True RMS power meter with load monitoring and control function. Why should you choose True RMS devices? What is RMS

Alternating voltages and currents can be characterized by various indicators. For example, for alternating periodic voltage of arbitrary shape u(t), in addition to amplitude values, can be characterized by:

average value(constant component)

average rectified value

effective or effective value

Most often, the effect of alternating voltage or current is judged by the average power over the period that heats up the active resistance R through which alternating current passes (or to which alternating voltage is applied). The heating process is inertial and usually its time is much longer than the period T alternating voltage or current. In this regard, it is customary to use the effective value of sinusoidal voltage and current. In this case:

From here it is clear that to measure the effective value of a sinusoidal voltage or current, it is enough to measure their amplitude value and divide by √2 = 1.414 (or multiply by 0.707).

AC voltmeters and ammeters are often used to measure AC voltage and current levels non-sinusoidal shape. Theoretically, such signals can be represented by a Fourier series, consisting of the sum of the constant component of the signal, its first harmonic and the sum of higher harmonics. For linear circuits, due to the principle of superposition, the power of a non-sinusoidal signal is determined by the power of all its components. It depends on the harmonic composition of the signal, determined by the signal shape.

As a rule, regardless of the measurement method, they are usually calibrated in effective values of sinusoidal alternating voltage or current. Usually in this case, with the help of a full-wave rectifier, voltages or currents are rectified and it is possible to measure their average rectified voltage (often it is simply called average, but this is not entirely accurate - see above). The deviation of the AC voltage shape from the sinusoidal one is usually taken into account by the shape factor:

k f =U d /U avg

For a square wave (meander) kФ =1, and for sinusoidal kФ =π/2√2=1.1107. This difference causes a large difference in readings even in these simple cases.

Nowadays they are widely used personal computers, Cell Phones with pulse mode transmitters, pulse and resonant voltage converters and power supplies, variable speed electric drives and other equipment that consumes currents in the form of short-term pulses or sinusoid segments. In this case, the root mean square value of the signals must take into account all harmonics of its spectrum. In this case they say that it is true rms value (TrueRMS or TRMS).

Unfortunately, when measuring voltages and currents with different time dependencies other than sinusoidal, big problems due to a violation of the relationship between the average rectified or amplitude values of alternating voltage or current and their effective values. Conventional voltage and current meters with averaged readings in this case give an unacceptably large error, see Fig. A simplified measurement of the effective value of currents can sometimes lead to an underestimation of up to 50% of the true results.

Rice. 1. Comparison of different types of measurement of varying voltages and currents

A user who does not know this may wonder for a long time why the fuse in a device with a current of 10 A regularly burns out, although according to the readings of an ammeter or a conventional multimeter, the current is an acceptable value of 10 A. If the curve of the measured voltage or current deviates from the ideal sinusoidal shape, refinement using a factor of 1 ,1107≈1.1 becomes unacceptable. For this reason, meters with averaged readings often give incorrect results when measuring currents in modern power networks. In this regard, instruments have been created that measure the truly true rms value of alternating voltage and current of any form, which is determined by the heating of a linear resistor connected to the measured voltage.

Nowadays, modern multimeters that measure the true rms value of alternating voltage or current (not necessarily sine wave) are usually marked with the True RMS label. Such meters use more advanced measurement circuits, often with microprocessor control and correction. This made it possible to significantly increase the measurement accuracy and reduce the dimensions and weight of the instruments.

Accurate measurements are a difficult task facing technologists and specialists in the maintenance of modern production facilities and equipment of various organizations. Our daily lives increasingly include personal computers, variable speed drives and other equipment that have non-sinusoidal characteristics of current consumption and operating voltage (in the form of short-term pulses, with distortions, etc.). Such equipment may cause inadequate readings from conventional averaging (rms) meters.

Why should you choose True-RMS devices?

When we talk about AC current values, we usually mean the average effective heat generated or the root mean square (RMS) current value. This value is equivalent to direct current, the action of which would cause the same thermal effect as the action of the measured alternating current, and is calculated by the following formula:

The most common way to measure such RMS current is using measuring instrument consists of rectifying alternating current, determining the average value of the rectified signal and multiplying the result by a coefficient 1,1 (the relationship between the mean and root mean square values of an ideal sine wave).

