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Power is the rate of doing work. It is equivalent to an amount of energy consumed per unit of time. The power of an electrical system is the multiplication of the voltage with the current, integrated over and then divided through the periodic time. We have to know the periodic time (equals frequency) to calculate the power of an electrical system.
In physics power is the rate of doing work. It is equivalent to an amount of energy consumed per unit of time. The unit of power is Joule per second [J/s], also known as Watt [W]. The integral of power over time defines the energy (performed work).
The power of an electrical system is calculated by multiplying the voltage with the current.
But is it really that simple? What about measuring a 7-phase system or measuring frequency inverters?
Power calculation can be very easy for example when measuring DC systems, but it can also be challenging when measuring inverters with a number of phases.
In this course, you will learn how to measure the electrical power of different systems (DC, AC, multiphase) and for different applications (grid, motor, inverter). The course starts with a theoretical part which includes theoretical background to the power calculations, the calculation of easy power parameters and explanations of how to configure the power module and how to visualize the power values in the measurement screen. The practical part will show you, step-by-step, how to measure DC power and single-phase power, 2-phase power, 3-phase power in star, delta, aron and V connection, what’s to consider when measuring inverters and an example how to calculate the power of a 6-phase motor.
Electrical power is the rate at which electric energy is transferred by an electric circuit. The SI unit of power is watt [W].
The following formula describes the calculation of the electric power for AC or DC systems.
So the power is not just voltage multiplied with current, it’s the integration over the periodic time of this term, divided through the periodic time. We see, that we have to know the period of time (frequency) to calculate the power of an electrical system.
Measuring the DC power is not difficult as the voltage and current are constant and there is no frequency. The time interval for the integration just defines the averaging interval of the power calculation.
For measuring AC systems you have to know the periodic time. It’s not done by taking the default grid frequency (e.g. 50 Hz) for granted because the grid frequency is never exactly 50 Hz, but varies depending on the balance of the energy-supply and electric load in every moment. At variable drives where the frequency continuously changes within a wide frequency range (1 Hz up to 2000 Hz), it’s even more difficult to calculate the power.
Therefore, the period time has to be determined. This is especially difficult when measuring inverters where the voltage is not a sinusoidal waveform anymore but packets of pulses.
This is one point where the concept of the Dewesoft power analysis is totally different to the conventional power analysers. Conventional power analyser uses a zero-point detection to determine the periodic time. This means they are looking when the voltage or current crosses the x-axis and then calculate the periodic time. This often works fine, but especially at strongly distorted signals this also can lead to errors.
However, Dewesoft has created a special FFT algorithm (software PLL) to determine the periodic time (frequency). The algorithm determines the period time of the signal via a special FFT algorithm at a sampling window of multiple periods (typically 10 periods … definable in power module). The calculated frequency is highly accurate (mHz) and works for every application (motor, inverter, grid, …).
A cheap wattmeter calculates the power of an AC system out of the peak values for the voltage and the current, according to this formula:
In order to get the power they simply multiplicate the RMS values of the voltage and current. This way of measuring the power works well when the waveform for both current and voltage is an ideal sinusoid (as it is produced at the generators in the power plants). Nowadays the waveform of both voltage and current are never ideal due to non-linear loads and also non-linear generation units. So this way to calculate the power is outdated, especially when measuring inverters you will get completely wrong results.
Conventional power analyser calculate the RMS values of the voltage and current out of each sample point. The RMS values are calculated out of the square root of all squared sample points of the curve divided by the number of samples.
While other power analysers calculate the power in the time domain, in Dewesoft it is calculated in the frequency domain. With the before determined period time, an FFT analysis for voltage and current is done for a definable number of periods (typically 10 with electrical applications) and a definable sampling rate. Out of this FFT analysis, we get an amplitude for the voltage, current and cos phi for each harmonic. One major benefit of this FFT transformation is that we can now correct the behaviour of amplifiers, current or voltage transducers in amplitude and phase for the whole frequency range (using the Sensor XML). This way of power analysis has the highest possible accuracy. Another benefit is that harmonic analysis and other power quality analysis can be done completely synchronized to the fundamental frequency.
