*2.1. Design Calculations for the Photo Voltaic-Inverter*

The design calculations for the inverter and the filter are presented in Table 2. An LCL filter (2 inductances-L connected in series with a capacitor-C in parallel) is often used to interconnect an inverter to the utility grid in order to filter the harmonics produced by the inverter. Since the PCC voltage is 415 V and the grid voltage is 11 kV, the grid side transformer with a transformation ratio of 11 kV/415 V with minimum 100 kVA rating is selected.

Due to the L-C-L filter used at the output side of the inverter, there is an voltage drop across the filter, so the inverter output voltage should be the sum of PCC voltage and the voltage drop across the filter. Considering the sinusoidal PWM (SPWM) technique for pulse generation, the minimum DC link voltage required is calculated based on the inverter output voltage. Since the inverter needs to be designed to handle the filter capacitor current in addition to the rated load current, an optimal filter capacitor is selected which draw less than 5% of rated current. The Inverter side inductor L1 is derived from the value of the capacitor C and the corner frequency Fc. After selecting the inductor L1, the grid side inductor L2 can be selected based on the maximum filter drop allowed. Inductance L2 can also be made part of the transformer on the grid side to eliminate the physical inductor L2 in the system.


**Table 2.** Design calculations for the photo voltaic-inverter.

#### *2.2. Selection of Battery Type*

The procedure for the calculation of PV power requirement for battery charging is explained in Table 3. As mentioned earlier, since the power requirement during nighttime is much lower than that during the daytime, an energy storage with 25% of the rated power of the PV array is selected. A Lithium-ion battery with a nominal voltage of 350 V is selected as an energy storage in this system. The ampere-hour rating of the battery is decided based on the minimum backup time required and the battery discharging current. Similarly, the charging current of the battery is calculated based on the charging time and ampere-hour rating of the battery. The power required from the PV array for charging the battery is determined from the battery nominal voltage and the charging current.


**Table 3.** Electrical parameters of the battery.

The battery selected for this system can be modeled as a voltage source [1,7,8] and the model was implemented based on the equation for the battery voltage expressed as below [9].

Battery Voltage:

$$\text{V}\_{\text{Batt}} = \text{E}\_0 - \text{K} \left[ \text{Q} / (\text{Q-I} \, ^\ast \text{T}) \right] + \text{Ae} \, ^\ast \text{I} \, ^\ast \text{T} - \left[ \text{I}\_{\text{Batt}} \, ^\ast \text{R} \right] \tag{1}$$

where VBatt is the battery voltage (V), IBatt is the battery current (A), E0 is the nominal voltage (V), Q is ampere-hour rating of the battery (Ah), B is the nominal discharge current (Ah)−1, K is the fully charged voltage (V)which is around 116%, A is the exponential voltage (V), which is around 105%, R is the internal resistance of the battery, and "I \* T" is the discharged capacity (Ah) which is determined by integrating the battery current.

State of charge of the battery can be obtained after integrating the battery current:

$$\% \text{ SOC} = 100 \times \left\{ 1 - \left[ \left( \text{I} \, ^\ast \text{T} \right) / \text{Q} \right] \right\} \tag{2}$$

#### *2.3. Selection of the PV Array*

From the above discussions, a PV array for a minimum power rating of 113 kW is required, since a power of 100 kW for the grid and 13 kW for battery charging is required from the PV array. Design calculations for the PV array using 435 watt PV module (Make: M/s Sunpower, Model: SPR-435NE-WHT-D) is explained and the procedure for selecting a number of series, parallel PV modules in a PV array is also presented in Table 4. An operating temperature range of 25 to 55 ◦C is considered for the calculations. PV module parameters such as MPP voltage, MPP current, open circuit voltage and short circuit current at 25 ◦C are obtained from the data sheet and the values at 55 ◦C are derived using the temperature coefficients of the PV modules. The operating range of PV module voltages and currents are tabulated.



**SL. NO Parameter Value Units Remarks Electrical Ratings of PV Array** 23 Minimum No. of Modules required (N) 260 No's PV power/Pmod\_max 24 Minimum No. of Modules in Series (Nse) 10 No's V\_PV\_Min/Vmod\_min 25 No. of Modules in parallel (Np) 26 No's N/Nse 26 Minimum Voltage of PV Array 658.9 V Vmod\_min × Nse 27 Maximum Voltage of PV Array 856 V Vmod\_max × Nse 28 Maximum power from PV Array 113 kW Nse × Np × Pmod\_max

**Table 4.** *Cont.*

The total number of PV modules required in the PV array is calculated based on the total power requirement and the power rating of each PV module. The number of series PV modules in a PV array is selected based on the minimum DC link voltage requirement for the PV-inverter. For this system, the minimum DC link voltage required is 620 Volts to match the inverter voltage with the PCC voltage. Hence the PV array minimum voltage should always be more than 620 V in the operating temperature range. The minimum number of parallel PV modules in the PV array is calculated from a total number of PV modules and the number of series PV modules selected.

The PV array can be modeled as a current source [1,7,10] and the mathematical expression for the PV array model is as given below [11].

