3-phase electric power (3ϕ, P3, or P3Ø) is a AC common way of AC current generation, transmission, and distribution and a type of polyphase system using 3 wires (or 4 with an optional neutral return wire), and the most common way used by electrical grids worldwide to send power.
3ϕ is independently invented by Galileo Ferraris, Mikhail Dolivo-Dobrovolsky, Jonas Wenström and Nikola Tesla in late 1880s.
[2.1]
[2.1] Identifying the connections in transformer banks
Liquid filled transformers installed indoors need a special room called a “vault.”
Note the transformer tank grounding.
Current Standard
use of steel bracket
single pole
What can we see?
3 x 37.5 kVA
grounded wye secondary
Most high power, outdoor installations are three phase transformers
We can tell from this installatino it's a 50/15 KV, 50MVA.
This is a 3-phase pole mounted power transformer for a telecommunications array in Uruguay, rare in Canada.
We can tell from this transformer
A balanced circuit is a 3ϕ AC system with all voltages and currents equal in magnitude and evenly spaced in phase (120° apart in three-phase systems), a symmetry ensuring good power transfer via minimal losses.
3ϕ systems mainly use Wye (Y) and Delta (Δ) configurations:
The delta (Δ) connection is a connection used in a 3ϕ electrical system where 3 elements in series form a triangle, the supply being input and output at the three junctions.
Delta applications:
240 V delta systems are rare but are in use.
600 V delta was commonly installed into the 1980’s (?) in Ottawa.
44 kV Hydro Ottawa – sub. transmission that feed Algonquin College
Medium and high voltage systems are sometimes delta connected.
Line voltage (Vline, Vl , or Eline): Voltage between any 2 phases/lines (e.g., 400V, 480V).
Phase voltage (Vₚ, Vpower, or Ephase): Voltage between a phase and neutral (Vₚ = Vₗ / √3).
Line current (IL or ): Current flowing per line.
Phase current (Iₚ or Ipower): In star (wye) systems, Iₚ = Iₗ; in delta, Iₚ = Iₗ / √3.
In Δ systems, line voltage = phase voltage
Current in delta
In delta connections, each load connect across 2 lines, so phase current flows through 1 load.
Line current (IL) is the vector sum of 2 phase currents at a node.
IL's formula: IL = Iphase x √3
That’s why IL is √3 times larger than phase current, assuming balanced loads.
Ammeter A1 measures line current in line 3
A2 measures current in phase B only
A3 measures current in phase A only
A1 is the vector sum of the phase currents.
Ground to a delta connection V1 here will read 0 V, as there's no connection to ground n the transformer and it's an open circuit.
An analog reads 0 V and a 100 V lamp also won't light:
There is a connection to ground through capacitive coupling, with high impedance so a digital meter will have a voltage but not enough current to light a lamp.
If we ground L3, V1 reads 0 V--both sides of the meter connect to ground.
The breaker won't trip as the only return to the transformer is through the capacitance--very high impedance and low current.
If V2 reads 240 V, and V1 reads 0 V, V3 reads the B phase voltage of 240 V and so does V4 (the A phase voltage).
This is a L2 to L3 short circuit. At 2 grounds, at least 1 overcurrent protection opens.
But we can use 1 ground.
If we center tap 1 phase, we get 120/240.
We must:
provide overcurrent protection
ground the neutral
keep the 2 systems separate
The Pythagorean theorem tells the x' value: 208 V.
Removing this transformer's B phase makes it an "open delta", but we'd still have a 3-phase power/
The transformer output power (in VA) is for a balanced transformer system for a closed delta connection (via phase current), giving:
3 phase power for delta: S = 3*Vph* I Phase …….1
S=3*Vph*I phase; Iphase=I line in open delta & Vph=Vline/1.732 sub in 1.
Delta connection formula: VA = √3VLIph
With the open delta ratio to closed delta power gives:
We divide by 3 VL as it’s 3 winding
Open delta This open delta system would still works, without closing the terminal (crossed by x)
An open delta transformer can only send 57.7% of a capacity of an equivalent 3ϕ delta transformer banks via akin voltage and load current or the total load carried by 3ϕ banks, open delta system is 57.7% of closed healthy 3ϕ transformer banks.
This open delta wouldn't have the same power capacity--58% of the rating of the 3 transformers rating only.
Why use open delta? If a transformer fails and a replacement is unavailable, we can run the load open delta, it would work.
Even if the transformers that were readily available were larger than needed, e can still run the load open delta.
