Synchronus Generator

•  Synchronous Generators
•  Synchronous machines are principally used as alternating current (AC) generators. They supply the electric power used by all sectors of modern societies: industrial, commercial, agricultural, and domestic.

•  Synchronous generators usually operate together (or in parallel), forming a large power system supplying electrical energy to the loads or consumers.

•  Synchronous generators are built in large units, their rating ranging from tens to hundreds of megawatts.

•  Synchronous generator converts mechanical power to ac electric power. The source of mechanical power, the prime mover, may be a diesel engine, a steam turbine, a water turbine, or any similar device.

• For high-speed machines, the prime movers are usually steam turbines employing fossil or nuclear energy resources.

•  Low-speed machines are often driven by hydro-turbines that employ water power for generation.

•  Smaller synchronous machines are sometimes used for private generation and as standby units, with diesel engines or gas turbines as prime movers.

Types of Synchronous Machine

According to the arrangement of the field and armature windings, synchronous machines may be classified as rotating-armature type or rotating-field type.

Rotating-Armature Type: The armature winding is on the rotor and the field system is on the stator.

Rotating-Field Type: The armature winding is on the stator and the field system is on the rotor.

 

INDUCED E.M.F:

e = B l v volts
where

B = flux density Wb/sqm
v = velocity (m/s) of movement
l = length of conductors in meters.

Frequency:

The frequency of the voltage generated is given by

f = NP/120

where P is the total number of poles and N is the speed in r.p.m.

Breadth factor:

(K_b) = Voltage obtained in multi-slots winding / Voltage obtained if the windings were all concentrated in one slot

Thus breadth factor is always less than unity.
Mathematically,

K_b= (sin δ n/2 )/ (π sin δ/2)

where n is the number of slot and is the slot pitch.

Pitch factor:

Shortening the pitch of the coil has the same effect as the distribution of the winding. When the turns of the windings do to span a complete pitch there occurs a slight loss in the induced emf. A pitch factor ( K_p ) is given by

K_p = cos θ/2

for a coil which extends over (180° - θ) instead of 180°.

Magnitude of Induced emf in alternators / phase:

E_RMS = 4.44 Kp Kb φ f.T. volts

Synchronous Reactance:

X_s = X_L + X_A

where
X_L = Leakage reactance;
X_A = Armature reactance.

Synchronous Impedance:

Z_s = (R² + X²_s )^1/2

SYNCHRONOUS GENERATOR CHARACTERISTICS:

(1) Open Circuit Characteristics:

(Magnetisation Curve).

(2) Short Circuit Characteristics:

(Terminal Voltage vs Current)

Synchronous Generator (Continued):

(3) Load Characteristics of Synchronous Generator:

While the exciting current and the speed remain constant, the terminal voltage changes with the load current in the armature and the relationship between the terminal voltage and load current of an alternator is known as its load characteristics.

When the armature current increases, the terminal voltage drops. This is mainly due to

(a) Resistance and reactance of armature winding, and
(b) Armature reaction.

The load characteristics of an alternator is shown in the figure.

Phasor diagram of synchronous generator under three types of leading conditions :

Simplified equivalent AC circuit (per phase) for synchronous generator:

AT POWER FACTOR LAGGING:

(A) When R_A is very small:

α = torque angle
P = 3 V_φE₀ sin α/ X_s

Torque induced,
T _ind = 3 V_φE₀ sin α/ X_s ω_m

where ω_m = speed.

(B) General case:

P = 3 E₀/Zs [ E₀cosθ – V (cosθ + α) ]
where cosθ = R_a / Z_s

:. Small R_a implies θ = 90.

For maximum power output:

cosφ = E₀/√ (E²₀ +V²φ)

α = 90⁰

3 P _max = (3 Vφ I _max E₀)/√ (E²₀ +V² φ) = 3 V_φ E₀ / X_s

Synchronous Generator (Continued):

BLONDELS TWO REACTION THEORY:

In case of cylindrical pole machines, the direct-axis and the quadrature axis mmfs act on the same magnetic circuits, hence they can be summed up as complexors. However, in a salient-pole machine, the two mmfs do not act on the same magnetic circuit. The direct axis component F_ad operates over a magnetic circuit identical with that of the field system, while the q-axis component F_aq is applied across the interpole space, producing a flux distribution different from that of F_ad or the Field mmf.

