Analysis of the Potential for Thermal Flexibility of Cooling Applications

Abstract

The feed-in of electricity from renewable energies, such as wind or solar power, fluctuates based on weather conditions. This unpredictability due to volatile feed-in can lead to sudden changes in energy generation so that solutions ensuring grid stability need to be implemented. The cooling sector offers the opportunity to create flexibilities for such balancing, with this study focusing on the thermal flexibilities that can be provided by cooling applications. Various cooling-demand profiles are investigated with respect to their load profile and their impact on flexibility is analysed. In addition to the cooling demand, scenarios of different storage dimensions are considered. As a result, it shows that an increasing base-load level and increasing operating-load duration have a negative effect on flexibility, while an increasing full-load duration is beneficial for flexibility. Storage size also has a strong impact as higher storage capacity and storage performance indicate higher flexibility, whereas above a certain size they only provide little added value.

1. Introduction

The use of fossil fuels causes significant environmental problems due to CO₂ emissions. It is therefore important to increase the use of renewable energy sources (RESs). However, the growing share of RESs poses considerable challenges to the existing energy infrastructure, particularly with respect to significant load changes. The unpredictable nature of RESs leads to sudden and significant fluctuations in energy supply that threaten grid stability. These large load changes can result in a mismatch between energy production and demand. In addition, the instability of energy supply creates an imbalance between supply and demand on the electricity grid, potentially leading to shortages or surpluses. Such instability can lead to unreliable electricity supplies and affect the operation of the networks. Existing transmission networks may not be able to cope with the sudden changes in energy production, increasing the risk of overloads and blackouts. In addition, intermittent supply can lead to higher peak loads, creating additional challenges for grid operators. These challenges are evidenced by the growing demand for electricity and the integration of renewable energy sources into the electricity grids. This is due to the inherently unpredictable and volatile nature of their generation. Unlike conventional power plants, solar PV and wind power do not supply electricity to the grid on demand but depend on the availability of the renewable energy source. This results in what is known as intermittent feed-in, which needs to be balanced to ensure security of supply. To counteract these fluctuations, existing supply structures need to be adapted, or new, flexible, and grid-friendly systems need to be developed. In this context, demand-side management is discussed as a promising strategy for creating flexibility within the energy grid. Special attention is given to the flexibility of cooling systems. The focus is on the inherent thermal flexibility of cooling applications. This flexibility refers to the fundamental ability of a thermal energy system to adjust its energy production or consumption without external signals. It enables the system to respond to changing demands and contributes to the stability of the electricity grid by storing or using excess electrical energy in the form of heat or cold [1,2].

To investigate inherent flexibility, applications are analysed based on their characteristic cooling-load profiles. The profiles are varied based on a typical air conditioning profile to determine how flexibility changes with different characteristics. In addition to the characteristics defined by the load profile, storage systems will also be integrated, and their dimensions will be varied. The aim of this research is to quantify and classify flexibility in relation to input parameters such as cooling system configuration, storage dimensioning, and cooling-load profile. Furthermore, the theoretically available flexibility within cooling applications allows for a first informed assessment of the extent to which the integration of demand-side management is worth considering.

2. State of the Art

2.1. Cooling Sector and Applications

Previously, load management in cooling supply was primarily associated with minimising energy costs for the consumer. This was achieved by minimising operating costs as much as possible, as the maximum peak demand in a defined period is used to calculate the power price for the entire electricity supply [3]. By reducing operating costs through efficient load management and avoiding peak demand times, the peak demand itself could be lowered. In recent years, however, as suggested in [4], cooling supply is also increasingly being discussed for load management of electricity grids. Since the electricity consumption for cooling technology, which at 73 TWh per year in 2017 accounts for 14% of total German electricity consumption [5], is not insignificant; the goal of this research project is to determine the flexibility potential of the cooling sector in Germany.

In this context, ‘flexibilisation’ refers to the deviation of both the time and amount of electricity required to operate a chiller using its normal operating parameters. For the purpose of this study, it is assumed that the normal operation of a chiller can be accurately characterised by a cooling-load profile. This model assumes that the cooling demand is consistently met by the chiller, providing exactly the cooling capacity required.

It is also important to note that the definition of normal operation does not include the use of a storage system, as such a mechanism is considered unnecessary under these conditions. The chiller operates continuously, adjusting its output in real time to match the immediate cooling demand.

