Authors: Dumitru Dobrea Laurentiu Aioanei Karlsruhe November 21, 2012

1. INR Pitesti, Romania Simulations of ALFRED Control Involving a More Detailed Model of the Secondary Circuit (Contribution to WP4 Task 4.4 DEL021, “Preliminary Definition of the Control Architecture”) Authors: Dumitru Dobrea Laurentiu Aioanei Karlsruhe November 21, 2012

2. INR Pitesti 1. Introduction • A more detailed model of the secondary circuit was developed, based on the last design option, in order to take account of pressure and temperature rising in the feedwater line, in order to involve the intermediate and low pressure ranges, and to have more realistic time constants. • The whole simulated system consists of reactor core and coolant, steam generator (SG), and secondary circuit. The electric generator was not introduced in the system. The coupled SG and core dynamics was developed in previous work [1], aiming to be close to the CIRTEN approach. That allowed inter-comparisons [1] that showed good agreement between the approaches. A first model involving core, SG and secondary circuit was developed in [2], but it did not perform control functions.

3. 2.Outline of the method • The model of the secondary (fig. 1) is simpler vs. design: preheaters were “collapsed” into a single preheater, deaerator tank and condenser controllers were simplified. • Deaerator tank level control is necessary; otherwise it could be emptied of condensate during simulations. The simplest solution: using condenser pump, as in [3]. It is active in all simulations. The condenser pressure control was based on cooling water flow. • Attemperator spray water is extracted from feeedwater pump outlet. • Feedwater outlet temperature control: through a mixing chamber between steam line and feedwater line, extracting steam from the steam line. • There is no atmospheric steam discharge valve. • The feedwater control valve (FCV) is fully open, while feedwater flow is controlled by the feedwater pump.

4. Fig. 1. Secondary circuit

5. 2.1. Normal mode • The reactor follows the generator power, as emphasized (fig. 2). After a load variation demanded by generator power regulator, the mechanical energy of the turbines is adjusted by requiring reactor power variation for obtaining the required load while keeping the steam pressure constant. By imposing constraints on cold leg lead temperature, it could be difficult to impose the pressure condition. • A variation of the electric power commands the HP turbine valve in order to adjust the flow through the turbines. Imposing the SG cold leg lead temperature control, in order to keep it constant, the reactor power setpoint is adjusted in order to reduce the reactor and SG power, while other controllers level out the important parameters: cold leg lead temperature, SG pressure and turbine inlet temperature.

6. SG power was considered because SG steam flow and SG steam enthalpy contribute to the plant load. Due to interference between I/O pairs in the control scheme, the lead temperature was included in the reactor power STP computation. Electric power, SG pressure and lead temperature are used as measured disturbances thus feedforward variables. • If pressure is controlled, without controlling the lead temperature during load reduction, the new steady-state lead temperature will decrease. Thus, weights in could be adjusted in order to minimize simultaneously the steam pressure variation and the lead temperature variation. • In the simulations the electric power is computed as the sum of HP and LP turbine powers based on inlet and extraction flows and the inlet/outlet enthalpies. To obtain enthalpies, temperature and pressure measurements are needed. • The SG powers need water/steam flows, pressures and temperatures measured at SG inlet/outlet.

7. Fig. 2. Normal mode control scheme

8. 2.2. Alternate mode • In alternate mode the generator power will follow the reactor power (fig. 3). Usually, this mode works during start-up, at low powers, or after setbacks/stepbacks. • The rate of power variation should account of temperature rate specifications and allowed flow and pressure variations at the turbine inlet. However, those conditions were not specified in the present simulations.

9. Fig. 3. Alternate mode control scheme

10. Setpoint Measurement Sensor Signal Error Controller Process Measurement Sensor Signal Fig. 4. General control scheme

11. 3. Results The figures 5-25 present results of simulations performed for normal and alternate modes.

12. INR Pitesti Fig. 5. N-mode. Free evolution after a step closing of the HPT valve

13. The steam and feedwater flows drop by ~4 kg/s, the SG and HP turbine output pressures rise by ~1.5 bar, while the SG outlet and core inlet lead temperatures rise by ~3.6 oC. • As could be seen in fig. 5, the temperature feedback in the core+coolant will level out the parameter values, with delays imposed by core, steam generator (SG) and secondary circuit dynamics. As the transient or final steady-state values could exceed allowable limits, the control should prevent that.

