Potential to balance load variability, induced by renewable power, using rock cavern thermal energy storage, heat pumps, and combined heat and power in Sweden

Large shares of variable renewable electricity (


Introduction
With large shares of variable renewable electricity (VRE) generation, e.g., wind/solar/wave/tidal power, there will likely be power balancing challenges in future power systems.Power system operators will be required to manage occasional power deficits and surpluses.Othercontrollablepower sources, are commonly used to cover power deficits, e.g., condensing thermal power, hydro power or imported power.Export, curtailment, conversion, and/or storage are, on the other hand, examples of potential VRE-surplus consumers.
The mentioned management possibilities are, however, limited in many systems.Insufficient access to height differences, dam capacities and river water flows limits the potential for hydro power.Condensing thermal power plants have poor fuel efficiency and/or use fossil fuels.Power import and export require enough cross-national transmission capacities, and available production capacities and/or power demand in neighbouring countries.Curtailment is a waste of installed VRE capacity, and finally, electric storages are generally expensive.
A further possibility to meet the power balancing challenges of VRE production would be to couple different energy sectors (e.g., electric, thermal, transportation, gas) [1].Thus, by integration of several different energy systems into one, synergetic effects can be achieved.For example, integration of district heating (DH) and power systems to provide power balancing services, would potentially also reduce DH-fuel use.To do this, combined heat and power (CHP) plants can produce electricity to cover VRE-induced power deficits, and compression heat pumps can consume VRE surpluses in what is generally referred to as power-to-heat (P2H).Furthermore, power utility managers in Sweden have reported capacity shortages in to and out from urban areas due to limitations in transmission lines [2].These shortages are the result of increasing power demands caused by urban densification, establishments of new industries, and electrification of transport.The matter of such capacity shortages is, for instance, acknowledged by the European Union via the collaboration project, CoordiNet, which aims to develop a more efficient use of existing power systems [3].In this context, the power generation potential from DH production systems is of significant relevance as these are commonly located within the cities, which is generally not the case with the other main power producing plants in Sweden, i.e., hydro and nuclear power.Thus, these Swedish urban area capacity shortages, in combination with national transmission limitations between electricity price areas and the above mentioned limited hydro power extension possibilities, stress the need for local urban power balancing capacity.
Hypothetically, local, and smart sector-coupled heat and electricity systems would be operated somewhat differently than conventional DH production systems.An electricity balancing demand could control the production in a CHP unit, instead of, as today, a local heat demand.Furthermore, P2H could contribute with power balancing by consuming VRE surpluses to produce heat and in that way avoid VRE-curtailment.
There are studies showing how P2H production can manage VREinduced surpluses in power systems [4,5,6].Also, the amount of VRE sold to the day ahead market is shown in [7] to be improved significantly with extended P2H production.Furthermore, in [8], P2H is shown to reduce the surplus of VRE from 45 % of the annually produced electricity to around 10 %, and thus significantly increase the potential for integrating VRE in energy systems.
Both for power production in CHP and P2H-power consumption, heat is co-produced.This heat is reasonably supplied the cover the local heat load.However, local heat loads will occasionally be smaller than the potential amount of co-produced heat, as shown in [9].The heat load therefore risks becoming limiting for the potential of the DH system to manage VRE deficits and surpluses.For instance, during low heat load season, i.e., summer, such a limiting impact is notable.Summer unfortunately coincides with significantly good conditions for solar power production in Sweden.However, introducing thermal energy storage (TES) units could help to increase heat load flexibility and reduce the limiting impact of the heat load, as shown in [9].Combining CHP and P2H units with large-scale TES can improve the VRE-managing capability of the system [10].In [8], the potential for such managing of VRE with TES is shown.In [9] and [11], the potentials for TES to increase flexibility in P2H and CHP production is shown.Furthermore, in [12] the ability for a combination of P2H, TES, and heat-only boilers to reduce the demand for biomass is investigated.Finally, in [13], TES, P2H and CHP that are operated together are shown to potentially increase cost-optimality.This accomplished by a replacement of heat-only production and maximized full-load operational hours for CHP units.
Holmér et al [13], conclude that the type of TES is crucial for the flexibility of heat production.Holmér also states that it is especially important with a high response-rate for charging/discharging TES when managing VRE production.Sensible TES, with water as heattransferring-and storage medium are considered as the storage technology with the highest potential response-rate [14].Examples of such TES technologies are heat accumulators (tanks) and water-filled ground pits, or rock caverns [15], of which the latter are in focus in this study.
In our previous studies, we investigated the power balancing potential for small-scale communities [16] and for DH systems aggregated on regional level for one Swedish electricity price area [17].However, the potential on a national level for Swedish DH systems to provide power balancing services, is yet not fully investigated.To the best of our knowledge, there has been no study investigating the potential for implementing a power balancing operation strategy for DH (or cooling) systems on national level for any country.Furthermore, several studies investigating the potential for DH systems to enable integration of VRE are limited in the sense that conventional cost-optimised heat load supply is presupposed.In the study presented here, this research gap is addressed by investigating how DH production can be optimised to supply a power balancing demand, facilitated by added system heat-load flexibility through inclusion of large-scale rock cavern TESs.
The National Swedish Board of Economic Defence built about rock cavern facilities between 1950 and 1990 in Sweden for storing petroleum products.These rock caverns are located all over Sweden, but with a concentration to the southern parts.For many of the rock caverns, the exact location is either classified due to national security, or not public for other reasons.About 80 of these caverns are uninsulated plain bedrock caverns, and the rest are steel cisterns mounted in the bedrock.The sizes of these caverns vary from 5,000 up to 150,000 m 3 [18].The Swedish Geological Survey has decommissioned, cleansed, and sealed many of the caverns today.A few DH utilities, however, have converted former fuel depot caverns into TES, while other caverns remain in use for other purposes.More rock caverns could be converted into TES units and used, at least those that are in close vicinity to a DH system.
Construction of new large-scale rock caverns is costly.Investment costs for large-scale rock caverns (>50,000 m 3 ) come close to 190 USD/ m 3 according to [19].This cost is in line with the costs estimated for rock cavern energy storage using compressed air presented in [20], and range between 111 and 245 USD/m 3 .However, the costs for conversion of existing non-TES rock caverns into TES are significantly lower.Numbers presented in [21] show that rock-cavern conversion into TES is about USD/m 3 .
We argue that investigating the potential to convert existing rockcaverns into TES for use in DH systems, is highly relevant.To enable a fully renewable energy system, it is crucial to fully grasp the potential of integrating heat and power systems.Rock-cavern TESs may provide the flexibility required to manage large shares of VRE.Even though increased flexibility from TESs has been previously shown, there is a need to investigate how additional TESs affect fuel use in sector-coupled energy systems.Also, the possible competition of these TESs with other heat producing units needs investigation.Thus, the originality of this study lies within the comprehensive approach taken to investigate how Swedish district heating production in coordination with large-scale conversion of rock caverns into TESs can potentially provide power for balancing the production from large amounts of VRE production units, on a national scale.

