Optimization for the Equipment in Combined Heating Systems

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Modern Applied Science; Vol. 9, No. 5; 2015

ISSN 1913-1844 E-ISSN 1913-1852
Published by Canadian Center of Science and Education

# Optimization for the Equipment in Combined Heating Systems

Andrey Gennadiievich Batuhtin 1, Maxim Stanislavovich Bass 1 & Sergey Gennadiievich Batuhtin 1

1 Energy Faculty, "Thermal power plants" Transbaikal State University, Chita, Russian Federation

Correspondence: Bass Maxim Stanislavovich, 672039 Russian Federation. Tel: 7-302-241-7085. E-mail:
bms77@mail.ru

Received: February, 2015      Accepted: March 15, 2015     Online Published: March 26, 2015

doi:10.5539/mas.v9n5p93      URL: http://dx.doi.org/10.5539/mas.v9n5p93

Abstract

The article discusses the prospects for using various types of renewable energy sources for continental climate
conditions (on the example of the Zabaikalye Territory). It is determined that the most efficient is the use of solar
energy for the heating needs. The method for optimizing the composition of the equipment in combined heating
systems, which allows quick determination of the optimal amount of solar collectors without reusability of
complex astronomical calculations needed to determine the exact position of the Sun in the required time.
Application of the developed methodology in conducting energy audit of heating supply objects can reasonably
represent the technical and economic advice on the implementation of renewable energy sources.

Keywords: non-traditional power source, solar installations, power supply, solar energy

1. Introduction

_1.1 Continental Climate Characteristic of the Russian Federation_

Climate of the biggest territory of Russia can be characterized as continental. The substantial part is located in
the areas of extreme continental climate (e.g. the Zabaikalye Territory). The average temperature of the coldest
month is -26.6 _°_ C, the minimal temperature can reach -55 _°_ C. The average temperature of the hottest month is
+18.8 _°_ C, the maximum temperature can reach +55 _°_ C. The quantitative indicator of the climatic features of
regions can serve as an integral characteristic of the heating season. It is estimated by the sum of average
monthly temperature differences of indoor and outdoor air during the heating period (Batuhtin, A. G., 2014;
Batuhtin, A. G., 2013; Semenov, B. A., 2002). The average value of this indicator in Russia is 5000 _°_ C · day,
which is almost 2 times higher than in Denmark and the United States. This value is higher than the value for
most northern European country - Sweden (4017 _°_ C·day.) (Department of Energy of Denmark, 1993). In this case,
integral characteristic of the regions of Siberia with extreme continental climate are much higher and reach
12045 _°_ C·day for Oimjakon (Semenov, B. A., 2002).

_1.2 The Problem of Low Efficiency of Heat Supply Systems of the Russian Federation_

Harsh climatic conditions predetermine widespread central heating systems in Russia. The efficiency of using
the fuel burned in central heating systems of the Russian Federation is extremely low. According to (SNiP
23-01-99 - RF), the average unit cost of primary energy carrier (fuel) for heating buildings in the heating system
during the heating season in Russia as a whole is 55 kg t.c./m 2 (1.528 MJ/m 2 ), and for areas with extreme
continental climate (eastern Siberia, Yakutia and the Zabaikalye Territory) - 110 kg t.c./m 2 or more (Matrosov Yu.
A., 1994). For comparison, the corresponding figures of energy consumption of buildings in Germany are
estimated to be 34 kg t.c./m 2 (944 MJ/m 2 ), in Sweden and Finland - the value of 18 kg t.c./m 2 (500 MJ/m 2 )
(Semenov, B. A., 2002). Multiple excess of unit costs determines the urgency of the problems in energy
conservation and the need to reduce fuel consumption in existing heating systems and during their development
(Goryachikh, N. V. et al., 2010). Currently, some installations of traditional and renewable energy are close in
terms of their cost, while the renewable energy has significant advantages in energy and environmental
efficiency (Bass, M. S., & Batuhtin, A. G., 2011). Without them, it is impossible to perform the introduction of
targets to improve energy efficiency inherent in long-term programs and the relevant laws of the Russian
Federation (Government of the Russian Federation, 2010, the President of the Russian Federation, 2008, the
President of the Russian Federation, 2009). Assessment of prospects for using alternative energy sources in the
continental climate of Russia (on the example of the Zabaikalye Territory) is provided in this article.