For this reason, it seems useful to identify the flexibility potential by identifying characteristic cooling-load profiles of different cooling applications, which serve as a basis for this flexibility assessment. Therefore, it is important to gain an overview of the cooling applications represented in the sector to be able to derive a potential for flexibilisation based on their characteristic cooling-load profiles. For this reason, a meta-study [6] was carried out to provide an overview of the cooling sector.

Various studies [7,8,9,10,11,12,13] serve as a basis. These studies focus on the cooling sector in Germany and are structured according to the classification in [6] into various sectors: the food industry; the trade, commerce, and services (TCS) sector; industry; households; transportation; and air conditioning (AC). The energy demand for air conditioning is recorded separately in these studies and is therefore designated as an independent sector.

Some of these studies [7,8,9] provide comprehensive coverage of all the mentioned sectors, while the remaining studies [10,11,12,13] focus on specific sub-areas, thereby contributing to the refinement of the overall overview. This diversity in approach allows for a differentiated analysis of the cooling demand across the various sectors and applications. Additionally, the studies have different reference years, which complicates the comparison of results. Nevertheless, they provide valuable data for quantifying the cooling demand in Germany and enhance the understanding of the relevance of the individual sectors. This methodological approach enables the creation of a holistic picture of cooling applications in Germany and allows for a clearer representation of the relevance of the individual sectors.

Table 1. Overview of the underlying studies [6].

Study	Reference Year	Food Industry	TCS Sector	Industry	Households	Transportation	AC
[7]	1999	x	x	x	x	x	x
[8]	2008/2009	x	x	x	x	x	x
[9]	2017	x	x	x	x	x	x
[10]	2012		x	x
[11]	2009–2011	x		x			x
[12]	2018	x	x	x			x
[13]	2018				x	x	x

provides an overview of which studies cover which sectors.

As part of the study, various applications that have a cooling demand were identified. These, for example, can be processes in the food industry or mechanical engineering and the cold supply for product storage in cold stores, as well as for air conditioning in office buildings. An extract of the applications is listed in [14]. To be able to make a generally valid statement about the flexibility potential of the entire cooling sector, an analysis of the cooling applications in the sector is required. Due to the large amount of cooling applications which differ in their application specific characteristics, an analysis of the flexibility potential is difficult to perform. In general, it is possible to use cooling-demand profiles to estimate at what times and to what extent a consumer has theoretical flexibility potential to shift loads within the application. This can especially be derived from the demand profiles and the load peaks [15]. Against this background, the meta-analysis can be used not only to identify a large number of applications but also to make a rough categorisation in terms of cooling usage, which serves as a basis for identifying characteristic load profiles. Further investigations can be carried out regarding the qualitative progression. The concise characteristics in which the load profiles are similar and different will be incorporated into scenarios in the further course, whereby the underlying inherent thermal flexibility can be derived.

Thus, the cooling-demand profile of an application can be qualitatively characterised by the duration of the operating load and full load. The operating load refers to the load that exists during a specific period of normal operation of a system and can vary. The duration of the operating load corresponds to the period in which another load occurs in addition to the base-load level, which is the constant and continuous load that a system must always provide. In this research, this corresponds to the period in which air conditioning is required, for example. The full load represents the maximum load that the system must handle. The duration of the full load refers to the period during which the system must maintain this maximum load to meet the current cooling demand. Furthermore, the level of the cooling load plays an essential role, which significantly impacts the shape of the profile. Some applications have a continuous demand for cooling, resulting in a base load that can be considered as an additional parameter. The base load remains relatively stable and forms the base load that exists to meet the minimum requirements, regardless of fluctuating demands. This can be considered as a further parameter.

To be able to cover the cooling demand of an application, cooling technologies are needed. A basic assumption is that a chiller in normal operation covers the cooling demand according to the demand-load profile. If the chiller is operated at times when there is no demand, this excess production can be stored in the storage system and drawn from the storage later. The resulting change in the operating mode of the chiller is the flexible-load profile.

2.2. Definition and Quantification of Flexibility

There are various definitions for the term flexibility [2,16,17,18], with the “ability to deviate from the plan” being used as a general definition in the energy sector [16]. Furthermore, the Federal Network Agency defines flexibility as “the change in feed-in or withdrawal in response to an external signal with the aim of providing a service in the energy system”. The parameters that characterise flexibility are the level of performance change, duration, rate of change, reaction time, and location. This can be achieved, for example, by adjusting process starts, machine utilisation, order sequence, and break times and shift times, as well as process parameters. Furthermore, this can be accomplished by interrupting processes and storing energy, as well as changing the energy source [17].

