Power is defined as the rate of flow of energy past a given point. In alternating current circuits, energy storage elements such as inductance and capacitance may result in periodic reversals of the direction of energy flow. The portion of power flow that, averaged over a complete cycle of the ac waveform, results in net transfer of energy in one direction is known as real power. That portion of power flow due to stored energy that returns to the source in each cycle, is known as reactive power.
Mostly this article will concentrate on single frequency systems. Unfortunately, unlike voltage and current, power cannot be calculated by superposition of calculations at the various frequency components due to the fact its calculation invovles the square of voltage or current.
The term mains usually refers to the general purpose AC electrical power supply (as in "I've connected the appliance to the mains"). The term is not usually used in the US and Canada, where it is known as household, or domestic power.
European and most other countries in the world use a supply that is within 10 % of 230 volts, whereas Japan and most of the Americas use between 100 and 127 volts.
Following voltage harmonisation co-ordinated with CENELEC countries, all electricity supply within the EU is now nominally 230 V, +/− 10% (though some countries have stricter specifications for example the UK specifies 230V +10% -6%). In practice this means that countries, such as the UK, that previously supplied 240 V continue to do so, and those that previously supplied 220 V continue to do so. However equipment should be designed to accept any voltages within the specified range, and in practice most does so. Similarly, Australia has converted to 230 V as the nominal standard, and like the UK, 240 V is within the allowable tolerance. "240 volt" spoken as "two forty volt" remains a synonym for mains in Australian and British English.
A close synonym to "mains" in Canadian provinces that use hydroelectric power would be "hydro".
ANSI standard C84.1 and Canadian CAN3-C235 specify that the nominal voltage at the output should be 120 V and allows a range of 114 to 126 V. California deliberately runs in the voltage range 114 to 120 V to reduce power consumption, however the reasoning behind such a move is debatable.
In Japan, the electrical power supply to households is at 100 V. Eastern and northern parts of Honshu (including Tokyo) as well as Hokkaido have a frequency of 50 Hz, whereas western Honshu (including Nagoya, Osaka, and Hiroshima), Shikoku, Kyushu and Okinawa operate at 60 Hz. To accommodate for the difference, appliances marketed in Japan can often be switched between the higher and lower frequencies.
The system of three-phase alternating current electrical generation and distribution was invented by Nikola Tesla in the nineteenth century. He considered that 60 Hz was the best frequency for alternating current (AC) power generating. He preferred 240 V, which was claimed to be better for long supply lines. Thomas Edison developed direct current (DC) systems at 110 V and this was claimed to be safer. For more information about the early battles between proponents of AC and DC supply systems see War of Currents.
The German company AEG built the first European generating facility to run at 50 Hz allegedly because the number 60 did not fit into the numerical unit sequence of 1, 2, 5…. At that time, AEG had a virtual monopoly and their standard spread to the rest of the continent. In Britain, differing frequencies proliferated, and the 50 Hz standard was only established after World War II.
Originally Europe was 110 V too, just like Japan and the US today. It was deemed necessary to increase voltage to draw more power with reduced loss and voltage drop from the same copper wire diameter. At the time the US also wanted to change, but it was deemed too costly to change all of the existing infrastructure.
Americans are still often confronted with the problems of the lower voltage. A device at 120 V draws twice as much current as a device with the same power draw at 240 V. A 3000 W domestic clothes dryer requires 12.5 A at 240 V or 25 A at 120 V. The end result is that wiring must be larger, and each outlet supplies less power. This may have been a factor in the use of circuit breakers in America long before they became common in Europe.
Smaller North American buildings get 240 V split in two 120 V supplies between neutral and hot wire. Larger buildings often have 3 phase with 208V between any two hots. Major appliances, such as dryers and ovens, are now connected to 240 V or 208 V supply. Americans who have European equipment can connect it to these outlets, as long as it can accept the U.S. frequency of 60 Hz rather than 50 Hz.
The unit for all forms of power is the watt (symbol: W). In practice, however, this is generally reserved for the real power component. Apparent power is conventionally expressed in volt-amperes (VA) since it is the simple multiple of rms voltage and current. The unit for reactive power is given the special name "var" which standard for volt-amperes-reactive in IEC 60027-1.