14. INR Pitesti Fig. 6. N-mode. Step decrease of electric power by 2%. All controllers active.

15. INR Pitesti Fig. 7. N-mode. Step decr. of el. power by 2%. All ctrls active. Short time interval.

16. SG pow. follows the react. pow. with ~ 1000 s delay. SG pressure has a sudden rise of ~ 2 bar, then BpV opens at 2 bar. BpC recovers the SG press. within 100 s. The HPT inlet chamber press. drops by ~ 2 bar when BpV opens, and recovers slowly in ~ 10000 s. SG and Fw flows have an inverse behavior vs. pressures. The HPT flow settles to a value less by ~ 4 kg/s, equal to the SG and Fw flows, but faster than the last. Bp flow rises quickly, then drops slowly to 0 in ~20000 s. TIT and the Fw outlet temperature are constant by the attemperator and by FwTC resp., at the expense of the SG steam temp. which behaves like the HPT press. TIT rate has a drop of 4 oC/min, then goes to 0. • Lead core inlet and SG outlet temp. have similar behavior, by dropping with ~ 1.7 oC, and recovering after ~ 10000 s. Lead core outlet and SG inlet temp. drop with ~ 2.3 oC, then settle at a lower value (-1.6 oC ) after ~ 10000 s. ΔT over core decreases from 80 to ~79 oC. Lead flows have different dynamics for a time interval of ~ 300 s, when core & SG dynamics dominate. The deareator tank level recovers after ~ 4000 s, with oscill. at the start of transient. The condenser pressure increases from 5.4 kPa to ~ 5.6 kPa, then settles at ~ 5.3 kPa after ~15000 s. • Actuators: the gov. valve closes by ~3% at the start of transient, then lifts to ~0.5%, followed by a slow closing to 2% after 1000 s. To keep pow. constant the CR follows core & SG dynamics in the first 100 s, then slowly continues insertion and settles after ~10000 s following sec. dynamics. BpV valve opening reproduces the Bp flow behavior. To keep condenser level the condenser pump slows down by 0.3% after ~15000s, with oscill. during the first 300 s. To keep constant SG lead outlet temperature the feedwater pump slows down by ~0.25% over ~15000s. Subcool., sat. & superheat. lengths have smooth behavior both for short and long time intervals. Efficiency = ~38.5%

17. One may observe that the core and SG powers will equal the electric power after a long time, because the commanded reactor power is constrained to allow settling two of the main controlled parameters LT, and SG pressure. • The governor valve regulates the electric power, thus is not involved in regulating the SG pressure. It would be useful to use a governor setpoint combining the power and the pressure, as done for reactor power regulator, or to include an HP inlet chamber pressure term in the reactor power setpoint computation. Usually a valve at the SG outlet header is dedicated to controlling the SG pressure.

18. If bypass valve control is not involved in the SG pressure control, TIT and HPT flow stay almost equal to their initial values, while SG pressure slowly decreases from ~ 2 bar to 0.2 bar during ~ 40000s, as shown in fig. 8 (upper graphs). The LT has a smaller decrease than in fig. 6. The SG outlet steam temperature drops by ~ 2 oC, while the SG inlet water temperature is constant, due to FwTC. The efficiency is ~39.3, close to the nominal steady state value of 39.43. • The short time dynamics (fig. 8, lower graphs) shows damped oscillations in almost all parameters. They could be generated by controller tunings, or to interference between the controllers due to correlated parameters. • One could observe that controlling SG pressure using only reactor power will interfere with LT control. A controller dealing with interferences, as designed in the last DEL21 revision by CIRTEN could be implemented in order to further damp the oscillations.

19. INR Pitesti Fig. 8. N-mode. Step decrease of el. power by 2%. All ctrls active, except BpC

20. The smooth behaviour of fig. 8 is seen in fig. 9 also, where FwTC was removed. The SG press. settles a little higher than in fig. 8, and SG outlet temp. drops by ~-2 oC, recovering slowly. The Fw outlet temp. rises by a little amount, because keeping the cold leg lead temperature constant is more important than keeping the feedwater outlet temperature constant by changing the water flow. Thus the effect of the FwTC is not important for small transients. • If LTC is not used, but only Att and FwTC are active, their effect in keeping TIT and Fw temperature constant is shown in fig. 10. In that case, the LT settles at a value less than the initial by 0.5 oC. This variation is small, while SG pressure and outlet temperature variations are not too large. Thus, the control architecture could account for LT ranges where LTC could be activated. Simulations could help to assess those ranges taking account of equipment constraints. • The role of the attemperator is stressed by fig. 11, where it was removed. The TIT drops by ~8 oC, while SG press. does not vary significantly. Lack of AttC increase also the LT drop, showing an important degree of interference in the system. However, one could see that the feedwater outlet temperature control alone does not recover the cold leg lead temperature. • The LTC and AttC can work together to bring the LT and TIT to their initial values, as fig. 12 shows. The SG and HPT pressures recover slightly, showing an impact of those controllers on these parameters.

