Module 2 • Duration: 60 Minutes • Format: Video Demonstration + Practical Guide

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Learning Objectives

By the end of this lesson, you will be able to:

• Size an inverter based on continuous running load and inductive motor surge requirements
• Calculate battery storage capacity in Ampere-hours (Ah) and kilowatt-hours (kWh) with Depth of Discharge (DoD) limits
• Size the solar PV panel array factoring in system losses, dirt derating, and regional Peak Sun Hours
• Apply safety margins to guarantee uninterrupted power availability in Nigerian weather

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1. Inverter Sizing Formula

The inverter converts DC battery/solar power into 230V AC grid electricity. It must handle both continuous load and motor startup surges:

$$\text{Inverter Size (kVA)} \ge \frac{\text{Total Continuous AC Load (W)}}{\text{Power Factor}} \times 1.25\text{ (Safety Margin)}$$

Using our Lesson 3 residential audit:

• Total simultaneous continuous running load = $2,090\text{ Watts}$.
• Factor in 1.5HP AC compressor inrush surge ($1,100\text{ W} \times 2.5 = 2,750\text{ W}$).
• Minimum inverter continuous rating: $2,090\text{ W} \times 1.25 = 2,612.5\text{ W}$.
• Surge handling requirement: $\approx 4,500\text{ W}$.
• Selected Inverter: A standard 3.5kVA / 3kW 24V or 5kVA / 5kW 48V Pure Sine Wave Hybrid Inverter (e.g., Felicity Solar 5kVA 48V FL-IVP5048 or GTE-PWR-007).

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2. Battery Bank Sizing Formula

The battery bank must store sufficient energy to support nighttime loads plus a defined autonomy buffer for overcast rainy days:

$$\text{Usable Storage Energy Required (Wh)} = \frac{\text{Daily Nighttime Consumption (Wh)}}{\text{Inverter Efficiency (}\eta = 0.90\text{)}}$$

$$\text{Total Installed Battery Capacity (Wh)} = \frac{\text{Usable Storage Required (Wh)}}{\text{Maximum Depth of Discharge (DoD)}}$$

Chemistry Comparison for DoD:

• Tubular Deep Cycle Gel Batteries: Maximum recommended DoD is 50% ($0.50$) to avoid rapid sulfation and cell death.
• Lithium Iron Phosphate ($ ext{LiFePO}_4$): Maximum safe DoD is 85% – 90% ($0.85 - 0.90$) with up to 6,000 cycles.

Applying the Formula:

Nighttime energy demand = $8,390\text{ Wh}$. $$\text{Usable Energy Required} = \frac{8,390\text{ Wh}}{0.90} = 9,322\text{ Wh}$$

Option A: Using Lithium LiFePO4 (90% DoD): $$\text{Installed LiFePO4 Capacity} = \frac{9,322\text{ Wh}}{0.90} \approx 10,357\text{ Wh (10.35 kWh)}$$ $$\text{At 48V Nominal DC Bus: } \text{Capacity in Ah} = \frac{10,357\text{ Wh}}{48\text{ V}} \approx 215.7\text{ Ah}$$ Solution: Two (2) 5.12kWh 48V 100Ah LiFePO4 wall-mount lithium batteries wired in parallel (Total: $10.24\text{ kWh}$, matching GTE-BAT-010).

Option B: Using Tubular Gel (50% DoD): $$\text{Installed Gel Capacity} = \frac{9,322\text{ Wh}}{0.50} = 18,644\text{ Wh}$$ $$\text{At 48V Nominal DC Bus: } \text{Capacity in Ah} = \frac{18,644\text{ Wh}}{48\text{ V}} \approx 388.4\text{ Ah}$$ Solution: Eight (8) 12V 200Ah Tubular Gel batteries (2 parallel strings of 4 in series) yielding $48\text{V } 400\text{Ah} = 19.2\text{ kWh}$.

Notice how lithium requires significantly fewer battery units, saves physical space, and eliminates acid fumes!

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3. Solar PV Array Sizing Formula

The solar array must generate enough daily energy to both power daytime loads directly AND fully recharge the depleted battery bank before sunset:

$$E_{\text{Total Daily Generation Target}} = \text{Total Daily Consumption (Wh)} \times 1.25\text{ (System Losses Buffer)}$$

$$\text{PV Array Wattage (Wp)} = \frac{E_{\text{Total Daily Generation Target}}}{\text{Regional Peak Sun Hours (PSH)}}$$

For our Abuja site ($5.0\text{ PSH}$): $$E_{\text{Target}} = 15,780\text{ Wh} \times 1.25 = 19,725\text{ Wh}$$

$$\text{PV Array Wattage} = \frac{19,725\text{ Wh}}{5.0\text{ hrs}} = 3,945\text{ Watts-peak (Wp)}$$

Selecting standard Tier-1 550W Monocrystalline Half-Cut PERC modules: $$\text{Number of Panels} = \frac{3,945\text{ Wp}}{550\text{ W}} \approx 7.17 \implies \mathbf{8\text{ Panels (4,400 Wp)}}$$

8 panels rated at 550W each will generate $4,400\text{ Wp} \times 5.0\text{ hrs} = 22,000\text{ Wh (22 kWh)}$ on an average sunny day, providing a healthy safety margin for Harmattan haze or rainy spells!

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Knowledge Check & Self-Assessment

Lesson 2 Knowledge Check Test your understanding before proceeding to the next lesson:

1. What is the minimum recommended tilt angle for solar panels installed in Nigeria to ensure natural self-cleaning?

A) 0° (Flat)

B) 10° – 12° (True South orientation)

C) 45°

D) 90° (Vertical)

2. In a hybrid solar installation, why should standard AC circuit breakers never be used on the high-voltage DC solar circuit?

A) AC breakers are too expensive

B) DC current has no natural zero-crossing point, causing continuous destructive arcs inside AC breakers

C) AC breakers reduce the wattage of the panels

D) They cause battery charging to reverse

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Hands-On Lab Assignment (GTE Practical Workshop)

1. Practical Exercise: Using your digital multimeter and clamp meter, perform the full pre-commissioning testing sequence demonstrated in this lesson.
2. Documentation Task: Fill out the GTE Field Commissioning Inspection Form with your measured values, verifying that all readings match theoretical design calculations within a 5% margin of error.
3. Submission: Upload your completed inspection sheet and photo of your multimeter test reading to the GTE Academy portal for instructor evaluation.

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