Analysis on the Thermal Balance and Operational Parameters for the District Heating System with Peak Load Boilers in Heating Substations

This study proposes to use gas-fired boilers as peak shaving heat sources in heating substations due to their capability to increase the reliability, flexibility and heat capacity without the need to change the district heating network (DHN). However, the design and operational requirements with different connection modes for this kind of DH system are still not clear. This paper presents a systematic study on this kind of DH system, analyzes the connection modes of series and parallel connections between the gas-fired boilers and the heat exchangers. For each connection mode, we figured out the thermal balances and obtained the design and operational parameters including the supply temperatures of the heat exchangers, gas-fired boilers and their variations under different network temperature levels and the base load ratios (β). Under the series connection mode, the design supply temperature of the heat exchangers has no relation with the design peak shaving flow ratio (ω′); it decreases linearly along with smaller β, and the decreasing slope is higher with bigger temperature difference (Δt) of the DHN. However, the design supply temperatures of gas-fired boilers increase linearly when β and/or ω′ are smaller, and the increasing speed is proportional to Δt. For the parallel connection mode, the design supply temperatures of the heat exchangers and gas-fired boilers are all affected by β, ω′ and Δt. The former decreases when β and/or ω′ are smaller, while the latter increases at the same time. Finally, the design peak shaving flow ratio ω′ are determined for the peak boilers with series and parallel connection modes. The study provides a theoretical basis for the design and operation of the DH system with peak heating boilers in substations in order to reach a lower investment and higher efficiency.


Introduction
Nowadays, most of the district heating (DH) systems have multiple heat sources, including the base load heat sources, e.g., combined heat and power (CHP) plants or large heat only boilers (HOB), and the peak shaving heat sources located either in the base plant or in the heating substations. Those parameter called peak shaving flow ratio, reflecting the ratio of the flowrate entering the PB and sheat exchanger. Determination of this parameter heavily affects the pumping energy consumption of the combined DH system. Therefore, a comprehensive and systematic study of the DH system with peak-shaving gas-fired boilers in heating substations is necessary in order to provide a theoretical and solid basis to support the design and operation of a real system. This paper focuses on peak-shaving heating with gas-fired boilers in heating substations, and tries to solve the problem of how to determine the design and operational parameters with series and parallel connection modes of the PBs considering different supply and return temperature levels in the DHN. Specifically, this study analyzed the connection modes based on series and parallel connections between the boilers and the heat exchangers in substations. For each connection mode, we carried out the simulation procedures and performed calculations based on the mass and heat balances and the second law of thermodynamics for the given design conditions. The design parameters of the peak boilers including the supply temperatures of the heat exchangers and PBs were determined, and their variations with the outdoor temperatures in a case study were analyzed. Then the determination method for the peak shaving flow ratio was summarized for both connection modes. The research results can help to understand the real operation mechanism of the DH system with peak boilers in the secondary side, and provide the theoretical basis for determining the operation strategy of this kind of DH system.

Connection Modes between Peak Boilers (PB) and Heat Exchangers
This paper proposes two connection modes according to the connections between the gas-fired PBs and the heat exchangers in the heating substations, namely series and parallel connection modes, as shown in Figures 1 and 2. Figure 1 indicates the series connection mode. For heating substation i, the gas-fired PB is placed after the heat exchanger with a series connection, and a bypass pipe is connected to the PB. The return water from the heat user in the secondary side is preheated by the base load heat plant through the heat exchanger, and then the water flow is divided into two streams: one stream with flowrate ωg 2,i enters the gas-fired boilers for reheating, while the other flows through the bypass pipe. The two water streams mix again at the outlet of the PB, but the value of ω, which is called peak shaving flow ratio should be determined to minimize the pumping cost and the heat output of PB should be controlled in order to provide supply water with the required temperature.
Energies 2020, 13, x FOR PEER REVIEW 3 of 17 and operated only according to the first law of thermodynamics without consideration of the second law of thermodynamics. This can lead to a waste of investment and the low overall efficiency of the peak boilers (PB) and sometimes may not satisfy the required supply temperatures. Moreover, few studies consider the very important parameter called peak shaving flow ratio, reflecting the ratio of the flowrate entering the PB and sheat exchanger. Determination of this parameter heavily affects the pumping energy consumption of the combined DH system. Therefore, a comprehensive and systematic study of the DH system with peak-shaving gas-fired boilers in heating substations is necessary in order to provide a theoretical and solid basis to support the design and operation of a real system. This paper focuses on peak-shaving heating with gas-fired boilers in heating substations, and tries to solve the problem of how to determine the design and operational parameters with series and parallel connection modes of the PBs considering different supply and return temperature levels in the DHN. Specifically, this study analyzed the connection modes based on series and parallel connections between the boilers and the heat exchangers in substations. For each connection mode, we carried out the simulation procedures and performed calculations based on the mass and heat balances and the second law of thermodynamics for the given design conditions. The design parameters of the peak boilers including the supply temperatures of the heat exchangers and PBs were determined, and their variations with the outdoor temperatures in a case study were analyzed. Then the determination method for the peak shaving flow ratio was summarized for both connection modes. The research results can help to understand the real operation mechanism of the DH system with peak boilers in the secondary side, and provide the theoretical basis for determining the operation strategy of this kind of DH system.