21. INR Pitesti Fig. 9. N-mode. Step decrease of el. power by 2%. All ctrl. active, except BpC & FwTC. Fig. 10. N-mode. Step decrease of el. power by 2%. AttC FwTC active.

22. INR Pitesti Fig. 11. N-mode. Step decrease of el. power by 2%. FwTC Fig. 12. N-mode. Step decrease of el. power by 2%. LTC and AttC active.

23. INR Pitesti Fig. 13. N-mode. Step decrease of el. power by 2%. LTC+PowPC+PowLTC active

24. INR Pitesti Fig. 14. N-mode. Step decrease of el. power by 2%. LTC active. Fig. 15. N-mode. Step decrease of el. power by 2%. PowEC+PowSGC active.

25. Fig. 13 shows that the combination of LTC, PowPC, and PowLTC also recovers the LT, almost recovers the SG and HPT pressures within the simulation interval, and would recover the TIT during longer time intervals. The feedwater outlet temperature does not increase significantly, and the water/steam flows does not decrease too much. • Some controllers or their combination does not ensure satisfactory control. In fig. 14 the LTC based on feedwater flow variation sustained shows oscillations that resisted to various attempts for tuning. A dominant small frequency characteristic for the whole circuit dynamics could be due to conflicting processes as steam temperature and pressure evolutions. Free dynamics temperature feedbacks modulated by secondary dynamics could conflict with control actions. A better designed controller accounting for the small frequency could solve the problem, but practically using only the LTC has to be avoided. • If only PowEC and PowSG components of the power controller are used, all variables diverge, as shown in fig. 15.

26. Using all controllers withstands more severe transients. Fig. 16: behaviour after a 10% step decrease of the el. pow. It is similar with the behaviour of 2% transient in fig. 6. The undershoots of LT, SG temp. & HPT in. ch. Press. increase quite proportionally with powers. The actuator variations are in range. The press. & temp. variations are within the range allowing linear approach. • Fig. 17 illustrates a more complicated transient. The powers match at each steady-state, the controlled params LT, SG press. and TIT recover to nominal values. The transient ampl. of LT, SG and HTP in. ch. temp. during step-down and step-up are almost equal. Compared with 2% and 10% steps they increase in proportion with power step. There are transient high and low pressures in condenser, and an ~0 transient subcooled length in SG. Almost actuators are in range, although shim rods may have to be inserted. The BpV starts from fully closed, and a negative value is not physical, but we did not impose saturation and anti-windup features during the simulations. • A 50% power decrease with all controllers active is shown in fig. 18. The behavior is similar to those in fig. 6, 15, and 16, with amplitudes of transient variations ~ scaled by power ratios, and all actuators in range. The short-term pattern of fig. 19 does deviate from the pattern of 2% power decrease. Scaling with power is due to linearity of the model, but it estimated that non-linearity would affect only transient amplitudes. • Since the mean relative variations of the tempe. and press. are small, and the peak variations < 30%, their influence upon amplitudes are not severe.

27. INR Pitesti Fig. 16. N-mode. Step decrease of el. power by 10%. All controllers active.

28. INR Pitesti Fig. 17. N-mode. 100 – 60 – 100 step el. power variations. All controllers active.

29. Fig. 18. N-mode. 50% step el. power decrease. All controllers active.

30. Fig. 19. N-mode. 50% step el. power decrease. Short time interval.

31. The simulations show that with simultaneous SG lead outlet temperature and pressure control the efficiency will be constant, thus the electric power will be strictly proportional to reactor power. Without lead outlet temperature control the efficiency will drop, and without pressure control the efficiency will raise. Without LT control the attemperator and FwTC will recover the efficiency to a value lower than the nominal one. • Fig. 20 illustrates ramp electric power variations in normal mode, using all controllers, except bypass valve controller. One can see that TIT, SG pressure and LT have moderate variation, and the reactor and SG powers follow well the electric power. The ramp slopes were -0.005 MW/s, 0.002 MW/s, and 0.02 to 0.0005.

32. Fig. 20. N-mode. Ramp electric power variations

33. In figs. 21-23 there is a mismatch between the electric power and the reactor or SG power at the final steady-state. Ramp or “manual” power variations as in the figures 24-25 do not show power mismatch at steady states. “Manual” power variations are obtained by combining ramping of reactor power with holding reactor power until generator and SG power come closer. • In some cases (figs. 23 & 24) the steam press. variation is slight, like flow variations, while the steam and lead temp. variations are larger. • Fig. 21 shows results fora a step decrease of the reactor power by 30 MW, without other controls than the reactor pow. ctrl. using ramps of given slopes. SG follows the reactor power with ~ 1000 sec delay. The electric power settles after the same time at a lower value, due to lower efficiency decrease. In simulations the reactor power was not calibrated against electric power, although the electric power has been calibrated vs. reactor power in normal mode. If that would be done, there would have been no mismatch of powers. Yet we let the reactor power uncalibrated in order to emphasize the efficiency effect.