Load management is a form of providing flexibility; the definition of load management is interpreted differently in the literature such that various measures can be included in this context [19]. The term load management generally refers to an adjustment of the usually demand-controlled energy demand or energy production according to externally introduced incentives or restrictive specifications. Possible manifestations of load management are demand-side management or the demand response potential (DRp). The term demand-side management is used differently in the literature. In some cases, demand-side management is equated with demand response and thus refers to the short-term deliberate change in consumer load in response to price signals in the market or to an activation within the framework of a contractual power reserve. In some cases, a distinction is made between demand-side management, where the consumer load is activated by a central control system and demand response, where the consumer must activate the load themself [1,20,21,22].

Thermal energy storage is a primary tool for enhancing the flexibility of an energy system [23]. For integration of load management in a cooling supply system, cold-storage systems are usually required [2], which enable loads to be shifted in time or load peaks to be changed, i.e., raised or lowered. Knowing the cooling demand or the load curve is essential for optimised load management as it allows planning future operating modes [20,24]. In order to make flexibility comparable and assessable, various indicators are used in the literature. Most of these indicators are formed from a comparison of a reference to the flexibilised state. The flexible-load profile, referred to as L_flex in the following equations, represents a deviation from normal operation that is caused by the utilisation of storage systems. Typically, the reference point is the nominal power at a specific moment or the electrical or thermal energy over a given period. The flexible parameter refers to the power or energy resulting from a flexible mode of operation. This flexible operation results from the response of an energy system to a signal, which is usually external but also internal. In context of this study, the activation of storage utilisation takes place according to the charging and discharging limits defined in Section 3.2. As soon as the cooling demand is met by the storage system or the cooling unit is operated to charge the storage, the operation deviates from the normal state and is classified as a flexible load. This deviation facilitates the creation of flexibilities that allow the shifting of energy quantities [25,26]. In the following, the key figures DRp and S_flex, as well as E_flex, are examined in more detail as examples of various key figures for quantifying flexibility.

DRp is the ratio of two consumption profiles, shown in Equation (1); it is calculated to show the savings potential of a flexibilised power compared to the original nominal power for a single time step. Each individual time step $i$ is considered and evaluated in isolation, so that DRp does not allow any conclusion as to the overall flexibility of a system but is only meaningful for the respective time step. The calculated DRp can represent both the positive and the negative deviation of the flexibilised performance compared to the reference performance. A positive DRp describes a power decrease and a negative DRp a power increase of the flexibilised power compared to the nominal power (cf. [27]).

$${DRp}_i={\displaystyle \frac{L_{\mathrm{ref},i}-L_{\mathrm{flex},i}}{L_{\mathrm{flex},i}}}$$

(1)

In comparison to DRp, the key indicator S_flex is also a ratio of two consumption curves, but in this case the flexibility is cumulated over a longer time period. Furthermore, only the negative deviation of the flexibilised performance is used for evaluation to avoid negative and positive results cancelling each other out in the calculation. This can be seen in Equation (2). The cumulative approach means that S_flex can be used for flexibility assessment over a longer observation period. Due to the limitation to the negative deviation, S_flex is an indication of the relatively saved power of the flexibilised operation mode compared to the reference [28].

$$S_{\mathrm{flex}}={\displaystyle \frac{{\sum }_{i=1}^n\max \left\{L_{\mathrm{ref},i}-L_{\mathrm{flex},i},0\right\}}{{\sum }_{i=1}^n{L}_{\mathrm{ref},i}}}$$

(2)

E_flex extends the calculation of S_flex by an external signal. Thus, not only the negative deviation is considered, but also the positive deviation. Through this weighted consideration, E_flex can be seen as a statement about the level of the total savings potential regarding the selected external signal over an observation period. The external signal is referred to as $c_i$ in Equation (3) and can, for example, represent the electricity price or the CO₂ emissions or other freely selectable external evaluation variables for the respective time step. For the calculation of E_flex, as for the previous key indicators, a reference and a flexibilised power are set in relation to each other for each individual time step and, as the S_flex, cumulated over an observation period [28].

$$E_{\mathrm{flex}}={\displaystyle \frac{{\sum }_{i=1}^n{c}_i·\left(L_{\mathrm{ref},i}-L_{\mathrm{flex},i}\right)}{{\sum }_{i=1}^n{c_i·L}_{\mathrm{ref},i}}}$$

