JSDEWES: Thermodynamic-based method for supporting design and operation of thermal grids in presence of distributed energy producers

Climate change and the recent energy crisis have pointed out the urgent need to move towards fully renewable energy systems [1]. District Heating and Cooling Networks are included among the key technologies for the achievement of this challenging goal [2]. More specifically, if coupled with power-to-heat technologies like air-to-water or water-to-water heat pumps (HP), they could help managing the unpredictable electricity production from renewable energy sources (RES) [3], which makes the operation of the distribution electric grid very complex [4]. In addition, they could allow for the sharing of heat produced from distributed thermal RES [5] and the exploitation of low-temperature waste heat (WH) from industries [6] and data centers [7]. Due to these capabilities, energy planning tools like EnergyPlan [8] or EnergyPro [9] include these systems among the key technologies in the development of 100% renewable energy systems.

District Heating Networks (DHN) are not new technologies, but great advances have been achieved during the last decades, in terms of thermal insulation, reduction of pressure drop, and operating temperature. Regarding the latter, DHNs are typically supplied by centralized combined heating and power plants (CHP) where fossil fuels or biomass are burnt, and they are operated at 85 °C (typical value for 3^rd generation DHN) [10]. However, this operating temperature of the networks does not allow for the inclusion of heat from RES or low-temperature WH flows. To solve this problem, the concept of 4^th [11] and 5^th-generation DHNs has been developed [12]. In the 4^th generation, DHNs are operated at a maximum temperature of about 60 °C. In the 5^th DH system, the grid is operated at almost ambient temperature with local boosting at the end-user by using heat pumps to achieve the required temperature level [13].

Attention has also been paid to the development of District Cooling Networks (DCN). In this respect, Østergaard et al. [14] provided a clear picture of the time evolution of this technology, by identifying four generations like in DHNs. Interestingly, in 4^th-generation DCNs, the cold demand of the users is met not only by diversified cold sources such as centralized systems (e.g., absorption chillers, compression chillers) and natural cooling sources (lakes, excess cold streams) but also with cold sharing among prosumers and consumers, with HPs operated in combined heating and cooling mode and with the implementation of distributed cold storages (such as water tank or seasonal storage).

Considering the recognized role played by DHNs in future energy systems, large efforts have been devoted by researchers to optimize DHN design [15]. Some researchers focused on the need to redesign substations in case of the lower operating temperature of 4^th and 5^th DHNs [16]. Some authors focused on the benefits achievable by prosumers in DHNs in terms of achievable energy saving and/or the reduction of carbon dioxide emissions [17]. Other studies, instead, focused on cost evaluation in DHNs. For instance, Gudmundsson et al. [18] found that 4^th DHNs could lead to greater economic benefits compared to 5^th DHNs. Li et al. [19] developed a dynamic price model for DHNs while comparing some criteria to allocate the costs burdening the heat production (e.g., fuels, maintenance, etc.). Tian et al. [20] found that a 5–9% reduction in heat unit cost could be achieved by using solar collectors. Millar et al. [21] found that a 5^th DHN allowed for a strong reduction in heat cost. Verda et al. [22] and Catrini et al. [23] showed the potential of Exergoeconomics for allocating capital and operating costs in DHNs. Finally, other authors addressed the issue of proper maintenance schedules in substations to reduce energy consumption [24]. Indeed, the diagnosis of anomalies in heat exchangers of DHN substations is an essential point to assure high comfort levels in buildings, as well as to save energy. Gadd et Werner [25] identified unsuitable heat load patterns, low average annual temperature difference, and poor substation control, as common faults in European DHNs. Kim et al. [26] developed virtual sensors for detecting fouling in DHN substations using datasets measured from a conventional building automation system. Results showed that by using virtual sensors a 61% improvement in the accuracy of fault detection was achieved.

Considering the strong interest in DHNs, it is useful to provide researchers in this field with simple indicators that could provide insights on the following aspects: (i) the rational uses of thermal energy resources with a different thermodynamic “quality” for DHN supply (e.g., WH at different temperatures or thermal energy from CHP plants), (ii) the effects of thermodynamic inefficiencies occurring in heat production and distribution on the cost of the heat supplied to the users, and (iii) the effect of the off-design operation of poorly-maintained substations. The first point is of utmost importance considering that sustainability issues are pushing society to a keen use of limited energy sources. Meantime, as the number of producers will increase (e.g., the presence of prosumers), there is a need to have indicators that classify them not only for the quantity of thermal energy supplied but also for the thermodynamic quality of the heat flows. Only a few papers have addressed the topic of thermodynamic efficiency in DHNs. For instance, Pass et al. [27] carried out an exergy analysis for a bidirectional network, which adopted a single circuit for both heating and cooling. The authors compared exergy destruction in the case of high- and low head load density vs. individual heating and cooling systems, and the effect of pumping on the exergy destruction was also quantified. Dorotić et al. [28] performed an economic, environmental, and exergetic multi-objective optimization of district heating systems. The minimization of exergy destruction led to the phase-out of natural gas-based technologies.