34. Fig. 21. A-mode. -30 MW step decrease of core power. Power control

35. In fig. 22 pow. mismatch is lower, as eff. has a smaller decrease, due to additional controls. The lead temp. decreases are lower. The HPT press. is constant, while the SG press. rises by ~ 7 bar. The flows decrease significantly st SG I & O. Due to attemp. TIT is constant at the expense of SG outlet temp. that decreases by ~ 15oC. Due to FwTC Fw outlet temp. is const. ΔT over core decreases from 80 to ~72 ~ 50 oC. The TIT rate is ~0, except ~ -25 oC/min at the start of the transient. The tank level recovers, while condenser pressure drops from 5.4 kPa to ~ 4.6 kPa. To keep power constant the CR continues insertion after the initial sudden drop. The cond. pump slows down 1% to keep constant the cond. level. The SG press. increase is due to AttC and FwTC, which distort the flows. • In fig. 23 the el. pow ~= core pow, as the eff. almost recovered, due to adding LT ctrl. to those involved in fig. 22 . The SG lead out and core in temp. is constant, with an undershoot at the start of the transient due to LTC. The undershoot is more manifest for SG press., with an ampl. of 10 bar. An improved controller, and a better tuning could damp the undershoot. The HPT press. is constant, while SG press. rises by ~ 1 bar. The flows decrease significantly both at SG I & O. Due to attemp. TIT is ~unchanged. The SG O temp. decreases by ~2 oC. Due to FwTC, sec. fw. outlet temp. = constant. ΔT over core decrease from 80 to ~72 ~ 50 oC. The TIT rate is ~0, except ~ -25 oC/min at the start of the transient. Tk level recovers, while cond. press. drops from 5.4 kPa to ~ 4.6 kPa. To keep power constant CRs continue insertion after the initial sudden drop. The cond. pump slows down 2% to keep const. the cond. level, while the Fw pump slows down by 1% to decrease fw. flow to keep SG lead outlet temp. const.

36. Fig. 22. A-mode. -30 MW step decr. of core power. PowC, AttC, FwTC and HPTC

37. Fig. 23. A-mode. -30 MW step decr. of core power. PowC, LTC, AttC, FWTC and HPTC

38. The stepback before emphasizes the combined effect of various controls, but it is not usual for alternate mode. Slow ramps are used to adjust the powers, as could be seen in fig. 24, where SG press. and temp., HPT inlet temp. variations are small, and the cold leg lead temp. is constant. • In fig. 25 a succession of ramps with different slopes and “hold power” commands brings the reactor to 1% FP, and then brings it close to 100% FB, continuing with a small slope until FP, then holding it at steady-state. The attemp. and SG lead O temp. controllers are active enabling moderate variations of TIT and HPT pressure, while SG press. and temp. vary moderately due to higher CR insertion rates. ΔT over core =~0 1% FP, and the HPT flow has a small negative value at that power. Because TIT and lead temp. ctrls are imposed, the powers keep close, while the cold leg lead temp. does not vary. • The alternate mode being used during startup for raising the reactor power to the nominal value, the ascending ramp illustrates that operation. As in the case above, the flows and steam pressures have slight variation, while steam and lead temperatures have large variations. Non-linearity may influence the results, although pressure and temperature variations are moderate.

39. Fig. 24. Alternate mode. 100-280-105% AttC+LTC

40. Fig. 25. Alternate mode. 100-1-100-90% AttC+LTC

41. INR Pitesti 4. Conclusions • Simulation results indicate that simultaneous control of SG pressure, cold leg lead temperature and turbine inlet temperature is possible both in normal and alternate mode using control rods, feedwater flow and turbine valve, bypass valve, attemperator and feedwater outlet temperature control. • The simulations suggest that automatic control down to 30% FP could be effective.

42. INR Pitesti References • [1] Laurentiu Aioanei, Dumitru Dobrea: Simulations of Coupled Core and Steam Generator Circuit Dynamics (Contribution to Task 4.4: “Preliminary definition of the Control Architecture” Status Report), INR, Pitesti, October 20, 2011 • [2] Laurentiu Aioanei, Dumitru Dobrea: Simulations of Coupled Core, Steam Generator and Secondary Circuit Dynamics (Contribution to Task 4.4: “Preliminary definition of the Control Architecture” Status Report), INR, Pitesti, May 07, 2012 • [3] Niels Larsen: Simulation Model of a PWR Plant, RISO-M-2640, March, 1987 • [4] A. Campedrer, F. Fineschi: Normal, transient and accidental operational modes: control and protection functions identification, DEL014/2011