ABSTRACT

BALANCING BOILER INPUTS TO ENERGY DEMAND-ONE OF THE BASIC CONSIDERATIONS IN THE DESIGN OF CONTROLS FOR DRUM TYPE BOILERS

Plant operators are demanding more and more from boiler controls - Maneuvering units over wide ranges at variable pressure is one tough requirement which, which, along with coal firing, has forced control designers to consider plant characteristics which has increased importance of plant performance. The author describes the basis of a boiler control system which combines a unique turbine energy demand with a unique measure of energy delivered to the boiler. Features to deal with pulverizer and boiler dynamics are described as well as the features which balance supply to demand during steady state operation.

INTRODUCTION

There is little disagreement about the basic objectives assigned to boiler controls in specifications today. Almost every list includes these along with others.

1. Maintain generation to meet demand.

2. Maintain boiler-turbine balance under all operating conditions.

3. Maintain a balance boiler inputs under all operating conditions.

A control system which meets these three objectives is, by definition, a coordinated control.

This paper limits itself to a discussion of control concepts which deal with objectives no. 1 and 2 under normal operating conditions.

COORDINATED CONTROLS (Normal Operation)

The concept of the coordinated boiler control is to develop a perfect turbine energy demand which is applied to the boiler control. It is now only necessary to furnish a perfect energy delivered signal and a perfect energy balance is obtained.

Alas, our world is imperfect. Compromises must be made, and provisions must be made for the imperfections which we deal with as well as the perverse natural characteristics of the equipment which is to be controlled.

Consider the boiler control by itself (figure 1).

Here we have the turbine energy demand compared to the boiler energy supply and the difference or error controls the energy input. What more do we need? Well, to make a control system complete, quite a lot - we must account for the dynamics of the boiler auxiliaries and for changes in stored energy over the load range, we must supply safety features and many others, but our discussion today is limited to boiler - turbine energy balance - what more do we need to achieve this balance?

Energy delivered is compared to turbine energy demand. A throttle pressure controller must be supplied because the measure of energy supplied to the turbine control as a feedback probably will not match the delivered energy signal to the boiler control. The throttle pressure controller integrates these differences and brings demand and supply into balance.

It is not our purpose to discuss the merit of using throttle pressure to determine a boiler-turbine balance - let us accept that if the throttle pressure is constant, the input equals the output and if the throttle pressure is at a set point, the plant is operating as desired. If throttle pressure is changing, for any reason, a mismatch in turbine demand and boiler input exists.

Most control systems in the past apply the throttle pressure controller to the boiler inputs as shown in figure 2.

Why would anybody want to improve on this arrangement? Well, let us see. If the energy demand and energy supply measurements are properly scaled and calibrated, the throttle pressure correction would be zero at steady state or at some fixed value to account for a fixed offset between the turbine energy demand and boiler energy supply measurements.

Let us now postulate a disturbance, one which creates a change in throttle pressure. This means that, temporarily, energy demand and energy supply are out of balance and the throttle pressure controller must modify the boiler input demand to restore throttle pressure to set point. After a time, when the energy demand and energy supply approach a balance - the output of the pressure controller adds to the energy demand and now we must have an overshoot in throttle pressure.

The throttle pressure controller must integrate back to zero. Then are energy supply and energy demand in the proper balance. Let us look at this on the chart shown in figure 3.

The above case is an example of a steady state load disturbance typical of a coal fired boiler.

The manifestation of the phenomenon becomes more severe during load changes and particularly during load changes with variable throttle pressure set point.

Let us consider an alternate control method which is free of this overshoot problem. We shall approach this by developing a model of a simple process.

THE PROPOSED CONTROL SCHEME

This simple process shown in figure 4 consists of a tank with something flowing out of the tank (F_i) and a valve (V) controlling the flow flowing out of the tank (F_o). the flow out of the tank is some function of the position of the valve and the level in the tank - expressed as follows:

(1) F_o = f (V,L)

Further, it can be seen that when the flow in and the flow out are equal, the level will be constant. On the other hand, when F_i and F_o are not equal, the level is changing, the rate depending on the magnitude of the unbalance between the two flows.