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_1.3 Overall Assessment of the Potential of NTRE Sources (Non-Traditional and Renewable Energy) in the_
_Zabaikalye Territory._

Renewable energy sources are the sources based on existing or constantly recurring processes in nature, as well
as the life cycle of the plant and animal world and the life of human society (Ministry of Regional Development,
2007)

The main types of renewable energy include the following:

1. Geothermal energy.

2. Tidal energy.

3. Biomass energy.

4. Water energy (mini-HPP).

5. Wind energy.

6. Solar energy.

_Geothermal energy._

Geothermal springs in the Zabaikalye Territory are located in the Kalar district, their energy potential is
underexplored. The area is sparsely populated. The prospects for being a source of heat and electricity supply
from the geothermal energy require a detailed feasibility study.

_Tidal energy._

The absence of sea or ocean coast in the Zabaikalye Territory makes it impossible to use this type of energy.

_Biomass energy._

Biomass energy is a promising direction of development in the field of alternative energy industry in the
Zabaikalye Territory, especially the gasification of wood wastes. The main problem is the high moisture content
of raw material, which requires additional energy for drying and preparing the primary substance. Technical and
economic benefits shall be determined based on this factor. In addition, the greatest effect from this method can
be achieved on large wood-processing industries. The evaluation of all possible factors requires a pilot project.
Using its example will give the chance for evaluation in practice of the pros and cons of the technology.

As for the production of biogas technology, China is one of the world leaders and cooperation of the Zabaikalye
Territory, as the border area, with China in this area is very promising. The main factor for obtaining significant
technical and economic effect is the presence of large agro-industrial complexes with significant quantities of
organic waste.

_Water energy (mini-HPP)._

The main limiting factors of widespread implementation of these energy sources in the Zabaikalye Territory are
the duration of the winter period and preservation of this equipment. Because nearly half of the year, the rivers in
the region are covered with ice, the number of hours of equipment use is low. In addition, during the period of
maximum power consumption, this equipment will not work, resulting in a long payback period. Furthermore, an
additional power source for equipment downtime will be required.

The most rational is using this type of energy for the seasonal works, e.g. gold mining cooperatives.

_Wind energy._

When choosing a wind turbine type, it is necessary to consider the weather conditions and terrain. The
Zabaikalye Territory, due to the rugged terrain and the presence of Lake Baikal, is characterised by the
well-developed local winds. It means that both in the mountains and on the coast of Lake Baikal are distinct for
phoenes, which cause thaws and snow cover loss in winter, and temperature increase and humidity decrease in
summer. The warm periods are characterised by the developed local mountain-valley winds. The area, adjacent
to Lake Baikal, is characterized by local winds in summer and spring from the lake to the land, and in winter, the
winds blow in the opposite direction.

Traditional wind turbines start operation at wind speeds above 3 m/s, leaving the nominal performance at speeds
of 10-16 m/s ( Li, H., & Zhe, C., 2008 ). The average wind speed in the Zabaikalye Territory in recent years is 1.7
m/s with an average maximum of 5.3 m/s, which does not allow these wind turbines to work throughout the year
with normal values.

A significant disadvantage of autonomous wind power is the presence of storage batteries in the circuit, as the

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life cycle of these batteries is 3-5 years. Their cost comprises from 30 to 50% of the cost of wind power
installation, which leads to a significant rise in price for this type of a renewable energy source.

_Solar energy_

The main ways of using solar energy is to convert it into electricity and heat (Sébastien, A., & Michael, R.,
2012).

Today, the most effective way to use solar energy is solar heating of water using solar collectors of various types
(E. Mohseni-Languri, et al., 2009, A. Saxena, et al., 2013, Ebru Kavak Akpinar and Fatih Kocyigit, 2012). The
lack of widespread use of this technology in Russia is due to the misconception that the possibility of collecting
solar energy is directly related to the ambient temperature. In fact, the power of solar collectors depends on the
intensity of solar radiation, air transparency and the day length (Batuhtin, A. G., & Batuhtin, S. G., 2009). This
provision gives the prerequisites for the use of solar collectors in the Zabaikalye Territory, which has
considerable number of cloudless days and the maximum value of solar activity in Russia.

