RU2566641C2 - Method of metering of heat energy supplied by heating device - Google Patents

Abstract

FIELD: instrumentation.

SUBSTANCE: invention relates to thermotechnical measurements and can be used for measurement of amount of consumed heat energy in heat supply systems. According to the offered method using Newton-Richmann law the difference of average temperatures of the heating device and air is measured which is multiplied by the heating device thermolysis coefficient. The heating device thermolysis coefficient is found by interruption in supply of the heat carrier into the heating device with subsequent measurement of temperature dependence of the cooled-down heating device, finding of rate of change of temperature and calculation of the named coefficient. After finding of the thermolysis coefficient the heating system is activated and the heat power is calculated.

EFFECT: improvement of accuracy of measurement of heat energy supplied by a heating device.

2 cl, 1 dwg, 2 tbl

Description

FIELD OF THE INVENTION

The invention relates to heat engineering measurements, allows you to determine the amount of heat energy consumed by the heating device, and can be used to measure the amount of heat consumed in heating systems.

State of the art

Description of the invention. Currently, there are two ways to measure the heat output of a heater. In the first of them, the thermal power entering the heater R _I. (W), calculated on the basis of measurements of temperatures and flow rate of the coolant through the supply pipe using a heat meter.

R _I = G · s · (T ₁ -T ₂ ),

where G is the coolant flow rate, [kg / s];

C is the heat capacity of water, [J / kg · ° C];

T ₁ , T ₂ - coolant temperature, [° C].

In the second case, the heat output given by the heater is determined from the Newton-Richmann law, according to which the heat output P is _warm. given by the heater is proportional to the difference between the average temperature of the heater T _East and the average room temperature T _in :

$$R_{tePl.}={\alpha }_{\mathrm{and}\mathrm{from}t}\cdot (T_{\mathrm{and}\mathrm{from}t}-T_{\mathrm{at}}).(\mathrm{one})$$

Here α _ist is the heat transfer coefficient of the heater taking into account its surface area. [W / ° C].

In stationary mode, when performing heat balance P heat _. = P _in. .

When finding the thermal power of an individual heating device, the first method has a high measurement error, since the temperature difference of the coolant of the supply and return pipelines (T _in- T _out ) is units of degrees, and the error of temperature sensors is about 0.3-0.5 ° C. Therefore, currently the second method is mainly used. In this case, the fundamental point is to find the heat transfer coefficient α _ist .

For the transition from thermal power to thermal energy, instantaneous values of thermal power are summed (integrated) over time.

$$Q={\displaystyle \sum _i{\alpha }_{i_{\mathrm{and}\mathrm{from}t}}\cdot (T_{i_{\mathrm{and}\mathrm{from}t}}-T_{i_{\mathrm{at}}})}\cdot \Delta t,(2)$$

where i is the reference number in time;

Δt is the interval for taking time samples. In general, Δt may be a function of the average operating temperature, which varies over time (for example, day, month, heating season).

A known method of accounting for the consumption of thermal energy of a heating device, which includes continuous measurement of the temperature of the heating device and the heated room for a certain time interval. From the difference in the instantaneous values of these temperatures, the instantaneous values of thermopower are continuously determined. These values of thermoEMF are converted into instantaneous values of the current of the discrete integrator. The instantaneous values of the recording current are converted to the amount of electricity per time interval. The amount of electricity is read by a direct current reading of a discrete action integrator. The value of the read time, the read current, taking into account the heat transfer coefficient and the area of the heating device, determine the consumption of thermal energy (RU No. 2145063 IPC G01K 17/20, G01K 17/08, 10.26.1998).

The disadvantage of this method is that when determining the consumption of thermal energy of the heating device, the heat transfer coefficient α is used, selected from predefined by known methods for the corresponding temperature conditions. Thus, the applied heat transfer coefficient does not take into account the individual characteristics of heating devices (changes during long-term operation, the state of clogging, paint on the surface, etc.). In turn, this leads to an increase in measurement error. Another source of measurement inaccuracy is the systematic error in measuring the temperature of the heater and air.

