*3.2. Economic Evaluations*

Let us now consider a case study of how to interpret those results from an economic perspective. Table 2 lists the parameters used for our economic analysis:



**Table 2.** Peak Shaving—Parameters for Economic Feasibility.

In order for the system to be profitable, the total peak shaving compensation has to be higher than the total cost (incl. battery and losses) over the payback period; this condition is expressed in Equation (14). Next, as shown in Equation (15), the peak reduction-to-capacity ratio can be expressed in function of all economic parameters. Finally, by replacing with the values of Table 2, it can be concluded that the ratio needs to be higher than 0.43–0.67 (Equation (16)).

> Rev·8760·ROI·<sup>Δ</sup>Ppeak > Cap·(Costbat + Ratecons incr·Pelect·8760·ROI) (14)

$$\frac{\Delta\text{P}\_{\text{peak}}}{\text{Cap}} > \frac{\text{Cost}\_{\text{bat}} + \text{Rate}\_{\text{cons incr}} \cdot \text{P}\_{\text{elect}} \cdot 8760 \cdot \text{ROI}}{\text{Rev} \cdot 8760 \cdot \text{ROI}} \tag{15}$$

$$\frac{\Delta P\_{\text{peak}}}{\text{Cap}} > 0.43 - 0.67 \tag{16}$$

where ΔPpeak is the peak reduction, ROI is the return of investment (payback period), Rev is the peak compensation (revenue), Cap is the battery capacity, Costbat is the battery capex, Ratecons incr is the rate of consumption increase and Pelect is the electricity price.

Over the 10-year period, the total capacity loss of the battery will be 20%. Consequently, to ensure that the peak threshold will always be met, we have to oversize the battery capacity. Finally, the results of the economic feasibility study are illustrated in Figure 8. Figure 8 can be made easily from Figure 6a (see Section 3.1) by adding a 20% margin to the minimum battery capacity requirement. The color at each point [x,y] represents the total number of users whose peak reduction-to-capacity exceeds the y value (similarly to the quantile plots of Figure 6a). The yellow and green dashed lines represent the profitability thresholds 0.43 and 0.67, respectively (see Equation (16)). As can be seen, there are several positive use cases; of course the number of positive cases depends on the battery size. To give an example, when the ratio capacity/mean power equals 2, there are 15–20 users exceeding the value 0.43 (lower profitability threshold), whereas when the ratio capacity/mean power becomes 10, there are only 0–5 users exceeding that value (0.43). With that being said, we do now have an estimation of the profitability margins for the Belgian use cases.

**Figure 8.** Peak shaving—results of economic feasibility study. At each point [x, y], the color represents the total number of users whose peak reduction-to-capacity exceeds the y value. The yellow and green dashed lines represent the profitability thresholds 0.43 and 0.67, respectively (see Equation (16)).

Needless to say that our estimation is strongly influenced by the considered parameter values (Table 2). Even without changing neither the electricity price nor the peak shaving compensation, simply by varying the payback period and/or the battery capex we would ge<sup>t</sup> different results. Here, it is worth noting that the battery capex at 500 €/kWh is very realistic for the time being and it is expected to decline further in the coming years [34]. (To define the battery capex we consulted manufacturers

and received offers.) As a general conclusion, we can note that given the current electricity prices (fixed, no ToU dependency) and capital expenditures, particularly for Belgium, peak shaving through battery storage seems to be interesting from an economic perspective for several low-voltage enterprises.

## **4. Discussion and Conclusions**

To summarize briefly what has been done, a model was developed in Matlab/Simulink for peak shaving. The dichotomy method was proposed as an optimization algorithm to find the minimum threshold above which we are 100% certain that the peak will never be exceeded. The model was tested for 40 low-voltage users with peak demand charge derived from the Belgian grid operator. We introduced five performance metrics to evaluate the simulation results. Furthermore, we gave an example how to interpret the results from economic perspective and explored the profitability of the application in Belgium. Below is a summary of the most important conclusions resulting from our analysis:


One of our main conclusions is that the battery utilization (SoC active time and number of cycles) is very low for almost all users. Consequently, there seems to be enough potential to let our battery provide additional services during those inactive periods in order to accelerate the payback period of our investment. Which services can be combined and how efficiently this can be done is certainly a topic to be addressed by future research works.

As an initial step, we sugges<sup>t</sup> studying the predictability of the load profile. In our study, we consider the battery to be available for peak shaving 100% of the time; therefore, there is no need to know in advance when the peak occurs. However, in hybrid applications, time must be allocated appropriately and as a result load prediction plays an important role. To better explain this argument, let us consider two different load profiles derived from our dataset, user A and B (Figures 9 and 10 respectively). Although the battery utilization is in both cases very low (peak occurs rarely), user A is by far more predictable than the user B. For user A, the peak occurrence is dependent on the day, the time of use and the temperature, whereas for user B, there seem to be no clear explanatory variables. Consequently, user B cannot know how to allocate his inactive time to other services; hence, the battery remains underutilized solely reserved for peak shaving. Closing this paragraph, we note that, so far, most research works on battery storage have addressed only single applications. In our view, the concept of hybridization will gain more attention in the coming years as users gradually acquire more incentives to interact with the grid.

**Figure 9.** Thermal image—predictable load profile.

**Figure 10.** Thermal image—unpredictable load profile.

**Supplementary Materials:** The following are available online at http://www.mdpi.com/1996-1073/13/5/1183/s1, Dataset S1: "40 LV consumers with peak demand pricing in Belgium, From 1-1-2014 to 31-12-2016.zip".

**Author Contributions:** Conceptualization, V.P. and J.D.; methodology, V.P. and J.D.; software, V.P.; validation, V.P.; formal analysis, V.P.; investigation, V.P. and J.D.; resources, J.D.; data curation, C.D.; writing—original draft preparation, V.P.; writing—review and editing, J.D., J.K. and C.D.; visualization, V.P.; supervision, J.D., J.K. and C.D.; project administration, V.P. and J.D.; funding acquisition, J.D. All authors have read and agreed to the published version of the manuscript.

**Funding:** The research received no external funding.

**Acknowledgments:** We would like to thank the Flemish distribution system operator for providing the dataset for experimentation. Normally, such large datasets are very difficult to find within the research community.

**Conflicts of Interest:** The authors declare no conflict of interest.
