**2.4 Modeling of electrochemical storage**

*Green Energy Advances*

with

equation [26]:

is 800 W/m<sup>2</sup>

calculated by the formula:

sources of losses are considered constant:

*P*AC = *P*PV,r ∙ \_\_\_\_ *<sup>G</sup>*

*<sup>T</sup>*<sup>c</sup> <sup>=</sup> *<sup>T</sup>*<sup>a</sup> <sup>∙</sup> *NOCT* <sup>−</sup> <sup>20</sup>°

The thermal losses and consequently the DC input power change, while the other

ηmix = *η*dirt ∙ *η*refl ∙ *η*mis ∙ *η*MPPT ∙ *η*cabl ∙ *η*shad (2)

Losses due to temperature ηtherm are due to the reduction in the voltage of the PV generation with increasing temperature. The power loss with respect to the standard test condition is linearly dependent on temperature with proportionality factor about *γth* ≈ 0.3 ÷ 0.5%/°C depending on the semiconductor of the photovoltaic generator [24]. According to [25], a value of 0.5%/°C, typical for c-Si PV modules, which is the most diffused PV technology for terrestrial applications, is used. In order to estimate temperature losses, at every time step, the temperature of the PV cells *Tc* is calculated starting from measured air temperature *Ta* by the following

> \_\_\_\_\_\_\_\_\_\_*C GNOCT*

; the overtemperature losses *η*therm (with respect to TSTC = 25°C) are

*NOCT* is the normal operating cell temperature, generally provided by the manufacturer of the PV modules; in this work, it corresponds to a typical value *NOCT* = 45°C. *G*NOCT is the solar irradiance occurring at *NOCT* condition and it

ηtherm = 1 − γ*th* ∙ (*Tc* − TSTC) (4)

Losses due to dirt *η*dirt provide an average 2% of reduction in energy production for the deposit of dust and other materials on the glass of the modules. Thus, a typical value *η*dirt = 0.98 is used in the present work [27, 28]. Note that in case of horizontal modules, the cleaning made by rain is reduced, and in case of emission of pollution close to the plants from special industrial processes [29], losses can be more than 7%. Losses due to reflection from the glass on the front of the PV module are inevitable losses due to a not ideal transparency of the glass; according to [30], they can be considered equal to ≈3% (*η*refl = 0.97). Mismatch losses are due to nonuniformity in *I-V* characteristics of modules connected in series or in parallel. Thus, the conversion unit imposes to the whole PV generator a working point not perfectly corresponding to the optimum. According to [31], a typical value of *η*mis = 0.97 is used. Joule losses take into account dissipation of electrical energy into heat by Joule effect in the cables. During design phase, cables should be sized in order to keep Joule losses within 3% in nominal conditions [30]. Since the PV system operates at nominal conditions (maximum power) for a short period during the year, and in other conditions (partial load) losses are lower, Joule losses are estimated equal to an average value of 1% (*η*cab l = 0.99) [30]. Losses for shadings are due to external causes, as a wrong design; thus, in the performed simulations, these losses are neglected (*ηshad* = 1). Regarding the accuracy of the maximum power point tracking (MPPT) system, it causes losses, because the optimum value is generally not perfectly tracked, especially at low power: on average, this loss can be estimated ≈1%. (*ηMPPT* = 0.99) [32]. Finally, the DC/AC conversion introduces losses, which

∙ *η*mix ∙ *η*therm ∙ *η*DC/AC (1)

∙ *G* (3)

*GSTC*

**78**

A correct model of the storage is fundamental to evaluate energy flows. Many electric models are present in literature and they permit to simulate operation of batteries with different pros and cons [34–37]. The simplest model describes a battery by an equivalent voltage source in series with an internal resistance. The equivalent voltage can easily be determined by measuring the open circuit voltage of the battery, while the measurement of the internal resistance requires a further test performed during battery charge. Obviously, this model has a limited use, because the parameters are constant: the accumulator results in having an infinite capacity and there is no way to determine the *SOC*. An upgrade with respect to the basic model is obtained using an equivalent resistive-capacitive model [36]. The values of resistances and capacitances can be determined through impulsive test of the battery. The advantage of this model is that it permits to evaluate the charge and discharge transients with variable loads in time. However, the SOC dependence on the voltage, which has to be determined, requires careful preliminary measurements on the battery. Another possible model consists of the impedance model, where a voltage source is in series with a resistance and an inductance. An additional series impedance is used to represent the electrochemical characteristics of the battery. Nevertheless, the definition of this impedance is complicated; in fact, it can be obtained starting from an electrochemical impedance spectroscopy to obtain an equivalent impedance in the frequency domain. In addition, the impedance has to be characterized varying the state of charge and the temperature [35].