A known method of determining heat consumption by local consumers (apartments) included in the integrated system of heat consumers (apartment building), which involves determining the heat consumption of the combined system of heat consumers (using a heat meter) for a specific time, measuring the temperature difference on the surface of the heat source of a local heat consumer and cooling medium of a local heat consumer. Then, according to the Newton-Richman formula, the average heat transfer coefficient is determined by the combined system of heat consumers (by the consumption of thermal energy for the whole house, the surface area of the heating devices of the whole house and the average temperature difference of the whole house). Using this coefficient, the heat consumption is determined by the local consumer for the same specific time of heat transfer by the heat source (RU No. 2138029 IPC G01K 17/08, 06/09/1998).

The disadvantage of this method is that the average heat transfer coefficient found by the combined system of heat consumers implies that each consumer has one type of heat sources (heating appliances) that differ only in the number of sections, which often does not correspond to reality. Failure to take into account the individual characteristics of heating appliances causes a sharp increase in measurement error. In addition, during measurements, individual heating devices may not be turned on at full power, which also introduces additional inaccuracies.

Thus, the disadvantages of this method are:

- low accuracy of the distribution of consumption for each apartment due to improper use of the Newton-Richmann formula, which suggests that the parameters included in it are applied from only one heat source, and then the resulting costs from each heat source can be added, but not vice versa, as the author of the patent suggested;

- the impossibility of applying this method if one or more apartments of an apartment building refuse to install an apartment device for determining the temperature difference and temperature sensors on batteries and in rooms.

A known metering device for the consumption of thermal energy of a heating device and a heating device. The device for measuring the heat energy consumption of the heating device contains temperature sensors connected to the calculation device, one of the temperature sensors is used to measure the temperature of the heating device and is installed on its surface, and the other is used to measure the temperature of the air surrounding the heating device and is installed outside the heating device.

According to the first invention, it further comprises a thermo-anemometric thermo-anemometric sensor of the heated air flow velocity that removes heat from the surface of the heating element of the heater located under its casing, the output of the thermo-anemometric sensor is connected to the input of the calculator, which determines the consumption of thermal energy spent on heating the room using a calibrated equation.

The heating device comprises a housing with a heating element and temperature sensors connected to the calculation device, according to the second invention, it further comprises a thermally insulated hot-wire anemometer sensor, which, together with the temperature sensors, is calibrated on the stand in a heated room, taking into account the speed of the upward air flow washing the heating element of the heating device according to a certain equation (RU No. 2403542 IPC G01K 17/20, G01K 17/08, 11.11.2009).

The disadvantage of this technical solution is the need to calibrate the heater on the bench in a heated room to obtain the coefficient of air flow rate used in calculating the flow of thermal energy from the heater. The complex process of calibration in laboratory conditions leads to a decrease in the accuracy of calculating the consumption of thermal energy directly from the consumer, and the use of a large number of temperature sensors leads to a rise in the cost of the device.

There is also a method of determining the consumption of thermal energy from a consumer with vertical and other types of wiring of the heating system. Essence: set the temperature difference range of the heat sources. Empirically determine the coefficient of heat consumption corresponding to each temperature range. With a frequency of 0.2-1.0 hours, the temperature difference between the surface of the heat source and the environment is determined in turn for all heat sources. The heat energy consumption of each heat source and the entire consumer is determined (RU No. 2273833, IPC G01K 17/08, 07/20/2004) (prototype).

This method cannot take into account the individual characteristics of each heater and the change in its characteristics during operation. In this regard, the actual value of the heat transfer coefficient for each individual device will have a large scatter in relation to the selected tabular value of the heat transfer coefficient, expressed through a curved functional dependence on the temperature difference of the heat sources. The physical formula used for the calculations and the table for determining the heat consumption coefficient were obtained by the applicant empirically. The ranges of the temperature difference of the heat sources indicated in the table significantly exceed the real temperature range of the heating devices (30-90 ° C).