Connection Modes between Peak Boilers (PB) and Heat Exchangers
This paper proposes two connection modes according to the connections between the gas-fired PBs and the heat exchangers in the heating substations, namely series and parallel connection modes, as shown in Figures 1 and 2.    Figure 1 indicates the series connection mode. For heating substation i, the gas-fired PB is placed after the heat exchanger with a series connection, and a bypass pipe is connected to the PB. The return water from the heat user in the secondary side is preheated by the base load heat plant through the heat exchanger, and then the water flow is divided into two streams: one stream with flowrate ωg2,i enters the gas-fired boilers for reheating, while the other flows through the bypass pipe. The two water streams mix again at the outlet of the PB, but the value of ω, which is called peak shaving flow ratio should be determined to minimize the pumping cost and the heat output of PB should be controlled in order to provide supply water with the required temperature.
The peak shaving flow ratio for the heating substation i is defined as, where gp,i and g2,i are the flow rates of the circulation pumps for the peak-shaving gas-fired boiler and for the secondary network of substation i, kg/s. Therefore, the peak shaving flow ratio under design condition for each heating substation can be written as, where , , and , , are the flow rates of the circulation pumps for the peak-shaving gas-fired boiler and for the secondary network of substation i under the design condition, kg/s. Design peak-shaving flow ratio is a very important parameter for the DH system with PBs in the heating substation. In this study, we assume that the peak shaving flow ratio for each heating substation is equal to the peak shaving flow ratio for the whole DH system, i.e., = , , ⁄ = , , ⁄ = Figure 2 shows the parallel connection mode. For heating substation i, the return water from the heat user in the secondary side is divided into two streams. One stream enters the heat exchanger with a flowrate of (1-ω)g2,i, while the other flows into the gas-fired PB with a flowrate of ωg2,i. It is clear that the PB and heat exchanger will heat up the return water independently, and the two streams mix with each other at the outlet of the PB, and the value of ω should be determined and the PB be controlled in order to provide supply water with the required temperature. It can be concluded that the water stream entering the PB in series mode is preheated by the heat exchanger, while the water stream entering PB in parallel mode is the return water without preheating. This makes the flowrate and water temperature variations and operation requirements quite different for the two connection modes. The peak shaving flow ratio for the heating substation i is defined as, where g p,i and g 2,i are the flow rates of the circulation pumps for the peak-shaving gas-fired boiler and for the secondary network of substation i, kg/s. Therefore, the peak shaving flow ratio under design condition for each heating substation can be written as, where g p,i and g 2,i are the flow rates of the circulation pumps for the peak-shaving gas-fired boiler and for the secondary network of substation i under the design condition, kg/s. Design peak-shaving flow ratio is a very important parameter for the DH system with PBs in the heating substation. In this study, we assume that the peak shaving flow ratio for each heating substation is equal to the peak shaving flow ratio for the whole DH system, i.e., ω i = g p,i /g 2,i = G p,i /G 2,i = ω. Figure 2 shows the parallel connection mode. For heating substation i, the return water from the heat user in the secondary side is divided into two streams. One stream enters the heat exchanger with a flowrate of (1 − ω)g 2,i , while the other flows into the gas-fired PB with a flowrate of ωg 2,i . It is clear that the PB and heat exchanger will heat up the return water independently, and the two streams mix with each other at the outlet of the PB, and the value of ω should be determined and the PB be controlled in order to provide supply water with the required temperature. It can be concluded that the water stream entering the PB in series mode is preheated by the heat exchanger, while the water stream entering PB in parallel mode is the return water without preheating. This makes the flowrate and water temperature variations and operation requirements quite different for the two connection modes.