However, if the sinusoidal curve deviates from perfect shape this coefficient ceases to apply. For this reason, averaging meters often give incorrect results when measuring currents in modern power networks.

Linear and non-linear loads

Rice. 1. Voltage curves of sinusoidal and distorted shape.

Linear loads, which consist only of resistors, coils and capacitors, are characterized by a sinusoidal current curve, so there are no problems when measuring their parameters. However, with non-linear loads such as variable frequency drives and office power supplies, distorted curves will occur when there is interference from large loads.

Rice. 2. Current and voltage curves of a personal computer power supply.

Measuring the root mean square value of currents using such distorted curves using conventional meters can give, depending on the nature of the load, a significant underestimation of the true results:

Device class	Load type/curve shape
Device class	PWM (meander)	single-phase diode rectifier	three-phase diode rectifier
RMS	correctly	overstatement by 10%	understatement by 40%	understatement 5%...30%
True RMS	correctly	correctly	correctly	correctly

Therefore, users of conventional appliances will wonder why, for example, a 14-amp fuse regularly blows, although according to the ammeter reading the current is only 10 A.

True RMS meters

To measure current with distorted waveforms, you need to use a waveform analyzer to check the shape of the sine wave, and then use the meter with averaging readings only if the waveform is truly a perfect sine wave. However, it is much more convenient to constantly use a meter with True RMS readings and always be confident in the accuracy of the measurements. Modern multimeters and current clamps of this class use advanced measurement technologies that allow you to determine the true effective values of alternating current, regardless of whether the current curve is a perfect sine wave or distorted. For this purpose, special converters are used, which cause the main difference in cost with budget analogues. The only limitation is that the curve must be within the permissible measurement range of the device used.

Everything that concerns the features of measuring nonlinear load currents is also true for measuring voltages. Voltage curves are also often not perfect sine waves, causing meters that average readings to give incorrect results.

Based on the examples described above, in modern high-tech electrical systems, it is recommended to use True RMS class instruments to measure currents and voltages.

Introduction

Measuring trueRMS of alternating voltage is not an entirely simple task, nor is it what it seems at first glance. First of all, because most often it is necessary to measure not a purely sinusoidal voltage, but something more complex, complicated by the presence of noise harmonics.

Therefore, a simple solution with an average value detector with conversion to rms is tempting. values does not work where the signal shape is very different from sinusoidal or is simply unknown.

Professional voltmeters Wed. sq. values are quite complex devices both in circuit design and algorithms. In most meters, which are auxiliary in nature and serve to monitor functioning, such complexity and accuracy are not required.

It is also required that the meter can be assembled on the simplest 8-bit microcontroller.

General measurement principle

Let there be a certain alternating voltage of the form shown in Fig. 1.

Quasi-sinusoidal voltage has a certain quasiperiod T.

The advantage of measuring RMS voltage is that in general the measurement time does not play a big role, it only affects the frequency bandwidth of the measurement. A longer time gives greater averaging, a shorter time makes it possible to see short-term changes.

Basic definition cf. sq. the values look like this:

where u(t) is the instantaneous voltage value
T - measurement period

Thus, the measurement time can, generally speaking, be anything.

For a real measurement with real equipment to calculate the integrand expression, it is necessary to quantize the signal with a certain frequency, which is obviously at least 10 times higher than the frequency of the quasi-sinusoid. When measuring signals with frequencies within 20 kHz, this does not pose a problem even for 8-bit microcontrollers.

Another thing is that everything standard controllers have unipolar power supply. Therefore, it is not possible to measure the instantaneous alternating voltage at the moment of the negative half-wave.

The work proposes a rather ingenious solution on how to introduce a constant component into the signal. At the same time, in that decision, determining the moment when it is worth starting or ending the process of calculating cf. sq. the meaning seems quite cumbersome.

This paper proposes a method to overcome this drawback, as well as to calculate the integral with greater accuracy, which allows reducing the number of sampling points to a minimum.

