Cascaded heat merit order for industrial energy systems to evaluate district heating potential

IES consist of a variety of centralized and decentralized energy converters, distribution networks, and energy storage to supply production systems and buildings with energy [1, 2]. Central thermal networks which are supplied by typical energy converters such as CHP, gas or electric boilers, cooling towers, and compression chillers [13] can achieve high energy efficiency levels through economies of scale, efficient technologies, or integration of waste heat [14]. These central thermal networks can be characterized by temperature level and application (Table 1). The integration of heat exchangers (HEX) and heat pumps (HP) between thermal networks can further increase efficiency, but also complexity of such IES [2]. Highly integrated thermal networks of different temperature levels within IES are described as cascaded thermal networks in the following.

Waste heat occurring at industrial sites is often dissipated passively into the air or actively removed from cooling networks by cooling systems. Reusing waste heat can replace heat supply based on fossil fuels and thus reduce energy consumption of IES [13]. Within industrial processes, various sources generate waste heat which can be distinguished as follows:The possible uses of waste heat include in-process, in-plant, or external use. The first two options describe usage within the industrial site. If the potentials of these variants are exhausted - the internal heat demand is met -, potential waste heat integration can be increased by a connection to DHS [15]. Besides waste heat, excess heat from energy converters such as CHP units can be utilized for the use in DHS (see Sect. 1), thus a holistic view on surplus (waste and excess) heat must be obtained in order to evaluate the overall potential.

Due to the introduction of industrial energy management systems, e. g. in the course of implementing ISO 50001 [16], data on IES such as energy flows, volume and mass flows, or temperature levels are often digitally recorded and evaluated. Data analysis can also target measures for increasing energy efficiency, so that waste heat potentials are also investigated and corresponding information is provided [17]. These data can be used for the aim of this paper (Sect. 4).

District heating describes the supply of heat mainly for space heating and hot water in buildings over long distances, i. e., heat generation and consumption are spatially separated. Fossil fuel, biomass, or waste-fired CHP plants often serve as heat suppliers in DHS [18]. By separating generation and consumption, however, other heat sources such as waste heat or renewables can also be integrated. Depending on temperature levels, converter structures, and topologies, DHS are characterized in different generations (Table 2). Especially fourth generation DHS are able to integrate (industrial) waste heat [19].

The heat demand in DHS fluctuates seasonally and with the time of day. This results in load peaks in winter months as well as in the morning and afternoon. Depending on the network, the flow temperature is adapted to the ambient temperature on a sliding basis to achieve necessary thermal power [18]. DHS customers’ retail prices are usually smoothed over the year including network costs, maintenance, cost for capacity provision, marginal cost, etc. [20]. For third parties such as industry which want to feed-in waste heat, the marginal costs of the network determine the maximum profit which can change over time depending on energy converters and energy prices, e. g. for electricity or gas from the energy supplier [11]. For feed-in from third parties, additional ecological requirements have to be met. DHS have to disclose a primary energy or emission factor which should not be worsened by third party feed in [18]. For feed-in planning, internal marginal cost and emission from potential surplus heat sources must be transparent, not only on DHS side, but also within IES.

During IES planning and operation different methods can be applied to address the assessment and integration of waste heat. Woolrey et al. present a systematic approach for waste heat assessment within IES [21]. For systematic waste heat integration, pinch analysis is a common approach in process industry [22] already expanded to manufacturing [23, 24].

Current research on waste or surplus heat potential of IES for DHS mainly focuses on spatial or sector analysis. Here, the assessment of an overall potential within a certain region (e. g. in [25]), country (e. g. in [26, 27]) or sector (e. g. in [6]) can be seen as a top down approach not addressing IES in detail. For specific IES, model based research is conducted such as [28, 29]. These approaches model single waste heat sources and its potential for integration in DHS, often neglecting the complexity of IES. Lastly, technology driven approaches analyse how different technologies can be integrated to utilize, e. g. low temperature waste heat for DHS [30, 31].