The most sophisticated models [38, 39] are developed to calculate also the state of health (*SOH*), which is a parameter useful to evaluate how the charge-discharge profiles affect the storage life and when the batteries have to be replaced. In fact, PV production is intermittent; thus, PV generators cannot guarantee the optimal charge-discharge cycles to have the longest possible life of storage and the highest efficiency. For example, the *real-time model* described in [39] is a blend of the previous battery models whose particular combination of components and dependencies eases the estimation of the equivalent parameters. In conclusion, this model permits to calculate the *SOC*, the *SOH*, and then the residual life. This information permits the evaluation of the economic investment of electrochemical storage system [40], taking in consideration the battery management. Nevertheless, the models that permit to estimate the *SOH* require a continuous measurement of battery parameters (i.e., voltage, current, and temperature of the batteries) [37]. For this reason, the calculation of the *SOH* cannot be performed with only simulations, but a real system with continuous measurements is required.

The *energy model* is used in the simulations presented in this chapter, because it permits to simulate the *SOC* with a good approximation (a few percent points) without measurements and with a low computation effort (only the formulas (5) and (6) are used). The *energy model* permits to estimate the state of charge of batteries; i.e., how much energy is stored or can be stored in a battery with rated energy capacity *Cbat*, by the comparison with the limits imposed to preserve life of batteries. The calculation of the *SOC*(*t*) at the instant *t* is a function of the state of charge *SOC*(*t* − 1) at the previous time step, of the power exchanged *P*bat during the time step *Δt* (in this chapter, *Δt* = 1 min) and of the charge efficiency *ηbat*. During the charge phase, the batteries behave as a generator (*P*bat > 0) and it is considered a charge efficiency *ηbat* = 0.88; during discharge (*P*bat < 0), efficiency is considered unitary.

 

$$\text{SOC(t)} \quad = \text{SOC(t-1)} + \frac{\eta\_{\text{bar}} \cdot P\_{\text{bar}} \cdot \Delta t}{C\_{\text{bar}}} \quad P\_{\text{bar}} \quad > \text{ O} \tag{5}$$

$$\text{SOC(t)} \quad = \text{SOC(t-1)} + \frac{P\_{\text{bar}} \cdot \Delta t}{C\_{\text{bar}}} \quad P\_{\text{bar}} < \text{ O} \tag{6}$$

### **3. Provisional energy balance and storage management**

The proposed BMS periodically defines the strategy to minimize the power absorption from the grid. The strategy selection is performed two times per day to better match the consumption peaks of domestic users, which occur early in the morning and during the evening. Thus, the day is divided in three time slots. The first time slot starts at midnight and ends at 6:00 a.m. Between 6:00 a.m. and 6:00 p.m., there is the second time slot: the production is dominant and in case of people at home, part of generation is self-consumed. In this period, the consumption peak in the morning due to preparation to work and school activity (such as hairdryers, electric boiler, etc.) is included. Obviously, this peak cannot be totally satisfied by PV production, especially in winter. The third time slot starts at 6:00 p.m. and finishes at midnight, when the second consumption peak occurs, and PV production is low or negligible.

The time 6:00 p.m. is selected for the download of raw weather forecasts for the next 24 h, for the calculation of provisional energy balance and the update of management strategy for batteries. In fact, at 6:00 p.m., the PV production is almost over: the BESS can accurately calculate the quantity of stored energy, which will be available for the next hours. In fact, during evening and night, the batteries will not be charged: supply from the grid is not considered.

#### **3.1 Comparison of estimated energy production and consumption**

The provisional energy balance for 1-day ahead is performed comparing estimated energy production and consumption. Regarding the energy consumption, this value is calculated on the basis of measurement of local consumption profiles. Loads are monitored, and average values of energy consumption are calculated for each of the three time slots composing the day, as described in the previous paragraph. In addition, a distinction of average energy consumption between working days and holidays is considered.