Disclosure of invention

The aim of the invention is to improve the accuracy of the measurement of thermal energy given by the heating device, taking into account its individual characteristics.

This is achieved by the fact that, in contrast to the known technical solutions that use the heat transfer coefficient of the heating device, found from the reference data, or when measured in laboratory conditions, the heat transfer coefficient of each heating device is determined under operating conditions. And the fact that there is a significant decrease in the influence of the systematic error in measuring the temperature of the room air and the surface of the heating device.

The process of measuring consumed thermal energy is carried out in three stages. At the first stage, the heat transfer coefficient of the heating device is found. The second stage is the thermal power. At the third stage, the thermal energy supplied by the heater for the entire observation period is calculated.

The first step is calibration. At this stage, we assume that the thermal regime is unsteady unlike the prototype. The temperature of the heater changes over time. Let us assume that measurements are carried out in a temperature range from T _H to T _B. Using temperature sensors at key points, the surface temperatures of the heater and indoor air are measured. The mathematical model of the heat balance for a heating device is described by a differential balance equation:

$$\frac{{\mathrm{FROM}}_{\mathrm{and}\mathrm{from}t}\cdot d{T}_{\mathrm{and}\mathrm{from}t}}{dt}=G\cdot c\cdot (T_{\mathrm{one}}-T_2)-{\alpha }_{\mathrm{and}\mathrm{from}t}\cdot (T_{\mathrm{and}\mathrm{from}t}-T_{\mathrm{at}}),(3)$$

where C _East - the heat capacity of the heater, [J / ° C].

In this equation, the profit of thermal energy occurs due to the supply of the coolant (G · c · (T ₁ -T ₂ )), and the expense due to the heat transfer of the battery to the air is α _ist · (T _ist -T _in ). If you stop the flow of coolant (G = 0), then from equation (3) you can find the heat transfer coefficient:

$${\alpha }_{\mathrm{and}\mathrm{from}t}=\frac{{\mathrm{FROM}}_{\mathrm{and}\mathrm{from}t.}\cdot \frac{d{T}_{\mathrm{and}\mathrm{from}t}}{dt}}{T_{\mathrm{and}\mathrm{from}t.}^{\mathrm{to}}-T_{\mathrm{at}}^{\mathrm{to}}},[\mathrm{AT}t/°\mathrm{FROM}](\mathrm{four})$$

, $${Т}_{в}^{к}$$

). Процедура измерения на этом этапе заключается в следующих действиях:In this case, the values of the air temperature and the surface of the heater are fixed ( $$T_{\mathrm{and}\mathrm{from}t.}^{\mathrm{to}}$$

, $$T_{\mathrm{at}}^{\mathrm{to}}$$

) The measurement procedure at this stage consists in the following actions:

- finding the temperature of the cooling heater as a function of time (T _source = f (t));

- measurement of air temperature, which is a constant value within the observation interval;

- the choice of the calibration point in the middle of the observed section from T _N to T _B on the curve of the function T _East = f (t). In this case, the observation period can be from a minute to several days, and the temperature of the heater at the calibration point can lie in the entire range of measured temperatures;

в точке калибровки, с последующим вычислением коэффициента теплоотдачи (формула 4) при известной теплоемкости отопительного прибора.- finding the rate of change of temperature of the heater in time $$\frac{d{T}_{\mathrm{and}\mathrm{from}t}}{dt}$$

at the calibration point, followed by the calculation of the heat transfer coefficient (formula 4) with the known heat capacity of the heater.

Unlike the prototype, in this case, the heat transfer coefficient is measured for each heating device, taking into account its individual characteristics. Another advantage of this method of measuring the heat transfer coefficient is that it takes into account the dependence of the heat transfer coefficient on the temperature of the heating device.