(2) F_i - F_o = dL/dt or L

(3) F_i = F_o + L

Finally, it can be seen that the level as it exists now (L_T) depends on the level at the time we began to consider this process (L_to) plus the integral of all of the rates of change of level that have existed in the meantime.

(4) L_T = L_to + L

Equations one through four describe a simple mathematical model of this process. For our discussion, it is preferred to diagram this model as shown in figure 4 labeled a "Simplified Process With Self Regulation".

This discussion is about boiler controls, why consider such a trivial process? The reason is that the process shown is a reasonable analog of the energy flow process in a boiler.* In this model, flow in (F_i) is the heat energy to the boiler, flow out (F_o) is the energy flow from the boiler and level (L) represents the energy stored in the process.

In figure 5, our simple process model is expanded slightly to show the super heater and the actual process variable listed below.

P_l - Energy flow from the boiler. (For purposes of this discussion, we will consider turbine first stage pressure- energy flow to the turbine). There are other methods used to calculate this variable depending on the plant design. The variable of interest is energy flow

*It depicts energy flow; in no way, is this a model of fluid in a drum boiler; that is a different model completely.

P_t - Throttle Pressure, or boiler or outlet pressure.

P_d - Drum pressure (the integral rates of changes of P_d)

Heat release in the furnace - That large mass of energy input which we would like to measure - particularly on a coal fired boiler.

In figure 6, we develop the very basic control system. Here, we apply a a megawatt control to the turbine through the governor. Figure 6 shows the boiler coordinated with the turbine by energy demand (P_l/P_t x P_s) which is based on turbine demand.

To develop the energy demand, the control system measures the effective governor value position by computing the ration of first state pressure to throttle pressure *(P_l/P_t) - this effective turbine valve position, is turbine energy demand at a fixed throttle pressure.

This is calibrated into turbine energy demand at any throttle pressure by multiplying P_l/P_t by the throttle pressure set point - designated P_s. This energy demand (P_l/P_t x P_s) is therefore the energy demanded by the turbine from the boiler.

Energy demand is compared to the measure of energy supply, called heat release and the fuel controller modulates the energy input to maintain a balance.

The heat release computation is an inferential measurement of the actual energy supplied to the furnace going back to our model we see that F_i = F_o + L. In the actual boiler, the heat release signal is comprised of the instantaneous energy flow out of the boiler (P_l) plus the rate of stored energy (P_d).**

* See reference no. 1

** See reference no. 2

With turbine energy demand developed as P_l/P_t x P_s and the boiler energy supply measured as

P_l + P_d, let us consider how throttle pressure is controlled.

In figure 7, we have added a set of equations which define the error the fuel controller (e_f).

(5) e_f = (energy demand) - (energy supply)

(6) e_f = P_l/P_t x P_s - (P_l + P_d)

(7) e_f = P_l (P_s)/(P_t) - P_l - P_d

(8) e_f = P_l (P_s - P_t) / (P_t) - P_d

Since P_s - P_t = e_pt (throttle pressure error)

(9) e_f = P_l/P_t e_pt - P_d

Since the fuel error (e_f) contains the throttle positions error, let us examine this in steady state and transient conditions. The fuel controller is a throttle pressure controller.

If steady condition P_d is zero and the integrating fuel controller forces ef to zero. This reduces equation (9) to:

(10) 0 = P_l/P_t e_pt

since P_l/P_t is not zero, then ept must be zero, and P_s = P_t.

Thus, at steady state, throttle pressure is controlled to desired set point without need for a separate integrating throttle pressure controller.

For the transient case as throttle pressure departs from set point in the increase direction - P_d is positive there by strongly assisting ept in the decrease of fuel to correct the pressure.

As the throttle pressure comes under control and begins toward a set point P_d reverses polarity and strongly damps the action of e_pt preventing an overshot of pressure.

Under pressure decreasing, the opposite affects take place.

By having a good fortune to select the proper computation of turbine energy demand and boiler energy supply, we obtain the fuel controller also functions as a throttle pressure controller. Now we have the ideal arrangement as shown in figure 8.