PV Current:

I=Iph <sup>−</sup> [Is <sup>×</sup> (e (V + I \* Rs )/N \* Vt <sup>−</sup> 1)] <sup>−</sup> [(V + I \* Rs )/Rp] (3)

where I is PV current and V is the PV voltage. Iph is the photon current and it is expressed as:

$$\mathbf{I}\_{\rm ph} = \mathbf{I} \mathbf{r} \mathbf{r} \text{adiance } \triangleq (\mathbf{I}\_{\rm gc} / \mathbf{I}\_{\rm ro}) \tag{4}$$

where Isc is the short circuit current of the PV array = Isc of each module, N represents the number of parallel modules, Iro is the measured irradiance = 1000 W/m<sup>2</sup> (from the datasheet), Is is the diode saturation current and expressed as:

$$\mathbf{I}\_{\mathsf{k}} = \mathbf{I}\_{\mathsf{k}\mathsf{C}} / \left( \exp(\mathsf{Voc} / (\mathsf{n} \, ^\star \mathsf{V}\_{\mathsf{l}})) - 1 \right) \tag{5}$$

where Isc is the short circuit current of the PV array, Voc is the open-circuit voltage= Voc of each module, multiply by the number of series modules, n is the quality factor and Vt is the thermal voltage and expressed as:

$$\mathbf{V\_{t} = k \,\,\,\mathbf{T}/q} \tag{6}$$

where k is Boltzmann's constant = 1.3806 × <sup>10</sup><sup>−</sup>23, T is the operating temperature = 25 ◦C, q is charge of an electron = 1.602 × <sup>10</sup><sup>−</sup>19, RS is the series resistance of the PV array, Rp is the parallel resistance of the PV array.

#### *2.4. Design Calculations for the Battery Charger*

Battery charger ratings are decided after selecting the PV array. Since the PV array and the battery charger are connected to the common DC link, the battery charger input voltage range is the PV array operating voltage range. The battery charger output voltage range is the battery operating voltage range. Based on the input and output voltage range of the battery charger, an isolation transformer with a transformation ratio of 1:2 is selected. Electrical parameters for the battery charger system are listed in Table 5.

Design calculations for the proposed system are explained briefly in this subsection. The control methodology for the battery charger and the PV-inverter are explained in next subsections.


**Table 5.** Electrical parameters of the battery charger system.

*2.5. Control of the Dual Active Bridge-Based Battery Charger*

The DAB-based DC-DC converter consists of two H-bridges and a high-frequency transformer. The source side H-bridge is connected to the DC link and the load side H-bridge is connected to the battery, as shown in Figure 3. A high-frequency transformer is required to match the battery voltage with the DC link voltage and also to provide isolation between the PV array and the battery. The transformer's leakage inductance helps in boost operation mode [12,13]. The transformer winding connected to the source side H-bridge is considered as the primary and the winding connected to the load side H-bridge is considered as the secondary. A control block diagram of the DAB-based battery charger is shown in Figure 4. Source side and load side H-bridges act like a simple square wave inverter. Square pulses with 50% duty cycle are provided to the load side and source side H-bridges. Power flow through the DAB is controlled using phase shift control. The pulse generator provides the gate pulses for the source side and load side H-bridges based on the phase shift obtained through a PI controller.

**Figure 4.** Control block diagram of the DAB-based battery charger.

During current control mode, when the battery current reference is zero, then the gate pulses for source side and load side H-bridges will be in phase with each other. During forward power flow i.e., for charging the battery, the gate pulse of the source side H-bridge will be in leading to the gate pulse of the load side H-bridge. Similarly, during reverse power flow i.e., during battery discharging mode, the load side gate pulse will be leading. The amount of power transfer depends on the phase angle between the gate pulses for the source side bridge and load side bridge. As the size and cost of a high-frequency transformer are much less than those of a high-frequency transformer for the same power rating, battery charger size and cost can be reduced by using a high-frequency transformer in a DAB.

During voltage control mode, the battery side H-bridge receives 50% duty cycle gate pulses and the DC link side H-bridge is controlled to maintain the DC link equal to the reference DC link voltage. The detailed control philosophy of the DAB-based battery charging system during various modes of operation is explained below:

	- The battery is in charging mode of operation hence the battery current reference is taken as positive.
	- Based on the battery SOC, the reference charging current is obtained through a look-up-table.
	- When the battery SOC is in the range of 80 to 115%, then the battery charging current is maintained at 0.12 C i.e., 36 A (0.12 \* amp-hour rating of battery) as shown in Table 3.
	- When the battery is fully charged, then the battery voltage will reach the maximum voltage, then the reference battery current is made zero to avoid overcharging. In this case, the operation can be transferred to Mode2, if the load requirement is more than the PV power.
	- When the battery is fully discharged, then the battery voltage will be less than 0.9 times the nominal voltage, then the charging current is adjusted to 0.2 C i.e., 57 A for fast charging.
	- In this mode, the battery is in discharging mode of operation hence the battery current reference is taken as negative.
	- In this case, if the PV array is in an inactive state i.e., PV voltage is more than the minimum DC link voltage required (i.e., 620 V) but the MPP of the PV array is less than the critical load requirement:
		- The battery discharging current is obtained from the Amp-hour rating of the battery and the discharging time.
		- Since the minimum backup time in this system is 4 h, the user can adjust the backup time to be more than 4 h.
	- In case the PV voltage is less than the minimum DC link voltage required then the battery charger needs to provide the required voltage to the DC link:
		- In this case, the DC link voltage reference (Vdc\_ref) is generated by the reference generator.
		- Vdc\_ref is always maintained at more than the minimum required DC link voltage (620 V).
