. Demnach bräuchte man für drei Phasen eigentlich sechs Leitungen. Die Rückleitungen können jedoch bei Drehstrom entfallen, da sich die drei Phasen in jedem Augenblick zu null ergänzen. Voraussetzung ist, daß der elektrische Verbraucher an alle drei Phasen angeschlossen wird und diese gleichmäßig belastet. Jedes Drehstrom-Gerät setzt sich deshalb aus drei gleichgearteten elektrischen Teil-Verbrauchern zusammen. Für den Anschluß dieser Teil-Verbraucher an die drei Phasen gibt es zwei Möglichkeiten:

Stern-Schaltung: Man legt jede Eingangsklemme der drei Teil-Verbraucher an eine der Phasen und verbindet die Ausgangsklemmen untereinander.

Dreieck-Schaltung: Die drei Teil-Verbraucher werden jeweils so zwischen zwei Phasen gelegt, daß jede Ausgangsklemme mit einer Eingangsklemme verbunden ist.

Je nach Art der Schaltung verketten sich die Stromstärken der drei Phasen oder deren Spannungen. So läßt sich zum Beispiel aus demselben Drehstrom durch Sternpunkt-Schaltung eine Spannung von 230 Volt oder durch Dreieck-Schaltung eine Spannung von 400 Volt gewinnen.

Die Transformatoren, die der Strom auf seinem Weg vom Kraftwerk zur Steckdose passieren muß, sind entweder im Stern oder Dreieck geschaltet. Zum Beispiel verwendet man beim Übergang von der Mittel- auf die Niederspannung üblicherweise die Dreiecksschaltung für die Oberspannungs-Seite des Transformators (30 kV oder 10 kV) und die Sternschaltung für die Niederspannungs-Seite (400/230 Volt).

Der Endverbraucher kann seine elektrischen Geräte wahlweise in Sternschaltung (mit 230 Volt) oder in Dreiecksschaltung (mit 400 Volt) betreiben. Die dafür erforderlichen Steckdosen erkennt man an den drei Kontakten für die drei Phasen-Leiter (außerdem verfügen sie über den üblichen Schutzkontakt). Eine besondere Führungs-"Nase" gewährleistet, daß die Phasen beim Einstöpseln des Steckers übereinstimmen. Beim Vertauschen der Phasen laufen Drehstrommotoren nämlich rückwärts, was unliebsame Folgen haben kann.

Drehstrom-Steckdosen und drehstromtaugliche Geräte findet man aber normalerweise nur in Gewerbe- und Industriebetrieben. In Haushalten sind sie auf Ausnahmefälle beschränkt, etwa auf einen besonderen "Kraft"-Anschluß für Waschmaschinen oder leistungsstarke Heizgeräte.

Das Prinzip der Drehstrom-Übertragung ist seit über hundert Jahren unverändert

Tony Locker

Director, Business Development
I-Gard
(888) 737-4787
Email

Tony Locker received a BSEE from Rose-Hulman Institute of Technology and a MSEE from Georgia Institute of Technology. He is presently Director, Business Development with I-Gard, Cincinnati, Ohio, where he is responsible for providing technical seminars and application assistance on resistance grounding and ground fault protection in the USA. Prior to joining I-Gard in 2005, he was Vice President – Engineering with Post Glover Resistors. Previously, he was Director of Engineering at Power Engineering Technology. His background includes leading design teams and managing installations of numerous multi-million dollar control and power systems for data centers, industrial plants, cogeneration facilities, and utilities. Before Power Engineering Technology, he was a R&D engineer for Square D Company.