With the FFT corrected values, the RMS voltages and currents are calculated out of the RMS values of each harmonic.
The power values for each harmonic and the total values are calculated with the following formulas:
Active power is measured in Watt (W) and refers to the energy transfer from an electric generator to a load. The active power is the power which can be used by electric loads (useful power).
The reactive power is measured in Volt-Ampere-reactive (VAr). The reactive power doesn’t consist of energy but is necessary for most types of magnetic equipment (motors, transformers) to work. Reactive power is provided by generators, synchronous condensers or electrostatic equipment such as capacitors and directly influences the electric system voltage and also the capacity of the power transmission line.
Apparent power is measured in Volt-Amperes (VA) and is the voltage on an AC system multiplied by the total current that flows in it. It is the vector sum of the active and the reactive power.
The ratio between active power and apparent power in a circuit is called the power factor. For two systems transmitting the same amount of active power, the system with the lower power factor will have higher circulating currents due to energy that returns to the source from the energy storage in the load. These higher currents produce higher losses and reduce the overall transmission efficiency. A lower power factor circuit will have a higher apparent power and higher losses for the same amount of active power.
The cos phi is the angle difference between a phase voltage relative to the current.
The difference between cos phi and the power factor is that the cos phi is calculated for each individual harmonic starting at the fundamental frequency compared to the power factor which includes the whole spectrum (all harmonics).
The power triangle illustrates the relation between active, reactive and apparent power.
In the diagram, P is the active power, Q is the reactive power (in this case positive), S is the complex power and the length of S is the apparent power. Reactive power does not do any work, so it is represented as the imaginary axis of the vector diagram. Active power does do work, so it is the real axis.
For easier understanding, the difference is shown with beer. Reactive power is like the foam on top of a glass of beer, where the liquid in the glass represents active power. The foam takes space in the glass and, therefore, reduces the beer containing capacity. By comparison, the reactive power reduces the electricity transport capacity of a power transmission line. Only the active (real) power can be used.
For easier understanding how the power of each harmonic component is calculated, take a look at the following visualization for the calculation of the several harmonic active power values. This is the same for apparent and reactive power considering the right formula.
Nowadays the typical power triangle doesn’t fit any more because other parameters like the distortion or harmonic reactive power have to be considered due to more and more non-linear loads (inverter, electronic ballast unit, etc...) and also generation units (the wind, PV, etc...). The new power triangle, therefore, has one dimension more:
The sum of the harmonic reactive power. This reactive power occurs through the phase shift between voltages and currents of the same frequency.
The combination of voltages and currents of different frequencies which produce the distortion power.
Distortion power considering everything except the first harmonic.
These are the power quality (PQ) parameters. All other PQ parameters which are calculated in Dewesoft (Harmonics, THD, Rapid voltage changes, Symmetrical components …) you will find in the POWER QUALITY PRO training.
The following table shows the calculation of the power values for different connections.
The power module is one of the most complex mathematic modules in Dewesoft X. It allows measurements of different frequency power grids in different configurations and even variable frequency sources. This section will demonstrate how to use it.
After the configuration of the voltage (see voltage pro training) and current inputs (see current pro training) we can add a new power module with the '+' button in the channel setup by clicking “Power grid analysis".
Then you see the "Power" icon available.
The following screenshot gives you an overview of the power module.
In the power module, there are several system configurations available. The most common are 1-phase and 3-phase star or delta. 2-phase is used with special motors or also in some parts of the grid. The Aron and V configuration are basically star or delta configuration but measuring only 2 currents instead of 3 (see 3-phase measurement). Special configurations like 6-, 7-, 9- or 12 phase motor measurement can be done with multiple single phase systems and adding up the power values in the Math library.
