In Europe, the heating and cooling demand accounts for more than 60% of the final energy use in the residential sector, yet renewables currently only supply a quarter of the EU's space heating needs [1]. District Heating and Cooling (DHC) networks, in particular the 5^th Generation (5GDHC), represent a valuable solution for the reduction of primary energy use and both global and local emissions [2]. The primary objective of 5GDHC is to increase the share of residual and renewable energy sources (R²ES) by lowering the supply temperature close to ground temperature (T_s < 30 °C), facilitating the exchange of low-quality thermal energy. While global warming is already progressing, the cooling of buildings is becoming more relevant in urban energy systems [3], which is another reason why 5^th generation district heating and cooling (5GDHC) networks are gaining interest as they allow for simultaneous heating and cooling through a bi-directional network. Heat pumps and/or chillers, in decentralized “active” substations, upgrade the low-exergy heat to the required quality, while a centralized balancing unit usually keeps the temperatures within a specified range [4].

However, the operation of these future-proof networks is not yet optimised, and the future enhancements of system performance through optimal integration and control of distributed heat and cold sources are needed, as highlighted in [4][5][6]. Meibodi et al. [7] introduced the use of the energy hub concept [8] for the design optimization of 5GDHC networks, but emphasized the necessity of new modelling approaches for the bidirectional energy flow in 5GDHC networks. Moreover, control strategies for 5GDHC networks vary significantly based on system configurations, temperature settings, and optimisation objectives, underscoring the need for advanced control strategies beyond rule-based controls [4].

Different classifications of 5GDHC networks exist, depending on the number of pipelines at different temperature levels and the direction of energy and medium flows. Buffa et al. [9] conducted a thorough survey on different 5GDHC networks in Europe and identified two main configurations of “prosumers” substations: i) Bidirectional energy - Non-Directional medium flow (BiND), ii) Bidirectional energy - Directional medium flow (BiD). In the most advanced solution with non-directional medium flow, the system is able to reject warm water (in active or free cooling mode) in the warm pipeline and cold water (in heating mode) in the cold pipeline. In this way, heat pumps will operate with higher COP thanks to optimal boundary conditions and both cooling and heating demands can be satisfied simultaneously. On the other hand, the directional medium flow configuration offers simpler hydraulics, but at the cost of lower performance in either heating or (not and) cooling mode. However, in the non-directional medium flow configurations, pump-to-pump interactions present a big challenge, as highlighted by Sommer et al. [10]. Large sizes of the decentralized pumps in the different substations strongly affect the mass flow rates through smaller proximal circulation pumps. These interactions may cause possible freezing problems in the heat pump due to lower mass flow rates or even reverse flows. For these reasons, a robust network control becomes crucial and challenging for the non-directional medium flow configuration, especially with increasing mass flow rates and extended networks.

Zanetti et al. [11] proposed an improved control strategy to reduce the energy use of pumps, highlighting the significant impact of pumping energy at low temperatures. Easiness, comfort, and affordability seem to dominate building owners’ preferences for heating system choices in households, with increasing environmental awareness [12]. In this context, Taylor et al. [13] presented Model Predictive Control (MPC) as a particularly promising control strategy for 5GDHC networks, being able to predict evolving system states, taking into account the physical behaviour of the system, building thermal inertia, and weather forecasts. This allows for Demand Side Management (DSM) through system control, enhancing overall system performance by shifting heat demand or leveraging building inertia [14]. Different optimal control approaches have been presented in the literature by Frison et al. [15] and Wirtz et al. [16], with mixed-integer nonlinear program (MINLP) MPC for a bidirectional energy - non directional medium flow configuration, although these show simplified control-oriented models. Bünning et al. [5] developed an agent-based control strategy with network temperature optimisation, comparing different scenarios with different heating and cooling demands and boundary conditions. Sommer et al. [10] contributed to the state of the art by providing insights into the effect of different 5GDHC network configurations on total energy use. They compared a base-case double pipe network with a reservoir network through Modelica dynamic simulations. The operational and economic feasibility of bidirectional energy - directional medium flow configuration has been investigated by different studies in literature. Bilardo et al. [17] focused on modelling a low-temperature 5GDHC system, demonstrating its potential for enhanced efficiency and flexibility. An advanced thermo-hydraulic network model for 5GDHC systems with directional medium flow was also developed in [18], enhancing the accuracy of pressure drop and heat loss calculations by incorporating temperature-dependent fluid viscosity and convection effects. However, both models rely on simplified demand profiles instead of detailed building simulations. Vivian et al. [19] explored smart control strategies for heat pumps in 5GDHC networks, yet their approach is constrained by post-processing control, limiting real-time adaptability. Saini et al. [20] conducted a techno-economic analysis, highlighting the economic viability of 5GDHC networks with a BiD configuration under various market conditions. However, the network and substations performance were evaluated in a co-simulation environment, increasing the complexity and neglecting key non-linearities in thermal and hydraulic behaviours. On the other hand, Penttinen et al. [14] highlighted the necessity to better understand the restrictions imposed by supply temperature reduction.

