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Wiring Unlimited

2. Theory

In this section:

You will get the most out of this book if you have knowledge of basic electrical theory. This will help you to understand the underlying factors that determine wiring thickness and fuse ratings. You might already have this basic understanding and can perhaps skip this chapter, but we highly recommend that you read this chapter.

2.1. Ohm's Law

Ohm’s law is the most important law of an electric circuit. It is the basis of almost all electrical calculations. It allows you to calculate the current that runs through a cable (or a fuse) at different voltages. Knowing how much current runs through a cable is essential knowledge to be able to choose the correct cable for your system. But first, some basic knowledge about electricity is needed.

What is electricity:

Electricity is the movement of electrons in a material, called a conductor. This movement creates an electric current. This current is measured in “Ampere” (amps for short) and the symbol is the letter A.

The force required to make the electrons flow is called voltage (or potential). It is measured in "Volt" and the symbol is the letter V (In Europe also referred to as U).

When an electrical current passes through a material, it meets a certain resistance. This resistance is measured in Ohm. The symbol is Ω.

Ohms_law_cartoon.png

How do voltage, current and resistance relate to each other:

  • When the resistance is low, many electrons move, and the current is high.

  • When the resistance is higher, fewer electrons move, and the current is lower.

  • When the resistance is very high, no electrons move at all, and the current has stopped.

Ohm's law:

You can say that the resistance of a conductor determines how much current runs through a material at a given voltage. This can be represented in a formula. The formula is called Ohm’s Law:

Ohms_law_formula.PNG

2.2. Power

Ohm’s law describes the relationship between resistance, current and voltage. But there is one more electrical unit that can be derived from Ohm’s law, and this is power.

Power is an expression of how much work an electric current can do. It is measured in Watts, and the symbol is P. It can be calculated using the following formula:

Power_formula.PNG

From Ohm’s law, other formulas can be derived as well. All possible formulas are listed in the below image. Please note that there are two symbols in use in the world that represent voltage. These are U or V.  

Ohmm_law_wheel.png

Some of these formulas are very useful when calculating the current in a cable. One often used formula is:

Current_law.PNG

This formula can calculate how much current runs through a cable when the voltage and the power are known.

An example of how this formula can be used:

Question:

  • If we have a 12V battery that is connected to a 2400W load. How much current is running through the cable?  

Answer:

  • V = 12V

  • P = 2400W

  • I = P/V = 2400/12 = 200A

Current_in_cable.png

The benefits of using power instead of current in calculations:

A big advantage of using power in calculations or for measurements is that power is independent of voltage. This is useful in systems where multiple voltages exist. An example of this would be a system with a DC battery, AC power and perhaps a solar panel with a different DC voltage than the battery.

Power remains the same across the different voltages. For example, if you run an AC load of 2400W via an inverter from a 12V battery, it will also take 2400W from the battery (ignoring the inverter inefficiencies).

Current_calculations_-_complete.png

2.3. Conductivity and resistance

Some materials conduct electricity better than other materials. Materials with a low resistance conduct electricity well, and materials with a high resistance conduct electricity poorly or not at all.

Metals have a low resistance, and they conduct electricity well. These materials are called conductors. This is the reason they are used as the core in electrical cables.  

Plastic or ceramics have a very high resistance; they do not conduct electricity at all. They are called insulators. This is why non-conductive materials, like plastic or rubber, are used on the outside of cables. You will not get an electrical shock when you touch the cable because electricity cannot travel through this material. Insulators are also used to prevent a short circuit should two cables touch each other.

Electron_flow.png

A: In a conductor, the electrons can move.

B: In an insulator, the electrons cannot move or move very slowly.

Each material has its own specific resistance. It is measured in Ohm meters (Ω.m). and the symbol is ρ (rho).

The conductivity of a material is inversely proportional to its resistance. It is represented by this formula: σ = 1/ρ. it is measured in Siemens per meter (S/m) meter, and its symbol is σ (sigma).

The table below lists various conductive materials, their electrical conductivity, and specific resistance. As shown, copper conducts electricity well and has a low resistance. As shown, copper is an excellent conductor with low resistance, which is why it is commonly used in electrical cables. In contrast, titanium has poor electrical conductivity and a higher specific resistance, making it less suitable as an electrical conductor.

Material

Electrical conductivity (10.E6 Siemens/m)

Electrical resistivity (10.E-8 Ohm.m)

Silver

62.1

1.6

Copper

58.5

1.7

Gold

44.2

2.3

Aluminium

36.9

2.7

Molybdenum

18.7

5.3

Zinc

16.6

6.0

Lithium

10.8

9.3

Brass

15.9

6.3

Nickel

14.3

7.0

Iron

10.1

9.9

Palladium

9.5

10.5

Platinum

9.3

10.8

Tungsten

8.9

11.2

Tin

8.7

11.5

Bronze

7.4

13.5

Carbon steel

5.9

16.9

Lead

4.7

21.3

Titanium

2.4

41.7

Two more factors determine cable resistance. These are the length and the thickness of the conductor (cable):

These factors relate in the following way:

  • A thin cable has a higher resistance than a thick cable of the same length.

