why do we use 3 phase power

There are several reasons 3-phase is desirable over 1-phase power. One advantage of 3-ph over 1-ph has to do with instantaneous power (i. e. power generated or consumed at any instant in time within the power cycle). For example, consider a heating element (power resistor) in a 1-phase circuit. Voltage and current are in phase. Both cross zero twice during a cycle as they go positive and then negative. Their product is power which is a sinusoid at 2x the fundamental frequency (multiply two sine waves and you get a new sine wave with twice the frequency). The power dissipated by the heating element has a sinusoidal waveshape that sits above the zero line (because the two V I sinusoids, when multiplied together, always give a positive value). The power sinusoid also reaches zero twice during the fundamental cycle at the same time V or I cross zero. The resistor doesn't produce heat (consume power) at these zero-crossing instants in time (resistor remains hot due to its thermal mass). Now replace the resistor with a 1-ph induction motor. For similar reasons, despite V I being out of phase, there are times in its power cycle when the motor doesn't produce mechanical power (it remains spinning due to its own and its load's inertia). In a 3-ph system, the phases are staggered by 120 electrical degrees.

If a 3-ph heating element is connected (Y or delta; doesn't matter for the purpose of this discussion), each individual resistor "sees" a zero crossing but collectively the three are producing heat at all times. There is no instant in time when heat is not being produced. Similarly, with a running 3-ph motor, there is no instant in time when it isn't producing mechanical power. The result is a simplified motor (no starting winding needed as is the case with a 1-phase motor), smaller frame for same horse-power because instantaneous power is never zero. Unlike the 1-ph motor, the 3-ph motor doesn't need the larger bulk to "coast through" a zero crossing.
In a symmetric three-phase power supply system, three conductors each carry an of the same frequency and voltage amplitude relative to a common reference but with a phase difference of one third of a cycle between each. The common reference is usually connected to ground and often to a current-carrying conductor called the neutral. Due to the phase difference, the voltage on any conductor reaches its peak at one third of a cycle after one of the other conductors and one third of a cycle before the remaining conductor. This phase delay gives constant power transfer to a balanced linear load. It also makes it possible to produce a rotating magnetic field in an and generate other phase arrangements using transformers (for instance, a two phase system using a ).

The symmetric three-phase systems described here are simply referred to as three-phase systems because, although it is possible to design and implement asymmetric three-phase power systems (i. e. , with unequal voltages or phase shifts), they are not used in practice because they lack the most important advantages of symmetric systems. In a three-phase system feeding a balanced and linear load, the sum of the instantaneous currents of the three conductors is zero. In other words, the current in each conductor is equal in magnitude to the sum of the currents in the other two, but with the opposite sign. The return path for the current in any phase conductor is the other two phase conductors. As compared to a single-phase AC power supply that uses two conductors (phase and ), a three-phase supply with no neutral and the same phase-to-ground voltage and current capacity per phase can transmit three times as much power using just 1. 5 times as many wires (i. e. , three instead of two). Thus, the ratio of capacity to conductor material is doubled. The ratio of capacity to conductor material increases to 3:1 with an ungrounded three-phase and center-grounded single-phase system (or 2. 25:1 if both employ grounds of the same gauge as the conductors).

Constant power transfer and cancelling phase currents would in theory be possible with any number (greater than one) of phases, maintaining the capacity-to-conductor material ratio that is twice that of single-phase power. However, two-phase power results in a less smooth (pulsating) torque in a generator or motor (making smooth power transfer a challenge), and more than three phases complicates infrastructure unnecessarily. Three-phase systems may also have a fourth wire, particularly in low-voltage distribution. This is the wire. The neutral allows three separate single-phase supplies to be provided at a constant voltage and is commonly used for supplying groups of domestic properties which are each loads. The connections are arranged so that, as far as possible in each group, equal power is drawn from each phase. Further up the, the currents are usually well balanced. Transformers may be wired in a way that they have a four-wire secondary but a three-wire primary while allowing unbalanced loads and the associated secondary-side neutral currents. The phase currents tend to cancel out one another, summing to zero in the case of a linear balanced load. This makes it possible to reduce the size of the neutral conductor because it carries little or no current.

With a balanced load, all the phase conductors carry the same current and so can be the same size. Power transfer into a linear balanced load is constant, which helps to reduce generator and motor vibrations. Three-phase systems can produce a with a specified direction and constant magnitude, which simplifies the design of electric motors, as no starting circuit is required. Most household loads are single-phase. In North American residences, three-phase power might feed a multiple-unit apartment block, but the household loads are connected only as single phase. In lower-density areas, only a single phase might be used for distribution. Some high-power domestic appliances such as electric stoves and clothes dryers are powered by or from two phases of a three phase system at 208 volts. Wiring for the three phases is typically identified by color codes which vary by country. Connection of the phases in the right order is required to ensure the intended direction of rotation of three-phase motors. For example, pumps and fans may not work in reverse. Maintaining the identity of phases is required if there is any possibility two sources can be connected at the same time; a direct interconnection between two different phases is a short-circuit.

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