Despite these advancements, the existing studies often rely on demand profiles, simplified building models, or linear models, and rarely combine the strengths of detailed physics-based models, non-linearities, and direct optimisation without the need for post-processing controls. Hermans et al. [21] contributed filling this gap by developing a detailed controller model that includes nonlinearities for the specific BiND configuration.

Therefore, this study aims to develop a similarly featured controller for the directional medium flow configuration (BiD) for 5GDHC networks in order to assess its performance compared to the BiND configuration. The BiD configuration has a simpler hydraulic design which might eliminate the shortcomings of the non-directional medium flow configuration (BiND), guaranteeing more robust operation conditions. To compare both configurations (BiD and BiND) in a fair way, Model Predictive Control (MPC) is used as a strategy to minimise energy use, while providing thermal comfort. To enhance understanding of the impact of the different configurations on the 5GDHC system performance, dynamic simulations are performed using a virtual district. For the BiND configuration, a mixed-integer nonlinear programming (MINLP) MPC has already been developed and analysed by Hermans et al. [21]. For the BiD configuration, a new approach is developed and employed in this paper to solve the nonlinear Programming (NLP) MPC.

In addition, this paper assesses the impact of several key factors on the optimisation results, among them: the building thermal performance, the pumps energy use and the thermal comfort constraint imposed on the floor surface temperature. These factors are integrated into the MPC framework for the BiD configuration to provide a comprehensive analysis of their influence on system performance.

This study introduces a novel nonlinear programming Model Predictive Control (MPC) formulation for the Bidirectional energy - Directional medium flow (BiD) configuration of a 5^th Generation District Heating and Cooling (5GDHC) network. The performance of the BiD configuration is evaluated under two distinct Scenarios:

• Scenario A: This Scenario considers a district with poorly performing buildings. The objective is to minimize the total energy use of heat pumps and thermal discomfort, without imposing any constraints on the minimum floor temperature.

• Scenario B: This Scenario considers district with better-performing buildings. The goal is to minimize the total energy use of both heat pumps and pumps, as well as thermal discomfort, while also imposing a constraint on the minimum floor temperature.

For Scenario A, the BiD configuration, using the novel NLP MPC formulation, is compared to the non-directional medium flow (BiND) configuration, for which a Mixed-Integer Nonlinear Programming (MINLP) MPC formulation developed by Hermans et al. [21] is employed. Both optimisation problems for the two configurations are evaluated using the same cost function to ensure a fair comparison.

Scenario B is then compared to Scenario A to assess the impact of improved building performance, the inclusion of pumping power in the cost function, and the additional constraint on floor temperature.

For both scenarios, detailed physics-based models of building envelopes, thermal systems, and hydraulic components are developed in Modelica, an object-oriented, equation-based, acausal, multi-domain modelling language. These models are integrated into the MPC framework to create a high-fidelity controller model, ensuring effective exploitation of the system's flexibility.