(3)

The focus of the study is to investigate the influence of the characteristic load profiles on the flexibility exhibited by a cooling application. This inherent thermal flexibility is not induced or influenced by an external signal, and therefore, E_flex cannot be used in this context. As only the effects of base load, duration of full load, and duration of operating load on flexibility are to be examined, the inclusion of external signals would distort the results, as the additional variables would then influence the flexibility. Therefore, this purely inherent flexibility should be considered theoretically, representing the theoretical maximum flexibility that can be found in an application. An adapted version of S_flex is therefore used, where the electrical power is replaced by the currently applied cooling load via Equations (4) and (5).

$$EER={\displaystyle \frac{{\dot{Q}}_0}{P_{el}}}$$

(4)

$${\dot{Q}}_{\mathrm{flex}}={\displaystyle \frac{{\sum }_{i=1}^n\max \left\{\left(L_{\mathrm{ref},i}·EER\right)-\left(L_{\mathrm{flex},i}·EER\right),0\right\}}{{\sum }_{i=1}^n{L}_{\mathrm{ref},i}·EER}}$$

(5)

3. Material and Methods

3.1. Cooling-Load Profile

To analyse the influences of different variants, within the cooling-load profiles, on the flexibility potential, a typical load profile of a cooling air-conditioning system for an office building has been chosen. The load profile consists of synthetic data, which is presented in a simplified manner and is based on load profile (1) of an air-conditioning system. This synthetic load profile is varied in its characteristics and adjusted to include a base load that also varies in different orders of magnitude. Furthermore, the durations of the operating load of the load profiles are varied, whereby the peak load of the system is considered at different times. These different variations of the cooling-load profile result in a number of scenarios in which the impact of each of these parameters on the flexibility potential of the cooling-load profiles can be determined.

When comparing the different load profiles and the inherent flexibility potentials two factors must be considered: First, there may not be an external signal or impact factor, as explained in Section 2.2, to start a flexible operation of the cooling system. Second, all load profiles must be standardised. Standardisation is achieved by normalisation based on the full load, which means that the cooling capacity is between 0% and 100%. In this way, the result can be transferred to different cooling applications that have the same profile with different load ranges. Taking this into account, different standardised load profiles are considered regarding base load, duration of operating load, and duration of full load, which are explained below.

Specifically, based on a cooling-load profile that has no base load and runs for an operating time of 10 h per day—from 8 a.m. to 5 p.m.—and has a full load for 1 h per day, further load profiles are generated. These are generated by adding a base-load level of 20% and 50% each. On this basis, the peak values are each varied with a duration of 4 and 6 h. To identify the impact of the operating time, the 0 h are extended to an operating-load duration of 17 h—from 4 a.m. to 8 p.m.—on the one hand and to 21 h per day—from 2 a.m. to 10 p.m.—on the other. This results in a total of 27 load profiles, which are examined regarding flexibility.

Table 2. Overview of the cooling-load profiles considered.

Load Profile	Base-Load Level [%]	Duration of Operating Load [h]	Duration of Full Load [h]
(1)	0	10	1
(2)	0	10	4
(3)	0	10	6
(4)	0	17	1
(5)	0	17	4
(6)	0	17	6
(7)	0	21	1
(8)	0	21	4
(9)	0	21	6
(10)	20	10	1
(11)	20	10	4
(12)	20	10	6
(13)	20	17	1
(14)	20	17	4
(15)	20	17	6
(16)	20	21	1
(17)	20	21	4
(18)	20	21	6
(19)	50	10	1
(20)	50	10	4
(21)	50	10	6
(22)	50	17	1
(23)	50	17	4
(24)	50	17	6
(25)	50	21	1
(26)	50	21	4
(27)	50	21	6

gives an overview of the described load profiles.

In accordance with Table 2, exemplary load profiles are shown in Figure 1, Figure 2 and Figure 3. Figure 1 shows three exemplary profiles that vary in their base-load level, while Figure 2 is differentiated regarding the duration of the full load. These load profiles are standardised so that the full load is 100%. Thus, the load profiles in which a base load was added differ slightly from each other, as these had to be re-standardised. The reason is that load was added to the entire profile, as otherwise, for example, the duration of the operating load would be reduced, and this would lead to a misrepresentation of the results. Finally, the duration of the operating load varies in Figure 3.

