barcode reader code in c# net Synchronous Motor Analysis in Software

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EXAMPLE 1710 Synchronous Motor Analysis
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Find the kVA rating, the induced voltage and the power angle of the rotor for a fully loaded synchronous motor
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Is + Vs = 460 0 3 Rs 1 jXS 12 + Eb
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Known Quantities: Motor ratings; motor synchronous impedance Find: S; Eb ; Schematics, Diagrams, Circuits, and Given Data: Motor ratings: 460 V; 3 ; pf = 0707 lagging; full-load stator current: 125 A ZS = 1 + j 12 Assumptions: Use per-phase analysis
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Figure 1736 Analysis: The circuit model for the motor is shown in Figure 1736 The per-phase
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current in the wye-connected stator winding is IS = |IS | = 125 A
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The per-phase voltage is 460 V VS = |VS | = = 26558 V 3 The kVA rating of the motor is expressed in terms of the apparent power, S (see 7): S = 3VS IS = 3 26558 V 125 A = 9,959 W From the equivalent circuit, we have Eb = VS IS (RS + j XS ) = 26558 (125 45 A) (1 + j 12 The induced line voltage is de ned to be Vline = 3Eb = 3 17931 V = 31057 V From the expression for Eb , we can nd the power angle: = 3283
Comments: The minus sign indicates that the machine is in the motor mode
) = 17931 3283 V
EXAMPLE 1711 Synchronous Motor Analysis
Problem
Find the stator current, the line current and the induced voltage for a synchronous motor
Solution
Known Quantities: Motor ratings; motor synchronous impedance Find: IS ; Iline ; Eb Schematics, Diagrams, Circuits, and Given Data: Motor ratings: 208 V; 3 ; 45 kVA;
60 Hz; pf = 08 leading; ZS = 0 + j 25 losses: 10 kW Load power: 15 hp
Assumptions: Use per-phase analysis
Friction and windage losses: 15 kW; core
Analysis: The output power of the motor is 15 hp; that is:
Pout = 15 hp 0746 kW/hp = 1119 kW The electric power supplied to the machine is Pin = Pout + Pmech + Pcore-loss + Pelec-loss = 1119 kW + 15 kW + 10 kW + 0 kW = 1369kW As discussed in 7, the resulting line current is Pin 13,690 W Iline = = = 475 A 3V cos 3 208 V 08 Because of the connection, the armature current is 1 IS = Iline = 274 3687 A 3
17
Introduction to Electric Machines
The emf may be found from the equivalent circuit and KVL: E b = V S j X S IS = 208 0 j 25 The power angle is = 124 (274 3687 A) = 255 124 V
Synchronous motors are not very commonly used in practice, for various reasons, among which are that they are essentially required to operate at constant speed (unless a variable-frequency AC supply is available) and that they are not self-starting Further, separate AC and DC supplies are required It will be seen shortly that the induction motor overcomes most of these drawbacks
Check Your Understanding
1711 A synchronous generator has a multipolar construction that permits changing its synchronous speed If only two poles are energized, at 50 Hz, the speed is 3,000 rev/min If the number of poles is progressively increased to 4, 6, 8, 10, and 12, nd the synchronous speed for each con guration 1712 Draw the complete equivalent circuit of a synchronous generator and its phasor
diagram
1713 Find an expression for the maximum pull-out torque of the synchronous motor
THE INDUCTION MOTOR
The induction motor is the most widely used electric machine, because of its relative simplicity of construction The stator winding of an induction machine is similar to that of a synchronous machine; thus, the description of the threephase winding of Figure 1725 also applies to induction machines The primary advantage of the induction machine, which is almost exclusively used as a motor (its performance as a generator is not very good), is that no separate excitation is required for the rotor The rotor typically consists of one of two arrangements: a squirrel cage, or a wound rotor The former contains conducting bars shortcircuited at the end and embedded within it; the latter consists of a multiphase winding similar to that used for the stator, but electrically short-circuited In either case, the induction motor operates by virtue of currents induced from the stator eld in the rotor In this respect, its operation is similar to that of a transformer, in that currents in the stator (which acts as a primary coil) induce currents in the rotor (acting as a secondary coil) In most induction motors, no external electrical connection is required for the rotor, thus permitting a simple, rugged construction, without the need for slip rings or brushes Unlike the synchronous motor, the induction motor does not operate at synchronous speed, but at a somewhat lower speed, which is dependent on the load Figure 1737 illustrates the appearance of a squirrel-cage induction motor The following discussion will focus mainly on this very common con guration
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