Module 3: Electrical Fundamentals, Site Assessment & System Design

24 sept. 2026

Introduction

Correct design and installation depend on understanding how electrical systems behave. This module covers the electrical principles, component characteristics, site assessment and sizing methods required to specify a safe and suitable solar and battery system. Each worked example should be reproduced with a calculator.

Learning outcomes

On completing this module, partners should be able to:

1. Apply the relationships between voltage, current, resistance, power and energy;
2. Distinguish between power (kW) and energy (kWh);
3. Calculate voltage and current for series and parallel connections;
4. Interpret a PV module datasheet and the effects of temperature, shading and soiling;
5. Describe the function and key ratings of inverters, charge controllers and batteries;
6. Identify the main system types;
7. Conduct a site assessment and load analysis;
8. Size an inverter, battery and PV array for a simple system;
9. Verify that a string configuration is within an inverter's voltage limits;
10. Explain cable selection and calculate voltage drop;
11. Verify equipment compatibility.

3.1 Electrical quantities

Example 1. A 230 V appliance draws 8 A. P = 230 × 8 = 1,840 W.

Example 2. A 2,000 W kettle operates at 230 V. I = 2,000 ÷ 230 = 8.7 A.

At 230 V, each ampere corresponds to approximately 230 W. Results should be checked against this order of magnitude.

Example 3: heat at a poor connection. A battery lug with a resistance of 0.05 Ω carries 40 A. Heat produced = 40² × 0.05 = 80 W, concentrated in a single joint, with a voltage loss of 40 × 0.05 = 2 V. Because heat is proportional to the square of the current, doubling the current produces four times the heat. This is the mechanism by which loose terminals, poor crimps and undersized conductors cause fires.

3.2 Energy: kW and kWh

Example. A 0.75 kW compressor runs for 6 hours: E = 0.75 × 6 = 4.5 kWh.

Confusion between kW and kWh is a common cause of mis-sized systems and customer misunderstanding. A request for "a 5 kW system" may refer to an inverter, a battery or an array, which are different quantities.

Battery capacity stated in ampere-hours is converted to energy as follows:

A 12 V, 100 Ah battery stores 12 × 100 ÷ 1,000 = 1.2 kWh.

3.3 AC and DC; single-phase and three-phase

Direct current (DC) flows in one direction and has positive and negative polarity. Alternating current (AC) reverses direction periodically; the Nigerian supply operates at 50 Hz.

Single-phase supplies have one line conductor and a neutral at approximately 230 V (240 V in older documentation) and serve most homes and small premises. Three-phase supplies have three line conductors, each at 230 V to neutral and approximately 400 V (415 V) between lines, and serve larger premises and loads. Three-phase loads should be balanced across the phases, and three-phase sites require a three-phase inverter or single-phase inverters designed to operate together.

For loads such as motors, pumps and compressors, current is not fully in phase with voltage. Such loads draw apparent power (kVA) greater than the real power (kW) they consume:

A 5 kVA inverter supplying loads with a power factor of 0.8 can deliver 5 × 0.8 = 4 kW.

3.4 Series and parallel connections

In series, the same current passes through each device in turn and each contributes its voltage. In parallel, each device is connected across the same two conductors and their currents combine.

PV modules (three identical modules, each Vmp 40 V, Imp 11 A):

Series connection is generally preferred because lower current reduces conductor size and I²R losses, subject to the inverter's voltage limits (unit 3.11).

Batteries (four identical 12 V, 200 Ah units):

Batteries connected together must be of the same type, capacity, age and condition.

3.5 PV modules

Irradiance and peak sun hours

Irradiance is the power of sunlight per unit area, in W/m²; full midday sun is approximately 1,000 W/m². Peak sun hours (PSH) express a day's total solar energy as the equivalent number of hours at 1,000 W/m². Typical values in Nigeria range from about 4 to 6.5 depending on location and season.

Datasheet parameters

Module ratings are stated at Standard Test Conditions (STC): 1,000 W/m² irradiance and 25 °C cell temperature.

Temperature effects

On Nigerian roofs, cell temperatures of 60–70 °C are common in full sun.

Example: high temperature. At 65 °C (40 °C above STC), power falls by 40 × 0.35% = 14%, giving approximately 550 × 0.86 = 473 W.

Example: low temperature. At 15 °C (10 °C below STC), Voc rises by 10 × 0.27% = 2.7%, to approximately 49.6 × 1.027 = 50.9 V.