Solar activity in the Zabaikalye Territory (ZT) in the maximum month is not much higher than, for example, in
Krasnodar, and the value of total solar radiation is significantly higher (Bass, M. S. et al., 2012). This is because
the quantity of solar activity in ZT is significantly higher than in other regions during the winter months. This
fact, along with the highest total solar activity value for the year gives considerable promise for using solar
heating in heating systems.

Table 1 presents a comparative analysis of solar radiation intensity on a number of regions (Bass, M. S. et al.,
2012). Table 1 shows that the solar activity in the Zabaikalye Territory (ZT) in the maximum month is not much
higher than, for example, in Krasnodar, and the value of total solar radiation is significantly higher. This is
because the quantity of solar activity in ZT is significantly higher than in other regions during the winter months.
This fact, along with the highest total solar activity value for the year gives considerable promise for using solar
heating in heating systems.

Table 1. Intensity of solar radiation

No.
No.

City The value of the
average radiation per
day in the most
intense month
kW·h/m 2 per day

Month of maximum
radiation

The total solar
radiation per year,
kW·h/m 2

1 Volgograd 5.95 June 1170
2 Irkutsk 5.2 May 1128
3 Kiev 6.0 May 1198
4 Krasnodar 6.2 June 1344
5 Moscow 5.15 May 962
6 Chita 6.3 June 1531

The magnitude of rainfall in the ZT is significantly below average within Russia. This is typical for the winter
months. Low snowy winters (and a very low value of annual rainfall) allow minimizing the operational costs in
the operation of solar heating systems in the winter months and significantly improving their performance
compared with other solar regions of Russia.

The use of solar collectors for heating and hot water in the Zabaikalye Territory is connected with certain
difficulties. The main one is the very low temperature of the ambient air in winter (design outdoor air
temperature for heating and ventilation systems -38 0 _С_ and average heating temperature is -11 0 _С_ ).

There are currently a number of different schemes for using solar energy in the hot water supply and water
heating. Warm air heating of premises based on different types of heat sources makes it possible in many cases to
reduce significantly capital and operating costs. In the harsh continental climate, the most justified is the use of
solar energy to heat the air. Solar heating using various types of solar collectors for air heating systems will
significantly increase the effectiveness of such systems, as well as increase the degree of substitution for the
traditional sources of heat. Such systems heat air or water depending on the temperature, or joint heating of the
water is made for heating hot water supply and air for heating. Since our ultimate goal is heating the air in the
room, it is precisely such complexes can achieve the maximum efficiency by eliminating all intermediate

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processes and transformations (Batuhtin et al., 2009; Batuhtin, A. G. & Kalugin, A. V., 2011).

Air collectors are mainly used in conditions of Canada similar to the Russian conditions. Currently, the most
efficient designs of flat solar collectors are developed by the company of Conserval Engineering Inc in
conjunction with a number of Canadian research centres. The average annual efficiency of the best examples is
as follows: Efficiency = 35-60% (SolarWall, 2008), at sufficiently low coefficient of heat transfer (Tabish et al.,
2014; Smith et al., 2012; Thianpong et al., 2012). The leader in the implementation of solar heating of air in the
Asian market is the company of "Himin", using vacuum capillary heat pipes for air heating (national patent 1 NO.
200820123062.7). These schematics are not widely used due to the low efficiency values (passport average
heating efficiency is 50%; average annual is less than 30%) at a high cost. Recently, there were developed
air-water solar collectors with an average year conversion efficiency of solar energy of more than 65%, due to
the benefits of gaseous and liquid heat carriers and as a result, year-round load of radiant heat absorbing surface
(RF patent No. 2403511). Universality of the system causes a wide scope of their application: from cottage
houses to heating giant industrial buildings and greenhouses. The majority of the advantages of this scheme is
only possible when using unfreezing liquids in solar collectors. Air heating can be performed in a heat
interchanger from the intermediate liquid heated both in the manifold, and directly in the interchanger. The
produced feasibility study on the use of solar heating systems demonstrated that the conditions for the
Zabaikalye Territory, the payback period is in the range of 9-11 years. A larger value corresponds to a lower
heating load of the building.

