# Thermal Energy Storage for Building Load Management: Application to Electrically Heated Floor
## 2 Materials and Methods
### Study of the Performance of an EHF
#### 2.2.3 Adaptation of Indicators for Sensible Thermal Storages

Table 3: _Cont._where:  
\[CES_{1} = \Biggl{(}\sum_{i=1}^{N_{d}}c_{e_{eff}peak}\times E_{offpeak\_1}+\ c_ {e_{peak}}\times E_{peak\_1}\Biggr{)}/E_{tot\_1} \tag{3}\] \[CES_{2} = \Biggl{(}\sum_{i=1}^{N_{d}}c_{e_{eff}peak}\times E_{offpeak\_2}+\ c_ {e_{peak}}\times E_{peak\_2}\Biggr{)}/E_{tot\_2} \tag{4}\]  
where  
* \(c_{ini_{1}}\) and \(c_{om\_1}\) are respectively the initial cost and maintenance cost of the system with storage
* \(c_{om\_2}\) is the maintenance cost of the system without storage
* \(c_{e_{eff}peak}\) and \(c_{e_{peak}}\) are the energy prices during off-peak and peak, respectively,
* \(E_{offpeak\_1}\) and \(E_{offpeak\_2}\) are the consumption during off-peak periods per day respectively with storage system and without storage system
* \(E_{peak\_1}\) and \(E_{peak\_2}\) are the consumption during peak periods per day respectively with storage system and without storage system
* \(E_{tot\_1}\) and \(E_{tot\_2}\) are the total consumption for space heating for \(N_{d}\) days respectively with storage system and without storage system, and
* \(CES_{1}\) and \(CES_{2}\) are the average energy price for \(N_{d}\) days with storage system and without storage system, respectively. Depending on the availability of the data and the goal of the study, some parameters may be considered differently:  
* For the consumption of the heating system for one year without the storage system (\(E_{tot\_2}\), historical data may be used to define the consumption of the system without storage in the case of an existing building. * In Equation (2), only the initial cost of the heating system associated with storage is considered. That means most of the installations are for retrofitted buildings. For a new building, the price difference between the price of the heating system with storage and the price of the heating system without storage may be considered. * Energy costs during peak and off-peak periods may be the cost for customers or for the supplier, depending if the study is done on the potential savings for the customer or for the supplier. In this study, the maintenance costs of the system with storage and without storage are considered equal. Moreover, in this study, the calculation of the ratio between peak and off-peak energy consumption has been done only for January, the critical period for space heating period. Finally, the reference building, with electric baseboards and with a set-point of 21 \({}^{\circ}\)C, had a total energy consumption of 81.7 kWh/day, with 55% of the consumption during the day. Energy Conversion Efficiency--\(\eta\)[-]  
The energy conversion efficiency is one of the most important indicators: it is the ratio of the useful output (the building demand during the discharging time) of a system to the input (the required energy consumption during the charging time). The complexity of efficiency definition is to define what the input is. In particular, for a storage system coupled with a heating or cooling systems, two different efficiencies can be defined: the efficiency of the storage system itself, and the efficiency of the whole system, from the heating/cooling system to the delivery system including the storage system, see Figure 5.  
[PERSON] et al. [32] provides three definitions of the efficiency for a sensible thermal storage (hot water tank): the storage fraction, which represents the usable portion of the heat stored (with a tank for example, a portion of the fluid cannot be used); the first law efficiency, which defines the ratio of the actual energy discharged to the stored thermal energy, taking into account losses; and the second law efficiency is the exergy definition, taking losses and potential ineffectiveness of a part of the storage system into account. The choice of a storage material also depends on the heating system type. For example, with a floor heating system embedded in concrete, the storage system is the concrete.