Aim of study
The overall aim of this study is to investigate the national potential for Swedish DH systems to provide power balancing services.The DH systems are simulated with a hypothetical access to large-scale rock cavern TES, P2H-assets, and CHP units.These components are operated in a coordinated way to manage an electricity balancing demand.This concept has not, to the best of our knowledge, yet been fully covered.The operation of a DH system to follow the electricity balancing demand will henceforth be called the 'Electricity strategy'.This is in opposite to the conventional operation of a DHS, which is to primarily supply a heat demand.This conventional operation strategy will henceforth in this paper be called the 'Heat strategy'.
For each of the four electricity price areas of Sweden, an electricity balancing demand is defined.The electricity balancing demand includes transmission of electricity between the areas.

Research questions
To investigate the potential for national and VRE-induced electricity net load variability to be reduced if an 'Electricity strategy' replaces the 'Heat strategy' in Swedish DHs, the following research questions are to be answered: 1. What impact do capacities in CHP units and/or heat pumps have on net electricity balancing load variability?
2. Is the fuel demand for CHP units different for the 'Electricity strategy' in comparison to the 'Heat strategy'?3. To what extent do TES-size influence reduction of net load variability?

Materials and method
In this section, the modelling of the DH production systems is described.Thereafter, the used simulation algorithm and the data used

Table 1
The five levels of the CHP capacity in the 'Heat strategy' acts as referencing cases for corresponding increments in CHP capacity in the simulation for the 'Electricity strategy'.for the simulations are presented.

Modelled system and study design
The modelled heat production systems consist of biomass-fuelled CHP units, large-scale heat pumps, DH distribution networks, and rock cavern TES units, as shown schematically in Fig. 1.The system configuration is inspired by the DH system in the Swedish city of Hudiksvall (15,000 inhabitants), located geographically in the mid part of Sweden.In this system, 180,000 m 3 former rock-cavern oil-depots have been converted into TES units and incorporated into the DH production system together with a biomass-fired CHP plant.The DH system in Hudiksvall proves that the system modelled in this study is realistic for practical implementation.Also, similar conversions of oil-depot rockcavern into TES are currently taking place as for instance at the DH system in Västerås, Sweden.
In this study, all DH production for each electricity price region is modelled as one large and aggregated system.The operation of these aggregated systems is thereafter simulated for a future scenario where the Swedish energy system is including large shares of VRE.To illustrate this, an electricity balancing demand is defined to control the systems operation.The heat loads for the DH systems are scaled to represent the aggregated heat loads for each of the four electricity price regions.Similarly, electricity balancing demands are also calculated for each price-region.It is assumed here that all existing rock caverns are geographically located so that a conversion to function as a TES is possible.This assumption is further explained and discussed in Section 2.4.3.To assess the power balancing potential for the systems, a business-as-usual reference case is defined in which biomass-fuelled CHP and heat-only boilers are operated to primarily supply the heat demand, i.e., following a 'Heat strategy'.This reference case includes no heat pumps and no storage.Hence, there is no flexibility in the heat load available to consume additional surplus VRE.Table 1 shows the relation between the business-as-usual reference case and the simulated cases.
Each increment of CHP capacity in the simulated 'Electricity strategy'cases are compared to the corresponding CHP capacity in the businessas-usual reference case (The column to the left in Table 1).

Heat load data generation
The heat load data used in the DH production simulations are generated by a heat demand generator described in detail in Åberg et al. (2013) [22].This generator calculates an hourly DH system heat load from hourly outdoor temperature data, building balancing temperature, and annual system heat load.Calculations are made separately for domestic hot water demand, building space heating demand, and DH Fig. 3.The electricity load, P L , production from wind, P W , and solar, P PV , the residual profile, P RL , and the balancing demand, P bal , for all electricity price areas.[23]).Temperature data for the four regions were obtained from SMHI [24] for Växjö (SE4), Enköping (SE3), Boden (SE1), and measured at Hudiksvall site (SE2).Fig. 2 shows the variation in distribution and duration of the heat load.The highest aggregated peak heat load is for price region SE1 with 39.3 MW th , and the lowest is 33.9 MW th for SE4.