Regarding the provisional production, every day at 6:00 p.m., the converter downloads raw weather forecasts for the next 24 h. Data are collected from commercial web services: they generally identify weather forecast with simplified symbols, i.e., showing a sun symbol for a clear sky day and lightning for rain. For the sake of simplicity, in the present work, it is considered a three-level forecast: a clear sky day, an average day with few clouds, and a cloudy/rainy day. These levels correspond to the three irradiance conditions provided by the database PVGIS. In this way, it is defined a raw correlation between the weather forecast and the expected production from the PV generator. The advantage consists of a free and easily accessible daily forecast of production, which can be used for free by the Internet-connected BESS to select the best battery management.

#### **3.2 Definition of the total discharge time**

**80** The first step in the smart management of batteries consists of the definition of the total discharge time (*TDT*): **Figure 4** shows the flowchart of the procedure.

**81**

**Figure 5.**

*Example of PV and load profiles for 2 days.*

*TDT* will be equal to 36 h.

*Definition of the total discharge time (TDT).*

**Figure 4.**

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

First, at 6:00 p.m., after weather forecast download, the provisional balance between expected production *E*PV\_1day-ahead and loads *E*loads\_1day-ahead, 6 a.m.-6 p.m. occur-

In case of PV energy production higher than loads *E*PV\_1day-ahead > *E*loads\_1day-ahead, 6 a.m.–6 p.m., a management of the storage to satisfy loads until 1-day ahead at 6:00 a.m. is performed. In this case, the *TDT* will be equal to 12 h. In fact, the day after, during light hours, energy will be self-consumed, and the surplus of PV production will charge the storage or will be injected into the grid. Vice versa, in case of low production and high loads *E*PV\_1day-ahead < *E*loads\_1day-ahead, 6 a.m.–6 p.m., an SBMS is necessary not only for 1-day head but also for the day after. In this case, the PV production cannot satisfy local loads and storage has to be able to reduce loads for two nights, and the

Batteries are expensive [40], and considering a storage with a too high capacity is not cost-effective for a grid-connected plant. For this reason, in the present work, the BESS can distribute the stored energy in a maximum *TDT* = 36 h. It means that

ring in the time slot 6:00 a.m.–6:00 p.m. of the day ahead is performed.

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

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

#### **Figure 4.**

*Green Energy Advances*

  *SOC*(*t*) <sup>=</sup> *SOC*(*<sup>t</sup>* <sup>−</sup> 1) <sup>+</sup> <sup>η</sup>*bat* <sup>∙</sup> *Pbat* <sup>∙</sup> <sup>∆</sup>*<sup>t</sup>* \_\_\_\_\_\_\_\_\_\_\_ *Cbat*

*SOC*(*t*) = *SOC*(*t* − 1) + *Pbat* <sup>∙</sup> <sup>∆</sup>*<sup>t</sup>* \_\_\_\_\_\_\_

**3. Provisional energy balance and storage management**

consumption peak occurs, and PV production is low or negligible.

**3.1 Comparison of estimated energy production and consumption**

Internet-connected BESS to select the best battery management.

**3.2 Definition of the total discharge time**

be charged: supply from the grid is not considered.

days and holidays is considered.

*Cbat*

The proposed BMS periodically defines the strategy to minimize the power absorp-

The time 6:00 p.m. is selected for the download of raw weather forecasts for the next 24 h, for the calculation of provisional energy balance and the update of management strategy for batteries. In fact, at 6:00 p.m., the PV production is almost over: the BESS can accurately calculate the quantity of stored energy, which will be available for the next hours. In fact, during evening and night, the batteries will not

The provisional energy balance for 1-day ahead is performed comparing estimated energy production and consumption. Regarding the energy consumption, this value is calculated on the basis of measurement of local consumption profiles. Loads are monitored, and average values of energy consumption are calculated for each of the three time slots composing the day, as described in the previous paragraph. In addition, a distinction of average energy consumption between working

Regarding the provisional production, every day at 6:00 p.m., the converter downloads raw weather forecasts for the next 24 h. Data are collected from commercial web services: they generally identify weather forecast with simplified symbols, i.e., showing a sun symbol for a clear sky day and lightning for rain. For the sake of simplicity, in the present work, it is considered a three-level forecast: a clear sky day, an average day with few clouds, and a cloudy/rainy day. These levels correspond to the three irradiance conditions provided by the database PVGIS. In this way, it is defined a raw correlation between the weather forecast and the expected production from the PV generator. The advantage consists of a free and easily accessible daily forecast of production, which can be used for free by the