Delta vs Wye comparison
1 fault on a delta system wont' open an overcurrent--can be fixed at a convenient time.
convenient: suitable
A line to ground is the most common fault/shock. The voltage to ground on a 600 volt delta system is 0 V or 600 V. A 600 volt wye system has a voltage to ground of 347 V.
2 ground faults on a delta system create a line to line fault with higher voltages and higher fault currents than a ground fault on a wye system.
Delta Connections are often used in applications which require high starting torque, higher voltages across windings, highest power!
The wye (Y) connection has its transformer coils connected at a common point, a neutral point, often grounded, giving a balanced voltage reference per phase and facilitating breaker and fuse operation. They're versatile, offering both line-to-line and line-to-neutral voltages, making them suitable for both single-phase and three-phase loads.
Canada's voltage of delta systems are often not grounded. A system to detect accidental grounds is needed. (10-106)
A usual set of ground
detector lamps.
If a system is free of grounds (no nodes are intentionally connected to a ground (0 V)), all lamps light up.
A ground fault causes lamps for a grounded phase to go out.
240 volt delta systems are rare but are in use.
600 volt delta was commonly installed into the 1980’s (?) in Ottawa.
44 kV Hydro Ottawa – sub. transmission that feed Algonquin College
Medium and high voltage systems are sometimes delta connected.
[1.2] A stator is a rotary system's stationary part, in electric generators, motors, sirens, mud motors, or biological rotors (like bacterial flagella or ATP synthase). Energy flows into a stator to/from the system's rotating component, the rotor. In an electric motor, the stator provides a magnetic field that drives the rotating armature; in a generator, the stator converts the rotating magnetic field to electric current. In fluid powered devices, the stator guides the flow of fluid to or from the rotating part of the system.
This has 3 transformers and 1 core, for a liquid filled transformer.
We can tell this is a transformer of core type configuration.
This is a usual dry-core, 3 phase transformer for indoor use.
[5] Reactive power (Q) is the zero power dissipated by reactive loads (inductors and capacitors), yet the fact that they drop voltage and draw current gives the deceptive impression that they actually do dissipate power. It's measured in the volt-amps-reactive (VAR) units, not watts.
True power (P) is the true power amount used/dissipated in circuits, measured in watts.
Apparent power (S) is the combo of reactive power and true power, the product of a circuit’s voltage and current, without reference to phase angle, measured in the unit of volt-amps (VA).
Power formula in 3-phase AC circuits: P3 = √3 x Vl x Il x cosϕ
Apparent power (S, in VA): P3 = √3 x Vl x Il
Reactive power (Q, in VAR): Q = √3 x Vl x Il x sinϕ
Power triangle relationship: S = √(P²+ Q²)
Power factor is the real power (P) ratio to apparent power (S).
Power factor formula
[3] A copper wire wraps into 2 coils across each other in a stator to make a circuit (Fig. 1). If the magnet is between these coils and rotate the magnet, the magnetic field will disturb the copper wire's free electrons and current will flow (Fig. 2).
As the magnet rotates so does the polarity of the magnetic field as you can see in the illustration the North and South Pole of the magnet are rotating and as they rotate they pass across the coils, causing electrons to move.
Fig. 1
Fig. 2
Fig. 3
The magnetic field lines are oval shaped at each side and meet in the central axis of the magnet (Fig. 3). See them as 1 side positive and the other being negative. In between these overalls the magnetic field is neutral you can see that the intensity of the magnetic field increases on either side until the center where it is at is maximum strength and then it decreases again until it gets back to the neutral point.
=
As the field rotates through the coil, which feels increasing intensity of the magnetic, causing positive half and during this increase the free electrons within the copper coil is pushed and gets faster in 1 direction til it gets at the magnetic field's max then as the field reduces, electrons flow slows slow down til reaches a neutral point without electrons flow.
Negative side of field So as the field rotates through the coil the coil will experience an increasing intensity of the magnetic cause positive half and during this increase the free electrons within the copper coil will be pushed and begin to move faster and faster in one direction up until it reaches the maximum point of the magnetic field then as the magnetic field decreases the flow of electrons will begin to slow all the way until it reaches a neutral point where no electrons will flow then comes a negative side of the magnetic field and
Sine wave graph On a graph, the electrons speed flowing in the rotation makes a sine wave, where electrons are motioneless initially in the neutral zone, the speed rises through the positive half to the max and then it reduce down to neutral without electrons flow. Again after this comes a negative half where the electrons speed up to the maximum point and then they begin to slow down again til the magnet does a full rotation, and so on.
The current also represents power.