High temperatures determine the minimum operating voltage of a string; low temperatures determine the maximum voltage the inverter must withstand (unit 3.11).

Shading, soiling and ageing

In a series string, all modules carry the same current, so a shaded module limits the string. Bypass diodes, typically three per module, allow current to pass around shaded cell groups; they reduce the loss and prevent overheating, but the output of the bypassed section is lost. Harmattan dust and bird droppings reduce output until modules are cleaned. Modules also degrade gradually, typically by about 0.4–0.7% per year. In Nigeria, modules generally face south at a tilt of at least 10–15° to allow rain to clean them.

3.6 Inverters and charge controllers

Most EcoStride systems are hybrid, reflecting the need for backup during grid outages.

A PWM charge controller connects the modules almost directly to the battery, holding them at battery voltage, well below their maximum power point. An MPPT controller converts the module voltage to the battery voltage while keeping the modules at their maximum power point.

Example. A module with Vmp 18 V and Imp 5.5 A (about 99 W) charges a 12 V battery at 13.5 V. With PWM, output is approximately 13.5 × 5.5 = 74 W. With MPPT, output is approximately 96 W after conversion losses.

3.7 Batteries

Cycle life depends strongly on depth of discharge and temperature; the manufacturer's data should be consulted. Lead-acid cells are 2 V (six per 12 V block). LFP cells are 3.2 V; a 16-cell battery has a nominal voltage of 51.2 V and is commonly described as "48 V".

Example. A 51.2 V, 100 Ah LFP battery at 90% depth of discharge supplies a 500 W load through an inverter of 92% efficiency.

1. Rated energy: 51.2 × 100 ÷ 1,000 = 5.12 kWh
2. Usable energy: 5.12 × 0.90 = 4.61 kWh
3. Delivered AC energy: 4.61 × 0.92 = 4.24 kWh
4. Runtime: 4.24 ÷ 0.5 = approximately 8.5 hours

The C-rate relates current to capacity: for a 100 Ah battery, 0.5C is 50 A. Maximum charge and discharge currents are stated on the datasheet. High temperature accelerates ageing; as a guide, a lead-acid battery operated at 35 °C rather than 25 °C may lose about half its service life.

The battery management system (BMS) of a lithium battery monitors cell voltages and temperatures, disconnects the battery outside safe limits, limits current, balances cells, estimates state of charge (SoC) and state of health (SoH), and communicates with the inverter.

3.8 System types

In a DC-coupled system, the PV array connects to the inverter's MPPT input and charges the battery on the DC side; this is the usual hybrid arrangement. In an AC-coupled system, a separate grid-tied PV inverter supplies AC, and a battery inverter charges the battery from AC.

3.9 Site assessment

In Nigeria the sun passes close to overhead, predominantly to the south, and is low in the east and west in the early morning and late afternoon. Obstructions above the array's horizon on the southern, eastern or western side will shade it at some time of day and should be recorded with photographs.

Many existing installations have missing earths, undersized cables, overloaded distribution boards or signs of overheating. Connecting a new system to an unsafe installation increases the hazard. Such defects must be recorded and reported as part of the assessment.

3.10 Load analysis

A bill of 300 kWh per month indicates average consumption of about 10 kWh per day. It does not show when energy is used, which loads operate together, which have starting surges, or which are essential during outages. Where supply is unreliable, it also reflects only the energy received, not the energy required.

Load table

The following example is a small shop open from 09:00 to 17:00.

Continuous power is the total of loads that may operate simultaneously: 705 W. Surge power is the continuous load with the largest motor at its starting power instead of its running power:

Motors, compressors and pumps typically draw 3 to 7 times their running power when starting. Where two motors may start simultaneously, both are included.

The customer should identify essential loads to be supplied during outages; these are normally connected to a separate backed-up distribution board and clearly labelled. Where appropriate, efficiency measures such as LED lighting, inverter-type appliances and scheduling heavy loads during daylight should be recommended to EcoStride.

3.11 System sizing

This worked example continues from unit 3.10: continuous load 705 W, surge 1,305 W, daily energy 6.04 kWh.

Step 1: Inverter

• Continuous rating with a 25% margin: 705 × 1.25 ≈ 0.9 kW
• Surge capability: at least 1.3 kW

A standard size providing capacity for future loads, such as a 3 kVA, 48 V hybrid inverter, would normally be selected.

