Energy Comparison and Selection of Central Control Systems in Existing Heat Supply Systems
Abstract Generated abstract
This paper examines how to choose central control systems for already operating district heat supply networks, where pipeline diameters and hydraulic conditions are fixed and design recommendations for new networks may not apply. It proposes an energy comparison method that minimizes seasonal dependent costs, including the fuel component of heat carrier pumping, heat losses in the network, and fuel costs associated with electricity generation at cogeneration and substitute condensing power plants. A calculation for Tomsk compares qualitative control by heating load with control by total heating and domestic hot water load, using seasonal flow, temperature, and heat consumption schedules. The example indicates that, despite lower design water flow under the elevated temperature schedule, total costs are about 4 percent higher, supporting selection by direct energy comparison for existing systems.
Full Text
Proceedings
of the Tomsk Polytechnic Institute named after S. M. Kirov,
awarded the Order of the October Revolution and the Order of the Red Banner of Labor
Volume 249 1973
Energy Comparison and Selection of Central Control Systems in Existing Heat Supply Systems
N. A. Popov
(Submitted by the Department of Industrial Heat Power Engineering)
Recently, a number of new modifications of central control have been developed. Recommendations have been given for their selection. However, these recommendations are applicable to the selection of a control system for newly designed heat networks, when the design flow rates of network water, and consequently the pipeline diameters that determine the costs in the heat supply system, will be determined depending on the adopted control method.
In existing heat supply systems, in which the pipeline diameters have already been specified, the conditions for selection are different and will depend on the particular local operating conditions that have developed in the heat supply system, such as the type of turbines installed, the steam pressure in extractions or back pressure, the cost of fuel and electric power, climatic conditions, and the ratio of the magnitudes of the heat loads for heating, ventilation, and hot-water supply.
The choice of one or another modification of the central control system when reassessing an already operating system can be made on the basis of the methodology presented below, in the preparation of which the works of Prof. E. Ya. Sokolov on the energy evaluation of the efficiency of district heating [1] were taken as a basis. This choice is made by minimizing the sum of dependent annual costs, including the costs of pumping the heat carrier \(S_{t}^{\mathrm{P}}\), heat losses \(S_{\mathrm{tp}}\), and fuel costs in the generation of electric power \(S_T\). With the same supply of electric and thermal energy to consumers, the economically expedient central control system will be the one for which
\[ S = S_{t}^{\mathrm{P}} + S_{\mathrm{tp}} + S_T \sim \min , \]
where, in determining the costs of pumping the heat carrier \(S_{t}^{\mathrm{P}}\), we take into account only the fuel component of these costs. When comparing variants, the indicated costs will be determined not for a year, but for a heating season, assuming that the operating conditions of the heat supply system in the summer period are the same for all variants.
The costs of pumping the heat carrier are
\[ S_{t}^{\mathrm{P}} = \frac{3.6 \cdot 10^{-6} V_{\mathrm{av}}^{\mathrm{P}} \cdot H_{\mathrm{av}} \cdot n_{\mathrm{os}} \cdot Z_T} {\eta_{\mathrm{n}} \cdot Q_{\mathrm{ut}} \cdot \eta_{\mathrm{k.t}} \cdot \eta_{\mathrm{em}}}, \quad \frac{\text{rub}}{\text{season}}, \]
where \(V_{\mathrm{av}}^{\mathrm{P}}\) is the average heat-carrier flow rate in the supply header of the CHP plant during the heating season, \(\mathrm{m^3/sec}\);
$H_{\mathrm{av}}$ — the required head of the network pumps corresponding to the season-average flow rates of network water in the supply and return headers of the CHP plant, $\dfrac{\mathrm{m}}{\mathrm{m}^2}$;
$Z_T^{\mathrm{CHP}}$ — cost of fuel delivered to the boiler house of the CHP plant, $\dfrac{\mathrm{rub}}{\mathrm{MJ}}$;
$n_{\mathrm{hs}}$ — duration of the heating season, yr;
$\eta_{\mathrm{p}}$ — efficiency of the pumping installation;
$Q_{\mathrm{cf}}$ — calorific value of standard fuel, $\dfrac{\mathrm{MJ}}{\mathrm{kg}}$.