In a previous paper [23], the authors of this work have developed an exergoeconomic modeling of a ring-shaped network for allocating capital and operating costs in DHN systems. The results highlighted the capability of the method in allocating sustained costs among different users, reflecting the effect of irreversibility on the variation of the unit cost of supplied heat. However, the following aspects were not addressed: (i) the capability of the method to account for different quality of heat sources (especially WH), (ii) the effect of the operating temperature of the grid, (iii) the percentage incidence of irreversibility sources in the heat unit cost (iv), the effect of proper design and maintenance of the DHNs substation on the unit cost of heat. To address the previous points, this paper proposes the Exergy Cost Theory (ECT) [29]. More specifically, ECT provides the unit exergetic cost of a given product (e.g., an energy flow or a stream of matter) which quantifies the resources (measured in exergy) used to produce a unit of exergy of the given product. If inefficient processes are involved along the productive chain of a given product, a large irreversibility is generated, and a high exergy cost is consequent. This property has been proven to make it suitable for allocating sustained costs[30], the consumed natural resources [31], and emissions [32] in multi-output systems. Moreover, it could support the diagnosis of malfunction [33] or be assumed as an index for the evaluation of urban sustainability [34].

In the case of DHNs, by using the unit exergetic cost of the heat supplied to the buildings, it is possible to account separately for inefficiencies occurring in the production units (e.g., CHP plant, RES systems, WH recovery, etc.), along the network (e.g., heat losses and pressure drop), and in substations (arising for instance due to poor maintenance, or wrong design). Moreover, the method allows for performing sensitivity analyses to design (e.g., DHN tube diameter, heat exchanger sizes in substation, etc.) and operating variables (such as heat load sharing among different production units). To show the capabilities of the method, a cluster of five buildings in the tertiary sectors is assumed as the case study. More specifically, a ring-shaped network with centralized fossil-fueled CHP is considered as the base case, and three alternative scenarios are characterized by the presence of waste heat from an industrial process, and prosumers. The paper is structured as follows. In the second section, a detailed description of the physical and exergetic cost modeling is provided. In the third section, the case study is presented together with the simulated scenarios. In the fourth section, results are shown and discussed. In the last section, conclusions are drawn.

To perform the exergy cost analysis of a given process, the definition of the Fuels and Products of each component is required [35]. The “fuel” F_i of the i-th component represents the exergy of consumed energy or matter flows. The “product” P_i is the exergy content of its useful output [35]. The exergy balance is set as shown in Eq. (1), where I_i is the exergy destroyed in the i-th component.

$F_i=P_i+I_i$ (1)

The unit exergy consumption “k_i” is a useful indicator and it is defined by the ratio between Fi and Pi as shown here follows:

$K_i=\frac{F_i}{P_i}$ (2)

To describe the “functional” interactions among components (in exergy terms), the “productive structure” of the given process is developed. This diagram provides a clear picture of the fuels and products exchanged among all components placed along the productive chain of given products. However, in energy systems, it is common to find components necessary for plant operation, (e.g., stacks, condensers, cooling towers, and dust separators), for which it is not possible to define a “productive scope” [36]. To model these units, a common approach consists in considering the exergy destroyed or lost as a “fictitious product” of these components, which is then allocated as additional fuel to the components that contributed to its formation. This “fictitious product” is usually named “residue” [36].

According to the well-known Cost Conservation Rule, all costs sustained along a given production process must be allocated to the final product’s cost. On this basis, the exergetic cost balance is set as shown in Eq. (3), where the exergetic cost of the product $(P_i^{*})$ is equal to the exergetic cost of the consumed fuels $(F_i^{*})$ and allocated residues $(R_i^{*})$ [29]. More specifically, the unit exergetic cost of a product $k_{P,i}^{*}$ (measured in W_ex/W_ex or J_ex/J_ex) indicates, for the generic i-th plant component, the amount of external resources (measured in exergy units) consumed per unit of exergy content of the product of the i-th component [29]. This indicator measures the irreversibility occurring along the production chain of a given stream of matter or energy flow. It follows that (as previously said) the higher the unit exergetic cost of a product, the higher the amount of resources used along the process. Alternatively, this indicator could be used to qualify the thermodynamic rational of different systems aimed at producing the same products.

