Comparison - classic cos-phi measurement

Measurement of the power factor as cos phi

• The power factor is a pure ratio calculated from the quotient P/S
• The measured variable "cos phi" traditionally used instead of the power factor (P/S) is essentially the result of the measurement technology used to date: the separate measurement of active power and apparent power with subsequent division P/S (= power factor) required to determine the power factor was not previously carried out with conventional cos phi converters due to the great measurement effort involved
• In these conventional converters, the measurement of the phase shift of current and voltage (angle phi, distance between the zero crossings of current and voltage), which is much easier to implement in terms of equipment technology, is used as a substitute. The corresponding measuring transducers generally 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 realized on the scales of the downstream devices by a corresponding non-linear scale division (scale curve proportional to the cosine curve, Fig. 1)
  

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Figure 1

• non-linear scale
• linear scale

The main advantage of this method so far is the simple and inexpensive realization of the device.

The disadvantages lie in two points:

• On the one hand, the downstream connection of indicators or evaluation devices that only allow a linear relationship between input and display cause difficulties (e.g. digital indicators: the desired cosine characteristic curve cannot be entered for most device types, which leads to misinterpretations)
• Secondly (and this is the most important aspect), the measurement result is only correct for undistorted curves. For distorted signals, the measurement provides incorrect results (distortions result in additional zero crossings, which means that the distance between the zero crossings of current and voltage is no longer determined solely by the phase shift)

However, if the boundary conditions of this measurement (e.g. pure sinusoidal shape of the measured variables) are clearly recognized and observed, the method can still be used today, even if such ideal conditions are practically no longer present in the networks, so that the replacement of the classic "cos-phi" measurement (described above) is required.

Measurement of power factor PF and power factor LF

• The microprocessor technology used in the multi-measurement transducers (M1004, M563, DME4...) enables the transition from angle difference measurement to genuine power factor measurement. In order to make the departure from the traditional "cos-phi" measurement clear, the terms power factor (PF) and power factor (LF) have been introduced in the new measurement method to differentiate between them
• In comparison to angle difference measurement, both measured variables offer a linear relationship between the measured variable and the analog output signal of the transducer (Fig. 2). In addition, harmonics up to the 16th harmonic are taken into account due to the type of measurement
• The power factor PF is used to determine the physically and mathematically exact cos phi as a quotient of active and apparent power. Its sign is determined by the sign of the active power (positive for power consumption, negative for power output; the apparent power itself has no sign).

The power factor PF therefore provides information about output and consumption

PF = Pw/Ss

• However, the most common requirement in practice is to identify the type of load (inductive or capacitive). The measured variable LF (for power factor) takes this into account
• In contrast to PF, the power factor LF does not provide the direction of energy flow in the sign, but the load type. So that the statement clearly depends only on the type of load (and not on the direction of energy flow), 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 inductive loads and negative for capacitive loads)

The LF is then calculated as follows.

LF = sgn Qn * lPwl / Ps
(inductive: Q+ at reference, Q- at output) (capacitive: Q- at supply, Q+ at discharge)

It should be noted that the measured variable LF can only be used for one energy flow direction due to the magnitude of the active power:

• If a four-quadrant power factor measurement is required, the PF should be used and the information on the load type should be obtained from a limit value monitoring of the reactive power (set limit value to e.g. 0 mA)
• A calibration according to the above formula for the LF would result in a jump in the output signal (Fig. 3). To counteract this, the LF is calculated for the device calibration as described below:
  

LF = sgn Qn * (1 - |Pw| / Ps)

• From a desired measuring range of e.g. cap. 0.5 … 1 … ind. 0.5 (i.e. -0.5...1...+0.5) corresponding to e.g. -20...0...+20 mA becomes -0.5...0...+0.5 for the internal design. This means that the characteristic curve passes through the zero point and can therefore be mapped without a jump point (kink) (Fig. 4)

Figure 3 Figure 4