When the machine is to be used as a motor, voltage is applied across the armature windings, and the reaction with the magnetic field produces rotary motion of the shaft. When the machine is to be used as a generator, mechanical energy is applied to rotate the shaft, and the rotation of the armature windings in the magnetic fields produces current in the armature windings. The current varies in magnitude and reverses direction as the shaft rotates.
Sine-Type Currents and Voltages. In generation of alternating current, rotation of the armature of a generator produces a current that starts from zero as a wire enters the magnetic field of a pole on the stator and increases as the wire moves through the field. When the wire is directly under the magnet, the wire is cutting across the field at right angles and the maximum flow of current results. The wire then moves out of the field and the current decreases to zero. The wire next moves into the magnetic field of the opposite pole, and the process repeats, except that the current now flows in the opposite direction in the wire. This current variation from zero to a maximum in one direction (positive direction), down to zero, then continuing down to a maximum in the opposite direction (negative direction), and back to zero takes the form of a sine wave.
The number of complete cycles per second of the wave is called the frequency of the current. This is usually 60 Hz (cycles per second) in the United States; 50 Hz in most other European countries.
If P is the number of poles on the stator of a generator, the frequency of the alternating current equals P x rpm/120, where rpm is the revolutions per minute of the armature. This relationship also holds for ac motors. Hence, for a frequency of 60 Hz, rpm = 60 x 120/P = 7200/P. This indicates that theoretically a standard four-pole motor would run at 1800 rpm, and a two-pole motor at 3600 rpm. Because of slippage, however, these speeds are usually 1760 and 3400 rpm, respectively.
Phases. Two currents or voltages in a circuit may have the same frequency but may pass through zero at different times. This time relationship is called phase. As explained in the preceding, the variation of the current (or voltage) from zero to maximum is a result of the rotation of a generator coil through 90 to a pole and back to zero in the subsequent 90. The particular phase of a current is therefore given as angle of rotation from the zero start. If current (or voltage) 1 passes through its zero value just as another current (or voltage) 2 passes through its maximum, current 2 is said to lead current 1 by 90. Conversely, current 1 is said to lag current 2 by 90.
Effective Current and Voltage. The instantaneous value of an alternating current (or voltage) is continuously varying. This current has a heating effect on wire equal to the effective current I times the resistance R. Mathematically, the effective current is 0.707 times the maximum instantaneous current of the sine wave. The same relationship holds true for the effective voltage.
Ohms law, E = IR, can be used in alternating circuits with E as the effective voltage, I, the effective current, A, and R, the resistance, .
Inductive Reactances and Susceptance. When alternating current flows through a coil, a magnetic field surrounds the coil. As the current decreases in instantaneous value from maximum to zero, the magnetic field increases in strength from zero to maximum. As the current increases in the opposite direction, from zero to maximum, the magnetic-field strength decreases to zero. When the current starts to decrease, a new magnetic field is produced that is continuously increasing in strength but has changed direction.
The magnetic field, in changing, induces a voltage and current in the wire, but the phase, or timing, of the zero and maximum values of this induced voltage and current are actually 90 behind the original voltage and current wave in the wire.
The induced voltage and current are proportional to a constant called the inductive reactance of the coil. This constant, unlike resistance, which depends on the material and cross-sectional area of the wire, depends on the number of turns in the coil and the material of the core on which the coil is wound. For example, a simple coil wound around an airspace has less inductive reactance than a coil wound around an iron core. Inductive voltage EL and inductive current IL, A, are related by
E L = IL XL
where XL is the constant for inductive reactance of the circuit, expressed in ohms, . The reciprocal 1/XL is called inductive susceptance.
When an inductive reactance is wired in a series circuit with a resistance, the inductive reactance does not draw any power (or heating effect) from the circuit.
This occurs because the induced current IL is 90 out of phase with the applied voltage E. In the variation of the instantaneous value of applied voltage, power is taken from the circuit in making the magnetic field. Then, as the magnetic field collapses, the power is returned to the circuit.
Capacitive Reactance and Susceptance. An electrostatic condenser, or capacitor, consists basically of two conductors, for example, flat metal plates, with an insulator between. Another familiar form in laboratory use is the arrangement of two large brass balls with an airspace between. Electrostatic charges accumulate on one plate when voltage is applied. When the voltage is high enough, a spark jumps across the air space. With direct current, the discharge is instantaneous and then stops??until the charge builds up again. With alternating current, as one plate is being charged, the other plate is discharging, and the flow of current is continuous. In this case, the circuit is called capacitive.
Power in AC Circuits. Pure inductance or capacitance circuits store energy in either electric or magnetic fields and, when the field declines to zero, this energy is restored to the electric circuit.
Power is consumed in an ac circuit only in the resistance part of the circuit and equals ER, the effective voltage across the resistance, times IR the effective current.
Conversion of AC to DC. Alternating current has the advantage of being convertible to high voltages by transformers. High voltages are desired for longdistance transmission. For these reasons, utilities produce and sell alternating current. However, many applications requiring accurate speed control need direct-current motors, for example, building elevators and railroad motors, including subways. In buildings, ac may be converted to dc by use of an ac motor to drive a dc generator, which, in turn, provides the power for a dc motor. The ac motor and dc generator are called a motor-generator set.
Another device used to convert ac to dc is a rectifier. This device allows current to flow in one direction but cuts off the sine wave in the opposite direction. The current obtained from the motor-generator set described previously is a similar unidirectional current of varying instantaneous value. The only truly nonvarying direct current is obtained from batteries. However, output filters can be added to rectifiers to reduce the amount of voltage variation to nearly zero. In most cases this is acceptable, and using a rectifier as a dc source eliminates the weight, cost, and hazards involved with large storage batteries.
Single-Phase and Multi-Phase Systems. A single-phase ac circuit requires two wires, just like a dc circuit. One wire is the live wire, and the other is the neutral, so called because it is usually grounded (Fig. 15.3a).
A voltage commonly used in the United States is 240 V, single-phase, two-wire, which is obtained from the two terminals of the secondary coil of transformers fed from utility high-voltage lines. If a third wire is connected to the midpoint of the
secondary coil as a neutral, the voltage between either of the two terminal wires and the neutral will be 120 V (Fig. 15.3b). This voltage, 120/240 V, single-phase, three-wire, is the voltage used for most residential electrical services.
The currents in the two terminal wires are 180 apart in phase. The neutral current from each is also 180 apart. These two currents, traveling in the same neutral wire, offset each other because of the phase difference. If the load currents in the two terminal wires are equal, the currents in the neutral will become zero.
Though there is a phase difference between the two live wires, this is still considered as a single-phase system, designated as single-phase, three-wire.
An outdated voltage system that may be encountered in renovation work is the two-phase system in which the live wires are 90 apart in phase. There are actually two types of two-phase systems, two-phase three-wire and two-phase five-wire.
In a similar way, three-phase electric service can be obtained directly from the utility company with three live wires and a grounded neutral (Fig. 15.3c). The currents in the three live wires, as well as their respective return flows in the neutral, are 120 apart in phase. If the currents are equal in the three live wires, the current in the neutral will be zero.
If the phase currents are not equal, the current in the neutral will be the phasor sum of the phase currents (Fig. 15.3d).
In many two-phase or three-phase systems, it is necessary therefore to balance the single-phase loads on each wire as much as possible. When the current in the neutral is zero, there is no voltage drop in the return circuit. Any voltage drop in the neutral subtracts from the voltage on the single-phase wires and affects the loads on these circuits. The voltage drop times the current flowing in the neutral times the cosine of the phase angle is the power consumed in the neutral wire, and this adds to the total metered power on the utility bill.
