Arab Journal of Nuclear Science and Applications, 94 (2), (85-98) 216 Design and Implementation of a Fuzzy Logic ontroller for the Pressurized Water Power Reactor ontrol S.A. Kotb 1 M.M. Metwally 2, and K.M. Rady 2 1 ETRR2, Atomic Energy Authority, airo, Egypt 2 Faculty of Engineering, airo University, airo, Egypt Received: 25/5/215 Accepted: 1/9/215 ABSTRAT The pressurized water reactor type power plant has a sophisticated automatic control systems. On the primary side, The ontrol rod system and the Soluble boron control the core neutron flux. On the secondary side, output steam is controlled by the turbine control valve and steam dump system. During the automatic control mode, the two sides work in a synchronized way so that transition to stabilized conditions will be achieved smoothly. This paper presents a detailed nuclear power model for the medium-term and long-term power system stability. This model can be used to analyze the difference transient fault on electrical grid. Also this work introduces the effect of utilizing the Fuzzy logic control methodology in the power control model of the PWR (pressurized water reactor). The fuzzy logic controller was tested on a PWR model using the Matlab Simulink Interface. Two case studies were performed on the model using both the fuzzy logic method and the traditional rod speed program for controlling the nuclear power plant variables. The proposed controller presented a higher performance than that of the traditional rod speed program controller. Key Words: Power system; Fuzzy Logic, Nuclear Power Plant Model INTRODUTION The power and temperature of a nuclear reactor should be properly controlled in order to maintain the performance of the reactor s operating conditions as well as to maximize the thermal efficiency of an entire nuclear power plant. However, power plants are highly complex, nonlinear, time-varying, and constrained systems. If a load-following operation is desired, the daily load cycles can change plant performance significantly. Advanced power tracking control of nuclear reactors has not been accepted mainly due to the safety concerns stemming from imprecise knowledge about the time-varying parameters, nonlinearity, and modeling uncertainty. However, rapid and smooth power maneuvering has its benefits in view of the economical and safe operation of reactors and the importance of a load-following strategy (1-4). Modern nuclear power plants should respond to the load demand on the power grid, which demand high plant operation performance, subject to various kinds of constraints. Meanwhile, nuclear safety and radioactive pollution prevention have long been much concerned problems. One of the early works on power control in nuclear reactors presented a water level controller in a PWR steam generator (5). In 1998, a nuclear power reactor fuzzy controller simulator using Matlab was developed (6). An analysis of the safety aspects of fuzzy controller implementation in nuclear reactors was reported in 2 (7,8). Also in this work, the results of a comparison study between a classical rod speed program and a fuzzy logic controller applied to nuclear reactors were presented (9). Subsequent work has been done evaluating the strengths and weaknesses of fuzzy controllers applied to nuclear reactors (1). Most of the work on power control of nuclear reactors using fuzzy logic shows, through computer simulations, the feasibility of its implementation (11,12). In this paper, a detailed nuclear power plant model is proposed. In this model, the steam turbine model is simplified, while the coolant pump model. Fuzzy logic and conventional rod speed program for the reactor power control system are included. Then a user-defined program of Matlab Simulink Interface modeling the nuclear power plant is implemented. The program can revise 58