In order to simplify the calculations, the author proposes the following formula for determining $H_{\mathrm{av}}$ in the variants being compared:
\[ H_{\mathrm{av}}=\Delta H'_{\mathrm{s}}\left(\varphi_{\mathrm{s}}^{2}+\varphi_{0}^{2}\right)+\Delta H'_{\mathrm{h.u}}\varphi_{\mathrm{s}}^{2}+\Delta H'_{\mathrm{ab}} . \]
According to this formula, in order to determine $H_{\mathrm{av}}$ it is sufficient to determine the calculated head losses in the supply pipeline $\Delta H'_{\mathrm{s}}$, in the heating installation of the CHP plant $\Delta H'_{\mathrm{h.u}}$, and at the end consumer $\Delta H'_{\mathrm{ab}}$, only for the existing central-control system. Then, knowing for the compared variants the season-average relative flow rates of the heat carrier in the supply $\varphi_{\mathrm{s}}$ and return pipeline $\varphi_{0}$, it is easy to find $H_{\mathrm{av}}$.
The values of the quantities are found from the formulas:
\[ \varphi_{\mathrm{s}}=\frac{V_{\mathrm{av}}^{\mathrm{s}}}{V_{\mathrm{s}}};\qquad \varphi_{0}=\frac{V_{\mathrm{av}}^{0}}{V_{\mathrm{s}}}, \]
where $V_{\mathrm{s}}$ is the total flow rate of the heat carrier in the supply header of the CHP plant under the existing control system;
Fig. 1. Graph of network-water flow rates under control according to the heating load
Fig. 2. Graph of network-water flow rates under control according to the total load
$V_{\mathrm{av}}^{\mathrm{s}}, V_{\mathrm{av}}^{0}$ — total flow rates of the heat carrier in the supply and return headers of the CHP plant, averaged over the heating season; they are found using heat-carrier flow-rate graphs (Figs. 1, 2) and data on the duration of outdoor-air temperatures, by the formula
\[ V_{\mathrm{avg}} = \frac{V_1 \cdot n_1 + V_2 \cdot n_2 + \ldots + V_n \cdot n_n} {n_1 + n_2 + \ldots + n_n}, \]
where \(n_1, n_2,\ldots,n_n\) is the number of hours in the operating season of the heat-supply system at flow rates \(V_1, V_2,\ldots,V_n\). When determining \(H_c\), throttling losses are not taken into account.
Costs of heat losses
In existing heat networks, heat losses during transport are determined by thermal tests or are estimated by one method or another.
Their cost is determined as
\[ S_{\mathrm{hl}} = \frac{Q_{\mathrm{hl}} \cdot Z_T^{\mathrm{TPP}}} {10^3 \cdot Q_{\mathrm{sf}} \cdot \eta_{\mathrm{b}} \cdot \eta_{\mathrm{em}}}, \quad \frac{\mathrm{rub}}{\mathrm{season}}, \]
where \(Q_{\mathrm{hl}}\) is heat losses, \(\dfrac{\mathrm{MJ}}{\mathrm{season}}\);
\(Z_T^{\mathrm{TPP}}\) is the cost of fuel delivered to the TPP boiler house, \(\dfrac{\mathrm{rub}}{\mathrm{t}}\).
If, under the existing central-control system, they are equal to \(Q_{\mathrm{hl}}^{c}\), then under another control method they are determined as
\[ Q_{\mathrm{hl}}^{x} = Q_{\mathrm{hl}}^{c} \frac{\left(\tau_{\mathrm{avg}}^{x} - t_o^{\mathrm{avg}}\right)} {\left(\tau_{\mathrm{avg}}^{c} - t_o^{\mathrm{avg}}\right)}, \quad \frac{\mathrm{MJ}}{\mathrm{season}}. \]
where \(\tau_{\mathrm{avg}}^{c}, \tau_{\mathrm{avg}}^{x}\) are the average seasonal heat-carrier temperatures under the existing and under any other control system, respectively, \({}^{\circ}\mathrm{C}\).
