*3.1. Results of the Case Study*

*3.1. Results of the Case Study*  Three RSOCHS systems as well as one reference system were optimized for different solar PV generation capacities using the interval halving optimization method presented in the paper. The reference system has no onsite energy generation or storage. It is only comprised of connections to the electricity grid, the district heating network and the solar PV panels. The idea of the optimization was to optimize the operation of the system by minimizing the OPEX. The results of the optimization are presented and analyzed in this chapter in order to form a conception of the behavior and benefits Three RSOCHS systems as well as one reference system were optimized for different solar PV generation capacities using the interval halving optimization method presented in the paper. The reference system has no onsite energy generation or storage. It is only comprised of connections to the electricity grid, the district heating network and the solar PV panels. The idea of the optimization was to optimize the operation of the system by minimizing the OPEX. The results of the optimization are presented and analyzed in this chapter in order to form a conception of the behavior and benefits of a RSOCHS system as a seasonal energy storage for buildings.

of a RSOCHS system as a seasonal energy storage for buildings. The optimal operation of the different RSOCHS systems was analyzed for three different solar PV installation areas (1000, 2000, and 3000 m2), with results presented in Figures A1–A9 in the Appendix. All of the systems show the same trend; storing energy during summer and consuming the stored energy during winter. One surprising remark, which also holds true for all storage systems, is that the system uses large amounts of electricity from the grid to fill up the hydrogen storage, even during the summer, when there is a surplus of energy generated by the solar PV panels. This indicates that it is cost-effective to convert electricity from the grid to hydrogen gas and then use it for heating The optimal operation of the different RSOCHS systems was analyzed for three different solar PV installation areas (1000, 2000, and 3000 m<sup>2</sup> ), with results presented in Figures A1–A9 in the Appendix A. All of the systems show the same trend; storing energy during summer and consuming the stored energy during winter. One surprising remark, which also holds true for all storage systems, is that the system uses large amounts of electricity from the grid to fill up the hydrogen storage, even during the summer, when there is a surplus of energy generated by the solar PV panels. This indicates that it is cost-effective to convert electricity from the grid to hydrogen gas and then use it for heating during the winter.

during the winter. By comparing the optimal operation of different system setups, it is shown that seasonal energy storage has some benefits for energy systems with large solar PV installations. This remark is supported by the results presented in Figures 7–10. It shall, however, be pointed out that the optimization model is formulated so that it does not allow the RSOC device to be turned off, since it might be complicated to ramp the RSOC up and down due to the high operation temperature. This By comparing the optimal operation of different system setups, it is shown that seasonal energy storage has some benefits for energy systems with large solar PV installations. This remark is supported by the results presented in Figures 7–10. It shall, however, be pointed out that the optimization model is formulated so that it does not allow the RSOC device to be turned off, since it might be complicated to ramp the RSOC up and down due to the high operation temperature. This is the reason why the RSOCHS systems perform worse than the reference system for smaller PV installations.

is the reason why the RSOCHS systems perform worse than the reference system for smaller PV

Figure 7 shows the optimal OPEX (for the optimal hydrogen storage size) as a function of installed PV area for the RSOCHS storages systems and the reference energy system (no RSOC). By examining the graph in Figure 7, it can be observed that increasing the solar PV area has a higher cost saving impact on the RSOCHS system than on the reference system. More installed PV panels entail drops below zero.

greater extent by a big RSOC device.

solar PV installations.

suitable for small RSOC devices, while the power generation of larger PV areas can be utilized to a

The same trend can be observed when the amount of imported energy is examined for the different energy systems. Figure 8 shows that the amount of imported energy can be reduced by investing in an RSOC and hydrogen storage system. It can also be observed that the energy savings increase when more solar PV panels are added to the system. This proves that the RSOCHS system works as intended, halving the need for annually imported energy for energy systems with large

Figure 9 and 10 show that reduced district heating consumption accounts for most of the energy savings generated by the RSOC and hydrogen storage system. The figures describing the optimal RSOC operation in the Appendix show that most of the time, heat is generated by the RSOC, but the peaks in the heat generation are caused by hydrogen combustion. Some of these peaks may be a

