Algoritm for optimal time heating facility

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Ogarev Mordovia State University

Algoritm for optimal time heating facility

post-graduate student Kabanov, O.V.

professor Panfilov S.A.



Abstract

algorithm autonomous temperature heating

This article is devoted to the description of the developed energy-saving algorithm for the autonomous heating systems installed in the heated rooms. The algorithm enables to determine the optimal time of switching on to move to a predetermined nominal temperature after the maintenance mode of the established minimum permissible temperature without using the ambient temperature sensors and under the results of studies of the active operation of heating system, depending on the ambient temperature and heating time of the object from the minimum allowable temperature to nominal one.

Keywords: algorithm, automation, autonomous heating, efficiency, energy saving, heating, heating time



Аннотация

Данная статья посвящена описанию разработанного алгоритма энергосбережения для автономных систем теплоснабжения, устанавливаемых в отапливаемых помещениях. Алгоритм позволяет без применения датчиков окружающей температуры, по результатам исследований активной работы системы теплоснабжения, в зависимости от температуры окружающей среды и времени разогрева объекта с минимально допустимой температуры до номинальной, определять оптимальный момент включения для перехода до заданной номинальной температуры, после режима поддержания установленной минимальной допустимой температуры.

Ключевые слова: автоматизация, автономное теплоснабжение, алгоритм, время разогрева, теплоснабжение, энергосбережение, эффективность



In recent years, according to the researchers conducted by Russian and foreign authors, it was published a considerable amount of papers related to the consideration of issues of operation mode automation of the autonomous (decentralized) heating systems [1]. It has been established that one of the ways to optimize the energy consumption in the heated buildings is the use of systems with the pre-installed control algorithm, in order to save the energy sources [3]. The main advantage of the autonomous heating systems with the pre-installed action algorithm is, according to [2], an independent heat provision of the consumers and an ability of effective control of the heating system. The autonomous heating systems are widely used in country houses, mini markets, shopping halls, petrol stations, where the objects cannot be connected to the district heating system. We should also note that in recent years the control devices (controllers) aimed at source energy saving have appeared in the management of the autonomous heating systems. The use of controllers in the autonomous heating systems to maintain the desired room temperature is becoming increasingly important due to the increase in energy source tariffs. The controllers for heating system control are produced by both domestic and foreign manufacturers. Nowadays the most known controllers are the controllers of heating systems of the American corporation “Honeywell” producing the electronic control and automation systems, the controllers of the Russian company “OWEN” producing the automation equipment, the controllers for automated control systems manufactured by the Swiss company “T.A.C.”, the controllers of such companies as Triton, Automix, Simens, Kontar, EQJW, Danfos, Smile SDC, RVD230 etc. These controllers have a wide range of opportunities for effective heat supply management.

Main part. The analysis of the properties of existing heating control systems has shown that, however, there are additional opportunities to improve the control systems that will increase the efficiency of the autonomous heating systems.

There are known the automated heating systems with different control algorithms, which automatically reduce the temperature in the room in order to save energy sources in the absence of the house owners or in the industrial premises in non-working hours [2-7, 19-29]. A relevant problem for the existing systems is the problem of determining the optimal time interval to raise the temperature in the room to the nominal one prior to the appearance of the house owners or to the beginning of production activity. In this paper, we propose an algorithm of discrete heating control with a precise access to the nominal temperature regime at the desired time point. The energy saving mode includes maintenance of the room temperature at the minimum acceptable level.

The denotations are as follows:

Internal T_min - minimum acceptable temperature in the room in the energy saving mode, internal T_nom - nominal temperature in the room corresponding to the given conditions, T_ambient - ambient temperature, K_a - coefficient of active work of the heating system in the discrete thermal stabilization mode at internal T_min temperature.

(1)

where - time of active work of the heating system during , Pconsumed - average power consumption, Рnominal- nominal power of the heating source.

To form the base algorithm dependence:

1) The experimental data is recorded and the dependence is found Ка=f (T_ambient)



Fig. 1. Dependence Ka=f (T_ambient)

2) The dependence of running time of the heating system t_{running time} is found for the transition from internal T_min temperature to internal T_nom for different ambient temperatures. The Fig. 2 includes the dependence graph t_{running time}=f (T_ambient)

Fig. 2. Dependence t_{running time}=f (T_ambient)

3) The combination of above dependencies enables to get new t_{running time}=f (K_a).The Fig. 3 includes the dependence graph t_{running time}=f (K_a)



Fig. 3. Dependence t_{running time}=f (K_a)

The table values of the latter dependence give the values of the time of room heating and the moment of switching on the heating system for the unconditional implementation of the requirements to the room temperature.

To receive the dependence of the heating time on the active operation coefficient it is necessary to identify the dependencies Ka=f (T_ambient), t_{running time}=f (T_ambient), which is not always possible due to the time constraints.

