Mathematical Modeling of Transient Processes of the Automatic Control System of Water Level in the Steam Generator

The methodology of creation of automatic control system (ACS) of water level in the steam generator is developed. The mathematical model of checking its working capacity is developed, which allows establishing the maximum deviations of water level without carrying out full-scale tests, without adjusting the settings of tripping actuation according to the water level in the drum. The foreign methods of PID-regulator adjustment in the cascade system of automatic water level control in the boiler drum are considered, on the basis of which an invariant cascade system of automatic control is proposed. The invariant Cascade-System of Automatic Control (CSAC) of water level in a boiler drum is offered. Simulation results of the invariant cascade-system of automatic control in comparison with CSAC, configured with best foreign method, showed a significant improvement in the quality of regulation in all the major disturbing influences. The results can be used in the development of adaptive control systems and other thermal power devices.


Introduction
Automation of power equipment of power plants is carried out in many directions, with one of the main being the regulation of the water level in the boiler drum (steam generator). The quality of regulation of the water level in the drum boilers of thermal power plants (TPP) and of steam generators of nuclear power plants (NPP) largely determine the reliability and efficiency of thermal power plants and nuclear power plants. In accordance with this, the issues of significant improvement in the quality of water level regulation in the boiler drum (steam generator) become urgent.
Three-pulse automatic control systems (ACS) of the water level in the drum are most widespread at TPP and NPP [1][2][3]. The use of classical regulators with a rigid feedback device in these ACS increases the stability of the system, but does not provide quality control of the water level in the boiler drum [4,5]. A typical three-pulse ACS of the water level in the boiler drum has such disadvantages as:  necessity of availability of three measurement sensors (level, superheated steam flow and feed water)  the presence of a static control error at the end of the transition process at the internal perturbation, as well as at the external perturbation of the flow rate of superheated steam with the phenomenon of "level swelling" [3].
For elimination of the specified shortcomings in [5] on the example of ACS of the boiler BKZ-210-140 it is offered to use structural-parametric optimization of cascade ACS. In this case, the elimination of the static control error in the development of internal perturbation is carried out by the stabilizing regulator, and elimination of a static error of regulation at working off of extreme external disturbance with the phenomenon of "level swelling" is made by the corresponding choice of structure of the correcting device, as well as with the correction of tasks to the last value of the static regulation error at the point of time when the main control value stabilizes. However, in this case, the integral of the control error module in terms of the level when testing external disturbances, although less than in a typical three-pulse ACS, however, there is a possibility of significant improvement in the quality of water level regulation.

Materials and Methods
Of all the typical control algorithms, PID-regulators 140 Mathematical Modeling of Transient Processes of the Automatic Control System of Water Level in the Steam Generator provide the best control quality for thermal power facilities. Cascade automatic control system is widely used in the field of automation of technological processes [6,7]. The water level in the drum of the steam generator when perturbed by the flow of feed water refers to objects without self-leveling and is described by the transfer functions of the ideal integrating link with delay The dynamics of the controlled object in terms of the perturbation of the flow rate of feed water and superheated steam of the steam generator BKZ-210-140 has the following parameter: [3]. The transfer function of the external perturbation of the flow rate of superheated steam with the phenomenon of "level swelling" of water in the boiler drum can be approximated by the difference between the transfer functions of the first-order inertial link and the ideal integrating link of the In this case, the value of the "level swelling" will be the greater the numerical value of the transfer coefficient of the inertial link of the first order 3 k . The transfer function of the flue perturbation has the form of an inertial link of the first order ( ) 1 30 where p k -the gain of the perturbation; p T -the time constant of the furnace perturbation. The transfer function of the leading section of the feed water flow rate during the abrupt movement of the control valve has the form of an inertial link of the second order where le  The method of determining the optimal parameters of the dynamic adjustment of the controllers of the standard CSAC is based on the possibility of calculating one circuit independently of the other. First, the stabilizing regulator is adjusted, and then the dynamic adjustment of the correcting regulator is calculated. Typically, the standard CSAC is used as a corrective and stabilizing regulator PI-regulators for the formation of regulatory impact, although it is known that of all linear regulators, PID-regulators provide the best quality of transients. In this regard, we will replace the PI-regulators of CSAC to PID-regulators. In this case, the output of the transfer function of the optimal stabilizing regulator is made on the basis of the inverse model of the controlled object and a given optimal transfer functions of closed ACS for the driving force. We write down the transfer function of the closed ACS ( ) The transfer function of the internal circuit is selected so that it meets the quality criterion for the driving force: where ( ) p W opt s1 -optimal transfer function of the internal circuit on the driving force.
Given (7), the transfer function (6) where ( ) p W t1 -the optimal transfer function of the controller, which implements a given optimal transfer function of the internal circuit of the ACS for the driving force s1 x .
We make a choice of structure and optimum dynamic adjustment of the stabilizing regulator. Since the transfer function of the leading section (5) has a second order, opt s W 1 we take the following form: where 1 s T -a given time constant of the inertial link of the second order.
Substituting (5) and (10) into (9), we obtain (for the stabilizing controller) the transfer function of the real PID-regulator with one parameter of dynamic adjustment Determination of the numerical value 1 s T is carried out using numbers of the Golden section rule [9], taking as an Adjustment of the corrective regulator (Table 1) can be carried out using some foreign methods. As a rational structure of the controller, we choose the classical PID-regulator, the transfer function of which has the following form [10]:

Discussion
According to [10], the selected controller is used in the following products: Toshiba TOSDIC 200 product with 10 ≤ ≤ 33 , 3 N 3.33 (McMillan, 1994)  From the transient graphs it can be seen that when a jump of the task is developed, an overshoot appears up to 50%, the minimum adjustment time is 250 s. When working out the internal and external disturbances static regulation errors are absent, the minimum regulation time is 300 seconds. The minimum values of the maximum dynamic regulation error are as follows: when practicing an internal disturbance, from + 3.0 to -2.5%; when developing external similar disturbances -from +36.0 to -25.0%; during the development of external excitation with steam consumption -from +58.0 to -22.0%. The best direct quality indicators for key impacts are consistent with the NI Labview method. (2001)  The disturbed influences affect the controlled value, the most dangerous being the disturbance of the flow of superheated steam applied to the ACS output. In the invariant ACS, the influence of the disturbance on the regulated value is compensated by introducing an additional signal to the regulator input from the output of the compensating device of the corresponding structure. The block diagram of the simulation of the proposed invariant CSAC of the steam generator power supply is shown in Fig. 3.
The choice of the rational structure and parameters of the optimal dynamic adjustment of the correction regulator is made on the basis of the transfer function of the optimal regulator. To do this, we determine the transfer function of the equivalent object, taking into account the transfer functions of the object (2) and the specified transfer function of the internal contour (10) The dynamics of control objects with self-leveling are described by the transfer functions of inertial links, and the dynamics of control objects without self-leveling, which include the water level in the boiler drum, by the transfer functions of integrating links. In this case, the graphs of transient processes for these objects with a jump in the regulating effect will coincide until the time when the controlled object with self-leveling does not begin to stabilize the graph at the steady-state value. Based on this property, up to a certain point there is no difference what transfer function describes the dynamics of the control object without self-leveling (transfer function of a real integrating link or transfer function of an inertial link of the second order). Stemming from this, the transfer function of an equivalent object can be represented in the form of a second-order inertial link, as for an object of regulation with self-leveling: ( ) ( ) ( ) In this case, the transfer function of the equivalent object (14) takes the following form: Where 2 s