Arab Journal of Nuclear Science and Applications, 94 (2), (85-98) 216 and debug very easily, for the user only need to modify the Matlab transfer function diagram of certain modules if needed. Based on this program, the response of nuclear power plant to the disturbance of power grid is simulated. Modeling the Nuclear Power Plant System The nuclear power plant system is very complicated. Factors that have close relationship with the power system should be kept, while the others should be ignored or simplified. In this paper, a detailed nuclear machine model is proposed. It includes the reactor neutron dynamics model, reactor thermal dynamics model, steam generator dynamics model, reactor power system model and coolant pump integrated parameter model (13). The model is relatively simple and fit for power system stability analysis. The diagram of the proposed detailed model is shown in Fig. (1). Thermal output dynamic model T Hot leg temperature model THL Steam generator model Turbine control system model w N TL ext Ps Turbine model PM Reactor control model PM Ps Neutron dynamics model Frist loop average temperature model TL old leg temperature model oolant pump model Fig (1) The diagram of the nuclear power plant model Reactivity and ore Kinetics The reactor neutron dynamic behavior is modeled by a group of equivalent delayed neutrons (13). The equations of neutron dynamic behavior are as follows d n(t) dt d (t) dt = ρ (t) l β l n(t) + = β l n(t) (t) (1) (t) (2) ρ = β ρ ext + α f T f + α c ( T θ1 T θ2 ) (3) Where: n ρ :the deviation in initial power, pu; :the reactivity deviation ρ ext : the reactivity change induced by control rod; T F : the fuel temperature deviation, c ; 58
Arab Journal of Nuclear Science and Applications, 94 (2), (85-98) 216 T θ1 : the coolant node 1 temperature deviation, c ; T θ2 : the coolant node 2 temperature deviation, c ; β : the delayed neutron group fraction; the equivalent decay constant, 1/s; α f : the fuel coefficient of reactivity, 1/c ; α c : the coolant coefficient of reactivity, 1/c. The Thermal Output Dynamics Model The thermal output dynamic model can be expressed by the first order differential equations, as is shown. dt dt f fp m F PF ha n m F ( T1 PF T F ) (4) dt dt 1 (1 f ) P n m Pc ha m Pc ( T F T 1 m ) m ( T L T 1 ) (5) dt dt 2 Where (1 f ) P n m Pc ha m Pc ( T F T 1 m ) m ( T 1 T 2 ) (6) P :the initial power level, Mw f h A :the fraction of the total power produced in the fuel :the heat transfer coefficient from fuel to coolant, w/m2.k :the heat transfer area, m2 m F :the mass of fuel, kg c :the specific heat of fuel, Kj/kg.k PF m :the mass of coolant, kg P :the specific heat of coolant, Kj/kg.k m :the mass flow rate in core, kg/s 58
Arab Journal of Nuclear Science and Applications, 94 (2), (85-98) 216 The Hot Leg and old Leg Temperature Model The hot leg and cold leg temperature model can be expressed by the first order differential equations, as: dt dt HL 1 HL ( T T 2 HL ) (7) dt dt L Where: 1 L ( T op T L ) (8) T HL : the hot leg temperature deviation, T L : the cold leg temperature deviation, T OP : the primary fluid lump temperature deviation, HL : the hot leg heat transfer time constant, s L : the cold leg heat transfer time constant, s The Reactor Rod Speed Program ontroller Reactor Power ontrol in PWR can be accomplished by ore Reactivity Regulation and Power Distribution ontrol. ore Reactivity Regulation accounts for reactivity changes due to power level changes, and transient xenon level resulting from the power level changes. It is achieved by a combination of control rod position adjustment, and boron concentration adjustment. The controls rods which perform the core reactivity regulation are reduced strength rods, known as Gray rods. They are moved up or down, when the deviation between primary power (Pav) and the reference power (Pref) obtained from the turbine load (secondary power; turbine first stage pressure), exceeds the predetermined setpoint. Power Distribution ontrol is performed to maintain the core thermal