* ROTARY GAP ANALYSIS (…continued)*

The previous section about internally ballasted supplies showed a method to choose the best tank capacitor size for a given NST in order to obtain maximum power throughput. It also highlighted the compromises which have to be accepted due to the fixed leakage inductance of the shunted transformer. Most notably, poor power throughput at high rotary speeds, and less than ideal power factor.

In theory the same design approach could be applied to a system which uses a power transformer and external ballast. The ballast could be fixed, so as to make the power transformer appear like an NST supply. Then the optimum tank capacitor could be found in order to maximise the power throughput. This approach is perfectly valid, but it does not remove the disadvantages described above, and there is so much to be gained by making the ballast inductance adjustable.

The next section goes on to describe how these disadvantages can be overcome when using a power transformer with an adjustable ballast.

* Externally ballasted supplies,*

In the case of a power transformer with an external inductive ballast, both the tank capacitor *Cp* and the ballast inductance *Lb* can be varied as desired. This represents a very flexible system indeed, since it allows the resonant charging frequency *Fr* and the effective impedance *Zr* to be influenced independently of each other. This means that the performance of an externally ballasted system can be optimised much better for any chosen rotary speed.

In the previous section on NST systems, the design target was to choose *Cp* to **maximise the real power throughput** from a given NST, since this is what gives maximum spark length. We could afford to make the power factor of less concern, because any reactive current flow would be quite small in an NST based system, and could easily be corrected by a small amount of PFC capacitance.

In a larger system based around a power transformer the situation is different, and a high power factor becomes much more important. This is because a poor power factor implies much higher reactive currents in a high power system than in a small NST based system. As a result, poor power factor in large a 20kW system is more troublesome and harder to correct. It would require a large quantity of PFC capacitors to reduce the supply current. (Even with PFC capacitors fitted, the reactive current still flows in the power transformer and ballast inductor windings causing unnecessary heating ! ) Heating is primarily a function of current squared, so even a little excess current produces significantly more heating. For these reasons the system should be designed with high power factor in mind from the outset.

In the case of a power transformer with external ballast, the designer now has the ability to juggle the values of *Cp* and *Lb* to get both high power factor and good power throughput at the same time. I propose the design approach explained below:

Choosing Lb and Cp for a given rotary firing rate,

The design objective should be to first choose the resonant frequency *Fr* of the charging system in order to obtain a good power factor at the chosen rotary firing rate. Then *Lb* and *Cp* can be manipulated together to change *Zr* and get the desired power throughput for the system.

The graph below was created using the results from a large number of Microsim simulations. It shows how power factor varies with changes in the resonant charging frequency *Fr* for a variety of different rotary firing rates. (At this stage we are not concerned with actual values of *Lb* or *Cp*, or even with actual power throughput. We are only concerned with the choice of the resonant charging frequency *Fr* that maximises the power factor.)

Each coloured line represents operation at a different rotary firing rate (BPS). Notice how low rotary firing rates require the resonant charging circuit to have a low resonant frequency. (This implies large values for Lb and Cp.) In contrast, high rotary firing rates require that the charging circuit has a high natural resonant frequency. (This implies small values for Lb and Cp.) This is to be expected since higher rotary break rates require the charging circuit to be more "responsive", in order to charge the tank capacitor in the shorter time between electrode presentations. |

The graph above shows that it is possible to design the resonant charging circuit of a TC to have a power factor above 0.9 for any chosen rotary firing rate, when an external adjustable ballast inductor is employed.

(In practice I have found that it is not possible to achieve a PF better than 0.93 because of the non-sinusoidal load current that the TC charging circuit draws. Significant harmonic distortion in the supply current sets an upper limit to the power factor even when there is no displacement between the voltage and current waveforms. However, for most practical purposes a PF of 0.9 is perfectly acceptable.)

At first it would appear that we should design our charging circuit to obtain the best power factor possible. i.e. Design the charging circuit to be resonant at whatever frequency gives a peak for the chosen break rate in the graph above. This is perfectly reasonable and does indeed result in excellent power factor. However, it tends to lead to fairly small tank capacitor and ballast inductance values. The small tank capacitance implies high peak voltages to get the required power throughput, and the small ballast inductance implies high short-circuit currents in the event of a short circuit.

For these reasons the author suggests that the designer chooses a **slightly lower **resonant frequency, and aims for a **power factor of 0.85**. As with most decisions in engineering, this is a compromise. The choice of 0.85 is still thought to represent a good power factor, without incurring excessive peak voltages or fault currents. Therefore, all of the text that follows will assume that the resonant charging frequency *Fr* is chosen to give a power factor of 0.85.

The recommended *Fr* values to achieve 0.85 power factor for a range of break rates were read off the graph above. The relationship between BPS and suggested resonant charging frequency is summarised below.

There are two lines on this graph because the optimum resonant charging frequency is influenced by the mains supply frequency. The blue line indicates the resonant charging frequency required for various rotary speeds when a 50Hz supply is used. The Magenta line shows the resonant charging frequencies required when a 60Hz supply is used. The equations show how the required resonant charging frequency can be estimated from the chosen break rate. |

The resonant charging frequency *Fr* is inversely proportional to the product *Lb Cp*. Therefore we have fixed the product *Lb Cp* by determining the required resonant frequency.

In fact there are an infinite number of combinations of *Lb* and *Cp* which result in the correct resonant charging frequency, and the designer still has considerable freedom in the exact choice of each component at this stage. As long as the *LbCp* product remains close to that determined above, the power factor, and timing aspects of the design will be good. Only the power throughput will vary depending on the ratio of *Lb* to *Cp*. Controlling the power throughput is the next step to the design.

Setting the power throughput

Now that the product LbCp is defined, we can adjust the ratio of Lb / Cp in order to change *Zr* and get the amount of power throughput that we desire. *Lb* can initially be chosen to ballast the power transformer to its faceplate VA rating. This provides a good starting point, but it's value will likely be decreased considerably to get the required power throughput at the chosen rotary speed.

More will be added here shortly…

What happens if the resonant charging frequency Fr is slightly wrong for the chosen BPS ?

Firstly, if *Fr* differs significantly from the optimum value, the power factor will deteriorate slightly as shown in the first graph on this page.

A large tank capacitor and lots of ballast inductance implies a low resonant frequency *Fr*.

If *Fr* is too low for a given firing rate, then the tank capacitor will not fully charge during the time between presentations. Power throughput is hindered, and the system appears predominantly inductive. Hence the reduced power factor.

There are a number of disadvantages to having *Fr* too high (ie. small ballast inductance and small tank capacitor):

- If
*Fr*is too high, the tank capacitor can re-charge too quickly between firings. A situation can arise where the capacitor voltage rockets upwards after each gap firing, reaches a maximum, and then rings back down to a low value before the gap fires again. If the resonant charging frequency is far too high it is even possible for there to be several cycles of oscillation between firings of the rotary spark gap ! (This is actually the underlying reason for the repeating smaller peaks on the first graph of this page !) - If
*Fr*is too high, the peak voltage to which the capacitor charges can become excessive. This can cause dielectric stress in the capacitor and the HV transformer. - If
*Fr*is too high, the average voltage can also increase. This can cause the iron core of the power transformer to saturate.