As an alternative, it is designed a portable automated plant for determining the TPP and a control program for it [16]. With its help, we determine the appropriate coefficients and values under the experiment conducted in the object studied using the following algorithm:

1. It is set the object temperature - T_internal.

2. It is determined the average ambient temperature during the study [°C]:

(2)

where - ambient temperature in the i-th time of the study.

3. It is determined the total area and volume of the object by exterior measurement.

4. It is determined the average power consumption for maintaining the desired temperature:

(3)

5. It is determined the heat transfer coefficient:

(4)

6. It is determined the specific thermal performance [W/(m³* є C)].

(5)

It was conducted a study on testing of this action algorithm.

The heat source with a power of 262 W was placed in the manufactured model. After carrying out all the necessary actions required to conduct the research, it was maintained the established temperature T_internal=25 ° C for a certain period of time in this facility, the ambient temperature at the initial time of the study was T_ambient=14.8 ° C, at the end of the study - T_ambient = 15 °С. The study time was 3600 sec. The time of heating source operation to maintain the temperature inside the object amounted to 455 sec. According to the data obtained during the study it was calculated the overall heat transfer coefficient for the object studied, which amounted to 2.48 W/(m² * ° C); the design heat transfer coefficient =2.40 is determined as follows.

The heat transfer resistance for the object studied was found from the dependence.

(6)

where - heat transfer coefficient of the inner surface of the building envelope, W/(m² * ° С);

- heat transfer coefficient of the outer surface of the building envelope, W/(m²* ° С);

- thermal conductivity of the i-th layer of the building envelope, W/(m * °С), W/(m * °С);

- thickness of the i-th layer of the building envelope, =0.010 m,=0.002 m.

W/(m² * °С).

The design heat transfer coefficient is calculated under the formula:

W/(m² * °С)

It was also calculated the specific thermal performance of the object studied as a whole, which amounted to 33.45 W/(m³ * °C).

The average power consumption expended in maintaining the required temperature inside the object studied, depending on the ambient temperature, is defined by the formula using the heat transfer coefficient and taking into account the total area of the object studied on the exterior measurement (W):



(7)

The average power consumption expended in maintaining the required temperature inside the object studied, depending on the ambient temperature, is defined by the formula [8, 9, 10, 11] using the specific heat performance and volume of the room by exterior measurement :

(8)

The coefficient of active work is determined by the formula (1).

It was conducted the natural experiment to verify the data obtained by calculation, compared with the experimental way.

The experiment was conducted at T_ambient in the range of 6, 7, 8,9,11, 10, 12 °C.

The Fig. 4 includes a graph K_a=f (T_ambient) obtained from the experimental and calculated data.

Fig. 4. Graph Ka=f (Tambient).



In order to find a warm-up time of the object, depending on the ambient temperature, it is necessary to know the equation of the heat mode of the object.

The heat mode of the heated object may be described by the following differential equation [17, 18].

(9)

where - - difference between the ambient and internal temperatures at each time point , Т_heating-heating time constant.

- transfer coefficient on the channel “power of the heating system - internal air temperature” is as follows:

(10)

To find the optimum time of the object heating, it is necessary to use the equation adopted in the automatic control theory [12, 13, 14].

(11)

For the analytical solution of the equation (11) by the method of variale separation, it is necessary to bring it to the following form:

(12)



A general solution of the equation (11) will be the function

(13)

were C -integrating constant.

For a given ambient temperature and a given initial value of internal temperature it is necessary to find the value :

(14)

(15)

A solution of the equation (11) will take the form

(16)

It is necessary to find a constantby the least square method using the experimental data obtained in the course of heating the room at a fixed power of the heating system.The Fig. 5 includes a graph of the object heating.



Fig. 5. Experimental curve during the heating of the object studied.

Let us assume that , where , , it is necessary to find .

As is a part of the degree exponent, then it will be the easiest way to it find out by creating a functional for the least square method as the square of difference of the natural logarithms.

(17)

To find the minimum of this functional, it is necessary to find its derivative and equate to 0.

(18)



Then it is necessary to solve the resulting equation for x

(19)

By substituting the experimental data, we obtain .

By substituting the data obtained, the time constant amounted to 16.4 h for this object.

And it is necessary to construct the dependence graph of t_{running time} on T_ambient for T_ambient from -30 °C to +12 °C by the formula:

(20)

The Fig. 6 includes the dependence graph of heating time t_{running time} on T_ambient.

Fig. 6. Dependence t_{running time}=f (T_ambient)



A combination of functional dependencies shown in Fig. 4 and 6 enables to obtain a dependence t_{running time}=f(Ka) on the results of experiment on determining the thermal-physical properties of the object.

Fig. 7. Dependence t_{running time}=f (Ka).

The dependencies obtained provide an opportunity to build the discrete control algorithm increasing the efficiency of the existing district heating control systems, which helps to reduce the costs and reduce the payback period of the automated heating control systems.



Conclusion

The effective management of heating system is one of the areas of study aimed at optimizing the energy source consumption. The equipment of existing autonomous heating systems with the control devices with the pre-installed algorithm increases the life of equipment and reduces the heating costs.



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