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Measurement and technology
II.
Electric power measurement
current division
voltage division
Instantaneous power:
depending on time
Active power: The time
average of the intantaneous
power. It gives amount of
dissipated energy
Effective values!
Apparent power
Reactive power
P/P_A called
power factor,
cos(fi)
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 few
gigahertz).
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
Result: sum of
P1,P2,P3
High frequency methods
Pulse power measurement