Without hydrogen storage, the operation of the RSOCHS systems and the reference system would be the same. Hence, the difference in OPEX between the systems in Figure 7 is only induced by the hydrogen storage size. It can be noted that the impact of the hydrogen storage size on the OPEX is marginal for PV installations below 5000 m2. For big PV installations, however, the significance of the hydrogen storage size is more crucial, especially when the OPEX of the systen

Figure 11 shows the optimal hydrogen storage capacity for different RSOCHS systems and solar PV areas. The figure indicates that the optimal size of the hydrogen storage increases with the size of both the solar PV installation and the RSOC device. The energy content of the hydrogen stroage is

consequence of the interval halving approach in the optimization method.

**Figure 7.** Optimal annual operating expense (OPEX) (for the optimal hydrogen storage size) as a function of installed solar photovoltaic (PV) panel area for the three RSOCHS systems and the reference system. **Figure 7.** Optimal annual operating expense (OPEX) (for the optimal hydrogen storage size) as a function of installed solar photovoltaic (PV) panel area for the three RSOCHS systems and the *Buildings*  reference system. **2020**, *10*, x FOR PEER REVIEW 12 of 27

*Buildings* **2020**, *10*, x FOR PEER REVIEW 12 of 27

**Figure 8.** Annual imported energy (electricity and heat) (for the optimal hydrogen storage size) as a function of installed solar PV panel area for the three RSOCHS systems and the reference system. **Figure 8.** Annual imported energy (electricity and heat) (for the optimal hydrogen storage size) as a function of installed solar PV panel area for the three RSOCHS systems and the reference system. **Figure 8.** Annual imported energy (electricity and heat) (for the optimal hydrogen storage size) as a function of installed solar PV panel area for the three RSOCHS systems and the reference system.

**Figure 9.** Annual imported electricity (for the optimal hydrogen storage size) as a function of installed solar PV panel area for the three RSOCHS systems and the reference system. **Figure 9.** Annual imported electricity (for the optimal hydrogen storage size) as a function of installed solar PV panel area for the three RSOCHS systems and the reference system. solar PV panel area for the three RSOCHS systems and the reference system. **Figure 9.** Annual imported electricity (for the optimal hydrogen storage size) as a function of installed solar PV panel area for the three RSOCHS systems and the reference system.

**Figure 10.** Annual imported heat (for the optimal hydrogen storage size) as a function of installed

**Figure 10.** Annual imported heat (for the optimal hydrogen storage size) as a function of installed

solar PV panel area for the three RSOCHS systems and the reference system.

solar PV panel area for the three RSOCHS systems and the reference system.

**Figure 8.** Annual imported energy (electricity and heat) (for the optimal hydrogen storage size) as a function of installed solar PV panel area for the three RSOCHS systems and the reference system.

**Figure 10.** Annual imported heat (for the optimal hydrogen storage size) as a function of installed solar PV panel area for the three RSOCHS systems and the reference system. **Figure 10.** Annual imported heat (for the optimal hydrogen storage size) as a function of installed solar PV panel area for the three RSOCHS systems and the reference system.

Figure 7 shows the optimal OPEX (for the optimal hydrogen storage size) as a function of installed PV area for the RSOCHS storages systems and the reference energy system (no RSOC). By examining the graph in Figure 7, it can be observed that increasing the solar PV area has a higher cost saving impact on the RSOCHS system than on the reference system. More installed PV panels entail a lower OPEX and an increased advantage of the RSOCHS system. It can also be observed that the optimal size of the RSOC is dependent on the installed PV area, as small PV areas appear to be more suitable for small RSOC devices, while the power generation of larger PV areas can be utilized to a greater extent by a big RSOC device.

The same trend can be observed when the amount of imported energy is examined for the different energy systems. Figure 8 shows that the amount of imported energy can be reduced by investing in an RSOC and hydrogen storage system. It can also be observed that the energy savings increase when more solar PV panels are added to the system. This proves that the RSOCHS system works as intended, halving the need for annually imported energy for energy systems with large solar PV installations.

