*3.2. Economical Model*

The cost of optimal PV array, CPV\_inv can be calculated as follows:

$$\mathbf{C}\_{\text{PV\\_inv}} = \mathbf{U}\_{\text{PV}} \, ^\ast \mathbf{P}\_{\text{PV\\_rated}} \tag{9}$$

where UPV\_kWp is the unit cost of PV array per kWp. Apart from that, reducing the cost of PV inverter system will lead to lower miscellaneous costs such as operation and maintenance costs and replacement costs. The overall cost of the solar PV system is the combination of both costs of power conversion units and cost of inverter. In this paper, the overall solar PV system cost, Ctotal\_PV\_inv is evaluated by referring to a specific planning period and is given by:

$$\mathbf{C\_{total\\_PV\\_inv}} \text{ (MYR)} = \mathbf{C\_{PV}} + \mathbf{C\_{O\&M\\_PV}} + \mathbf{C\_{RC\\_PV}} \tag{10}$$

The cost of batteries, CBat is calculated as follows:

$$\mathbf{C\_{bat}}\text{ (MYR)} = \mathbf{U\_{bat}}\text{ (MYR/kWh)}\text{ \* }\mathbf{P\_{bat}}\text{ (kWh)}\tag{11}$$

where UBat is the unit cost of the batteries in kWh, PBat is the rated capacity of the batteries. The cost of power conversion units, Cconv is as follows:

$$\mathbf{C\_{curv}}\text{ (MYR)} = \mathbf{U\_{curv}}\text{ (MYR/kWh)} \times \mathbf{P\_{curv}}\text{ (kW)}\tag{12}$$

where UConv is the unit cost of the power conversion units in kW and Pconv is the power rating of the converter. The overall cost of the BESS is the combination of both costs of power conversion units and cost of batteries. In this paper, the total overall BESS cost, Ctotal\_BESS is evaluated by referring to a specific planning period and is given by:

$$\mathcal{C}\_{\text{BESS}} = \mathcal{C}\_{\text{bat}} + \mathcal{C}\_{\text{conv}} \tag{13}$$

$$\text{C}\_{\text{total\\_BESS}} \text{ (MYR)} = \text{C}\_{\text{BESS}} + \text{C}\_{\text{cohm\\_BESS}} + \text{C}\_{\text{rep\\_BESS}} + \text{C}\_{\text{disp\\_bat}} + \text{C}\_{\text{LS\\_bat}} \tag{14}$$

where CBESS is the capital cost, Co&m\_BESS is the operation and maintenance cost, Crep\_BESS is the replacement cost, Cdisp\_bat is the disposal cost related to the potential cost achievable from recycling old batteries and lifespan cost (CLS\_bat) of all the main components including its system. However, this is not added in MDRed modeling since the cost of the BESS is very high and will lead to longer ROI. Cost of energy savings on net consumption and MD are according to Malaysian electricity tariff allocated for each category of commercial and industrial customers. For commercial consumers with tariff rates of C1 category, the annual savings, Syr\_shave can be calculated as follows:

$$P\_{\text{share\\_MD}} = \text{[max} \left( \sum P\_{\text{load\\_net}} \right) \tag{15}$$

$$\text{S}\_{\text{yr\\_share}} = \left(\sum \text{P}\_{\text{load\\_share}} \, \, ^\ast \text{E}\_{\text{load\\_net}}\right) + \left(\text{P}\_{\text{share\\_MD}} \, \, ^\ast \text{E}\_{\text{MD}}\right) + \left(\sum \text{P}\_{\text{PV\\_supplus}} \, ^\ast \text{E}\_{\text{surplus}}\right) \, ^\ast 12 \tag{16}$$

Under the NEM scheme, the rate of surplus generation, E\_surplus has been formulated at MYR 0.238 (USD 0.05)/kWh for medium voltage interconnection. Apart from that, overall loan paymen<sup>t</sup> is important to include all the incurred cost such as operation and maintenance cost (CO&M), replacement cost (CRC) and lifespan cost (CLS) of all the main components including its system. This is applied to PV-inverter and BESS components which includes the batteries and converter unit. Therefore, the overall cost of the system comprises of:

$$\mathbf{C\_{full\\_learn}} = (\mathbf{C\_{total\\_PV}} + \mathbf{C\_{total\\_BESS}}) \text{ \* interest rate (\%)}\tag{17}$$

The energy flow schedule of solar PV-battery system integration has been included to lower the daily operating cost mainly on the MD reduction at the specific limit. For GA optimization, 7% of interest rate for total load paymen<sup>t</sup> has been included.

