Insane Hydraulics
Bold and audacious blog about fluid power
I have a little bit of theory for you today. Solenoid-valve-related, because this is an industrial hydraulics blog, after all. If you have an engineering background, you already know everything I am about to say, but if you are, like me, a self-taught, hands-on hydraulic tech, you may actually learn a couple of "good-to-knows." This post stems from a question I was asked just the other day, which led to a discussion that brought up some very interesting points. The only things you need to know to follow along are: the difference between Direct Current (DC - the electric charge flows in one, constant direction) and Alternating Current (AC - the electric charge periodically reverses its direction, flowing back and forth), what a diode is, and, of course, understand the good old Ohm's law:
V = I x R
If the formula above is something new to you - brush up on your basics before going further down this blog - it won't make much sense otherwise. I will keep the math to the barest minimum, and I will use the typical European industrial voltage values for my examples, but the theory is, obviously, valid for the American standard as well.
Let me first show you the thing that brought this up:
What you see here is a solenoid-operated directional control valve, and here's the question I was asked:
"...The coil says 230V RAC, which stands for Rectified Alternating Current. So far, so good. We do see that the coil has a DIN plug with a built-in full-wave rectifier, and if we follow the wiring, we will see that the solenoid switch draws its power from a single phase and the neutral, which, given our location, indeed, amounts to 230V. But then... why does it also say 207VDC? What's with the 207? Shouldn't rectified 230VAC be 230VDC? Isn't this whole rectifying with diodes thing just redirecting the flow of the electric charges in a single direction, just like we do with them check valves?..."
This is a very good question, and to give it a more or less complete answer, I'd like to start right at the source - namely - the power source, which, in our case, is the European industrial power grid specified at 400/230V @ 50Hz. Why do people use three-phase sine-wave AC anyway? In short, because the alternating sine wave is the natural "electrical power format" generated by a rotating mechanical device (a.k.a. generator), and because the three-phase AC is, by far, the most most efficient and convenient way to transmit and distribute the generated power to consumers. I made this drawing representing the typical voltage wave forms for a standard European three-phase supply:
But hold on for just a minute... there's surely a mistake here! Our grid, like you just said, is spec'd as 400V/230V. Why the hell do you have the 325V and the 563V here? 563V is like half a kilovolt, dude! Are you insane?
No, my friends, this is not insanity - this is nothing but pure convention. Let me explain. The values in the graph above are correct, because they stand for the amplitude - i.e., the maximum voltage at the crest of the waveform. If we wanted, we could totally define an AC source by its amplitude. For example, in this case, referring to a single phase, we could absolutely say "it's a sine-wave AC with an amplitude of 325V" if we chose to (by the way, I am hoping the graph clearly shows why the line-lo-line voltage in a three-phase supply is higher than a single phase to neutral). However, the amplitude figure would not be very convenient for performing power calculations for a given resistive load (for example, a 23-ohm heater). With a constant-voltage DC, calculating power is super simple - the power (in Watts) is Amps times Volts, and so if we have a given R and a given V, the power is P = V²/R. Now, tell me, how would you perform a power calculation for this heater given a sine-wave AC with an amplitude of 325V?
Let's think about it. The power dissipated by our resistance heater would, naturally, follow the sine wave of the supply voltage, but it would make no sense for us to say something along the lines of "the power at the crest of the sine-wave is ... kW." This figure has no real meaning, because what we're really interested in is the average power generated by our heater. So, to calculate it, we could plot out a bunch of voltages along the sine wave, calculate instant powers using the P = V²/R equation, and then average them out. That would be totally correct! And, in the end, we would come to a realization that since we used squared voltage values for our power calculations, if we calculated the mean of all of the squared voltages from our plot points, we could use the square root of this figure as the "magic" voltage that gives us "instant access" to super-convenient power calculations! This voltage is called RMS voltage (Root-Mean-Square, for, as you just saw, the root of the mean of the squares) and this is how most alternating voltages (and currents) are conventionally expressed. It is also often referred to as the "effective" voltage, and for a sine waveform, the RMS voltage is the amplitude divided by √2 (≈1.414). Hence, a sine wave with an amplitude of 325V becomes 230V RMS, and, of course, 563V becomes 400V RMS (rounded 398V, actually. The customary 400V figure is nothing but an agreed target equipment manufacturers and power suppliers should aim for). Knowing the RMS voltage of our AC supply makes calculating the dissipated power of the 23-ohm heater a breeze - P = V²/R => 230 x 230 / 23 = 230 x 10 = 2.3 kW.