The first step in the smart management of batteries consists of the definition of the total discharge time (*TDT*): **Figure 4** shows the flowchart of the procedure.

tion from the grid. The strategy selection is performed two times per day to better match the consumption peaks of domestic users, which occur early in the morning and during the evening. Thus, the day is divided in three time slots. The first time slot starts at midnight and ends at 6:00 a.m. Between 6:00 a.m. and 6:00 p.m., there is the second time slot: the production is dominant and in case of people at home, part of generation is self-consumed. In this period, the consumption peak in the morning due to preparation to work and school activity (such as hairdryers, electric boiler, etc.) is included. Obviously, this peak cannot be totally satisfied by PV production, especially in winter. The third time slot starts at 6:00 p.m. and finishes at midnight, when the second

*Pbat* < 0

*Pbat* > 0 (5)

(6)

**80**

*Definition of the total discharge time (TDT).*

First, at 6:00 p.m., after weather forecast download, the provisional balance between expected production *E*PV\_1day-ahead and loads *E*loads\_1day-ahead, 6 a.m.-6 p.m. occurring in the time slot 6:00 a.m.–6:00 p.m. of the day ahead is performed.

In case of PV energy production higher than loads *E*PV\_1day-ahead > *E*loads\_1day-ahead, 6 a.m.–6 p.m., a management of the storage to satisfy loads until 1-day ahead at 6:00 a.m. is performed. In this case, the *TDT* will be equal to 12 h. In fact, the day after, during light hours, energy will be self-consumed, and the surplus of PV production will charge the storage or will be injected into the grid. Vice versa, in case of low production and high loads *E*PV\_1day-ahead < *E*loads\_1day-ahead, 6 a.m.–6 p.m., an SBMS is necessary not only for 1-day head but also for the day after. In this case, the PV production cannot satisfy local loads and storage has to be able to reduce loads for two nights, and the *TDT* will be equal to 36 h.

Batteries are expensive [40], and considering a storage with a too high capacity is not cost-effective for a grid-connected plant. For this reason, in the present work, the BESS can distribute the stored energy in a maximum *TDT* = 36 h. It means that

**81 Figure 5.** *Example of PV and load profiles for 2 days.*

storage must be able to supply the load when a single cloudy day occurs (2 nights and 1 day).

**Figure 5** shows an example of PV and load profiles for 2 days: in the first day, the PV production is low, while the second one is a clear sky day. At 6:00 p.m. of day #1, the procedure starts with the converter downloading forecast for day #2: supposing a correct forecast, the result is a provisional high PV production. Thus, the BESS will manage the discharge of the storage from the evening of day #1 at 6:00 p.m. to the morning of day #2 at 6:00 a.m. (12 h). After 6:00 a.m. of day #2, storage and loads will again be mainly supplied by the PV production.

The second case is shown in **Figure 6**. It presents an example of PV and load profiles for 3 days: in the first and second days, the real PV production is low, while the third one is a clear sky day. At 6:00 p.m. of day #1, the converter downloads forecast for day #2: supposing a correct forecast, the result is a provisional low PV production. Thus, the BESS will manage the discharge of the storage until the morning of day #3 (a total of 36 h, from 18 to 54 h in **Figure 6**).

### **3.3 Selection of the storage management strategy**

After the definition of the total discharge time (*TDT*), the procedure continues with the second part; i.e., the definition of the storage management strategy. The *SOC* is calculated at 6:00 p.m. by the BESS, which uses appropriate models starting from the real-time measurement of voltage and ambient temperature of batteries, as described in Section 2.1. The rated capacity of the storage and the *SOC* permit to calculate the energy that can be provided to the loads *E*batt,disch. The estimated energy production *E*PV\_1day-ahead is the same quantity used in the previous step, while the consumption *E*load,*TDT* corresponds to the estimated loads during the *TDT* (**Figure 7**). These raw energy quantities are compared and it is defined if there is an energy deficit *E*PV\_1day-ahead + *E*batt,disch ≥ *E*load,TDT or surplus *E*PV\_1day-ahead + *E*batt,disch < *E*load,TDT.

