Corresponding author: Maksim A. Trofimov (
Academic editor: Georgy Tikhomirov
The paper considers the construction of a mathematical model for an electrohydraulic system to control automatically the Т-63-13,0/0,25 product manufactured by JSC Kaluga Turbine Plant. Mathematical simulation of control systems makes it possible to improve considerably the quality of control, that is, the accuracy and reliability of such systems, as well as to accelerate greatly the development and calculation of the control system and the parameters of its individual components. The T-63-13,0/0,25 mathematical model of the ASTCS allows estimating the effects of design parameters during any load dropping (in a range of 0 to 100%) and the quality of control for the monitored parameters both in the process of operation as part of an isolated power system (generator output, frequency) and an integrated power system (generator output). A mathematical representation has been developed in the model for the control units, the T-63-13,0/0,25 product model, and the electronic controlling part of each of the control units. It has been proposed that pulse-width modulation be used to control the synchronous motors which makes it possible to control the synchronous machine shaft speed by changing the supply voltage frequency. To this end, the control system’s model uses a frequency converter which is proposed to be used in the real control system. The developed control system with one adjustable steam extraction in the T-63-13,0/0,25 steam turbine is coupled and autonomous, that is, each of the two meters for the turbine’s controlled parameters has effect on both steam distribution systems such that a deviation for one of the controlled parameters does not lead to excitations in the other.
Mathemetical methods are of special importance in investigating the dynamic performance of the power turbine automatic control systems (ACS). They not only form the basis fo analytical methods but also become an integral part of experimental studies. The key to success in this shall be mathematical models that reflect correctly the dynamic properties of components. A mathematical model makes it possible to determine the quantitative indicators of the quality of turbine control, this being a critical task since neither existing ACSs (and, accordingly, the turbines equipped with these) can be operated nor new ones developed without knowing these quality indicators. Mathematical simulation allows improving significantly the quality of control, that is, the accuracy and reliability of such systems, as well as speeding up greatly the development and analysis of the ACS and some of its components. The level of the model complexity shall not preferably exceed that required for the given type of studies. To build a model, the researcher always keeps in mind the objectives pursued, taking into account only those facts that are of most importance for achieving these objectives. Any model is not therefore identical to the original object and is, thus, incomplete since it is only the facts the researcher believes to be most important that are taken into account in the model construction process.
The mathematical model of the turbine control system is important for identifying at the design development stage the influence of such design parameters of the ACS actuators as the servomotor time constants, cutoff slide valve port areas and other components on the quality of transients, as well as for
testing the stability of the turbine generator control process; and
exploring the dynamic qualities of the control system during load sheddings (dynamic overshoots for the control system links, transient duration, etc.).
The objectives at hand allow estimating the ACS operation efficiency and the system reliability in conditions of long-term operation.
In the overwhelming majority of cases, steam turbines (ST) are used in power engineering as primary motors to drive synchronous generators. Since no generated electricity is accumulated anywhere in the grid, electricity generation shall at any time correspond to consumption. The criterion for this correspondence is the persistance of the grid frequency, a parameter the value of which in a steady-state mode is the same for any grid point. The rated power value of the grid frequency in Russia is equal to 50 Hz and shall be maintained with high accuracy (T-63-13.0/0.25, Technical Requirements,
The key objective pursued in this paper is to build a model of an ACS with the facility being controlled to identify the influence of design parameters on the ST dynamics; this actually involves the problem of the closed ST ACS analysis.
The purpose of the closed nonlinear automatic control system analysis is to determine the output signal (transient) or error signal characteristic.
It should be noted that a number of assumptions shall be introduced both in analyzing and synthesizing the ST control systems, that is, the most important mode (100% electrical load shedding) is considered. This mode shall not lead to the operation of protection when shutoff valves stop to feed steam into the turbine. If the ST ACS develops this mode, the control system is assumed to operate normally (
A mathematical model has been built for the T-63-13,0/0,25 ST ACS, which makes it possible to assess the influence of design parameters at any load shedding (from 0 to 100%), as well as the quality of control for the monitored parameters in the process of operation both for an isolated grid (generator output power, frequency) and for an integrated grid (generator output power). The ACS mathematical model is presented in a functional form in Fig.
Functional diagram of the automatic control system for product T-63-13,0/0,25 (condensation mode).
The mathematical model comprises the following key nodes.
Control units (CU1 through CH4).
Operator control unit.
T-63-13,0/0,25 turbine model.
Electronic control part of each of the control units (CU1 ECP through CU4 ECP).
Electronic control part (ECP).