The optimal control problems are formulated in TACO (Toolchain for Automated Control and Optimization), an in-house developed Modelica-based toolchain for nonlinear white-box MPC [22]. MPC simulations are conducted over an 8-month period (from January to August) to investigate and analyse the control behaviour of the two configurations. The energy use and thermal discomfort levels are then compared for the BiD and BiND configurations, as well as for the two MPC frameworks used for the BiD configuration.

Use case and model description

A small virtual 5GDHC network consisting of 4 residential buildings, 1 office building and a central balancing unit, serves as an example district to compare both configurations. The buildings are selected in order to simulate a typical Belgian district, with a variation in building quality (different UA values) and functions (residential and office). Linear two-zone white-box models for all buildings are created using the approach of De Jaeger et al. [23], with a day and night zone representative for the dwellings and a north and south zone for the office building.

Figure 1 shows the UA-value distribution of a typical Belgian district and the UA-value ranges of the buildings selected for the two Scenarios. In the transition from Scenario A to B, House 2 was replaced with a more energy-efficient building, still representative of the distribution but no longer at the extreme end. House 4 was also replaced, but the new building remains within the same UA range, however a building with improved window and roof transmittance was chosen to better accommodate low-temperature heating. As a result, two different buildings with distinct geometries were selected from the Belgian archetype buildings while maintaining consistency with the UA-value considerations. Table 1 reports the main building parameters of the districts in both Scenarios. The heat power design value Q is calculated taking into account all heat loss terms (transmission, reheating, infiltration), using a setpoint of 21 °C and 18 °C for the day zone and the night zone respectively.

Figure 1.

Typical Belgian district UA-value distribution [23]

Table 1.

Summary of buildings specifications [23]

	House 1	House 2		House 3	House 4		Office
	A and B	A	B	A and B	A	B	A and B
A floor [m2]	81	307	449	334	153	167	200
V [m3]	269	1,093	1,394	1,027	517	565	600
UAbuilding [W/K]	89	1,820	1224	392	550	542	173.1
Uwall [W/m2/K]	0.145	2.359	2.335	0.48	2.100	2.27	0.333
Uground floor [W/m2/K]	0.889	1.467	0.824	0.784	0.380	0.638	0.040
Uwindows [W/m2/K]	1.631	5.86	3.534	2.055	3.028	1.909	1.400
Uroof [W/m2/K]	0.345	3.107	0.572	0.336	1.400	0.605	0.349
n50 [1/h]	8	8	8	8	8	8	3
Q ˙ designdayzone [W]	2,835	28,325	23138	10,312	11,204	13,728	4,400
Q ˙ designnightzone [W]	2,664	29,699	23,267	10,073	9810	7,098	4,400

The considered central balancing unit then comprises of i) a large buffer tank (20 m³), in order to dampen the seasonal temperature fluctuations in the network, ii) a large modulating air-source chiller (ASCH), and iii) a large modulating air-source heat pump (ASHP). The heat pump and chiller are necessary to maintain the buffer tank's temperature within the range of 3–16 °C. This network temperature range is set to avoid freezing and, at the same time, enable direct cooling, according to the average temperature adopted in 5GDHC networks [10], [24]. To keep new model development limited, the choice to use separate units (ASHP and ASCH) instead of a single reversible air-source heat pump was made without impacting the main findings. To model the HVAC components and the buildings the IDEAS Modelica Library is used for most parts [25]. The fundamental equations of these models can be found in the APPENDIX of this paper. However, as TACO requires that all model equations are continuous and twice differentiable, an in-house developed Modelica optimisation component library is used to model pumps, valves, and heat pumps.

The uninsulated district heating/cooling pipes (typically used in existing 5GDHC networks) are explicitly modelled by a single volume to account for the hydraulic limitations and heat losses of the network [24].