The second stage is measurements. At this stage, the heating system is in working condition (operating mode). Using the same measuring instruments, the temperature of the air and the surface of the heater are measured. These data are supplied to the Newton-Richmann equation (1), in which the heat transfer coefficient is represented by the expression (4). Moreover, the expression for thermal power takes the following form:

, $$P_{tePl.}=\frac{{\mathrm{FROM}}_{\mathrm{and}\mathrm{from}t.}\cdot \frac{d{T}_{\mathrm{and}\mathrm{from}t}}{dt}}{T_{\mathrm{and}\mathrm{from}t.}^{\mathrm{to}}-T_{\mathrm{at}}^{\mathrm{to}}}\cdot (T_{\mathrm{and}\mathrm{from}t}-T_{\mathrm{at}})$$

,

, то в этом случае выражение для тепловой мощности примет вид:It is easy to see that in this expression the errors in the measurement of thermal power are determined by the errors in the measurement of temperatures. If we represent the temperature difference between the source and air as the true value and the absolute systematic error $$[(T_{\mathrm{and}\mathrm{from}t}^0\pm \delta T_{\mathrm{and}\mathrm{from}t})-(T_{\mathrm{at}}^0\pm \delta T_{\mathrm{at}})]$$

, then in this case the expression for thermal power will take the form:

, $$\begin{array}{l}{R}_{tePl.}={\mathrm{FROM}}_{\mathrm{and}\mathrm{from}t.}\cdot \frac{d{T}_{\mathrm{and}\mathrm{from}t}}{dt}\cdot \frac{T_{\mathrm{and}\mathrm{from}t}^0\pm \Delta T_{\mathrm{and}\mathrm{from}t}-T_{\mathrm{at}}^0\mp \Delta T_{\mathrm{at}}}{T_{\mathrm{and}\mathrm{from}t}^{0\mathrm{to}}\pm \Delta T_{\mathrm{and}\mathrm{from}t}^{\mathrm{to}}-T_{\mathrm{at}}^{0\mathrm{to}}\mp \Delta T_{\mathrm{at}}^{\mathrm{to}}}={\mathrm{FROM}}_{\mathrm{and}\mathrm{from}t.}\cdot \frac{d{T}_{\mathrm{and}\mathrm{from}t}}{dt}\cdot \frac{T_{\mathrm{and}\mathrm{from}t}^0-T_{\mathrm{at}}^0}{T_{\mathrm{and}\mathrm{from}t}^{0\mathrm{to}}-T_{\mathrm{at}}^{0\mathrm{to}}}\cdot \frac{\mathrm{one}\pm \frac{\Delta T_{\mathrm{and}\mathrm{from}t}-\Delta T_{\mathrm{at}}}{T_{\mathrm{and}\mathrm{from}t}^0-T_{\mathrm{at}}^0}}{\mathrm{one}\pm \frac{\Delta T_{\mathrm{and}\mathrm{from}t}^{\mathrm{to}}-\Delta T_{\mathrm{at}}^{\mathrm{to}}}{T_{\mathrm{and}\mathrm{from}t}^{0\mathrm{to}}-T_{\mathrm{at}}^{0\mathrm{to}}}}=\\ ={\mathrm{FROM}}_{\mathrm{and}\mathrm{from}t.}\cdot \frac{d{T}_{\mathrm{and}\mathrm{from}t}}{dt}\cdot \frac{T_{\mathrm{and}\mathrm{from}t}^0-T_{\mathrm{at}}^0}{T_{\mathrm{and}\mathrm{from}t}^{0\mathrm{to}}-T_{\mathrm{at}}^{0\mathrm{to}}}\cdot \frac{\mathrm{one}+{\delta }_{\mathrm{one}}}{\mathrm{one}+{\delta }_2}\end{array}$$

,

where δ ₁ , δ ₂ are the systematic errors (δ ₁ << 1, δ ₂ << 1).