To increase economic transparency for potential decentralized heat suppliers in DHS such as industrial waste heat, Moser et al. present the heat merit order transferring the marginal cost approach from electricity markets to heating networks [11]. The heat merit order lists all heat generating units in DHS according to their specific heat costs and energy quantities per time unit (Fig. 1). According to the heating demand, the currently achievable price for a feed-in source can be determined. The profit of a feed-in can then be determined by the difference between the generation costs of the feed-in and the current price. From this, possible investment cost or operational planning can be derived [11].

For the simplified, transparent representation of the heat merit order, part load behavior and grid restrictions are omitted. Furthermore, compared to the electricity market, there are significantly fewer generation units in the merit order and CHP processes with corresponding electricity prices can also result in negative specific cost [11]. The approach is based on the assumption that the supplier (industry) wants to evaluate a waste heat source in terms of economic potential, but omits the fact that IES have different (waste) heat sources, which should be investigated as a whole in terms of potential analysis. Furthermore, information about the ecological impact is only indirectly addressed.

As outlined in Sect. 1, industrial companies seek to reduce energy cost. By economizing industrial waste or excess heat through DHS, their overall site specific energy cost can be reduced [33, 34]. Moreover, due to ecological challenges, states provide incentives for increasing energy efficiency and emission reduction, e. g. taxation-benefits after certification within ISO 50001 [16]. After analysing and integrating industrial waste heat on-site, data on the amounts, specific cost, and specific emissions of surplus energy which can be traded with DHS must be obtained. As feed-in into DHS in operation depends on marginal cost, an estimation of time dependent available feed-in at a (potential) coupling point must be calculated and evaluated. The obtained information can be used to communicate with energy suppliers for operational or investment planning in order to develop business models around industrial waste heat (Sect. 4.7). The two main goals / business models can be described as follows:

In Sect. 2, the cascaded characteristics of thermal networks in IES are outlined. To apply the presented methodology, the specific network topology and characteristics such as temperature levels of an IES must be known. Figure 4 gives an example of a cascaded IES with a high and low temperature heating network as well as a cooling network to supply production systems and buildings with thermal energy.

Besides the network topology, data of available energy converters such as nominal power and efficiencies, thermal power of integrated waste heat sources from production processes and energy demands as well as prices for external energy supply such as gas and electricity have to be collected. These data are typically available in implemented energy management systems. If the methodology is applied for operational planning, e. g. day ahead, forecasting of energy demands and waste heat supply must be integrated.

Some thermal energy demands such as steam and cooling supply are usually recorded in other formats than power or energy. The former is often tracked in mass \(\textrm{m}\) (tons), the latter in volume \(\textrm{V}\) (\(\text {m}^{3}\)). In order to apply the heat merit order, the time dependent thermal demand of steam \({\dot{\textrm{Q}}}^{\textrm{steam}}_{\textrm{t}}\) and cooling supply \({\dot{\textrm{Q}}}^{\textrm{cooling}}_{\textrm{t}}\) must be converted as shown in Eqs. 1 and 2:The steam demand is calculated with the pressure dependent specific enthalpy of steam \(\Delta \textrm{h}\) while cooling demand is dependent on the temperature difference between flow and return temperature of the cooling network. \(\Delta \textrm{t}\) describes the time step length.

Lastly, information on the heat transfer station (HTS) between the IES and the DHS—especially on its subsystems—is necessary. For investment planning, potential transfer points must be evaluated. For operational planning, the IES is already connected via HTS to the DHS.

To set up the cascaded heat merit order and store data for the analysis, a data model for each component of IES is generated. An overall factory model includes data models of thermal networks, energy converters, waste heat sources, energy demands, and the DHS as displayed in Fig. 5. The relational multiplicities are also illustrated.

The IES superstructure is represented in the data model by a Factory object which contains all thermal networks that are part of the IES as a list of HeatNetwork objects as well as a list of NetworkConnector objects which establish relations between the IES thermal networks, e. g. via HP or HEX. A Factory object must consist of a minimum of one HeatNetwork and one DHS object. HeatNetwork objects contain functions for establishing their internal heat merit order as well as a list of EnergyConverter objects and Demand objects.