Base Load Ratio
The design heat load of a DH system with PBs in the secondary side can be written as Energies 2020, 13, 6180 5 of 16 where Q load,b and Q load,p are the design heat load of the base load heat plant and the PBs, W. The base load ratio β can be defined as and thus the peak load ratio α = 1 − β.
In this study, we assume that the base load ratio for each heating substation is equal to the base load ratio of the DH system, namely, where β i is the base load ratio for the ith substation; q load,b,i is the design heat load of the heat exchanger in the ith substation, W; q load,i is the design heat load of the ith substation, W. The base load ratio β is influenced by the characteristics of the base load plant and the PBs, e.g., the initial investment and operating cost for them, as well as the configuration of the base load heat plant and the PBs. The derivation of optimal base load ratio with CHP as base plant can be found in [12].

System Characteristics
The DH system with peak shaving gas-fired boilers in heating substations has the following characteristics depending on whether the system is newly built or retrofitted. For the newly built system: (1) the diameter of the primary DHN can be reduced because the primary DHN only provides the base load, and this will reduce the initial investment of the DHN; (2) the peak shaving heat sources are installed in heating substations, therefore even the most disadvantageous accident happens and the heat supply from the primary DHN is cut down, the gas-fired PBs can still provide a certain level of the district heat to reduce the impact of the accident and prolong the repair time; (3) the gas-fired PB has good flexibility and higher efficiency, which is slightly affected by the heat demand. As for the retrofitted system, the system can also provide back-up capacity for the base load heat plant and thus reduce the impact of the accident. In addition, the most obvious advantage is to extend the heating capacity of the existing DH system without changing old pipelines in the primary DHN. Of course, the use of gas-fired boilers will add extra investment and operating cost to the boilers and gas supply pipes, however the overall economic performance can be better with proper base load ratio and compared to the DH system with only base load heat plant [12].

Thermal Balance of the DH System with Peak Shaving Gas-Fired Boilers in Heating Substations
The use of PBs in substations introduces the design and operating parameters of the gas-fired boilers, which will affect the design and operating parameters of the heat exchanger. In this paper, we analyze the relationship between those parameters and the base load ratio β as well as the design peak shaving flow ratio ω . For this purpose, the thermal balance of the DH system should first be established.
During the whole heating season, the thermal balance of the DH system can be written as where Q load,b is the heat load of the base load heat plant at outdoor temperature tout, W; Q hr is the heat load of all heat exchangers, W; q hr,i is the heat load of the heat exchanger in the ith substation, W. When the peak heating is not needed, the thermal balance is, Energies 2020, 13, 6180 where Q network is the heat load that users receive from the DHN, W; c water is the specific heat capacity of water, 4186.8 J/(kg· • C); t s , t r are the supply and return water temperatures of the secondary DHN at outdoor temperature tout, • C. However, during the peak heating season, the thermal balance of the whole DH system will take the form where Q hr is the design heat load of all heat exchangers, W; q hr,i is the design heat load of the heat exchanger in the ith substation, W; Q load,p is the peak shaving heat load during the peak heating period at outdoor temperature t out , W.