Features of the analog part of the meter

In Fig. Figure 2 shows the core of the analog signal pre-processing circuit.

The signal is supplied through capacitor C1 to the shaper amplifier, assembled on the operational amplifier DA1. The AC voltage signal is mixed at the non-inverting input of the amplifier with half the reference voltage used in the ADC. The voltage chosen is 2.048 V, since compact devices often use a supply voltage of +3.6 V or less. In other cases, it is convenient to use 4.048 V, as in.

From the output of the shaper amplifier, through the integrating chain R3-C2, the signal is supplied to the input of the ADC, which serves to measure the DC component of the signal (U0). From the shaper amplifier, the signal U’ is the measured signal shifted by half the reference voltage. Thus, to obtain the variable component, it is enough to calculate the difference U’-U0.
The U0 signal is also used as a reference for the comparator DA2. When U' passes through the value of U0, the comparator generates an edge, which is used to generate an interrupt procedure for collecting measurement readings.

It is important that many modern microcontrollers have both operational amplifiers and comparators built in, not to mention ADCs.

Basic algorithm

In Fig. Figure 3 shows the basic algorithm for the case of measuring an alternating voltage with a fundamental frequency of 50 Hz.

The measurement can be triggered by any external event, even a button pressed manually.

After startup, the DC component in the ADC input signal is first measured, and then the controller waits for a positive drop at the comparator output. As soon as the edge interrupt occurs, the controller samples 20 points with a time step corresponding to 1/20 of the quasi-period.

The algorithm says X ms because the low-end controller has its own latency. To ensure that the measurement occurs at the correct times, this delay must be taken into account. Therefore, the actual delay will be less than 1 ms.

In this example, the delay corresponds to measurements of quasi-sine waves in the range of 50 Hz, but can be any depending on the quasi-period of the measured signal within the speed limits of a particular controller.

When measuring rms. the voltage value of an arbitrary quasi-periodic signal, if it is a priori unknown what kind of signal it is, it is advisable to measure its period using the timer built into the controller and the same comparator output. And based on this measurement, set the delay when sampling.

RMS calculation

After the ADC has created a sample, we have an array of U"[i] values, a total of 21 values, including the value U0. Now, if we apply the Simpson (more precisely, Cotes) formula for numerical integration, as the most accurate for this application, we get the following expression:

where h is the measurement step, and the zero component of the formula is absent, since it is equal to 0 by definition.

As a result of the calculation, we will obtain the value of the integral in its pure form in the format of ADC samples. To convert to real values, the resulting value must be scaled taking into account the value of the reference voltage and divided by the integration time interval.

where Uop is the ADC reference voltage.

If everything is converted to mV, K is approximately equal to just 2. The scale factor refers to differences in square brackets. After recalculation and calculation, S is divided by the measurement interval. Taking into account the multiplier h, we actually obtain division by an integer instead of multiplication by h followed by division by the measurement time interval.

And finally we extract the square root.

And here the most interesting and difficult thing comes. You can, of course, use floating point for calculations, since the C language allows this even for 8-bit controllers, and perform calculations directly using the given formulas. However, the calculation speed will drop significantly. It is also possible to go beyond the microcontroller's very small RAM.

To prevent this from happening, you need, as correctly stated in , to use a fixed point and operate with a maximum of 16-bit words.

The author managed to solve this problem and measure the voltage with an error of Uop/1024, i.e. for the given example with an accuracy of 2 mV with a total measurement range of ±500 mV at a supply voltage of +3.3 V, which is sufficient for many process monitoring tasks.

The software trick is to do all division processes, if possible, before multiplication or exponentiation processes, so that the intermediate result of the operations does not exceed 65535 (or 32768 for signed operations).

Specific software solution is beyond the scope of this article.

Conclusion

This article discusses the features of measuring rms voltage values using 8-bit microcontrollers, shows a variant of the circuit implementation and the main algorithm for obtaining quantization samples of a real quasi-sinusoidal signal.

