10 Integration of stochasticity

In this chapter, our focus is on investigating the influence of stochasticity through the time shift. This effect of stochasticity is incorporated into the analysis to make the mode more realistic, as it considers the inherent variability in individuals’ behavior over the given period. The time shift follows a Gaussian distribution centered at 0, with a variance represented by the sigma value. In our analysis, we examine three different sigma values: 0.5, 1, and 2. The greater the variance, the more the hypothesis of heterogeneous behaviour is taken into account, while the case without stochasticity corresponds to a case with variance 0.

Analysing the impact of stochasticity, we observe that the results demonstrate similarities across all three districts. Therefore, we will focus our analysis solely on Vessy. Figure 10.1 illustrates that as the variance increases, there is a slight decrease in TOTEX. More specifically, the difference between the case without stochasticity and the case with maximum stochasticity, i.e. when the variance is 2, amounts to 1.8%. Incorporating variance leads to a decrease in peak consumption, resulting in improved self-consumption, as indicated by the SC in the KPIs from Table 10.1. This improvement explains the reduction in TOTEX with similar installed power, as shown in Table 10.2.

Table 10.1: KPI for different standard deviation of the stochasticity of Vessy
Standard deviation	SC	SS	PVC	GUs	GUd	PVP	LCoE1
sd=0	0.488	0.551	0.108	2	2	1.13	-0.114
sd=0.5	0.496	0.562	0.103	2.01	2.14	1.131	-0.115
sd=1	0.499	0.566	0.100	1.87	2.17	1.135	-0.116
sd=2	0.496	0.565	0.104	1.88	2.18	1.138	-0.115

Table 10.2: Installed capacity of the units for different standard deviation of the stochasticity of Vessy
Standard deviation	PV	Electrical Heater SH	Heat pump Air	Heat pump Geothermal	Water Tank SH	Electrical Heater DHW	Water Tank DHW
sd=0	311.15	98.79	63.51	0	9.35	4.71	2.36
sd=0.5	308.84	93.86	59.96	3.21	8.73	4.52	2.36
sd=1	309.65	93.54	59.99	3.24	8.04	4.59	2.36
sd=2	310.61	89.32	64.11	0	7.82	4.40	2.36

Figure 10.1: TOTEX comparison between the different standard deviation of the stochasticity of Vessy

Figure 10.2: GWP comparison between the different standard deviation of the stochasticity of Vessy

Introducing stochasticity into the system yields slight improvements in performance without causing significant differences in the units. The results obtained show that the introduction of stochasticity makes the model more realistic from a conceptual point of view without producing major differences in the results. For the subsequent analysis, the time shift follows a centered and standardized normal distribution. In addition, some of the plots generated that are not included in this section of the results are included in the appendix.