# Household Energy Management
## 4 Simulation Studies of the EEM Algorithm for a Single Household
### Analysis of Test Results  
To illustrate the effects of the developed algorithms in a single household, the following analysis of energy consumption in a household were carried out using:  
* the ToU price program (without EEM),
* the ToU price program and the EEM algorithm, without and with RES. The results of these analyses are presented in Table 3, where each analyzed case contains the value of energy consumed and its costs in each time zone and their sums per day. The comparison of the analysis of the obtained results of the tests for the first group (Table 3--without RES) shows that the use of the EEM algorithm resulted in a reduction in the cost of daily energy consumption by Polish monetary unit PLN 0.76 (\(-\)5.6%), despite an increase in energy consumption by 0.8 kWh (+3.2%). The shifting of switching on of the washing machine and dryer from \(t\_z\) = 2 (07:00-10:00) to \(t\_z\) = 1 (21:00-24:00) had a significant impact on reducing energy costs. The increase in energy consumption was caused by the extended operation time of the boiler and air conditioner in their next work cycle, occurring after their earlier switching off by EEM1. Extending the working time of these appliances resulted from ensuring the required water and air temperature. On the other hand, activation of EEM2 ensured the implementation of power reduction with excess in the desired period of time. Turning off the boiler for a period of 1 h resulted in the extension of its work time in \(t\_z\) = 3 and shortening in \(t\_z\) = 1. During this period, the EEM2 algorithm also prevented turning on the air conditioner. However, the comparison of the analysis of the obtained results of the tests for the second group (Table 3--with RES) shows that the use of the EEM algorithm resulted in a simultaneous reduction in daily energy consumption by 2 kWh (11.2%) and its costs by PLN 1.03 (13.6%). It was influenced by the amount of power generated by RES, part of \begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline  & & \multicolumn{6}{c}{**ToU Pricing Program**} \\ \hline  & & \multicolumn{6}{c}{without RES} \\ \hline Time zones (\(t\_z\)) & 1 & 2 & 3 & 2 & 3 & 1 & Sum \\ \hline \multirow{3}{*}{without EEM} & \(E_{1}\) [kWh] & 5.9 & 5.7 & 2.9 & 3.9 & 4.1 & 2.1 & 24.6 \\  & \(C_{1}\) [PLN] & 1.59 & 2.91 & 2.64 & 1.99 & 3.73 & 0.57 & 13.43 \\ \hline \multirow{3}{*}{with EEM} & \(E_{2}\) [kWh] & 5.9 & 3.4 & 1.9 & 5.4 & 3.9 & 4.9 & 25.4 \\  & \(C_{2}\) [PLN] & 1.59 & 1.73 & 1.73 & 2.75 & 3.55 & 1.32 & 12.67 \\ \hline \multicolumn{6}{c}{with RES} \\ \hline \multirow{3}{*}{without EEM} & \(E_{3}\) [kWh] & 5.9 & 4.6 & \(-\)2.7 & 3.8 & 4.1 & 2.1 & 17.8 \\  & \(C_{3}\) [PLN] & 1.59 & 2.32 & \(-\)2.50 & 1.93 & 3.69 & 0.56 & 7.59 \\ \hline \multirow{3}{*}{with EEM} & \(E_{4}\) [kWh] & 5.9 & 2.8 & \(-\)1.1 & 3.8 & 2.3 & 2.1 & 15.8 \\  & \(C_{4}\) [PLN] & 1.59 & 1.43 & \(-\)1.01 & 1.92 & 2.07 & 0.56 & 6.56 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Energy consumption (\(E\)) and its costs (C) for 1 day in particular \(t\_z\) from the ToU pricing program without and with the EEM algorithm. which was transferred in the zone \(t\_z=3\) to NPS. This power did not exceed the value of 5 kW reported by the DSO; therefore, there was no reaction of the EEM algorithm to the limitation of this power by the inverter. When calculating the costs of energy consumption for the zone \(t\_z=3\), it was assumed that the selling price of the surplus energy from RES is equal to its purchase in this zone. The use of the EEM algorithm also resulted in lower delays in the use of the washing machine, dryer and dishwasher, which significantly increased the comfort of their use by household residents. The evaluation studies carried out clearly show that the use of RES in the household has a significant impact on the reduction of daily energy consumption and its costs. This is indicated by the results of simulation tests (Table 3) for both groups (without and with RES).