## 3 Results
### Dynamic Analysis of the System  
The results of the dynamic analysis for the heating period (October to April) are included in this section. It is interesting to say that these results are given for a representative design case A\({}_{\text{col}}\) = 30 m\({}^{2}\) and V = 3 m\({}^{3}\) in order to show how the system behaves during the different heating needs. The first step in this investigation is the presentation of the weather data of the examined city. Figure 4 shows the variation in the ambient temperature during the heating period, as well as the cumulative solar irradiation on the tilted surface per area for the heating period. It is clear that the minimum ambient temperature is about 0 \({}^{\circ}\)C while the solar potential is 661 kWh/m\({}^{2}\). These results show that in the examined location, (i) there are no extremely low ambient temperature levels, (ii) there are significant heating needs and (iii) there is adequate solar potential for solar thermal technology utilization. Figure 3: Depiction for the accuracy of the approximation formula for the heat pump COP. Figure 5 depicts the heating demand expressed in terms of power (kW) and in terms of cumulative energy (kWh). The maximum heating load is calculated close to 6 kW and the seasonal heating demand is at 6785 kWh. Moreover, it is useful to state that the coldest period in Greece is the months of December, January and February, while April presents restricted heating loads. The next stage is the presentation of the system performance results during the winter period. Figure 6 illustrates the variation in the mean tank temperature during the heating season. The minimum obtained temperature is around 10 \({}^{\circ}\)C due to the activation of the  
Figure 4: Climate conditions of Athens in the winter period (1 October to 30 April). Figure 5: Heating load and cumulative heating demand for the examined building (1 October to 30 April). auxiliary system when lower values are obtained. Moreover, the maximum temperature in the tank is 95 \({}^{\circ}\)C because there is a proper control system to stop the collector operation when this limit is reached. The low temperatures in the tank are found in the period of high heating loads, while in the period of low heating loads the tank temperature increases. Moreover, it is significant to add that the low heating loads are usually associated with increased solar potential, something that makes it possible on some days to have a very high solar potential and a very small heating demand. These facts justify the increase in the tank temperature up to 95 \({}^{\circ}\)C. These relatively high values are detected in the months with a relatively small heating demand (November, March and April). More specifically, on days of low heating loads, the tank temperature increases because there is higher useful heat production from the solar system than the heat input demand in the heat pump. So, it is possible to transfer stored solar energy to the next days and to assist them in the case of increased heating needs on them. Figure 7 depicts the electricity consumption during the heating period which is consumed by the compressor and by the auxiliary electrical heater. It is useful to note that the auxiliary electrical resistance is activated when the temperature of the stored water is very low, and its activation aims to keep it at 10-12 \({}^{\circ}\)C for a safe operation. Practically, the avoidance of the extremely low water temperature levels makes the efficient operation of the compressor possible and so the COP is kept at acceptable levels in the system's overall daily cycle. It is obvious that the auxiliary heater is activated only in some restricted cases during the period, and more specifically, it operates for 187 h during the heating period. On the other hand, the heat pump operates for 3008 h; thus, the auxiliary system is activated only for 6.2% of the heating time. This fact indicates that the auxiliary system is the minor energy unit in the present system.