Electric Machines (2)

Question 1

What are the features of a single phase synchronous AC generator?

Answer 1

• A Rotor made of either a perminant or electromagnet of two poles (North and South) at opposite ends, that spin round the middle, as shown below.
• A Stator, made of laminated steel (which has low reluctance) that directs magnetic flux from the rotor round the stator. Stator will have conductors (or bunches of coils within the stator) at specific points so they are in phase.

Large vs Small generators:
* for large generators the coils often stay still and the rotor (or magnets) spin
* for small generators the coils may spin while the magnets stay still.

Question 2

Explain how magnetic flux and therefore E.M.F (or generated voltage) varies for each of the positions of the Single Phase Synchronous AC generator, below? Use relevant equations or derivations to explain.

Answer 2

Explaination:
* We know that magnetic flux is the flux density times the area. Therefore the magnetic flux is greatest when the magnet is perpendicular to the coil, therefore when θ =π/2.
* The flux varies by ϕ = ϕmax sin(θ) = ϕmax sin(ωt), this can be measured as the flux will alternate in a sinosidal way.
* Since EMF is a function of flux, E = -d(Nϕ)/dt, we can then derive it as an equation E = -Emax cos(2πft), or if we change the starting point of the rotor and make it start where EMF is initially zero then the equation is E = Emax sin(2πft).
* We can plot these equation on a graph and show the variation is sinosiodal for both.

Question 3

What is the circuit configuration and the EMF equations for each phase of a three-phase synchronous AC generator as shown below?

Answer 3

For Phase A:
* EA = Emax sin(2πft)

**For Phase B: **
* EB = Emax sin(2πft - 2π/3) (as it’s 120° out of phase of A)

For Phase C:
* EC = Emax sin(2πft - 4π/3) (as it’s 120° out of phase of B, therefore 240° out of phase of A).

Circuit configuration is shown below. Notice how its connected.

Question 4

Why would we use a Three-phase over a single-phase synchronous AC generator?

Answer 4

Simply put, we aren’t utalising all the available space in the stator by using a single phase. We can easily generatre more electricity or emf by adding multiple phases and these can then be used to power other loads.

Question 5

What are the two main types of load connections for a three-phase synchronous AC generator?

Answer 5

• Star connection
• Delta connection

Question 6

What is the benefit of using a star connection for your load connection for a three-phase synchronous AC generator?

Answer 6

• If the loads are balanced: R = Ra = Rb = Rc
• Then the current through the neutral wire, iN = ia + ib + ic = 0.
• Therefore the electrical power generator/consumed is a constant, P = Eaia + Ebib + Ecic = 3(Em^2) / 2R

Try deriving the power and the current equation using trigonometry and the understanding that A, B and C are out of phase by 120 degrees each.