I must say that the "RMS trick" works for all waveforms (I am definitely getting carried away here, but I really want to make the RMS voltage notion super clear). For example, if you have, say, a pulsed DC source with an amplitude of 10V and a 50% duty cycle:
The RMS value of this waveform would be 7.07V. So, for a 1-ohm resistor, the dissipated power would be P = 7.07²/1 = 50W. See why an RMS voltage representation of an alternating source is much more useful than the amplitude?
Anyway, back to our solenoid valves. We know now that our single-phase AC voltage source has an amplitude of 325V and an RMS of 230V. When we pass it though a full-wave rectifier, we will get a pulsating DC made out of "flipped" sine wave bumps, like so (for simplicity, let us forget about the 1.5V voltage drop of the two diodes):
As far as the RMS value goes, it should be the same as before, right? We just flipped the negative portion of the wave, but we didn't change its shape, which means the RMS value should be exactly the same. But then... why do we read 207 VDC when we measure the voltage at the outlet of our rectifier? Where did 23 V go? (By the way, taking this reading with one hand while trying to take a picture with the other was not easy at all):
Now, a coil is an inductor, so, maybe it has something to do with this? Let's check. Here, I recreated the same circuit at home - and now I have just the rectifier plug (four BY 228 diodes and a V250K7 varistor) with no coil connected to it. You can see that my mains read 236V (it's actually even more - about 238V - I live not far from the transformer), and the outlet from the rectifier - only 215V. Where did the 20-odd volts go?
And this, my friends, is another convention you should be aware of. When we measure AC voltage with our digital multimeters, they're generally calibrated to output an RMS value. But when we measure DC voltages, most multimeters are designed to show a value averaged over a given (usually sub-second) period of time. If you think about it, this is exactly what analog voltmeters do. Firstly, they deflect a coil in a magnetic field in direct proportion to the current that flows through it (which, in turn, is directly proportional to the voltage it's connected to). Secondly, they employ damping of the needle movement (usually eddy-current based) that integrates current fluctuations into an average position of the needle. Pretty cool, if you think about it.
Now, if you're smart enough to do the math, you will see that for a full-wave rectified sine wave, the average DC voltage is equal to its peak value times 2/π, and, if you want to use the ever-convenient Vrms - it is almost exactly 0.9 times Vrms (very easy to remember!). So, in the case of 230V RMS AC the average DC voltage downstream of a full-wave rectifier is 230 x 0.9 = 207V. This is why many manufacturers put this figure in their catalogs and on their solenoid coils.
So, let me translate this from "OEM-speak" to normal:
When manufacturers put a "RAC" voltage on a coil, what they really mean is:
"... Connect this coil to an AC source with this RMS voltage via a full-bridge rectifier, and it will work perfectly fine. No filtering is required!..."
When they put a DC value next to the RAC, it basically means:
"... If you, however, wanted to use a filtered DC source for this coil, you should somehow come up with this voltage. (Although, to be honest, nobody here understands why you would ever want to do that, nor where you would find a source with such a weird value)..."
Phew... This post turned out to be much longer than I expected, and I haven't even started to cover the real AC coils - something you don't see much of these days, but definitely should know about. I'll leave this for next week.
P.S.:
If you really need to know, my Brymen is a true-RMS multimeter, and it can actually calculate the total effective RMS of a pulsed DC source when measuring it in AC+DC mode:
