CHAPTER 3 MODELING OF DEAERATOR AND SIMULATION OF FAULTS

Transcription

1 27 CHAPTER 3 MODELING OF DEAERATOR AND SIMULATION OF FAULTS 3.1 INTRODUCTION Modeling plays an important role in the prediction and assessment of plant performance. There are two ways of getting the model for any plant i.e., theoretical model established by physical principles and behaviour model derived from input and output data of the plant. This chapter deals with simulation of the deaerator using mathematical model. An analytical model for the deaerator is obtained in the state space form based on fundamental physical laws. The model is linearised around the operating point and the possible faults are simulated by varying the system parameters using the linearised differential equations. The mathematical model is validated by the parameters obtained through RLS technique from the real time data obtained from the plant under normal operating conditions. 3.2 OPERATION OF DEAERATOR Modern power plants are operated at high pressure and temperatures. The presence of oxygen in dissolved form in feed water results in harmful corrosive attack. Of the many measures adopted to contain corrosion in boilers and associated plant, removal of oxygen from feed water

2 28 is the most important one. This removal of air or deaeration is done by incorporating a deaerating unit in the feed system. In addition to the function deaeration, the deaerator also serves for the following purposes. The deaerator functions as a surge tank of feed water capable of meeting the variable demands of the plant. The deaerator also forms part of the regenerative heating system improving the temperature of condensate and It also acts as a heat conversion unit. The deaerator consists of a vertical deaerating tower and a horizontal deaerating water storage tank as shown in Figure 3.1. The tower is connected to the storage tank through two balance pipes. A safety valve is provided at the top of the tower. In order to avoid buckling of tower due to any possible vacuum, a vacuum breaker is also provided at the top. The operation of the deaerator is based on the fact that the solubility of gases in defined mass of liquid is inversely proportional to the temperature of the liquid. Thus if water is heated up to the saturation temperature and kept at this temperature for a sufficient time, all gases present therein can be removed and vented to the atmosphere due to their reduced solubility. In order to increase the deaerating efficiency, water is broken up into small droplets through spray nozzles and perforated trays. There are four perforated trays in the deaerating tower. The water enters the tower at the top and gets divided into small droplets by means of spray nozzles. Then it is distributed uniformly over the trays. The steam extracted from the turbine is given out from the bottom of the tower.

3 29 The deaerator is operated in the variable pressure mode. The pressure in the deaerator is varied according to the operating status of the turbine. Fourth extraction steam, the normal source, is feeding the steam to deaerator at a pressure which is varying along with operating load on the turbine. Since the load on the turbine is getting varied during normal operation of the unit, the operating pressure of the deaerator will also vary and it is maintained by pressure PID controller. The water level in the deaerator storage tank is maintained by regulating the make up water flow. The actual level is sensed by a level transmitter and the deviation is fed to the level PI controller. Thus the deaerator always responds to any change in operating conditions. For any increase in incoming main water flow, there will be a corresponding increase in the steam demand. For any decrease in incoming main water temperature also, there will be a corresponding increase in the steam demand. For any increase in steam pressure, there will be an increase in the deaerator water temperature till the saturation temperature is reached. 3.3 MATHEMATICAL MODELING The deaerator in general is a second order multivariable nonlinear system. The model is developed in state space form based on the differential equation considered by Abdennour et al (1993). The state variables considered are pressure and enthalpy, the output variables are pressure and water level and the manipulated variables are water valve and steam valve positions.

4 30 SP Setpoint PC Pressure Controller LT Level Transmitter PS Level Controller PT Pressure Transmitter Figure 3.1 Schematic diagram of a deaerator The state space representation of the deaerator model is given by X k+1 = AX(k) + BU(k) (3.1) Y k = CX k + DU k (3.2) where X, U and Y are state, control and output vectors, respectively. In order to obtain the state space model for the system, X(k) as 2 1 state vector, U(k) as 2 1 input vector and Y(k) as 2 1 output vector are defined. k x1 k p X k = = x 2 h (3.3)

5 31 T U k = y y (3.4) c s Y k = p L T (3.5) The real time plant data obtained from 110 Atm deaerator supplied by M/s Thermax Pune for Madras Fertilizers Limited, Chennai is used for obtaining the model shown in Figure 3.2. The nominal values of the variables of the deaerator are p = 1.2kg/cm 2, h = 277kJ/kg, y c = % open, y s = % open, and L = 1.62m. The water valve is normally in a closed condition and in Figure 3.2 it represents the percentage of opening. The steam valve is normally of open type and in Figure 3.2 it represents the percentage of closure. The height of the deaerator tank is 2m and in Figure 3.2 it is represented in terms of percentage. Figure 3.2 Real time plant data 1 1 p: pressure (kg/cm 2 ), L: level (in %), h: enthalpy (kj/kg), y s : steam valve position (% of closure), y c : water valve position (% of opening)

6 PARAMETER ESTIMATION USING RLS TECHNIQUE In this section, the system identification technique is used for developing an alternative model for the deaerator. The RLS method is used for parameter estimation. The multivariable discrete data system is described by X k = A Xk -1 + B Uk -1 n 1 n nn nn mm 1 (3.6) The problem of identifying the matrices A and B of the system from knowledge of the sequence X() and U()was taken as a type of adaptive identification problem. The following notations are used for obtaining RLS model. ψ A B (3.7) ˆ ˆ ψ k A k B k (3.8) Y T k X T k U T k (3.9) X k = ψ k Y k-1 (3.10) X k = ψˆ ky k-1 ek = X k-x k (3.11) (3.12) Thus the algorithm ˆ T kpk T e k+1 Y ψˆ k+1 = ψ k + (3.13) 1+Y k P k Y k gives a stable estimate of the sequence ψ() for ψ, where the symmetric positive definite matrix P = 1. The stability of the scheme is provided by

7 33 Janakiraman et al (1981). Thus the recursive parameter estimation algorithm for the deaerator is formulated in which the new estimate is given by the old estimate plus a correction term based on the error e(k+1), P(k) and the observation vector Y(k). Figure 3.3 shows the block diagram of the generalised RLS. The computational algorithm comprises the following steps (Renganathan 2003). Figure 3.3 Block diagram representation of RLS technique 1. Set initial values at time index k = 0, ψ (k) = 0, P (k) = α I, where α is a large number and I is the identity matrix. 2. Obtain measurement Y(k). 3. Estimate state vector X(k-1) = ψ(k) Y(k) 4. Compute error in state estimate e(k+1) = X(k+1) - X(k+1) 5. Perform recursive parameter estimation e k+1 Y ψˆ k+1 = ψˆ k + 1+Y T kpk T k P k Y k 6. Compute covariance matrix of error in estimate recursively

8 34 P k+1 = P k T kp k T 1+Y kp ky k P k Y k Y 7. Continue from step 2 for next sampling instant k =1. The same procedure is used for obtaining C matrix. The parameters matrices A, B, C are obtained by RLS technique and its convergence plot is shown in Figure 3.4 for a given operating condition. The results are given in Equations (3.14) and (3.15). x 1(k+1) 5.611e e-03 x 1(k) e e-03 u 1(k) x 2(k+1) e e-01 x 2(k) e e-01 u 2(k) (3.14) y 1(k) e e-005 x 1(k) y (k) e e-005 x (k) 2 2 (3.15) From Equations (3.14) and (3.15) it is inferred that the obtained parameters of the state matrix for the deaerator model indicate instability. Hence, a state feedback control system based on the pole placement technique is employed to make the system open loop-stable. The closed loop poles of the system using pole placement controller are {0, -0.5}. The K-state feed back gain matrix is obtained as K (3.16) The control input U(k) of the pole placement controller is U(k) = - K X(k) (3.17)

9 35 The control system performance of the deaerator is obtained using Matlab / Simulink package with change in setpoint and load disturbance. A PID controller with K P = 0.795, T i = 1.75, T d = is used for the pressure control loop and a PI controller with K P = 0.6 and T i = 3 is employed for the level control loop. The block diagrams of two control loops are shown in Figure 3.5. Figure 3.4 Parameter estimation using RLS technique The variations of deaerator output such as pressure and level are plotted in Figure 3.6a and 3.6b for a positive and negative step change in level and pressure respectively introduced at 2500 th instant. It is evident that the controllers are able to track the changes.