To be able to determine the impact of the individual parameters, it is assumed that the daily profiles occur periodically throughout the year. This indicates that every day of the year has the same load profile. Dependencies due to given boundary conditions, such as the storage level at the start of the simulation, ensure that the evaluable equilibrium state only occurs after a subsequent point in time. This means that the impact of the parameters can only be evaluated after several charging and discharging cycles, as the equilibrium state of ongoing operation only occurs later with a given storage system dimensioning. Depending on how high the base-load level or how long the duration of the operating load is, the number of charging and discharging cycles to run through may differ. In one scenario, operation can be stabilised after one day and in other scenarios after a few days. This further validates the implementation of a full year simulation.

3.2. Cold Storage and Limits for Charging and Discharging

The next step is to define the cooling system. A standardised method is being used for the cooling load levels; the power supply and the capacity of the storage system are also standardised. This offers the possibility to vary the storage performance, defined as the maximum energy that a storage system can discharge or store within a specific time period, and the storage capacity, which describes the total amount of energy that a storage system can store, for each load profile in the same way. The standardised storage performance equals the performance of the chiller in the cooling application. A storage performance of 100% thus equals 100% of the thermal performance of the chiller and would cover the maximum load of the cooling application. Furthermore, in terms of load shifting from full load to off-peak times, the storage system only supports the chiller in covering the load during times of high cooling demand. The dimensioning of the storage unit is selected in such a way that it can be used for all load profiles considered. Based on the charging and discharging limits of the storage described below and the increasing base-load level in the scenarios, the storage performance varies between 10%, 15%, and 20%. This corresponds to the unit [kW_storage/kW_cold]. Higher storage performances are not applicable for every scenario, as with higher base-load levels the charging limit would be above the discharging limit and the storage would thus simultaneously charge and discharge. For this reason, the maximum storage performance is limited to 20%. Furthermore, lower storage performance results in significantly lower flexibilities, which is the reason why these are not considered in the scenarios below 10%. In addition, a storage capacity of 100% represents the optimal design case of the storage system, allowing the maximum load of 100% to be theoretically covered for a duration of one hour. In contrast, a capacity of 50% is considered an under-dimensioning, as only half of the required capacity is available. Conversely, a capacity of 200% reflects an over-dimensioning, representing a doubling of the storage capacity. The aim of this study is to analyse the impact of storage sizing on flexibility. Firstly, the design case of 100% is used, then both undersizing and oversizing are considered. The capacities are varied at 50%, 100%, 150%, and 200%, focusing on the ratio of the actual capacity in relation to the designed capacity [kWh_real/kWh_design]. Lastly, no storage losses are considered, as flexibility is to be evaluated independently of external impacts. This is because storage losses are directly related to the outside air temperature. Rising outdoor temperatures can lead to increased heat flow to the outside, causing the storage tank to operate less efficiently. Conversely, lower outdoor temperatures can reduce heat losses and increase storage efficiency.

Since external signals should not serve as initiators, another basis for flexible operation is identified, which is based on the cooling application and thus the cooling-demand profile itself. Two limits are defined, which, depending on the current load, can lead to a change in the operation of the cooling application. The flexibilisation itself is based on load shift [18], in which the load is shifted from times of high load to times of low load. Thus, if the load is higher than the defined discharge level limit, the cold storage is activated to support the cooling application. On the other hand, if the load is lower than the defined cold storage charging level threshold, the cooling application must run with the additional load to charge the cold storage.

The limits depend on the curve of the load profiles. Depending on a given base-load level, limits for storage loading are defined differently. In order to ensure comprehensive coverage of all load profiles, the storage limits were set at a level that would adequately accommodate the base load. This indicates that load profiles without a base load demonstrate a consistent storage level, as do those with 20% and 50% base load. This approach enables meaningful comparisons to be made between the various load profiles. The storage limit for load profiles which do not include a base load is set at 20%. Concurrently, the extraction limit for all load profiles is set at 80%, thereby ensuring comparability between the various scenarios. The storage limit is contingent on the existing base loads [29].