  • A long cable has a higher resistance than a short cable of the same thickness.

The resistance of a length of cable can be calculated by the following formula:

Specific_resistance_fromula.PNG

As in the above formula, three factors determine cable resistance. Namely:

  • The electrical resistance of the material used.

  • The length of the cable, a longer cable equals more resistance.

  • The diameter of the cable, a thinner cable equals more resistance.  

It is important to know the resistance of a cable because when a current passes through a cable, the cable resistance is responsible for these two effects:

  • There will be a voltage drop (loss) over the cable length.   

  • The cable heats up.

If the current increases, these effects will worsen. An increased current will increase the voltage drop and the cable will heat up more.

An example of how to calculate the resistance of a cable:

Question:

  • What is the resistance of a 1.5-meter, 16mm² cable?  

Given:                                                                          

  • ρ copper = 1.7 x 10-8Ω/m

  • l = 1.5m

  • A = 16 mm2 = 16 x 10-6 m2

Answer:

  • R = ρ x I/A

  • R = 1.7 x 10 -8 x 1.5/(16 x 10-6)

  • R= 1.7 x 10-2 x 1.5/16

  • R = 0.16 x 10-2 = 1.6 x 10-3

  • R = 1.6mΩ

The effect of cable length:

Let’s use the previous example and calculate the resistance for a 5-meter cable. The result will be that the resistance is 5.3mΩ. If you increase the cable length, the resistance will increase.  

The effect of cable thickness:

Let’s take the original example and calculate the resistance for a cable with a cross-section of 2.5mm². The result will be that the resistance is 10.2mΩ. If you make the cable thinner, the resistance will increase.  

Conclusion:

Both cable thickness and cable length have a big impact on cable resistance.

2.4. Electrical insulation

Electrical insulators are used to prevent the flow of electrical current from one part of an electrical circuit to another and to protect people and equipment from electric shock.

As we saw in the table in the previous chapter, if a material does not conduct electricity well, it is called an insulator.

Examples of electrical insulators include rubber, plastic, glass, ceramics, and air. These materials are used in various electrical applications, such as insulation for wires, insulators for electrical equipment, and coatings for electrical components.

Electrical insulators play a critical role in ensuring the safe and efficient operation of electrical systems and in preventing electrical hazards.

As a rule of thumb, the higher the voltage, the thicker or better the insulation needs to be. This is why, for example, special cables are required to and from a high-voltage solar array.

Insulated cables and electrical tools are rated for a specific maximum voltage. Ensure that this voltage rating matches your application.

2.5. Connection resistance

Resistance in an electrical installation is not solely determined by the resistance of the cable, as the resistance of the electrical connections also contributes to the total resistance.

How is connection resistance created:

Whenever a connection is made between a cable and an appliance or between a cable and a cable terminal the resistance of the circuit increases. The degree of resistance is influenced by the quality of the connection and the size of the connecting area.

  • A tight connection will have less resistance than a loose connection.

  • A large connection area will have less resistance than a small connection area.

How to limit connection resistances:

  • Make tight and secure connections. Ensure that connectors are fastened correctly while not exceeding the maximum torque. For more information, see the Torque chapter.

  • In case of a nut or bolt connection, always add a washer and spring washer in the correct order, as indicated in the image on the right.

  • Correctly crimp cable terminals to a cable. Use an appropriate crimping tool and use a correctly sized cable terminal. For more information, see the Crimp terminals chapter:

MP-II_connection_of_battery_cables.png

Be aware that resistance will also create heat:

A poor connection with high resistance will generate excessive heat. The relationship between power, current, and resistance is described by the formula P = I²R. In extra-low voltage DC, even a small amount of resistance can result in a dangerous level of heat that can cause equipment and cables to become damaged, or even cause a fire in severe cases.

2.6. Torque

As described in the previous chapter, tight electrical connections are important, as loose connections will lead to resistance, heat, and potential corrosion due to arcing. However, be aware not to over-tighten these connections, as damage to the connector fastener might occur.

Electrical connection fasteners, screws or bolts are often made of tin-plated brass. It is a common misconception to assume that these fasteners are made of stainless steel with over-tightening and damage to the fastener as a result.

Always use a torque wrench (or torque screwdriver), so you know the bolt or screw is tightened correctly.

Note that our products have metric connection bolts. Commonly used threads are M4, M5, M6, M8, and M10. The recommended torque values in our documentation are listed in N.m (Newton meter).

Torque_screwdriver.jpg

Insulated torque screwdriver.

Torque_wrench.JPG

Insulated torque wrench.