разложим в ряд Тейлора. Учтем, что систематические погрешности ΔT_ист и ΔТ_в линейно зависят от текущих измерений температуры отопительного прибора и воздуха соответственно:Fraction $$\frac{\mathrm{one}+{\delta }_{\mathrm{one}}}{\mathrm{one}+{\delta }_2}$$

expand into a Taylor series. We assume that a systematic error? T and ΔT _{ist in} linearly dependent on the current measurement and the heater temperature accordingly:

, $$\Delta T_{\mathrm{and}\mathrm{from}t}-\Delta T_{\mathrm{at}}=k_{\mathrm{one}}\cdot T_{\mathrm{and}\mathrm{from}t}^0-k_2\cdot T_{\mathrm{at}}^0$$

,

(k=1÷10%). На практике за счет ряда факторов (выбор оптимальной точки измерения на поверхности отопительного прибора - несоответствие температуры в точке измерения и средней температуры батареи, тепловой контакт) систематическая погрешность ΔТ_ист значительно выше ΔТ_в. В связи с этим, рассмотрим предельный случай, когда k₂=0.where k is the coefficient of proportionality, may be several percent of $$T_{\mathrm{and}\mathrm{from}t}^0$$

(k = 1 ÷ 10%). In practice due to a number of factors (choice of the optimal measurement point on the surface of the heater - temperature mismatch at the measuring point and the average battery temperature, thermal contact) systematic error? T _ist significantly higher delta T _in. In this regard, we consider the limiting case when k ₂ = 0.

Error of measurements of thermal power ΔР heat _. will be determined by the following expression:

. $$\Delta R_{tePl.}={\delta }_{\mathrm{one}}-{\delta }_2=k_{\mathrm{one}}\cdot \left(\frac{T_{\mathrm{and}\mathrm{from}t}^0}{T_{\mathrm{and}\mathrm{from}t}^0-T_{\mathrm{at}}^0}-\frac{T_{\mathrm{and}\mathrm{from}t}^{0\mathrm{to}}}{T_{\mathrm{and}\mathrm{from}t}^{0\mathrm{to}}-T_{\mathrm{at}}^{0\mathrm{to}}}\right)$$

.

It is easy to see that, unlike the prototype, errors in the measurement and calibration will partially compensate each other. Therefore, systematic errors in the measurement of thermal power can be significantly reduced.

Table 1 shows the results of calculating the error in measuring the thermal power of the heating device at different values of the source temperature. The following data were used in these calculations: air temperature - 20 ° С, the systematic error in measuring the battery temperature is proportional to the battery temperature itself, and this proportionality coefficient is taken to be sufficiently large k = 0.1. The calibration temperature was 50 ° C.

Table 1

от температуры отопительного прибора Т_ист The dependence of the relative systematic error of measurements of thermal power $$\delta R_{tePl.}=\frac{\Delta R_{tePl.}}{R}$$

from the temperature of the heater T _East Temperature T _East , ° C δР _warm % Without calibration $$T_{{}_{\mathrm{to}\mathrm{but}l}^{\mathrm{and}\mathrm{from}t}}^0=\mathrm{fifty}°\mathrm{FROM}$$

thirty thirty 13.33 40 twenty 3.33 fifty 16.66 0 60 fifteen -1.66 70 fourteen -2.66 80 13.33 -3.66

равна нулю. Вместе с тем даже максимальная погрешность на краях диапазона существенно меньше (примерно в два раза), чем погрешность измерения без калибровки.The table shows that the systematic error δP heat _. depends on the temperature of the heater. At the edges of the measuring range, it is maximum, and at the calibration point $$(T_{\mathrm{and}\mathrm{from}t}^{0\mathrm{to}}=\mathrm{fifty}°\mathrm{FROM})$$

equals zero. At the same time, even the maximum error at the edges of the range is significantly less (about two times) than the measurement error without calibration.

At the third stage, the calculation of the consumed thermal energy occurs as follows. All instantaneous power values are summed, the resulting sum is multiplied by the interval of taking time samples Δt according to formula (2). In this case, the systematic error δР heat will also be summed up _. , since it has a variable sign depending on the instantaneous value of the source temperature, then when summing δP heat _. the relative systematic error of the heat output will be significantly reduced:

. $$\delta Q_{tePl}(T_{{}_{\mathrm{to}\mathrm{but}l}^{\mathrm{and}\mathrm{from}t}}^0=\mathrm{fifty}°\mathrm{FROM})=\frac{\mathrm{one}}{6}\cdot (13.33+3.33+0-1.66-2.66-3.66)=1.45\%$$

.