Power balancing demand
In the Swedish power distribution system, transmission limitations separate the four electricity market price regions (denoted SE j in the following equations where j represents one of the four areas).For every time step i in the system simulations, with the Electricity strategy applied, the DH operation is controlled by a power balancing demand, P SEj bal .This demand is calculated separately for the four market regions, j, according to equation (1).
P SE k NRL is the negative residual load (NRL), i.e., VRE surplus, for area k.P SEj PRL is the positive residual load (PRL), i.e., VRE deficit, for area j.These two loads are given by and

P SEj
L is the electricity consumption per hour i in the electricity price area j in Sweden for the year 2020.The P SE k NRL is also influenced by electricity transfer between price regions.The capacity to do this is, however, limited.Transmission limitations are considered in the sense that equation (3) does not apply if P SE k NRL (i) ≤ T cap (l).T cap is the transmission capacity from electricity price region SE j to SE k .The study does not, however, include trans-border transmission of electricity to neighbouring countries.This limitation is necessary due to the increased complexity of the problem, and the large amounts of additional data that a transnational study would require.P SEj VRE is the electricity production from wind and solar power in area j defined as P Wj and P PVj are electricity produced in area j for hour i from wind and solar power in 2020, respectively.C 1 and C 2 are scaling factors that, on an aggregated national level (including all four electricity price areas), scale up the electricity production from wind and PV to represent 60% and 10% of the annual electricity demand respectively.C 1 and C 2 are defined as and Here, P L is the electricity consumption, and P W , and P PV are national aggregated electricity production from wind and solar.Hence, the estimated increased VRE production capacity corresponds to the current geographical distribution of wind and PV production.Fig. 3 and Table 2 shows data used in the derivation of the control signal, P SE j bal .

Heat production units
The following section describes how the production units in the DH systems have been modelled.It is important to note here that the coordination of the operation of the heat production units and the TES aims to reduce the power balancing demand, P SEx bal , described in the previous section.The production units contribute to supply this power balancing demand by either producing, or consuming electricity in their respective electricity price area.The part of the balancing demand not met by the production units is described in a net load profile (P SEj net ) as P SEj net contains the remaining deficits, and surpluses that needs to be managed by other non-variable power production (such as hydro power), end-user flexibility, export/import, and/or electrical storage.
The final management of the net power balancing demand is, however, beyond the scope of this study.P el CHP in equation ( 7) is the power produced in the CHP plants, and P el HP is power consumed in large scale heat pumps.Both CHP and heat pumps produce heat while providing power balancing services to the electricity network.The produced heat is either supplied to the DH network or stored in the TES.Thus, the total heat load and not just the current heat load level, as mentioned in the introduction, limits the systems over-all potential for providing power balancing services.In turn, this limitation affects power consumption in heat pumps (reduction of NRL); and production from CHP units (reduction of PRL).Furthermore, the use of biomass in CHP production is also an important aspect.VRE-induced heat production in heat pumps can reduce fuel use in CHP.There is, therefore, a trade-off between the capacities in heat pumps and the capacity of the CHP units that relates to the potential power balancing load reduction and the potential to reduce fuel use.In the simulations, capacities in CHP and heat pumps have been varied to investigate this trade-off.

Combined Heat and Power plant
The CHP units are described in the model by a thermal output capacity, an electricity-to-heat output ratio (α-value), an overall plant efficiency, and a ramping rate.These are further described in the following section.The thermal output capacities are varied in steps of 5 MW th , from 30 MW th to 50 MW th .For all simulations, the electricity-to-heat output ratio is 0.5 which represents the ratio for a conventional biomass-fired CHP plant in Sweden [25].The co-generated heat output includes heat extracted while condensing the vapour in the flue gases, which gives an overall fuel-to-heat plant efficiency (η fuel ) of 1.1 [25].
Fuel use, Q fuel , is calculated based on the simulated produced heat, P th , and electricity, P el , as for all hours i.An averaged heating value for wood of 2.88 GJ/m 3 is assumed [26].
In the real case, a partial load output from the CHP units would reduce the fuel conversion efficiency to some extent.This is not considered here due to the increased complexity this would add to the calculations.However, the general efficiency of the CHP units assumed here can be considered to be of sufficiently accuracy on the aggregated level the calculations are performed at.
Finally, the ramping rate, i.e., the rate for boiler thermal output adjustment is 4% of the nominal boiler output per minute.The latter is based on reported data from [27].Cold starts of the CHP units are also S.W. Monie and M. Åberg considered and are based on reported figures from [27] where CHP units in Denmark, optimised for quick response, are shown to be able to reach 90% of nominal output after 170 min.The cold start of a CHP unit is modelled to be a linear increase of the production output during the first 3 h following idle operation periods.This is described as P nominal is the thermal output of the boiler, t is the time during cold start, and τ is the total time (hours) of the cold start, i.e., 3.During cold start, no electricity is generated.

Heat pumps
In the simulations, the heat pumps are assumed to have suitable heat resource in close vicinity for heat production.This could be low-grade waste heat (~20 • C), sewage water or similar resources.It can even be considered to use large-scale air-to-air heat pumps as a significant part of the NRL occurs during the part of the year when the average outdoor temperature is significantly higher than sewage and sea water temperatures.This solution has been used for similar applications in Denmark [28].
The coefficient of performance (COP) of the heat pumps is assumed to be 3.8 which corresponds to a situation where the temperature source is about 20 • C and the supply temperature for DH is 85 • C.These are common temperatures for DH heat pumps using water in Swedish water treatment plants.
The relation between electricity consumption in the heat pumps, P el HP , and heat production, P th HP , is defined by using the COP as

Rock cavern thermal energy storage
This section describes how the TES are modelled and distributed over the four electricity price areas.Also, the estimations made of potential storage sizes are presented.
The simulation of the TES storage use is based on the energy balance for every hour i of a TES which is here described as P th in is heat produced in the CHP unit and/or heat pumps that exceeds the current heat load, P th out is heat discharged from the TES to the DHS when production in CHP and/or heat pumps does not supply the entire load.The thermal losses, P th loss , from the TES are assumed to have reached close to a thermal balance with the surrounding bedrock.For a fully charged rock cavern as the ones in Hudiksvall with a capacity of 5.23 GWh th TES, the losses are 0.24 MW th /h, based on simulations of the rock caverns in the software Heat3 [29].Electricity for circulation pumps etc. is neglected.Heat exchangers are assumed to be of large-enough capacity and exchange losses are neglected.
In order to measure the total amount of heat discharged from the TES relative to the storage capacity, the storage degree of utilization is used, which is defined as where P max TES is the maximal storage capacity, i.e., for Hudiksvall these capacities are 5.23 GWh th and 10.25 GWh th for the 90,000 m 3 and the 180,000 m 3 TES, respectively.Energy efficiency of a thermal storage is defined as the amount of heat discharged relative to the amount of heat charged The number of existing rock caverns suitable for conversion to TES is unknown due to that this information is classified since it is a national security interest.However, the Swedish Geological Survey supervises 32 former fuel depot rock caverns for environmental reasons and the locations of these relative to the four electricity-price areas of Sweden are