Fig. 3. Normal temperature schedule
Fig. 4. Elevated temperature schedule
\[ \tau_{\mathrm{avg}} = \frac{\tau_{\mathrm{avg}}^{\mathrm{s}} + \tau_{\mathrm{avg}}^{\mathrm{r}}}{2}, \quad {}^{\circ}\mathrm{C}, \]
\(\tau_{\mathrm{avg}}^{\mathrm{s}}, \tau_{\mathrm{avg}}^{\mathrm{r}}\) are the heat-carrier temperatures in the supply and return pipelines of the network, averaged over the season, \({}^{\circ}\mathrm{C}\). They are found—
... according to the temperature charts (Figs. 3, 4) and data on the duration of occurrence of outdoor-air temperatures, by the formula:
\[ \tau_{\mathrm{av}}= \frac{\tau_1\cdot n_1+\tau_2\cdot n_2+\ldots+\tau_n\cdot n_n} {n_1+n_2+\ldots+n_n},\ ^\circ\mathrm{C}, \]
where \(n_1, n_2 \ldots n_n\) is the number of hours of operation of the heat pipeline during the heating season at heat-carrier temperatures \(\tau_1, \tau_2 \ldots \tau_n\);
\(t_0^{\mathrm{av}}\) is the temperature of the medium surrounding the heat pipeline, averaged over the season, °C.
Fuel Costs in the Generation of Electric Power
With the same supply of electric and thermal energy to consumers, the difference in fuel costs among the variants will be determined by the different generation of electric power on heat consumption. The cost of fuel by variants is
\[ S_{\mathrm{t}}^{\mathrm{I}}=B_{\mathrm{TE}}^{\mathrm{I}}\cdot Z_{\mathrm{t}}^{\mathrm{TEC}}, \quad \frac{\mathrm{rub}}{\mathrm{season}}, \]
\[ S_{\mathrm{t}}^{\mathrm{II}}=B_{\mathrm{TE}}^{\mathrm{II}}\cdot Z_{\mathrm{t}}^{\mathrm{TEC}} +\Delta B_{\mathrm{CES}}\cdot Z_{\mathrm{t}}^{\mathrm{CES}}, \quad \frac{\mathrm{rub}}{\mathrm{season}}. \]
In these formulas
\(B_{\mathrm{TE}}^{\mathrm{I}}, B_{\mathrm{TE}}^{\mathrm{II}}\) is the fuel consumption for electric-power generation on heat consumption, in the compared variants,
\[ \frac{t}{\mathrm{season}}; \]
\(\Delta B_{\mathrm{CES}}=B_{\mathrm{TE}}^{\mathrm{I}}-B_{\mathrm{TE}}^{\mathrm{II}}\) is the fuel consumption due to the generation of part of the electric power in one of the variants at the substituting CES,
\[ \mathrm{CES},\ \frac{t}{\mathrm{season}}; \]
\(Z_{\mathrm{t}}^{\mathrm{TEC}},\ Z_{\mathrm{t}}^{\mathrm{CES}}\) is the ex-boiler-house cost of fuel for the TEC and CES,
\[ \frac{\mathrm{rub}}{t}. \]
The fuel consumption for electric-power generation on heat consumption is determined as
\[ B_{\mathrm{TE}}=b_{\mathrm{t}}^{\mathrm{e}}\cdot E =\frac{E}{Q_{\mathrm{u.t}}\cdot \eta_{\mathrm{k.s}}\cdot \eta_{\mathrm{em}}}, \quad \frac{t}{\mathrm{season}}, \]
where \(E\) is the generation of electric power on heat consumption in the compared variants,
\[ \frac{\mathrm{MJ}}{\mathrm{season}}; \]
\(Q_{\mathrm{u.t}}\) is the calorific value of reference fuel,
\[ \frac{\mathrm{MJ}}{\mathrm{kg}}, \]
\(\eta_{\mathrm{k.t}}, \eta_{\mathrm{em}}\) are the efficiency of the boiler station and of the electromechanical turbogenerator.