Solar photovoltaic installations carry out direct conversion of solar energy into electricity via solar cells.

Their main disadvantage is the low power output from the area of photovoltaic panels. Therefore, huge areas are
required to obtain a significant amount of electricity.

2. Methodology

_2.1 The Method for Optimizing the Proportion of Replacing Power at the Base Source of Power Supply by Solar_
_Heating Units_

As shown above, the most reasonable way to use renewable energy sources in a continental climate is solar
heating of water using solar collectors of various types.

Technical and economic characteristics of solar power plants depend mainly on the following factors: climatic
conditions of the area under consideration, determining the amount of generated energy (solar radiation,
cloudiness, number of sunny days per year, etc.); specific investments in solar installation; availability and cost
of the spent fuel and energy. Low density of solar energy distribution in the territory, the volatility of energy
supply in time, the dependence on climatic conditions determine the increase in the size of solar power and
complexity of their designs, which in turn causes an increase in specific capital investments and consumption of
materials in the construction of solar power plants.

An important factor in the cost-effectiveness of renewable energy is the proportion of replacing power base
power supply. When choosing the number of solar collectors (hereinafter SC), one shall take into account the
two important factors - the maximum heating load of the consumer and reliability of solar heating systems. If
solar energy is the only source of heat, it is required to install a large number of both SC and heat storage tanks
that are guaranteed to provide the consumer with the maximum load in the absence of solar radiation. In this case,
during the biggest part of the heating period, the equipment shall be operated at partial power. Consequently, this
approach is inefficient and SC shall be combined with the heat power sources, in particular with electric boilers.
The goal of the methodology is the feasibility in determining the optimal number of SC carrying the base load
with additional heating of the heat carrier in the boiler. The optimality criterion is the minimum payback period
of heating.

Determining the optimal number of collectors shall be made in the following order:

1. Calculation of the heat of the object by month.

2. Determination of the amount of incoming solar energy.

3. Selection of the required number of solar collectors for different values of the proportion of replacement heat
consumption with the heat from the solar collectors and the determination of the optimal quantity.

_Determination of the heat of the object by month._

Heating consumption is determined based on the calculation of heat loss through the building envelope, for a
given heat load depending on the ambient temperature or heat meter readings.

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_р_ _н_
_мi_ = _Q_ _p_ ⋅ _tвр_ − _tнвзд_ . _р_ . ⋅τ _м_

_tв_      - _tвзд_

_р_

_Qмi_ = _Q_ _p_ ⋅ _tв_ − _t_

. _р_ .

_р_ _н_

= _Q_ _p_ ⋅ _tвр_ − _tнвзд_ . _р_ . ⋅τ

_tв_     - _tвзд_

, (1)

_р_

_tв_ - _t_

where _Qp_ - is the heat load of the building, kW;

_t_ _р_ _в_ - is the design temperature inside the building, °C;

_t_ _н.р._ _взд_ - is the design outdoor temperature, °C;

_t_ _н_

_взд_ - is the average outdoor temperature, °C;

τ _м_  - is the number of operation hours of the heating system, h

_Determination of the amount of incoming solar energy._

Determination of the amount of incoming solar energy requires specific data calculated by region:

_E_ - is the total solar radiation (direct and indirect) on a horizontal surface under cloudless skies MJ/m 2 ;

_Eв_ - is the total solar radiation (direct and indirect) on a vertical surface under cloudless skies MJ/m 2 ;

_Е0_ - is the average daily arrival of solar radiation on a horizontal surface outside the earth's atmosphere, MJ/m 2 .

Then, based on the data, it is possible to determine the ratio of average monthly inflows of daily total radiation
on inclined and horizontal surfaces

_Eд_ _Eд_ 1+ cosβ 1− cosβ
_R_ = (1− ) ⋅ _Rn_ + ⋅ + ρ⋅, (2)
_Е_ _Е_ 2 2

where _Eд_ - is average daily arrival of diffuse radiation (scattered radiation) on a horizontal surface;

_Rn_   - is the ratio of average monthly inflow of direct radiation onto

inclined and horizontal surface;

_β_   - is the collector inclination angle to the horizon, deg;

_ρ_   - is the coefficient characterizing soil reflectivity (from 0.2 to 0.7).