The considered emission system that provides both heating and cooling in each zone of the buildings is an embedded floor system controlled by two valves. The heating demand is satisfied by a modulating water-source heat pump (WSHP), while a heat exchanger (HEx) is used for direct cooling. The two configurations (BiD and BiND), compared in the present paper, mainly differ in the hydraulic scheme of the substation, presented in Figure 2 and Figure 3. The BiD configuration is characterized by a centralized on-off pump, which determines a unique flow direction in the network. The flow can be directed through the direct-cooling heat exchanger or the WSHP depending on the positions of the three-way valves, which select the heating or cooling mode. In the more flexible BiND configuration, two decentralized on-off pumps provide the fluid flow through the HEx or the WSHP depending on the mode selected by each prosumer.

Figure 2.

Simplified hydraulic scheme of bidirectional energy - directional medium flow (BiD) substation configuration

Figure 3.

Simplified hydraulic scheme of bidirectional energy - non-directional medium flow (BiND) substation configuration [21]

The thermal system sizing and modelling is in line with the approach used in [21]. A nominal temperature difference of 3 K is considered across each substation, while a nominal temperature difference of 5 K is taken across the floor heating/cooling system. The total heat demand, Q ˙ design , of the connected buildings is then used for the heat pump and pipeline sizing.

The modelling approach used considers prescribed pressure head pumps, valves with linear opening characteristics, and a constant effectiveness (0.8) heat exchanger. The central buffer tank is modelled as a perfectly stratified two-layers tank, with two mixing volumes of each 10 m³. The substation heat pumps (WSHP) and central heat pump (ASHP) coefficients of performance (COP) and the central chiller (ASCH) energy efficiency ratio (EER) take into account the temperatures dependency, according to eqs. (1a), (1b), (1c) respectively [26]:

COP WSHP =6.4−0.16( T con,out −29)+0.1( T eva,out −11) (1a) COP ASHP =4.7−0.16( T con,out −20)+0.1( T eva,out −6.98) (1b) EER ASCH =3.7−0.16( T con,out −20)+0.1( T eva,out −6.98) (1c)

where T_con,out [°C] and T_eva,out [°C] are respectively the condenser and evaporator outlet temperatures. The part-load limitations and efficiencies are not taken into account in this case.

Occupancy schedules and related temperature setpoints are used to assess the thermal comfort inside the buildings. Standard office hours spanning from 8 a.m. to 6 p.m. during weekdays are considered. In the residential buildings, the setpoint temperatures are between 21–23 °C and 18–25 °C for the day and night zone respectively, when people are present (which is outside the office hours), while between 15–27 °C when no one is present. No internal gains are considered for the residential occupants. The temperature ranges for the office building are set between 21–23 °C during the office hours and 15–27 °C when no people are present. 20 people are assumed to be present in the office and a fixed internal heat gain of 55 W/person is considered. The metabolic heat gains are set to 45 W latent heat production per person and 73 W sensible heat production per person [27]. IDEAS library's TMY-file (Typical Meteorological Year) for the Belgian region of Uccle is used for the ambient temperature and solar irradiation information.

This section presents the results of the 8-month MPC simulation for the two configurations and settings analysed. In the first step, the directional and non-directional configurations are compared. Table 2 summarises the main results for Scenario A, in terms of electricity use of the decentralised heat pumps and central units (ASHP and ASCH), and thermal discomfort. Based on the ASHRAE standard 55 [28] and the ISO7730 standard [29], the need for thermal comfort in the Belgian climate can be converted into a requirement on the operative temperature. Therefore, according to [30], thermal discomfort can be measured in Kelvin-hours.

