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Three-Phase Electric Power

Figure 8 The homemade generator up and running, connected to a DSO-X 3024A Keysight scope for test, through three safety-insulated differential probes. Note: Here, scope does not show 3-phase power. The probe for the blue signal was accidently inverted.
Written by Robert Lacoste

Build Your Own Source

Three-phase power is ubiquitous, and it’s an important electrical engineering concept to understand. Here, Robert explains three-phase power distribution, why it’s so common and how to use it. He also guides us through building a small, experimental three-phase power source on your own.

  • How three-phase power distribution works

  • How to build a small, experimental three-phase power source

  • Single-phase vs. three-phase power

  • Wye and Delta configurations

  • How to use direct digital synthesis (DDS) technology

  • What the the safety precautions to take?

  • Analog Devices (ADI) AD9959 DDS IC

  • ADI AD9959-based generator card

  • STMicroelectronics STM32 MCU controller card

  • GPX1000.4 automotive amplifier from Crunch

Welcome to “The Darker Side.” Since the first electric networks were developed in the late 1880s, three-phase electric power has been the most common electricity delivery method worldwide. I guess that the majority of Circuit Cellar readers are more used to 5V or 3.3V DC voltages, but three-phase is the norm for electric networks, even if your house is supplied with a single phase.

For the first time in years, my company was recently tasked to design a product directly connected to a three-phase source. For proprietary reasons, I can’t explain what this design was about, but it gave me the idea for this article. This month, I will explain what a three-phase distribution actually is, how they are so common and how to use them. Moreover, I will also show you how to build a small, experimental three-phase power source for $300 or so. As usual, I will not use any difficult math. So, take a seat and stay cool!

SINGLE PHASE

In the early days of electric networks, the use of direct (continuous) current (DC) or alternating current (AC) was a technical, commercial, public-safety and patent conflict for years, known as the “War of the Currents.” In particular, Thomas Edison was a supporter of DC, whereas George Westinghouse was leading the AC camp. To make a long story short, the AC guys won, but I encourage you to read the Wikipedia article on that interesting piece of history [1].

As you know, an AC current is transmitted over a pair of wires. The voltage between the two wires is alternatively positive and negative, and more exactly follows a sine function of time. The power transmission is differential, so only the voltage difference between these two lines is important. Nevertheless, usually one of the two lines, called the “neutral,” has a voltage that stays close to ground voltage, while the other line, the “phase,” oscillates around this reference. To make our lives more interesting, the frequency and amplitude of this voltage is country dependent, as every traveler knows. For example, if, like me, you live in France, then the AC voltage as a function of time is:

Phase(t) = 325 × sin(2π × 50 × t)

Therefore, the instantaneous voltage in our plugs varies from -325V to +325V with a frequency of 50Hz. The equivalent RMS (root mean square) voltage is 325V divided by the square root of 2 (√2 ), which gives 230VRMS. That means that our AC sources provide, on average, the same power as a 230V DC source.

THREE PHASES?

I will explain in a minute why, but single-phase electric sources nearly always come from a three-phase electric distribution network. What is a three-phase power supply system? As the name implies, there is no longer one but three phase conductors, each carrying an alternating current of the same frequency and voltage as that measured from a given neutral reference. However, there is a phase difference of 120 degrees between each of them, which is exactly one-third of a cycle (360 degrees/3=120 degrees, or 2π/3 when expressed in radians). As in the case of single-phase distribution, the neutral reference is usually connected to ground somewhere. 

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Figure 1 (top) shows the line voltages of a three-phase distribution system in the example of France. Each phase has a ±325V peak-to-peak voltage and 50Hz frequency, just like single phase, but has a phase shift of 120 degrees with respect to the two others. So, in a nutshell:

Phase1(t) = 325 × sin(2π × 50 × t + 0)

Phase2(t) = 325 × sin(2π × 50 × t + 2π/3)

Phase3(t) = 325 × sin(2π × 50 × t + 2π/3)

Figure 1 Top: A three-phase source is three sine voltages with 120-degree phase shifts. Bottom The voltage, when measured between any pairs of phases, is 1.73 times higher than between a phase and the neutral
Figure 1 Top: A three-phase source is three sine voltages with 120-degree phase shifts. Bottom The voltage, when measured between any pairs of phases, is 1.73 times higher than between a phase and the neutral

In that example, the voltage between each phase and the neutral is still ±325VP-P (peak-to-peak), or 230VRMS. But what is the voltage measured between any two of the three phases? It is still a sine with the same frequency, here 50Hz, but with a voltage multiplied by √3, which is 1.73. Therefore, the instantaneous voltage between two phases in France is ±562VP-P, or 400VRMS. Why this factor of √3? There are three ways to understand it. The first is to simply look at the graph in Figure 1. Measure the difference between two phases on the top graph for the same time step or look at the graph in Figure 1 (bottom), which shows the voltage between any two pairs of phases. You will see that the peak voltage is 1.73 times higher than when measured between one phase and the neutral.