10 36 Figure 3.5 Block diagram representation of deaerator control loops Figure 3.6a System output for 10% positive and negative step change in level setpoint Figure 3.6b System output for 10% positive and negative step change in pressure setpoint

11 SIMULATION OF FAULTS Introduction The introduction of fault in a real healthy system may not be acceptable. But the same fault can be easily simulated in a simulation environment. The possible faults in the deaerator are simulated using a linearised mathematical model. The occurrence of fault will alter the parameters of the system namely A, B and C. Since A and B parameters are affected more than C parameter, the variations in A and B parameters are considered for fault diagnosis. The simulation of fault in deaerator is carried out through the following steps: i. a fault and its magnitude is specified, ii. iii. iv. the effect of this fault on the process variables is determined, the variations in A and B parameters for the above fault is obtained using the linearised mathematical model (discussed in 3.5.2) with the changed process variables, and the specified fault is simulated by using A B parameters as determined above. The model obtained by the RLS technique using the real time data cannot be used to find the change in A and B parameters for different faults, as the introduction of the faults in real system is not feasible. Hence, efforts are made to obtain a mathematical model using fundamental laws and the model is then employed to simulate fault.

12 Linearised mathematical model An analytical model proposed by Abdennour (1993) for the deaerator is considered for fault simulation in state space form. As the introduction of faults in the nonlinear model is very difficult, the model is linearised around the operating point and then used for fault simulation. The analytical model is given by Equations (3.18) and (3.19). h = 1 w e - w l ρ p ρ 3600v t p h (3.18) where p = p (w - w ) + h - w h - w h ρ h ρ ρ p v t + ρ 778 h e l e e l l (3.19) w e = w c +w s w = c ρ p - p c qc c c 19 w s = cv ρ s s ps - p 30 c = qc c = Y c s c c 2 2 vc pc 3 vs s v max c = Y c c 3 vc c v max

13 39 The variables are defined as follows p: Pressure (kg/cm 2 ), w: flow rate (T/hr), h: enthalpy (kj/kg), L: level (m), y: valve position (in %), : bulk density over the entire vessel(kg/m 3 ), w e : flow rate entering feed water + steam (T/hr), w l : flow rate leaving (T/hr), h e : enthalpy of fluid entering the vessel (kj/kg), h f : enthalpy of fluid leaving the vessel (kj/kg), v t : total volume of deaerating and storage tank (m 3 ), c v : valve conduction, c p : pipe conduction. The subscript c stands for water and s stands for steam. The process variables in the deaerator and their nominal values are given in Table 3.1. Table 3.1 Process variables of the deaerator Sl.No. Process Variables Unit Nominal Value 1. p pressure in the deaerator kg/cm h enthalpy in the deaerator kj/kg y c water inlet valve position (opening) % y s steam valve position (opening) % w l water flow rate leaving T/hr h e enthalpy of fluid entering the vessel kj/kg c density of water in the deaerator kg/m s density of steam in the deaerator kg/m p c inlet water pressure kg/cm p s inlet steam pressure kg/cm The Equations (3.18) and (3.19) are linearised around the equilibrium point (setpoint) as the same values considered in the real time system. The linearisation depends on five variables namely, pressure, enthalpy, feed water level, water valve position and steam valve position. The

14 40 linearised differential equations that govern the operation of deaerator are expressed in Equations (3.20) and (3.21). w 0.01 ρ p 0.1 ρ p ρ p c c s c s s l p = - p + h e yc-h e ys 3600 vt 3600 vt 3600 vt (3.20) 2 w 0.02 ρ p 0.2 ρ p ρ p h = - h + h y -h y 3600 v 3600 v 3600 v c c s c s s l e c e s t t t (3.21) By substituting the steady state values in Equations (3.22) and (3.23) the state model is obtained as follows: x 1(k+1) e-03 0 x 1(k) e e-04 u 1(k) x (k+1) e-03 0 x (k) e e-04 u (k) (3.22) y 1(k) e e-005 x 1(k) y (k) e e-005 x (k) 2 2 (3.23) In general, the dynamics of the system is influenced in a larger measure by the state matrix (A) and input matrix (B). Hence, for simulation, the output matrix (C) for the mathematical model is considered from the estimated model. The variations of deaerator output such as pressure and level are plotted in Figure 3.7a and 3.7b for a positive and negative step change in level and pressure respectively introduced at 2500 th instant. It is evident that the controllers are able to track the changes.

