In order to develop a comprehensive method for supporting the strategic decision of fuel procurement of independent heat producers with coal- and gas-based generation portfolios, this study proposes a practical method for estimating the long-term thermal energy demand of an urban area considering the fluctuations in the residential and commercial property market dynamics, the annual rate of customer acquisition by the network operator, customer disconnections, and the thermal modernization of buildings. Moreover, to tackle the issue of the strategic planning of fuel procurement combined with the simultaneous minimization of production costs, this paper develops a computable model with high enough accuracy to allow the capture of the techno-economic characteristics of the heat sources of an independent heat producer.
Figure 1 shows a diagram of the method developed in this study.
To the best of the authors’ knowledge, no previous study has reported or proposed a practical solution for long-term fuel procurement in complex CHP systems considering the fluctuations in property market dynamics, customer acquisition rate, and the thermal modernization of the building stock. The following sections provide more detailed information on the elements of the proposed method.
2.1. Heat Demand Model
Thus far, the modeling and approximation of changes in thermal energy demand at the city level—mainly due to variation in heat use for space heating and hot water preparation—have been performed using top-down approaches that rely on predictive variables such as heating degree days, number of persons per household, GDP, among others [
26,
27]. Although these approaches have been essential for developing policies and estimating the use of energy for heating, the existing approaches tend to ignore the future trends of the local property market (e.g., property market development, customer acquisition, improvement in energy performance of residential and commercial units) and the market activity of independent district heating producers.
Therefore, this paper contributes to the state of the art by proposing a practical model for projecting the thermal demand of a defined urban area considering five components:
Heat demand in the previous year
Heat demand from the primary market
Heat demand from the secondary market
Heat demand reduction due to customer disconnections
Heat demand reduction due to the thermal modernization of buildings
The proposed heat demand model uses information that is often available to district heating planners and independent district heating suppliers. Moreover, it is a simple and intuitive method for projecting the heat demand of an urban area that can be implemented on a spreadsheet program. Equation (1) describes the relationship between the five components.
where
stands for the heat demand in year
(MWt),
is the heat demand in the previous year
(MWt), and
is the annual increase in heat demand due to changes in the primary heat market (MWt). The annual increase in heat demand from changes in the secondary heat market is described by
(MWt). Moreover,
represents the annual reduction in heat demand resulting from permanent disconnections of district heating consumers (MWt), and
is the annual reduction in heat demand resulting from the thermal modernization of existing buildings (MWt).
2.1.1. Primary Heat Market
The overall change in demand in the primary heat market
is linked to residential and commercial property market dynamics. This relationship can be disaggregated into three components: annual increase in heat demand due to newly built residential properties
(MWt), annual increase in heat demand from newly constructed non-residential buildings
(MWt), and annual increase in demand arising from new products and services offered by the district heating network operator
(MWt). The annual increase in the primary heat market can be found as formulated in Equation (2):
For newly built residential and non-residential buildings, the annual increase in heat demand can be estimated from the cadastral data of usable floor area (building typology) and energy performance indicators for heating, ventilation and domestic hot water preparation [
28]. The calculations should also take into account the share of district heating in the city’s heat demand balance as well as the share of a specific producer in the local district heating market.
The annual increase in heat demand for investments other than residential (office buildings, commercial, cultural and entertainment facilities, etc.) can be computed in a similar way considering the annual increase in the usable area of these types of buildings and their corresponding energy performance indicators.
In the coming years, new products and services offered by the network operator are expected to be available to consumers. Consequently, the proposed heat model may also be expanded to account for the increase in heat demand from new products/services such as the production of cooling for air conditioning. Such services in district energy systems can be achieved using various types of absorption and adsorption chillers and vapor-compression chillers [
29].
2.1.2. Secondary Heat Market
The change in the annual thermal demand of a defined urban area can also be attributed to the fluctuation in the yearly rate of customer acquisition by the network operator. In the proposed model, the changes in the structure of the secondary heat market are associated with the market potential of new customers from areas outside the district heating network (i.e., potential customers are in locations where preliminary plans exist to extend the district heating network). It is worth highlighting that the changes in this market segment can also be attributed to the implementation of hot water programs that support the replacement of old boilers and incentivize the utilization of highly efficient heat generation sources such as central hot water installations. New customers in this market segment comprise owners of existing buildings that can connect to the district heating system and are expected to replace their small-scale fuel-powered boilers used to prepare domestic hot water (e.g., individual sources powered by gas or electricity). Therefore, the overall thermal demand in the secondary heat market can be calculated as the sum of the demand from new customers (driven by expansion of the district heating network) and demand through customer acquisition from the replacement of small-scale fuel-powered boilers. These two components are accounted for using Equation (3).
where
stands for the heat demand of the secondary market in year
(MW
t),
is the heat demand from new customers due to network expansion (MW
t), and
is the additional demand from replacing small-scale fuel-powered boilers (MW
t).
2.1.3. Customer Disconnections and Thermal Modernization of Buildings
In recent years, numerous studies have reported that the building sector accounts for nearly one-third of total global final energy use [
30] prompting governments to roll out ambitious measures to increase the energy efficiency of national stocks of existing buildings. For example, in 2018, the European Commission revised the Energy Performance of Buildings Directive (EPBD) and established the requirement for EU countries to adopt long-term building renovation strategies that include policies and actions to target the renovation of the worst-performing buildings and mobilize the financial institutes to support the transformation of existing buildings into near zero-energy buildings [
31]. Consequently, in the proposed heat demand model, the long-term projections consider (a) the reduction in annual demand
because of the permanent disconnections of customers from the district heating network, and (b) the heat demand reduction resulting from the thermal modernization of the existing building stock
, as presented in Equation (1).
