3. Simulator development

ð29Þ

Figure 12 shows the steam temperature control system that uses vapor attemperation to regulate the main steam thermal conditions going to the superheater system. The system compares the steam temperature at the superheater 2 outlet with the set point to generate the error. Then the PID controller generates the demand signal to open or close the spray valve,

which brings water/vapor at lower temperature than the superheat leaving the drum.

Figure 12. Steam temperature using feedwater attemperation. Control system diagram.

Figure 11. Drum pressure control system diagram.

18 Modeling and Computer Simulation

Once the equations have been derived, a computer simulation model is developed to initiate the test of the steam generation system predicted performance both, in steady state and dynamic conditions. One of the objectives is to validate a modular simulation feature that permits a fully integration of blocks when additional components are added to the system. The simulation tool would be useful to provide predicted performance behaviors for a wide variety of system configurations based in elementary modules such as preheaters, economizers, evaporators, superheaters, and reheaters. Figure 13 describes the general operation of a typical computer simulation program where the main computing blocks and variables are described. Further details on the simulation blocks and programs can be found in Ref. [16].

### 3.1. Case study 1: Modeling and simulation of an industrial boiler

An industrial boiler was modeled and simulated having a traditional PID control strategy. The boiler under test was a VU 60 Industrial system that produces 180,000 pounds of steam per hour [7]. The mathematical model of the plant was a scaled version model of the one obtained for a thermoelectric unit [6]. The model represented only the behavior of the drum-evaporator system having a combustion process with a simplified control system and a three element boiler feed-water controller. The simulations were performed using the SIMULINK® shell running under the MATLAB® platform.

The computational model obtained is compared with the measurements from the real boiler at steady state as well as during transient conditions. In steady state, four steam loads were studied and they are shown in Tables 2–5. In all cases, a small steady state error is observed

Figure 13. Computer simulation flow diagram.




Table 3. Measurement vs. simulation comparison for a load of 65 <sup>10</sup><sup>3</sup> lb/h.


3.2. Case study 2: Modeling and simulation of HRSG

Figure 14. Drum level behavior and error comparing simulation and measurements.

Table 5. Measurement vs. simulation comparison for a load of 170 <sup>10</sup><sup>3</sup> lb/h.

This case shows a heat recovery steam generator (HRSG) operating at different ramping conditions and then settling a steady state operating. The modular simulation methodology permits a full integration of blocks when additional components are added to the system. The simulation tool provides predicted performance behaviors for a wide variety of HRSG configurations based in elementary modules such as preheaters, economizers, evaporators, superheaters, and reheaters. Further details on the simulation blocks and programs can be found in

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The case in point describes the behavior of a load rejection from 100–75% in the turbine gas capacity, by making reductions in the amount of combustion gases as well as in their

Ref. [16]. Tables 6 and 7 shows the dimensions and geometries of the system.

Table 4. Measurement vs. simulation comparison for a load of 135 <sup>10</sup><sup>3</sup> lb/h.

for the feed-water flow. This error might be produced by a purge located before the sensor position. This way the flow will always be higher in the simulation values.

The simulation of the transient behavior was performed using a load ramp of 1.9% per minute. The results for the critical variables are shown in Figures 14 and 15. The error in the feed-water flow is due to a non-minimal phase effect that was not replicated exactly in the model simulation.


Table 5. Measurement vs. simulation comparison for a load of 170 <sup>10</sup><sup>3</sup> lb/h.

Figure 14. Drum level behavior and error comparing simulation and measurements.

#### 3.2. Case study 2: Modeling and simulation of HRSG

for the feed-water flow. This error might be produced by a purge located before the sensor

The simulation of the transient behavior was performed using a load ramp of 1.9% per minute. The results for the critical variables are shown in Figures 14 and 15. The error in the feed-water flow is due to a non-minimal phase effect that was not replicated exactly in the model simulation.

position. This way the flow will always be higher in the simulation values.

Table 2. Measurement vs. simulation comparison for a load of 56 <sup>10</sup><sup>3</sup> lb/h.

20 Modeling and Computer Simulation

Table 3. Measurement vs. simulation comparison for a load of 65 <sup>10</sup><sup>3</sup> lb/h.