A further decrease in the error in calculating thermal energy can be obtained using another method of finding the calibration point - the statistical method. When measuring during operation of the heater for a long time (months), the calibration point is in the middle of the section from T _N to T _B on the curve of the function T _source. = f (t) will be inappropriate (since the probability of occurrence of temperature T _{East is} not uniform). Therefore, the calibration point must be calculated by finding the density of the probability distribution of the temperature difference between the source and air over the observation period. Consider the case when the average temperature over a long period of time varies from T _N to T _B , but the probability of occurrence of temperature T _{East is} not uniform. We denote (T _source -T _in ) a random variable x, then f (x) is the probability density of a random variable x. The condition for normalizing probabilities in this case is as follows:

. $${\displaystyle \underset{T_N}{\overset{T_B}{\int }}f(x)dx=\mathrm{one}}$$

.

The expected value of the random variable x will be the calculated temperature at the calibration point. The obtained value can serve to clarify the temperature at the calibration point used in calculating the consumed thermal energy according to the third stage and formula (2).

Comparison of the present invention with known technical solutions shows that it has a set of new essential features (taking into account the individual characteristics of the heating device under operating conditions, improving the accuracy of measuring the thermal energy supplied by the heating device), which together with the known features can successfully achieve the goal.

Description of drawings

In FIG. presents the probability density for the temperature of the heater.

The implementation of the invention

This method is implemented as follows. On the surface of the heater at an arbitrary point is a temperature sensor that measures the temperature of the source. Another sensor measures air temperature. The data of these sensors using a wired or wireless communication line is transmitted to the processing device (computer), this device using a special program calculates the heat transfer coefficient (calibration), thermal power and thermal energy (operation).

An experimental verification of this method was carried out in a living area of 10 m ² , equipped with a heating device - a cast-iron sectional radiator type M-140-AO. The cooling rate of the battery was 50 min at an average temperature of T _East = 30 ° C. In this case, the heat transfer coefficient was 27 W / ° C in the range of air temperatures 19-22 ° C. The calculated value of this value is 25 W / ° C.

In operating mode, measurements were carried out during the four winter months. The minimum measured value of the heater temperature is 34.5 ° С, the maximum - 54.5 ° С.

The probability distribution density for the temperature of the heater is shown in FIG. We take a sample of the temperature at 0.5 ° C in the range from 34.5 to 54.5 ° C, and we take the air temperature to be 20 ° C. We perform calibration for several values of T _cal, the results represented in Table 2.

table 2 The value of the error δP heat _. at different calibration temperatures

, °С $$T_{{}_{\mathrm{to}\mathrm{but}l}^{\mathrm{and}\mathrm{from}t}}^0$$

° C $$\frac{{\Delta }_P}{P}$$

% 36 -3.3 38 -1.9 42 0.12 46 1,5 fifty 2,5

, систематическая погрешность измерения тепловой мощности δР_тепл при этой температуре равна 0,12%. Относительная систематическая погрешность отдаваемой тепловой энергии составит:Note that the error δP is _warm. it is small and that by choosing the most optimal calibration point, one can reduce the relative systematic error of the heat energy supplied by measuring the temperature to almost zero. In our case, the optimal calibration point is $$T_{{}_{\mathrm{to}\mathrm{but}l}^{\mathrm{and}\mathrm{from}t}}^0=42°\mathrm{FROM}$$

The systematic measurement error of the thermal power Dp _heat at this temperature is equal to 0.12%. The relative systematic error of the given heat energy will be:

. $$\left|\delta Q_{tePl}\left(T_{{}_{\mathrm{to}\mathrm{but}l}^{\mathrm{and}\mathrm{from}t}}^0=42°\mathrm{FROM}\right)\right|=\left|\frac{\mathrm{one}}{5}\cdot (2.5+\mathrm{1,5}+0.12-1.9-3.3)\right|=0.22\%$$

.