$F_i^{*}=P_i^{*}+R_i^{*}$ (3)

$k_{P,i}^{*}{P}_i=k_{F,i}^{*}{F}_i+k_{R,i}^{*}{R}_i$ (4)

Note that regarding the allocation of residues, some allocation criteria have been proposed in the literature. In this paper, the criterion presented by Torres et al. [36] was adopted. More specifically, the exergy cost of a residue is allocated to the components proportionally to their contribution to the production of the exergy flow finally destroyed or lost in the dissipative component.

When performing exergy cost analysis, it is useful to gain insights on two aspects: (i) the contribution of the exergy cost of the fuel used to supply the i-th component on the final $k_{P,i}^{*}$; and (ii) the contribution of the irreversibility generated in components placed upstream (including also the i-th component itself) on $k_{P,i}^{*}$. To this purpose, in Symbolic Exergoeconomics [37], researchers have developed general equations that relate $k_{P,i}^{*}$ to the specific cost of the fuels consumed, or to the irreversibility generated along the production process. Regarding the first points, the “technical coefficients” presented in Eqs. (5) and (6) can be adopted. More specifically, κ_ij is the ratio between the exergy produced by the j-th component and used as a fuel by the i-th unit (indicated as E_ji) and the total product of the i-th component. θ_ij is defined as the ratio between the fraction of the residue generated by the j-th component, which is allocated as input to the i-th component, R_ji, and the same product.

$k_{ij}=\frac{E_{ji}}{P_i}$ (5)

${\theta }_{ij}=\frac{R_{ji}}{P_i}$ (6)

It is possible to show that, by combining Eq. (4) with Eqs (5) and (6), the unit exergy cost of the i-th component can be written as follows [29]:

$k_{P,i}^{*}=k_{0,i}^{*}{\kappa }_{e,i}+\sum _{\begin{array}{c}i=1\\ j\ne i\end{array}}^N(k_{P,i}^{*}{k}_{j,i}+k_{R,i}^{*}{\theta }_{j,i})$ (7)

In Eq. (7), κ_e,i quantifies the amount of external exergy resources used to produce the unit exergy of P_i, and $k_{0,i}^{*}$ is the unit exergy cost of these sources. Worth noting that, following ECT rules, in the absence of external assessment, the exergy cost of the flows entering the plant equals their exergy, thus meaning that $k_{0,i}^{*}$ = 1. ECT provides alternative coefficients which directly relate the unit exergetic cost of a product to the irreversibility generated along the productive process of the same product [29]. More specifically, the factors ϕ_ji and ψ_ji, represent the irreversibility and the residue generated in the j-th component to produce the unit of exergy of the product P_i. Using these coefficients, it is possible to rewrite Eq. (4) as follows:

$k_{P,i}^{*}=1+\sum _{i=1}^N({\varphi }_{j,i}+{\psi }_{j,i})$ (8)

Eq. (8) allows for an in-depth analysis of the effects on $k_{P,i}^{*}$ of the irreversibility generated not only in the components that fuel the i-th component, but also in the same i-th component. If no irreversibility was generated along the production of P_i, then $k_{P,i}^{*}$ would be equal to one.

Before providing details on the productive structure for a ring-shaped thermal network, it is useful to briefly present the thermohydraulic modeling, from which the productive structure is then developed. Worth noting that some aspects of thermohydraulic and exergy modeling were already presented in another paper by the authors [23]. However, for the self-consistency of the proposed work, some equations are here repeated.

A cluster of five buildings (briefly indicated as BLD in the following) of the tertiary sector was considered as the case study (Figure 3). It was assumed that the cluster was in Sicily (Italy), and it consisted of the following BLDs: three offices, one hospital, and one hotel. In Table 2, distances among substations are reported. The peak value of the thermal demand of each BLD is also presented. As shown in Figure 3, air-to-water HPs or natural gas (NG) boilers were installed at each consumer not only to supply the uncovered part of thermal demands (for instance, in case of low thermal demand during night-time when it was not economically viable to operate the centralized plant) but also for the sake of redundancy. The nominal heating capacity of local generators is shown in Table 2.

Regarding substations, the UA values are reported in Table 1. These values were calculated according to Eq. 7, by considering an operating temperature of the SR equal to 85 °C and a minimum temperature difference among the water flow drawn from the network and water circulating in the hydronic loop of the building equal to 5 °C. In this respect, the hot water produced in the substations was not the same for all BLDs. For BLD no. 1 and BLD no. 5, it was assumed that water returning from the hydronic circuit was heated up to 78-80 °C. For BLDs no. 2-3-4, instead, hot water at 55 °C was produced. NG gas turbines (GT) were assumed as prime movers in the CHP plant (located in “Node 0” in Figure 3). Moreover, the SR was operated at 85 °C as in the case of 3^rd generation of DHNs. The UA value of the CHP plant substation is also reported in Table 2.

