**4. Simulation results**

*Green Energy Advances*

**Figure 8.**

energy consumptions:

*Example of load and SOC profiles in case of basic BMS.*

In the other case, if the energy stored in the batteries is slightly lower than loads, the charge is used both for baseload supply and peak shaving (BMS Strategy #3). Nevertheless, the exact time schedule of loads is not predictable and it is not possible to know when the load peaks will occur. In the worst case, storage will be discharged soon in the evening, while the peak will be in the next early morning, when batteries are already empty. For this reason, the SBMS limits the discharge of batteries during time with the definition of different levels of minimum *SOC*min,x for an user-defined number of time slots *x*, in which the *TDT* is divided. According to the procedure proposed in Section 3.2, in case of *TDT* = 12 h, the number of time slots *x* = 2, otherwise with *TDT* = 36 h, the time slots are 5 (*x* = 5). The *SOC*min,x limits are defined in order to distribute the stored energy proportionally to the provisional energy consumption. Thus, *SOC*min,x limits are calculated starting from the *SOC* of the storage, measured in real time by the BMS, and the provisional

where *E*load, slot x is the provisional energy that will be required by loads in the time slot *x*. For example, let us suppose that the TDT is 12 h and the overall required load will be 10 kWh. In particular, during the evening (from 6:00 p.m. to midnight), the required load will be 4 kWh, and during the next night (from midnight to 6:00 a.m.), the load will be 6 kWh. The stored energy will be discharged as follows: 40% during the evening and 60% during the night. In this example, the

**Figure 8** shows an example of load and *SOC* profiles in case of a basic battery management. In this case, the storage is charged when PV production is higher than loads and batteries are empty; on the contrary, storage is discharged if PV production is lower than loads [23]. The only limitation in charge/discharge is performed to avoid fast degradation of batteries, by limiting the *SOC* in a safety range *SOC*min,safety < SOC < *SOC*max,safety. For sake of simplicity, it is considered a rainy day and the production from the PV generator is negligible. In case of lithium batteries (**Figure 8**), the minimum level *SOC*min,safety generally corresponds to *SOC*safety ≈ 20%, while in case of lead-acid batteries, it can reach 50% [41, 42]. In the example of **Figure 8**, the storage supplies the loads until 10:50 a.m., when the *SOC*min,safety is reached. After that, only the grid supplies the load and the highest

storage is considered initially full and with a minimum *SOC*min,safety = 0.2.

*Eload*.*TDT*) (8)

*SOCmin*,*slot <sup>x</sup>* <sup>=</sup> *SOC* <sup>∙</sup> (<sup>1</sup> <sup>−</sup> *Eload*,*slot <sup>x</sup>* \_\_\_\_\_\_\_\_\_\_\_

**84**

absorption peak is not limited ≈2.9 kW.

#### **4.1 Inputs parameters and constraints of the simulations**

Simulations of the PV-storage system are performed for the entire month of December with a 1-min time step for both basic and proposed BMS to compare their performance. During winter, the PV production is low, batteries are often empty, and the development of an efficient BMS is necessary to reduce the absorption peaks from the grid. On the contrary, in summer, PV generation generally charges storage and directly supplies part of the loads.

The optimal management of the storage is investigated in case of different sizes of the PV system *P*PV,r and different capacities of the battery *C*bat. Regarding *P*PV,r, it ranges between 2 and 6 kWp with a step of 1 kW, while the storage capacity *C*bat is in the range 1–5 kWh (step of 1 kWh). The management parameters are the power value *P*load,max beyond which the peak shaving strategy works and the threshold *R*thres. The power limitation *P*load,max ranges between 0.5 and 2 kW with a step of 0.5 kW, while the user-defined threshold *R*thres varies between 50 and 80% (step of 10%). Regarding the loads, the measured consumption profile of a domestic user (a family composed of two persons) located in Northern Italy (45.05° Nord, 7° 40' Est) is used. The annual consumption of

the domestic user analyzed in the case study is ≈2800 kWh/year and its loads correspond to typical home appliances (e.g., hairdryer, oven, personal computer, lighting, and electric water heater).

