# Thermal Energy Storage for Building Load Management: Application to Electrically Heated Floor
## 3 Results
### Indicators
#### 3.3.2 Economic Analysis  
Considering the economic point of view, an EHF suffers from two issues: the initial cost of an EHF is important, and it can increase the electrical energy consumption due to heat losses to the ground. In addition to studying the thermal comfort or the peak shaving of the system, an economic feasibility analysis is required both from the point of view of the customer or the supplier.  
The focus of this study is on the load management due to an EHF. Then, from an economical point of view, the customer and the supplier may both benefit from the peak shifting.  
In fact, as it was discussed previously, from the customer point of view, a time-of-use tariff is available in many countries, differentiating peak periods (higher cost) and off-peak periods (lower cost). On the other hand, from the supplier point of view, peak periods lead to an increase of the electricity production cost. Then, the shift of a part of the consumption will provide financial savings for the supplier.  
Due to the shift of the consumption from peak periods to off-peak periods, the greatest the difference between off-peak and peak electricity prices is, the more financially profitable the EHF is. To study the financial profitability of the EHF, the peak electricity price is calculated as a function of  
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Parameters** & **Unit** & **Value** \\ \hline Concrete price (per m\({}^{2}\) of surface and cm of thickness) & \(\$/\)m\({}^{2}\)/cm & 2.1 \\ XPS price (per m\({}^{2}\) of surface and cm of thickness) & \(\$/\)m\({}^{2}\)/cm & 2.5 \\ Electrically Heated Floor System & \(\$/\)m\({}^{2}\) & 65 \\ Cost of the electricity (same during off-peak and peak periods) & \(\$/\)kWh & 0.10 \\ \hline \hline \end{tabular}
\end{table}
Table 8: Considered parameters to calculate the indicators.  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Indicators** & **Unit** & **Reference Case** & \(R\) = 5 m\({}^{2}\cdot\) K/W \\ \hline ESD & kWh/m\({}^{3}\) & 5.75 & 5.75 \\ Efficiency & - & 0.80 & 0.89 \\ CDR & - & 0.48 & 0.43 \\ \hline \hline \end{tabular}
\end{table}
Table 9: Indicators for the EHF system for two different insulation thicknesses.  
the off-peak electricity price from Equations (2) to (4) to have a payback amount per year equal to 0 (Equation (10)). A payback period of 15 years is considered.  
\[c_{e_{peak}}=\frac{N_{PB}*c_{e_{off,peak}}*(\sum_{i=1}^{N_{d}}\frac{E_{effpeak_{ i}}}{E_{tot_{2}}}*E_{tot-2_{par}}-\sum_{i=1}^{N_{d}}\frac{E_{effpeak_{i}}}{E_{tot_{1}}}*E_{ tot-1_{par}})-c_{init_{1}}-c_{om,1}}{N_{PB}*(\sum_{i=1}^{N_{d}}\frac{E_{peak_{i}}}{E_{tot_{1}}}*E_{ tot-1_{par}}-\sum_{i=1}^{N_{d}}\frac{E_{peak_{i}}}{E_{tot_{2}}}*E_{tot-2_{par}})} \tag{10}\]  
In the case of the studied EHF, Equation (11) is obtained, and results are presented in Figure 9.  
\[c_{e_{peak}}=\ 1.6211\times c_{e_{off}peak}+0.1742 \tag{11}\]  
Equation (10) can be considered from the customer point of view in considering the electricity tariff, or for the supplier considering production costs. One can observe that the required peak/off-peak electricity price ratio decreases when the off-peak price increases. In fact, when the electricity price is higher, savings will be higher for the same peak/off-peak electricity ratio: a lower ratio between peak and off-peak electricity prices is required to have a profitable system.  
Because of the initial cost of the system, the difference has to be important. However, in countries with high electricity price, the required ratio may be less than 3. For example, for residential buildings, the average electricity price in Massachusetts (US) is higher than 0.20 $/kWh. Thus, proposing an off-peak electricity price of 0.15 $/kWh and a peak electricity price of 0.42 $/kWh will allow to decrease at the same time bills of customers and peak period consumption for the supplier.