Three Phase and Wye To Wye or Wye To Delta

Three-phase electric power 
 A common method of alternating-current electric power generation, transmission, anddistribution.[1] It is a type of polyphase system and is the most common method used by electrical grids worldwide to transfer power. It is also used to power large motors and other heavy loads. A three-phase system is usually more economical than an equivalent single-phase at the same line to ground voltage because it uses less conductor material to transmit electrical power.[2] The three-phase system was independently invented by Galileo Ferraris, Mikhail Dolivo-Dobrovolsky, Jonas Wenström and Nikola Tesla in the late 1880s.

Why 3-Phase?


To understand electric power in the data center, you need to first understand single- and 3-phase power distribution. Most homes are wired with single-phase that uses one ac voltage delivered over two hot wires and one neutral wire. The voltage across the two hot wires measures 240VAC (for your oven or dryer) and across any hot to neutral measures 120VAC (for everything else).
Most commercial businesses are wired with 3-phase that consists of three ac voltages separated from each other by 120 electrical degrees, or by a third of a cycle. These systems deliver power over three hot wires where the voltage across any two hot wires measures 208VAC.
B23_3_phase_AC_waveformAnother way to look at 3-phase power is as a combination of three single-phase circuits that deliver power in a way that it never falls to zero, meaning that the load is the same at any instant (the concept is easy to grasp when you look at the waveform).
Because the load is constant, 3-phase power is ideal for motors—it eliminates the need for starting capacitors. It also allows for smaller wires (i.e., less copper) and lower voltages for the same power transmission as single-phase, making it less expensive and safer.

Why Wye?


There are two types of circuits used to maintain equal load across the three hot wires in a 3-phase system—Delta and Wye. The Delta configuration has the three phases connected like a triangle, whereas the Wye (or “star”) configuration has all three loads connected at a single neutral point.
Delta systems have four wires—three hot and one ground. Wye systems have five wires—three hot, one neutral and one ground. While both Delta and Wye systems measure 208VAC between any two hot wires, Wye systems also measure 120VAC between any hot wire and neutral. In other words, it’s the neutral wire of the Wye system that allows for providing two different voltages and powering both 3-phase and single-phase devices in the data center.
That’s not to say that Delta doesn’t have its place—we mainly see Delta used for any large motors or heaters that don’t need a neutral. Delta is also used in power transmission because it’s expensive to run a fourth neutral wire all those miles. That’s why distribution transformers are wired as Delta-Wye. This creates the neutral that allows the transformer to deliver power for single-phase loads.
Delta-wired devices can also be fed from a Wye source by simply omitting the neutral. That means that in a data center, a Delta power distribution unit (PDU) can be used when there is only a need for 208VAC, while Wye PDUs are used when there is a need for both 120VAC and 208VAC.
B23_WyevsDeltaMany of today’s larger blade servers only accept 208VAC because their power requirements can’t be met with 120VAC. However, most data centers still need the flexibility of also being able to power 120VAC devices. So now you know why 3-phase Wye power distribution is the best option for today’s data center.
Belden’s wide range of three-phase rack-mounted and vertical PDUs available in both Delta and Wye configurations to accommodate a broad range of electrical characteristics, outlet requirements, plug and receptacle styles, and remote monitoring and management.

Balanced circuits[edit]

In the perfectly balanced case all three lines share equivalent loads. Examining the circuits we can derive relationships between line voltage and current, and load voltage and current for wye and delta connected loads.
In a balanced system each line will produce equal voltage magnitudes at phase angles equally spaced from each other. With V1 as our reference and V3 lagging V2 lagging V1, using angle notation, we have:[12]
V_1 = V_\text{LN}\angle 0^\circ,
V_2 = V_\text{LN}\angle{-120}^\circ,
V_3 = V_\text{LN}\angle{+120}^\circ.
These voltages feed into either a wye or delta connected load.

Wye[edit]

Three-phase AC generator connected as a wye source to a wye-connected load
For the wye case, all loads see their respective line voltages, and so:[12]
I_1 = \frac{V_1}{|Z_\text{total}|}\angle (-\theta),
I_2 = \frac{V_2}{|Z_\text{total}|}\angle (-120^\circ - \theta),
I_3 = \frac{V_3}{|Z_\text{total}|}\angle (120^\circ - \theta),
where Ztotal is the sum of line and load impedances (Ztotal = ZLN + ZY), and θ is the phase of the total impedance (Ztotal).
The phase angle difference between voltage and current of each phase is not necessarily 0 and is dependent on the type of load impedance, Zy. Inductive and capacitive loads will cause current to either lag or lead the voltage. However, the relative phase angle between each pair of lines (1 to 2, 2 to 3,and 3 to 1) will still be −120°.
By applying Kirchhoff's current law (KCL) to the neutral node, the three phase currents sum to the total current in the neutral line. In the balanced case:
I_1 + I_2 + I_3 = I_\text{N} = 0.

Delta[edit]

Three-phase AC generator connected as a wye source to a delta-connected load
In the delta circuit, loads are connected across the lines, and so loads see line-to-line voltages:[12]
\begin{align} V_{12} &= V_1 - V_2 = (V_\text{LN}\angle 0^\circ) - (V_\text{LN}\angle {-120}^\circ) \\ &= \sqrt{3}V_\text{LN}\angle 30^\circ = \sqrt{3}V_{1}\angle (\phi_{V_1} + 30^\circ), \\ V_{23} &= V_2 - V_3 = (V_\text{LN}\angle {-120}^\circ) - (V_\text{LN}\angle 120^\circ) \\ &= \sqrt{3}V_\text{LN}\angle {-90}^\circ = \sqrt{3}V_{2}\angle (\phi_{V_2} + 30^\circ), \\ V_{31} &= V_3 - V_1 = (V_\text{LN}\angle 120^\circ) - (V_\text{LN}\angle 0^\circ) \\ &= \sqrt{3}V_\text{LN}\angle 150^\circ = \sqrt{3}V_{3}\angle (\phi_{V_3} + 30^\circ). \\ \end{align}
Further:
I_{12} = \frac{V_{12}}{|Z_\Delta|} \angle (30^\circ - \theta),
I_{23} = \frac{V_{23}}{|Z_\Delta|} \angle (-90^\circ - \theta),
I_{31} = \frac{V_{31}}{|Z_\Delta|} \angle (150^\circ - \theta),
where θ is the phase of delta impedance (ZΔ).
Relative angles are preserved, so I31 lags I23 lags I12 by 120°. Calculating line currents by using KCL at each delta node gives:
\begin{align} I_1 &= I_{12} - I_{31} = I_{12} - I_{12}\angle 120^\circ \\ &= \sqrt{3}I_{12} \angle (\phi_{I_{12}} - 30^\circ) = \sqrt{3}I_{12} \angle (-\theta) \end{align}
and similarly for each other line:
I_2 = \sqrt{3}I_{23} \angle (\phi_{I_{23}}-30^\circ) = \sqrt{3}I_{23} \angle (-120^\circ - \theta),
I_3 = \sqrt{3}I_{31} \angle (\phi_{I_{31}}-30^\circ) = \sqrt{3}I_{31} \angle (120^\circ - \theta),
where, again, θ is the phase of delta impedance (ZΔ).


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