15 41 Figure 3.7a System output for 10% positive and negative step change in level setpoint in linearised model Figure 3.7b System output for 10% positive and negative step change in pressure setpoint in linearised model By comparing the deaerator responses plotted in Figures 3.6a and 3.6b to Figures3.7a and 3.7b respectively, it may be observed that both models (model obtained using RLS technique and analytical linearised model) give almost same output responses.

16 Simulation of faults using linearised model There are many reasons for the appearance of faults, like ageing, corrosion, wear during normal operation, wrong operation, improper maintenance and so on. They may appear suddenly with a large size or in steps with smaller size or slow like a drift. In this work the large step size fault are simulated using the Matlab / Simulink. Eight important faults that occur in the deaerator are given below: 1. Leakage in tank 2. Sedimentation deposit 3. Positive bias in the inlet water valve 4. Negative bias in the inlet water valve 5. Positive bias in the inlet steam valve 6. Negative bias in the inlet steam valve 7. Decrease in inlet water temperature and 8. Steam mixing with water in preheater. Fault 1: The simulation of fault, water leakage in the tank is shown in Figure 3.8. This is simulated by increasing the outlet flow by 10% at 2000 th instant. It can be seen from the graph that as level decreases the pressure also decreases. For example if a 11 and a 21 is increased by 10% from their nominal value and b 11, b 12, b 21, b 22 are normal, then the fault is water leakage in the tank and the magnitude of leakage is 10%. The inference is as follows. An excess of outlet flow in the outlet pipe from its nominal value can be assumed as leakage in the tank. Equations (3.20) and (3.21) are used to obtain the

17 43 modified values of plant parameters (a 11, a 21, b 11, b 12, b 21, b 22 ) due to 10% increase in output flow rate. The change in plant parameters thus determined is +10% for a 11 and a 21 and 0% for b 11, b 12, b 21 and b 22. Fault 2: A decrease in outflow is the result of the sedimentation deposit in the water outlet pipe. This is simulated by decreasing the outlet flow by 10% at 3500 th instant. It can be seen from the graph that as level increases the pressure also increases. The fault is represented in Figure 3.8. For example, if a 11 and a 21 is decreased by 10% from their nominal value and b 11, b 12, b 21, b 22 are normal then the fault is sedimentation deposit and the magnitude of leakage is 10%. This inference is as follows. When sedimentation gets deposited in the outlet water pipe, the water outlet flow gets reduced by 10%. Equations (3.20) and (3.21) are used to obtain the modified values of plant parameters (a 11, a 21, b 11, b 12, b 21, b 22 ) due to 10% increase in output flow rate. The change in plant parameters thus determined is -10% for a 11 and a 21 and 0% for b 11, b 12, b 21 and b 22. Similarly, the outflow is assumed as 99% to 90% of normal flow when the fault sedimentation deposit has a severity of 1% to 10%. Thus the change in A and B parameters for the faults with severity of 1% to 10% is determined. Fault 3 and 4: The inlet water valve to the deaerator is normally of closed type. The positive and negative bias in the inlet water valve will cause an increase and decrease in flow rate respectively. The negative bias to the valve is introduced by increasing the upstream pressure, the pressure upstream to the water inlet valve, and the positive bias is simulated by decreasing the same. The positive bias is simulated at 2000 th instant, which causes an increase in level and pressure in the deaerator. The negative bias will create a decrease in flow rate, which will cause a decrease in level and pressure in the deaerator, which is simulated at 3500 th instant. Both the faults are represented in Figure 3.9 and the severity of the faults is 10%.

18 44 Fault 5 and 6: The inlet steam valve to the deaerator is normally of open type. The positive and negative bias in the inlet steam valve will cause an increase and decrease in flow rate respectively. The negative bias to the valve is introduced by increasing the upsteam pressure by 10% at 2000 th instant, the pressure upstream to the steam inlet valve, and the positive bias is simulated by decreasing the steam pressure by 10% at 3500 th instant. Both the faults are represented in Figure Fault 7: The decrease in temperature of the inlet water to the deaerator is represented by decreasing the enthalpy of inlet water by 10% at 3500 th instant. The response is given in Figure Fault 8: The mixing of steam with water in the preheater will increase the temperature of the inlet water. This causes an increase in pressure and level in the deaerator tank. The simulation is done, by increasing the enthalpy of the inlet water by 10% at 2000 th instant. The response is shown in Figure 3.11.