The units in items 4 and 5 form the general structure of the ECP for the electrohydraulic automatic control system (EHACS).
the ECP control signal conversion to the CSVTD control signal (voltage- and current-sensitive control, signal amplitude matching, etc., as specified in the technical assignment (Technical Requirements));
control of CU1 through CU4 during load shedding.
deliver the required electric power to the grid, with regard for the given setting;
keep the given setting of the turbine generator electric power in the event of deviations from the rated steam parameters upstream of the turbine (integrated grid);
keep the given setting of the turbine generator electric power in the event of deviations from the rated steam parameters upstream of the turbine (isolated grid);
maintain the required T-63-13,0/0,25 ST speed during electrical load fluctuations at the consuming end (isolated grid);
control the turbine generator during load shedding from 0 to 100%.
Structurally, an FC normally consists of the following key functional parts: a voltage rectifier (VR); power keys (PK), a PWM module.
Vector PWM is viewed as a special-purpose circuit including six high-power transistors of a three-phase converter operating in a key mode. Such converter circuit that feeds the synchronous motor has such form as shown in Fig.
ST synchronous motor feed circuit.
The mathematical model of T-63-13,0/0,25 is shown in Fig.
Т-63-13,0/0,25 block diagram.
Signals from CU1 through CU4 corresponding to the movement of the SM rods (
If there is a signal (equal to 1 in the model as set by the operator from the control desk), key K2 is closed, and key K1 changes to state 2, which matches the mode of operation for an isolated grid. The monitored parameters in this are Nel (output electric power of the turbine generator, MW), and n (ST speed, rpm).
If there is no signal (equal to 0), K2 is opened and K1 is in state 1, while the lower branch in the circuit is off (mode of operation for an integrated grid). The monitored parameter is Nel (output electric power of the turbine generator, MW).
The complexity of simulating the disturbing impacts arising during operation both for an isolated grid and an integrated grid is noted also in [14]. To solve the problem, the proposed block diagram (see Fig.
The monitored parameters are maintained through the ST steam feed control provided in the CU EHACS, the purpose of which is to control the ST steam supply during
The functional diagram for CU1 ECP is presented in Fig.
Functional diagram of the CU1 control unit with a control device (CU1 CD).
We shall discuss in brief the CU CD mathematical model and action using an example of the block diagram for the control device of control unit 1 (see Fig.
Block diagram of the control device for CU1 control unit.
The signal received at K1 indicates that this CU is on. Partial or complete load shedding leads to some of the CUs operating to close fully the steam control valves the number of which depends on the algorithm „weaved“ in the ECP. As soon as there is a signal to operate for the SCV full closure, K1 is opened; the output signal from the CU CD in this case is defined by the setting value equal to 4 V. This setting is taken with a negative sign, which is explained by a conditional coordinate grid introduced for simplifying the CU model. The movement of the cutoff slide valve (CSV) to close is assumed to correspond to the negative input signal from the ECP and its movement to open is assumed to correspond to the positive sign. Accordingly, when the CSV moves to close, the servomotor rod protracts, this corresponding to the steam supply stoppage, and the SCV opens in the opposite case. Such assumption is connected with a peculiarity of the CU design which suggests that both SM cavities are filled and emptied in the course of control. The setting value has been determined based on the following considerations: in accordance with technical documentation (T-63-13.0/0.25), the control signal received at the CSVTD varies in terms of voltage in the limits of 1 to 5 V (the variation range is 4 V). Conversion uses the same pattern if control is based on a current signal (4 to 20 mA).
Coefficients
Diagrams of steam flows through the HPS control valves (SCV1 through SCV4) as a function of their strokes.
It is possible to adjust the valve opening sequence and extent in the process of design and commissioning, this being provided by the turbine set control algorithm. This algorithm includes a program segment which supports the CU switching depending on the total steam flow to the turbine and the operator-set output electric power.
The CU switching algorithm is implemented in the model in the form of a unit referred to conventionally as the decision making box (DMB). Its functions are to
identify active CUs for the steam feed control;
switch on in series the CUs during the ST speedup to the required output electric power in accordance with the setting;
connect CU1 through CU4 to the turbine control algorithm.
A full disjunctive normal form (FDNF) of the finite state automaton, a logical sequence reflecting the DMB action, was prepared based on the tabular SCV status data. Fig.
Constitutional diagram of control valves, SCV1 through SCV4, in control of steam supply to the T-63-13,0/0,25 ST.
The EHACS mathematical model (
mathematical models of the ACS actuators (CU1 – CU4 models and the T-63-13,0/0,25 model);
a mathematical model of the ECP (ECP CD, DMB and the turbine control algorithm);
a model of disturbing impacts (D n for the ST speed; D Nin for the ST internal power).
The developed mathematical model of the steam turbine automatic control system makes it possible to take into account different disturbing impacts in the process of the turbine testing and operation. The control system with single steam extraction in the T-63-13,0/0,25 ST has been designed as coupled and standalone, that is each of the two meters for the controlled turbine parameters acts for both steam distribution systems such that the deviation of one of the controlled parameters would not lead to disturbances in another.
* Russian text published: Izvestiya vuzov. Yadernaya Energetika (ISSN 0204-3327), 2021, n. 4, pp. 99–109.