The second way is to draw a so-called “vector diagram,” as illustrated in Figure 2. The length of each vector corresponds to the amplitude of the sinusoid, whereas their angular position corresponds to their respective phases. The amplitudes could be either peak to peak or RMS values. Here the three vectors in green show the respective voltage and phase for each of the three phases. The voltage difference between two phases is represented by the orange vectors, and they are without doubt longer. Do the trigonometry or measure it on the diagram, and you will find that the ratio is √3 .

Figure 2 This vector diagram enables us to understand where the 1.73 ratio comes from. On the right, the most common three-phase voltages are listed.
Figure 2
This vector diagram enables us to understand where the 1.73 ratio comes from. On the right, the most common three-phase voltages are listed.

The last way is to use the equations for Phase1 and Phase2 given above. Subtract them and remember the small formula for the difference of two sine functions. (I will not offend you by reminding you). You will find out that the difference is:

2 × sin(π/3), which is √3

WYE AND DELTA

As explained, each phase of a three-phase distribution provides an AC power source with the neutral as a return line. This neutral line is usually provided through a fourth line, and allows the use of three-phases as three independent, single-phase networks: Just use one of the phases and the neutral as a return path, and you have a single-phase equivalent. This is, in fact, how single-phase distribution is provided to our homes.

Such a setup, where loads are connected between one of the phases and the neutral, is called a “wye configuration” (Y), or star configuration. Here, the neutral wire is mandatory and is usually grounded at the delivery station. This neutral must, of course, not be confused with the safety ground connection, which is always independent and used solely for fault protection. It doesn’t carry any current in normal use.

When using a wye configuration, the loads connected on each phase are arranged so that, as far as possible, equal power is drawn from each phase. In such a perfectly balanced configuration, and when the loads are purely resistive, the math shows that the sum of the currents of the three phases is zero. This means that the current going through the neutral wire is also zero! In fact, the return current of the loads connected to, for example, Phase1, precisely counterbalances the return current of the loads connected to the two other phases, which are, respectively, 120 degrees and 240 degrees out of phase. I will not go through the demonstration here, but if you are interested there is a nice article on that topic on Wikipedia [2].

So, for a wye configuration, the neutral line theoretically may be omitted if the loads were exactly balanced. In real life they aren’t, and the neutral line is absolutely mandatory. If you cut the neutral line on an unbalanced wye configuration, then the voltage at the center connection is no longer fixed, and voltages applied to the loads on the three phases are no longer the same: Some get a voltage considerably lower than nominal, whereas others get an overvoltage.

LOOSE SCREW

We experienced such a situation some years ago in the building where my company is located. It was caused by a loose screw on one of the main building power distribution bars. The consequence was fortunately limited to a lot of smoke from several appliances, a fire in a laser printer and about $10,000 of damage.

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Now let’s see the other way to use a three-phase network, called “delta configuration” (Δ). As you may have guessed, here the loads are connected between each pair of phases, and get a higher voltage as explained. Therefore, a delta configuration requires only three wires for transmission, since no neutral is involved. Once again, this doesn’t include the safety ground connection, which is always independent but doesn’t carry any current, except when a fault occurs. Delta configuration is less common that wye for domestic installations but is largely used in industrial sites—for example, for powering motors or high-power transformers. Delta configuration is also used for long-distance power transmission, just because it precludes the need of a fourth conductor.

Finally, you have to know that there are plenty of ways to transform a wye connection into a delta or vice versa, or to isolate two wye or two delta networks. You just need to use the proper kind of transformer. For example, a transformer with a four-wire wye secondary and a three-wire delta primary is used to connect unbalanced loads, while maintaining a fully balanced current on the distribution lines.

PROS AND CONS?

