Measuring the power factor as cos phi
The power factor is a pure ratio, which is calculated from the quotient P / S.
The measured variable "cos phi" traditionally used instead of the power factor (P / S) essentially results from the previously used measuring technology: The separate measurement of active power and apparent power required for the determination of the power factor with subsequent division P / S (= Power factor) was previously not performed because of the large metrological effort with conventional cos-phi converters.
In these conventional converters, the apparatus-based measurement of the phase shift of current and voltage (angle phi, distance between the zero crossings of current and voltage) is used as a substitute, much easier to implement. The corresponding transducers typically provide an output signal that is linearly proportional to the angle phi (not the cos phi) (e.g., -20 mA ... 0 ... 20 mA).
The desired cosine function is implemented on the scales of the downstream units by a corresponding unlinear scale division (scale progression proportional to the cosine curve, Fig. 1).
1) non-linear scale 2) linear scale
The main advantage of this method has so far been the simple and inexpensive implementation of the device.
The disadvantages are due to two reasons:
- On the one hand, the subsequent connection of indicators or evaluation devices presents difficulties that allow only a linear relationship between input and display (example digital display: here the desired cosine characteristic is not matched in most types of equipment, resulting in misinterpretations).
- On the other hand (and this is the essential aspect), the measurement result is correct only for undistorted bends. For distorted signals the measurement will give wrong results (distortions will give extra zero crossings, so the distance between the zero crossings of current and voltage is no longer just determined by the phase shift).
However, if the boundary conditions of this measurement (e.g. pure sinusoidal shape of the measured quantities) are clearly recognized and considered, the method can still be used today even if ideal conditions in the nets are practically no longer present, so that the replacement of the classical ( described above) "cos-phi" measurement.
The microprocessor technology used in the multi-measurement converters (M1004, M563, DME4 ...) enables the transition from angle differential measurement to true power factor measurement. In order to make clear the departure from the traditional "cos-phi" measurement, the new measurement technique introduced the terms power factor (PF) and power factor (LF).
In comparison to the angle difference measurement, both measured values provide a linear relationship between the measured variable and the analogue output signal of the transmitter (Fig. 2).. In addition, due to the type of measurement, the harmonics up to the 16th harmonic are taken into account.
The power factor PF is used to determine the physically and mathematically exact cos phi as the quotient of active power and apparent power. For him, the sign is determined by the sign of the active power (positive for power reference, negative for power output, the apparent power itself is unsigned).
The power factor PF thus provides information about delivery and reference.
PF = P w / S
However, the most common requirement in practice is to identify the type of load (inductive or capacitive). This is taken into account by the measured variable LF (for power factor).
Unlike the PF, the power factor LF does not provide the direction of the energy flow but the load type. So that the statement clearly depends only on the load type (and not on the energy flow direction), only the amount of active power (P) is included in the calculation rule. The sign itself is obtained from the measurement of the fundamental wave phase reactive power (by definition, the sign is positive for reference for inductive load and negative for capacitive load).
The LF is then calculated as follows.
| LF = sgn Qn * | P w | / P s |
(inductive: Q + at reference, Q- at output) Please note that due to the absolute value of the active power, the measured variable LF can only be used for one energy flow direction. In the event that a four-quadrant power factor measurement is desired, the PF should be used, and the indication of the load type should be obtained from a reactive power limit monitor (set limit to, for example, 0 mA). A calibration according to the above formula for the LF would give a jump in the output signal (Fig. 3). To counter this, the LF is calculated as follows for device calibration: LF = sgn Qn * (1 - | P w | / P s) From a desired measuring range of e.g. cape. 0.5 ... 1 ... ind. 0.5 (i.e. -0.5 ... 1 ... + 0.5) in accordance with e.g. -20 ... 0 ... + 20 mA will be for the internal design -0.5 ... 0 ... + 0.5. Thus, the characteristic passes through the zero point, so it can be reproduced without a discontinuity (kink) (Fig. 4).
Fig. 3 Fig. 4 |