Table 4
The table lists the volumes of some rock caverns used for storage of petroleum products.In parenthesis is the electricity price market area given for respective location.Fig. 6.The top row shows changes in power output from CHP units relative to the reference case for all electricity price regions in Sweden.Data points highlighted in red are system configurations that need a heat-only boiler to fully supply the heat demand.The bottom row shows total heat production in heat pumps (dashed lines) and heat supplied directly to the DH network (solid lines).

Location of cavern
known.Applying the distribution of these 32 known caverns to the approximately 80 uninsulated caverns make it possible to estimate a potential for flexible power balancing in DH systems.Also included in this study is a few large-scale rock caverns constructed as TESs during the 1980 s (see Table 3).
The volume of the rock caverns supervised by SGU varies between 12,000 and 170,000 m 3 [30] and the caverns originally built as TESs have a volume in the range of 15,000 -850,000 [31].A brief literature research shows that the volume of rock caverns used for oil storage varies significantly.In Table 4 and in Fig. 4 this spread is shown.Typically, several oblong rock caverns were constructed in parallel.The dimensions of these caverns are quite similar in width (15-20 m) and height (20-30 m), while the length can vary significantly, 50-500 m.It is thus not possible to specify a standard size for these caverns.In the range between 70,000 and 120,000 m 3 there are 23 caverns with an average size of approximately 93,000 m 3 .Thus, in this study, each system had access to either one cavern of the size of 90,000 m 3 , or twice as much, which corresponds to the sizes of the caverns in Hudiksvall.In Hudiksvall's experience, the full volume of the TES is not available due to geometric irregularities, e.g., sloping bottom, and arched roof.But also due to exergy destruction along the walls, where hot water near the wall is cooled down by intrusion of colder groundwater, causing cold water to circulate down the wall and rendering part of the bottom water unusable.Therefore, is only 80% of the total volume available in the simulations, which equals 4.21 GWh th or a heat storage capacity of 3% relative to the annual heat demand for a 90,000 m 3 storage.The available volume will be called "active volume" in the presentation of the results.

Simulation algorithm
The control signal for the algorithm is the electricity balancing demand as defined in (1) (see also Fig. 5).If P SEj bal is greater than zero, electricity is produced by the CHP plant.Co-produced surplus heat is stored in TES according to (11).In each time-step, the ramping rate is limiting the CHP production output change.If P SEj bal is less than zero for hour i, the heat pumps consume electricity (10) and the produced excess heat is stored in the TES as described in (11).Neither heat pumps nor CHP produce any heat if P SEj bal equals zero for hour i.For these conditions, the heat demand is supplied with stored heat from the TES.
The algorithm overrides the control signal, P SEj bal , if the storage is full, and discharges the storage until a storage capacity equivalent to 40 h of (maximal) heat production from the CHP unit, is available.The CHP unit is not available for production during the discharge of the TES.However, the heat pumps are available to respond to the control signal and produce heat if there is an NRL during this discharging period.The reason for this forced discharge is to avoid an operation of the CHP unit that ramps up and down every hour because the TES is almost fully charged and instead the operator shuts down the unit.The length of this shutdown is of relevance as it disables power balancing production from the CHP plant on these occasions.Therefore, a sensitivity analysis evaluates how the length of the discharge period affects the power balancing potential.
To mimic the fact that production is based on placed bids at the dayahead market at NordPool, an assumption is made.If the coming 48 h after the current hour of operation contain PRL, the turbine of the CHP is bypassed, and the boiler is downregulated to minimum output.If the coming 48 h contain no PRL, the operator shuts down the boiler.Since the day-ahead auction closes, at noon, 36 h before the latest hour of operation, 48 h as time horizon, thus, gives room for 12 h of planning before the first hour of operation.
Two weeks before the period of maintenance of the CHP unit, the algorithm ensures that the stored heat will cover the heat demand during maintenance.Extra heat production in the CHP unit in advance ensures this.Furthermore, if the stored heat in the TES drops below the capacity of supplying the heat demand at peak level during 3 h, CHP units increase heat production, if possible, to uphold a required buffer capacity.Fig. 7.The top row shows changes in power output from CHP units relative to the reference case for all electricity price regions in Sweden.The bottom row shows total heat produced in heat pumps (dashed lines) and the amount of heat supplied from heat pumps directly to the DH network (solid lines).Inset graph, b, shows the energy transaction in the TES in the scenarios with 20 MW th heat pump capacity and 40 and 50 MW th capacitiy in CHP units, respectively for SE3.

Results
In this section the results are presented corresponding to the order of the research questions.

