The zero power factor characteristics (ZPFC) is the graph plotted between the armature terminal voltage per phase and the field current, when the machine being operating with constant rated armature current at synchronous speed and zero lagging power factor. The ZPFC is also known as Potier Characteristics after its originator.In order to maintain the power factor very low, the alternator is loaded by means of reactors or by an under-excited synchronous motor. The shape of the ZPFC is very much like that of the open-circuit characteristic (O.C.C.) displaced downwards and to the right.Phasor DiagramFigure-1 shows the phasor diagram of the ... Read More

When the flux density distribution in the alternator is non-sinusoidal, the induced voltage in the winding will also be non-sinusoidal. Thus, the pitch factor or coil span factor, distribution factor and winding factor will be different for each harmonic voltage.Pitch Factor for nth HarmonicAs the electrical angle is directly proportional to the number of poles and the angle between the adjacent slots, i.e., $$\mathrm{𝜃_{𝑒} =\frac{𝑃}{2}𝜃_{𝑚} … (1)}$$The chording angle increases with an increase in the order of the harmonics (n). In a short pitch coil, the chording angle is α° (electrical) for the fundamental flux wave. For the nth harmonic, ... Read More

When a synchronous machine is synchronised to infinite busbars, it has an inherent tendency to remain in synchronism.Rotor is accelerated – Consider an alternator delivering a steady power P at a steady load angle δ. Suppose, due to some transient disturbance, the rotor is accelerated so that the load angle increases by an angle $dδ$. The operating point of the machine shifts to a new constant power line and the load on the machine increases to (𝑃 + 𝑑𝑃)). As the power input to the machine remains unchanged, this additional load decreases the speed of the machine and brings it ... Read More

A synchronous generator is a synchronous machine which converts mechanical power into AC electric power through the process of electromagnetic induction.Synchronous generators are also referred to as alternators or AC generators. The term "alternator" is used since it produces AC power. It is called synchronous generator because it must be driven at synchronous speed to produce AC power of the desired frequency.A synchronous generator can be either single-phase or poly-phase (generally 3phase).Construction of Synchronous Generator or AlternatorAs alternator consists of two main parts viz.Stator – The stator is the stationary part of the alternator. It carries the armature winding in ... Read More

Short Circuit RatioThe ratio of the field current required to generate rated voltage on open-circuit to the field current required to circulate rated armature current on short circuit is called as the short-circuit ratio (SCR) of a synchronous machine.Calculation of SCRThe short circuit ratio of a synchronous machine can be calculated from the open-circuit characteristic (O.C.C.) and the short-circuit characteristic (S.C.C.) of the synchronous machine, which are shown in the figure.From the figure, the SCR is given by, $$\mathrm{SCR =\frac{𝐼_{𝑓}\:for\:rated\:open \:circuit\:voltage}{𝐼_{𝑓}\:for\:rated\:short\:circuit\: current}=\frac{𝑂𝑎}{𝑂𝑑}… (1)}$$Since the triangles "Oab" and "Ode" are similar triangles, $$\mathrm{SCR =\frac{𝑂𝑎}{𝑂𝑑}=\frac{𝑎𝑏}{𝑑𝑒}… (2)}$$Also, from the figure, for a field ... Read More

The frequency of the generated voltage by the alternator depends upon the number of field poles and the speed at which the field poles are rotated. One complete cycle of the voltage being generated in an armature coil when a pair of field poles i.e. one north pole and one south pole passes over the coil.Let, 𝑃 = Number of rotor field poles𝑁 = Speed of rotor or field poles in RPM𝑓 = Frequency of the generated voltage in HzIn one revolution of the rotor, an armature coil is cut by (P/2) north poles and (P/2) south poles. Since one ... Read More