All typical thermal supply and demand systems are modeled as objects inheriting the base functionality of HeatDemand and EnergyConverter objects, respectively, and are extended with methods in order to represent their specific cost and supply structure. HP and HEX are modeled as subclasses of NetworkConnector objects and provide the necessary methods for applying penalties for transporting heat between thermal networks.

Necessary input parameters for the cascaded heat merit order are calculated and stored within the data model. These parameters include time dependent capacities \({\dot{\textrm{Q}}}_{\mathrm{i/j,t}}\cdot \Delta \hbox {t}\) of energy converters \(\textrm{i}\) and waste heat sources \(\textrm{j}\) as well as their marginal cost \(\textrm{c}_{\mathrm{i/j,t}}\) and specific emissions \(\textrm{e}_{\mathrm{i/j,t}}\). Moreover energy demands \({\dot{\textrm{Q}}}^{\textrm{dem}}_{\textrm{n,t}}\) for each thermal network \(\textrm{n}\) are calculated as the sum of all demands in this network.

The marginal cost of heat sources such as energy converters or waste heat from production processes can include the following variable cost parameters [11]:The following equations show the basic calculations for energy converters such as boilers (Eq. 3), CHP units (Eq. 4), HP (Eq. 5), and a single waste heat source (Eq. 6) with corresponding efficiency measures (\(\eta ^{\mathrm{th/el}}_{\textrm{i}}\) and \(\textrm{COP}_{\textrm{i}}\)):The specific emissions e for each energy source are calculated in the same way as energy cost (Eqs. 7–10).The calculated specific emission can be used to integrate cost for \(\hbox {CO}_2\) certificates by multiplying with the \(\hbox {CO}_2\) price. If the direct waste heat source does not need to be cooled such as waste heat from heat treatment furnaces, the term for cooling in Eqs. 6 and 10 is set to zero.

By applying the cascaded heat merit order, the waste and excess heat potential for every time step is quantified. How the heat merit order is set up for a single thermal network is described in Sect. 3.2 and [11]. As IES can consist of several interconnected thermal networks, the cascaded heat merit order must be set up for each network after which the heat exchange between networks must be evaluated. Figure 6 shows the cascaded heat merit order exemplarly for three networks. The high temperature heating network (HN-HT) is connected via HEX to the low temperature heating network (HN-LT). Thus, depending on maximum power of the HEX, thermal energy can be transferred from HN-HT to HN-LT. Moreover, heat from the cooling network which contains waste heat from production processes can be integrated into the HN-LT via HP. Depending on the COP of the HP, the heating power differs from the cooling power. If the DHS is connected to the HN-LT of the IES, a heat merit order for the transfer station can be derived. The parameters of the heat sources are calculated as stated in Sect. 4.3. As explained in [11], the cascaded heat merit order must neglect part load behavior of energy converters to enable a linear calculation for single networks with focus on the maximum potential output of surplus heat.

To calculate a generic cascaded heat merit order for n heating and cooling networks with i energy converters and j waste heat sources, an algorithm as displayed in Fig. 7 is developed and integrated. The algorithm is divided into two levels, the factory level and the thermal network level. First, the factory is initialized with all components such as thermal networks, network connections, energy converters, waste heat sources, and energy demands. Then, on the network level, iteratively for each thermal network, the supply merit order (energy converters and waste heat sources) is set up for each thermal network which can supply into the current thermal network (parent networks). Thus, all thermal sources to meet the internal demand are considered to match supply and demand for each thermal network. For example, in a heat network which is connected to a higher temperature steam network via HEX, all internal sources are considered as well as all sources within the connected steam network. On the factory level, overall demand and supply matching can be conducted. Due to the network connections, some energy supply sources may appear more than once in the total set of all network-level merit orders. This is why in the next step only the cheapest match between supply and demand is subsequently chosen. The transferred energy amount is then subtracted from both the energy supply source as a capacity reduction and from the energy demand. If the specific energy demand is met or the full capacity of an energy supply source is exhausted, these are removed from the factory. The merit orders of the networks within the resulting factory with adapted energy supply sources and energy demands are then recursively calculated again until no matching energy demands and energy supply sources are left.