Power balancing service
Fig. 6 shows the change in annual power balancing production for different CHP capacities compared to the "business-as-usual" reference with 90,000 m 3 TES.System configurations that require heat-only boilers to supply the heat demand are highlighted with red circles.The lower panels in Fig. 6, show the amounts of heat produced in heat pumps and supplied to the DH network.The potential to provide power balancing services differs between the different electricity price areas.
One explanation for this is the difference in control signal P SEj bal for the different regions (see Fig. 3 and Table 2).For instance, for SE1, 2, and 4 the amount of NRL relative to the amount of PRL is significantly higher than in SE3.The point is that with large amounts of NRL, heat pumps can consume more electricity for production of heat, and with increasing capacity in the heat pumps, this heat will limit production in CHP units.This competing relation explains the continuously reduced CHP power production as heat pump capacities increase as is shown in the upper panels in Fig. 6.For SE3, the amount of NRL is quite small, and the reduction in CHP power production is not as prominent as for the other three regions.It would be reasonable to expect that power production would increase compared to the reference case with the operation of the CHP units controlled by electricity balancing demand.However, due to competing heat from heat pumps, this is not always the case.For several scenarios, power production is less than in the reference case.The lower power production is an effect of competing production of heat in heat pumps combined with the overall limiting heat demand.Still, the results indicate that with higher capacity installed in the CHP units, power production is more likely to increase, relative to the reference case, despite competing heat from heat pumps.With higher capacities in the CHP units, production is however, not necessarily increased compared to the reference case, as Fig. 6 shows.
The bottom panel in Fig. 6 shows the amount of heat supplied directly to the DH network (solid lines) and the total amount of heat produced in heat pumps (dashed lines).Increasing the capacity of the heat pumps does not give an increase in heat supplied directly to the DH network.Capacities higher than 30 MW th does increase the total heat production from heat pumps, but not the amount of heat supplied directly to the DH network.This discrepancy relates to the temporal mismatch between the NRL and the heat demand, and therefore an increased heat pump capacity mainly yields a higher demand for flexible storage capacity.For SE3, such a peak cannot be identified since the total amount of NRL is too small.With a larger storage capacity (Fig. 7), CHP power production is generally higher compared to cases with smaller storage capacities.The total amount of heat produced in heat pumps (dashed lines) and the amount of heat supplied directly to the DH network (solid lines) does not change significantly, as shown in the bottom panels.The major difference is that cases with high capacities in the heat pumps and low capacities in the CHP units, increase the amount of produced heat when the storage size increases.Furthermore, higher storage capacity reduces the need for heat-only boilers to cover heat demand.Only 46 system configurations required heat-only boilers with the large storage compared to 56 system configurations with a smaller storage.The temporal mismatch between production and demand for heat can explain this.The storage must be large enough to store enough heat to cover the heat demand not directly supplied by the producing unit, i.e., CHP or heat pump.At peak demand periods, i.e., the colder part of the year, this becomes particularly crucial.With the smaller storage size, stored heat is not sufficient to cover all load and heat-only boilers are required to cover demand peaks.With higher capacities in CHP units, on the other hand, co-produced heat is sufficient, and heat-only boilers become redundant.Also, larger TES can more easily store heat for longer time, which aids in making heat-only boilers redundant.The surplus heat to store comes partly with increased capacity in the CHP units, but also with increased capacity in the heat pumps.Capacities higher than 40 MW th and 35 MW th in SE3 and SE4, respectively, do not increase power production significantly compared to the reference case.In some cases, total production is less at maximum capacity compared to slightly lower capacities.With high capacity in CHP units comes large amounts of co-produced excess heat that is stored.This stored surplus heat will in turn, when used, compete with additional CHP production (see inset diagram b in Fig. 7), forcing the CHP unit to bypass the turbine and ramp down production until there is either sufficient heat demand or capacity in the TES available.Why this is not seen for SE1 and 2 relates to the amount of PRL and NRL in these regions.In SE1 and 2, PRL and NRL are fairly equal in amount and somewhat evenly distributed in time, while for SE3 and 4, there is significantly more PRL compared to NRL.In SE3, heat produced in heat pumps from NRL is merely a few percent of total heat demand.Thus, heat from heat pumps never really competes with the production in CHP units, as is the case in other regions.
In Table 5, different system configurations for different main objectives of operation are shown.The configurations are based on the lowest standard deviation of the residual loads' variability.In the first column, together with the name of the region, is the standard deviation of the electricity balancing demand shown for comparison (in parenthesis).If the main objective is to maximise the positive power balancing production, it shows, as one might expect, that high capacity in the CHP and small capacity in heat pumps is preferred.If the main objective instead is to reduce the NRL, not surprisingly, the opposite relation is preferable.The last column shows configurations that, without the need for HoB, manage to minimise net load variability the most, i.e., lowest standard deviation.Systems requiring a HoB are excluded as these are considered not using the storage potential to replace peak load units fully.In italics is the standard deviation of the net demand for the reference businessas-usual case also shown.
A national power balancing potential can be estimated by applying configurations that minimise the net load variability (from Table 5) times the approximated amount of available rock cavern TESs in the respective SE-area.Table 3 gives the amount of rock cavern TESs for each SE-area.Table 6 shows the resulting power balancing potential for these systems with access to either 90,000 m 3 or 180,000 m 3 of storage.

Fuel demand
In Fig. 8, the fuel use for all system configurations with access to 90,000 or 180,000 m 3 rock cavern TES is shown.Generally, the results show that high-capacity heat pumps reduce fuel demand.Furthermore, in all configurations the fuel use is less when compared to the reference case, except for in SE3.The low amount of available NRL used to run    Table 7 shows the fuel use in the configurations that reduce net load variability the most.When compared to Fig. 8, the configurations that reduce net variability the most are not the same as the ones that reduce fuel demand the most.The trade-off between fuel-replacing heat production in heat pumps and power balancing production in CHP units explains this discrepancy.All regions, but SE3, show significant reductions in fuel use.The large amount of PRL, i.e., consequently thus also a relatively low share of NRL causes the increased fuel use in SE3.Although the size of production differs markedly between the regions, where SE3 stands out with more than six times production compared with the region with the second most production, SE4, the total fuel use is nevertheless lower compared with the reference.The large reduction in fuel use in SE1, SE2, and SE4 simply compensates for the increased fuel use in SE3.