### **4.2 Case study**

The results of the simulation show that the proposed BMS decreases the peaks of absorption from the grid with respect to a traditional management. The results are interesting especially in case of a small storage, while in case of higher storage capacity, there are negligible differences between the two managements. **Figure 10** shows case #1: it corresponds to the analysis of 2 days of simulation for a PV system with *P*PV,r = 4 kW and a storage system with *C*bat = 2 kWh. In the graphs, in case of battery discharge, the sign of the power supplied by the storage to the loads is negative. The 2 days are characterized by cloudy and rainy conditions, and the PV production is low. The proposed BMS calculates the provisional energy balance and a huge lack in storage is predicted; thus, the peak shaving method is used (BMS Strategy #2). Before 6:00 p.m., all the loads are supplied by PV and storage; then, peak shaving is applied and only the quota exceeding *P*load,max = 2 kW is satisfied by batteries. The saved energy is then preserved and used to shave loads during the second day, with the result of keeping the absorption from the grid always ≤2 kW.

On the contrary, if a standard BMS is used (**Figure 11**), all the stored energy is consumed before the end of the evening of the first day; furthermore, there is no energy from storage to supply the load peaks during the second day. The result is a maximum absorption peak of ≈4.2 kW: during these days, the proposed SBMS reduces the absorption peak of ≈50%.

**Table 2** shows the energy balance of the case #1 related to **Figures 10** and **11**. With the proposed SBMS, the maximum power absorbed from the grid is half, while the deviations in terms of self-sufficiency and injected energy into the grid are negligible. Nevertheless, there is an increase in grid absorption: to guarantee power for peak shaving, a residual energy is kept in the storage, and at 6:00 p.m. of the second day *SOC*≈0.7.

A second simulation is shown in **Figure 12**. The case #2 is characterized by two different days with respect to case #1: a negligible PV production occurs in both days, while the sizes of PV and storage systems and loads are the same of case #1. The provisional energy balance predicts that the energy in the storage will supply great part of the loads, but it will be not sufficient to supply them totally. The

**87**

**Table 2.**

*Energy results for case #1.*

*A Smart Battery Management System for Photovoltaic Plants in Households Based on Raw…*

provisional self-sufficiency parameter is *R*suff > *R*thres (with *R*thres *=* 50%); thus, the converter selects the BMS Strategy #3. The most interesting part corresponds to the time window 6:00 a.m.–6:00 p.m. of the second day. Batteries start discharging at 6:00 a.m. and when peaks occur (10:00–12:00 a.m.), only the quota exceeding *P*load,max = 2 kW is satisfied by batteries. In the same way, the other absorption peak occurring at 9:00 p.m. is shaved, thanks to the preserved energy in the storage. The

On the contrary, in the same conditions, a traditional BMS would discharge the battery before 10:00 a.m. and the absorption peak would be 2.8 kW (higher than

Finally, in **Table 3**, the above-described combination #A and other three combinations of PV and storage sizes, which permit to obtain significant improvements, are presented. The power and energy results of the proposed SBMS are compared to the standard BMS. In all the other cases, the improvement in terms of maximum absorption from the grid is confirmed, ranging from ~9 to ~10%. Regarding the maximum injection into the grid and the energy quantities, their deviations are negligible. The combination #A shows much better results, confirming that the

Load (kWh) 11.45 11.45 Self-consumption (kWh) 3.2 3.2 Grid absorption (kWh) 5.5 4.58 Grid injection (kWh) 0.52 0.52 Self-sufficiency/load (%) 28 28 Self-consumption/PV production (%) 43 43 Grid injection/load (%) 4.5 4.5 *P*load,max (kW) 2 4.22 Injection peak (kW) −0.81 −0.81

**Proposed BMS Standard BMS**

*DOI: http://dx.doi.org/10.5772/intechopen.80562*

maximum absorption peak is 2.4 kW.

