Motor equations

Generators and motors are often connected to their associated switchboards or networks by an impedance. This impedance can be a cable, an overhead line, a unit transformer or a combination of these components. The intermediate circuit introduced in the stator circuit will contain resistance and inductive reactance, the effect of which is to modify the time constants in the generator and motor equations, and the performance of these machines under most transiently disturbed conditions. This aspect has been mentioned in the literature e.g. References 24, 25 and 26 but is easily overlooked when developing computer programs. 

Equation 2.2 is obviously not exact since the heat of melting and other thermal effects have been ignored. Equation 2.2 coupled with Equation 2.1 enables one to obtain an estimate of AT. Thus, for processing of poly(methyl methacrylate), for which Cp is about 0.6 Btu/lb °F, in a 2-in. extruder run by a 10-hp motor, Equation 2.1 gives Q =74 Ib/h, and Equation 2.2 indicates that AT=430°F. In practice, a AT of 350 F is usually adequate for this polymer. 

The minimum required actuation force Fmi can also be defined in the same way with Tl replaced with IT.. When the motorization equation is applied to mechanisms which have to fulfil a specified acceleration requirement or for which an indirect acceleration requirement can be deduced, then the external torque or force is increased by a factor of 1.25. 

Power, Energy, and Drives. Centrifuges accomplish their function by subjecting fluids and soHds to centrifugal fields produced by rotation. Electric motors are the drive device most frequently used however, hydrauHc motors, internal combustion engines, and steam or air turbines are also used. One power equation appHes to all types of centrifuges and drive devices. 

From equation 60 one can obtain a theoretical power requirement of about 900 kWh/SWU for uranium isotope separation assuming a reasonable operating temperature. A comparison of this number with the specific power requirements of the United States (2433 kWh/SWU) or Eurodif plants (2538 kWh/SWU) indicates that real gaseous diffusion plants have an efficiency of about 37%. This represents not only the barrier efficiency, the value of which has not been reported, but also electrical distribution losses, motor and compressor efficiencies, and frictional losses in the process gas flow. 

Within these basic principles there are many types of electric motors. Each has its own individual operating characteristics peculiarly suited to specific drive applications. Equations (29-1) through (29-9), presented in Table 29-1, describe the general operating characteristics of alternating-current motors. When several types are suitable, selection is based on initial installed cost and operating costs (including maintenance and consideration of rehability). 

The speed-torque characteristics of a motor will largely depend upon its rotor parameters such as ( 2 The higher the rotor resistance / 2. the higher will be the torque. From equation (1.3) we cun draw a speed-torque curve of a motor as shown in Figures 1.5(a) and (b). 

During a run, if the supply voltage to a motor terminal drops to 85% of its rated value, then the full load torque of the motor will decrease to 72.25%. Since the load and its torque requirement will remain the same, the motor will star to drop speed until the torque available on its speed-torque curve has a value as high as 100/0.7225 or 138.4% of T to sustain this situation. The motor will now operate at a higher slip, increasing the rotor slip losses also in the same proportion. See equation (1.9) and Figure 1.7. 

The higher the full load slip, the higher will be the rotor losses and rotor heat. This is clear from the circle diagram and also from equation (1.9). An attempt to limit the start-up current by increasing the slip and the rotor resistance in a squirrel cage motor may thus jeopardize the motor s performance. The selection of starling current and rotor resistance is thus a compromise to achieve optimum performance. 

GD of the load, as referred to the motor speed, will be different. Equating the work done at the two speeds ... 

This expression, except for the mechanical design, is totally independent of the type of start and the electrical design of the motor. Electrically also, this is demonstrated in I he subsequent example. The expression, however, does not hold good for an ON-LOAD start. On load, the accelerating torque diminishes substantially with the type of load and the method of start, as can be seen from Figure 2.14, and so diminishes the denominator of equation (2.5), raising the time of start. 

In such a condition, if the heat generated in the windings raises the temperature of the windings by 6 above the temperature, the motor was operating just before stalling. Then by a differential form of the heat equation ... 

With the help of this equation the thermal curve of a machine can be drawn on a log-log graph for a known r, I versus /j//, for different conditions of motor heating prior to a trip (Figure 3.12). The relay can be set for the most appropriate thermal curve, after assessing the motor s actual operating conditions and hence achieving a true thermal replica protection. 

The inverter may be a current source inverter, rather than a voltage source inverter (.Section 6.9.4) since it will be the rotor current that is required to be vtiried (equation (1.7)) to control the speed of a wound rotor motor, and this can be independently varied through the control of the rotor current. The speed and torque of the motor can be smoothly and steplessly controlled by this method, without any power loss. Figures 6.47 and 6.48 illustrate a typical slip recovery system and its control scheme, respectively. 

The brakes should be suitable to counter at least the torque developed by the motor. They must therefore develop at least this amount of torque. To find the least braking torque, the brake drums must be able to develop, in either of the above typies of mechanical brakes, the torque shown in equation (1.10) may be used i.e. 

In addition to electrical braking, a mechanical brake, as discussed in Section 6.20.1(A) may also be essential if the motor is required to be stopped completely because, at any value of excitation current, the motor will never reach a standstill condition. The heat of braking up to the standstill condition (N = 0) is roughly equal to one start and is expressed by equation (6.9). 

This output coixesponds to a continuous duty of drive. It must be suitably corrected for the duty cycle the motor has to perform (see equation (3,11)), i.e. 

Whenever a motor is installed in a humid atmosphere and is switched on after a long shutdown, insulation resistance must be checked before energizing the motor. As a precaution, insulation resistance must be checked before a restart after a long shutdown, even in temperate conditions. If the insulation level is found to be below the recommended level as shown in equation (9.1) it must be made up as noted below. 

One can thus easily obtain the significance of the factor 6 to represent the status of the most affected winding of the motor in the event of a voltage unbalance resulting in a negative sequence current component. For more clarity, consider equations (12.4) and (12.6) to ascertain the similarity in both these equations. Since both must represent the maximum heating effect... 

Overcurrent protection. To provide a thermal replica protection, the relay is set according to motor s heating and cooling (/ - 1) curves supplied by the motor manufacturer. If these curves are not available, they can be established with the help of motor heating and cooling time constants, as in equations (3.2) and (3.4). A brief procedure to establish the motor thermal curves when they are not available is explained in Section 3.6. 

If the field excitation is also lost, the generator will run as an induction motor again driving the primer mover as above. As an induction motor, it will now operate at less than the synchronous speed and cause slip frequency current and slip losses in the rotor circuit, which may overheat the rotor and damage it, see also Section. 1.3 and equation (1.9). A reverse power relay under such a condition will disconnect the generator from the mains and protect the machine. 

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