.,    (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)

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)

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)

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• º 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: 

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.

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].}

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

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

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.

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.

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

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.

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.

Summary. 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.

Hydrogen energy has become one of the most promising components of the global energy transition, driven by the need to reduce greenhouse gas emissions and ensure sustainable industrial growth. In the United States, hydrogen is increasingly viewed not only as a clean energy carrier but also as a strategic resource for enhancing energy security and supporting decarbonization across multiple sectors [1]. Recent developments in production technologies, storage systems, and infrastructure have accelerated the integration of hydrogen into industrial processes, transportation, and power generation. At the same time, government initiatives and private investments are fostering large-scale pilot projects and expanding the scope of hydrogen applications.

This article aims to analyze the practical use of hydrogen energy in the United States, focusing on its role in industry and its contribution to energy saving. Particular attention is given to technological advancements, economic implications, and the challenges associated with scaling hydrogen solutions.

Industrial use of hydrogen in the USA

One of the key areas where hydrogen is gaining practical importance in the United States is the industrial sector. It is widely applied in oil refining, chemical production, metallurgy, and, more recently, in the development of green steel and ammonia [2]. The U.S. Department of Energy reports that hydrogen consumption is steadily growing, especially in sectors with high energy intensity and demand for decarbonization. Figure 1 illustrates the distribution of hydrogen consumption by industry in the United States.

Figure 1. Distribution of hydrogen consumption by industry in the USA (2024)

The analysis shows that hydrogen use in the USA remains concentrated in traditional sectors such as refining and fertilizers, while its expansion into metallurgy and energy is only beginning. This indicates both the dependence of current hydrogen demand on established industries and the potential for diversification as new technologies mature.

Hydrogen and energy saving potential in the USA

Hydrogen is considered one of the most promising tools for improving energy efficiency and reducing greenhouse gas emissions in the United States. Its use as an alternative fuel in transport, power generation, and energy-intensive industries allows for partial replacement of fossil fuels and contributes to decarbonization strategies [3, 4].

According to projections by the International Energy Agency (IEA) and the U.S. Department of Energy (DOE), large-scale adoption of hydrogen could reduce primary energy demand and significantly cut emissions by 2030–2040. Figure 2 illustrates estimated scenarios of energy savings resulting from hydrogen integration in different sectors of the U.S. economy.

Figure 2. Estimated energy savings from hydrogen adoption in the USA by 2030 and 2040

The results indicate that hydrogen can make a substantial contribution to energy efficiency, particularly in transportation and heavy industry [5]. The growing gap between the 2030 and 2040 scenarios highlights the importance of long-term investment and supportive policies for scaling hydrogen infrastructure in the United States [6].

Barriers and challenges of hydrogen deployment in the USA

While hydrogen energy has strong potential for decarbonization and energy saving, large-scale adoption in the United States faces technological, economic, and infrastructural challenges. Production of low-carbon hydrogen via electrolysis remains costly due to high electricity prices and limited efficiency of electrolyzers, while storage and transportation require specialized pipelines and cryogenic systems. Economically, hydrogen projects demand higher upfront investments compared to conventional energy. The price gap between fossil-based grey hydrogen and renewable-based green hydrogen hinders industrial adoption without subsidies. Although the Inflation Reduction Act and Bipartisan Infrastructure Law provide incentives, long-term market stability is still uncertain [7]. Infrastructure is another barrier, as the U.S. lacks a nationwide network of refueling stations and pipelines, and regional differences in renewable energy resources limit large-scale production. Regulatory issues, such as safety standards and certification of hydrogen origin, also slow down adoption [8].

One of the most critical obstacles remains cost. Grey hydrogen is the cheapest at about $1.5/kg, blue hydrogen costs around $2.5/kg, while green hydrogen reaches $4.0/kg, making it the most expensive option (figure 3).

Figure 3. Estimated production costs of different types of hydrogen in the USA

The comparison shows that while grey hydrogen remains economically dominant, the transition to blue and green hydrogen will require substantial policy support and technological innovation [9]. Without reducing production costs, industries may be reluctant to scale the adoption of clean hydrogen solutions.

Conclusion

Hydrogen energy in the United States demonstrates considerable potential for industrial application and energy saving. Current consumption is concentrated in refining and chemical production, while new opportunities emerge in metallurgy, transport, and power generation. Despite clear advantages for decarbonization, large-scale deployment faces technological, economic, and infrastructural barriers. Government initiatives and private investment will play a decisive role in reducing costs, expanding infrastructure, and ensuring the integration of hydrogen into the national energy system. Overall, hydrogen is positioned as a strategic element of the U.S. energy transition, with significant long-term benefits for industry and sustainability.