CHAPTER 2 REACTIVE POWER

2.1       INDUCTIVE CASE

In Chapter 1 it was shown that the true power transmitted where the load is purely resistive is given by:

                                                                     P  =  VI watts

where V and I are the rms values of voltage and current.

Consider now the purely inductive case, where there is no resistance, as represented by Figure 2.1.

FIGURE 2.1

A.C. POWER - PURE INDUCTIVE LOAD

It has already been shown in the manual ‘Fundamentals of Electricity 2’, Chapter 9, that, if the top wave represents the alternating voltage, the second wave represents the current, which now lags one-quarter of a cycle, or 90°, behind the voltage.

Using the same method as in Chapter 1, multiply the voltage and current at each instant.  We now have:

At points A, B, C, D and E either the voltage or the current is zero, so that their product at all these points is zero.

FIGURE 2.2

A.C. POWER - PURE CAPACITIVE LOAD

If the product (power) curve is now drawn, it will be as the third wave of Figure 2.1.  It will be, as before, of double frequency but now it is symmetrical about the zero line, and therefore the average power will be zero.  Power is put in at each positive part and taken out again at each negative part, giving a net power transmission of NIL.

2.2       CAPACITIVE CASE

It has been shown above that a current lagging 90° on the voltage, in the purely inductive case, gives rise to a double-frequency power wave which is symmetrical about the axis and therefore has no net or average power.

The purely capacitive case is quite similar except that the current wave leads the voltage by 90°, as shown in Figure 2.2.

Exactly the same treatment as that given in para. 2.1 will produce the power wave at the bottom of Figure 2.2.  Compared with that of Figure 2.1 it will be reversed in sign, but it will still be symmetrical about the axis and therefore will have no net or average power.

2.3       THE ‘VAR’ UNIT

The conclusions of both paras. 2.1 and 2.2 - namely that no net power is passed in either a purely inductive or purely capacitive circuit - lead to a certain re-thinking of the power rules if we are used only to d.c.  If the d.c. voltmeter reading is multiplied by the d.c. ammeter reading, the result is the d.c. power in watts.  In the a.c. case however this is only true if the load is purely resistive (as in Chapter 1), which it seldom is.

In the reactive cases (inductive or capacitive) the voltmeter and ammeter readings can still be multiplied together, but they do not now represent true power in watts.  Yet the product is a perfectly good figure.  What then is it?  It represents a ‘false power’ (the Germans call it ‘blind power’) and it is measured in a unit called the ‘var’ (short for volt-ampere-reactive).  It is called ‘reactive power’, or sometimes ‘wattless power’ with symbol ‘Q’, and is a measure of the energy stored (but not consumed) in a magnetised system.  Since a platform or shore installation consists of a vast number of transformers, motors, etc. which all need to be magnetised, the demand for vars is considerable, as will be shown by the varmeter (also a dynamometer instrument) now installed on most switchboards.

It is convenient for system operators to consider the true, or useful, or ‘active’ power (P) in watts quite separately from the ‘reactive’ or wattless power (Q) in vars, though in practice both are present together, travel down the same cables and are produced by the same generator.  Separate wattmeters and varmeters are usually installed at switchboards