The overshoot is gone because the mis-calibrating integral is gone, and the rate of change of drum pressure acts as a strong stabilizing influence - opposing all throttle deviations from set point and stabilizing all actions to return to set point.

Another advantage of this new arrangement is the variable gain adaptive feature available naturally from e_f = P_l/P_t x e_pt. Consider figure 9, here we show load versus throttle pressure curves assuming fixed turbine governor value positions of 100%, and 50% open. Load is also recognized as fuel input, then it can be seen that when the valves are 50% open the slope of throttle pressure change for incremental change in fuel is much greater than at 100% valve position. It can be seen that a fuel controller attempting to correct the throttle pressure disturbance needs a smaller change in fuel as the governor valves are further closed.

Hence, e_f = P_l/P_t x e_pt naturally adapts the gain of the fuel controller to the operating conditions of the plant.

SUMMARY AND CONCLUSION

What we have discussed is a simple is a simplified structure supporting the energy balance scheme of a boiler control. Many details remain to develop the complete system - a few important ones are air flow demand development and how to deal with boiler stored energy change with load or variable pressure and most particularly, how to deal with the dynamics of the pulverizers. These are presented on figure 10 and are discussed in the appendix.

More stringent requirements placed on boiler controls for variable pressure operations focused our attention on the way we were accomplishing the function of balancing boiler inputs to energy demand. By combining a unique signal representing turbine energy demand with a unique signal representing energy supply to the boiler, a very stable method was found to balance boiler input to energy demand.

ACKNOWLEDGMENT

The author appreciates constructive inputs to this paper by J.M. Finan and H.C. Gery, both of Leeds & Northrup Company.

REFERENCES

1. Daniels, J.H., "Boiler-Turbine Control System", U.S. Patent No. 3,247,672, April 26, 1966.

2. Jenkins, Jr., T.W., Garber, I. and Stewart, F.L., "Heat release Computer for Combustion Control Systems", Proceedings of the American Power Conference. Vol. XXVI, pp. 333-343, 1964.

3. Jenkins, Jr., T.W., and Littman, B., "Response Capability in the Control of Large Generating Units", IEEE Paper No. 71 CP 73 PWR, Presented at IEEE Winter Power Meeting, New York, NY, January 31 to Fbruary 5, 1971

4. Morse, R.H., "Boiler Control System", U.S. Patent No. 4,213,304, July 22, 1980.

APPENDIX

The basic control discussed in this paper relates to the measurement of energy input under steady state conditions. To successfully control the firing rate to a boiler under all conditions requires developing the demand for air flow, and in addition, to develop the techniques to manage energy input during changes in demand. This latter requires dealing properly with the dynamics of the boiler and its auxiliaries, in particular, the coal pulverizing mills.

Considerable study has been devoted to the behavior of coal pulverizers from the standpoint of the boiler control system. It is hoped someday that this work will be published. For the present, it is sufficient to consider the pulverizer as a time constant in series with the boiler time constant as shown on the left in figure 10. Process model in figure 10 indicates the pulverizer in series of the boiler dynamics. The control system in figure 10 shows the air flow demand and the three feed forwards which deal with the boiler dynamics as perceived in this model.

1. Feed forward 1 - A lead on fuel demand dedicated to pulverizer dynamics. This lead has a gain and decay time which is adjusted top compensate for the pulverizer dynamics as determined by field testing and tuning.

2. Feed forward 2 - A lead on energy demand dedicated to the change in stored energy with load at constant throttle pressure. This is best understood by considering the behavior of drum pressure with load. At zero or very low steam flow, drum and throttle pressure are equal. As flow through the superheater increases, drum pressure rises with respect to the throttle pressure as the square of the flow. The effect of this feed forward is non-linear., more is needed at high load. Consequently, the rate of change of energy demand is multiplied by the demand and added to the demand as a feed forward.

3. Feed forward 3 - A lead on throttle pressure set point. This is employed during variable pressure operation and accounts for the large change in stored energy required when throttle pressure is varied from one level to another.