The Blondel's two reaction theory hence considers the results of the cross and direct-reaction components separately and if saturation is neglected, accounts for their different effects by assigning to each an appropriate value for armature-reaction "reactive" respectively X_aq and X_ad .

Considering the leakage reactance, the combined reactance values becomes

X_ad = X + X _ad and X _sq = X _aq

X_sq < X_sd as a given current component of the q-axis gives rise to a smaller flux due to the higher reluctance of the magnetic path.



Let l_q and I_d be the q and d-axis components of the current I in the armature reference to the phasor diagram in Figure. We get the following relationships

I_q= I cos (σ+θ) I_a = I cosφ

I_d = I sin (σ+ φ) I_r = I sinφ

And I = √(I_d² + I_q²)= = √(I_d² + I_r²)
 
where I_a and I_r are the active and reactive components of current I.

Voltage Regulation:

voltage regulation of an alternator is defined as "the rise in voltage when full load is removed (field excitation and speed remaining unaltered) divided by the rated terminal voltage. Thus

% regulation =( E₀ – V ) / V x 100

In case of leading load pf the regulation is negative.

Parallel Operation of Synchronous Generators:

A stationary synchronous generator should not be connected to five bus bars because, stator induced e.mf. being zero, a short circuit will result. For proper paralleling of Generators the following three conditions must be satisfied :

1. The terminal voltage of the incoming generator must be same as bus-bar voltage.

2. The speed of the incoming generator must be such that its frequency (PN/120) equal bus-bar frequency.

3. The phase of the synchronous generator voltage must be identical with the phase of the bus voltage.

Parallel-Generator Theorem:

Reference to Figure given above , where 2 generators are connected in parallel. Let the load be I amps at V volts such that V / I = Z.

Then , V = (I₁+I₂ )Z = [( E₁-V)/Zs₁+ ( E₂-V)/Zs₂ ]

= [ E₁/Zs₁ + E₂/Zs₂ ] Z – V[1/Zs₁ + 2/Zs₂]Z

i.e. V [1/Z +1/Zs₁ + 1/Zs₂]

= E₁/Zs₁ + E₂/Zs₂ i.e. V [1/Z₀] = I_sc

where I_sc is the total short circuit current obtained by summing the terms E₁/Zs₁ and E₂/Zs₂ where

1/Z₀=1/Z +1/Zs₁ + 1/Zs₂

This theorem holds true for any number of generator.

The characteristics of a synchronous generator on infinite bus-bars are quite different from those when it operates on its own local load. In the latter case, a change in the excitation changes the terminal voltage, while the pf is determined by the load. When working on infinite bus-bars, on the other hand, no alternation of the excitation can change the terminal voltage which is fixed by the network, the point however, is affected. In both cases the power developed by a generator (or received by a motor) depends solely upon the mechanical power provided (or load applied to it).



Consider 2 alternators operating in parallel on infinite bus-bars, with identical initial operating conditions, i.e. the active and reactive powers are divided equally. Now suppose the excitation of alternator 1 is increased then as stated earlier, the kW loading of the 2 alternators remains unchanged as the mechanical input remains the same. The change is seen in the KVAR loading due to the changes in the individual load currents and points.



Similarly with change in steam supply of one of the alternator with excitation kept same, the change is observed in the kW loading of the 2 alternators. While the KVAR loading remains unaltered.

SYNCHRONIZING POWER (P_s):

Let for same cause the angle δ changes to δ I δ’.

The synchronous power, P_s = (E+ V) Z_s sin (θ + δ) sinδ’

For large generator, Z_x =S_x

i.e. θ = 90⁰

P_s = ( E+ V ) Z_s cos δ sinδ’

When an unloaded M/c is synchronized to a constant voltage bus bar
δ = 0,

P_s = (E+ V) Z_s sin δ/ ph

when δ is small enough

P_s = (E+ V) Z_s sin δ’/ ph

=V I_sc δ’ / ph where I_sc = E_f / Z_s