margin within operating and safety limits. Power distributions, as determined by the core neutron power axial shapes, are monitored and controlled during power maneuvers. This controller gives the reactor control rod speed. The reactor power is adjusted indirectly because this controller in fact controls the reactor average temperature, calculated as the mean value of the cold and hot leg temperature. This value is delayed and lead/lag compensated. The set point for the average temperature is calculated as a piecewise linear function of relative HP-turbine inlet pressure which is a measure of turbine power. The power mismatch signal is sent through nonlinear and variable gains. The error signal, corrected for power mismatch is transformed into control rod speed in the rod speed program as shown in Fig (2). (12) 55
Arab Journal of Nuclear Science and Applications, 94 (2), (85-98) 216 The time constant T as showing in table (1) Fig (2) Reactor rod speed program controller. Table (1) time constant of T. onstant Values sec T1 4 T2 3 T3 8 T4 5 T5 1 The error signal, corrected for power mismatch is transformed into control rod speed in the rod speed function of which the graph is shown in Fig. (3). (12) Fig (3) Rod Speed Program. 58
Arab Journal of Nuclear Science and Applications, 94 (2), (85-98) 216 The following equation is described the traditional rod speed program with function of error. Where RS: Er : R S = = 3.3115e ( 3) Er, If Er 2.8 = ((((3.315e 3 3.68e 4 ) Er (3.68e 4 2.8 3.315e 3 1.7))/(2.8 1.7)) +3.68e 4 Er If Er 2.8 = ( ( 3.315e 3 3.68e 4 ) Er 3.68e 4 2.8 3.315e 3 1.7 ) + (3.68e 4 Er) (2.8 1.7) (If Er 1.7) 4 3.68e = (3.68e 4 +.55 ) Er If (Er >.55) { Rod speed Error = (3.68e 4 3.68e 4.55 ) Er If (Er >.55) = ( ( 3.315e 3 3.68e 4 ) Er + (3.68e 4 2.8 3.315e 3 1.7) ) (2.8 1.7) (3.68e 4 Er) (If Er 1.7) = (((3.315e 3 3.68e 4 ) Er + (3.68e 4 2.8 3.315e 3 1.7))/(2.8 1.7)) 3.315e 3 ) Er If Er 2.8 Implementation of Fuzzy Logic Power ontroller Fuzzy Logic ontroller Design The fuzzy logic controller implemented in the rod speed control module is demonstrated in fig (3). The difference in the nuclear power and the turbine load which represents the load demands is transferred to temperature using a certain transfer function along with the mean temperature difference inside the reactor core, the product is a single output signal the temperature changes. The main objective in the design of the current ontroller is to achieve a control system response that resembles the output of the rod speed program function. As a result the Fuzzy Logic controller can easily replace the conventional rod speed program controller with interfering with safety features established in the reactors model safety regulations as shown in Fig (4). (9) Fig (4) Reactor rod speed program via Fuzzy Logic controller. 89
Arab Journal of Nuclear Science and Applications, 94 (2), (85-98) 216 The control module that is used in this paper will be Matlab FIS toolbox as a simplified approach for artificial intelligence. The Mamdani-type inference method will be chosen for its optimization simplicity, it is divided into four major steps: fuzzification, rule evaluation, aggregation of the rule outputs and defuzzification. Max aggregation method and entroid Defuzzification method were used since they had proved to be the most efficient methods for this model. Fuzzification for Antecedent The Antecedent Membership functions will be a Single input DeltaT temperature difference, the fuzzy set consists of five membership functions: if DeltaT is less than -1.8,a Gaussian membership functions is selected; if DeltaT is between (-2.1,-.45),a triangular membership functions is selected; if DeltaT is between (-.45,.45), a triangular membership functions is selected; if DeltaT is between (.45,2.1), a triangular membership functions is selected; if DeltaT is less than 1.8, a Gaussian membership functions is selected as shown in Fig (5)and (6). Fig. (5)The antecedent membership function. Fig (6) The consequent membership function. Fuzzification for onsequent: The onsequent Membership functions will be a Single output Rlvl ontrol rod position that would be sent to the control rod drive mechanism explained earlier, the fuzzy sets consists of five membership functions: if Rlvl is less than (-.332), a triangular membership functions is selected; if Rlvl is between (-.6,.3), a triangular membership functions is selected; if Rlvl is between (-.16,.16), a triangular membership functions is selected; if Rlvl is between (-.3,.6), a triangular membership function is selected; if Rlvl is higher than (.332), a triangular membership function is selected as shown in Fig (6). The membership function rules are show in table (2). Table (2) Rule of membership function. ondition If DeltaT is okay If (DeltaT is rt_high) If (DeltaT is high) If (DeltaT is rt_low) If (DeltaT is low) Action then (Rlvl is no_change) then (Rlvl is increase_fast), then (Rlvl is increase_slow), then (Rlvl is decrease_fast), then (Rlvl is decrease_slow). The Antecedents and the onsequents were optimized using genetic algorithm based on the surface view GUI output to resemble the initially discussed Rod speed program. 89
Arab Journal of Nuclear Science and Applications, 94 (2), (85-98) 216 Testing the NPP ontroller The model in this paper was tested on a single machine infinite bus system (Fig 7). (13) ase 1: Transient Fault on Bus 1 (NPP) Fig (7) The single unit infinite system diagram. A three-phase short circuit is applied to the generator terminal on bus 1 (Nuclear Power Plant Busbar) when t= 3 sec and cleared when t = 3.2 sec, with the line being tripped at the same time. The simulation result is shown in Fig. (8). As shown in Fig. (8, a, b, c, d, e, f, g, h), when the fault can be cleared correctly, the system can run stable and the nuclear plant can operate without dropping the unit. The change in mechanical power, change in control rod speed, change in rod distance, and change in the pressures, the change in reactor power and change in temperatures are shows in its figures. Summarizing the important variables for the results is shown in table (2). The frequency of several large central power generators is shown in Fig (8.i). learly, short circuit occurrence at its bus changes the frequency of other connected generators. They oscillate severely during the fault duration (from t = 3 to 3.2 sec). then, the oscillations start to damp from t=3.2 sec till 6 sec and goes to steady state situation which is the same as the new initial conditions. Figure (8.j) shows the change in generators rotor angle behaviour. It is accompanying to the oscillations start to damp from t = 3.2 sec till 8 sec and goes to a steady state situation which is similar to the initial conditions. Finally Figure (8.k) shows the surrounding buses voltage violations, the voltage dips to zero P.U suddenly during the fault time.2. After fault clearance, the voltage starts to recover itself..9 4 x 1-3 Pmech.8.7.6.5 2 4 6 8 1 Time in Sec Fig (8.a) Mechanical power with fault at t= 3 sec hange of Rod Speed m/s 2-2 Without FL With FL -4 2 4 6 8 1 Time in sec Fig (8.b) hange Rod Speed with fault at t= 3 sec 89
Arab Journal of Nuclear Science and Applications, 94 (2), (85-98) 216 hange Distance of Rod m.1.5 -.5 Without FL With FL -.1 2 4 6 8 1 Time in sec Fig (8.c) hange in Rod distance with fault at t= 3 sec DPp Mpa.1.5 -.5 -.1 Withot FL With FL -.15 2 4 6 8 1 Time in sec Fig (8.d) hange in pressurizer pressure with fault at t= 3sec Fig. (8) Effect the fault from 3 to 3.2 sec on bus (1) with and without FL. dp SG Mpa.1 -.1 Without FL With FL dp MWth 1 5-5 Without FL With FL -.2-1 -.3 2 4 6 8 1 Time in sec Fig. (8.e) hange in steam generator pressure with fault -15 2 4 6 8 1 Time in sec Fig. (8.f) hange in Reactor power with fault at t= 3sec dtl F.2.1 -.1 -.2 Without FL With FL dthl F.2 -.2 Without FL With FL -.3 -.4 2 4 6 8 1 Time in sec Fig. (8.g) hange in cold-leg temperature at fault at t=3 sec -.4 2 4 6 8 1 Time in sec Fig. (8.h) hange in Hot-leg temper at fault at t= 3 sec 89