The generation of electric power on heat consumption by variants is
\[ E=E_{\mathrm{t}}+E_{\mathrm{r}}=e_{\mathrm{t}}(1+c_{\mathrm{t}})\cdot Q_{\mathrm{sez}}^{\mathrm{T}}, \quad \frac{\mathrm{MJ}}{\mathrm{season}}, \]
where \(\mathcal{E}_{T}\) is the generation of electric power for external heat consumption,
\[ \frac{\mathrm{MJ}}{\text{season}}; \]
\(\mathcal{E}_{R}\) is that for internal heat consumption (on the basis of regenerative condensate heating),
\[ \frac{\mathrm{MJ}}{\text{season}}; \]
\(e_{T}\) is the specific generation of electric power for external heat consumption,
\[ \frac{\mathrm{MJ}}{\mathrm{MJ}}; \]
\[ C_{T}=\frac{e_{R}}{e_{T}} \]
is the relative generation of electric power for internal heat consumption,
\[ \frac{\mathrm{MJ}}{\mathrm{MJ}}; \]
\(Q_{\mathrm{seas}}^{T}\) is the amount of heat supplied for external heat consumption from the corresponding condensate extraction when it operates under deteriorated vacuum or back pressure,
\[ \frac{\mathrm{MJ}}{\text{season}}. \]
The value of \(e_{T}\) for each steam flow is
\[ e_{T}=\frac{H_{T}\cdot\eta_{0i}\cdot\eta_{\mathrm{em}}\cdot4.186\cdot10^{3}} {\left(i_{\mathrm{sr}}^{T}-\bar{t}_{H}^{\mathrm{sr}}\right)}, \quad \frac{\mathrm{MJ}}{\mathrm{MJ}}, \]
where \(H_{T}\) is the adiabatic drop of the corresponding steam flow from the initial pressure before the turbine to the seasonal average steam pressure in the extractions, condenser, and back pressure,
\[ \frac{\mathrm{MJ}}{\mathrm{kg}}; \]
\(i_{\mathrm{sr}}^{T}\) is the steam enthalpy corresponding to the seasonal average steam pressure in the extractions, condenser, and back pressure,
\[ \frac{\mathrm{MJ}}{\mathrm{kg}}; \]
\(\bar{t}_{H}^{\mathrm{sr}}\) is the enthalpy of the steam condensate in the extractions, condenser, and back pressure, averaged over the season,
\[ \frac{\mathrm{MJ}}{\mathrm{kg}}; \]
\(\eta_{0i}\) is the relative internal efficiency of the turbine.
The relative generation for internal heat consumption \(C_{T}\) in comparative techno-economic calculations may be determined on the basis of a simplified method for determining the generation of electric power on the basis of regenerative condensate heating by the formula
\[ C_{T}=\frac{H_{R}\left(\bar{t}_{\mathrm{pv}}-t_{H}^{\mathrm{sr}}\right)} {H_{T}\left(i_{R}-\bar{t}_{\mathrm{pv}}\right)}, \]
where \(H_{R}\) is the adiabatic drop from the initial steam parameters to the steam pressure in the regenerative extraction,
\[ \frac{\mathrm{MJ}}{\mathrm{kg}}; \]
\(\bar{t}_{\mathrm{pv}}\) is the enthalpy of the feedwater,
\[ \frac{\mathrm{MJ}}{\mathrm{kg}}. \]
The essence of this method is that the actual regenerative-heating scheme can be replaced by a conventional scheme consisting of
regenerative mixing heaters (one heater for each condensate stream). The schematic diagram of regenerative heating, in the general case for condensate streams from district-heating heaters and from the condenser when it operates at a degraded vacuum, will have the form shown in Fig. 5.
Fig. 5. Schematic diagram of regenerative heating of condensate at a CHP plant
\(P\)—steam generator; \(T\)—turbine; \(TP\)—district-heating heater; \(RP\)—regenerative heater; \(K\)—condenser with a built-in bundle
In regenerative mixing heaters, the condensate streams are heated from their initial temperature to the feedwater temperature. The saturation temperature of the heating steam in each of the regenerative heaters \(t_p\) is taken as equal to
\[ t_p=\frac{t_{\mathrm{n}}^{\mathrm{sr}}+t_{\mathrm{pv}}}{2},\ ^\circ\mathrm{C}, \]
where \(t_{\mathrm{n}}^{\mathrm{sr}}\) is the temperature of the condensate of the corresponding steam stream going for external heat consumption, °C.
