Ferranti Effect

A long transmission line draws a substantial quantity of charging current. If such a line is open
circuited or very lightly loaded at the receiving end, the voltage at receiving end may become greater
than voltage at sending end. This is known as Ferranti Effect and is due to the voltage drop across the
line inductance (due to charging current) being in phase with the sending end voltages. Therefore both
capacitance and inductance is responsible to produce this phenomenon.
The capacitance (and charging current) is negligible in short line but significant in medium line and
appreciable in long line. Therefore this phenomenon occurs in medium and long lines.

Represent line by equivalent -model.

C P
N
Vs
Ic

Vr
O M

Line capacitance is assumed to be concentrated at the receiving end.

OM = receiving end voltage Vr

OC = Current drawn by capacitance = Ic
MN = Resistance drop
NP = Inductive reactance drop

Therefore;
OP = Sending end voltage at no load and is less than receiving end voltage (Vr)

Since, resistance is small compared to reactance; resistance can be neglected in calculating Ferranti
effect.

From -model,

YZ
Vs = 1 + Vr + ZI r {refer eq. 5, in -model ckt. derivation}
2
For open circuit line; Ir = 0
YZ
∴ Vs = 1 + Vr
2

YZ YZ
or; V s − Vr = 1 + Vr − Vr = Vr 1 + −1
2 2

or; Vs − Vr =
YZ
Vr =
( jωCl ) (r + jωL )l V
r
2 2
Neglecting resistance;
− Vr ω 2 l 2 LC
V s − Vr =
2
1
The quantity is constant in all line and is equal to velocity of propagation of electromagnetic
LC
waves (= 3 × 105 km/sec)
1 1
LC = LC =
(
3 × 10 5
) 3 × 10 5
2
( )
Substituting the value in above equation;
− Vr ω 2 l 2
Vs − Vr =
2 3 × 10 5( 2
)
− Vr ω 2 l 2 × 10 −10
∴ V s − Vr =
18

ω 2 l 2 × 10 −10
∴ Vs = Vr 1 −
18

Now, from above expression;

ω 2 l 2 × 10 −10
1− < 1
18

So,
Vs < Vr or; Vr > Vs

i.e. receiving end voltage is greater than sending end voltage and this effect is called Ferranti Effect. It
is valid for open circuit condition of long line.
Proximity Effect:
Proximity means nearness in space or time, so as the name suggests, proximity effect in
transmission lines indicates the effect in one conductor for other neighbouring conductors.
When the alternating current is flowing through a conductor, alternating magnetic flux is
generated surrounding the conductor. This magnetic flux associates with the neighbouring wires
and generates a circulating current (it can be termed as ‘eddy current’ also). This
circulating current increases the resistance of the conductor and push away the flowing current
through the conductor, which causes the crowding effect.

When the gaps between two wires are greater the proximity effect is less and it rises when
the gap reduces. The flux due to central conductor links with right side conductor. In a
two wire system more lines of flux link elements farther apart than the elements nearest to
each other as shown above. Therefore, the inductance of the elements farther apart is more as
compared to the elements near to each other and hence the current density is less in the
elements farther apart than the current density in the element near to each other. As a result the
effective resistance of the conductor is increased due to non uniform distribution of
current. This phenomenon is actually referred as proximity effect. This effect is pronounced in
the case of cables where the distance between the conductor is small whereas proximity
effect in transmission lines in the case of overhead system, with usual spacing is negligibly
small.

Series and shunt compensation:

The demand of active power is expressing Kilo watt (kw) or mega watt (mw). This power should
be supplied from electrical generating station. All the arrangements in electrical pomes system
are done to meet up this basic requirement. Although in alternating power system, reactive power
always comes in to picture. This reactive power is expressed in Kilo VAR or Mega VAR. The
demand of this reactive power is mainly originated from inductive load connected to the system.
These inductive loads are generally electromagnetic circuit of electric motors, electrical
transformers, inductance of transmission and distribution networks, induction furnaces,
fluorescent lightings etc. This reactive power should be properly compensated otherwise, the
ratio of actual power consumed by the load, to the total power i.e. vector sum of active and
reactive power, of the system becomes quite less. This ratio is alternatively known as electrical
power factor, and fewer ratios indicates poor power factor of the system. If the power factor of
the system is poor, the ampere burden of the transmission, distribution network, transformers,
alternators and other equipments connected to the system, becomes high for required active
power. And hence reactive power compensation becomes so important. This is commonly done
by capacitor bank.

Let’s explain in details,

we know that active power is expressed =VIcosθ
where,cosθ is the power factor of the system. Hence, if this power factor has got less valve, the
corresponding current (I) increases for same active power P.