### **4. Modeling of System Reliability**

Several approaches have been used to achieve the optimal configuration of solar PV-battery systems from the technical and economical perspective. In this paper, the technical algorithm for the optimal sizing is developed according to the concept of MDRed model to evaluate the reliability of solar PV-battery system. The GA model attains the optimal size in terms of various degrees of reliability. A binary coded GA was introduced to solve the optimal capacity of solar PV and battery. Input data includes hourly data per year, solar irradiation by indirect power calculation, load power consumption and timeframe of battery DOD and SOC with respect to peak hours and o ff-peak hour's tari ff charges. The flowchart of the GA process applied to PV-battery sizing problem with respect to MDRed modelling is illustrated in Figure 5. One of the key parameters that represent the battery sizing is the capacity of battery charging, Pbat\_chg and battery discharging, Pbat\_dischg. Based on Figure 5 and Table 7, the amount of maximum demand reduction (MDRed) is based on battery discharging capacity (Pbat\_dischg) to maintain the maximum demand limit (PMD\_limit), in the presence and/or absence of generated PV power (PPV) during peak hours from 8.00 a.m. and 10.00 p.m. Battery charging capacity (Pbat\_chg) will be in operation during o ff-peak hours in between 10.00 p.m. and 8.00 a.m. As per Figure 7, the battery energy managemen<sup>t</sup> system works to monitor the net load continuously in the presence of solar PV and will immediately activate the battery operation to discharge if the new net load exceeds the MD limit. Besides that, the battery discharging will not take place if the new net load is below the MD limit. Besides that, as per Figure 7, the Battery Energy managemen<sup>t</sup> system scenarios for MDRed modeling approach is based on any scenarios (e fficient, intermittent or zero solar PV). Therefore, the proposed optimization method will deliver the optimal operation condition or optimal sizing of solar PV-battery in real time scenario.

**Figure 5.** Flowchart of MDRed model for optimal sizing simulation using Genetic Algorithm.

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**Table 7.** Battery Energy managemen<sup>t</sup> system for MDRed modeling approach.

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As per Equation (18), the generated PV power, PPV will be supplied for self-consumption to reduce the actual load, Pload\_actual. Therefore, new net load, Pload\_net will be obtained. However, the battery will not discharge if the Pload\_net is below PMD\_limit. Due to the intermittent solar irradiance during bad weather condition, the optimal battery sizing can be calculated using Equations (19) and (20) to cater for the MD limit. If the Pload\_net is above PMD\_limit, the battery will discharge (Pbat\_dischg) to maintain the required MD limit. During off-peak hours, the batteries will be charged (Pbat\_chg) during off-peak hours until minimum DOD is reached. Therefore, new net load, Pload\_net can be calculated as:

[Condition #1: PMD\_limit < Pload\_net with solar PV]:- Condition #1: PMD\_limit < Pload\_net with solar PV

$$
\int \mathbf{P}\_{\text{load\\_net}} = \int \mathbf{P}\_{\text{load\\_actual}} - \int \mathbf{P}\_{\text{PV}} \tag{18}
$$

[Condition #2: PMD\_limit > Pload\_net with solar PV]:-

> Pload\_net = [Pload\_actual + Pbat\_chg] − [PPV + Pbat\_dischg] (19)

[Condition #3: PMD\_limit > Pload\_net without solar PV]:-

$$\text{P}\_{\text{load\\_net}} = \text{[P}\_{\text{load\\_actual}} + \text{P}\_{\text{bat\\_chg}}\text{]} - \text{[P}\_{\text{bat\\_dischg}}\text{]}\tag{20}$$

The total load net consumption reduction will be based on sum of the new net load mainly due to generated PV power. Therefore, total load shaving (Pload\_shave) can be calculated as:

$$\sum \mathbf{P}\_{\text{load\\_shave}} = \sum \mathbf{P}\_{\text{load\\_actual}} - \sum \mathbf{P}\_{\text{PV}} \tag{21}$$

MD reduction shaving varies according to system performance which mainly relies on total generated PV power and battery capacity. The excess PV power, PPV\_suplus will be achieved when generated PV power is more than actual load and it can be calculated as: [Condition #4: PPV > Pload\_actual with solar PV]:

$$\text{P}\_{\text{PV\\_supulus}} = \sum \text{[P}\_{\text{PV}} - \text{P}\_{\text{load\\_actual}}] \tag{22}$$

The basic Return on Investment (ROI) is calculated based on paymen<sup>t</sup> of loan in regard to interest rate using total profit achieved using solar PV-battery system. The ROI can be calculated as:

$$\text{ROI (in years)} = \text{C}\_{\text{load\\_payment}} \text{\%}\_{\text{yr\\_share}} \tag{23}$$