Operation and size of the TES
Figs. 9 and 10 show the operation of the TESs for the scenarios that reduce net load variability the most.Fig. 9 shows scenarios with access to 90,000 m 3 TES, and Fig. 10 shows scenarios with access to 180,000 m 3 TES.The blue dashed line represents the energy content in the TES (right y-axis) in both figures.The black solid line represents surplus heat from heat pumps, while the light grey solid line represents surplus heat from co-generation in CHP units, both supplied to TES.Negative values represent discharged heat supplied to the DH network, shown as medium grey solid line.Comparing Figs. 9 and 10, the frequency of charging/discharging is not significantly different between the smaller and larger TESs.However, due to the smaller size, the degree of utilization, η U is approximately twice as high for the small TESs compared to the larger storages.It can also be seen that the storages are only fully  Fig.11.Energy transactions and content in the storage for four of the sensitivity cases.
S.W. Monie and M. Åberg discharged on a few occasions per year, typically during seasonal peak demand periods and/or during maintenance of the CHP unit.For SE4, however, storage is never fully discharged during the entire year.For the 180,000 m 3 TES, only 21% of the capacity is used, and for the 90,000 m 3 TES, about 37% is used.Also, for SE3, the depth of discharge (DoD) only reaches 49% at the most for the 180,000 m 3 TES.The reason for this is that the operational strategy of the storage is not designated to specifically target a reduction in peak heat demands.It is merely acting as a flexible load where surplus heat from CHP and/or heat pumps is stored and later supplied to the DH network when CHP and/or heat pumps are not producing enough heat.The poor DoD either implies that the storage is unnecessary large in these three mentioned cases, or that the operational strategy should be adjusted to ensure full cycling of the energy content in the storage.
In Table 8, key figures for the operation of the TESs are presented.The table gives aggregated values for both total and active volumes as well as the energy capacity of the active volumes and the heat losses.Generally, the degree of utilization,η U , is about twice as high for smaller storages compared to larger.The energy efficiency, η E , is fairly constant, around 95% for the large TESs, and 8 percentage units lower for the smaller TESs.The depth of discharge, DoD, represents how deep the energy content is discharged at the most.For all systems the DoD is 95% or more, except for the large storage in SE3 or any of the SE4 systems.In these three systems the DoD is merely some 50% or even less.

Sensitivity analysis
To better understand the impact of operational strategy of the TES on power balancing services, the sensitivity for the case of SE4 with 180,000 m 3 TES was analysed.The TESs are available if there is enough capacity left in the TES to store an amount of heat equivalent to 40 h peak balancing power production from the CHP units, i.e., or an equivalent amount of heat of 2 GWh th .If the available TES-capacity is less than this, the CHP units are shut down, while TESs and heat pumps supply the heat demand until enough storage capacity is available.For example, in Fig. 10 it can be seen for SE4, that at the beginning of December, the TES has no capacity left to store heat and the operator shuts down the CHP unit, while the TES supplies the heat demand.The first discharge-period covers the heat demand for about 3 full days (68 h), after which the operator re-starts the CHP unit.The CHP then operates for almost six full days (139 h) before the heat demand and the TES capacity is limiting the production again.This limitation of CHP production is, however, challenging and is here analysed further.Excessive starts and stops of a CHP unit are undesirable due to thermal stress of components as well as costly cold starts due to inefficient fuel use.Also, there are no power production possible at these times.The choice of using 40 h in this study was an estimated trade-off between available production capacity and sufficiently long periods of shutting the unit down, based on practises reported from industry.
The sensitivity analysis changes the required capacity available in the TESs before shutting down the CHP production unit in five steps.The first analysis has no restriction and allows CHP units to produce whenever there is heat demand and/or capacity available in the storage.In the following analyses, the required available capacity in the TES, based on the specified number of hours of maximum heat production in the CHP units, is increased.Table 9 shows all analysed cases in the  sensitivity analysis for SE4 with 180,000 m 3 TES and the same capacities in CHP (50 MW th ) and heat pumps (60 MW th ) that reduced net load variability the most, i.e., as presented in previous section.
Fig. 11 shows the energy transactions in the TES for four of the analysed cases, "No restriction", "20 ′′ , "80 ′′ , and "120 ′′ .The dashed blue line represents the energy content in the TES and, with increasing required available capacity, increased charge/discharge cycling of the heat follows.Surplus heat from CHP production stored in TES is shown with light grey lines (positive values).By analysing the cycling of the heat in the TES during December, significant differences in the operation of the TES can be seen.In the case with no restriction, the TES is charged and discharged every hour, which means that the CHP unit is ramping up and down in production continuously during this period.In the case "20 ′′ , there are 7 distinct discharge periods during which the operator shuts down the CHP unit.The length of these discharges is approximately 30 h each.With increasing amounts of required available storage capacity, these periods of discharge become longer.In the last case "120 ′′ , there is only one charge/discharge period, during December.In mid-December, a discharge of the TES starts during which the operator shuts down the CHP unit.This period lasts for 8 full days before the CHP unit is re-started.Fig. 12 A shows the change in net load variability relative to P SE4 bal with increasing thresholds for available TES capacity.Fig. 12 B similarly shows how the DoD and the share of heat produced in heat pumps change with increasing thresholds for available TES capacity.In 12 A with increased required storage capacity, the variability in the net NRL is almost linearly decreasing.Larger amounts of NRL can, thus, be consumed in heat pumps.The reason for this is the fact that with increasing length of the downtime for the CHP unit, follows an increased share of the heat demand that the heat pumps can supply.The change in the variability for the net PRL, though, does not follow a similar trend as the net NRL.In the unconstrained case "No restriction", the operator runs the CHP unit on partial load for basically half of the operating hours.When introducing a threshold for the required available storage capacity, this partial load time is reduced to about one third of the total production time.Almost all the partial load production in the "No restriction" case is a result of the CHP unit ramping up to initiate power production as a response to a PRL in the P SE4 bal .However, since the TES is almost full, the unit immediately needs to ramp down production, most of the time shortly after starting power production.The effect of this is the production of a lot of surplus heat, directly stored due to insufficient heat demand.In turn, this hampers the heat production in the heat pumps since there is not sufficient heat load available; thus, the quite low reduction of net NRL variability for the "No restriction" case compared to the other cases.When increasing the threshold for required available storage capacity from 1 GWh th , case "20 ′′ , to the maximum of 6 GWh th , case "120 ′′ , power production gradually reduces.However, not to the same extent that NRL consumption increases.In case "120 ′′ , the balancing power production is about 14% less compared to case "20 ′′ , while the consumption of NRL in heat pumps is 30% higher.The result of this discrepancy between the reduction of PRL and NRL means that net profile variability is not significantly affected at all for cases with a threshold greater than zero.The reduced net profile variability was about 6% larger for all these cases when compared to P SE4 bal .Fig. 12 B confirms the relation between higher thresholds for the available storage capacity and increased NRL consumption in heat pumps.The DoD of the TES also increases with higher thresholds, as can be seen in Fig. 11.
In the storage algorithm, when fully charged, the TES discharges and continues to discharge until a predetermined threshold of required available storage capacity has been reached.During discharge, the CHP units are forced to shut down, and thus the CHP units might not be available at critical peak PRL hours.Generally, the results indicate that with larger TESs follows a greater possibility that the CHP is available at critical peak PRL.However, this also relates to the capacity of the heat pumps.Fig. 13 exemplifies this for the scenario of SE1 and a CHP capacity of 40 MW th together with varied capacities in the heat pumps.The Figure shows the energy transactions in the TES for all five levels of heat pump capacity.The dashed black line indicates the hour of peak PRL when the CHP unit preferably should be available.With low capacity in the heat pumps, the available capacity in TESs is sufficient for a flexible operation of the CHP unit.However, when the capacity in the heat pumps exceeds 40 MW th , the available capacity is significantly reduced, which hampers the flexible operation of the CHP unit.Hence, one may argue that if the CHP units should be available at critical peak PRL hours, it is crucial that the capacity in the heat pumps is not too high.One can, on the other hand, also argue that with suitable probabilistic forecast methods, it may be possible to plan the operation of the TES and heat pumps to maximise the availability of the CHP units.A noteworthy result, however, is that for the other SE-regions, this conflict is not as prominent as for SE1, which in turn relates to the temporal distribution of the PRL and NRL in the electricity balance demand profiles.In SE1, a significant amount of NRL occurs during the week before the peak PRL hour, which the heat pumps consume for production of heat.The heat pumps are, thus, operated almost continuously during the preceding week, which rapidly charges the TESs.The higher the capacity in the heat pumps, the more rapidly the TESs are charged.