If the PV production and the storage can satisfy the load *E*PV\_1dayahead + *E*batt,disch ≥ *E*load,TDT in the selected *TDT*, no advanced management of the batteries is required (BMS Strategy #1).

On the contrary, if loads are too high *E*PV\_1day-ahead + *E*batt,disch < *E*load,TDT, peak shaving strategy (BMS Strategy #2) or appropriate discharge profiles (BMS Strategy #3) are adopted. To select the most appropriate method between BMS

**83**

low.

**Figure 7.**

*Definition of storage management strategy.*

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

Strategy #2 and BMS Strategy #3, a provisional self-sufficiency *R*suff parameter, that is, the ratio between the provisional PV production plus the available energy from

When the ratio *R*suff is lower than a user-defined threshold *R*thres, the BMS Strategy #2 is adopted: the local generators and the storage will provide a low quantity of energy to the loads, which will be mainly supplied by the grid. It can result in high absorption peaks. In this case, the low energy quantity stored in the batteries will be used only when loads exceed a maximum limit *P*load,max, such as the contracted power absorption limit or another user-defined threshold. The BMS Strategy #3 is adopted when the ratio *R*suff is higher than the user-defined threshold *R*thres and lower than unit value. This case is better than the previous one, because great part of loads will be supplied by PV and storage and the quote from the grid is

The storage management strategies consist of peak shaving and of a timedependent discharge profile. According to the procedure described in the previous subsection, when the storage energy is much lower than loads, only the peak shaving technique is adopted (BMS Strategy #2). Thus, batteries are discharged only when strictly necessary, i.e., when a load peak occurs. In particular, storage will be

discharged only by the quota exceeding an user-defined limit *P*load,max.

(7)

the battery, and the provisional local loads, is calculated:

**3.4 Implementation of storage management strategies**

*<sup>R</sup>*suff <sup>=</sup> *EPV*<sup>1</sup>*day*−*ahead* <sup>+</sup> *<sup>E</sup>*batt,disch \_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_ *Eload*,*TDT*

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

**Figure 6.** *Example of PV and load profiles for 3 days.*

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

**Figure 7.** *Definition of storage management strategy.*

*Green Energy Advances*

and 1 day).

storage must be able to supply the load when a single cloudy day occurs (2 nights

loads will again be mainly supplied by the PV production.

morning of day #3 (a total of 36 h, from 18 to 54 h in **Figure 6**).

**3.3 Selection of the storage management strategy**

*E*PV\_1day-ahead + *E*batt,disch < *E*load,TDT.

batteries is required (BMS Strategy #1).

**Figure 5** shows an example of PV and load profiles for 2 days: in the first day, the PV production is low, while the second one is a clear sky day. At 6:00 p.m. of day #1, the procedure starts with the converter downloading forecast for day #2: supposing a correct forecast, the result is a provisional high PV production. Thus, the BESS will manage the discharge of the storage from the evening of day #1 at 6:00 p.m. to the morning of day #2 at 6:00 a.m. (12 h). After 6:00 a.m. of day #2, storage and

The second case is shown in **Figure 6**. It presents an example of PV and load profiles for 3 days: in the first and second days, the real PV production is low, while the third one is a clear sky day. At 6:00 p.m. of day #1, the converter downloads forecast for day #2: supposing a correct forecast, the result is a provisional low PV production. Thus, the BESS will manage the discharge of the storage until the

After the definition of the total discharge time (*TDT*), the procedure continues

with the second part; i.e., the definition of the storage management strategy. The *SOC* is calculated at 6:00 p.m. by the BESS, which uses appropriate models starting from the real-time measurement of voltage and ambient temperature of batteries, as described in Section 2.1. The rated capacity of the storage and the *SOC* permit to calculate the energy that can be provided to the loads *E*batt,disch. The estimated energy production *E*PV\_1day-ahead is the same quantity used in the previous step, while the consumption *E*load,*TDT* corresponds to the estimated loads during the *TDT* (**Figure 7**). These raw energy quantities are compared and it is defined if there is an energy deficit *E*PV\_1day-ahead + *E*batt,disch ≥ *E*load,TDT or surplus

If the PV production and the storage can satisfy the load *E*PV\_1day-

ahead + *E*batt,disch ≥ *E*load,TDT in the selected *TDT*, no advanced management of the

