(3) Consider a synchronous machine air gap of width g and average radius r. Ther
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(3) Consider a synchronous machine air gap of width g and average radius r. There is a flux density wave cos(O ? wt) in the air gap moving at synchronous speed w = 377 rad/s. Assume that the machine is length L. Consider a concentrated full pitch stator coil at 0 90 degree and 90 degree. (a) What is the total flux A linking the stator coil as a function of time t? (b) If the concentrated coil has N turns, use Faraday?s law to derive the voltage Ca induced in the coil. (ea is proportional to w and is called the speed voltage.) (c) What is the voltage Cb induced in a similar concentrated stator coil at theta = 150 degree and 30 degree ? (4) Consider a,b,c full pitch stator coils that arc equally spaced around the stator and with 3 phase balanced 60 Hz AC currents. Assume that each of the coils is designed so that produces a flux density in the air gap that is sinusoidally distributed around the air gap and has maximum value Bmax. Assume that the iron has infinite permeability ?i,.. Show that the total air gap flux density is a sinusoidal wave of flux density rotating at synchronous speed. Draw pictures of the wave at several times in the unwrapped version of the air gap to Convince yourself that it is a moving wave. Then look at the Mathematica applet on the course web page to verify that you have understood what is happening. The following questions use the per phase circuit model of the 3 phase syn chronous machine that is the no-load AC voltage E in series with the synchronous reactance Xs. (Leakage reactance and resistance of the windings are neglected.) (5) A 3 phase synchronous generator has a synchronous reactance of 9 per phase, a no-load line to neutral AC voltage of E = 12 kV and a line to line terminal voltage of 17.3 kV. You will need your formula for power produced by the generator (you can get this by adapting your answer from homework 7 or the class notes) (a) The power angle sigma m = 30 degree. (6m is the angle between E and V.) Calculate the 3 phase real power delivered to the grid at the terminals of the generator. (b) The real power increases when the power angle 6m increases, but there is a maximum possible theoretical power that the generator can produce. Calculate the maximum 3 phase real power. Consider a synchronous machine air gap of width g and average radius r.Explanation / Answer
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