was developed. A method of mathematical modeling of the centralized heating control system based on

mathematical models of distributed power systems and experimental studies has been developed, which allows

for determining the parameters of the coolant when the outdoor temperature changes, qualitative regulation of

heat in autonomous sources, quantitative regulation in automated individual heating devices, etc. The method

makes it possible to study the interaction of an automated individual heating point to increase the efficiency of

the management of distributed power systems of buildings. As a result of studying the controller created by the

R2 control unit, for the PI controller, the calculated heat consumption of the building imperceptibly increases

from 1.08502 kJ to 1.085888 kJ when an oscillatory transient occurs, and for the I controller, the calculated

heat consumption of the building remains at the same level. The level, as for the PI controller, increases slightly

during the oscillatory transition from 1.08456 GJ to 1.08535 GJ.

element requires intellectualization. Accurate

calculations are necessary to ensure heat supply and

energy saving. The development of mathematical

models directly affects the user's convenience and

economical operation of the heating system.

investigated, in addition to monitoring and adjusting

the operating parameters, it is necessary to

coordinate the heat supply in accordance with the

season, outdoor air temperature, and the user's heat

avoiding unnecessary heat costs to ensure

economical maintenance of heating systems. Several

studies have been conducted on optimizing the

increase overall fuel efficiency.

the heating network was developed; based on this

modification, the peak valley method and the ratio

analysis method were introduced, respectively, and

it also became possible to calculate two important

parameters related to the dynamic data of the

heating system - the delay time and the degree of

comparative attenuation. In, [8], a hydraulic pump

was compared with the classical main circulating

mathematical research and computer modeling. By

finding a rational combination of water supply

temperature and flow rate in the heating system, a

low temperature of the main recurrent water was

obtained, which allowed to reduce operating costs.

In, [10], a mathematical model was developed for an

integrated direct heat supply system that combines

wind energy, solar energy, natural gas, and

electricity. By approving a purposeful function of

rational management behavior under time-

flexibility and efficiency of the system. Basing on

the monitoring of outdoor air temperature and the

history of scientific and technical data. In, [14], a

mathematical distribution model was created and an

error-free optimizer was developed to minimize

pumping costs and heat costs; by optimizing the

water supply temperature and fuel consumption, the

heating design could do efficiently and smoothly.

In, [15], presented all possible approaches to simple

forecasting of district heating networks to optimize

models were solved analytically using the Laplace

transform method. The temperature distribution in

the longitudinal edge is measured using the

residuals in a single plane theorem for the inverse

perfectly at the same level, and, therefore, there is a

possibility of utilitarian use of the I-regulator to

regulate the flow of heating of premises and

buildings, because it is easier to introduce and

configure. It is also possible to say that the present

study of the transient motion, taking into account

the temperature of the coolant in the return pipeline

of the structure, shows that an ultra-low-frequency

filter arrives under control concerning full-fledged

oscillations at its inlet (in the output pipeline). In

possible to establish not only suitable options for the

control unit but, above all, the characteristics of the

coolant with probable changes both in the structure

of components of an automated personal heating

point and in the heating systems of a building or

structure.

automated IHP with known standard regulators are

investigated using mathematical modeling. The heat

supply system is a complex of distributed heat

current). If we neglect a small change in the mass of

the coolant, then the rate of change in its

temperature will be proportional to the amount of

heat:

electric drives ED1 and ED2, a control valve RV1

with an actuator A1, a check valve BV1, a direct-

acting differential pressure regulator PR1 with an

RV2 valve, temperature sensors of the coolant DT1

and TG2 accordingly, in the supply and return

pipelines, pressure sensors PT1 and PT2, an outdoor

temperature sensor TG3, as well as a thermal energy

metering unit, for example, a heat meter with a set

of sensors.

Figure 2. The circuit contains the following

elements: WC – weather compensation unit

(interference control); CU – control unit (deviation

control, Figure 2.); PU – protection unit (control of

the permissible temperature range of the coolant in

the return pipeline);

and depending on temperature; Elements CE1 –

CE3 converters of output values (resistances) of

temperature sensors S1 – S3 to the physical

networks and the return pipeline of the building

heating system through a jumper with a check valve;

the control object is CO (control object), which is

the building heating system (HS).

functional scheme: – outdoor air temperature; –

converted outdoor air temperature; – calculated

temperature of the coolant in the supply pipeline of

the building heating system; – control deviation of

the movement of the regulatory body (RB);

the internal circuit RB of the building;

measured temperature of the coolant in the building

heating system;

in the return pipeline heating systems of the

building;

coolant at the inlet to R2.

System (1) includes the following equations:

Equations of motion of temperature sensors S3 and

thermal power

account the use of an automated IHP, is as follows:

Simulation parameters. We believe that at the initial

The initial parameters for modeling are presented in

Table 1.

presented in Table 2.

temperature of the

heating systems (Figure 5b) shows that an

oscillatory transition process is observed for. The

estimated heat consumption of the building in the

studied case is about 1.08535 GJ.

In equation (3) we take the following parameter

movement of the valve stem using the actuator

(Table 4). The simulation results taking into account

the selected values of

Figure 6.