CHAPTER 1 ACTIVE POWER

1.1       POWER

The purpose of most electrical systems is to generate real electrical power and to convey it to those consumer installations which will use it.

True ‘power’ may be used to provide a mechanical drive, or to provide heating and lighting, or to energise control and communication systems such as instrumentation or radio and telephone installations.  All of these things consume energy, and that energy is absorbed at a stated rate: the rate of consuming energy is defined as the true power consumption of that system.  In electrical installations it is measured in the unit ‘watt’ (W).  For practical power purposes this unit is generally found to be too small, and more often used is the kilowatt (kW), one thousand watts, or even the megawatt (MW), one million watts.

Electric power is most usually obtained from an electric generator, but this in turn receives its power from the engine which drives it (termed the ‘prime mover’).  It may be of many types: a steam or gas engine, a diesel, a steam or gas-turbine, a water-wheel or even a windmill, though in some installations only gas-turbines or diesel engines are used.  With the exception of water- and wind-driven sets, the energy delivered by these engines to the generator is derived from the fuel which they burn - that is to say, the energy source is ultimately a chemical one.

What has been said so far refers to energy and to the rate at which it is delivered (the power).  When an electric generator is delivering this energy it is at the same time usually delivering also another type of ‘false energy’ which too is required by certain consumer equipment.  To distinguish between them the true power, which represents real energy, is called ‘active power’ (sometimes also called ‘wattful power’).  The other kind, which is the rate of delivering ‘false energy’, is termed ‘reactive power’ (sometimes also called ‘wattless power ‘or ‘blind power’).

Reactive power is dealt with separately in Chapter 2.

1.2       ELECTRICAL POWER

Voltage is a pressure, and current is a flow.  In mechanical engineering, power - the rate of doing work - is the product of pressure and volume flow; in electrical circuits, power is the product of voltage and current - that is, power = V x I.  If V is measured in volts and I in amperes, their product is the power in watts (W).

In d.c. this presents no problem.  Both V and I are steady quantities and their product is a direct measure of the power in watts. Indicating instruments - wattmeters - are made which do this multiplication internally.

With a.c. rather more care must be taken.  The same rule applies: namely that the watts at any instant are the product of the volts and the amperes at that instant, but these quantities are constantly changing as the voltage and current alternate. It is therefore necessary to look at this product instant by instant to see whether it has any average value.

FIGURE 1.1

A.C. POWER - PURE RESISTIVE LOAD

Consider an a.c. voltage feeding a purely resistive load.  If the top wave of Figure 1.1 represents the alternating voltage, the second wave represents the current, which, as has been shown for a resistive circuit, is in phase with the voltage.  Thus both voltage and current have their positive parts together, and also their negative parts together.

The power at any instant is the product of the voltage and current at that instant. Clearly at times t₀, t₄ and t₈ both waves are at zero, so their product is also zero.  At any time, say t₁, in the first half-cycle voltage and current are both positive, so their product is also positive and is greatest at time t₂, where both are at their maximum.

At any time, say t₅, in the second half-cycle voltage and current are both negative, so their product is again positive and is greatest at time t₆, where both are at their negative peaks.

The power wave is therefore the third in Figure 1.1.  It is of double frequency (i.e., two peaks for every one voltage peak) and is wholly above the line (positive).  It represents pulses of power, always positive, and the average value of that power is midway between the power peaks and valleys.

So from (i) above the mean power (symbol ‘P’) is given by:

P          = ½ x √ 2V x √ 2I

= ½ x 2VI

   = VI (watts)

That is to say, in the purely resistive case the mean power is the true or active power (P) and is measured in watts.  It is the product of the rms voltage and rms current (in amperes), exactly similar to the d.c. case.

The dynamometer wattmeter, described in the manual ‘Fundamentals of Electricity 1’ and also in Chapter 9 of this manual, does this multiplication automatically for a.c. as well as d.c., and it will indicate the average watts being transmitted.