As the current of the system increases, the ohmic loss of the system increases. Ohmic loss
means, generated electrical power is lost as unwanted heat originated in the system. The cross-
section of the conducting parts of the system may also have to be increased for carrying extra
ampere burden, which is also not economical in the commercial point of view. Another major
disadvantage, is poor voltage regulation of the system, which mainly caused due to poor power
factor.

The equipments used to compensate reactive power.

There are mainly two equipments used for this purpose.
(1) Synchronous condensers
(2) Static capacitors or Capacitor Bank

Synchronous condensers, can produce reactive power and the production of reactive power can
be regulated. Due to this regulating advantage, the synchronous condensers are very suitable for
correcting power factor of the system, but this equipment is quite expensive compared to static
capacitors. That is why synchronous condensers, are justified to use only for voltage regulation
of very high voltage transmission system. The regulation in static capacitors can also be achieved
to some extend by split the total capacitor bank in 3 sectors of ratio 1: 2:2. This division enables
the capacitor to run in 1, 2, 1+2=3, 2+2=4, 1+2+2=5 steps. If still further steps are required, the
division may be made in the ratio 1:2:3 or 1:2:4. These divisions make the static capacitor bank
more expensive but still the cost is much lower them synchronous condensers.
It is found that maximum benefit from compensating equipments can be achieved when they are
connected to the individual load side. This is practically and economically possible only by using
small rated capacitors with individual load not by using synchronous condensers.
Static capacitor Bank.

Static capacitor can further be subdivided in to two categories,

(a) Shunt capacitors
(b) Series capacitor
v. The ohmic values of impedances are refereed to secondary is different from the value as referee to
primary. However, if base values are selected properly, the p.u impedance is the same on the two
sides of the transformer.
vi. The circuit laws are valid in p.u systems, and the power and voltages equations are simplified
since the factors of √3 and 3 are eliminated.

Change the base impedance from one set of base values to another set

Let Z=Actual impedance ,Ω

Zb=Base impedance ,Ω
𝑍 𝑍 𝑍×𝑀𝑉𝐴 𝑏
Per unit impedance of a circuit element= = 2 = (1)
𝑍𝑏 𝑘𝑉𝑏 𝑘𝑉𝑏 2
𝑀𝑉𝐴 𝑏

The eqn 1 show that the per unit impedance is directly proportional to base
megavoltampere and inversely proportional to the square of the base voltage.

Using Eqn 1 we can derive an expression to convert the p.u impedance expressed
in one base value ( old base) to another base (new base)

Let kVb,oldand MVAb,old represents old base values and kVb,newand MVA b ,new
represent new base value

Let Zp.u,old=p.u. impedance of a circuit element calculated on old base

Zp.u,new=p.u. impedance of a circuit element calculated on new base

If old base values are used to compute the p.u.impedance of a circuit element ,with
impedance Z then eqn 1 can be written as
𝑍 × 𝑀𝑉𝐴𝑏,𝑜𝑙𝑑
𝑍𝑝.𝑢 ,𝑜𝑙𝑑 = 2
𝑘𝑉𝑏,𝑜𝑙𝑑
2
𝑘𝑉 𝑏 ,𝑜𝑙𝑑
𝑍 = 𝑍𝑝.𝑢 ,𝑜𝑙𝑑 (2)
𝑀𝑉𝐴 𝑏 ,𝑜𝑙𝑑

If the new base values are used to compute thep.u. impedance of a circuit element
with impedance Z, then eqn 1 can be written as
 𝑍×𝑀𝑉𝐴 𝑏 ,𝑛𝑒𝑤
𝑍𝑝.𝑢 ,𝑛𝑒𝑤 = 2 (3)
𝑘𝑉 𝑏 ,𝑛𝑒𝑤

On substituting for Z from eqn 2 in eqn 3 we get

2
𝑘𝑉𝑏,𝑜𝑙𝑑 𝑀𝑉𝐴𝑏,𝑛𝑒𝑤
𝑍𝑝.𝑢 ,𝑛𝑒𝑤 = 𝑍𝑝.𝑢.𝑜𝑙𝑑 × 2
𝑀𝑉𝐴𝑏,𝑜𝑙𝑑 𝑘𝑉𝑏,𝑛𝑒𝑤
2
𝑘𝑉 𝑏 ,𝑜𝑙𝑑 𝑀𝑉𝐴 𝑏 ,𝑛𝑒𝑤
𝑍𝑝.𝑢,𝑛𝑒𝑤 = 𝑍𝑝𝑢 ,𝑜𝑙𝑑 × 𝑘𝑉 𝑏,𝑛𝑒𝑤
×
𝑀𝑉𝐴 𝑏,𝑜𝑙𝑑
(4)

The eqn 4 is used to convert the p.u.impedance expressed on one base value to another base

MODELLING OF GENERATOR AND SYNCHRONOUS MOTOR

1Φ equivalent circuit of generator 1Φ equivalent circuit of synchronous motor