At the next step, the line frequency has to be set. With standard grid measurements, the frequency of 50 Hz (e.g. Europe) or 60 Hz (e.g. USA) has to be set. There are also other line frequencies available (16,7 Hz, 400 Hz, 800 Hz) for special applications. For inverter measurements “variable frequency” has to be selected. The “variable frequency” setting searches automatically for the fundamental frequency in the signal via an FFT algorithm (highest peak). This algorithm calculates the frequency with high accuracy (mHz) but is also very CPU intensive (CPU power). For optimal performance, it’s recommended to set a range (start and the end frequency) where the fundamental frequency can be via the “Exact frequency settings”. For example if you're measuring an inverter driven motor and you know that the fundamental frequency is never higher than 200 Hz, it’s recommended to set the end frequency to 250 Hz for example.
When measuring high power, it could be useful to change the output unit to a higher unit. Available are Watt, Kilowatt and Megawatt.
A special functionality in the power module is the selection of the frequency source. As a source, the voltage, the current or an external signal can be selected. As you can see in the next picture of an inverter measurement, the voltage (green) isn't a sinusoidal waveform any more. It’s a packet of pulses. If you select the voltage as the frequency source the frequency determination can be faulty. The waveform of the current is a lot more sinusoidal and should be selected as a frequency source to get correct results. The oscilloscope functionality in Dewesoft is very helpful for analysing the signal.
In this option, the number of cycles for the power calculation can be set. As standard, this value is 10 periods for 50 Hz measurements and 12 periods for 60 Hz applications (required in 61000-4-30). The lower level for the number of periods is 5. For all applications, if you need faster values the “period values” functionality can be used.
The entry of the nominal voltage is important if you want to calculate the Flicker. Also for other measurements the voltage should be set to at least an approximate voltage. If this value is set very high (e.g. measuring inverter with 20 V output and the nominal voltage is selected to 400V) the frequency determination can fail.
The calculation rate in the power module is like a sample rate divider for the power calculations. At high sampling rate (>100 kHz) this is often necessary due to performance problems (CPU power at the limit). So just select the calculation rate you need for your measurement. If you store all data in the full sampling rate (always fast) you also can calculate the power in the full calculation rate via the post-processing functionality.
Typical calculation rate:
After doing the configurations, you see in the channel list which parameters are calculated by Dewesoft:
The power module calculates a lot of parameters. Most of the time there are a lot of parameters calculated which are not necessary for a certain application. In this case, you can deselect in the channel list all the channels you do not want to store. So you can reduce your data file sizes.
The vector scope functionality in the power module gives a fast overview if all voltage and current channels are connected correctly to the measurement device.
In the bottom right of the vector scope, you see how the voltages and currents should look like. If you connected a voltage or a current incorrectly you don’t have to change the hardware connection, you just can correct this in the wiring schematics. Additionally to the correct position of the phase you also see if you have connected the current transducers in the right direction. If there is one connected wrong you again can simple edit this in the software the analog setup via the scaling by adding a minus.
In Dewesoft X you can create multiple power modules. So you can measure the power at multiple points completely synchronous. Via the math library you can further process the data of the power modules and for example automatically calculate the efficiency (see efficiency calculation).
These features will be described in the Power quality course on PRO training.
Period values are needed for detailed analysis of electrical equipment (e.g. analysing behaviour at faults or switching processes) and for fault recording (as a trigger argument). The period values are calculated for voltages, currents, active, reactive, apparent power, power factor and other parameters.
The period values can be calculated with a definable overlap (up to 99%) and for a definable number of periods (up to 4). Using an overlap of 99% at a 50 Hz measurement you can calculate the power values for every 0,2 ms. That’s a unique feature of Dewesoft.
Overlap: 25%, 50%, 75%, 90%, 95%, 99%
Periods: 1/2, 1, 2, 4
The period values are not corrected in amplitude and phase as it is done for the other power calculations in the power module.
Considering also the period values for the symmetrical components (see more details in Power Quality Pro training) there are more than 50 parameters available.