Figures 9 and 10 show that reduced district heating consumption accounts for most of the energy savings generated by the RSOC and hydrogen storage system. The figures describing the optimal RSOC operation in the Appendix A show that most of the time, heat is generated by the RSOC, but the peaks in the heat generation are caused by hydrogen combustion. Some of these peaks may be a consequence of the interval halving approach in the optimization method.

Without hydrogen storage, the operation of the RSOCHS systems and the reference system would be the same. Hence, the difference in OPEX between the systems in Figure 7 is only induced by the hydrogen storage size. It can be noted that the impact of the hydrogen storage size on the OPEX is marginal for PV installations below 5000 m<sup>2</sup> . For big PV installations, however, the significance of the hydrogen storage size is more crucial, especially when the OPEX of the systen drops below zero.

Figure 11 shows the optimal hydrogen storage capacity for different RSOCHS systems and solar PV areas. The figure indicates that the optimal size of the hydrogen storage increases with the size of both the solar PV installation and the RSOC device. The energy content of the hydrogen stroage is calculated using the LHV of hydrogen gas.

*Buildings* **2020**, *10*, x FOR PEER REVIEW 13 of 27

**Figure 11.** Optimal hydrogen storage size as a function of installed solar PV panel area for the three RSOCHS systems and the reference system. **Figure 11.** Optimal hydrogen storage size as a function of installed solar PV panel area for the three RSOCHS systems and the reference system.

#### *3.2. Optimization Model Perfomance 3.2. Optimization Model Perfomance*

generating some heat [15].

variables.

problems with cumulative constraints.

could be able to solve a larger variety of optimization problems.

The model is evaluated by examining the optimization results of various RSOCHS system setups and investigating whether an increased degree of freedom in the energy system can result in lower OPEX values or not. Figure 12 shows the optimal OPEX of the 50/200 kW RSOC system as a function of the hydrogen storage capacity for different solar PV installations. The OPEX should decrease with increasing storage capacity, since more storage entails more relaxed constraints in the optimization problem. This is however not exactly valid for all the results. In the graphs, it can be observed that the trend lines are all decreasing when the storage capacity is increasing, but this is not exactly followed by the individual optimized points. It can be presumed that this small but noticeable inconsistency in the results is caused by some inaccuracy of the optimization model. One of the main sources of inaccuracy in the method could be the halving approach. Fixing a The model is evaluated by examining the optimization results of various RSOCHS system setups and investigating whether an increased degree of freedom in the energy system can result in lower OPEX values or not. Figure 12 shows the optimal OPEX of the 50/200 kW RSOC system as a function of the hydrogen storage capacity for different solar PV installations. The OPEX should decrease with increasing storage capacity, since more storage entails more relaxed constraints in the optimization problem. This is however not exactly valid for all the results. In the graphs, it can be observed that the trend lines are all decreasing when the storage capacity is increasing, but this is not exactly followed by the individual optimized points. It can be presumed that this small but noticeable inconsistency in the results is caused by some inaccuracy of the optimization model. *Buildings* **2020**, *10*, x FOR PEER REVIEW 14 of 27

optimization-based design of energy storage systems with many different components, as it is impossible to include the component investment costs in the objective function. A more accurate evaluation of the optimization method performance would require a **Figure 12.** Optimal OPEX of the 50/200 kW RSOC system as a function of the hydrogen storage capacity for different solar PV installations. **Figure 12.** Optimal OPEX of the 50/200 kW RSOC system as a function of the hydrogen storage capacity for different solar PV installations.

comparative analysis with other optimization methods. For the time being, no other optimization tools are available for solving the type of optimization problems presented in the case study. **4. Conclusions**  An interval halving MILP optimization method for seasonal storages was presented and tested by applying it to a case study. The novelty of the method is that it allows integer variables in each time step of the annual energy storage operation. The aim of the case study was to examine the One of the main sources of inaccuracy in the method could be the halving approach. Fixing a few points in the first optimizations steps will add more constraints on the following optimization steps which, in turn, will prevent the solution from reaching the global optimum. The peaks in the heat generation graphs in Figures A1–A9 in the Appendix A are visible indications of the inaccuracy