The BiND configuration presents a total heat pump electricity use of 41 MWh, while the BiD configuration outperforms it with 38 MWh over the 8-month period. A similar approach as the one used in [21] is adopted for the comparison of the seasonal performance factor (SPF) in the two configurations, evaluating the total benefit in each building, in terms of heat provided in winter period Q ˙ WSHP,con,n and extracted in summer period | Q ˙ HEx,n | , versus the total heat pump electric energy use over the simulation period E_tot , eq. (4):

Both configurations show an SPF value of 3.34. This indicates that the electricity use reduction reflects into a lower thermal benefit in the directional medium flow configuration compared to the non-directional one, as expected from the observed thermal discomfort inside the buildings. This is clearly noticeable in House 2, where a particularly high level of thermal discomfort is balanced with limited energy use, due to the poor performance of the building envelope. The average COPs and EER of the different components in the buildings (Houses and Office) and in the central balancing unit are compared in Figure 4. It can be observed that the average COPs of the decentralised and centralised heat pumps in the BiND configuration are higher, leading to lower thermal discomfort for similar energy use. On the other hand, the efficiency of the centralised chiller is higher in the BiD configuration, with significantly lower energy use.

Figure 4.

Energy performance (COP or EER) comparison of the different components (decentralised heat pumps, centralised heat pump and chiller) in the two configurations in Scenario A

The difference between the two configurations mainly occurs due to different supply temperatures to the heat pumps. Figure 5 shows the daily average network temperatures as the daily average temperatures of the buffer tank for the BiD configuration and BiND configuration. The supply temperature is represented by the average temperature of mixing volume 1 (i.e. upper part of the stratified tank), while the return temperature corresponds to the one of mixing volume 2 (i.e. lower part of the stratified tank). It can be observed that the BiND configuration, compared to the BiD configuration, allows for higher average network temperatures on the primary side during the heating season, due to its enhanced flexibility and self-balanced network. Indeed, the excess heat resulting from high internal heat gains in the office is injected directly in the warm pipe, enabling a lower energy use from the central ASHP. This results in an average supply temperature for the period January-March of 10 °C for the BiND configuration, versus 7 °C for the BiD configuration. Based on eq. (1a), the temperature difference at the primary side (WSHP evaporator side) between the two configurations can lead on average to a COP difference of 0.3 in the decentralized units for the same condenser outlet temperature. Conversely, an average supply temperature for the period June-August of 9 °C is achieved for the BiND configuration compared to a higher average temperature of 13 °C in the BiD configuration. The lower network temperatures in the cooling season result in a decreased EER of the central chiller (ASCH) for the BiND configuration.

Figure 5.

Comparison of the daily average buffer tank temperatures (T vol1- supply temperature, T vol2 - return temperature)

As a consequence, higher supply temperatures can be reached on the secondary side at the condenser outlet in the substations for the BiND configuration. Thereby, thermal discomfort in the buildings can be reduced, while maintaining acceptable COPs with an overall heat pump electricity use of 22.4 MWh in the substations. In contrast, the BiD configuration, compared to the more advanced BiND configuration, results in lower indoor thermal comfort for a similar energy use of 22.8 MWh in the substations. However, the higher EER in the BiD configuration results in lower electricity use of the central chiller, reducing it to 1.4 MWh compared to 5.5 MWh in the BiND configuration, ultimately leading to lower overall energy use.

In the first district analysed in Scenario A, Houses 2 and 4 exhibit a poorly performing building envelope compared to the other residential buildings. This results in higher thermal discomfort in these buildings and elevated floor surface temperatures to achieve the desired temperature setpoint, often exceeding the maximum allowable limit of 31 °C during the heating season [28]. Consequently, it can be concluded that these buildings are not suitable for a 5GDHC network.

To investigate the effect of improving the building envelope quality, adding pump energy to the objective and including a floor surface temperature constraint, Scenario A is compared to Scenario B for the bidirectional energy - directional medium flow (BiD) configuration. The main results in terms of total electric energy use and thermal discomfort are reported in Table 3 for both Scenarios. The district of better-performing buildings in Scenario B achieves lower energy use while maintaining comparable average COPs and ensuring good thermal comfort inside the houses. This results in an overall reduction of energy use of 43%. The optimal solution in Scenario B leads in general to low thermal discomfort in the unchanged Houses 1 and 3, for a similar heat pump electricity use compared to Scenario A. The refined Houses 2 and 4 show thermal discomfort values below 101 Kh/zone, with consistent reduction in the heat pump electricity use, particularly for House 2 from 15.4 MWh in Scenario A to 7.2 MWh in Scenario B. Additionally, it is observed that the circulation pump electricity use in Scenario B is significantly reduced in all buildings and in the central circulation pump, with a total reduction of 76%. This is achieved thanks to lower mass flow rates at both the primary and secondary side of the substations. Figure 6 shows the mass flow rates ranges for the two Scenarios A and B in the substations at the secondary side and in the network.