In Figure 4.a, the overall thermal demand of the cluster is shown. The thermal demand profile was derived from a previous study [40]. A peak of around 6.1 MW_th was observed. Moreover, in Figure 4.b, the hourly profile of a typical weekday in winter (beginning of February) is shown. According to the methodological scope of this paper, the following analysis will focus only on the exergy cost analysis for the peak hour in the considered day (indicated by the black dot in Fig 4.b). More specifically, the peak value was around 5,690 kW_th.

The unit exergy cost values are shown in Figure 6.b. Regarding the unit exergetic cost of the heat supplied to the BLDs, k_p*, a value of 3.29 kW_ex/kW_ex was found for BLD no. 5 and 4.15 kWex /kWex for BLD no. 2. The decomposition of the unit exergy cost of the heat supplied to the users (as shown by the different colored bars in Figure 6.b) show that irreversibility generated by the CHP plant (red striped area) play a key role in determining the final unit cost. The irreversibility generated with substation slightly contributes to the final exergy cost of BLD no. 2, conversely, its contribution is negligible for BLD no. 5. The irreversibility generated in the pumps and in the network does not affect the unit exergetic cost of the heat supplied to the buildings.

Regarding the unit exergetic cost of the heat supplied to the BLDs (shown in Figure 8.b), it is possible to observe that it increases up to 4.84 kW_ex /kW_ex for BLD no. 2 and it decreases down to 2.63 kW_ex/kW_ex for BLD no. 5. Moreover, worth noting that the unit exergetic cost of BLD no. 2 is highly influenced by the irreversibility occurring in the CHP plant and LT-WH substation. Regarding BLD no. 5, although the exergy destruction in the substation is increased due to the presence of the booster-HP (blue area), the reduction of the thermal exergy drawn from the network leads to a reduction in the unit exergetic cost.

As previously clarified, the first sensitivity analysis investigated for Scenario no. 1 is the effect of the temperature of the WH on the unit exergy cost of the heat. More specifically, the WH temperature was varied from 100 °C up to 300 °C. The results of this analysis are shown in Figure 10. Note that when the WH temperature is increased, the unit exergy cost of the heat steeply increases. For instance, for BLD no. 2, the unit exergetic cost increases from 3.80 kW_ex/kW_ex when a WH flow at 100 °C is assumed, up to 16.69 kWex/kWex for the WH at 300 °C. This large variation in the unit exergetic cost of the heat suggested that the use of medium-temperature WH flows for producing low-temperature hot water within building substations is not rational.

The second sensitivity analysis investigated the effect of substations’ maintenance on the unit exergetic cost of the heat supplied to the considered buildings. Results are shown in Figure 11. Note that, when the U_sub value is reduced from 100% to 80%, a gradual increase in the unit exergetic cost of heat for BLD no. 2 is observed (+6.83%). However, when U_sub is decreased from 80% to 70% of the nominal value (which would occur in the case of very poor maintenance) a higher change in the unit exergy consumption is observed (+18.5%). Regarding the unit exergy cost of heat supplied to BLD no. 5, it is possible to observe that its value is not sensitive to off- design operation in the substation on BLD no. 2, in case of a low and moderate reduction in U_sub. However, in case of a heavy reduction of U_sub, also the unit exergy cost of heat supplied to BLD no. 5 increases. This result is very important as it shows that this indicator could allow for the prediction of off-design operations of substations and then support the scheduling of proper maintenance programs.

This work proposed ECT for supporting the design and operation of heating networks serving a cluster of buildings. To show the capabilities of this method, a cluster of five buildings in the tertiary sector was assumed as the case study. Some scenarios were compared, respectively characterized by a centralized GT-based CHP plant, the integration of WH, and the presence of prosumers. Results demonstrated that the use of unit exergetic cost of heat could help identify which steps along the heat production process highly contribute to lowering the thermodynamic efficiency, and then leading to high operating costs. More specifically, from this analysis, it was found that the inefficiencies occurring in the CHP plant accounted for almost 50% of the unit exergy cost of the heat supplied to the buildings. Moreover, it was found that a lower operating temperature of the network did not lead to better thermodynamic efficiency if the same heat production units were assumed to supply the network, by keeping the same systems for heat generation. Finally, the analysis revealed a 30% reduction in unit exergy cost of heat when moving from a centralized to a decentralized production, although booster HPs should be installed within substations, The proposed model was useful for performing sensitivity analyses. For instance, when the WH temperature increases, the unit exergy cost of the heat consumed by buildings steeply increases because of the higher exergy destruction occurring in the substation. This trend justified the poor rationale for using medium-temperature WH for space heating. Moreover, in case of poor maintenance in building substations, the increasing value of unit exergy cost of the heat provided not only a quantitative assessment of extra resources consumed for heat production in the off-design condition but also a support for scheduling of proper maintenance program. In conclusion, ECT could provide support in the design, operation, and monitoring of thermal grids.