Figure 4 and Figure 5 illustrate two load profiles each, demonstrating the applicability of the selected storage limits to the specific load profiles. Figure 4 depicts load profile (1) in the first diagram and load profile (7) in the second diagram. The shaded areas represent the shifted quantities of energy that can be shifted by the storage system in accordance with its design specifications. The boundaries of these areas are indicated by the respective reference profile and the flexibilised load profile, which is a consequence of the operational mode of the cooling system used in conjunction with the storage tank. The flexibilised load profile is indicated in red and purple. In this example, a storage system with 100% storage capacity and 20% storage performance is considered. It is evident that in load profile (7), the peak load on the first day cannot be covered by the storage system, as it was initially empty and therefore requires a period of initial filling before it can be fully operational. From the second day onwards, the stabilisation of operations is facilitated by the storage system. This emphasises the importance of selecting the appropriate storage system dimensioning, as the peak load cannot be fully covered due to the insufficient capacity of the storage system.

As the base load increases to 20%, the charge limit is increased to 40% to ensure optimum utilisation of the cold store and to take advantage of the additional capacity. Figure 5 compares load profiles (19) and (23), also displaying a storage capacity of 100% and a storage performance of 20% to enable a direct comparison. As demonstrated in Figure 4, it is also shown here that with a static base load, the varying characteristics of the load profiles can be covered by the chosen storage limits. In this figure, the shifted energy quantities are represented by the shaded areas, resulting from the reference profile and the flexibilised load profile. The flexibilised load profile is indicated in light red.

At a base load of 50%, the charging limit is increased to 70% to ensure that the cooling storage can be sufficiently charged to provide the required constant cooling capacity.

3.3. Simulation

The simulation of the storage level depends on the selected storage dimensioning. An example is given that involves a storage with a storage performance of 20% and a capacity of 100%. In each scenario, it is assumed that the storage is empty at the beginning. Figure 6 shows the simulation of the quantity of energy that can be shifted due to the flexible load resulting from operation with the integrated storage system, using load profile (1) as an example, which has a charging limit of 20% and, as defined in Section 3.2, a discharging limit of 80%.

Table 3. Storage level in connection with Figure 6 at a storage performance of 20% and capacity of 100%.

	Hour per Day [h]	Cooling Demand [%]	Storage Level [%]
Starting condition	1	0	0
(1)	4	0	80
(2)	8	55	100
(3)	11	95	75
(4)	14	85	35
(5)	16	35	35
(6)	18	0	75

gives an overview of the storage level that results for the plotted points 1 to 6 when the storage is in operation at the specified limits.

If it is assumed that the storage unit is empty at the beginning, it will therefore be full at hour 4 (point 1) as the cooling demand during this time is below the loading limit and the chiller can use the entire performance of 20% to fill the storage. The second point is in the range between the limits, which means that the cooling demand is completely covered by the chiller and the storage unit is not used. In contrast, points 3 and 4 are above the discharge limit. Since the storage is only used to support the coverage of the load above the limit, only the difference between the cooling demand and the discharge limit is covered. Thus, the new storage level is the difference between the previous level and the cooling demand minus the discharge limit, resulting in a level of 95% at point 3. The storage unit is then used to cover the demand, resulting in a filling level of 35% at point 4. As soon as the demand falls below the discharge limit, neither charging nor discharging takes place, keeping the storage level unchanged while the demand is covered by the chiller again (point 5). Point 6 is once more below the storage limit, which indicates that the cooling system is once again charging the storage tank. In the case of a storage point being below the charging limit and a cooling demand occurring simultaneously, this represents a situation in which the storage unit is also charged in addition to meeting the demand. In this instance, only the discrepancy between the cooling demand and the charging capacity is stored in the storage tank.

4. Results and Discussion

The aim is to investigate the impact of the load profile on the theoretically achievable flexibility. Figure 7, Figure 8 and Figure 9 each show the flexibility ${\dot{Q}}_{\mathrm{flex}}$ depending on the base-load level, the duration of the operating load, and the duration of the full load with various storage capacities.

The figures show a non-linear relationship within storage dimensioning between storage performance and storage capacity: an increase in storage performance from 10% to 15% has a significantly greater impact on flexibility than an increase from 15% to 20%. This can be illustrated with the following example: an increase in flexibility from 10% to 15% corresponds to a doubling of storage performance, while the increase from 15% to 20% represents only a one-third increase. This relationship is crucial as it shows that storage performance has a greater effect, particularly when starting from a low baseline.

Furthermore, the figures indicate that at low storage capacities, the full storage potential is severely limited. When the storage capacity is insufficient to efficiently meet the required cooling demand, the maximum possible flexibility cannot be utilised. This is particularly important, as inadequate capacity can lead to bottlenecks in cooling supply. It becomes clear that storage performance plays a crucial role, especially at higher storage capacities. Optimal resource utilisation is essential to ensure the efficiency of the system and to prevent potential bottlenecks.

