Electric power measurement

voltage divisioncurrent division

VL

VL RR

RII

VRR

RV

AL

LL

Instantaneous power: depending on time

Active power: The time average of the intantaneous power. It gives the real amount of dissipated energy

Apparent power

Reactive power, its average over T equals to 0

cos(fi) called power factor

)cos( rmsrms VIP

rmsrmsA IVP

)sin( rmsrms VIQ

The above has presented the power definitions applied to ac circuits with the restrictions of sinusoidal quantities. In the most general case of distorted quantities, obviously symbolic representation can no longer be applied. In any case, active power is always defined as the mean power dissipated in one period.

As far as methods and instruments for ac power measurements are concerned, some circuit classification is required. In fact, the problems are different, arising in circuits as the frequency of power supply increases. Therefore, in the following, ac circuits will be classified into

(1) line-frequency circuits,(2) lowand medium-frequency circuits (up to a few megahertz), (3) and (3) high-frequency circuits (up to a fewgigahertz). Line-frequency circuits: related specifically to the three-phase power supply

Three voltmeter method

Because of the load, a delta e voltage imbalance arises proportional with the active power of the load

Wattmeters Based on Multipliers

The multiplication and averaging processes (Figure 3.8) involved in power measurements can be undertaken by electronic means.

Electronic wattmeters fall into two categories: analog (continous) or discrete

In continuous methods, multiplications are mainly carried out by means of analog electronic multipliers.

In discrete methods, sampling wattmeters take simultaneous samples of voltage and current waveforms, digitize these values, and provide

multiplication and averaging using digital techniques.

Errors:1. resistances of the voltage and current circuits have to be taken into account 2. phase errors of both current and voltage circuits increase the relative uncertainty of power measurement,3. sinusoidal conditions.

The main analog multipliers are based on a transistor-based popular circuit such as

Four-quadrant multiplier [3], which processes voltage and current to give the instantaneous

power, and an integrator to provide the mean power (Figure 3.9)

Time Division Multipliers (TDMs)

Hall effect-based multipliers.

Discrete utilities

Approx. periodic time synchronous sampling

Line applications

High frequency methods