3.3 Evaluation of the configurations
3.3.1 Parametric analysis
Having established the need for a storage system to overcome the different distribu-tion in the day of the producdistribu-tion and consumpdistribu-tion of energy, the relative influence of the sizes of the photovoltaic installation and the battery on the configuration’s performances can be addressed. For this purpose, the tool has been used to perform a ‘parametric’ analysis both on of them. Hence, keeping constant the characteristics of the aggregate (and the consumption profiles previously simulated), a number of configurations has been simulated, which are identified by the coupling between:
A photovoltaic system’s size, which can either be 15, 20, 25, 30 or 35 kWp;
A battery’s size, which can either be 0, 10, 20, 30 or 40 kWh.
The objective of the optimisation has been set initially to the minimisation of the interactions with the grid. The results of the parametric analysis are shown in Figure 3.14, where the configurations are placed in a space identified by their yearly
3It should be noticed that ‘consumption’, which has always been used as a synonyms of ‘load’
so far, is here intended as the energy that is used by the households, either to fulfill the power demand from the electric loads or to store energy in the battery. However, in the following the two terms are used again as synonyms, since the energy that flows in the battery is addressed as
‘battery charge’.
self-consumption and self-sufficiency indices. A chart of such type is useful when varying simultaneously the sizes of both the photovoltaic system and the battery, since it allows to easily assess how the configuration’s performances are affected by each one or both of them. Ideally, the aim is to have a configuration where all the energy that is self-generated is also consumed locally, i.e. shared, and where the shared energy is enough to fulfill the whole energy demand. In other words, this means having the largest self-consumption and self-sufficiency indices as possible.
Therefore, configurations that are located in the top-right region of the chart are to be considered as better-performing (from an energetic point of view). Consequently, a variation in the size of the battery or of the photovoltaic system is to be considered more valuable when it shifts the configuration towards this region.
Figure 3.14: Influence of the photovoltaic system’s and battery’s sizes on the yearly performance indicators in the minimisation of the exchanges with the grid. [Self-processing]
Gianmarco Lorenti Chapter 3. Simulation results and discussion
As previously mentioned, increasing the size of the photovoltaic system allows to share a larger quantity of energy, thus increasing the configuration’s self-sufficiency.
Anyway, if the battery’s size is not simultaneously increased (continuous lines in the figure), the shared energy increases in a slower way than the production, since an always smaller portion of the latter can be shared hence the self-consumption in-dex decreases. Moreover, the self-sufficiency inin-dex does not increase constantly but tends to be saturated. This holds for all configurations, regardless of the presence of a storage system. Anyway, when the battery’s size is larger, the increase in the self-sufficiency index is faster and at the same time the decrease in the self-consumption index is slower, thus confirming the important role played by the battery. As to the latter, instead, increasing its size while keeping constant the photovoltaic sys-tem’s (dashed lines in Figure 3.14), the self-sufficiency and self-consumption indices increase in the same proportion (linear trend). This is true until the maximum self-consumption is reached: moving along the line relating to the photovoltaic system’s size of 15 kWp, it can be noticed that, from that point on, a further increase in the battery’s size does not bring any increase in the self-sufficiency, since all the production is shared already.
Interestingly, when the same configurations have been simulated using the max-imisation of the shared energy as the optmax-imisation objective, the same results have been obtained, not only in relative terms but also as absolute values. This means that the minimisation of the interactions with the grid also leads to the maximi-sation of the shared energy, under the definition of the latter used in the routine.
The yearly performances of some of these configurations, simulated using the max-imisation of the shared energy as the objective of the optmax-imisation, are shown in Figure 3.15 and 3.16. In the latter, either the size of photovoltaic system is varied, while keeping constant the battery’s, or vice versa.
(a)
(b)
Figure 3.15: Variation of the self-consumption and self-sufficiency indices and yearly shared energy with the photovoltaic system’s size, for a battery’s size of: (a) 10 kW h and (b) 30 kW h. [Self-processing]
Gianmarco Lorenti Chapter 3. Simulation results and discussion
(a)
(b)
Figure 3.16: Variation of the self-consumption and self-sufficiency indices and yearly shared energy with the battery’s size, for a photovoltaic system’s size of: (a) 20 kWp, (b) 30 kWp. [Self-processing]
If the single configurations’ self-consumption and self-sufficiency indices were transposed into a chart such as the one previously shown, it could be checked that the two optimisation objectives lead to the same results. Moreover, it can be noticed that, while all the previous considerations on the self-consumption and self-sufficiency indices hold, the energy that is yearly shared increases anyway (until eventually being saturated), whether the photovoltaic system’s size is increased alone or together with the battery’s size. However, this should not shade the fact that increasing the size of the photovoltaic system means a higher capital cost. Hence the full exploitation of the production from the installation should be pursued, which is clearly not the case when the self-consumption index is small.
For sake of completeness, the yearly performances (shared energy and indices of self-sufficiency/self-consumption) of the various configurations simulated are shown in Table 3.1. From the point of view of the absolute values, it is interesting to notice that even when the yearly production from the photovoltaic installation is large enough to fulfill the whole consumption of the aggregate, i.e. for a size of 35 kWp, the maximum self-sufficiency of the configuration is around 67.5 %. This means that in order to exploit the whole production from the renewable installation, thus fulfilling the whole aggregate’s consumption by virtually sharing the former, a larger battery is needed. As a matter of fact, keeping the same battery’s size but reducing the photovoltaic system’s to 25 kWp would only slightly decrease the shared energy, therefore the self-sufficiency index, which decreases to around 66.5 %.
On the other hand the self-consumption index would increase from 67 % to around 77 %, since the total production is much smaller in proportion, hence the excess that is fed into the grid decreases. As to the configurations with a photovoltaic system of 15 kWp, it is interesting to notice that when the maximum self-consumption is reached (saturation of the shared energy despite increasing the battery’s size), the
Gianmarco Lorenti Chapter 3. Simulation results and discussion
self-consumption index is actually around 98 %. This is to be ascribed to the charge, discharge and self-discharge efficiencies of the battery, which cause the energy that can be discharged from it to be slightly smaller than the energy that is charged. For this reason, the energy that is injected into the grid when discharging the battery is smaller than the excess production that is sent to the battery.
Table 3.1: Comparison between the yearly performances of various configurations (aggre-gate of 20 households). [Self-processing]
Configuration Yearly energy (kWh/year) Indices (%)
PV size Battery size
Production Consumption Shared SSI SCI
(kWp) (kWh)
15
0
20796.8 48092.6
17359 36.09 83.47
10 19443.8 40.43 93.49
20 20505.7 42.64 98.6
30 20499.5 42.63 98.57
40 20493.3 42.61 98.54
20
0
27729.1 48092.6
19135.2 39.79 69.01
10 22010.1 45.77 79.38
20 24193.1 50.31 87.25
30 25893.6 53.84 93.38
40 27000.7 56.14 97.37
25
0
34661.4 48092.6
20015.7 41.62 57.75
10 22924.3 47.67 66.14
20 25823.6 53.7 74.5
30 28259.7 58.76 81.53
40 30136.1 62.66 86.94
30
0
41593.6 48092.6
20567.1 42.77 49.45
10 23476.3 48.81 56.44
20 26384.6 54.86 63.43
30 29291.1 60.91 70.42
40 31936.6 66.41 76.78
35
0
48525.9 48092.6
20902.6 43.46 43.08
10 23812 49.51 49.07
20 26720.6 55.56 55.06
30 29627.5 61.61 61.05
40 32532.7 67.65 67.04