Mr. Locker is active in the Industry Applications and Power Engineering Societies of IEEE, where he serves on several Subcommittees and Working Groups, as well as NSPE. He is a registered Professional Engineer in Ohio and has two patents.

regarding the neutral and ground

July 18, 2006 @ 5:05 am


Q.		When a current of 100A is passing through the phase, what will be the status of neutral and ground, will the same current will be passing even from them,,,,,


A.		I am assuming that you are referring to a single-phase circuit (because ideally no current would be flowing in a three-phase circuit a solidly grounded system. In a single-phase circuit, the “flowing” current must flow to the load via the phase conductor and return via the neutral conductor. So, the current flow must return via the neutral conductor (in your case, 100A). The ground conductor should not have any current. In fact, this is how a GFCI works on a single-phase circuit. Generally speaking, both the phase and neutral conductors are fed thru a window CT. The current (from the source) in the phase conductor (100A) produces a flux in the CT in one direction, and the current in the neutral (traveling the other way back to the source) produces a flux in the CT in the other direction. The net result … 0 flux IF the currents are the same. If the currents are not, the flux will not be the same and a voltage will be generated by the CT, which can be detected by a relay. The most common way for a difference in current is current returning back to source via ground conductor. So, if the phase conductor is 100A and the neutral is 95A, 5A must be traveling back to source via ground conductor. (This will be detected by the CT and relay.) Zero-sequence CT’s will the same way, except all three phase conductors are fed thru one window CT, which measures the net flux. If the current traveling down one conductor returns thru the other two, then the net flux is 0. If some current returns thru ground conductor, then the net flux is NOT 0 and a ground fault relay will alarm.

Neutral connection during paralleling process

July 13, 2006 @ 4:23 am


Q.		Although you recommend that only one generator need to be grounded during parallel operation, do we need to connect the follower generator’s ground during paralleling process?, if we do, what the reason for that?


A.		I do not recommend that only one generator be grounded during paralleling operation, I would rather see either the paralleling bus have a common ground or each generator have a resistance-ground to avoid circulating currents. Please see my responses dated on July 7th and 8th.

Correction to Previous Q&A

July 12, 2006 @ 9:10 am


Q.		Tony, One of our astute readers read your Q&A item on “using a GFCI in lieu of a grounding conductor” and then sent me an NEC reference that allows for replacement of a non-grounding type receptacle with a GFCI. I think it would be valuable if you added this reference and some additional text to your existing answer to help clarify this situation. See 406.3(D)(3)(b) of the 2005 NEC.


A.		The original question was: can a gfci be used in lieu of a grounding conductor? is there a specific NEC paragraph that addresses this? It is my understanding of the question that the questioner has a choice, either to install a grounding conductor or gfci. I do not recommend doing this. Whenever possible, install a grounding conductor. When giving a choice, I am not aware of a NEC paragraph that addresses this issue. NEC 406.3 (D) (3) (b) addresses replaces an old-style non-grounding type receptacle with a new gfci. This is permissible given that a grounding conductor is not available as the gfci must be labeled “No Equipment Ground”.

Circuit breaker triped .

July 12, 2006 @ 6:36 am


Q.		Dear Sir, In over network Main Circuit breaker Tripped due to one small Circuit Photo Cell Short Circuit occurred. In this circuit having 05 NOS Circuit Breakers having different rating like 20Amps, 50Amps, 100Amps,350Amps,1600Amps and 2000Amps. So, Main 2000Amps tripped on Ground Tripped set 1200Amps set as @ 0.4 and time 0.1 sec, We can change/increase this setting? On safe side. Our Natural & Ground is same. Not Repeat this trip or no?