The ratio _ЕЕд_ is a function of the coefficient К _т_ (Saransk, 2004):

_Ед_ 2 3

1,39                     - 4,03⋅ _Кт_ + 5,53⋅ _Кт_                     - 3,11⋅ _Кт_, (3)

_Е_ =

where Кт=Е/Е0.

The average daily inflow of total solar radiation on a horizontal surface equals to Eк=R·Е.

As the collector cannot be installed not perpendicular to the sun's rays, it is necessary to use the method by
(Vissarionov V. I., et al., 2008). The angle of ray incidence on the location of the site arbitrarily inclined to the
horizon at an angle β and oriented to the north at an angle γ:

_i_ = arccos(( _A_                  - _B_ ) ⋅sin( _Decl_ ) + ( _C_ ⋅sin( _HA_ ) + ( _D_ + _E_ ) ⋅ cos( _HA_ )) ⋅ cos( _Decl_ )), (4)
where

sin( _lat_ ) ⋅ cos(β);
cos( _lat_ ) ⋅sin(β) ⋅ cos(γ);

_A_ = sin( _lat_ )
_B_ = cos( _lat_ )

= sin( _lat_ ) ⋅ cos(β);
= cos( _lat_ ) ⋅sin(β) ⋅

β);
β) ⋅ cos(γ

_C_

sin(β) ⋅sin(γ);

β) ⋅sin(γ

= sin(β) ⋅

cos( _lat_ ) ⋅ cos(β);
sin( _lat_ ) ⋅sin(β) ⋅ cos(γ);

_D_ = cos( _lat_
_E_ = sin( _lat_ )

β);
β) ⋅ cos(γ

= cos( _lat_ ) ⋅ cos(β);
= sin( _lat_ ) ⋅sin(β) ⋅

_Decl_ - The Sun inclination, in degrees;

_HA_ - Meridian angle;

_lat_ - Latitude in degrees;

Then the power of direct solar radiation on an inclined area is defined as follows:

_ид_
_IS_ = _IS_ ⋅cos( ) _i_ . (5)

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The ratio _IS_

_ISид_

indicates the efficacy of the pad orientation by direct radiation and can be calculated both for the

given moment (in this case coincides with the value of cos(i)), and for days or months.
A more accurate calculation shall take into account the characteristics of the heat exchanger and the storage tank
using the method (Batuhtin A. G., 2010).

When calculating for the storage tank, the input data are as follows: tank parameters, costs for intermediate heat
carrier and tap water, the temperature of the intermediate coolant at the tank inlet.

The calculation starts with the definition of tubes flow section:

2
_fтр_ = 0,785 ⋅ _dB_ ⋅ _z_, (6)

where _dB – is the inner tube diameter, mm; z – q-ty of tubes._

Next we define the cross-section of tubular annulus:

2 2
_f_ _м_ = 0,785⋅ ( _DB_ −⋅ _z_ _dH_ ) (7)

and the equivalent diameter of the tubular annulus:

2 2
_экв_ = _DB_ −⋅ _z_ _dH_

_dэкв_ = _DB_ −⋅ _z_ _d_

= _DB_ −⋅ _z_

_DB_ + _z_ ⋅ _d_

, (8)

+ _z_ ⋅

_B_ + _z_ ⋅ _dH_

where _dн – is external tubes diameter, mm;_

_Dв – is internal case diameter_ of the storage tank, mm _._

_Then the velocity for heat carrying and heated mediums is defined:_

_G_

ω _T_ = _GT_

_тр_

ω _T_ = _T_, (9)

3600 ⋅ _fтр_

3600

_G_

_м_ = _Gм_

ω _м_ = _м_

3600 ⋅ _f_

_м_

. (10)

3600

where _GТ – is the flow for heat carrying medium, m_ _3_ _/h;_

_fтр – is the tubular space area, m_ _2_ _;_

_GМ – is flow for heated medium, m_ _3_ _/h;_

_fм – is the tubular annulus area, m_ _2_ _._

Using the known velocities of the medium and the average temperature of the corresponding heat carriers, heat
transfer coefficients for heat carrying and heated mediums are determined:

0,8
1 = (1400+18⋅− _T_ 0,035⋅ _T_ 2)⋅ω _dT_ 0,2

0,8

α1 = (1400+18⋅− _T_ 0,035⋅ _T_ 2)⋅ω _T_, (11)

⋅− _T_ 0,035⋅ _T_ 2)⋅ _T_

_dB_

_d_

0,8
2 = (1400 +18⋅− _t_ 0,035⋅ _t_ 2)⋅ω _dT_ 0,2

0,8

α2 = (1400 +18⋅− _t_ 0,035⋅ _t_ 2)⋅ω _T_ 0,2, (12)

⋅− _t_ 0,035⋅ _t_ 2)⋅ _T_

_dB_

_d_

where _Т_ - is the average temperature of the heating water, К;

_t_       - is the average temperature of the heated water, К.

Known _α_ and tubes characteristics, heat transmission coefficient _k_ can be determined. After that, the transferred
heat amount can be determined:

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_Q_ = μ⋅⋅Δ _k_ _tcp_ ⋅ _F_, (13)

where _μ_ - is the coefficient taking into account the scale and dirt of the heater tubes;

Δ _tcp_   - is the mean log temperature difference is determined by the method of successive

approximations, °C;
_F_ - is the heat exchange surface area, _m_ _2_ _._

Knowing the amount of the transferred heat, one can find the heat carriers temperature at the outlet of the heat
exchanger:

_Q_
_T_ 2 = _T_ 1 +, (14)
_GT_ ⋅ _c_ _p_ ( _Т_ )

_Q_
_t_ 2 = _t_ 1 +, (15)
_GМ_ ⋅ _c_ _p_ ( _М_ )

where _Т_ 1 and _t_ 1 are respectively the temperature of heat carrying and heated heat carrier temperature at the inlet
to the heat exchanger, ºС.

Since the storage tank has a volume of accumulated fluid, it is necessary to determine the average temperature of
tap water at the outlet of the considered time and the average temperature in the tank at the beginning of the next
time:

_н_

_tб_ = _Gм_ ⋅⋅τ _t_ 2 + _Vб_ ⋅ _tб_

_tб_ = _Gм_ ⋅⋅τ _t_ 2 + _Vб_ ⋅ _t_
_Gм_ ⋅+τ _Vб_

= _Gм_ ⋅⋅τ _t_ 2 + _Vб_ ⋅

_Gм_ ⋅+τ _Vб_

, (16)

_м_ ⋅+τ _Vб_

Where _Vб_ - is the tank volume, _m_ _3_ ;

_t_ _бн_ - is the initial temperature in the storage tank, °C.

_Determination of the solar collectors’ number_

The optimal amount of solar collectors will match the ratio of electricity and solar heating with a minimum
payback period of additional capital investments.

1) The amount of heat coming from the solar collectors in the past month, kW·h:

_i_ _i_
_Qс к_ . . = _nк_ ⋅ _Fк_ ⋅η _к_ ⋅ _Ек_, (17)

where _n_ к – is the number of collectors;

η _к_   - The efficiency of the solar collector;

_Fк_ - is the unit surface area of the collector receiving solar energy, m 2 .

2) Determining the cost of electricity spent by the electric boiler:

_i_ _i_ _i_
_Пс_ = _цээ_ ⋅ ( _Qм_                    - _Qc к_ . .), (18)

where _ц_ ээ – is the electricity cost, RUR/kW.

Since the value of _Пс_

_i_ in the summer months due to the excess of the value of _Qс кi_ . . on _Qмi_ can be negative, it

is necessary to apply the Heaviside function for zeroing negative values.

=  0, _Псi_ ≤

_i_ _i_

_ci_ =  0, _Псi_ ≤

 _Псi_, _Псi_

_Пci_ =  0, _П_

_i_

0, _Пс_ ≤ 0

_i_ _i_

 _Пс_, _Пс_

_Псi_, _П_

_i_

, _Пс_ - 0

(19)

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3) The optimality criterion is the minimum payback time considering the time factor. In this case, the costs of
reconstruction are defined as follows (Batuhtin A. G., 2014, Batuhtin et al., 2014):

_И=nк·цк+цмонт+царм+цант+цб.ак+цавт,_
where _цк_ - is the solar collector cost; _цмонт_ - is the installation costs; _царм_ - is the reinforcement cost; _цант_ - is the
non-freezing heat carrier cost; _цб.ак_ - is the storage tank cost; _цавт_ - is the automation cost.