Discussion
Currently, the shares of VRE increases in the Swedish energy system and as already stated, the heat production strategy providing power balancing services that is applied in this study requires significantly higher shares of VRE than today.The power balancing demand is difficult to approximate since the precise variability and production pattern for future VRE is difficult to predict.This because it depends on geographical distribution of future production units, the weather, as well as inter-regional transmission capacities.Furthermore, the currently limited transmission capacities between the Swedish electricity price regions will possibly improve in the future, but when and to what extent is difficult to foresee.The impact of a common electricity balancing demand for the entire SE-area can, however, be derived.This situation would be represented by the data in Table 2 and under the assumption that price-region transmission capacities are unlimited.This total national power balancing demand is presented in Fig. B1 in appendix B. A simulation of the operation for all 85 DH systems controlled by this total balancing demand, yields approximately 6% reduction of PRL and 24% reduction of NRL.Also, unlimited transmission capacities yield a reduction in fuel use of 45%, meaning that more NRL would potentially be available for heat production that replace fuel use.The simulations further indicate that a total balancing demand would reduce the required size of TESs.This because of a low storage capacity utilisation for both the 90,000 m 3 TES and for the 180,000 m 3 .This, on the other hand, opens for the possibility to use the produced and stored heat for other purposes, i.e., district cooling via sorption chillers or even electricity production via technologies using low enthalpy thermal energy, such as Sterling engines, Kalina-/Organic Rankine cycles, or thermal electric generators.
The amount and whereabouts of rock caverns in Sweden that can potentially be converted into TESs are not public information due to strategic defence concerns.This provides some significant uncertainty to the applicability of the storage-based scenarios.It may be that caverns are too far away from any urban areas to be potentially used in a DH production system.On the national level, every TES that is not in vicinity of a DH system hampers the potential reduction of PRL and NRL by 0.1 percentage units relative the total balancing demand.On the regional level, the corresponding impact of one unavailable rock cavern for PRL-reduction would vary between 0.2 percentage units in SE3 to 1.1 percentage units in SE2.For reduction of NRL, the reduction would be 0.6 percentage units for SE2, and 1.1 percentage units for SE4.
In the system configurations that reduced net balancing load variability most, the thermal capacities of both CHP and heat pumps are higher than peak heat demands.In general, heat production unit capacities are optimised to reduce heat production costs in the local DH system.It is not common in Swedish DH systems to have capacities that the results presented here would require.This is an aspect that is not further investigated here, but should be addressed and recognised as challenging, since it would require significant production capacity investments.Inline with this, it is of relevance to also consider business models that would enable production capacity investments based on power balancing potential rather than heat production cost.
Also, the economic value of balancing power is an aspect that would need further attention.The economic viability of operating DH production primarily for power balancing rather than heat load supply, needs to be considered in relation to the cost of the alternatives.The costs and availabilities of hydro power and/or power electronics and electric storage systems are crucial for the rationality of using DH production units for power balancing.Thus, the costs for these alternatives and/or increased capacities in power distributions systems must be compared with the savings from reduced fuel use, costs for converting rock caverns into TESs and the costs for increasing power production capacities in CHP and heat pumps.The latter is, however, an analysis that goes beyond the scope of this study.
Furthermore, a minor note on the reference case simulation results in comparison to official statistics on electricity production data from Swedish DH systems in 2020.The simulated CHP electricity production is about twice as large, 4.25 TWh el compared to 2.3 TWh el [41,42,23].This excludes CHP production from waste incineration plants as well as industry.This discrepancy is significant, but not particularly relevant since the reference case is not an attempt to represent the current production but rather represents the potential CHP power production.Also, there are explanations to why CHP electricity production is currently not fully utilised in Sweden.Svebio, for example, reports circumstances explaining why power production from biomass-fuelled CHP units is lower than expected, where heat being the primary product is one [43].Other relevant factors are actively restraining the electricity production to avoid costly net tariffs from grid owners, the need to increase the temperature of the feeder water to the DH network during colder parts of the year and thus reducing the temperature difference at the turbine which negatively affects the electricity production, or the need for more (and higher quality) fuel [43].These would potentially constitute obstacles also for the systems configuration simulated in this study.This could, thus, further indicate that there is a need for changed tariffs, policies, and/or economic compensations to make these systems possible to implement and that this is not merely a matter of changed operational strategy within the DH sector.
Finally, this study focuses on the Swedish case, and the specific Swedish conditions for providing balancing power using DH-production systems do have a crucial impact on the results.This means that the results presented are not fully applicable to other systems unless the conditions are similar to those of Sweden.However, the concept of coupling thermal energy systems with power systems in order to increase flexibility and provide balancing services and local urban power supply capacity is generally applicable.At least for systems where DH and/or district cooling infrastructures are either existing or potentially will exist in the future.Several insights from this study concerns aspects that will need consideration for any similar system regardless of the specific conditions.Such aspects are; limitations from thermal loads, power generation/consumption capacities, TES-capacities, competing heat-and/or cooling production units.