Design Supply Water Temperatures of Heat Exchanger and the Gas-Fired Boiler
According to the aforementioned thermal balances in Equations (6)- (8), we can obtain the supply water temperatures of heat exchangers and peak-shaving gas-fired boilers under working conditions when the outdoor temperature is t out and under design condition at outdoor temperature t out .
For series connection, the design heat load of all heat exchangers and all peak-shaving gas-fired boilers are, According to the heat balance in the substation, Equations (9) and (10) can also be written as, Then the design supply water temperature of the heat exchangers can be obtained from Equations (9) and (11), Similarly, design supply water temperature of the gas-fired boilers can be deduced from Equations (10) and (12), Figure 3 shows the variation of the design supply water temperature of the heat exchanger (t s,hr ) with the base load ratio (β) and different DHN temperature levels for series connection. The selected temperature levels are to cover more real situations. It can be found that t s,hr under series connection mode decreases linearly when β is smaller and the decreasing slope is only determined by the network temperature difference (∆t) and irrelevant from the design supply temperatures.
For safety and economic reasons, we assume that the highest supply water temperature of the gas-fired boilers is 135 • C. So the design supply temperature of the peak-shaving gas-fired boiler is affected not only by the base load ratio (β) and peak shaving flow ratio, but also it will be restricted by the maximum supply temperature of the gas-fired boilers. With this constraint and according to Equation (14), Figure 4 illustrates the variation of the design supply water temperature of the gas-fired boiler (t s,p ) with different DHN temperature levels, base load ratio β and design peak shaving flow ratio (ω ) for series connection. It can be concluded that when ω is chosen, t s,p decreases linearly with increasing value of β, and the decreasing speed of t s,p is only affected by the network temperature difference (∆t). In addition, t s,p increases rapidly when ω is decreasing, and the increasing speed is faster with bigger temperature differences. This also makes t s,p with low DH temperature levels can even be higher than those with high temperature levels, as indicated by the rectangle in Figure 4d, Energies 2020, 13, 6180 7 of 16 e.g., when β = 0.7 for t s , t r = {85 • C, 70 • C} with ∆t = 15 • C compared with the situation of t s , t r = {70 • C, 45 • C} with ∆t = 25 • C, t s,p for low DH temperature level is higher than that for the high temperature level.
Energies 2020, 13, x FOR PEER REVIEW 7 of 17 to cover more real situations. It can be found that , , under series connection mode decreases linearly when β is smaller and the decreasing slope is only determined by the network temperature difference (Δt) and irrelevant from the design supply temperatures. For safety and economic reasons, we assume that the highest supply water temperature of the gas-fired boilers is 135 °C. So the design supply temperature of the peak-shaving gas-fired boiler is affected not only by the base load ratio (β) and peak shaving flow ratio, but also it will be restricted by the maximum supply temperature of the gas-fired boilers. With this constraint and according to Equation (14), Figure 4 illustrates the variation of the design supply water temperature of the gasfired boiler ( , , ) with different DHN temperature levels, base load ratio β and design peak shaving flow ratio (ω') for series connection. It can be concluded that when ω' is chosen, , , decreases linearly with increasing value of β, and the decreasing speed of , , is only affected by the network temperature difference (Δt). In addition, , , increases rapidly when ω' is decreasing, and the increasing speed is faster with bigger temperature differences. This also makes , , with low DH temperature levels can even be higher than those with high temperature levels, as indicated by the rectangle in Figure 4d for low DH temperature level is higher than that for the high temperature level.
Base load ratio β Design supply water temperature of heat exchanger (°C) 0.6 0.
Design supply water temperature of the gas-fired boiler (°C) Base load ratio β 0.6 0.
Design supply water temperature of the gas-fired boiler (°C) Base load ratio β  For safety and economic reasons, we assume that the highest supply water temperature of the gas-fired boilers is 135 °C. So the design supply temperature of the peak-shaving gas-fired boiler is affected not only by the base load ratio (β) and peak shaving flow ratio, but also it will be restricted by the maximum supply temperature of the gas-fired boilers. With this constraint and according to Equation (14), Figure 4 illustrates the variation of the design supply water temperature of the gasfired boiler ( , , ) with different DHN temperature levels, base load ratio β and design peak shaving flow ratio (ω') for series connection. It can be concluded that when ω' is chosen, , , decreases linearly with increasing value of β, and the decreasing speed of , , is only affected by the network temperature difference (Δt). In addition, , , increases rapidly when ω' is decreasing, and the increasing speed is faster with bigger temperature differences. This also makes , , with low DH temperature levels can even be higher than those with high temperature levels, as indicated by the rectangle in Figure 4d for low DH temperature level is higher than that for the high temperature level.
Design supply water temperature of the gas-fired boiler (°C)  For the parallel connection mode, we can also obtain the design supply water temperatures for heat exchanger and the gas-fired boilers as follows. Design supply water temperature of the gas-fired boiler (°C) Base load ratio β Figure 4. Variation of the design supply water temperature of the PB (t s,p ) with different network temperature levels, base load ratio (β) and design peak shaving flow ratio (ω ) for series connection. For the parallel connection mode, we can also obtain the design supply water temperatures for heat exchanger and the gas-fired boilers as follows.
It can be seen from Figure 5 that when the design peak shaving flow ratio ω = 1 − β, the design supply water temperatures of the heat exchangers are all equal to the design supply water temperature of the DHN and irrelevant to the temperature levels. When smaller ω is chosen, i.e., ω < 1 − β, then t s,hr is lowered linearly with decreasing value of β, and the decreasing speed is faster for systems with larger temperature differences ∆t. Note that ω can be further lowered provided higher temperature water can be supplied by the peak-shaving gas-fired boilers, but the highest supply temperature is restricted to 135 • C as explained before. For example, in Figure 5d, when ω = 0.1, t s,hr is not defined for the DH system with an excessively low base load ratio since the required supply water temperature of the peak shaving gas-fired boiler is higher than 135 • C. On the other hand, ω cannot be larger than 1 − β, because t s,hr should be smaller than the DHN design supply water temperatures, according to the second law of thermodynamics. The upper and lower constraints of ω are detailed in Section 3.2 and Table 1.  For the parallel connection mode, we can also obtain the design supply water temperatures for heat exchanger and the gas-fired boilers as follows.
, ′ It can be seen from Figure 5 that when the design peak shaving flow ratio ω' = 1 − β, the design supply water temperatures of the heat exchangers are all equal to the design supply water temperature of the DHN and irrelevant to the temperature levels. When smaller ω' is chosen, i.e., ω' < 1 − β, then , , is lowered linearly with decreasing value of β, and the decreasing speed is faster for systems with larger temperature differences Δt. Note that ω' can be further lowered provided higher temperature water can be supplied by the peak-shaving gas-fired boilers, but the highest supply temperature is restricted to 135 °C as explained before. For example, in Figure 5d, when ω' = 0.1, , , is not defined for the DH system with an excessively low base load ratio since the required supply water temperature of the peak shaving gas-fired boiler is higher than 135 °C. On the other hand, ω' cannot be larger than 1 − β, because , , should be smaller than the DHN design supply water temperatures, according to the second law of thermodynamics. The upper and lower constraints of ω' are detailed in Section 3.2 and Table 1. ) with different network temperature levels, base load ratio (β) and design peak shaving flow ratio (ω') for parallel connection. Figure 6 shows the variation of , , with different DHN temperature levels, base load ratio (β) and design peak shaving flow ratio (ω') for parallel connection mode. Unlike the , , , , , varies with different temperature differences even when ω' = 1-β, and clearly , , is higher for bigger temperature differences within the same DHN supply temperature level. When ω' < 1-β, , Design supply water temperature of the heat exchanger (°C) Base load ratio β Figure 5. Variation of the design supply water temperature of the heat exchanger (t s,hr ) with different network temperature levels, base load ratio (β) and design peak shaving flow ratio (ω ) for parallel connection. Table 1. The supply water temperatures of the heat exchanger and peak shaving gas-fired boilers as well as the determination of the design peak shaving flow ratio ω .