After setting up the configurations in the power module, you can switch to the measure mode and define your measurement screen(s). As you already know, the different visualizations can be inserted by switching to design mode. The possible visualizations are located at the top of the window. On the right side you find the channel list and on the left side the properties to the individual visualizations.
The most interesting visualizations for power analysis are:
In the channel list you now find all the parameters which are automatically calculated out of the power module. They are categorized to easily find the desired values:
The Vector Scope and Harmonic FFT visualization are now described in more detail because they are specially implemented for the power calculation.
The name „Vector scope“ comes from the fact that not only absolute values of the voltage and current are important but also the phase relations between them. Why is the phase information so important? This is essential because only the part of the current that is in phase with the voltage can be used for producing the work. Therefore we measure the phase angle between the voltage and current as angle phi (e.g. 12,8 deg), and from that also the cos phi (which is just a cosine of that angle, but it is very nice because it is directly the ratio of work against the total consumed current). In the vector scope the voltage vector (hollow arrow) and the current vector (full arrow) for each harmonic can be shown.
A special feature in Dewesoft X is to change the vector scope orientation. So you can choose whether the vector scope should visualize clockwise or counter clockwise. For some special applications you can also change the orientation of the vector scope to the right side. You can change this in the „Settings“ – „Extension“ – „Power grid analysis“. By default the scope is shown for the first harmonic. Via the input field „shown harmonic“ in the visualization properties each individual harmonic can be selected. Furthermore, the scaling for voltage and current can be defined there manually or automatically. The option “Show measured values” adds digital values of basic power parameters for each phase on the right and left a side of the vector scope. The option “Tick count” defines the number of circles to be shown.
In the power module the harmonics can be calculated for apparent, active and reactive power for each individual harmonic. But do we need to calculate the harmonics?
In theory, voltage and current have a perfect 50 (or 60) Hz sine wave. This is the case if there are just linear loads connected to the grid (e.g. light bulbs). But as there are more and more non-linear loads connected (ballast unit, inverter, etc,) and also the generation units are not linear any more (Wind, PV, etc.), the waveform of voltage is not an ideal sinus any more. The following picture shows the voltage and current of a light bulb (left) and an LED (right). You see that at the light bulb the waveform of the current (blue) is sinusoidal but the current of the LED is everything but not sinusoidal.
The Harmonic FFT nicely shows the big difference of those two different loads (current harmonics):
What is the effect of the harmonics? Imagine we have an AC electromotor. The first harmonic (line frequency) is driving the motor. The rest of the harmonics are producing vibrations and noise, but the ironic truth is that there are bad and even worse harmonics. The 2nd, 5th, 8th... harmonics are really bad ones since they are breaking the motor. The 3rd, 6th, 9th... harmonics are either driving or braking, while 4th, 7th, 10th... harmonic are driving the motor, but they are still producing higher noise and vibrations.
The Harmonic FFT shows the harmonics of voltage, current, active and reactive power each fully synchronized to the fundamental frequency.
In the visualization properties, you have additional options:
More details about harmonics and fullFFT will be given in the Power Quality Pro training.
Let's start the practical part with a simple DC power measurement.
For a simple DC measurement please connect the voltage and the current to the Sirius as it is shown in the following picture.
In Dewesoft X you just have to create a math formula and multiply the DC voltage with the DC current to get the DC power.
Note: Never calculate the DC power with a one-phase power module. This won’t work and will produce incorrect results.
If you switch to the Measurement screen you can visualize the voltage, the current and the power. In this example, the battery power of an electric vehicle is shown. As you can see the voltage (purple) is relatively constant while the current is just present if power (acceleration) is required.
For a single-phase AC measurement please connect the voltage and the current to the Sirius as it is shown in the following picture.
Hint: Use your certain current transducer the Sensor XML correction (see current pro training) to get the highest accuracy for your power calculation.
In the power module, the wiring has to be set to single phase and the configurations for the certain application have to be done.