By analyzing the results of the optimization problem for the investigated case study, it can be noted that the solution of the optimization problem is a relatively accurate estimation of the optimal seasonal storage operation. Moreover, it shall be pointed out that the optimization problem presented in the case study is computationally too expensive to be solved by conventional optimization methods and that no other alternative optimization method suitable for the problem has been found in the literature so far. The model is hence ideal for optimizing MILP seasonal storage problems, but it could also be implemented in other computationally demanding linear scheduling optimization

There are, however, a few minor shortcomings that can be discussed regarding the interval halving optimization method. The most significant drawback of the method is caused by the interval halving approach itself. Bisecting the time interval and fixing its boundaries adds constraints to the optimization problem that are not present in a real situation. Consequently, the global optimum of the problem cannot be reached with the method, even if MILP problems can be solved to global optimality. Due to the nature of the interval halving approach, it is also impossible to include the investment cost in the objective function. Hence, it is somewhat inconvenient to use the method as an optimization-based design method for energy storage systems with a large number of design

Further algorithm development could increase the application area of the interval halving optimization method. Other MILP solvers and perhaps even mixed integer non-linear programming (MINLP) solvers could be applied in the model in the subproblem optimization. Thereby, the method

Apart from the restrictions of the optimization model, the mathematical assumptions in the optimization problem formulation also affect the reliability of the case study results. Some mathematical assumptions are made in order to attune the problem to fit the optimization approach,

optimal operation and setup of an RSOCHS system and evaluate its suitability as a seasonal energy

caused by the interval halving method. These peaks are most likely a consequence of forced hydrogen combustion due to the additional constraints produced by the interval halving process.

By analyzing deviation from the trend line in the graphs in Figure 12, it can be concluded that the optimization method is still relatively precise. The deviation from the trend line is namely below 2% for each optimized point in Figure 12. We also tried shifting the start of the year by 1400 h (58 days 8 h), but this action did only affect the value of the objective function (the OPEX) by less than 1%. This remark also supports the statement that the optimization method is relatively precise.

An additional drawback of the proposed optimization method is that the system component dimensions cannot be used as design variables in the optimization problem, as the optimization problem is divided into several subproblems with problem-speci0fic variables. Moreover, introducing the RSOC size as a variable would render the problem an MINLP (mixed integer non-linear programming) problem, which cannot be solved by the presented method. Hence, the optimal design of the energy storage system is found by performing several optimizations using different system component dimension combinations. This makes it complicated to use the method for the optimization-based design of energy storage systems with many different components, as it is impossible to include the component investment costs in the objective function.

A more accurate evaluation of the optimization method performance would require a comparative analysis with other optimization methods. For the time being, no other optimization tools are available for solving the type of optimization problems presented in the case study.

#### **4. Conclusions**

An interval halving MILP optimization method for seasonal storages was presented and tested by applying it to a case study. The novelty of the method is that it allows integer variables in each time step of the annual energy storage operation. The aim of the case study was to examine the optimal operation and setup of an RSOCHS system and evaluate its suitability as a seasonal energy storage. The operating principle of the RSOCHS system is to use RSOC technology to convert electrical energy to hydrogen gas and to convert hydrogen gas back to electricity while also generating some heat [15].

By analyzing the results of the optimization problem for the investigated case study, it can be noted that the solution of the optimization problem is a relatively accurate estimation of the optimal seasonal storage operation. Moreover, it shall be pointed out that the optimization problem presented in the case study is computationally too expensive to be solved by conventional optimization methods and that no other alternative optimization method suitable for the problem has been found in the literature so far. The model is hence ideal for optimizing MILP seasonal storage problems, but it could also be implemented in other computationally demanding linear scheduling optimization problems with cumulative constraints.