Design Parameters
Gas-fired boilers closed N.A.
Design peak shaving flow ratio ω Note: when peak heating starts, the regulation method adopted for secondary network is quality control which means that the flow rate is constant but the supply and return water temperatures are controlled to adapt the load variation. Figure 6 shows the variation of t s,p with different DHN temperature levels, base load ratio (β) and design peak shaving flow ratio (ω ) for parallel connection mode. Unlike the t s,hr , t s,p varies with different temperature differences even when ω = 1 − β, and clearly t s,p is higher for bigger temperature differences within the same DHN supply temperature level. When ω < 1 − β, t s,p increases linearly with decreasing value of β, and the increasing speed is faster for the system with the larger temperature difference. This makes it possible for t s,p with lower temperature level to exceed that with higher temperature level, e.g., in Figure 6c, when β is smaller than 0.7 for t s , t r = {85 • C, 70 • C} with ∆t = 15 • C compared with the lower temperature level of t s , t r = {70 • C, 45 • C} with ∆t = 25 • C. In Figure 6d, ω is further lowered with the highest supply temperature restricted at 135 • C. On the other hand, ω cannot be larger than 1 − β, because in this case the mixed water temperature of heat exchanger and gas-fired boiler cannot meet the DHN requirement according to the heat balance and the second law of thermodynamics. ) with different network temperature levels, base load ratio (β) and design peak shaving flow ratio (ω') for parallel connection. Figure 6 shows the variation of , , with different DHN temperature levels, base load ratio (β) and design peak shaving flow ratio (ω') for parallel connection mode. Unlike the , , , , , varies with different temperature differences even when ω' = 1-β, and clearly , , is higher for bigger temperature differences within the same DHN supply temperature level. When ω' < 1-β, , , increases linearly with decreasing value of β, and the increasing speed is faster for the system with the larger temperature difference. This makes it possible for , , with lower temperature level to exceed that with higher temperature level, e.g., in Figure 6c, when β is smaller than 0.7 for , , , = {85 °C, 70 °C} with Δt = 15 °C compared with the lower temperature level of , , , = {70 °C, 45 °C} with Δt = 25 °C. In Figure 6d, ω' is further lowered with the highest supply temperature restricted at 135 °C. On the other hand, ω' cannot be larger than 1-β, because in this case the mixed water temperature of heat exchanger and gas-fired boiler cannot meet the DHN requirement according to the heat balance and the second law of thermodynamics.  Design supply water temperature of the gas-fired boiler (°C) Base load ratio β

