Proportional Load Allocation vs. PID Load Allocation

Some might argue that summating all the Feedback Process Variables (PV's) for units contributing to the load, as a PV to a Load Allocating PID controller is the easiest approach to allocating load to units and I guess in most cases this is done to save some development time and get the process online faster. However, if you think about this solution, long term it causes more problems and could be a costly approach as process cycling will undoubtedly become a factor as the equipment wear over time. It is hard to allocate load in a stable manner when following this approach.

Let's take an example scenario of allocating fuel flow demand to a number of coal grinding mills at an old power utility. Usually, the load demand is allocated by a Fuel Master controller, it would demand a certain amount of coal flow from each coal grinding mill that is online.

This total coal flow is controlled by controlling the Primary Air (PA) Flow through each of the coal grinding mills. The air flowing through a mill would then pick up fine coal particles and carry it to the furnace. Coal Flow through the mill needs to be controlled in such a manner as to maintain a stable particle size distribution for the air to carry it into the furnace and ensure a stable flame at the burner.

Too large coal particles could drop in the pipes and not be carried all the way to the furnace which would cause a very dangerous situation over time, as a sudden high velocity of PA Flow could pick up a large amount of these stationary coal particles and carry them to into the furnace all at once. It is important to never build up coal within the Pulverized Fuel (PF) pipes.

Also, when the airflow through the mill is picked up too rapidly, it would cause all of the finer particles in the mill to be depleted and could result in a flameout on the PF burner, when there is not enough fine particles coming from the mill. The Coal Flow into the mill is usually regulated by a PID controller acting in parallel to the PA Flow Controller but with cross limitation.

There are many articles on how to control the coal flow to the mill in order to always remain air rich, employing a cross limit between Primary Air Flow and Coal Flow, and also between Total Air Flow and the Fuel Master demand. Stochiometric combustion is a whole study on its own but for the purpose of this article, it is enough to say that the mixture should always be air rich, i.e. more air than is required to completely burn the coal particles.

Therefore, the coal flowing into the mill should be controlled in relation to the air as to ensure that there is always more air to carry the coal particles than coal being fed into the mill, due to environmental considerations such as NOx reduction and safety considerations such as that the Primary Fuel pipeline is always kept clear of stationary coal particles.

The Primary Air Controller Set Point (SP) is usually calculated from a curve that describes the relation between coal flow and air flow. The Fuel Master demands a certain amount of coal flow per mill, and based on this Coal Flow - Air Flow Curve the Primary Air Controller SP is calculated for each mill based on that mill's load percentage. Usually, the Primary Air PV is used with the inverse of this Coal Flow - Air Flow curve, the Air Flow - Coal Flow curve, as the high limit of the Coal Feed controller SP for each mill. The Coal Feed PV in turn, through the Coal Flow - Air Flow curve is usually used as a low limit on the SP of the PA Flow controller to complete the Air Fuel Cross Limit action.

This creates quite some instabilities during load swings as you can imagine since a load increase has a delayed Coal Flow vs Primary Air Flow, and a load decrease has a delayed PA Flow vs Coal Flow. If you combine this with inaccurate or unreliable coal flow measurements which only adds to the problem, it is almost impossible to tune a PID Fuel Master Controller for stable operation throughout the load of the mills and combinations of running mills.

This is why I would argue that it is better to switch the Fuel Master Controller to a Proportional Load allocation instead.

In the PID case, a load swing could cause a lot of resonant reactions i.e Fuel Master PV, Coal Feed or PA Flow cycles which in turn causes cycling on the Main Steam pressure upon which the Main Steam Pressure Controller acts again.

The cycling of the PA Flow and Coal Feed affects the PV of the Fuel Master, and the Fuel Master allocates a different load to all the mills based on this action and this just becomes a never-ending story.

Over the lifetime of the plant, how much unnecessary control action are you introducing on actuators, speed drives, fan loads etc., you can see very quickly how it becomes very important to have stable Fuel Demand on your mills. You may also end up needing to employ someone to maintain the tuning of the controllers as the plant conditions change and the control of the system deteriorates.

