Three phase systems:

Three phase AC system can be analyze by considering Three phase generator, at generator terminal we consider armature winding in star or delta and output supply will have 3 phase R,Y,V, as shown in fig 38(a) and (b) having 3 phase at 120 degree phase displacement

**If we consider load is balance as show in fig 38 (b) 3 phase load is connected to 3 phase senator if we want studies each phase of generator load system we have study only one phase assuming per unit system and compare other phase to it. **

**Two-wattmeter Method of Power Measurement in a Three phase Circuit**

Connection diagram for two-wattmeter method of power measurement in a three-phase balanced system with star-connected load

Phasor diagram for a three-phase balanced star-connected circuit

**Three Phase Synchronous Generators**

**Synchronous Generators** : synchronous generator is a double excited machine it has two part 1- rotating part and 2- stationary part rotating part is called rotor (as show in Fig -)where as stationary part is call stator ,both stationary and rotating part is excited by individual source that s why synchronous machine called double excited machine 3 phase is applied to the stature terminal at armature winding that s why a rotating flux will setup in air gap ( gap between stator and rotor ) , the current flow flowing through the field coil will set up a constant flux of alternate North and South.

**Rotating part of synchronous generator : Rotating part of synchronous generator call rotor having field winding on it field winding is excited by dc supply ,**stationary flux setup in air gap now air gap has tow type of flux on is due to armature winding and second is due to field winding both fluxes are try to alien in direction and due to this rotor rotate .

Stationary part of synchronous machine : Its the outer part of machine consisting field winding field winding is excited by dc supply which stable stationary flux in air gap.

**Methods of starting synchronous motor**: Synchronous motor is not self starting machine it need external source to start. Synchronous motor rotate with synchronous speed it cant rotate other than synchronous speed ,

Voltage induce in generator is depend on the flux and speed of rotation so induce voltage can be written as

Assume machine is not connected to load then terminal voltage should be equal to internal voltage there is no load current so voltage drop in armature resistance will be zero thats why both voltage will be in same phase . If we consider synchronous reactance X and armature resistance Ra=0 and load is connected then

When i current flow in load then armature drop will be IRa and drop in armature reactance will be Ia XJ .If B net is the net magnetic flux density B_{R }is the magnetic flux density due to armature reaction and Bs is the main magnetic flux density then Bnet and V_{Φ} can be written as

X_{A }is the reactance due to armature reaction , Ra is the armature resistance and X is the armature inductance then V_{Φ} (terminal voltage) can be written as

Xs = X + Xa

and the circuit diagram can be drain as as we know field winding of synchronous machine can be excited by dc supply R_{F} is the field winding resistance and X_{f} is the reactance of field winding Rex is the external resistance added in the armature resistance to control the flux as well speed . Synchronous machine is operate on 3 pf leading pf ,lagging pf and unity pf .Here we are drawing pharoses diagram for each case. If we consider lagging case then armature current will lagg by armature voltage and terminal voltage also voltage drop in synchronous reactance will perpendicular on armature current as show in fig

If we consider leading case of synchronous machine then in this case current will lead to terminal voltage and voltage drop in armature resistance will be in phase of armature current and drop in synchronous reactance will be perpendicular to the armature current. E_{A }will be the vector some of V_{Φ}, IaRa, and IaX.

If u consider unity pf V_{Φ}, and armature current will be in same phase drop of synchronous reactance will be perpendicular to it

From above phasor diagram we can find v curve is the curve between armature current and field current .

As we increase field current armature current will decrease and after unity pf point armature current will increase as shown in above fig .

**Module-5**

TRANSFORMER:- Transformer is a device which can change voltage/ current level but it cant change the frequency and power , Transformer work on electro magnetic induction principle. Transformer consist 2 winding primary and secondary winding the winding which excited by ac source called primary winding and winding in which load is connected is called secondary winding. Transformer can work only on ac supply it cant work on dc supply because in dc supply there is no rate of change flux where as according to Faraday law for the induction there is variation of flux required. Transformer can be categories in 2 category 1- Step up transformer 2- Step down transformer .

**Step up transformer**: Those transformer which has N_{2} > N_{1} it implies that V_{2} > V_{1} and I_{1} > I_{2}

Where I1 is primary current

I2 is secondary current

V1 is primary voltage

V2 is secondary voltage as show in fig -33

TRANSFORMER WORKING :-When a ac supply is applied on primary of transformer the time varying flux of primary winding link with the secondary winding too due to this flux emf will induce in secondary winding

As show in above fig flux of primary winding linkage with primary as well secondary winding and as per faraday law.

Transformer can be categories in Two category Core type and shell Type as show in Fig - core is stranded by winding is called core type and when winding is surrounded by core is called shell type , core type transformer used for high voltage application where as shell type transformer used for low voltage applications.

OPEN – CIRCUIT AND SHORT – CIRCUIT TEST :-

Open circuit (or No –load) test:-

There are two type of losses in transformer 1- Core loss 2- Ohmic loss .

For the calculation of core loss we will use Open circuit test where as for the calculation of ohmic loss we use Short circuit test

**Open circuit test. **

In this test primary winding is excited by ac supply and secondary is short circuited (no load On secondary winding, only no load current flow in primary winding , no load current 3 to 5 % of full load current ) and the input only loss in core loss so.

Short –circuit test:-

Short circuit test can perform for calculation of ohmic loss in this test secondary is short circuited and primary excited by ac source and the input will loss in ohmic loss that can be calculated as

W is the full load copper loss

V1 is the applied voltage

I1 is the rated current

Ro1 resistance of primary side

X01 reactance of primary side

W01= IO^{2} Ro1

VOLTAGE REGULATION OF A TRANSFORMER:-

It is defined as the change in magnitude of the secondary terminal voltage, expressed as a percentage (or per unit) of the secondary rated voltage, when load at a given power factor is reduced to zero, with primary applied voltage held constant. If

V2 = secondary terminal voltage at any load,

E2 = secondary terminal voltage at no load

Then at a given power factor and specified load, the voltage regulation is -

**Condition for zero voltage regulation**:-

**Condition for maximum voltage regulation can be calculated **

TRANSFORMER EFFICIENCY:-

The efficiency of a transformer is defined as the ratio of output power to the input power.

Condition for maximum efficiency :-

- Given an iron core with 500 turns, a length of 0.50m and an area of 2x10
^{-4}m^{2}, determine the inductance. - A 20:1 transformer has N
_{P}= 200, V_{P}= 220V and I_{P}= 4A. Determine N_{S}, V_{S}, and I_{s}. - Four inductors of values 5mH, 9mH, 15mH, and 17mH are connected in series. Determine the total inductance.
- Four inductors of values 5mH, 9mH, 15mH, and 17mH are connected in parallel. Determine the total equivalent inductance.
- Calculate the energy store in a 15mH inductor with a current of 5mA flowing through it.

L_{tot}= L1+ L2+L3+L4= (5+9+15+17)=46 mH