The first four components are dependent on the number of solar collectors, the latter two - are not.

The payback period is defined as follows

_И_
_Ток_ = , (20)
_Э_

where _Э_ - is cost savings during the installation of solar collectors.

For the conditions of the Zabaikalye Territory, there were developed analytical dependences which allow large
simplification of the determining the optimal composition of the equipment in the combined system.

_р_ _н_

_tв_ − _tвзд_

_р_ _н_ . _р_ .

_tв_ - _tвзд_

_р_

_tв_ − _t_

_р_

_tв_ - _t_

−

In the Zabaikalye Territory, the complex _θ_ = _в_ _взд_

_t_ _р_ _t_ _н_ . _р_ .

during the year is shown in Figure 1.

0.9

0.8

0.7

0.6

0.5

0.4

0.3

0.2

0.1

0 1000 2000 3000 4000 5000 6000 7000 8000

Hours

Actual value Design value

Фактические значения Расчетные значения

Figure 1. The values of the complex _θ_ during the year to the conditions of the Zabaikalye Territory

Complex _θ_ dependence on time for any object with sufficient precision can be described by the following
empirical formula:

2 ⋅π⋅τ
_θ_ = _a_ + _b_ - sin( + _c_ ), (21)
_d_

where _τ_ - is time, h; _a_, _b_, _c_, _d_ - are the empirical coefficients.

For the Zabaikalye Territory: _a_ =0.4; _b_ =0.4; _c_ =1.5; _d_ =9793.

The average daily inflow of total solar radiation on a horizontal surface _Eк_ are quite accurately described by the
formula (20), where the coefficients are as follows _a_ =185.5; _b_ =42.6; _c_ =3.9; _d_ =4022.

Thus, the amount of heat required by the consumer for heating the premises based on the equations (1) and (5)

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shall look as follows:

_i_ 2 ⋅π⋅τ _i_
_Qм_ = _Q_ p· (0.4+0.4· sin( +1,5) )· _τ_ м. (22)
9793

The amount of heat coming from the solar collectors in the past month, shall be defined as follows:

_i_ 2 ⋅π⋅τ _i_
_Qс к_ . . = _nк_ ⋅ _Fк_ ⋅η _к_ ·(185,5+42,6· sin( + 3,9) ). (23)
4022

In the absence of hot water supply on-site, the question of heat recovery in the summer months is of high
importance. Dependence of the time of heat consumption with a considerable degree of accuracy can be
determined according to the method by (Bass M. S., et al., 2009) by the formula:

_a_
_месяц_   τ−τmax  

_a_

_Qмесяц_   τ−τmax   _Q_ max
=  cos  2⋅π  +1  ⋅ + _q_
_Qгод_   _T_   2 ⋅⋅ _b_ _Qгод_

 τ−τmax   _Q_ max

cos  2⋅π  +1  ⋅

 _T_   2 ⋅⋅ _b_ _Q_

=  cos  2⋅π  +1  ⋅ + _qгвс_

_год_   _T_   2 ⋅⋅ _b_ _Qгод_

(24)

where _τ_ max - is the time by which the highest load of boiler _Q_ max is achieved, _Т_ - is the year duration, _q_ гвс - is the
proportion of generated heat that goes to the hot water supply, _a_ and _b_ - are the empirical coefficients.

Sufficient accuracy is achieved at _a_ =3/2 и _b_ =1.35. The dimension of time can be any - months, days, hours.

_2.2 Example for Optimizing the Proportion of Replacing Power at the Base Source of Power Supply by Solar_
_Heating Units_

The example of application for the developed methods, Tables 2-3 present the results of calculations of the
optimal number of solar collectors for combined heating systems of the two-way car border crossing point
"Olochi". Design characteristics of the object were identified because of the energy audit.