For example measuring a load connected to the public grid the line frequency will be set to 50 Hz (60 Hz in North America, parts of South America, Japan, etc.) , the output unit should be Watts, the frequency source is voltage, number of cycles are 10 and the nominal voltage (line to earth) is 230 Volts.
After switching to the measurement mode, you can design the measurement screen.
2-phase measurements are really seldom, but some motors (e.g. step motor) for example are operated with two phases (one phase has a phase shift of 90°).
For a 2-phase AC measurement please connect the voltage and the current to the Sirius as it is shown in the following picture.
Hint: Use your certain current transducer the Sensor XML correction (see current pro training) to get the highest accuracy for your power calculation.
In the power module, the wiring has to be set to 2-phase and the configurations for the certain application have to be done.
After switching to measurement mode, you can design the measurement screen. In this case, the scope and vector scope of a 2-phase step motor is shown as well as the single-phase voltage and current of the grid.
The star connection is mainly used for measuring 3-phase systems, especially if a neutral line of grid or the start point of a motor is available. The three phase voltages are connected to the Sirius HV modules on the high side. The low side of the three inputs is on the potential of the neutral line or motor star point. If both are not available an artificial star-point can be made by short-circuiting the low sides of the amplifiers.
The following picture shows the connection for a 3-phase star measurement with the usage of zero flux transducers for current measurement. Therefore, you additionally need the Sirius MCTS power supply slice.
Hint: Use your certain current transducer the Sensor XML correction (see current pro training) to get the highest accuracy for your power calculation.
In the power module, the wiring has to be set to 3-phase star and the configurations for a certain application have to be done.
After switching to the measurement mode, you can design the measurement screen. In this case, you see the measurement of a load profile of a household. The left scope shows the waveform of the voltage, the right one the waveform of the current (which is quite distorted) and at the bottom of the screen you see the load profile in a recorder.
The delta connection is used if there is no neutral line or star point at motor measurements available. The three phase voltages are connected again to the high-side of the amplifier. Every low side of the HV amplifier has to be connected to the next high side (low side L1 to high side L2, low side L2 to high side L3), the low side of the last phase L3 to the high side of the first phase L1.
The following picture shows you the connection for a 3-phase delta measurement with the usage of zero flux transducers for current measurement. Therefore, you will additionally need the Sirius MCTS power supply slice.
In the power module, the wiring has to be set to 3-phase delta and the configurations for a certain application have to be done.
After switching to the measurement mode, you can design the measurement screen. In this case, you see the measurement of a PV inverter in the delta configuration. As you can see in the vector scope, the power is fed into the grid and, therefore, the current vectors have a phase shift of 180° compared to if they would take power. The waveform of voltages and currents can be seen in the scope and they have a very nice sinusoidal waveform.
Just for comparison in the next picture you see a one-phase PV inverter with a very bad waveform of voltage and current. The voltage is just a rectangle waveform. Such electrical devices strongly stress the grid. Learn more in Power Quality training.
A special feature in the Dewesoft X power module is the star-delta calculation.
It allows you to calculateall values of a delta connection out of a star connection (waveform, RMS values) and vice versa. Therefore it doesn't matter how you connect the voltages to your system, you can calculate all parameters nonetheless.
To see the analog voltage signal of a delta connection if you have connected in star and vice versa, you have to select the option “Waveforms”.
Formula: Star - Delta calculation
Formula: Delta - Star calculation
If you also select the option „Calculate line voltages“ also the RMS values and Harmonics are available.
This feature is implemented in the power module as standard and completely free of charge (with other power analysers you have to buy for this feature).
With some applications, only two currents are measured instead of three in a three-phase arrangement. The main reason is to save costs. With measurements where you can be completely sure that the load is completely synchronous you can calculate the third current out of the other two measured ones. This is often done with grid measurements (expensive current transducers, symmetrical load).
Hint: This schematic can be used ONLY when there is NO neutral line!
Hint: Never do this with inverter measurements. You will get wrong results.