Understanding the relationship between these three quantities lies at the heart of understanding power engineering. The mathematical relationship among them can be represented by vectors and is typically expressed using complex numbers
S = P + jQ (where j is the imaginary unit)
This complex value S is often referred to as the complex power.
Consider an ideal alternating current (AC) circuit consisting of a source and a generalized load, where both the current and voltage are sinusoidal. If the load is purely resistive, the two quantities reverse their polarity at the same time; the direction of energy flow does not reverse; and there is only real power flowing. If the load is purely inductive or capacitive, then the voltage and current are 90 degrees out of phase (for a capacitor, current leads voltage; for an inductor, current lags voltage) and there is no net power flow. This energy flowing backwards and forwards is known as reactive power. If a capacitor and an inductor are placed in parallel, then the currents caused by the inductor and the capacitor are 180 degrees out of phase with each other and therefore partially cancel out rather than adding to each other. Conventionally, capacitors are considered to generate reactive power and inductors to consume it. In reality, the load is likely to have resistive, inductive, and capactive parts; and so both real and reactive power will flow to the load. The apparent power is the result of a naïve calculation of power from the voltage and current that is simply multiplying the rms voltage by the rms current. Apparent power is handy for rough sizing of generators or wiring, especially when the power factor is close to 1. However, adding the apparent power for two loads will not give the total apparent power unless the two loads have the same phase difference between voltage and current.
Apparent Power
The definition of Apparent Power is considered to be one of the most controversal topics in Power Engineering. Originally, Apparent Power arose merely as a figure of merit. Major delineations of the concept are attributed to Stanley's Phenomena of Retardation in the Induction Coil (1888) and Steinmetz's Theoretical Elements of Engineering (1915). However, with the development of three-phase power distribution it became clear that the definition of Apparent Power and the power factor could not be applied to unbalanced poly-phase systems. In 1920, a "Special Joint Committee of the AIEE and the National Electric Light Association) met to resolve the issue. They considered two definitions:
pf = (Pa + Pb + Pc) / (Sa + Sb + Sc) i.e., the quotient of the sums of the real powers for each phase over the sum of the apparent power for each phase.
pf = (Pa + Pb + Pc) / ( | Pa + Pb + C + j(Qa + Qb + Qc) | ) i.e., the quotient of the sums of the real powers for each over the magnitude of the sum of the complex powers for each phase).
The 1920 committee found no consensus and the topic continued to dominate discussions. In 1930 another committee formed and once again failed to resolve the question. The transcripts of their discussions are the lengthiest and most controversial ever published by the AIEE (Emanuel, 1993). Further resolution of this debate did not come until the late 1990s.
Power Factor
The ratio between real power and apparent power in a circuit is called the Power factor. Where the waveforms are purely sinusoidal, the power factor is the cosine of the phase angle between the current and voltage sinusoid waveforms. Equipment data sheets and nameplates often will abbreviate power factor as " cos φ" for this reason.
Power factor equals unity (1) when the voltage and current is in phase, and is zero when the current leads or lags the voltage by 90 degrees. Power factor must be specified as leading or lagging. For two systems transmitting the same amount of real power, the system with the lower power factor will have higher circulating currents due to energy that returns to the source from energy storage in the load. These higher currents in a practical system may produce higher losses and reduce over all transmission efficiency. A lower power factor circuit will have a higher apparent power and higher losses for the same amount of real power transfer.
Capacitive circuits cause reactive power with the current waveform leading the voltage wave by 90 degrees, while inductive circuits cause reactive power with the current waveform lagging the voltage waveform by 90 degrees. The result of this is that capacitive and inductive circuit elements tend to cancel each other out. By convention, capacitors are said to generate reactive power whilst inductors are said to consume it (this probably comes from the fact that most real life loads are inductive and so reactive power has to be supplied to them from power factor correction capacitors).
In power transmission and distribution, significant effort is made to control the reactive power flow. This is typically done automatically by switching in/out inductors or capacitor banks, by adjusting generator excitation, and by other means. Electricity retailers may use electricity meters which measure reactive power to financially penalise customers with low power factor loads (especially larger customers).