Arab Journal of Nuclear Science and Applications, 94 (2), (85-98) 216 Rotor Angle ( Degree) 1 8 6 4 Gen1 2 2 4 6 8 1 time in Sec Fig. (8.i) hange in rotor angle at fault at t=3 sec hange in Frequency Hz.15.1.5 -.5 Gen 1 -.1 2 4 6 8 1 Time Sec Fig. (8.g) hange in frequency at fault at t=3 sec 1.5 Bus 1 voltage pu 1.5 2 4 Time Sec 6 8 1 Fig. (8.k) hange voltage bus at fault at t=3 sec Fig (8) Effect the fault from 3 to 3.2 sec on bus (1) with and without FL cont. Table (2) summarizing the important variables for the results. a se ase I ( Transient Fault ) Variables Important data Proposed ontroller onventional ontroller Pressurizer pressure Steam pressure Reactor power Hot leg temperature cold leg temperature Max Overshoot.83.6 Max Undershoot -.86 -.146 Settling time 7.4 7.55 Max Overshoot.64.51 Max Undershoot -.12 -.2 Settling time 9.5 9.5 Max Overshoot 77.8 77.8 Max Undershoot -64.91-113.5 Settling time 7.8 7.8 Max Overshoot.19.7 Max Undershoot -.28 -.47 Settling time 8.5 8.5 Max Overshoot.12.8 Max Undershoot -.2 -.34 Settling time 8.84 8.84 89
Arab Journal of Nuclear Science and Applications, 94 (2), (85-98) 216 ase 2 Total Load Rejection A loss of load is a 1% load rejection, that is, the entire external load connected to the power station is suddenly lost, or the breaker at the station s generator output is opened. Under this severe condition, it may still be possible to island the NPP so that it powers only its own auxiliary systems. During this house-load operating mode, the reactor operates at a reduced power level that is still sufficient to assure enough electricity for its own needs, typically 5% of full power. Once the grid disturbance has been eliminated, the NPP can be re-synchronized to the grid and its production quickly raised again to full power. This operational characteristic of the NPP is important when the loss of load is expected to last for just a short time. (14) A three-phase short circuit is applied to the generator terminal on bus 2 (Nuclear Power Plant Busbar) when t= 3 sec and the protection system was not able to clear this fault. Hence, this caused a total load rejection from infinite bus system and the NPP only operates on the domestic loads (5% of its total power). (14,15,16) As shown from Fig. (9), The sudden outage of the nominal load caused an over speed in the generator, triggering the generators governor to lockout the steam valves that drives the mechanical power for the steam turbine for the generators over-speed protection. Hence, the mechanical power suffers a decay Fig. (9.a), since the residual heat still exist the control rod system is triggered for changing the rods speed Fig. (9.b) and distance Fig. (9.c), thus changes the pressures Fig. (9:d,e), the reactor power Fig. (9.f) and temperatures Fig. (9:g, h), The results were achieved using both the conventional Rod ontroller and the Fuzzy logic controller for comparison. Summarizing the important variables for the results as shown in table (3). An outage of the NPP will cause a substantial loss of generation of both MW and Mvar for the grid. Figure (9.i,j) shows the bus frequency, and generator rotor angle are loss after outage of the nuclear power plant at 3 sec. also figure (9.k) show the voltage terminal in bus 1 is zero after 3 sec. Mechanical Power Pu.8 Gen 1.6.4.2 2 Time 4 Sec 6 8 1 Fig (9.a) Mechanical power with fault at t= 3 sec hange in Rod Speed m/s 4 x 1 3 2 1-1 -2-3 hange in Speed of ontrol Rod W/ fuzzylogic ctrlr W/ LASSI ctrlr -4 1 2 3 4 5 6 7 8 9 1 time in sec Fig (9.b) hange Rod Speed with fault at t= 3 sec.1 hange in Distance of Rod m W/ fuzzylogic ctrlr W/ LASSI ctrlr.2.15 Pressurizer Pressure W/ fuzzylogic ctrlr W/ LASSI ctrlr.1 Distance in m -.1 DPp Mpa.5 -.5 -.1 -.15 -.2 -.25 -.2 1 2 3 4 5 6 7 8 9 1 time in sec Fig. (9.c) hange in Rod distance with fault at t= 3 sec 1 2 3 4 5 6 7 8 9 1 time in sec Fig. (9.d) hange in pressurizer pressure with fault at t= 3sec 88