Supply Water Temperatures of Heat Exchanger and Gas-Fired PB under Working Conditions
In this section, working condition means the situation when outdoor temperature tout is higher than the design outdoor temperature . The calculation of the supply water temperatures of heat exchanger and gas-fired boiler depends on whether the peak heating period begins or not. Therefore, we can divide the heating season into two periods, i.e., during peak heating period when tout falls below the critical peak heating temperature , ′ [2] (peak heating is needed) and the period when peak heating is not needed.

During the Peak Heating Period
When peak heating starts, all heat exchangers are operated in full load and according to the second equation in Equation (8), for series connection we can obtain Because = βQ' and , ′ = (1-β)Q', the supply water temperature of the heat exchanger can be obtained via the following equation In addition, the supply water streams of the heat exchanger and the gas-fired boiler will be mixed to reach the supply water temperature of ts, so the following heat balance exists in the heating substation Therefore, the supply water temperature of the gas-fired boiler can be calculated by The aforementioned results are for the series connection system, and similarly for the parallel connection mode, the supply water temperature of the heat exchanger is Design supply water temperature of the gas-fired boiler (°C) Base load ratio β Figure 6. Variation of the design supply water temperature of the PB (t s,p ) with different network temperature levels, base load ratio (β) and design peak shaving flow ratio (ω ) for parallel connection.

Supply Water Temperatures of Heat Exchanger and Gas-Fired PB under Working Conditions
In this section, working condition means the situation when outdoor temperature t out is higher than the design outdoor temperature t out . The calculation of the supply water temperatures of heat exchanger and gas-fired boiler depends on whether the peak heating period begins or not. Therefore, we can divide the heating season into two periods, i.e., during peak heating period when t out falls below the critical peak heating temperature t out,p [2] (peak heating is needed) and the period when peak heating is not needed.

During the Peak Heating Period
When peak heating starts, all heat exchangers are operated in full load and according to the second equation in Equation (8), for series connection we can obtain Q hr = Q 3 − Q f h,t f = G 2 c water (t s − t r ) − G 2 c water t s − t s,hr = G 2 c water t s,hr − t r (17) Q load,p = Q − Q hr = G 2 c water (t s − t r ) − G 2 c water t s,hr − t r = G 2 c water t s − t s,hr Because Q hr = βQ' and Q load,p = (1 − β)Q , the supply water temperature of the heat exchanger can be obtained via the following equation In addition, the supply water streams of the heat exchanger and the gas-fired boiler will be mixed to reach the supply water temperature of t s , so the following heat balance exists in the heating substation G 2 c water t s,hr − t r + ω G 2 c water t s,p − t s,hr = G 2 c water (t s − t r ) Therefore, the supply water temperature of the gas-fired boiler can be calculated by Energies 2020, 13, 6180 11 of 16 The aforementioned results are for the series connection system, and similarly for the parallel connection mode, the supply water temperature of the heat exchanger is However, the supply water temperature of the gas-fired boiler is the same as Equation (21) for parallel connection, because they have the same heat load balance in the heating substation during the peak heating period.

