Negative excitation for a Synchronous Condenser

I had posted a question recently about the possibility of an out of step protection on a synchronous condenser actually being forced to operate, and like many good discussions, it morphed into something completely different - namely whether it was possible to apply negative excitation to a synchronous condenser to extend its operating range.

I'm going to ruin the suspense by saying "Yes, it has been done and I have seen it operate", but the purpose of this article is to say HOW it manages to work. Note that I don't consider myself to be a synchronous machine expert, so I may leave out important things like machine saturation, X'''''''''d, vector diagrams, etc... This will be a dead simple, "lumber crayon on the back of an envelope" introduction to the math and I won't claim for the results to have much accuracy past the first significant digit, but it will be close enough to get the point across.

Before I get into my dissertation, here are a couple of snapshots from the most recent WECC testing of the machine in question, just to show that I'm not making this up.

Now that we have that out of the way...

Synchronous machines in utilities are of two main types - salient pole machines and round rotor machines. The word Salient comes from the Latin salire, which means to leap. Merriam Webster says that "Salire?also occurs in the etymologies of some other English words, including?somersault?and?sally, as well as?Salientia, the name for an order of amphibians that includes frogs, toads, and other notable jumpers. Today,?salient?is usually used to describe things that are physically prominent (such as a salient nose) or that stand out figuratively (such as the salient features of a painting or the salient points in an argument)." When talking about synchronous machines, a salient pole machine is one whose pole faces "stick out". Here is a drawing (borrowed from here) showing a salient pole rotor vs a cylindrical rotor.

The important thing about a salient pole rotor is that the act of making the rotor non-uniform means that the rotor itself acts as a reluctance motor. If you can get the rotor up to synchronous speed, the pole faces will align themselves with the rotating flux from the stator because that is the configuration which has the least reluctance (similar to how solenoids and control relays work). This is important, because with normal generators, we are very concerned about pole slipping occurring during a loss of excitation event, because we normally consider the synchronizing torque due to the field current as being the major factor contributing to the synchronous machine remaining synchronous. This is true, but in a synchronous condenser, we have to remember that there is no prime mover, and so the only power going in or out of the machine is solely due to windage and friction losses, and changes in power system frequency (more correctly, I mean changes in the rate of change of the power system angle, as that includes not only an actual change in frequency as well as deviations from the normal 377 radians/second rate of angle change (314 in various places I don't live). Since the power transfer requirements are much lower (less than a couple percent), we can reduce excitation substantially without fear of slipping poles. The synchronous condensers I was most familiar with were fully capable of operating with zero field current (once you managed to get them synchronized in the first place). How does this work?

I grabbed the image below from here, which seems to get the math across in a fairly concise manner.

Looking at the equations, we can see two terms in the power equation, once which indirectly contains rotor current (via the internal voltage of the machine), and another due simply to asymmetry in the rotor. The (Xd - Xq) portion of the equation signifies the difference in rotor reluctance between the d and q axes, and it is this difference which results in a synchronizing torque even if there is no field current.

Once we know this, we can play a bit. If we have sufficient reluctance torque to maintain synchronism, we can entertain the idea of actually reversing the polarity of the rotor magnetic field by applying field current in the other (or wrong) direction. If the torque from this term is less than that of the reluctance torque, the machine will remain synchronized and not slip a pole, however, the internal voltage of the machine will change polarity as well, allowing the machine to absorb even more VARs from the system.

In the absence of real power transfer across a synchronous machine, the machine internal voltage (the three phase voltage which would be produced by the field current if we ran the machine open circuit) aligns with the stator voltage provided by the system, and the MVAR output of the machine is simply determined by the voltage across the synchronous impedance of the machine, or MVAR = (V_internal - V_terminal)^2/Xd. If the internal voltage equals the terminal voltage, the machine neither absorbs or produces VARs. If the internal voltage is lower than the terminal voltage (underexcited) , then the machine absorbs VARs and looks like a shunt reactor to the system. Likewise if the machine internal voltage is higher than the terminal voltage, the machine produces VARs and appears like a shunt capacitor to the system. The Xd of the machine and the field current limit jointly determine the MVAR range of the synchronous condenser (disregarding saturation effects). At zero field current, the machine looks like a shunt reactor of value Xd, and at 2 pu field current, the machine should look like a shunt capacitor of value Xd. For the synchronous condensers I have seen, this range is asymmetrical, with the boosting capacity of the SC exceeding the bucking capacity. One of these machines was rated at +50/-35 MVAR, but during a rebuild, a second bridge was added to the exciter to allow negative excitation. There were also some software interlocks required inside the exciter to prevent both bridges from conducting simultaneously, as that would produce a virtual short circuit across the exciter transformer secondary, so the transition from positive to negative excitation involves a short time at zero current. The big question is "How much negative excitation can we apply before we completely cancel out the rotor saliency?". In order to see just how far we could go, I took the equations above and the machine parameters and did some math. The machine parameters are listed below:

• Sbase = 50 MVA
• Zbase = 3 ohms
• Xd = 1.31 pu = 3.93 ohms
• Xq = 0.72 pu = 2.16 ohms
• Qmax = 56.6 MVAR (nameplate is +50)
• Qmin = -48.2 MVAR (old nameplate was -35, new nameplate is -50)
• Pmax = -0.63 MW (maximum windage and frictional losses)
• poles = 6
• air gap field current @ 1 pu voltage = 600 A

First, let's see what kind of rating this machine might have had as an actual generator if it were attached to a prime mover. If we assume a maximum steady state rotor angle of 30° and a machine internal voltage of 1 pu, then the power output, ignoring the saliency (the second half of the equation above) is P = 3*(12.6 * 12.6)*sin(30)/3.93 = 61 MW. This is close enough to the 50 MVAR nameplate rating to make sense.

Now, let's see how much power we could get out of the machine depending only on the rotor saliency. Since the saliency torque changes at twice the rate of the excitation torque, we will assume a 15° rotor angle to use the same proportion of available torque as in the example above. Using only the saliency term above, we get P = 3*(12.6^2 * (3.93 - 2.16))*sin (2*15)/(2*3.93*2.16) = 25 MW. This is pretty surprising. Even with no field current, we retain nearly half of the synchronizing torque of the machine. Given that the machine losses are under 1 MW, there is plenty of room to apply negative excitation without losing the ability of the machine to remain synchronized to the system. Here is the power vs angle chart for this set of machine parameters, assuming 1 pu internal voltage.

And here is the chart using the same parameters, but dropping the internal voltage to zero (no field current). Note that while the max synchronizing torque (which is proportional to power) is around 33% of what it was with excitation, it is still positive and certainly much larger than the steady state losses. If somebody wanted to do the math, they could take the machine inertia H and calculate the maximum dF/dt which would result in loss of synchronism. A 45° jump in the system voltage phasor might also do the trick.

Finally, here is the chart using the same machine parameters, but applying 0.25 pu negative excitation. Note that the polarity of the electromagnetic torque has reversed, but the total torque has not changed sign. Our maximum torque has dropped in half from the previous example, so that it is even easier to lose synchronism in the absolute sense, however, it would still take a frequency ramp or a phase angle jump of nearly 40° to cause the machine to slip a pole.

Finally, we show a simplistic estimate of machine VARs vs pu field current. This chart does not take saturation into account, so the right hand side of it is most certainly wrong, but it gets the point across. The portion of the plotline in blue is the extension of the bucking capability of the machine through the use of negative excitation. Note that not very much negative excitation is needed to make the capability of the synchronous condenser fully symmetrical.