Conclusions
This study shows that applying an operation approach where electricity balancing demand controls the heat production in DH systems can be a way to provide power balancing services.The potential varies between the electricity price regions investigated and with the size of the TES applied.The potential is mainly dependent on the distribution of TES with respect to the electricity price regions, but also on the share and temporal distribution of PRL and NRL within each region.The national Swedish potential is a 9 % reduction of PRL (≈ 4,000 TWh el ) and of NRL (≈ 600 TWh el ) with rock cavern TESs of either 90,000 m 3 or 180,000 m 3 .The results show that the shares of PRL and NRL are more important for the potential than actual installed capacities in CHP and/ or heat pumps.For SE1 and SE2, with fairly equal shares of NRL and PRL, the potential per system is higher than for SE3 and SE4 with more unequal shares.
One conclusion is that a focus on reducing NRL, significantly reduces fuel use.A further conclusion is that it is possible to reduce both PRL and NRL and at the same time also reduce fuel use.However, this is strongly dependent on shares of PRL and NRL, where PRL risks to cause increased fuel use while NRL generally reduces fuel use.The results further show that, on an aggregated level, the system configuration that reduces net load variability the most, also reduces fuel use by approximately 8-11 % depending on the size of the TES.
The way that the TES is operated is crucial since this occasionally limits the CHP units' availability at high demand peak.With larger TES capacity, CHP production is more flexible during peak demand periods, i.e., in wintertime.If reducing peak PRL is not the main objective for power balancing production, a third conclusion, based on the sensitivity analysis, is that possibilities exist to offer significant reduction of NRL combined with significant reduction of PRL.Furthermore, the operation of the simulated systems would benefit from improved transmission capacities between the electricity price areas regarding reduced fuel use and reduced size of storages needed.

Declaration of Competing Interest
The authors declare the following financial interests/personal relationships which may be considered as potential competing interests: Magnus Aberg reports financial support was provided by The Swedish Energy Agency.

Fig. 2 .
Fig. 2. Distribution and duration of heat load calculated for each of the four electricity price regions of Sweden.

Fig. 5 .
Fig. 5. General decision tree for the algorithm.A detailed description is given in Appendix A. The colours highlight the three different modes of operation in response to electricity balancing demand.

Fig. 8 .
Fig. 8.The figure shows changed fuel use relative to the reference case for all configurations of CHP and heat pumps capacities with access to 90,000 or 180,000 m 3 TES.

Fig. 9 .
Fig. 9.The figure shows the utilization of the 90,000 m 3 rock cavern TES for the configurations that reduce net load variability the most.Blue dashed line (right yaxis) represents the energy content in the storage.

Fig. 10 .
Fig. 10.The figure shows the utilization of the 180,000 m 3 rock cavern TES for the configurations that reduce net load variability the most.Blue dashed line (right yaxis) represents the energy content in the storage.

Fig. 12 .
Fig. 12. Figure A shows how the variability in the residual load is changed compared to P SE4 bal when the discharge threshold is changed for the TES. Figure B shows how changing the threshold affects the maximum DoD as well as the heat pumps' share of total heat production.

Fig. 13 .
Fig. 13.Energy transactions in a 180,000 m 3 TES in SE1 with a CHP unit with 40 MW th and varied thermal capacities in heat pumps.

Fig. B1 .
Fig. B1.The top left figure shows the electricity load, wind-and solar power, total electricity production from VRE, and the electricity balancing demand for the entire SE when all transmission limitations have been removed.Top right table shows key parameters for the derivation of the electricity balancing demand.Bottom figure shows usage of the TES.

Table 2
Annual numbers of data used to derive the P bal -profile.

Table 3
Distribution of the caverns supervised by SGU in Sweden.The distribution of the 32 known caverns is applied to the location of the unknown 80 uninsulated rock caverns in this study.

Table 5
Thermal capacities [MW th ], standard deviations [MW], and main objectives at different system configurations.

Table 6
Power balancing potential for configurations that minimise net load variability.

Table 7
Changed fuel use for configurations that reduce net load variability the most.

Table 8
Key figures for the operation of the rock cavern TES.Active volume refers to the available part of the total volume.

Table 9
Cases analysed in the sensitivity analysis.Scenario analysed is SE4 with 180,000 m 3 TES and the thermal capacities 50 and 60 MW in the CHP and heat pumps, respectively.The previously presented results show case "40 ′′ .