Figure 6.

Mass flow rates comparison for Scenario A and B for BiD configuration

Thermal comfort in the heating season in the buildings is ensured by higher average supply temperatures at the condenser outlet in the Scenario B. Figure 7 compares the distributions of the temperatures at condenser outlet in the decentralised WSHPs. The average temperatures at the condenser outlet for the unchanged buildings (House 1, 3 and Office) are clearly higher in Scenario B, with the inclusion of the pumping power into the objective function. This result allows for lower mass flow rates, minimizing the circulation pumping power, still meeting the thermal demand of the different buildings in the heating season. For House 2 and 4 it is observed that the better performing buildings in Scenario B show acceptable supply temperature ranges compared to Scenario A, with a significant reduction for House 2.

Figure 7.

Condenser outlet temperature distributions for Scenario A and B for BiD configuration

However, the total thermal discomfort in the cooling season in the office has increased in Scenario B, resulting in a total thermal discomfort of 1010 Kh. This is a result of the extra constraint on the minimum floor surface temperature (to avoid condensation) in the cost function of the optimisation problem. Figure 8 shows the evolution of the temperatures in the north and south zone of the office building in the period 20-25 August for Scenario A and Scenario B. It is observed that the temperatures in Scenario B are exceeding the upper setpoint temperature of 23 °C when there are occupants. In this case, the significant heat gains from occupancy and large windows in the office are no longer adequately compensated because of the limited cooling potential with a minimum allowed floor surface temperature of 17 °C.

Figure 8.

Evolution of the temperature in the north and south zone of the office building in summer period for BiD configuration

This paper presents a comparison between a novel NLP-based MPC control strategy for a bidirectional energy - directional medium flow (BiD) configuration, and an existing MINLP-based MPC control for a bidirectional energy - non-directional medium flow (BiND) configuration. Both strategies are applied to a small, virtual 5GDHC network, incorporating the non-linear dynamics of the hydraulic system and directly determining the optimal control inputs to realistic systems. An 8-month MPC simulation is conducted for both approaches in Scenario A, minimizing the total energy use of heat pumps and thermal discomfort in a base-case district with low performing buildings. Additionally, the study evaluates the impact of building thermal performance, pumps energy use and floor surface temperature constraint for the BiD configuration in Scenario B. It can be concluded that the two configurations show similar performances with a seasonal performance factor (SPF) of 3.34 in both configurations. However, the BiND configuration demonstrates an advantage by leveraging system flexibility to achieve higher thermal comfort while reducing energy use. The full potential of the BiND configuration is only partially exploited in this use case, due to a heating dominated cluster of buildings. A more diversified range of building functions could lead to higher COPs in the decentralised systems and to lower electric energy consumptions in the balancing units. Conversely, the BiD configuration maintains low energy use with 38 MWh, outperforming the BiND configuration with 41 MWh in Scenario A. However, the BiD configuration results to be infeasible if low performing building are included in the district, reaching high thermal discomfort values of 1096 Kh/zone in the badly performing House 2.

Moreover, the BiD configuration in Scenario B reaches effective thermal comfort values in the residential buildings, while achieving an overall reduction of energy use of 43% compared to Scenario A. However, the constraints on the floor surface temperature limit the heating/cooling capacity of the thermal system. This limitation results in higher thermal discomfort particularly during the cooling season for well-insulated and high-occupancy buildings. Additionally, the pumping power required is significantly reduced from 8.4 MWh to 1.9 MWh, when it is incorporated into the optimisation objective.