In electrical engineering, three-phase electric power systems have at least three conductors carrying alternating voltages that are offset in time by one-third of the period. A three-phase system may be arranged in delta (∆) or star (Y) (also denoted as wye in some areas, as symbolically it is similar to the letter 'Y'). A wye system allows the use of two different voltages from all three phases, such as a 230/400 V system which provides 230 V between the neutral (centre hub) and any one of the phases, and 400 V across any two phases. A delta system arrangement only provides one voltage, but it has a greater redundancy as it may continue to operate normally with one of the three supply windings offline, albeit at 57.7% of total capacity. Harmonic current in the neutral may become very large if nonlinear loads are connected. Definitions In a star (wye) connected topology, with rotation sequence L1 - L2 - L3, the time-varying instantaneous voltages can be calculated for each phase A,C,B respectively by: where: is the peak voltage, is the phase angle in radians is the time in seconds is the frequency in cycles per second and voltages L1-N, L2-N and L3-N are referenced to the star connection point. Diagrams The below images demonstrate how a system of six wires delivering three phases from an alternator may be replaced by just three. A three-phase transformer is also shown. Balanced loads Generally, in electric power systems, the loads are distributed as evenly as is 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. Constant power transfer An important property of three-phase power is that the instantaneous power available to a resistive load, , is constant at all times. Indeed, let To simplify the mathematics, we define a nondimensionalized power for intermediate calculations, Hence (substituting back): Since we have eliminated we can see that the total power does not vary with time. This is essential for keeping large generators and motors running smoothly. Notice also that using the root mean square voltage , the expression for above takes the following more classic form: . The load need not be resistive for achieving a constant instantaneous power since, as long as it is balanced or the same for all phases, it may be written as