Found 1006 Articles for Electronics & Electrical

The resistance $R_{a}$ of the armature can be neglected since it has negligible effect on the relationship between the power output of a synchronous machine and its torque angle $\delta$. The phasor diagram at lagging power factor for a salient pole synchronous machine, neglecting $R_{a}$ is shown in Figure-1. The power-angle characteristics of a salient-pole machine may be derived from the phasor diagram.The complex power output per phase of the alternator is, $$\mathrm{𝑆_{1𝜑} =𝑉{𝐼^{*}_{𝑎}}… (1)}$$Taking excitation voltage ($E_{f}$) as the reference phasor, then, $$\mathrm{𝑉 = 𝑉\angle − \delta = 𝑉\:cos\:\delta − 𝑗𝑉\:sin\:\delta … (2)}$$$$\mathrm{𝐼_{𝑎} = 𝐼_{𝑞} − 𝑗𝐼_{𝑑}}$$$$\mathrm{∴\:{𝐼^{*}_{𝑎}}= 𝐼_{𝑞} + ... Read More

The circuit model of a cylindrical rotor synchronous generator or alternator is shown in Figure-1.Let, 𝑉 = Terminal voltage per phase$𝐸_{𝑓}$ = Excitation voltage per phase$𝐼_{𝑎}$ = Armature current$\delta$ = Load angle (between 𝑉 and $𝐸_{𝑓}$ )By applying KVL in the circuit, we get, $$\mathrm{𝑬_{𝒇} = 𝑽 + 𝑰_{𝒂}𝒁_{𝒔} … (1)}$$$$\mathrm{∴\:𝑰_{𝒂} =\frac{𝑬_{𝒇} − 𝑽}{𝒁_{𝒔}}… (2)}$$Where, $$\mathrm{Synchronous\:impedance, \:𝒁_{𝒔} = 𝑅_{𝑎}+ 𝑗𝑋_{𝑎} = 𝑍_{𝑠}\angle 𝜃_{𝑧} … (3)}$$Also, for a synchronous generator the excitation voltage ($𝐸_{𝑓}$) leads the terminal voltage (V) by the load angle ($\delta$). Thus, $$\mathrm{𝑽 = 𝑉 \angle 0°\:\:then\:\:𝑬_{𝒇} = 𝐸_{𝒇} \angle \delta}$$Complex Power Output of the Alternator per Phase$$\mathrm{𝑆_{𝑜𝑔} ... Read More

The circuit model of a cylindrical rotor synchronous generator or alternator is shown in Figure-1.Let, 𝑉 = Terminal voltage per phase$𝐸_{𝑓}$ = Excitation voltage per phase$𝐼_{𝑎}$ = Armature current$\delta$ = Load angle (between 𝑉 and $𝐸_{𝑓}$ )By applying KVL in the circuit, we get, $$\mathrm{𝑬_{𝒇} = 𝑽 + 𝑰_{𝒂}𝒁_{𝒔} … (1)}$$$$\mathrm{∴\:𝑰_{𝒂} =\frac{𝑬_{𝒇} − 𝑽}{𝒁_{𝒔}}… (2)}$$Where, $$\mathrm{Synchronous\:impedance, \:𝒁_{𝒔} = 𝑅_{𝑎}+ 𝑗𝑋_{𝑎} = 𝑍_{𝑠}\angle 𝜃_{𝑧} … (3)}$$Also, for a synchronous generator the excitation voltage ($𝐸_{𝑓}$) leads the terminal voltage (V) by the load angle ($\delta$). Thus, $$\mathrm{𝑽 = 𝑉 \angle 0°\:\:then\:\:𝑬_{𝒇} = 𝐸_{𝒇} \angle \delta}$$Complex Power Input to the Alternator per PhaseThe ... Read More

The circuit model of a cylindrical rotor synchronous generator is shown in Figure-1.Let, 𝑉 = Terminal voltage per phase$𝐸_{𝑓}$ = Excitation voltage per phase$𝐼_{𝑎}$ = Armature current$\delta$ = Load angle or angle between 𝑉 and $𝐸_{𝑓}$Also, the phasor diagram of the alternator at lagging power factor is shown in Figure-2.For an alternator or synchronous generator, the excitation voltage ($𝐸_{𝑓}$) leads the terminal voltage (V) by the load angle ($\delta$) of the machine. Thus, $$\mathrm{𝑽 = 𝑉\angle0°\:\:and\:\:𝑬_{𝒇} = 𝐸_{𝑓}\angle \delta}$$The synchronous impedance of the alternator is given by, $$\mathrm{𝒁_{𝒔} = 𝑅_{𝑎} + 𝑗𝑋_{𝑠} = 𝑍_{𝑠}\angle𝜃_{𝑧} … (1)}$$Where, the angle ($𝜃_{𝑧}$) is ... Read More

The Potier Triangle Method is used in determining the voltage regulation of alternators. It is also known as the Zero Power Factor (ZPF) method. The following assumptions are made in the Potier triangle method −The armature reaction MMF is constant.The open-circuit characteristic (O.C.C.) taken on no-load accurately represents the relation between MMF and voltage under loaded conditions.The voltage drop due to the armature leakage reactance ($𝐼_{𝑎}𝑋_{𝑎𝐿}$) is independent of the excitation.Procedure to Obtain Voltage Regulation by ZPF MethodThe following procedure is followed to determine the voltage regulation of an alternator or synchronous generator by the zero power factor (ZPF) method ... Read More

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