19 45 (a) (b) Figure 3.8 Simulation of tank leakage and sedimentation deposit by increasing/decreasing the outflow (a) pressure variation (b) level variation

20 46 (a) (b) Figure 3.9 Simulation of positive and negative bias of inlet water valve by increasing/decreasing upstream water pressure (a) pressure variation (b) level variation

21 47 (a) (b) Figure 3.10 Simulation of positive and negative bias of inlet steam valve by decreasing/increasing upstream steam pressure (a) pressure variation (b) level variation

22 48 (a) (b) Figure 3.11 Simulation of steam mixing with water in preheater and decrease in inlet water temperature by increasing/ decreasing the temperature of the inlet water (a) pressure variation (b) level variation

23 49 The values of A and B parameters for the fault leakage in tank of severity ranging from 0% to 10% in steps of 1% are given in Table 3.2. Similarly the changes in A and B parameters for the other seven faults with severity ranging from 1% to 10% in steps of 1% is also determined. The parameters values are given in Table 3.3 to Table 3.9. The ranges for the occurrence of double fault are a11 [ ], a12 [0 0], a21 [ ], a22 [0 0], b11 [ ], b12 [ ], b21 [ ] and b22 [ ]. 3.6 PARAMETER IDENTIFICATION USING ANN In this section an attempt is made to use a single layer neural network for identifying the parameters of the linear deaerator system. The RLS algorithms have been used to train the single layer back propagation linear neural network. Given a training set of input-output pair which defines a function, such a network is considered to learn the function. The learning process involves the determination of the weights, which is nothing but the parameters of the system.

24 Table 3.2 Values of A and B parameters for the fault leakage in tank Sl. No. Severity of fault a 11 a 21 b 11 b 12 b 21 b % E E E E E E % E E E E E E % E E E E E E % E E E E E E % E E E E E E % E E E E E E % E E E E E E % E E E E E E % E E E E E E % E E E E E E % E E E E E E-04 50

25 Table 3.3 Values of A and B parameters for the fault sedimentation deposit Sl. No. Severity of fault a 11 a 21 b 11 b 12 b 21 b % E E E E E E % E E E E E E % E E E E E E % E E E E E E % E E E E E E % E E E E E E % E E E E E E % E E E E E E % E E E E E E % E E E E E E-04 51

26 Table 3.4 Values of A and B parameters for the fault positive bias in water valve Sl. No. Severity of fault a 11 a 21 b 11 b 12 b 21 b % E E E E E E % E E E E E E % E E E E E E % E E E E E E % E E E E E E % E E E E E E % E E E E E E % E E E E E E % E E E E E E % E E E E E E-04 52

27 Table 3.5 Values of A and B parameters for the fault negative bias in water valve Sl. No. Severity of fault a 11 a 21 b 11 b 12 b 21 b % E E E E E E % E E E E E E % E E E E E E % E E E E E E % E E E E E E % E E E E E E % E E E E E E % E E E E E E % E E E E E E % E E E E E E-04 53

28 Table 3.6 Values of A and B parameters for the fault positive bias in steam valve Sl. No. Severity of fault a 11 a 21 b 11 b 12 b 21 b % E E E E E E % E E E E E E % E E E E E E % E E E E E E % E E E E E E % E E E E E E % E E E E E E % E E E E E E % E E E E E E % E E E E E E-04 54

29 Table 3.7 Values of A and B parameters for the fault negative bias in steam valve Sl. No. Severity of fault a 11 a 21 b 11 b 12 b 21 b % E E E E E E % E E E E E E % E E E E E E % E E E E E E % E E E E E E % E E E E E E % E E E E E E % E E E E E E % E E E E E E % E E E E E E-04 55

30 Table 3.8 Values of A and B parameters for the fault decrease in inlet water temperature Sl. No. Severity of fault a 11 a 21 b 11 b 12 b 21 b % E E E E E E % E E E E E E % E E E E E E % E E E E E E % E E E E E E % E E E E E E % E E E E E E % E E E E E E % E E E E E E % E E E E E E-04 56

31 Table 3.9 Values of A and B parameters for the fault steam mixing with water in preheater Sl. No. Severity of fault a 11 a 21 b 11 b 12 b 21 b % E E E E E E % E E E E E E % E E E E E E % E E E E E E % E E E E E E % E E E E E E % E E E E E E % E E E E E E % E E E E E E % E E E E E E-04 57