Table 4. Measurement vs. simulation comparison for a load of 135 <sup>10</sup><sup>3</sup> lb/h.

This case shows a heat recovery steam generator (HRSG) operating at different ramping conditions and then settling a steady state operating. The modular simulation methodology permits a full integration of blocks when additional components are added to the system. The simulation tool provides predicted performance behaviors for a wide variety of HRSG configurations based in elementary modules such as preheaters, economizers, evaporators, superheaters, and reheaters. Further details on the simulation blocks and programs can be found in Ref. [16]. Tables 6 and 7 shows the dimensions and geometries of the system.

The case in point describes the behavior of a load rejection from 100–75% in the turbine gas capacity, by making reductions in the amount of combustion gases as well as in their

predicted performance for the superheater systems. Table 10 compares the simulated experiment results with the predicted performance for the evaporator and economizer systems.

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Table 8. Variations of temperature, mass flow and pressures for 100–75% ramp.

Table 9. Comparison between initial and final loads for a download change from 100–75%.

Table 9 shows a 1.56% difference between the simulated steam flow at superheater 1 from the steady state predicted performance at 100% load. This result is due to a slight overestimation of the steam temperature at superheater 3 that induces the control system to inject spray water to regulate the steam temperature according to the reference value. Table 10 shows also an overestimation of feedwater temperature at economizer 2. This temperature difference is 3.3% higher than the predicted performance for the HRSG system. However, those differences are well within the desired specifications of similar computer simulation systems. At the 75% load

Figure 15. Feedwater flow behavior and error comparing simulation and measurements.


Table 6. Geometric configuration of the drum tank.


Table 7. Geometric configuration of the heat exchanger elements in the HRSG system.

temperatures. Table 8 shows the how the variables change in the 900 seconds test. The control system generates corrective actions in order to sustain the liquid level and drum fluid pressure at the predicted performance. Table 9 compares the simulated experiment results with the


Table 8. Variations of temperature, mass flow and pressures for 100–75% ramp.

predicted performance for the superheater systems. Table 10 compares the simulated experiment results with the predicted performance for the evaporator and economizer systems.

Table 9 shows a 1.56% difference between the simulated steam flow at superheater 1 from the steady state predicted performance at 100% load. This result is due to a slight overestimation of the steam temperature at superheater 3 that induces the control system to inject spray water to regulate the steam temperature according to the reference value. Table 10 shows also an overestimation of feedwater temperature at economizer 2. This temperature difference is 3.3% higher than the predicted performance for the HRSG system. However, those differences are well within the desired specifications of similar computer simulation systems. At the 75% load


Table 9. Comparison between initial and final loads for a download change from 100–75%.

temperatures. Table 8 shows the how the variables change in the 900 seconds test. The control system generates corrective actions in order to sustain the liquid level and drum fluid pressure at the predicted performance. Table 9 compares the simulated experiment results with the

Table 7. Geometric configuration of the heat exchanger elements in the HRSG system.

Figure 15. Feedwater flow behavior and error comparing simulation and measurements.

Table 6. Geometric configuration of the drum tank.

22 Modeling and Computer Simulation


the main steam demand as expected and the hot flue gases have a slight overshoot when the ramp ends at full nominal load. The controller showed a good performance maintaining the drum liquid level steady during all simulation exercises. Finally, the modular approach used can be expanded to include different geometric configurations and operating conditions, as

well as different tuning alternatives for the control system [19–22].

specific heat at constant pressure (J/kg K) specific heat at constant volume (J/kg K)

area (m2 )

diameter (m)

transfer function gravity (m/s<sup>2</sup>

proportional gain

mass flow rate (kg/s)

pressure (bar)

Prandtl number

radius (m)

time (s)

heat transfer rate (W)

Reynolds number

number of tubes per bed

longitudinal step (m) transversal step (m)

molecular weight (kg/moles)

number of tube beds (or levels)

length (m) mass (kg)

error as a function of time

)

heat recovery steam generator

entalpy (J/kg) or heat transfer coefficient (W/m<sup>2</sup>

K)

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Glossary

Table 10. Comparison between initial and final loads for a download change from 100 to 75%.

a hot flue gases temperature error of 4.07% above the predicted performance is obtained from the computer simulation.