During the Heating Period When Peak Heating Is Not Needed
When peak heating is not needed, t s,hr = t s no matter for the series or parallel connection modes, and t s,p = 0 because gas-fired boilers are shut down.
In this section, we also show the variation of t s,hr and t s,p with the supply and return water temperature and outdoor temperature of a case DH system located in Dalian, China. The design outdoor temperature t out is −11 • C, the heating season is 150 days, and the heating degree days (HDD18) are 93.25 • C·d. The selected base load ratio β is 0.8, and the design supply and return water temperature are 70 • C and 45 • C. The heat supply of the DHN is controlled by changing the supply and return water temperature and as a result, the temperature differences.
The variation of t s,hr and t s,p with the outdoor temperature for series and parallel connection are shown in Figures 7 and 8. The critical peak shaving temperature of the case DH system is −5.2 • C, when the relative heat load ratio Q = t in − t out / t in − t out equal to the base load ratio β = 0.8. This is also highlighted with an arrow and dotted line in these two figures. Therefore, the peak-shaving gas-fired boilers are not utilized when t out is higher than −5.2 • C, and naturally the supply water temperature of the heat exchanger is equal to t s , regardless of whether they are for series or parallel connection modes. However, when t out is lower than −5.2 • C, the peak shaving gas-fired boilers need to be activated. As shown in Figure 7, for series connection mode, t s,hr is irrelevant to the value of ω , and it is lower than the required DHN supply temperature t s due to the insufficient heat supply from the base load heat source. This means that the gas-fired boilers must provide a hotter water stream (ω g 2,i ) to make the mixed water meet the supply water temperature requirement. Further, the smaller the ω is, the higher the t s,p will be.
Energies 2020, 13, x FOR PEER REVIEW 11 of 17 However, the supply water temperature of the gas-fired boiler is the same as Equation (21) for parallel connection, because they have the same heat load balance in the heating substation during the peak heating period.

During the Heating Period when Peak Heating is not Needed
When peak heating is not needed, ts,hr = ts no matter for the series or parallel connection modes, and ts,p = 0 because gas-fired boilers are shut down.
In this section, we also show the variation of ts,hr and ts,p with the supply and return water temperature and outdoor temperature of a case DH system located in Dalian, China. The design outdoor temperature ′ is −11 °C, the heating season is 150 days, and the heating degree days (HDD18) are 93.25 °C·d. The selected base load ratio β is 0.8, and the design supply and return water temperature are 70 °C and 45 °C. The heat supply of the DHN is controlled by changing the supply and return water temperature and as a result, the temperature differences.
The variation of ts,hr and ts,p with the outdoor temperature for series and parallel connection are shown in Figures 7 and 8. The critical peak shaving temperature of the case DH system is −5.2 °C, when the relative heat load ratio = ( − )/( − ) equal to the base load ratio β = 0.8. This is also highlighted with an arrow and dotted line in these two figures. Therefore, the peak-shaving gas-fired boilers are not utilized when tout is higher than −5.2 °C, and naturally the supply water temperature of the heat exchanger is equal to ts, regardless of whether they are for series or parallel connection modes. However, when tout is lower than −5.2 °C, the peak shaving gas-fired boilers need to be activated. As shown in Figure 7, for series connection mode, ts,hr is irrelevant to the value of ω', and it is lower than the required DHN supply temperature ts due to the insufficient heat supply from the base load heat source. This means that the gas-fired boilers must provide a hotter water stream (ω'g2,i) to make the mixed water meet the supply water temperature requirement. Further, the smaller the ω' is, the higher the ts,p will be.  For parallel connection mode, ts,hr is influenced by the value of ω', and it is higher with saller ω'. When peak heating begins, ts,hr is higher than the required DHN supply temperature ts, because part of the return water (ω'g2,i) flows into the gas-fired boiler, and the rest water will be heated up to a higher temperature since it received the same amount of heat (and also maximum heat) from the base load heat source. This means that the peak shaving gas-fired boiler does not need to provide hightemperature water at the beginning of the peak heating period when tout is not too low. In addition, when ω' = 1-β, ts,p is always lower than the ts, and they are equal only under design working conditions at outdoor temperature of ′ . When ω' < 1-β, e.g., in this case ω' = 0.1, the water flow in the gasfired boiler is smaller and thus ts,p increases faster but ts,hr increases slower with decreasing tout compared to the situation of ω' = 0.2, which makes ts,p and ts,hr intersect with each other during the peak heating period. In any case, the mixed water flow should meet the required temperature of the DHN according to the thermal balance and the second law of thermodynamics.
From another point of view, when peak heating begins, we have the following equation for both series and parallel connection modes.
Furthermore, the design heat load of all heat exchangers can be written as According to Equation (24), we conclude an important property for both series and parallel connection modes, namely the fact that the temperature difference between the supply water temperature of the heat exchanger and the return water temperature is a constant which equals the design temperature difference of , and ′ . Therefore, we can use this property to calculate the supply temperature of the heat exchanger without knowing β and ω', but only with information of tr.

