3.1.2. Solar PV Model

The di fficulty of calculating the energy generated by a solar PV has been extensively studied in the technical literature. The calculation of solar PV power of a grid-connected solar PV system is classified under two categories which is indirect method and direct method. As the operation and the performance of a PV focuses mainly on its maximum power, the indirect method describing the PV module's maximum power output behaviors are more theoretical for solar PV system valuation. Indirect method directly calculates the maximum power without calculating first the I-V curve of the solar PV array [25]. This simplified indirect method provides the modelled power to be used in MDRed modelling. Based on Rus-Casa et al., indirect method directly provides power from atmospheric parameters and information provided by the manufacturers in the datasheets. PV modelled power in per-unit conversion is based on PV module temperature and solar irradiance level at Standard Testing Condition (STC). The formula for PV modelled power in per-unit convention, Pmod is given as follows [25]:

$$\mathbf{P\_{mod}} = \mathbf{P\_{PV\\_kwp}}^\* \left(\mathbf{G/G\_{STC}}\right) \left[1 - \mathbf{y}^\* \left(\mathbf{T\_C} - \mathbf{T\_{STC}}\right)\right] \tag{4}$$

where Gs (t) is the measured solar irradiance (hourly) and PPV\_kwp is the rated PV power at Standard Testing Condition (STC). GSTC and TSTC is the solar irradiance (1000 <sup>W</sup>/m2) and PV module temperature (25 degC) at Standard Testing Conditions (STC), respectively. Besides that, γ is the temperature correction based on measured polycrystalline silicon PV module temperatures with a power decrease in between 0.30%/ ◦C and 0.5%/ ◦C.

The measured module temperature, TC is set at 50 ◦C at solar irradiance of 3.5 up to 4 h per day averagely based on Malaysian climate. Solar irradiance measurement was taken at Nilai, Negeri Sembilan, Malaysia using a CMP3 pyranometer (KIPP & ZONEN, Delft, The Netherlands). Apart from the measured solar irradiance, the actual generated power will be obtained with respect to solar irradiance and PV module temperature. The cost of the solar PV system and batteries are the important parameters for optimal sizing of the solar PV-battery system. Table 5 shows the historical prices of the solar PV-inverter system from the year 2010–2016 in Peninsular Malaysia [26]. The PPV\_rated can be calculated as follows:

$$\mathbf{P}\_{\text{PV\\_rated}} = \mathbf{P}\_{\text{PV\\_kWp}} / \eta\_{\text{inv}} \tag{5}$$

where PPV\_rated is the rated dc output power of the proposed PV array in kWp and ηinv is the conversion efficiency from dc to ac according to inverter e fficiency. Nowadays, the PV inverters can operate at 90% of conversion e fficiency.


**Table 5.** National trends in PV-inverter system prices.

3.1.3. Battery Energy Storage System (BESS) Model

The battery energy storage system (BESS) comprises batteries, control and power conditioning system (C-PCS). Typically, batteries will absorb power from the grid during the o ff-peak hours and discharge power during peak demand. Currently, significant research and development in battery technology are being carried out. Tesla (Arizona, AZ, USA) has designed and commercialized the Powerwall 2, the second iteration of its home battery system. Tesla Powerwall 2 costs MYR24,200 (USD5500) and delivers 14 kWh of capacity [27].

As the core battery technology matures and the unit pricing decays, bi-directional converters providing both battery charging (AC to DC) and battery inverting (DC to AC) will grow due to the new market for power converters. Various technologies for BESS are available, namely lead acid (LA), vanadium redox flow (VRB), zinc–bromine flow (ZnBr), polysulfide bromide battery (PSB), nickel–cadmium battery (NiCd), sodium sulfur and lithium-ion (Li-ion) battery [28]. Four battery technologies are chosen for the investigation of BESS systems such as LA, VRB, ZnBr, and Li-ion. The key parameters for these batteries are tabulated in Table 6.


**Table 6.** Key parameters of batteries.

a Data is collected from [29]; b Data is collected from [30]; c Data is collected from [31].

The batteries are rated in terms of their energy and power capacities. Some of the other essential features of a battery are its efficiency, life span, operating temperature, depth of discharge (DOD), self-discharge and energy density. In most cases, lithium-ion batteries and lead-acid batteries are the best choices for peak shaving techniques, although other battery types can be more affordable [32]. While lead-acid batteries have a relatively short lifespan and lower DOD than other battery types, they are also one of the least expensive options in the energy storage sector. Lithium-ion batteries are lighter and better than lead-acid batteries [33]. They also have higher DOD and longer lifespan when compared to lead-acid batteries. Since the battery is also operated on DC, an AC-to-DC converter is necessary for charging the battery and a DC-to-AC converter is necessary during discharging the battery. For simplicity, we assumed that both converters have the identical constant conversion efficiency satisfying:

$$\mathbf{P\_{conv}(t)} = \begin{cases} \begin{array}{c} \eta\_{\rm B} \mathbf{P\_{B}(t)}, & \text{if } \mathbf{P\_{B}(t)} < 0 \\ \frac{\mathbf{P\_{B}(t)}}{\eta\_{\rm B}} & \text{otherwise} \end{array} \tag{6} \\\end{cases} \tag{7}$$

Note that, ηB is the round trip efficiency of the battery converters. In other words, Pconv is the power exchanged with the AC bus when the converters and the battery are treated as a single entity. Similarly, we can derive:

$$P(\mathbf{t}) = \begin{cases} \frac{\mathbb{P}\_{\text{conv}}(\mathbf{t})}{\eta\_{\text{B}}} \text{ if } \mathbb{P}\_{\text{conv}}(\mathbf{t}) < 0\\ \eta\_{\text{B}} \mathbb{P}\_{\text{conv}}(\mathbf{t}) \text{ otherwise} \end{cases} \tag{7}$$

Apart from that, the rated capacity of the battery, PBat is calculated by considering the optimal size of the battery, Ebat as follows:

$$\text{Pbat}(\text{kWh}) = \text{E}\_{\text{bat}}(\text{kWh}) \* \frac{\eta\_{\text{bat}}}{\text{DOD}} \tag{8}$$

The battery Depth of Discharge (DOD) has a significant impact on a battery's life cycle. The battery life cycle is inversely proportional to the DOD. The DOD of a battery defines the fraction of the power that can be withdrawn from the battery. For instance, if a battery system is 100% fully charged, it means the DOD of this battery is 0% and vice +Generally, battery state of charge (SOC) provides the ratio of the amount of energy presently stored in the battery to the nominal rated capacity.