*Power profiles for case #1 with standard BMS.*

the proposed SBMS of ≈14%).

**Figure 11.**

**Figure 10.** *Power profiles for case #1 with the proposed SBMS.*

*A Smart Battery Management System for Photovoltaic Plants in Households Based on Raw… DOI: http://dx.doi.org/10.5772/intechopen.80562*

**Figure 11.** *Power profiles for case #1 with standard BMS.*

*Green Energy Advances*

**4.2 Case study**

puter, lighting, and electric water heater).

reduces the absorption peak of ≈50%.

*Power profiles for case #1 with the proposed SBMS.*

the second day *SOC*≈0.7.

the domestic user analyzed in the case study is ≈2800 kWh/year and its loads correspond to typical home appliances (e.g., hairdryer, oven, personal com-

The results of the simulation show that the proposed BMS decreases the peaks of absorption from the grid with respect to a traditional management. The results are interesting especially in case of a small storage, while in case of higher storage capacity, there are negligible differences between the two managements. **Figure 10** shows case #1: it corresponds to the analysis of 2 days of simulation for a PV system with *P*PV,r = 4 kW and a storage system with *C*bat = 2 kWh. In the graphs, in case of battery discharge, the sign of the power supplied by the storage to the loads is negative. The 2 days are characterized by cloudy and rainy conditions, and the PV production is low. The proposed BMS calculates the provisional energy balance and a huge lack in storage is predicted; thus, the peak shaving method is used (BMS Strategy #2). Before 6:00 p.m., all the loads are supplied by PV and storage; then, peak shaving is applied and only the quota exceeding *P*load,max = 2 kW is satisfied by batteries. The saved energy is then preserved and used to shave loads during the second day, with

On the contrary, if a standard BMS is used (**Figure 11**), all the stored energy is consumed before the end of the evening of the first day; furthermore, there is no energy from storage to supply the load peaks during the second day. The result is a maximum absorption peak of ≈4.2 kW: during these days, the proposed SBMS

**Table 2** shows the energy balance of the case #1 related to **Figures 10** and **11**. With the proposed SBMS, the maximum power absorbed from the grid is half, while the deviations in terms of self-sufficiency and injected energy into the grid are negligible. Nevertheless, there is an increase in grid absorption: to guarantee power for peak shaving, a residual energy is kept in the storage, and at 6:00 p.m. of

A second simulation is shown in **Figure 12**. The case #2 is characterized by two different days with respect to case #1: a negligible PV production occurs in both days, while the sizes of PV and storage systems and loads are the same of case #1. The provisional energy balance predicts that the energy in the storage will supply great part of the loads, but it will be not sufficient to supply them totally. The

the result of keeping the absorption from the grid always ≤2 kW.

**86**

**Figure 10.**

provisional self-sufficiency parameter is *R*suff > *R*thres (with *R*thres *=* 50%); thus, the converter selects the BMS Strategy #3. The most interesting part corresponds to the time window 6:00 a.m.–6:00 p.m. of the second day. Batteries start discharging at 6:00 a.m. and when peaks occur (10:00–12:00 a.m.), only the quota exceeding *P*load,max = 2 kW is satisfied by batteries. In the same way, the other absorption peak occurring at 9:00 p.m. is shaved, thanks to the preserved energy in the storage. The maximum absorption peak is 2.4 kW.

On the contrary, in the same conditions, a traditional BMS would discharge the battery before 10:00 a.m. and the absorption peak would be 2.8 kW (higher than the proposed SBMS of ≈14%).

Finally, in **Table 3**, the above-described combination #A and other three combinations of PV and storage sizes, which permit to obtain significant improvements, are presented. The power and energy results of the proposed SBMS are compared to the standard BMS. In all the other cases, the improvement in terms of maximum absorption from the grid is confirmed, ranging from ~9 to ~10%. Regarding the maximum injection into the grid and the energy quantities, their deviations are negligible. The combination #A shows much better results, confirming that the