The resulting heat merit order is stored to be analysed with further data in the analysis block.

The results of the cascaded heat merit order calculation can be used for different applications. Depending on whether the heat merit order of the DHS is known or unknown as well as if an operational or investment planning is the goal, different analyses can be conducted.

For investment planning and if the heat merit order of the DHS is known, time dependent values of both merit orders can be compared as described in [11]. Depending on the marginal cost in the DHS which can be replaced by the surplus heat of the IES, a maximum profit can be calculated. This way, maximum investment cost for a heat transfer station can be derived e. g. on the basis of one year of data. If the DHS heat merit order is unknown, the results of the cascaded heat merit order can be analysed regarding the energetic potential of single energy sources, e. g. the cooling network, as well as the base load potential of the IES. The base load potential describes how much energy the IES can supply continuously over a certain time period, e. g. a month, a quarter or a year. The base load may vary depending on price of emission restrictions. Compared to a uncertain feed-in, base load supply ensures security of supply for the energy supplier.

For operational planning and if the DHS heat merit order or if a pricing scheme is known, as in Stockholm Open District Heating,² the industrial company can plan which amount of energy it will provide based on the profits it can make. If the pricing scheme is not known, the cascaded heat merit order can be used to communicate offers to the energy supplier. These offers can be used in direct communication with the energy supplier in order to establish a long-time cooperation or to participate in dynamic heat market structures.

Exemplary analysis of the cascaded heat merit order are presented in Sect. 5.2

The analysis of the cascaded heat merit order can provide indications whether it is economically viable to feed in surplus heat. In an exchange with the energy supplier, further information can be requested, e. g. the merit order of the DHS. Based on this information, feed-in potentials can be specified—if necessary with iterative repetition of the merit order calculation—and further steps can be initiated together with the energy supplier (Fig. 2).

After deciding on traded energy amounts, further steps can be initiated. Depending on the application, further steps can be the technical planning (engineering) of the heat transfer station (investment planning) or setting up control signals for operational planning.

The following use case represents an industrial company which is planning a connection to a nearby DHS, thus aiming to utilize and trade waste and excess heat. The presented methodology can support the goal by creating transparency about the potential of connecting the IES to the DHS.

The IES of the industrial company consists of five thermal networks:The steam network is connected to the high temperature network via HEX and the high temperature network to the low temperature network, respectively. Waste heat, e. g. from production processes within the cooling and cold water network are connected to the low temperature network via HP. The efficiency of the HP depends on the temperature difference between low temperature network and the respective cooling or cold water network. The provision of heat from cooling or cold water networks via HP can be a cost-effective source for space heating in low temperature networks [35]. Moreover, waste heat from compressors for compressed air is integrated into the low temperature network. It is assumed, that a potential coupling point to the DHS is via low temperature heating network. Surplus heat is upgraded via HP to meet the temperature requirement in the DHS. Through the coupling point via low temperature heating network, excess heat from the two CHP units as well as waste heat from the compressors, cooling network and cold water network is available for the integration into the DHS. Depending on internal energy demands, the potential of the energy sources changes over time. Parameters on cost, energy converter capacity and energy demands of the networks are known and data for one year is available. For the IES, the data model is set up and necessary parameters to calculate the cascaded heat merit order are derived.

In the case study the cascaded heat merit order was calculated on an hourly basis for 2021. In the following, resulting heat merit order diagrams are exemplarily shown and discussed. The identified heat supply potential throughout the year within the case study is analysed. Based on all hourly merit orders, the base load potential of the IES is evaluated and discussed.