Table 2. Heat consumption of an object

Heat
consumptio

n, Gkal

Heat
consumptio

The
number

of
operatio

n hours

of the
heating
system,

h

i month

kW*h

Heat
load,

Designe

d heat

load,

Design
ambient air

temperatur

e, C

Month Ambient

air
temperatur

e, C

Design
internal air
temperatur

e, C

n, Q i

15.75
January -24 18 -38 21 0 744 11718 10.08

21 13.87

February -19 18 -38 5 672 9324 8.02

March -7.9 18 -38 21 9.713 744 7226 6.21
April 1.8 18 -38 21 6.075 720 4374 3.76
May 5.75 18 -38 21 4.594 384 1764 1.52
Septemb 18 21

February -19 18 -38

Septemb 18 21

er 4.75 -38 4.969 360 1789 1.54

October 0.2 18 -38 21 6.675 744 4966 4.27
Novemb 18 21 11.13

Septemb 18

er 4.75 -38

Novemb 18 21 11.13

er -11.7 -38 8 720 8019 6.90

Decembe 18 21 15.71

er -11.7

Decembe 18 21 15.71

r -23.9 -38 3 744 11690 10.05

Year 18 -38 21 5832 60870 52.35

r -23.9

18
-38

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Table 3. Characteristics of the incoming solar radiation

Month Е /3/, Еv /3/, MJ/m 2 n, day E*0, MJ/ E0, MJ/m 2
MJ/m 2 N NE/NW E/W SE/SW S (m 2 ·day)

January 164 143 371 495 31 9 279
February 270 210 424 566 28 14.5 406
March 528 152 365 572 692 31 22.3 691.3
April 678 110 243 459 557 558 30 31.2 936
May 850 176 332 512 573 497 31 38.1 1181.1
June 880 206 370 512 514 427 30 41.2 1236
July 882 212 340 518 511 452 31 39.6 1227.6
August 719 130 268 457 542 520 31 33.8 1047.8
September 540 191 371 530 584 30 25.4 762
October 344 110 263 490 611 31 16.7 517.7
November 194 166 392 543 30 10.3 309
December 126 121 305 475 31 7.6 235.6

- For the conditions of 50 degrees latitude.

Month Е /3/,
MJ/m 2

Еv /3/, MJ/m 2 n, day E*0, MJ/

E/W SE/SW S (m 2 ·day)

The calculations determined the optimal number of solar collectors equal to 10 (when the unit collector area
equals to 1.38 m 2 ) with a minimum payback period of about 8 years (Figure 2).

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

number of collectors

Figure 2. The optimal amount of solar collectors for heating system conditions in TWCBCP "Olochi"

3. Discussion and Conclusions

The article discusses the prospects for using various types of renewable energy sources for continental climate
conditions (on the example of the Zabaikalye Territory). The main types of renewable energy sources for the
region include the following:

1. Geothermal energy.

2. Biomass energy.

3. Water energy (mini-HPP).

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4. Wind energy.

5. Solar energy.

It is determined that the most efficient is the use of solar energy for the heating needs. The estimation of solar
activity in the Zabaikalye Territory in comparison with a number of regions of the former USSR is characterized
by high solar activity.

The method for optimizing the composition of the equipment in combined heating systems, which allows quick
determination of the optimal amount of solar collectors without reusability of complex astronomical calculations
needed to determine the exact position of the Sun in the required time. This methodology is based on obtaining
the integral characteristics of thermal loads and tributaries of useful operation of solar radiation based on
determining the heat consumption of the object by months. High solar activity is characterised with high
unevenness during the year, and in the summer months, the excess heat is generated. Mathematical interpretation
of this excess needs the application of the Heaviside function for zeroing negative values. The analytical
dependence has a high degree of convergence with the real data.

Application of the developed methodology in conducting energy audit of heating supply objects can reasonably
represent the technical and economic advice on the implementation of renewable energy sources.

The produced calculation of the optimal amount of solar collectors for heating supply of an operative object
(TWCBCP - two-way car border crossing point "Olochi") demonstrated that the payback period of renewable
energy installations is largely dependent on the proportion of rational choice of replaced power. The payback
period of the installation of solar collectors ranged from 37 to 8 years. Such a large variation of key performance
indicators of investment determines the relevance of the present study and the need for careful calculations to
optimize the structure of the equipment in combined heating systems for more efficient use of the potential of
renewable energy sources.

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