Root mean square (RMS) value. Current or effective value
True Root Mean Square (RMS)

Root-mean-square (RMS) - root mean square value - English.
True Root-Mean-Square (TRMS)

For anyone periodic function(for example, current or voltage) of the form f = f(t) the root mean square value of the function is defined as:

then the effective value of a periodic non-sinusoidal function is expressed by the formula

Since Fn is the amplitude of the nth harmonic, then Fn / √2 is the effective value of the harmonic. Thus, the resulting expression shows that the effective value of a periodic non-sinusoidal function is equal to the square root of the sum of the squares of the effective values of the harmonics and the square of the constant component.

For example, if a non-sinusoidal current is expressed by the formula:

then the rms value of the current is:

All of the above ratios are used in calculations in testers that measure ISKZ, in UPS current measurement circuits, in network analyzers and in other equipment.

True Root-Mean-Square (TRMS)

Most simple testers cannot accurately measure the RMS value of a non-sinusoidal signal (that is, a signal with large harmonic distortion, such as a square wave). They correctly determine RMS voltage only for sinusoidal signals. If you measure the RMS voltage of a rectangular shape with such a device, the reading will be erroneous. The reason for the error is that when calculating, conventional testers take into account the fundamental harmonic (for a regular network - 50 Hz), but do not take into account the higher harmonics of the signal.

To solve this problem, there are special instruments that accurately measure RMS, taking into account higher harmonics (usually up to 30-50 harmonics). They are marked with the symbol TRMS or ISKZ (true root-mean-square) - true root-mean-square value, True RMS, true RMS.

So, for example, a conventional tester can measure with error the voltage at the output of a UPS with an approximated sinusoid, while the APPA 106 TRUE RMS MULTIMETER tester measures the voltage (RMS) correctly.

Notes

For a sinusoidal signal, the phase voltage in the network (neutral - phase, phase voltage) is equal to:

Urms f = Umax f / (√2)

For a sinusoidal signal, the linear voltage in the network (phase - phase, interlinear voltage) is equal to:

Urms l = Umax l / (√2)

Relationship between phase and line voltage:

USKZ l = USKZ f * √3

Designations:

f – linear (voltage)

l – phase (voltage)

RMS – root mean square value

max – maximum or amplitude value (voltage)

Examples:

Phase voltage 220 V corresponds to linear voltage 380 V

Phase voltage 230 V corresponds to line voltage 400 V

Phase voltage 240 V corresponds to linear voltage 415 V

Phase voltage:

Mains voltage 220 V (RMS), - amplitude voltage value about ±310 V

Mains voltage 230 V (RMS), - amplitude voltage value about ±325 V

Mains voltage 240 V (RMS), - amplitude voltage value about ±340 V

Line voltage:

Mains voltage 380 V (RMS), - amplitude voltage value about ±537 V

Mains voltage 400 V (RMS), - amplitude voltage value about ±565 V

Mains voltage 415 V (RMS), - amplitude voltage value about ±587 V

Below is a common example phase voltages in a 3-phase network:

G.I. Atabekov Fundamentals of Circuit Theory p. 176, 434 pp.

Why should you choose True-RMS devices?

When we talk about AC current values, we usually mean the average effective heat generated or the root mean square (RMS) current value. This value is equivalent to the value of direct current, the action of which would cause the same thermal effect as the action of the measured alternating current, and is calculated using the following formula:

The most common way to measure such RMS current using a meter is to rectify the AC current, take the average of the rectified signal, and multiply the result by a factor of 1.1 (the ratio between the average and the RMS values of an ideal sine wave).

However, if the sinusoidal curve deviates from the ideal shape, this coefficient ceases to apply. For this reason, averaging meters often give incorrect results when measuring currents in modern power networks.

Linear and non-linear loads

Rice. 1. Voltage curves of sinusoidal and distorted shape.

Rice. 2. Current and voltage curves of a personal computer power supply.

Device class	Load type/curve shape
Device class	PWM (meander)	single-phase diode rectifier	three-phase diode rectifier
RMS	correctly	overstatement by 10%	understatement by 40%	understatement 5%...30%
True RMS	correctly	correctly	correctly	correctly

Therefore, users of conventional appliances will wonder why, for example, a 14-amp fuse regularly blows, although according to the ammeter reading the current is only 10 A.