η at full load = η at half load = 0.98

η at full load of the transformer

P_co + P_cufl = 2.0408

η at half load =

Solving the equation

P_co  = 0.6802 KW

P_cufl = 1.3605 KW

P_cufl > P_co

• Magnetic reluctance, or magnetic resistance, is a concept used in the analysis of magnetic circuits. It is analogous to resistance in an electrical circuit, but rather than dissipating electric energy it stores magnetic energy.
• Low the reluctance, less the opposition to flux therefore more flux can pass through the transformer core.
• Therefore the transformer core is made of magnetic steel that has high permeability (low reluctance) to the magnetic flux.

Leakage transformers are transformers where the magnetic flux of the secondary is loosely coupled to the flux of the primary.  This loose coupling ensures that the transformer can withstand short circuit conditions.

The output and input current of the leakage transformer is low enough to prevent thermal overload under load condition even if the secondary is shorted. Leakage Transformers are also known as Stray field Transformers.

Leakage transformers are used for arc welding and high-voltage discharge lamps (neon lights and cold cathode fluorescent lamps, which are series-connected up to 7.5 kV AC). They act as both a voltage transformer and a magnetic ballast. Other applications are short-circuit-proof extra-low voltage transformers for toys or doorbell installations.

Starting torque if 3 phase induction motor is given as

Where ns = synchronous speed in r.p.s i.e Ns/60

V = Rotor voltage

R₂ = Rotor resistance

X₂ = Rotor Reactance

∴ T_st ∝ V²

So starting torque of a 3-phase induction motor is directly proportional to V²

Let Pg = Air gap power

P_cu = Rotor copper loss = sP_g

P_m = Mechanical power or Gross power output

P_m = Air gap power – Rotor copper loss

= Pg – sP_g

P_m = (1 – s)P_g

Negative phase sequence current in Synchronous motor

• Negative sequence currents are produced because of the unbalanced voltage in the power system.
• The flow of negative sequence currents in electrical machines (generators and motors) is undesirable as these currents generate high and possibly dangerous temperatures in a very short time.
• Phase current and voltage in the three-phase system can be represented in the form of three single-phase components.
• Positive sequence components, Negative sequence components, and Zero sequence components.
• Positive sequence currents exist during the balanced load condition.

The ammeter has 30 oscillations in one minute. So, rotor current has a frequency

f” = 30/60 = 0.5 Hz

Rotor frequency f” = s×f

s= f”/f = 0.5/50 = 0.01 Hz.

Synchronous speed Ns = 120f/p = 120 x 50/6 = 1000 RPM

Slip s = (Ns – Nr)/Ns

0.01 = (1000 – Nr)/1000

Nr = 990 RPM

According to CENTRAL ELECTRICITY REGULATORY COMMISSION OF INDIA

Ideal Range of frequency variation

f = 50 ± 1%

49.5 to 50.5 Hz

Practical permissible Range of frequency variation

f = 50 ± 3%

48.5 to 51.5 Hz

The grid frequency should be maintained at 48.6 Hz. and above at all times.

Why is hydrogen used for Alternator cooling?

Hydrogen is the least expensive, has less weight, has high thermal conductivity, less density, and has less viscosity. Less weight, less density & less viscosity are attributed to its flow rate. High thermal conductivity helps in better heat exchange. The least expensive help in balance sheets, more power in fewer investments.

In order to reduce the high temperature of the alternator hydrogen gas is used as a coolant. The coolant, Hydrogen gas is allowed to flow in a closed cyclic path around the rotor. Heat exchange takes place and the temperature of hydrogen gas increases, for better cooling of the rotor in the next cycle it has to be cooled.

Cooling of hydrogen gas is done by passing it through heat exchangers generally constituted with water. Now Hydrogen gas after cooling is allowed to pass through driers ( mainly silica gel which absorbs moisture) and allowed to pass again through the rotor.

Demand factor is the ratio of the sum of the maximum demand of a system (or part of a system) to the total connected load on the system (or part of the system) under consideration.

Demand factor = Pmax / Sum of connected load

= 1.5/2 = 0.75