32 Architecture of the neural network A single layer neural network used to identify the parameters of the deaerator is shown in Figure The learning process involves the determination of the weights which directly indicate the parameters of the system. The number of input neurons is equal to the number of input and state variables and the number of output neurons is equal to the number of predicted states. In the deaerator, there are four inputs namely enthalpy, pressure, steam valve position and water valve position and the two output variables are the predicted state variables. The weight associated with each neuron represents the adaptable weight corresponding to one of the system parameters to be estimated (say a 11 ). The estimation algorithm trains the network weights with sequential updates. Whenever the parameters of the deaerator changes, it is reflected as an error in the predicted state variable value ˆX k+1. The predicted value of state variable ˆX k and actual value of state variable X k+1 are different and this difference is utilised by the algorithm to change the weights (parameters) till convergence take place. The neural network thus trained with a set of data corresponding to normal and fault conditions gets converged and the parameters thus obtained are used for detecting the faults by different types of neural network. The activation function purelin is used for this neural network. The computer used for this work is pentium IV intel 3.4 GHz CPU. And 504MB RAM. A sampling period of once again has been used in all the computer wok (and graphs) reported in this thesis.

33 59 Figure 3.12 Single layer neural network used for parameter estimation Fault simulation by single layer neural network Fault simulation essentially means introduction of fault (by varying the appropriate system parameters) through a simulated process. This exercise is required in order to carry out fault diagnosis in the simulated deaerator. The changes of the system parameters (A and B) due to occurrence of eight faults have been determined using the linear model of deaerator (section 3.5.2). These changes are effected (one set of changes at a given time) in the single layer neural network, which is equivalent to introducing a fault and this is termed as fault simulation. For example, various steps involved in the simulation of fault, leakage in tank are given below: i. The values of A and B parameters during fault leakage in tank are noted down

34 60 ii. iii. iv. The fault is introduced (Matlab program) by effecting the changes in system parameters at the 500 th sampling instant in the Equations (3.20) and (3.21) The input and state variables which are continuously fed to the single layer neural network are subjected to changes at the 500 th sampling instant (after the introduction of the fault). These changes lead to the changes of the weights of the neural network (which are nothing but the system parameters). The steady state values of the parameters as determined by the single layer neural network is then fed to the next stage for fault diagnosis. v. The above fault is with drawn at 750 th sampling instant and another fault sedimentation deposit is introduced from 1000 th to 1250 th sampling instant. Figure 3.13 gives the variation of system parameters as determined by single layer neural network due to the introduction of above two faults. vi. Similarly the simulation for two faults positive bias in water valve (from 500 th to 750 th ) and negative bias in water valve (from1000 th to 1250 th ) are illustrated in Figure Figure 3.15 illustrate the fault simulation for the faults positive bias in steam valve and negative bias in steam valve. Figure 3.16 illustrate the fault steam mixing with water in preheater and decrease in inlet water temperature.

35 61 Figure 3.13 Simulation of faults leakage in tank and sedimentation deposit (variation in a 11 and a 21 ) Figure 3.14 Simulation of faults positive bias in water valve and negative bias in water valve (variation in b 12, b 21 and b 22 )

36 62 Figure 3.15 Simulation of faults positive bias in steam valve and negative bias in steam valve (variation in b 12 and b 22 ) Figure 3.16 Simulation of faults steam mixing with water in preheater and decrease in inlet water temperature (variation in b 11, b 12, b 21 and b 22 )

37 SUMMARY This chapter describes the procedure used for identifying the parameters of the deaerator plant using RLS algorithm utilising the plant data. The method described is recursive in nature and suitable for both on-line and off-line implementation. As the model is unstable it was stabilized using pole placement technique. As the simulation of fault using RLS model is not feasible, a linearised mathematical model using fundamental laws was developed. A PI controller is used for level loop and PID controller is used for pressure loop. The closed-loop responses obtained with both models are almost same. Eight different faults are simulated (in closed-loop conditions) by varying A and B parameters of the deaerator and the responses during faulty conditions are also plotted. It is lasso observed that the ANN takes about 200s for estimating parameters (weights) initially. Any further change in parameter (due to fault) in estimated in a very short time, ie. 1s.