A.		Unfortunately this is a common problem with solidly grounded systems. Per the National Electric Code 230-95, Ground Fault Protection is required for solidly grounded systems <600V and >1000A. The maximum setting is 1200A and 1sec. If I understand your question, you have a 1200A GFI set at 0.4, or 480A at 0.1sec. With this setting, you are hoping that a downstream circuit breaker (CB) clears the fault before the main circuit breaker (MCB) does. Since I do not know the manufacturer and type of CB’s, I am going to use IEC 60898-1 to check coordination. The instantaneous trip at 0.1sec can range from 5 to 20 times rated current. So, let’s look at each downstream CB that you mentioned: 20A * 5 = 100A 20A * 20 = 400A (20A CB will trip prior to MCB) 50A * 5 = 250A 50A * 20 = 1000A (50A CB may or may not trip prior to MCB) 100A * 5 = 500A 100A * 20 = 2000A (100A CB will not trip prior to MCB) 350A * 5 = 1750A 350A * 20 = 7000A (350A CB will not trip prior to MCB) As you can see, your system does not appear to be coordinated i.e. a 100A CB will not clear a low level ground fault before the MCB. What causes a low level ground fault? An arcing fault is resistive in nature, so an arcing ground fault is ~35% of a bolted fault. Often times, the fault current will not be high enough to for the CB to react quickly to trip. The result is a low magnitude fault current that lasts until the MCB clears as shown above ONLY IF you are lucky. If not, the fault escalates into a severe arc flash / blast incident. It is estimated that 85-95% of all electrical faults are ground faults, which typically start out as an arcing fault. There are several ways to solve your problem. 1) You could increase your current setting and/or time. Even though this may help with coordination, your system has become less safe. Your exposure to Arc Flash / Blast will significantly increase. The base equation below shows that an increase in time is directly proportional to an increase in energy and an increase in current is proportional by the square. Energy = Current * Current * Resistance * time 2) A better solution is to install Zone-Selective Interlocking Protection (see our Application Guide on MGFR relays http://www.i-gard.com/appguides.htm). This will prevent the MCB from unwanted tripping on a ground fault downstream AND significantly reduces your exposure to Arc Flash / Blasts.

ELCBs in parallel circuits

July 12, 2006 @ 6:05 am


Q.		In a circuit for Emergency lighting fixtures (one with built-in battery) there are two ELCBs installed, one in lighting power and one in charger circuit. Both circuits are single phase and are derived from common main busbars. The problem is that these fixtures have a common Neutral terminal for both supplies, thus neccesiating to terminate neutral of both circuits together. When one circuit is switched on, it is fine, but when the second ELCB is turned on, the neutral current gets divided and ELCBs trip. Request explain what practice should be followed when there are 2 ELCBs and loads having common neutral.


A.		You have three possibilities to consider. 1) Separate the neutrals and feed them through the elcb to each load separately. This may not be possible with outopening the fixture and changing the wiring. 2) Use 1 phase 120/240 V circuit. This comprises of phase to phase voltage of 240V and you will have a two pole elcb with common neutral. This is common in North America and may not be possible in your distribution system. 3) Change the two breakers to normal mcbs and add elcb serving both loads on the line side. This will use the common neutral and will not cause the trip.

The Three-Phase Generator

Generator design, frame size 710-1250

From Wikipedia, the free encyclopedia

Contents

Generation and distribution

Single-phase loads

Connecting phase-to-phase

Three-phase loads

Phase converters

Small scale applications

Alternatives to three-phase

Color codes

Variable setup and basic definitions

Balanced loads

Star connected systems with neutral

Constant power transfer

No neutral current

Star connected systems without neutral

Three-Phase

Unbalanced systems

Revolving magnetic field

Conversion to other phase systems

Three-phase Y and Δ configurations

Three-phase Y and Δ configurations

Three-phase power systems

Three-phase power systems

Technische Stromarten: Gleichstrom, Wechselstrom und Drehstrom

Gleichstrom

Wechselstrom

Drehstrom - die wundersame Dreieinigkeit von drei verketteten Wechselströmen

Drehfeld für robuste Motoren

Stern-und Dreieck-Schaltung

Das Prinzip der Drehstrom-Übertragung ist seit über hundert Jahren unverändert


INVERSE PHASES ROTATION	PARALLELE OPERATION FORBIDDEN	SYNCHRONISING AND CONNECTION GIVE A SHORT CIRCUIT