Another point highlighted is that the curves tend to flatten out. This is particularly pronounced at higher storage capacities, where thermal storage is often oversized. In such cases, the available storage performance can no longer be utilised optimally, resulting in a reduction in the overall efficiency of the system. This suggests that the sizing of storage systems must be carefully reconsidered to ensure they are not only sufficient but also efficient.

In relation to Figure 9, the impact of the variability in the characteristics of the duration of full load is demonstrated in Figure 10. The first diagram in the figure depicts load profile (1) in dark blue, while the second diagram presents load profile (3) in light blue. Load profile (3) is distinguished by a longer duration of full load in comparison to load profile (1), with the remaining characteristics, such as the absence of a base load and the duration of operational load, remaining unaltered. Furthermore, the storage dimensioning is also identical, with a storage capacity of 100% and a storage performance of 20%. The shaded areas in the figures represent the quantity of energy that can be shifted from peak load to off-peak times. This energy is highlighted by the reference load profile and the flexible-load profile, which is established when the operating mode of the storage systems is considered and the chiller is operated accordingly.

It is evident that the quantity of energy that can be shifted from the load profile with a higher full-load duration is greater than that of the profile with a full-load duration of just one hour. This corroborates the statements presented in Figure 9, indicating that a higher full load offers greater flexibility, as the amount of energy that can be shifted is correspondingly larger. Furthermore, it is evident that the storage system for load profile (3) is not adequately dimensioned. This implies that if the storage were optimally sized in this case, the flexibility would indeed be enhanced.

To analyse the impacts in more detail, Figure 11 and Figure 12 show the scenarios from Table 2 according to increasing base-load level, duration of the operating load, and the full load. For the sake of a clear overview, Figure 11 shows the flexibilities with storage capacities of 50% and 200% and a fixed storage performance of 20%, so that the impacts can be demonstrated. In contrast, Figure 12 shows the calculated flexibilities for the scenarios with a fixed storage capacity of 200% and storage performances of 10% and 20%.

In general, an increasing base-load level and an increase in the duration of the operating load reduce the flexibility of a system. This is evident from the drop in flexibilities in the scenarios with an increasing base-load level and duration of the operating load. In contrast, an increasing duration of the full load shows an increase in flexibility. When also comparing the influence of the three factors with various storage capacities and performances, it can generally be seen that an increase significantly increases flexibility. This is shown in Figure 7, Figure 8, Figure 9, Figure 10, Figure 11 and Figure 12. Furthermore, a statement can be made about the distance between the data points within a class or the spread of the achievable flexibilities. The lower the spread, the more the investigated factor limits the achievable flexibility. It can be assumed that with a higher storage capacity, the duration of the operating load restricts flexibility the most, whereas an increased base-load level is the restricting factor with a low storage capacity. Furthermore, Figure 12 also shows that a minimum performance of the storage is necessary to be able to achieve any flexibilities. This is due to the utilisation level of the storage: an increasing base-load level increases the total energy demand, whereas the stored energy, the area above the storage limit, is constant. Increasing the duration of the full load, on the other hand, increases the stored energy and thus also increases flexibility. The duration of the operating load, on the other hand, has a special characteristic, because both the total energy and the stored energy increase, whereby the ratio of both stays the same and the spread of flexibility is low. With a duration of the operating load of 17 h, a higher flexibility is achieved with a low storage performance, as the storage is better utilised. For a better understanding, the first diagram in Figure 13 shows a load profile with a high base-load level and a duration of the operating load of 10 h (load profile (19)), whereas the second diagram shows a profile which has a duration of the operating load of 17 h (load profile (22)). It can be seen that ${\displaystyle \frac{{\alpha }_2}{{\alpha }_1}}>{\displaystyle \frac{{\beta }_2}{{\beta }_1}}$, which explains the difference between the achievable minimum flexibilities. The achievable flexibilities at 21 h are severely limited, as the storage is never fully utilised because there is too little time for storage.

The calculation and evaluation of the flexibilities refer to full year simulations. Thus, depending on the scenario, almost 3% to about 15% of the total thermal energy quantity can be shifted from full load to off-peak times.