There are, however, a few minor shortcomings that can be discussed regarding the interval halving optimization method. The most significant drawback of the method is caused by the interval halving approach itself. Bisecting the time interval and fixing its boundaries adds constraints to the optimization problem that are not present in a real situation. Consequently, the global optimum of the problem cannot be reached with the method, even if MILP problems can be solved to global optimality. Due to the nature of the interval halving approach, it is also impossible to include the investment cost in the objective function. Hence, it is somewhat inconvenient to use the method as an optimization-based design method for energy storage systems with a large number of design variables.

Further algorithm development could increase the application area of the interval halving optimization method. Other MILP solvers and perhaps even mixed integer non-linear programming (MINLP) solvers could be applied in the model in the subproblem optimization. Thereby, the method could be able to solve a larger variety of optimization problems.

Apart from the restrictions of the optimization model, the mathematical assumptions in the optimization problem formulation also affect the reliability of the case study results. Some mathematical assumptions are made in order to attune the problem to fit the optimization approach, while some assumptions are just made due to the lack of available RSOC operation data. The RSOC operation, for example, is assumed to be linear, even though the RSOC operation is slightly non-linear according to several sources [21,30]. The performance of the RSOC is, in practice, also highly dependent on the operation temperature [30], which is not taken into account in this study, since it would considerably complicate the problem formulation. Uncertain technical factors such as the time required to switch between operational modes and balance of plant energy losses etc. are not taken into account in the model either. It is, however, complicated to create a proper mathematical RSOC model, since ROSC technology is still in an early development phase. A more thorough optimization of the RSOCHS system would therefore have to be postponed until the technology is mature enough to provide sufficient technical and operational data.

The results of the optimization show that the operating cost benefits as well as the self-sufficiency of an RSOCHS system increase when more solar PV panels are installed. The RSOC and hydrogen storage system enables the consumer to utilize more of the generated PV power, which means that less energy has to be imported. An RSOCHS system could hence be an important contributor in achieving a net zero annual energy balance for individual buildings. In building energy systems with big solar PV panel installations, the annual imported energy could be halved by installing an RSOCHS system. This reduction in imported energy would mostly be in the form of a reduction in district heating.

However, installing an RSOCHS system does have a relatively low impact on the OPEX of the energy systems. The maximum capital savings in terms of annual OPEX is only about 5000 EUR, which is only a fraction of the investment cost of the hydrogen gas compressor [15]. The payback time of the RSOCHS system might thus be greater than the total life of the investment.

The optimal hydrogen storage size varies between 50 and 5000 kWh, depending on the RSOC size and the solar PV panel area. The optimal size of the hydrogen storage tends to increase as the RSOC size and the solar PV panel area increases.

The analysis of the ROSCHS system operation optimization showed that the hydrogen storage should be filled during the summer using both electricity generated by the solar PV and electricity imported from the grid. This behavior can be motivated by high PV generation during the summer period and the high district heating prices in the winter period. Because of the high district heating prices in the winter, it is economically feasible to charge the energy storage with electricity from the grid and use it for heating.

The case study in this paper only focuses on the optimal operation of the RSOCHS system and its operational benefits compared to a system without energy storage. To better understand the economic value of the RSOCHS system, a life-cycle cost analysis is required. RSOC technology is still in a development phase and the cost of an ROSCHS system is thus not yet competitive compared with other energy storage technologies [31]. Mass manufacturing of RSOC components is envisaged to bring down the investment cost of the technology, but exactly by how much is still difficult to predict. Hence, RSOC technology might play a significant role in future energy storage and power-to-gas systems.

**Author Contributions:** Conceptualization, O.L., R.W., F.P., A.H. and J.S.; methodology, O.L.; validation, O.L.; formal analysis, O.L.; investigation, O.L.; writing—original draft preparation, O.L.; writing—review and editing, O.L., A.H., R.W. and F.P.; visualization, O.L.; supervision, A.H., R.W. and F.P. All authors have read and agreed to the published version of the manuscript.

**Funding:** The authors would like to thank Business Finland. The work was part of Smart Otaniemi innovation ecosystem (Smart Otaniemi Pilot Phase 2, 8194/31/2018) financed by Business Finland.

**Conflicts of Interest:** The authors declare no conflict of interest.