On the contrary, if loads are too high *E*PV\_1day-ahead + *E*batt,disch < *E*load,TDT, peak shaving strategy (BMS Strategy #2) or appropriate discharge profiles (BMS Strategy #3) are adopted. To select the most appropriate method between BMS

**82**

**Figure 6.**

*Example of PV and load profiles for 3 days.*

Strategy #2 and BMS Strategy #3, a provisional self-sufficiency *R*suff parameter, that is, the ratio between the provisional PV production plus the available energy from the battery, and the provisional local loads, is calculated:

between, and the propositional local loads, is calculated:

$$R\_{\text{surff}} = \frac{E\_{PV\_{i\text{obs}}\text{-}ahad} + E\_{\text{bat,dish}}}{E\_{load,TOT}}\tag{7}$$

When the ratio *R*suff is lower than a user-defined threshold *R*thres, the BMS Strategy #2 is adopted: the local generators and the storage will provide a low quantity of energy to the loads, which will be mainly supplied by the grid. It can result in high absorption peaks. In this case, the low energy quantity stored in the batteries will be used only when loads exceed a maximum limit *P*load,max, such as the contracted power absorption limit or another user-defined threshold. The BMS Strategy #3 is adopted when the ratio *R*suff is higher than the user-defined threshold *R*thres and lower than unit value. This case is better than the previous one, because great part of loads will be supplied by PV and storage and the quote from the grid is low.

#### **3.4 Implementation of storage management strategies**

The storage management strategies consist of peak shaving and of a timedependent discharge profile. According to the procedure described in the previous subsection, when the storage energy is much lower than loads, only the peak shaving technique is adopted (BMS Strategy #2). Thus, batteries are discharged only when strictly necessary, i.e., when a load peak occurs. In particular, storage will be discharged only by the quota exceeding an user-defined limit *P*load,max.

**Figure 8.** *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 energy consumptions:

$$\text{SOC}\_{\text{min}, \text{dot } x} = \text{SOC} \cdot \left( \mathbf{1} - \frac{E\_{\text{load}, \text{dot } x}}{E\_{\text{load}, \text{TDT}}} \right) \tag{8}$$

**85**

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

**Figure 9** shows an example of load and *SOC* profiles in case of the SBMS, which reduces the absorption peaks from the grid. In this case, the *SOC* cannot drop down under a temporary minimum *SOC*min,a = 75% before midnight; then, the discharge is limited by *SOC*min,b = 70% between midnight and 06:00 a.m. Between 06:00 a.m. and 06:00 p.m., the minimum admitted *SOC*min,c is 37%. Then, between 06:00 p.m. and midnight, the limit *SOC*min,d = 22%. Finally, after 06:00 p.m., the last limit corresponds to the same level of the basic management *SOC*safety ≈ 20%, which is a typical value to preserve life of lithium batteries. The main difference from the basic management consists of a small reserve in storage, which is always present, and the absorption peaks are always reduced. On the other hand, preserving the storage partially charged could reduce the self-sufficiency. The best solution consists of the abovementioned *SOC* levels selected to reduce absorption peak and keep as high as

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

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

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

*Example of load and SOC profiles in case of the proposed SBMS.*

possible the self-sufficiency level.

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

storage and directly supplies part of the loads.

**4. Simulation results**

**Figure 9.**

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

**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 absorption peak is not limited ≈2.9 kW.

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

**Figure 9.** *Example of load and SOC profiles in case of the proposed SBMS.*

**Figure 9** shows an example of load and *SOC* profiles in case of the SBMS, which reduces the absorption peaks from the grid. In this case, the *SOC* cannot drop down under a temporary minimum *SOC*min,a = 75% before midnight; then, the discharge is limited by *SOC*min,b = 70% between midnight and 06:00 a.m. Between 06:00 a.m. and 06:00 p.m., the minimum admitted *SOC*min,c is 37%. Then, between 06:00 p.m. and midnight, the limit *SOC*min,d = 22%. Finally, after 06:00 p.m., the last limit corresponds to the same level of the basic management *SOC*safety ≈ 20%, which is a typical value to preserve life of lithium batteries. The main difference from the basic management consists of a small reserve in storage, which is always present, and the absorption peaks are always reduced. On the other hand, preserving the storage partially charged could reduce the self-sufficiency. The best solution consists of the abovementioned *SOC* levels selected to reduce absorption peak and keep as high as possible the self-sufficiency level.