2.2. Optimization Model
In the energy sector, optimization models are often used by decision-makers as normative tools. In other words, they are used in practice to identify the most efficient or optimal path towards achieving an objective while satisfying a set of constraints. This section develops a mathematical program for (1) optimizing the fuel acquisition requirements and usage in large-scale cogeneration systems connected to district heating networks and (2) establishing the long-term operational plan of the constituent elements in the CHP system (peaking boilers and steam turbines).
An important characteristic of cogeneration systems is their ability to satisfy the heat and electricity demand of a specific region of interest. In this context, Equations (4) and (5) present the main assumptions adopted for the definition of the heat and electricity supply–demand requirements. Equation (4) expresses the system’s heat supply–demand relationship. This constraint implies that the sum of the thermal energy production of turbogenerators and peaking boilers
must be greater than or equal to the heat demand
in time slice
in year
.
In a similar way, Equation (5) expresses the electricity supply–demand requirements. In this case, the electricity demand
in time slice
in year
must be satisfied by the total electricity generated in production units that are mainly intended for cogeneration processes. The calculation of the electricity output from production units
is based on the power-to-heat ratio
. We would point out that this modeling approach has been used extensively to represent the electricity–heat production possibility sets of cogeneration activities [
32,
33].
Equation (6) defines the upper bound of the thermal energy production of turbogenerators and peaking boilers
in time slice
in year
. It guarantees that the thermal output of each production unit
is lower than or equal to its maximum continuous rating considering fuel types, grid constraints, and planned/unplanned downtimes, among other factors [
34,
35].
is defined as the fraction of time duration that a unit is available to produce heat or electricity at its rated capacity.
is the maximum achievable thermal power output of production unit
in year
, and
is the duration of time slice
. It is worth noting that the average availability factors of production unit
can be estimated from historical plant datasets.
Equation (7) defines the upper bound of the electricity generated in cogeneration activities. The electrical output of production unit
, calculated as the product of the thermal power output and power-to-heat ratio
, cannot exceed its maximum continuous rating
in year
.
Note that for production units without steam condensation, the power-to-heat ratio can be calculated using Equation (8), while for production units with steam condensation, the power-to-heat ratio can be determined using Equation (9) [
36].
where
stands for the efficiency of total electricity generation and
for the overall efficiency threshold established for a given technology. The power-to-heat ratio presented in Equation (9) considers the efficiency of the total electricity generation of the CHP equipped with steam condensation
and the loss of electricity generation per unit of heat extracted
.
To properly reflect the operating characteristics of the turbogenerators and peaking boilers, it is also necessary to model their technical minimum production levels. Equation (10) sets the lower bound of the allowable thermal output of production unit
in time slice
in year
. The lower bound
is defined as a percentage of the operational capacity of the production unit [
37].
In addition to the previously identified technical constraints, combined heat and power systems often face specific limitations imposed by the requirements of the district heating system operator. For instance, the operators may introduce contractual limitations on the maximum flow rate and temperature of the heat carrier injected into the network. As a result, the production capacity of simultaneously operating units equipped with a particular type of steam turbine (e.g., extraction-condensing steam turbines) should be within the permissible range established by the CHP system owner and the district heating network operator. Equation (11) enforces the contractual limitations that preclude the CHP system owner from operating all turbogenerators simultaneously, preventing flow rates of the heat carrier which exceed the allowable levels of the district heating network.
The reduction in pollutants and carbon dioxide emissions has become a major global concern. In this context, EU member states have developed and adopted specific policies and standards to reduce carbon dioxide (CO
2) and other pollutant emissions (SO
2, NOx, PM) [
38]. Equation (13) sets the upper bound of the total emissions in a calendar year according to the notifications submitted by the operators of installations covered by the Transitional National Plan (TNP) [
39]. In this study, the total quantity of pollutants emitted from the combustion of fossil fuels in year
is calculated as the sum of the products of the thermal power produced
, duration
and emission factors of a given pollutant
. Equation (12) indicates that the total pollutants emitted from the combustion of fossil fuels must be lower or equal to the emission limits set in the TNP for a given year
.
The objective function minimizes the TC while meeting all the constraints formulated in the optimization model. The total production costs are discounted for the base year using Equation (13). The total discounted production costs
of the CHP system are calculated using Equation (14).
The individual components of the objective function are presented in Equations (15)–(18) and can be described as follows:
Fixed costs: calculated as the sum of the product of the power output of production unit and the corresponding fixed cost per unit of installed capacity, Equation (15).
Variable costs (excluding fuel and environmental costs): calculated as the sum of the product of the power generated by unit and the variable costs per unit of heat output, Equation (16).
Fuel costs: computed using the amount of heat and electricity produced, power generation efficiency of unit , and the corresponding prices of the energy carriers , Equation (17).
Greenhouse gas emission costs: computed using the amount of heat produced, emission factors of individual pollutants per unit of heat produced, and prices of emission permits for pollutants , Equation (18).