Let’s spend a minute on the advantages of a three-phase distribution compared to a single phase. Why do all electricity suppliers use three-phase, which requires more wires? Simply because a three-phase circuit is more economical. It uses less conductor material to transmit the same amount of power. More precisely, for the same total conductors’ weight, a three-phase system allows the transmission of no less than twice the energy! You don’t believe me? Let’s do some very simple math. Imagine that you have a single-phase, 230VRMS network, with a current limited to 100A due to the maximum current rating of the two wires. That gives an available power of 230 × 100 = 23kW.

Now, move to a three-phase network. If you use a delta configuration for the long lines, you will need three wires rather than two, so your wire budget will be multiplied by 1.5 for the same 100A rating. However, you will now get up to 23kW from each phase, or 69kW total. That’s 3 times more power, for 1.5 times more wire cost, so the net gain is a ratio of 3/1.5 = 2, not a small gain.

On the downside, there are some disadvantages of three-phase compared to single phase for electric installation: They include higher complexity, more costly transformers and slightly more safety risks, because the voltages are higher between pairs of phases. However, for the electronic designer or experimenter, there is another disadvantage: Playing safely with three-phase networks is not so easy. In particular, there isn’t anything like a low-cost, three-phase, configurable lab generator around.

Faced with this difficulty for our specific project, my company decided to assemble a small homemade three-phase generator. The goal was not to get any significant power out of it, but just to get three AC sources with 120-degree phase shifts, and an easy way to change the voltage from 0 to 250VRMS, and the frequency from 50Hz to 60Hz. Just keep reading if you want to know how.

DDS AROUND?

The first building block for such a generator must be a three-output sine wave generator, with a way to define as precisely as possible the phase shift between outputs. Regular readers may remember a column I wrote a long time ago on direct digital synthesis (DDS) technology (“Direct Digital Synthesis 101,” Circuit Cellar 217, August 2008) [3]. To make a long story short, a DDS is a fully digital solution to generate a sine wave with a fine control on all parameters of the generated waveform (Figure 3).

Figure 3 A direct digital synthesis (DDS) circuit is a full-digital way to generate sine wave forms.
Figure 3
A direct digital synthesis (DDS) circuit is a full-digital way to generate sine wave forms.

The circuit is based on a phase register, which is incremented by a given amount at each clock cycle. The resulting phase is then used as an address to a sine wave look-up table, and then routed to a digital-to-analog converter and filtered. The nice thing is that a precise phase control is then possible by simply adding a constant value to the phase register.

To implement an actual DDS, you may design your own either in hardware or firmware, but the easiest solution is to buy a DDS chip from the market leader, Analog Devices. In particular, this manufacturer offers a chip that seems exactly designed for what we need, the AD9959 [4]. Look at its architecture (Figure 4). This piece of silicon integrates four independent DDS generators, with independent frequency, phase and amplitude controls. Using three of them with the same frequency but phase offsets of 120 degrees is a nice starting point for a three-phase generator. These DDS ICs may generate frequencies up to 200MHz, but nothing prevents us from configuring them for 50Hz.

Figure 4 The internal structure of the AD9959 from Analog Devices, a quad DDS generator that’s ideal for this project
Figure 4
The internal structure of the AD9959 from Analog Devices, a quad DDS generator that’s ideal for this project
AN EXPERIMENTAL GENERATOR

Because we were, as usual, in a hurry, we took the path of least resistance, searched eBay for a ready-made board based on this AD9959 chip, and found a setup proposed by several China-based dealers (Figure 5). For a little more than $100, we got an AD9959-based generator card, a STMicroelectronics STM32 MCU controller card with ready-to-run firmware and even a tactile TFT display to configure it.

We then needed to amplify the outputs of the AD9959 from hundreds of millivolts to more than 325V peak-to-peak. How? Once again, we took the lazy route (Figure 6). Since the frequency of 50Hz or 60Hz is in the lower audio frequencies, we bought and connected a quad channel audio amplifier—a GPX1000.4 automotive amplifier from German supplier Crunch, specified for 4 × 70WRMS [5]. This amplifier provides a huge power gain, but the output voltage is still quite low, because it is designed for 4Ω or 8Ω speakers.

