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THREE-PHASE SYSTEMS
The three-phase systems are used for
- generation
- transmission
- distribution
of electrical power because
- The three-phase generators are less bulky and have a lower weight than the other electrical systems single-phase and d.c.
- The three-phase electrical lines have a lower weight than the other match all electrical parameters.
From the electrical point of view, a three-phase generator is composed of three single-phase generators with voltages of equal amplitudes and phase differences of 120°, according to the following relationships:
The phase voltage is the voltage of each of the single phase generator
These generator can be connected in different ways:
- Wye or Star connection (Y): the three voltage sources are connected to a common point with or without neutral wire;
- delta (Δ) connection
The three-phase systems are classified according to the sets of three electromotive forces (emf) and currents.
A " Symmetric 3-phase set " is a three phase system where the set of three sinusoidal voltages satisfy these requirements:
All three voltages have the same amplitude All three voltages have the same frequency All three voltages are 120o^ in phase So is called symmetric a system where the emfs
A " balanced 3-phase set " is a three phase system where the set of three sinusoidal currents satisfy these requirements:
All three currents have the same amplitude All three currents have the same frequency All three currentes are 120o^ in phase
So is called balanced a three phase system where the currents
If the load (Wye or Delta) has equal impedances, the system is Balanced
If the load (Wye or Delta) hasn’t equal impedances, the system is Unbalanced
If we compare the line-to-neutral voltages with the line-to-line voltages, we find the following relationships:
Line to line voltages in terms of line to neutral voltages
In any Symmetric and balanced three-phase systems (symmetric voltages and balanced load impedances), the resulting currents are balanced. This way, there is necessary to analyze all three phases. We may analyze one phase to determine its current, and deduce the currents in the other phases based on a simple balanced phase shift (120° phase difference between any two line currents).
Symmetric and balanced three-phase systems ( DELTA-DELTA CONNECTION)
The Line currents are different than the load currents
Line currents ≠ load currents
I 1 = I 12 – I 31 I 2 = I 23 – I 12 I 3 = I 31 – I 23
Z 12 = Z 23 = Z 31 = Z inductive resistive load
relationship between the line currents and phase:
Symmetric and balanced three-phase systems ( WYE-DELTA CONNECTION)
We can use the Wye-Delta transformation to get the case of wye load already studied
Symmetric and balanced three-phase systems (DELTA-WYE CONNECTION)
We can use the Delta-Wye transformation to get the case of wye sources already studied: Z 12 = Z 23 = Z 31 = Z = 3 Z Y
Sistema di distribuzione in bassa tensione di tipo T.T.
Carichi irregolari con sistema trifase squilibrato nella corrente, ma simmetrico nella tensioni (supponendo trascurabili le cadute di tensione sulle fasi del generatore)
SYMMETRIC AND UNBALANCED THREE-PHASE SYSTEMS WITH NEUTRAL WIRE (WYE-WYE CONNECTION)
E 1 , E 2 , E 3: the set of three symmetric voltages
Z 1 ≠ Z 2 ≠ Z 3: the set of three unbalanced impedances
The presence of the neutral wire ensures that O and O 'are at the same potential and then we have three independent phases:
In neutral wire circulates a current equal to
SYMMETRIC AND UNBALANCED THREE-PHASE SYSTEMS (DELTA-DELTA
CONNECTION)
E 1 , E 2 , E 3 the set of three symmetric voltages
Z 1 ≠ Z 2 ≠ Z 3: the set of three unbalanced impedances
POWER IN THREE PHASE SYSTEM
The total power of the system is given by the sum of the three powers of each phase
A) Symmetric and balanced system
Voltage on the load current
φ = phase angle between the current and the voltage
The total power supplied to the load is constant (unlike transmission with three-phase generators
S = apparent power P = active power Q = reactive power
Wye load Delta load
The power factor (P.F)