It is taken equal to the season-average temperature of saturated steam. The value \(t_{\mathrm{n}}^{\mathrm{sr}}\) is determined as
\[ t_{\mathrm{n}}^{\mathrm{sr}}= \frac{ t_{\mathrm{n}1}\cdot Q_1^{T}+t_{\mathrm{n}2}\cdot Q_2^{T}+\ldots+t_{\mathrm{n}n}\cdot Q_n^{T} }{ Q_1^{T}+Q_2^{T}+\ldots+Q_n^{T} },\ ^\circ\mathrm{C}, \]
where \(t_{\mathrm{n}1}, t_{\mathrm{n}2}, \ldots, t_{\mathrm{n}n}\) are the temperatures of saturated steam at the pressures in the extractions \(P_1^{T}, P_2^{T}, \ldots, P_n^{T}\). They are found from the network-water temperature graphs (Figs. 3, 4). The water underheating in the heaters may be taken as 4–8°C. \(Q_1^{T}, Q_2^{T}, \ldots, Q_n^{T}\) is the amount of heat supplied from the extractions at pressures \(P_1^{T}, P_2^{T}, \ldots, P_n^{T}\). They are found from the heat-consumption duration graphs, Fig. 6.
The enthalpies of the steam in the district-heating and regenerative extractions will be
\[ i_{\mathrm{sr}}^{T}=i_0-H_T\cdot \eta_{0e}, \]
\[ i_p=i_0-H_p\cdot \eta_{0e}. \]
At pressures below the critical pressure, with accuracy sufficient for practical calculations, the adiabatic expansion drops of water vapor may be determined as
\[ H = a \Delta t_{\mathrm{n}}, \quad \frac{\mathrm{MJ}}{\mathrm{kg}}; \]
where \(\Delta t_{\mathrm{n}}\) is the difference between the saturation temperatures of the steam at the beginning and at the end of the adiabatic expansion process, \({}^{\circ}\mathrm{C}\);
Fig. 6. Graph of heat consumption versus duration
\(a\) is a constant coefficient depending on the initial parameters of the steam, \(\dfrac{\mathrm{MJ}}{\mathrm{kg}\,{}^{\circ}\mathrm{C}}\); for its values see [1], p. 20;
\(i_0\) is the enthalpy of the steam before the turbine, \(\dfrac{\mathrm{MJ}}{\mathrm{kg}}\).
The fuel consumption at the substituted condensing power plant for electricity generation is
\[ \Delta B_{\mathrm{K\!E}} = b_{\mathrm{k}}^{\mathrm{E}} \Delta E = \frac{\Delta E} {10^3 \cdot Q_{\mathrm{u.t}} \cdot \eta_{\mathrm{k.s}} \cdot \eta_{\mathrm{em}}(\eta_i - 0.2\,c_{\mathrm{k}})} ,\quad \frac{\mathrm{t}}{\mathrm{season}}, \]
where \(\Delta E = E_{\mathrm{I}} - E_{\mathrm{II}}\) is the difference in electricity generation for heat consumption in the variants being compared, \(\dfrac{\mathrm{MJ}}{\mathrm{season}}\);
\(\eta_i\) is the internal absolute efficiency of purely condensing electricity generation.
With intermediate superheating,
\[ \eta_i = \frac{H_{\mathrm{K}} \cdot \eta_{0i}} {(i_0 - \bar{t}_{\mathrm{K}}) + \Delta i_{\mathrm{pp}}}, \]
where \(H_{\mathrm{K}}\) is the adiabatic drop from the steam parameters before the turbine to the pressure in the condenser, \(\dfrac{\mathrm{MJ}}{\mathrm{kg}}\);
\[ H_{\mathrm{K}} = H_{\mathrm{K}}' + H_{\mathrm{K}}''; \]
\(H_{\mathrm{K}}'\), \(H_{\mathrm{K}}''\) are the adiabatic drops before and after intermediate superheating, \(\dfrac{\mathrm{MJ}}{\mathrm{kg}}\);
\(\bar{t}_{\mathrm{K}}\) is the enthalpy of the condensate after the condenser, \(\dfrac{\mathrm{MJ}}{\mathrm{kg}}\);
$c_K$ is the ratio of the combined generation of electric power from internal heat consumption to purely condensing generation:
\[ c_K=\frac{H_P(\bar t_{\mathrm{pv}}-\bar t_K)}{H_K(t_P-\bar t_{\mathrm{pv}})}. \]
The designations are given above.