We wired three small 230V-to-12V transformers backward, to increase the voltage by a factor of about 20, and this provided the required output voltage range. Last, we added an off-the-shelf 230V-to-12V AC/DC power supply to power the audio amplifier from the main line, and a small 12V-to-±5V DC/DC isolated converter for the AD9959 and controller board. And that’s it! The total cost of all the parts was around $300, enclosure excluded.

For safety and comfort, one of my colleagues integrated the full device into a 3U rack (thanks Antoine!) and added voltmeters on the output. We even assembled the fourth channel, which could be used as a separate, single-phase source. You can see the final internals of the assembly in Figure 7, keeping in mind that this was just a quickly assembled tool for bench tests, not intended to be a finished product.

Figure 5 $118 for a quad DDS generator board, a TFT tactile display and a controller board. Reasonable, isn’t it?
Figure 5
$118 for a quad DDS generator board, a TFT tactile display and a controller board. Reasonable, isn’t it?
Figure 6 The overall architecture of our three-phase test generator
Figure 6
The overall architecture of our three-phase test generator
Figure 8 The homemade generator up and running, connected to a DSO-X 3024A Keysight scope for test, through three safety-insulated differential probes. Note: Here, scope does not show 3-phase power. The probe for the blue signal was accidently inverted.
Figure 7
The internals of the assembled generator. The DDS board and controller are right behind the front panel on the top left. The audio amplifier is on the bottom, and the four 230V/12V transformers are clearly visible. The unit on the right is the AC/DC power supply. Small extra boards were added for our specific tests needs.
WRAPPING UP AND CAUTION

Here we are. I know that the subject of three-phase power may seem a little awkward for electronics designers, but you might, as we did, have to dig into the subject someday. Moreover, I hope that the way we built our small test generator will give you some ideas for your own projects.

At this point, and even if I am sure that Circuit Cellar readers already know this, I must emphasize that working on such projects can be deadly—even if the high voltages are generated by a 12V-powered audio amplifier that seems harmless. Do not try to reproduce these experiments if you are not qualified and trained on high voltages. And in any case, always follows the three basic safety rules:

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1) Never work alone when voltages higher than 24V could be present, so at a minimum, someone can call for help if something goes wrong.
2) Always completely disconnect the power line cord and wait for capacitor discharge before opening the device, even, and especially, if you are in a hurry.
3) If you need to do any measurement, use safety-class insulated probes, always keep one hand in your pocket and think twice.

As an example, Figure 8 shows our test generator connected to an oscilloscope. The three small boxes between the scope and the generator are 2kV safety-class insulated differential probes, one of the only ways to connect a non-safety-insulated test instrument like an oscilloscope to a high-voltage source.

Experimenting is fun, but don’t take any risks and don’t play, if you don’t know the rules. 

Figure 8 The homemade generator up and running, connected to a DSO-X 3024A Keysight scope for test, through three safety-insulated differential probes. Note: Here, scope does not show 3-phase power. The probe for the blue signal was accidently inverted.
Figure 8
The homemade generator up and running, connected to a DSO-X 3024A Keysight scope for test, through three safety-insulated differential probes. Note: Here, scope does not show 3-phase power. The probe for the blue signal was accidently inverted.

RESOURCES

References:
[1] https://en.wikipedia.org/wiki/War_of_the_currents
[2] https://en.wikipedia.org/wiki/Mathematics_of_three-phase_electric_power
[3] “Direct Digital Synthesis 101,” Circuit Cellar 217, August 2008
[4] AD9959
https://www.analog.com/en/products/ad9959.html#product-overview
[5] GPX1000.4 power amplifier
https://www.crunchaudio.de/english/gpx1000.4-amplifier.html

https://en.wikipedia.org/wiki/Three-phase_electric_power

https://www.ecmag.com/section/your-business/wye-does-it-matter

https://www.electronicshub.org/comparison-star-delta-connections

http://www.chauvin-arnoux.com/sites/default/files/documents/d00vai84_representations_of_a_three-phase_signal_gb.pdf

Analog Devices | www.analog.com
Crunch | www.crunchaudio.de
Keysight Technologies | www.keysight.com
STMicroelectronics | www.st.com

PUBLISHED IN CIRCUIT CELLAR MAGAZINE • AUGUST 2021 #373 – Get a PDF of the issue

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Founder at Alciom | + posts

Robert Lacoste, France (Founder, Alciom; Columnist, Circuit Cellar)

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Three-Phase Electric Power

by Robert Lacoste time to read: 12 min