Conditions Required for Paralleling AlternatorsIn order to connect an alternator in parallel with another alternator or an alternator to the infinite busbars, the following conditions are met −The phase sequence of the voltages of the incoming alternator should be the same as that of the busbars.The incoming alternator voltages must be in phase with the busbar voltages.The terminal voltage of the incoming alternator must be the same as the busbar voltage.The frequency of the generated voltage of the incoming alternator must be equal to frequency of the busbar voltage.Synchronization by a SynchroscopeA stationary alternator must not be connected to live ... Read More

A set of three synchronizing lamps can be used to check the conditions for paralleling the incoming machine with other machines. The dark lamp method along with a voltmeter used for synchronising is shown in figure. This method is used for synchronizing low-power machines.In this method, one lamp is connected between corresponding phases while the other two lamps are cross-connected between the other two phases, i.e., R1 is connected to R2, Y1 to B2 and B1 to Y2 as shown in the figure.Now, the prime mover of the incoming machine is started and the alternator is brought up to near ... Read More

Short circuits at the terminals of the unloaded alternators or synchronous generators are very rare. They generally occur due to insulation failure or accidental damage on some part of the power system supplied by the generator. Therefore, it is important to deal with the case of a 3-phase alternator delivering power to a load or to an infinite bus.If a short circuit occurs across the armature terminals of the alternator, the short circuit armature current will pass through a sub-transient period, a transient period and finally will settle down to a steady-state condition. Also, when the short circuit occurs, the ... Read More

A sudden 3-phase short-circuit at the armature terminals of a synchronous machine is used to analyse the transient phenomenon. This is the most severe transient condition that can occur in a synchronous generator. It is assumed that the machine is to be initially unloaded and to continue operating at synchronous speed after short-circuit occurs.The machine being producing normal voltage under no-load condition and their instantaneous values are given by, $$\mathrm{𝑒_{𝑅} = 𝐸_{𝑚}\:sin\:𝜔𝑡}$$$$\mathrm{𝑒_{𝑌} = 𝐸_{𝑚}\:sin(𝜔𝑡 − 120°)}$$$$\mathrm{𝑒_{𝐵} = 𝐸_{𝑚}\:sin(𝜔𝑡 + 120°)}$$Since the machine is initially unloaded, the only pre-disturbance current in the machine is the field current. When the rotor rotates, ... Read More

The prime-mover governor characteristic is a graph plotted between the speed of the prime-mover (or generator frequency) and the active power. A typical prime-mover governor characteristic is shown in the figure.The prime mover characteristic usually drawn as a straight line, but the actual characteristic has a slight curve.For the successful parallel operation of the alternators or synchronous generators, the load-speed characteristics of the prime movers should be drooping, i.e., the speed of the prime mover should decrease slightly with increasing loads. The drooping characteristic provides inherent stability of the operation of an alternator when paralleled with the other alternators. The ... Read More

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