Arab Journal of Nuclear Science and Applications, 94 (2), (85-98) 216.2.1 -.1 hange in Steam Generation Pressure. W/ fuzzylogic ctrlr W/ LASSI ctrlr 8 6 4 2 W/ fuzzylogic ctrlr W/ LASSI ctrlr dps Mpa -.2 -.3 -.4 dp in MWth -2-4 -6 -.5 -.6-8 -1-12 -.7-14 -.8 1 2 3 4 5 6 7 8 9 1 time in sec Fig. (8.e) hange in steam generator pressure with fault.2 W/ fuzzylogic ctrlr W/ LASSI ctrlr 1 2 3 4 5 6 7 8 9 1 time in sec Fig. (8.f) hange in Reactor power with fault at t= 3 sec.2 W/ fuzzylogic ctrlr W/ LASSI ctrlr -.2 -.2 dthl in F -.4 -.6 -.8 dtl in F -.4 -.6 -.8 -.1 -.1 -.12 1 2 3 4 5 6 7 8 9 1 time in sec Fig. (9.g) hange in Hot-leg temper with fault at t= 3 sec Rotor Angle (Degree) 15 1 5 Gen 1 1 2 3 4 5 6 7 8 9 1 time Sec Fig. (9.i) rotor angle with fault at t= 3sec -.12 1 2 3 4 5 6 7 8 9 1 time in sec Fig. (9.h) hange in cold-leg temperature with fault at t= 3sec hange in Frequency.2.15.1.5 1 2 3 4 5 6 7 8 9 1 Time Sec Fig. (9.j) hange in frequency with fault at t= 3sec 1 Bus Voltage Pu.8.6.4.2 1 2 3 4 5 6 7 8 9 1 Time Sec Fig. (9.h) hange in bus voltage with fault at t= 3sec Fig. (9) Effect the fault from 3 and outage Genenerator on bus (1). 88
Arab Journal of Nuclear Science and Applications, 94 (2), (85-98) 216 Table (3) Important variables for the results. ase Variables Important data With FL Without FL ase I ( Total load loss ) Pressurizer pressure Steam pressure Reactor power Hot leg temperature cold leg temperature Max Overshoot N/A N/A Max Undershoot -.23 Mpa -.29 Settling time 9.41 Sec 9.41 Max Overshoot N/A N/A Max Undershoot N/A -.29 Settling time 7.63 9.59 Max Overshoot N/A -23.6 Max Undershoot -53.7-135.6 Settling time 6 6.5 Max Overshoot N/A N/A Max Undershoot -.11 -.13 Settling time 5.4 7.31 Max Overshoot N/A N/A Max Undershoot -.15 -.117 Settling time 5.6 6.96 ONLUSION This paper presented an approach for designing a robust power controller, based upon fuzzy logic methodology. It aimed to control, track and regulate the power of a pressurized water reactor type nuclear power plant. The consequents of the fuzzy logic controller were based upon the data of the rod speed program approved by the IAEA. The proposed and the conventional rod speed program were tested on a P based dynamic detailed model for the pressurized water reactor through the Matlab/ Simulink Interface using case study on infinite bus system: transient fault and total load rejection. The fuzzy logic controller has successfully achieved an improved performance than that of the conventional rod speed program through transient and normal operation modes in the following: 1. The designed controller output showed an improved smooth transition between the different control rods level. 2. The controller output response caused an improved damping for different nuclear power plant parameters such as power, pressures and temperatures. 3. The final value of the nuclear power plant parameters seems to be more stable and the error band seems less at using the fuzzy logic controller. The only drawback of the fuzzy logic controller was the fast variation in the control rod speed. REFERENES (1) J.H. Bickel Grid Stability and Safety Issues Associated with Nuclear Power Plants, Evergreen Safety and Reliability Technologies, LL (2) T.W. Kerlin, E.M. Katz, Pressurized Water Reactor Modeling for Long-Term Power System Dynamics Simulations, EPRI Final Report EL-387.1983. (3) Zhang Xuecheng, the Pressurized Water Reactor Nuclear Power Plant Model for the Power System Dynamics Simulation, Power System Technology, no. 4, pp. 71-77, Nov 199. (4) T. Ichikawa and T. Inoue, Light Water Reactor Plant Modeling for Power System Dynamic Simulation, IEEE TRANS ON PS, vol. 3, no. 2, may, 1988. 88
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