Take the time, develop the proportional load control and save yourself a lot money over time.

Now in our power utility example, let's say for instance there is an additional steam consumer that needs a large increase in steam flow, for a short duration of time, this would cause the Main Steam Pressure to start dropping and the pressure controller demanding more fuel and air to compensate while trying to maintain the pressure. The steam pressure controller can only be well tuned if its base layer is stable and reacts proportionally to the increase in demand.

If you have a cascade controller as the Fuel Master controller, with cascading controllers for each of the Air Flow controllers, and cross limiting on the Coal Feed, the Primary Air increase is the leading action in a load increase scenario due to the Air Coal cross limiting, there is some delay between the PA PV starting to pick up and the Coal Feed Controller SP being increased.

If you are measuring coal flow and totalizing this to form your total fuel flow PV to be used for the Fuel Master Controller, then you usually end up with a situation where the Fuel Master Controller overcompensates due to the integral action over time and needs to start reducing the load again, causing the reverse action on the PA Flow / Coal Feed cross limiting. Usually, people also add some long filter action on the PV of the Fuel Master to try to stabilize the total fuel flow feedback signal.

When reducing the Fuel Flow on the other hand, the coal flow has to reduce first due to the Cross Limit Action, and then the Air Flow. In this direction the proportional gain is thus more direct on the Fuel Flow, and it is able to reduce the load faster. At the same time, the Master Pressure controller could have started reducing the Fuel Master demand since the pressure started coming back to SP, but my guess is that it would overshoot its Pressure SP since the Process Gain is not the same for increasing Fuel Demand and Decreasing Fuel Demand.

Let's say now the opposite is true, in that the additional consumer now reduces its steam consumption, then the Pressure Controller reduces the demand on the Fuel Master Controller as the pressure starts to increase, which in turn acts faster in the reducing direction, or at least it does not have the same process gain which causes a whole cycle effect again on the Fuel Master Controller's PV and unstable Pressure Control.

Another problem that arises is the fact that during the increase in fuel demand, the Primary Air through the mill is first increased, picking up more coarse coal particles together with all the fine coal particles for a duration of time until the Coal Flow into the mill is increased and the coal has had time to grind back to the same particle size distribution. This effect on the Pulverized Fuel (PF) burner flame in the furnace causes a sudden increase in steam pressure followed by a less intense flame as the fine coal particles are depleted and need to go through this stabilization phase. This usually causes the Master Pressure Controller to first slow down the demand for fuel due to the fast increase in pressure, starting to reduce the increase in demand, and then continues to increase again by demanding more as this reduction in flame intensity effect comes in to action.

As the PF Flow starts to stabilize through the mill at the higher load, the Master Pressure controller would start pulling back and the Fuel Master SP. This load reduction has a quicker (greater proportional) action since the coal is reduced before the air flow through the mill.

The question then becomes, how do you tune the Master Pressure Controller with its Cascade Fuel Master Controller and cascaded parallel Primary Air Flow and Coal Flow controllers in a stable manner to maintain a constant pressure?

Simple. You remove the PID controller controlling the fuel flow, or energy demand, and make it proportional. This needs to be a calculation however, a PID cannot simply be tuned to operate proportional. The number of mills online need to be considered, the load of each mill that is online, the Coal CV, the oil burners that are in use and their contribution to the total energy input and so on.

If you think of a mill being started and another being stopped at the same time, everything needs to be stable. The mill shutting down needs to be de-loaded either by the operator reducing the SP on the air flow controller, or by bias reduction function that de-loads the mill to minimum causing the others to start increasing proportionally, and the mill that is being started should only contribute to the equation once there is coal flowing through it and so on.

Then to make things more complicated, a mill that tripped while it was online, is full of coal when it starts up, how do you manage that? Once the mill is started it would grind coal and you would immediately have some fuel going into the furnace, the Coal Feeder cannot run before the mill is online as this would cause a blockage of coal, so the mill has to start before the feeder and the air needs to start before the mill.

Well, if you have this proportional load allocation you could easily have a stronger derivative action on your Main Pressure controller which would take care of most of these kinds of issues and in the end have a much more stable base control layer.