A comparison of central control systems is shown for a particular example for the conditions of the city of Tomsk. For comparison, the following are adopted:
Fig. 7. Hourly heat-consumption schedule
a) central qualitative control according to the heating load (normal temperature schedule of network water),
b) central qualitative control according to the total load of heating and hot-water supply (elevated temperature schedule). The subscriber connection scheme is two-stage series. The magnitude of the heat loads and their ratio are given in Fig. 7.
The average specific linear pressure loss in the main pipeline in the existing variant is taken as \(R_l=100\ \frac{\mathrm{N}}{\mathrm{m}^2\cdot \mathrm{m}}\). The coefficient of local hydraulic losses is \(\alpha=0.25\). The initial steam parameters at the cogeneration plant are: \(880\ \frac{\mathrm{N}}{\mathrm{m}^2}\), \(535^\circ\mathrm{C}\),
\[ t_{\mathrm{pv}}=215^\circ\mathrm{C}, \quad \text{at the condensing power plant } 1275\ \frac{\mathrm{N}}{\mathrm{m}^2},\quad 565^\circ\mathrm{C},\quad t_{\mathrm{pv}}=230^\circ\mathrm{C}, \]
reheat at \(314\ \frac{\mathrm{N}}{\mathrm{m}^2}\), \(565^\circ\mathrm{C}\). The average annual steam pressure in the condenser is \(0.392\ \frac{\mathrm{N}}{\mathrm{m}^2}\).
\[ \eta_{\mathrm{KT}}=\eta_{\mathrm{KK}}=0.9;\quad \eta_{0iT}=0.78;\quad \eta_{0iK}=0.8;\quad \eta_{\mathrm{EMT}}=0.95; \]
\[ \eta_{\mathrm{EMK}}=0.98;\quad Z_T^{\mathrm{CHP}}=3.81\ \frac{\mathrm{rub}}{\mathrm{t}};\quad Z_T^{\mathrm{CPP}}=2.01\ \frac{\mathrm{rub}}{\mathrm{t}}. \]
The Belovskaya condensing power plant is taken as the replaced condensing power plant. In comparing the variants, turbines with one heating extraction are adopted. As a result of the calculations performed, the following is obtained:
Total costs under control
a) according to the heating load
\[ S_I=S_T^{\mathrm{P}}+S_{\mathrm{TP}}+S_g=25.5+122.5+1190=1338\ \frac{\mathrm{rub}}{\mathrm{season}}; \]
b) according to the total load
\[ S_{II}=S_T^{\mathrm{P}}+S_{\mathrm{TP}}+S_g=15.2+138+1241=1394\ \frac{\mathrm{rub}}{\mathrm{season}}. \]
Conclusion
- The energy comparison of central control systems for a closed heat network, carried out for the particular example in which the share of the domestic-hot-water load is a significant value,
\[ \frac{Q_{r}^{\mathrm{av}}}{Q_{0}^{\mathrm{I}}}=0.3, \]
shows that, despite the reduction of the design water flow rate under the elevated temperature schedule as compared with the design flow rate under the normal schedule by 24%, the total costs under the elevated schedule are 4% greater than under the normal one.
Thus, according to the calculation results obtained, the economically expedient variant proved to be central control according to the heating load. According to the conditions for selecting control systems given in [1], p. 26, however, at
\[ \frac{Q_{r}^{\mathrm{av}}}{Q_{0}^{\mathrm{I}}}=0.3, \]
the use of control according to the total load is recommended. The latter indicates that, for existing networks, when the pipeline diameters of the heat network in the variants being compared are identical, the recommendations given in [1] do not yield the correct solution. Therefore, the selection of central control systems in existing heat-supply systems must be made on the basis of their energy comparison.
- It should be noted that in the particular example presented, the specific linear pressure losses for the main line under control according to the heating load were taken to be 25% higher than the maximum values permissible under the standards for designing heat networks. However, such an increase in the specific linear pressure losses did not lead to a noticeable increase in total costs, since the expenditures on the fuel component for pumping the heat-transfer medium amount to only 1–2% of the total expenditures. This indicates that there is no need to fear an increase in heat-transfer-medium velocities above the standard values.
References
- E. Ya. Sokolov. District Heating and Heat Networks. GEI, 1963.
- Comparative Technical-and-Economic Indicators for Fuel Extraction and Transport by Regions of the USSR. Moscow, “Nauka,” 1964.