If a lamp connects to the circuit, its increase brightness to the peak then down to a neutral point where it's off as no current flows, then it rises again as a negative half cycle comes and electrons flow back through in the opposite til it reaches the neutral point again.
At some points, the lamp is off, and bright so this gets annoying in a room as the flickers like this.
To improve it, add another coils set--a 2nd phase in the generator by putting the coils at 120° from the first set, via a 2nd lamp.
Such rotation means the coils feel the the magnetic field's changing intensity at some points in time.
The 1st coil reaches max current and brightness. As it reduces, the 2nd coil rises.
But there's still a gap causing flickers so add in a 3rd coils set--a 3rd phase, so one of the lamps are almost always at its max brightness, with some gaps. We can add more but it gets more costly, so P3Ø is widely accepted.
Irl, we won't use different lamps of different phases to light them all at one phase. House lamps do use flicker, just too fast for eyes to see unless seen in slow motion.
A single-phase alternator is an AC generator creating single-phase AC power. Unlike a P3Ø (makes 3 V waveforms 120° apart), this makes 1 AC voltage waveform.
Generating a single AC phase
Adding a 2nd phase
[6] The power triangle shows the bond between true power (P), reactive power (Q) and apparent power (S).
E.g. 1# A transformer draws 160W from a 120V line and sends 24V at 5A. Find its efficiency.
160W = 5A*24V = 120W = Pout
Efficiency: (Pout/Pin)x100% = (120/160)x100 = 75%
E.g. 2# How much power a load consumes if it draws 75 A at 600 V, 3-phase via a 0.83 power factor?
WP3Ø = Eline x Iline x √3 x FP
= 600 x 75 x √3 x 0.83
= 64.7 kW
E.g. 3# What's the HV side's rated current? A pioneer 6 MVA transformer has high voltage of 24940/14400V, grounded wye connection, and a low voltage of 4260 Delta connection.
Iline = S3Ø/Eline x √3 = 6x10⁶/(24.940 x √3) = 139 A--It's 6 MVA so it's 6,000,000
E.g. 3.1# What's LV side's rated current of the same transformer?
S3Ø = Eline x Iline x √3
Iline = S3Ø/(Eline x √3) = (6x10⁶)/(4160x√3) = 833 A
Advantages
Depending on systems, we can move the same power by 87% conductor capacity. Other views of higher number don’t let for the number of conductors (Fig. 4).
Fig. 4
The impedance triangle shows the bond between resistance (R), reactance (X), and impedance (Z) in an AC circuit. Resistance is the opposition to current flow due to the circuit's physical components, while reactance is the opposition to current flow due to the presence of capacitors and inductors. The impedance (Z) is the overall opposition to current flow and is the hypotenuse of the triangle.
[1.3] A single-phase (P1Ø) is
Single-phase or 1-phase power formula: P1 = VI*Cos
1-phase AC circuit apparent power = S1
3-phase AC circuit apparent power = S3
Advantages of 3-phase P3Ø motors have ~50% more horsepower than P1Ø motor of same sizes.
Transformer's kVA rating at 3-phase is ~150% of 1-phase transformers of the same size.
P1Ø power goes to 0 twice a cycle; P3Ø power never does.
P3Ø:
don't need special starting windings.
are highly efficient
all motors over 10 hp are P3Ø motors.
Single-phase transformer bank:
Smaller
Can supply single phase only
Easier to move
If one fails, still have the others
Less power/bank
Less cost.
Used for power distributions (home and lighter load).
3-phase transformer:
Bigger size but more compact
Lighter
More power
Can supply both.
Simpler installation/ maintenance in larger sizes
More costly and repairing inconveniences.
Used for power transmission purposes like industrial and commercial uses.
E.g. 4# A single phase transformer's KVA rating is 2 and the load power sent is 2.6HP. What's the transformer's PF at 100% efficiency?
[1]
It's independently invented by Galileo Ferraris, Mikhail Dolivo-Dobrovolsky, Jonas Wenström and Nikola Tesla in late 1880s.
[1] Wikipedia
[1.1] Single-phase generator
[1.2] Stator
[1.4] Delta-wye transformer
[1.5] Y-Δ transform
[1.8] High-leg delta
[2] WK3 THREE PHASE POWER STBS PART 1 PRESENTATION 2024 - (Algonquin College) Canva
[2.2]
[2.3]
[3] How Three Phase Electricity works | The basics explained - YT
[4] Electrical Power Explained | Part 3: Balanced three-phase AC power - Fluke
[8] DELTA CONNECTION definition and meaning - Collin Dictionnary
[9]
[10]
[Q1]