Power setup - in the power module, the wiring has to be set to 3-phase V and the configurations for the certain application have to be done.
When measuring inverters or after the inverters you have to be especially careful and have considered some things to get correct results with high accuracy.
Always use high-speed (HS-HV and HS-LV) amplifiers for measuring inverters. As the voltage is a modulated (amplitude or phase) with switching frequencies up to several hundred kilohertz it is absolutely necessary to use high-speed amplifiers to get correct results.
As there are a lot of higher frequency components and also DC components after inverters always use current sensors with high bandwidth which are capable of measuring DC and AC currents.
The best way is to use the Dewesoft zero-flux transducers or hall-compensated AC-clamps.
It is important to set the current as frequency source because the voltage out of an inverter hasn't got a sinusoidal waveform any more. The inverter has modulated the signal by pulse width or amplitude, so it’s a packet of pulses. You can see an inverter modulated voltage in the next picture (orange). The current (green) is a lot more sinusoidal and should therefore be used as a frequency source.
You can choose whether you use the delta or the star connection for measuring after inverters. Never use Aron or V connection.
For basic power analysis, the delta connection is very good and recommended if there is no star-point available. The fact that you measure between voltages this connection is not always suitable for detailed inverter analysis (analysis of switching pulses).
If you measure in star connection you should always use a star point adapter. The artificial star-point via the modules doesn't fit due to different impedances. The active power analysis won’t be affected but the analog signal you see is not true and also the apparent power and power factor will be wrong.
If you measure in a star connection with a star-point adapter you gain high accurate power values and also the true analog signal which can be used for detailed inverter analysis.
So the best way measuring an inverter is using a star-point adapter. If not possible then choose the delta configuration
A frequently asked question when measuring an inverter is if there is a difference measuring with or without shielded motor cable.
Yes, there could be a difference. Due to the high switching frequencies of the inverter there can be leakage currents via the shield of the cable.
This leakage current can affect the results in the following way:
Therefore, this capacitive leakage can have low-pass characteristics (phase shift, no higher frequencies) and can affect the measurement results.
All configuration setups which can be chosen in the Dewesoft power module are the most common ones. But especially for E-Mobility applications there are also other configurations for 6-, 7-, 9- or even 12 –phase motors needed. There can be various reasons for this like lowering the voltage level or reducing the stress of the components.
With common power analysers it’s absolutely not possible to do a comprehensive analysis of such motors. But with our modular hardware system in combination with the powerful software of Dewesoft these appliations are no challenge!
For example, you can measure a 6-phase motor by using 6 single-phase power modules and calculating the total power in the power module.
This application should show you how powerful the Dewesoft Power analyser is. If you have a special application and you are not sure to measure just contact: Bernhard Grasel, firstname.lastname@example.org, +43 660 38 155 86
In Dewesoft X the energy can automatically be calculated using the power module. It’s possible to calculate the total energy consumption or you can even split up into positive (energy consumption) and negative energy (energy delivery). This is for example helpful when measuring electric vehicles with recuperation or when measuring the load profile of households / industry which also have a power generation unit (e.g. photovoltaic).
The energy calculation is a simple integration of all power values. To get the positive energy, the positive power values are integrated, for the negative energy the negative power values are integrate.
P is power in Watt [W] and E in energy in Watt hours [Wh].
In the following picture the settings for the Energy calculation in the power module are shown.
In addition to the basic power calculation it is also possible to start/reset the energy calculation at trigger events. Otherwise, the energy will be calculated as soon as you switch into measure mode.
The efficiency of electrical devices can easily be calculated with the Dewesoft X Math library, using the Formula editor. It can be calculated for power or for energy values also during measurement.
Where η is efficiency in [%].
Some customers measure the efficiency of e.g. electric vehicles at multiple points online. A result can be a diagram with the visualisation of the energy flow like this:
This course will end with a last few tips if the computing power of your computer is not sufficient.
If the computing power of your measurement device is not sufficiently to calculate all the required power parameters you have the following options: