In an ac system, the voltage across a resistor and the current flowing thought it are said to be in phase, that is, their zero value and their maximum values occur at the same times. There are two types of fields associated with an ac electric system; electric fields and magnetic fields. Electric fields relate to the voltage and magnetic fields relate to the current.12 The waveforms of the voltage and current associated with both of these characteristics are not in phase, that is, the times of the maximum and zero values are not identical.
Induction and Inductive Reactance
When we discussed the operation of a generator, we noted that an electric voltage is induced in a wire when a moving magnetic field “cuts” that wire. Similarly, a current varying with time (an alternating current) will produce a magnetic field around the wire carrying the current. Since the current is
varying so will the magnetic field. This varying magnetic field “cuts” the conductor and a voltage is induced in the wire which acts to impede the originating current.
The relationship between the current and the induced voltage is defined by a quantity called the inductance. One Henry is the amount of inductance required to induce one volt when the current is changing at the rate of one ampere per second. The letter L is used to represent the inductance in Henries.
The inductance, L, of one phase of a transmission or distribution line is calculated by considering the self-inductance of the individual phase conductor and the mutual inductance between that phase and all other nearby phases both of the same circuit/feeder and other nearby circuits/feeders.These quantities
are calculated based on the physical dimensions of the wires and the distances between them. The induced voltage across an inductor will be a maximum when the rate of change of current is greatest.
Because of the sinusoidal shape of the current, this occurs when the actual current is zero. Thus the induced voltage reaches its maximum value a quarter-cycle before the current does—the voltage across an inductor is said to lead the current by 90 degrees, or conversely, the current lags the voltage by 90 degrees.
The inductive reactance, XL is a term defined to enable us to calculate the magnitude of the voltage drop across an inductor.The inductive reactance is measured in Ohms and it is equal to 2*p* f* L, where 2pf is the rotational speed in radians per second; p is called pi and its value is 3.1416, f = frequency in hertz and L = inductance in Henries. Inductances consume reactive power or VARs equal to I2XL.
Capacitance and Capacitive Reactance
An electric field around the conductor results from a potential difference between the conductor and ground. There is also a potential difference between each conductor in a three phase circuit and with any other nearby transmission lines. The relationship between the charge and the potential difference
is defined by a quantity called the capacitance. One Farad is the amount of capacitance present when one coulomb produces a potential difference of one volt. The letter F is used to represent the capacitance in Farads.
The capacitance C, depends on the dimensions of the conductor and the spacing between the adjacent lines and ground. Since the charge on a capacitor varies directly with the voltage, when an alternating voltage is impressed across a capacitor, the flow of charge (or current) will be greatest when the rate of change of voltage is at a maximum.
This occurs when the voltage wave crosses the zero point. Thus in an alternating current system, the current across a capacitor reaches its maximum value a quarter-cycle before the voltage does—the voltage is said to lag the current by 90 degrees, or conversely, the current leads the voltage by 90 degrees.
The capacitive reactance, XC, is a term defined equal to 1/2*p * f*C, where C = capacitance in Farads. The unit of the capacitive reactance is Ohms. In a power system the capacitive reactance is viewed as a shunt connecting the conductor to ground. Capacitors supply reactive power or VARs equal to I2Xc.
Both inductive reactance and capacitive reactance have an impact on the relationship between voltage and current in electric circuits. Although they are both measured in Ohms, they cannot be added to the resistance of the circuit since their impacts are quite different from that of resistance.
In fact, their impacts differ one from the other. The current through an inductor leads the voltage by 90 degrees, while current through a capacitor lags the voltage by 90 degrees. Because of this difference, their effects will cancel one another.
The convention is to consider the effect associated with the inductive reactance a positive value and that with the capacitive reactance a negative value and VARs as consumed by inductive reactance and supplied by capacitive reactance. A general term, reactance, is defined which represents the net effect of the capacitive reactance and inductive reactance. It is denoted by the capital letter X.
Once determined, the reactance is combined with the resistance of a circuit to form a new quantity called Impedance which is denoted by the capital letter Z.To determine a single number representation of the impedance, the concept known as complex numbers is employed. Simply speaking, resistance and reactance are treated as both legs of a right triangle separated by 90 degrees. A common way of representing the impedance term is:
where the letter j, is used as a convention to indicate that the reactance is not to be directly added to the resistance. The magnitude of the impedance is determined by Pythagoras’ Theorem, that is, the square of the impedance is equal to the sum of the squares of the resistance and the reactance.