Coil span or coil pitch is defined as the distance between the two sides of a coil.Pole pitch is defined as the angular distance between the central line of one pole to the central line of the next pole. A pole pitch is always 180° electrical regardless of the number of poles on the machine.When a coil is having a span of 180° electrical, it is called as a full-pitch coil.When the coil is having a span less than 180° electrical, it is known as a short-pitch coil or fractional-pitch coil.The fractional-pitch coil is also known as chorded coil. A ... Read More

For a salient-pole synchronous generator or alternator, the per phase reactive power is given by, $$\mathrm{𝑄_{1𝜑} =\frac{𝑉𝐸_{𝑓}}{𝑋_{𝑑}}cos\:𝛿 −\frac{𝑉^{2}}{2𝑋_{𝑑}𝑋_{𝑞}}\lbrace{(𝑋_{𝑑} + 𝑋_{𝑞} ) − (𝑋_{𝑑} − 𝑋_{𝑞})\:cos\:2\delta}\rbrace … (1)}$$Where, V is the terminal voltage per phase.Ef is the excitation voltage per phase.$\delta$ is the per phase angle between Ef and V.Xd is the direct-axis synchronous reactance.Xq is the quadrature-axis synchronous reactance.For reactive power to be maximum, $$\mathrm{\frac{𝑑𝑄_{1𝜑}}{𝑑\delta}= 0}$$$$\mathrm{\Rightarrow\:\frac{𝑑}{𝑑\delta} \left(\frac{𝑉𝐸_{𝑓}}{𝑋_{𝑑}}cos\:\delta −\frac{𝑉^{2}}{2𝑋_{𝑑}𝑋_{𝑞}}\lbrace(𝑋_{𝑑} + 𝑋_{𝑞}) − (𝑋_{𝑑} − 𝑋_{𝑞}) cos\:2\delta\rbrace \right)= 0}$$$$\mathrm{−\frac{𝑉𝐸_{𝑓}}{𝑋_{𝑑}}sin\:\delta −\frac{2𝑉^{2}}{2𝑋_{𝑑}𝑋_{𝑞}}(𝑋_{𝑑} − 𝑋_{𝑞})sin\:2\delta = 0}$$$$\mathrm{\Rightarrow\:𝐸_{𝑓}\:sin\:\delta +\frac{𝑉}{𝑋_{𝑑}}(𝑋_{𝑑} − 𝑋_{𝑞})(2\:sin\:\delta\:cos\:\delta) = 0}$$$$\mathrm{\Rightarrow\:cos\:\delta = −\frac{𝐸_{𝑓}𝑋_{𝑞}}{2\:𝑉(𝑋_{𝑑} − 𝑋_{𝑞} )}… (2)}$$By putting the value of from eq. (2) ... Read More

Losses in an AlternatorThe losses that occur in an alternator can be divided into the following categories −Copper Losses or I2R LossesThe copper losses or I2R losses occur in the armature winding and rotor winding of the alternator. These losses occur due to the resistance of the windings.$$\mathrm{Armature\:winding\:cu\:loss = {𝐼^{2}_{𝑎}} 𝑅_{𝑎}}$$$$\mathrm{Rotor\:winding\:cu\:loss={𝐼^{2}_{𝑟}} 𝑅_{𝑟}}$$Core LossesThe core losses or iron losses occur in the pole faces, teeth and stator core of the alternator. The core losses in the alternator occur because the various iron parts of the machine are subjected to the varying magnetic field. The core losses consist of eddy current loss ... Read More

Hydrogen gas is used as cooling medium for cooling the alternators because of its superior cooling properties. The hydrogen cooling of the alternators requires completely seated circulated system. Mainly, oil-seated glands are used between shaft and casing of the alternator. The oil absorbs both hydrogen leaking-out and air leaking-in, so it should be purified periodically.In the hydrogen cooling of the alternators, the hydrogen gas is circulated by blowers and fans through the stator and rotor. Then, the heated hydrogen gas is passes over cooling coils inside the seated casing. The cooling coils carry oil or water to extract the heat ... Read More