Figure 8 shows an exemplary heat merit order during production times in a summer month. The main heat source at this time stems from coupling the cooling demand of the cold water and cooling networks into the low temperature heat network and upgrading the resulting heat surplus to the temperature requested by the DHS. A remaining CHP waste heat potential which is not used up internally can be provided at the lowest specific price. The price of the cooling and cold water demand result from the difference of HP expenses and avoided cooling costs such as from cooling towers and compression chillers. The increased cooling cost within the cold water network results in a lower specific price compared to heat provided via the cooling network even though HP expenses are higher for cold water sources. It should be noted that the resulting heat merit orders can vary within a day and between days, depending heavily on plant operation and ambient temperatures. The effects of this dependence are discussed at a later point within this section.

A merit order for a colder month is presented in Fig. 9. The cooling demand and thus potential for this date is significantly reduced, mainly due to the difference in ambient temperature compared to the summer date discussed above. Waste heat resulting from air compressors is similar in amount to operation in the summer months and can be provided here at the lowest price. For this date, all CHP waste heat was used internally and is thus not provided to the DHS. Instead a more expensive gas boiler supply can use the available HEX capacity and cover some of the supply difference compared to the summer case discussed above.

In application of the methodology presented in this paper, the potential surplus heat throughout the year is of interest to the industrial company and the local energy supplier. Figure 10 shows the monthly mean supply potential after applying the cascaded heat merit order for 2021. To provide a clear representation, the supply is averaged over each month. In further steps of investment planning, heat storage sizing can be used to smooth the available supply. The different heat sources are stacked by their price from bottom to top. A clear trend of heat surplus in the summer months due to increased cooling operation is visible. This inversely corresponds to the decreased DHS demand during summer months as previously shown in [11]. Available waste heat from the IES compressed air source is steady throughout the year. During the winter months, boiler operation can cover some of the deficiencies from missing cooling demand. From this graph, a first conclusion of available waste heat throughout the year can be drawn.

Due to the variable nature of the available heat, an indicator to assess constantly available heat for a given time frame is presented in the following. This metric is of especial interest for communication, as a guaranteed base load is often part of bilateral agreements between industrial sites and energy suppliers. For this approach, all merit orders within a specified time frame are taken into account. The minimum available amount of heat that can be provided for each time step defines the maximum supportable base load for a given time frame. The average specific heat price is calculated for \(\textrm{n}\) grid points and plotted over the corresponding heat supply. The resulting graph for the whole year of 2021, June of 2021 and December of 2021 is shown in Fig. 11.

The graph shows a clear difference in marginal cost between the summer and winter months. This information can be taken into account by an industrial company in finding a profitable pricing model for year-round feed in. A continuous supply of 0.8 MW can be achieved by the IES over different heat sources for marginal cost of around 27 €/MWh. If the DHS only needs base load over winter months marginal costs rise to 35 €/MWh. The cascaded merit order was calculated in an economic manner so that it does not necessarily suggest the most \({CO_2}\) effective feed-in. Thus, in the summer month, the specific \({CO_2}\) emissions decrease with increasing base load.

The presented methodology for deriving and analysing the cascaded heat merit order for IES can increase transparency in an economic and ecological view for the coupling with DHS. The marginal cost, specific emissions, and time dependent energetic potential of heat sources for DHS are integrated into the heat merit order to achieve a holistic view on the energetic potential. The economic view corresponding to [11] follows the goal of profit maximization in industrial companies. As the supply of surplus energy is not the main business of industrial companies, the approach aims to support the industrial energy management and to decrease information deficits for a more effective communication with energy suppliers.

The presented algorithm can handle the complexity of several thermal networks with potential waste and excess heat sources for DHS. As the heat merit order assumes that the energy demands of the internal production systems are met before energy is traded with the DHS, the internal security of supply is ensured.

Due to the high level economic and ecological focus, technical requirements are simplified such as part load behavior of energy converters, heat storage or flexibility in production processes. The cascaded heat merit order gives a first impression of the potential feed-in regarding energy amount and base load potential. Further engineering in investment planning must be conducted subsequent to the approach. Although the use case focuses on a potential estimation for investment planning, the approach can be used for both operational and investment planning.