Step 2: Battery

The customer requires the chiller to operate overnight and normal loads to run for 3 hours during a cloudy grid outage.

• Overnight chiller: 150 W × 16 h × 0.5 duty = 1.2 kWh
• Daytime loads without chiller: 555 W × 3 h = 1.67 kWh
• Energy required at the loads: 2.87 kWh
• Allowing for inverter efficiency (92%): 2.87 ÷ 0.92 = 3.12 kWh usable
• Allowing for depth of discharge (90%): 3.12 ÷ 0.90 = 3.47 kWh rated

A 51.2 V, 100 Ah LFP battery (5.12 kWh) meets the requirement with margin for ageing and growth.

Step 3: PV array

A performance factor of approximately 0.75 allows for temperature, soiling, cable and battery losses.

With 5 peak sun hours: 6.04 ÷ (5 × 0.75) ≈ 1.61 kWp, requiring at least three 550 W modules.

Step 4: String voltage

The inverter has an MPPT range of 120–450 V and a maximum PV input of 500 V. Using the module in unit 3.5, hot Vmp is approximately 41.9 × 0.86 = 36.0 V and cold Voc approximately 50.9 V per module.

The design therefore uses 4 modules (2.2 kWp). The voltage check increased the array size above the energy requirement, and the 10-module case shows that open-circuit voltage at low temperature, not operating voltage, sets the maximum string length. String current (Isc 14.0 A) must also be within the inverter's input current limit.

3.12 Cables and voltage drop

A cable's rated current-carrying capacity applies to reference conditions. High ambient temperatures (air beneath a roof sheet can greatly exceed 40 °C), grouping with other cables, and enclosure in conduit or insulation reduce it, in combination often by a third or more. Correction factors are given in manufacturers' tables and the applicable standards.

For DC and single-phase circuits, where current flows out and back:

where L is the one-way length (m), I the current (A), A the conductor cross-section (mm²) and ρ the resistivity of copper, approximately 0.0175 Ω·mm²/m at 20 °C.

Example 1: battery cable (48 V, 100 A, 3 m one way).

Undersized battery cables waste energy as heat and reduce the voltage at the inverter, which can cause false low-battery shutdowns under load.

Example 2: PV string cable (approximately 168 V, 13.13 A, 30 m one way).

Designers commonly limit DC voltage drop to about 1–3%. The overcurrent device must not exceed the derated capacity of the cable (Module 2, unit 2.9), and the conductor must suit the equipment terminals.

3.13 Equipment compatibility

A 16-cell LFP battery is 51.2 V nominal and operates between approximately 44.8 V and 57.6 V. A 48 V lead-acid bank charges at approximately 57–58 V and floats at approximately 54 V. Equipment described as "48 V" may therefore not be compatible.

Before equipment is approved, the following must be confirmed:

Equipment is not approved until every item has been confirmed.

Case studies

The following cases are based on situations commonly encountered on Nigerian sites. Names and places are illustrative.

Case 1: kVA and kWh confused. A customer in Owerri was told he had "a 5 kVA system" and expected it to supply his home overnight. The system had a 5 kVA inverter but a 2.4 kWh battery, which was exhausted by midnight. Principle: units 3.2 and 3.7.

Case 2: Motor starting. A hotel in Jos operated a 3 kW borehole pump from a 5 kVA inverter. The pump ran satisfactorily but tripped the inverter at every start, requiring approximately 12 kW momentarily. A soft starter resolved the problem. Principle: unit 3.10.

Case 3: Cold-morning overvoltage. Twelve modules with a datasheet Voc of 41 V (492 V in total) were connected to an inverter rated for 500 V maximum input. On a cold harmattan morning the string voltage exceeded 500 V and the inverter input was damaged. Principle: unit 3.11.

Relationship to performance rating

Practical activities

1. Prepare a load table for a home or small business and calculate continuous power, surge power and daily energy.
2. From a module datasheet, record Pmax, Vmp, Imp, Voc, Isc and the temperature coefficients, and calculate the output at 65 °C.
3. Using the same module and any hybrid inverter datasheet, determine the minimum and maximum number of modules per string.
4. Calculate the rated and usable energy of an installed battery and its runtime at 400 W.
5. Measure a cable route on site and calculate the voltage drop for two conductor sizes.
6. Record all potential sources of shading at a building.

Formulas

Glossary