The results of the analysis must be considered with limitations, in particular regarding the question whether the method developed for analysing the flexibility of cooling systems can be transferred to other load profiles. It should be noted that these results refer to periodic load profiles, which show the same pattern every day of the year and have recurring characteristics. In practice, these characteristics do not exist in this way. Therefore, if the load limits are set based on the annual hydrograph, days with lower full loads cannot be taken into account in terms of flexibility.

Key aspects are both the influence of external factors and the neglect of external signals. The current analysis does not account for factors such as temperature variations, market price changes, fluctuations in network demand, and the storage and release of energy into or from storage. These external influences can contribute significantly to the flexibility of a system and should therefore be included in future studies. Ignoring them results in an analysis of flexibility that is limited in its significance and may lead to overly optimistic assessments of the flexibility potential.

In addition, it is possible to determine the loading and unloading limits dynamically, which would allow a more realistic assessment of flexibility. The assessment of flexibility should be application specific, but it is difficult to translate the qualitative assessment into a quantitative assessment of flexibility. As such assessments can only be made using year-round simulations, and cooling demand is never periodic, flexibility would need to be assessed on a weekly basis.

Moreover, the thermal properties of, e.g., products in cold storage and building characteristics such as thermal inertia, should not be overlooked as they also influence flexibility. The result is purely a measure of the flexibility that can be provided by the characteristics of the load profile and the dimensioning of the storage in the system. Redundant systems, which could provide additional degrees of freedom, are also not included because flexibility through system dimensioning, i.e., the installed capacity of chillers and number of modules, requires external signals such as a price time series.

5. Conclusions and Outlook

The results presented illustrate the significant influence of the load profile on the theoretically achievable flexibility within cooling systems. The analysis shows that high storage capacity combined with high storage performance leads to increased flexibility. In particular, an increase in storage performance from 10% to 15% has a much greater effect on flexibility than an increase from 15% to 20%. The non-linear relationship between storage performance and capacity highlights the need for careful dimensioning of storage systems to ensure both efficiency and optimal utilisation. The results suggest that at low storage capacities, maximum flexibility cannot be fully realised, resulting in cooling bottlenecks. The research also shows that exceeding the storage capacity results in a flattening of the flexibility curves, which reduces the efficiency of the system.

The scenario analysis shows that an increasing base-load value and longer operating times reduce the flexibility of the system. For example, at a base load of 50%, the achievable flexibility drops to around 10%, while an increase to 75% reduces flexibility to just 5%. On the other hand, a longer period of full load increases flexibility; with a full load period of 10 h, flexibility can even increase to 15%. It is also clear that a minimum level of storage performance is required to achieve any level of flexibility. The analysis shows that a storage performance of at least 20% is required to ensure significant flexibility.

Several important conclusions can be drawn from the results presented. To maximise flexibility within cooling systems, careful sizing of storage capacity and performance is critical. Higher storage performance, especially in the 10% to 15% range, has a significant impact on flexibility. Therefore, the storage capacity should be dimensioned to maintain an optimal ratio to the required performance.

The analysis also shows that a high base load significantly reduces the flexibility that can be achieved. With a view to maximising flexibility, it would be beneficial to keep the base load as low as possible. An optimal base load value could be below 50% to ensure a flexibility of at least 10%. A longer duration of full load also leads to increased flexibility. Therefore, it would be ideal to design load profiles that include longer periods of full load to increase the flexibility of the system; for example, load profiles that aim for a full-load duration of 10 h or more could be selected. The operating period should be structured in a suitable way to allow optimal use of storage. An operating period that is proportional to the storage capacity could significantly increase flexibility.

It can be concluded that the greatest flexibility is provided by a load profile with a reduced base load of less than 50%, extended periods of full load of more than 10 h, and careful dimensioning of storage capacity and performance. These aspects are critical to ensure high efficiency. Implementing such a load profile contributes significantly to maximising the flexibility within the cooling systems, thereby improving the efficiency of the whole energy system.

In conclusion, this research provides valuable insights into the flexibility of cooling systems, while having limitations in terms of the transferability of results to other load profiles. As a perspective for future work, it would be beneficial to consider external signals, such as storage losses, in order to reflect more realistic conditions. Moreover, further investigations should be carried out that account for other factors, such as temperature variations due to seasonal weather conditions and different operating modes such as weekday, weekend, and holiday operation. Finally, the inclusion of daily dynamic charge and discharge limits offers the potential to gain a more comprehensive understanding of inherent thermal flexibility over the course of a year.