The proposed technical solution can be used in monitoring systems, control, accounting and management of heat consumption as a separate room, and the building as a whole.

Claims (2)

1. The method of accounting for the thermal energy supplied by the heating device, which consists in the fact that in accordance with Newton-Richmann's law, the difference in the average temperatures of the heating device and air is measured, which is multiplied by the heat transfer coefficient of the heating device, found according to the reference data, or when measured in special laboratory conditions and the subsequent integration of the values of the obtained heat capacity in time for the selected observation interval, for example, for a month, characterized in that in order to increase the accuracy STI measurements at the beginning is the heat transfer coefficient for a given sample measured by discontinuing the heat supply to the heater, then measuring the temperature dependence of the cooling heating device, finding a rate of temperature change of said coefficient and calculating according to the formula:
$${\alpha }_{\mathrm{and}\mathrm{from}t}=\frac{{\mathrm{FROM}}_{\mathrm{and}\mathrm{from}t.}\cdot \frac{d{T}_{\mathrm{and}\mathrm{from}t}}{dt}}{T_{\mathrm{and}\mathrm{from}t.}^{\mathrm{to}}-T_{\mathrm{at}}^{\mathrm{to}}}$$

,
where α _East - heat transfer coefficient of the heating device [W / ° C];
With _East - the heat capacity of the heater, [J / ° C];
$$\frac{d{T}_{\mathrm{and}\mathrm{from}t}}{dt}|(T_{\mathrm{and}\mathrm{from}t.}=T_{\mathrm{and}\mathrm{from}t.}^{\mathrm{to}}|$$

- the rate of change of the temperature of the heater at the calibration point, where the calibration point is located as the arithmetic average between the maximum and minimum temperatures of the heater for the observed period; the observation period can be from a minute to several days, and the temperature of the heater at the calibration point can lie in the entire range of measured temperatures;
t - current time [sec];
$$T_{\mathrm{and}\mathrm{from}t.}^{\mathrm{to}}$$

- the value of the average surface temperature of the heater at the calibration point [° C];
$$T_{\mathrm{at}.}^{\mathrm{to}}$$

- the value of the air temperature in the room at the calibration point [° C];
t - current time [sec],
after finding the heat transfer coefficient, the heating system is brought into working condition and the thermal power is found by the formula:
$$P_{tePl}={\alpha }_{\mathrm{and}\mathrm{from}t}\cdot (T_{\mathrm{and}\mathrm{from}t.}-T_{\mathrm{at}})={\mathrm{FROM}}_{\mathrm{and}\mathrm{from}t.}\cdot \frac{d{T}_{\mathrm{and}\mathrm{from}t}}{dt}\cdot \frac{(T_{\mathrm{and}\mathrm{from}t.}-T_{\mathrm{at}})}{T_{\mathrm{and}\mathrm{from}t.}^{\mathrm{to}}-T_{\mathrm{at}}^{\mathrm{to}}}$$

,
Where $$T_{\mathrm{and}\mathrm{from}t.}^{\mathrm{to}}$$

and $$T_{\mathrm{at}.}^{\mathrm{to}}$$

- current values of the surface temperature of the heater and air at the calibration point [° C],
for the transition from thermal power to thermal energy, instantaneous values of thermal power are summed (integrated) in time:
$$Q={\displaystyle \sum _i{\alpha }_{i_{\mathrm{and}\mathrm{from}t}}\cdot (T_{i_{\mathrm{and}\mathrm{from}t}}-T_{i_{\mathrm{at}}})}\cdot \Delta t$$

,
where i is the reference number in time;
Δt is the interval for taking time samples; in general, Δt may be a function of the average operating temperature, which varies over time (for example, day, month, heating season). 2. The method of accounting for thermal energy given off by a heating device according to claim 1, characterized in that the calibration point is calculated by finding the probability density distribution of the temperature difference of the source and air during the observation period and finding the mathematical expectation, which will be the calculated temperature at the calibration point .