In this exercise, we propose to study a three-phase alternator with smooth poles and a wound rotor. The three phases are star-connected. We measured its electromotive force E as a function of the excitation current Ie at the speed of 3000rpm. The measurement of E (Ie) is shown in Table bellow:
The alternator has a nominal apparent rated power of 250kVA and a nominal phase-neutral voltage 230V.
1- Represent the connection scheme of the three phases corresponding to the star coupling of the alternator. In addition, draw the equivalent circuit of the synchronous machine (for one phase) according to Behn-Eschenburg.
2- The frequency of the phase voltages is 50Hz. Specify the number of poles of the alternator.
3- Calculate the nominal current value: In.
4- At short-circuit, the current of the alternator reaches the calculated nominal value In for a value of the excitation current: Ie = 6 A. Calculate the value of the synchronous reactance Xs if we neglect the resistance of the windings that constitute the phases.
5- The alternator is now connected to a set of unit power factor loads. These loads are three-phase balanced and star wired to the alternator. What is the value of the excitation current Ie allowing supplying 150kW to all the loads under a voltage between two phases of 400 V?
(Make a Fresnel diagram of the magnitudes of the equivalent single-phase circuit before starting any calculation.)