In practice, a very large number of 3-phase alternators operate in parallel because the various power stations are interconnected through the national grid. The electric power systems are interconnected for economy and reliable operation. This interconnection of power systems requires alternators to operate in parallel with each other.In a generating station, two or more alternators are connected in parallel (as shown in Figure). Also, in an interconnected system forming a grid the alternators are located at different places and they are connected in parallel by means of transformers and transmission lines. Under normal operating conditions, all the alternators in an ... Read More

Consider two synchronous generators or alternators are operating in parallel and their load-frequency characteristics are shown in the figure.Let$𝑓_{1(𝑛𝑙)}$ = No load frequency of alternator 1$𝑓_{2(𝑛𝑙)}$ = No load frequency of alternator 2$𝑓_{1(𝑓𝑙)}$ = Full load frequency of alternator 1$𝑓_{2(𝑓𝑙)}$ = Full load frequency of alternator 2𝑓 = Common operating frequency when the two alternators are operating in parallel$𝑊_{1}$ = Full load power rating of alternator 1$𝑊_{2}$ = Full load power rating of alternator 2$𝑃_{1}$ = Power shared by alternator 1$𝑃_{2}$ = Power shared by alternator 2𝑃 = Total power delivered by the two alternatorsFor Alternator 1:$$\mathrm{Drop\:in\:frequency\:from\:no\:load\:to \:full\:load = 𝑓_{1(𝑛𝑙)} ... Read More

The slip test is a simple no-load test, which is used to determine the direct-axis and quadrature-axis synchronous reactances of a salient-pole synchronous machine. In this test, a small voltage at rated frequency is applied to the 3-phase stator winding of the synchronous machine. The field winding is unexcited and left open circuited.Circuit Arrangement for Slip TestThe circuit arrangement for slip test is shown in Figure-1.The rotor is driven by an auxiliary motor at a speed slightly less than or more than the synchronous speed. The direction of rotation should be same as that of the rotating magnetic field produced ... Read More

A synchronous machine may be subjected to various disturbances. Any cause of disturbance will produce electrical and mechanical transients. These transients may result from switching, from sudden changes of load, from sudden short-circuits between line and ground or between double lines or between all the three lines. These disturbances produce large mechanical stresses which may damage the machine. The synchronous machine may also lose synchronism.Constant Flux Linkage Theorem: StatementThe constant flux linkage theorem is used in studying alternator transients. This theorem is stated as follows −“The flux linkage after sudden disturbance in a closed circuit having zero resistance and zero ... Read More

Magnetic Axes of RotorThe figure shows the direct axis and the quadrature axis of a rotor −Direct AxisThe axis of symmetry of the magnetic poles of the rotor is called as direct axis or d-axis. The axis of symmetry of the north magnetic poles of the rotor is known as the positive d-axis while the axis of symmetry of the south magnetic poles is known as the negative d-axis.Quadrature AxisThe axis of symmetry halfway between the adjacent north and south poles is known as quadrature axis or q-axis. The q-axis lagging the north pole is taken as the positive q-axis. ... Read More

A synchronous machine under steady running conditions has a driving torque at every instant balancing its retarding torque. The retarding torque is developed by phase displacement ($\delta$) between the axis of the stator and rotor poles. A mechanical rotary system possesses inertia and restoring torque that tends to restore its position when displaced, thus the system has a natural frequency of oscillations.A synchronous machine operating in parallel with other machines or infinite busbars forms such an oscillatory system. Here, the restoring torque is due to the synchronizing torque that depends upon the phase displacement and opposes the displacement. The inertia ... Read More

In the ampere-turn method (which is also known as the MMF method), the effect of armature leakage reactance is replaced by an equivalent additional armature reaction MMF so that this MMF can be combined with the armature reaction MMF.In order to predict the voltage regulation of the alternator by the MMF method, the following information is required −Resistance of the armature (or stator) winding per phase.Open-circuit characteristic of the alternator.Short-circuit characteristic of the alternator.The MMF method uses the phasor diagram of the alternator for determining the voltage regulation. In order to draw the phasor diagram at lagging power factor, the ... Read More

Metadyne is a cross-field machine. The cross-field machines are special DC machines having an additional set of brushes on the direct-axis or d-axis. This arrangement of brushes enables the use of armature MMF to provide most of the excitation and achieve high power gains.Construction and Working of MetadyneAn ordinary DC generator can be converted into a metadyne by providing an additional pair of brushes on the direct-axis or d-axis (see the figure). The brushes lie on the quadrature axis or q-axis are short-circuited and the output of the machine is obtained from the d-axis brushes. The stator consists of a ... Read More

The synchronising torque coefficient is defined as the torque at which the synchronous speed gives the synchronising power. If represents the synchronising torque coefficient, then$$\mathrm{𝜏_{𝑠𝑦𝑛} =\frac{1}{𝜔_{𝑠}}𝑚\frac{𝑑𝑃}{𝑑𝛿}\:Nm/electrical\:radian …(1)}$$Also, $$\mathrm{𝜏_{𝑠𝑦𝑛} =\left (\frac{1}{𝜔_{𝑠}}𝑚\frac{𝑑𝑃}{𝑑𝛿} \right)\cdot \frac{𝜋𝑝}{180°}\:Nm/mechanical \:degree …(2)}$$Where, m is the number of phase of the machine, 𝜔𝑠 = 2𝜋𝑛𝑠 is the angular synchronous speed, 𝑛𝑠 is the synchronous speed in r.p.s.𝑝 is the total number of pair of poles of the machine.The synchronising torque coefficient may also be given by, $$\mathrm{𝜏_{𝑠𝑦𝑛} =\frac{𝑑𝜏}{𝑑𝛿}=\frac{1}{2𝜋𝑛_{𝑠}}\frac{𝑑𝑃}{𝑑𝛿}… (3)}$$$$\mathrm{∵\:\frac{𝑑𝑃}{𝑑𝛿}=𝑃_{𝑠𝑦𝑛} =\frac{𝑉𝐸_{𝑓}}{𝑍_{𝑠}}sin(𝜃_{𝑧} − 𝛿)}$$$$\mathrm{∴\:𝜏_{𝑠𝑦𝑛} =\frac{𝑉𝐸_{𝑓}}{2𝜋𝑛_{𝑠 }\cdot 𝑍_{𝑠}}sin(𝜃_{𝑧} − 𝛿) … (4)}$$In many synchronous machines, Xs >>R. Therefore, for a cylindrical rotor ... Read More

What is an Infinite Bus?Normally, in a power system, more than one synchronous generators or alternators operate in parallel. The alternators may be located at different places.A group of alternators located at a single place may be treated as a single large alternator.Also, the alternators connected to the same busbar but separated by transmission lines of low reactance may be considered as a single large machine.The capacity of this power system is so large that its terminal voltage and frequency may be taken constant. The connection or disconnection of a single alternator or a single small load would not affect ... Read More