Discussion on the Design Peak-Shaving Flow Ratio
Apart from the supply water temperatures, the design peak shaving flow ratio ω' is another parameter that heavily affects the DH system from the perspective of the pumping energy consumption of circulation water pump for peak-shaving gas-fired boilers and for the secondary DHN. If the value of ω' is too large, the pumping energy consumption of the peak-shaving circulation pump will be increased, otherwise the supply temperature of gas-fired boilers will be dramatically   For parallel connection mode, t s,hr is influenced by the value of ω , and it is higher with saller ω . When peak heating begins, t s,hr is higher than the required DHN supply temperature t s , because part of the return water (ω g 2,i ) flows into the gas-fired boiler, and the rest water will be heated up to a higher temperature since it received the same amount of heat (and also maximum heat) from the base load heat source. This means that the peak shaving gas-fired boiler does not need to provide high-temperature water at the beginning of the peak heating period when t out is not too low. In addition, when ω = 1 − β, t s,p is always lower than the t s , and they are equal only under design working conditions at outdoor temperature of t out . When ω < 1 − β, e.g., in this case ω = 0.1, the water flow in the gas-fired boiler is smaller and thus t s,p increases faster but t s,hr increases slower with decreasing t out compared to the situation of ω = 0.2, which makes t s,p and t s,hr intersect with each other during the peak heating period. In any case, the mixed water flow should meet the required temperature of the DHN according to the thermal balance and the second law of thermodynamics.
From another point of view, when peak heating begins, we have the following equation for both series and parallel connection modes. Q hr = Q hr = G 2 c water t s,hr − t r (23) Furthermore, the design heat load of all heat exchangers can be written as Q hr = G 2 c water t s,hr − t r , therefore, t s,hr − t r = t s,hr − t r ⇒ t s,hr = t r + t s,hr − t r According to Equation (24), we conclude an important property for both series and parallel connection modes, namely the fact that the temperature difference between the supply water temperature of the heat exchanger and the return water temperature is a constant which equals the design temperature difference of t s,hr and t r . Therefore, we can use this property to calculate the supply temperature of the heat exchanger without knowing β and ω , but only with information of t r .

Discussion on the Design Peak-Shaving Flow Ratio
Apart from the supply water temperatures, the design peak shaving flow ratio ω is another parameter that heavily affects the DH system from the perspective of the pumping energy consumption of circulation water pump for peak-shaving gas-fired boilers and for the secondary DHN. If the value of ω is too large, the pumping energy consumption of the peak-shaving circulation pump will be • Under series connection mode, the design supply temperature of heat exchangers t s,hr decreases linearly while the design supply temperature of t s,p increases linearly with decreasing value of β; and their variation speeds are only proportional to the network temperature difference (∆t) but has no relation to the network temperature levels. This makes t s,p with low DH temperature level but at bigger ∆t can even be higher than that with high temperature level at smaller ∆t.

•
For the parallel connection mode, when the design peak shaving flow ratio ω = 1 − β, t s,hr are equal to the design supply water temperature of the DHN and irrelevant to the ∆t. Unlike the t s,hr , t s,p varies with different ∆t even when ω = 1 − β. When ω < 1 − β (Note that ω can not be larger than 1 − β according to the thermal balance), t s,hr decreases linearly but t s,p increases linearly when β is smaller, and the increasing speed is faster for the system with the bigger ∆t. This also makes it possible for t s,p with lower temperature level to exceed that with higher temperature level.
• After examining the variation of those parameters under working conditions with arbitrary t out , an important property for both series and parallel connection modes was revealed, i.e., the temperature difference between the supply water temperature of the heat exchanger t s,hr and the return water temperature t r is a constant which equals to (t s,hr − t r ).
• This study proposed a very important variable called the design peak shaving flow ratio ω , which heavily affects the system from the perspective of the pumping energy consumption. If the value of ω is too large, the pumping energy consumption of the peak-shaving circulation pump will be increased, otherwise the supply temperature of gas-fired boilers will be dramatically increased due to the small flow rate at a certain heat output. There exists an upper and lower limit of ω for both connection modes. The upper limits of ω are 1 and (1 − β) for series and parallel connection modes, but the lower limits should be determined according to the chosen of other parameters, e.g., t s,hr , t s,p , t s and t r . It is recommended to use the smallest possible peak shaving flow ratio for both series or parallel connection modes in order to save pumping energy.
The obtained results can be used in the design of peak heating installations and contribute to the efficiency improvement taking full use of the existing district heating network DHN. Future work is necessary to analyze the optimal operating strategies and pumping energy-saving potential based on the derived thermal balances and operating parameters.