How to correctly use a torque wrench

To use a torque wrench, follow these steps:

  1. Choose the correct torque setting as per the manual. The torque wrench should have a scale or dial that can be adjusted to the desired torque value.

  2. Place the torque wrench on the fastener (bolt, nut or screw).

  3. Use the torque wrench to apply force to the fastener, turning it until you reach the desired torque setting.

  4. The torque wrench will typically click or indicate when the desired torque setting has been reached. If a torque-checking device is available, double-check the torque value.

Notice

Note that it is important to follow the manufacturer's instructions and guidelines when using a torque wrench to ensure accuracy and prevent damage to the tool or the equipment being worked on.

The maximum torque for brass bolts can vary based on factors such as the type of brass, the size and length of the bolt, and the intended use. Generally, the maximum torque for brass bolts is lower than for steel bolts of the same size.

The product manual normally states the maximum torque moment for the electrical connections. But if this information is missing, use the below table for brass bolts, nuts or screws.

Maximum torque values for brass (H62) fasteners:

Thread

Maximum torque in N.m

Equivalent in lbf.ft

Equivalent in lbf.in

M2.5

0.6

0.4

5

M3

1

0.7

49

M4

2.9

2.1

26

M5

5

3.7

44

M6

6

4.4

53

M8

12

8.9

106

M10

24

17

212

M12

40

30

354

Notice

Note that these are rough estimates and may vary based on the specific application, so it is important to consult the product manual or engineering guidelines to determine the appropriate torque value. Over-torquing a bolt can lead to damage or failure of the bolt or the components being fastened.

2.7. Current, cable resistance and voltage drop

A low voltage results in a high current:

As already explained, the current that flows through an electrical circuit for a fixed load is different for a variety of circuit voltages. The higher the voltage, the lower the current will be.

Below is an overview of the amount of current that flows in three different circuits where the load is the same, but the battery voltage in each circuit is different:

Current_calculations_-_Battery_bank_voltages.png

Cable resistance creates a voltage drop over the cable:

Also, as explained already, a cable has a certain amount of resistance. The cable is part of the electrical circuit and can be treated as a resistor.

When current flows through a resistor, the resistor heats up. The same happens in a cable; when current flows through a cable, the cable heats up and, power is lost in the form of heat. These losses are called cable losses. The lost power can be calculated with the following formula:

Power_formula_2.PNG

Another effect of cable loss is that a voltage drop will be created over the length of the cable. The voltage drop can be calculated with the following formula:

Voltage_formula.PNG

The 1st and 2nd law of Kirchhoff:

To be able to calculate the effect of a cable voltage drop, you will need to know two more electric laws, namely the first and second law of Kirchhoff:

Kirchhoff's current law (1st law):

The current flowing into a junction must be equal to the current flowing out of it.

An example of this is a parallel circuit. The voltage over each resistor is the same while the sum of current flowing through each resistor equals the overall current.

Current_calculations_-_paralell_circuit.png

Kirchhoff's voltage law (2nd law):

The sum of all voltages around any closed loop in a circuit must equal zero.

Here the exact opposite is the case. In a series circuit, the current through each resistor is the same, while the sum of the voltages over each resistor equals the overall voltage.

Current_calculations_-_series_circuit.png

Voltage drop calculation example:

Now, let’s use a real-world example of an inverter that is connected to a 12V battery and calculate the cable losses. In the circuit diagram on the right, you find a 2400W inverter connected to a 12V battery using two 1.5-meter-long, 16 mm2 cables.

As we calculated earlier, each cable has a resistance of 1.6mΩ. Knowing this, we can now calculate the voltage drop over one cable:

  • A 2400W load at 12V creates a current of 200A.

  • The voltage drop over one cable is: V = I x R = 200 x 0.0016 = 0.32V.

  • Since there are two cables, the positive and the negative cable, the total voltage loss in this system is 0.64V.

  • Because of the 0.64V voltage drop, the inverter does not get 12V anymore, but 12 - 0.64 = 11.36V.

Cable_resistance_-_Simple.png

The power of the inverter is constant in this circuit. So, when the voltage to the inverter drops, the current will increase. Remember I = P/V.

The battery will now deliver more current to compensate for the losses. This means, in the earlier example, that the current will increase to 210A.

This makes the system inefficient because we now have lost 5% (0.64/12) of the total energy. This lost energy has been turned into heat.

voltage_drop_circuit.png

How to reduce voltage drop:

It is important to keep the voltage drop as low as possible. The obvious way to do that is to increase the thickness of the cable or to keep the cable length as short as possible. But there is something else you can do. This is to increase the voltage of the electric circuit. The cable voltage drop varies for different battery (system) voltages. Generally speaking, the higher the voltage of the circuit, the lower the voltage drop will be.  

Example:

If we look at the same 2400W load, but now the system voltage is 24 or 48V:  

  • The 2400W load at 24V will create a current of 2400/24 = 100A.

  • The total voltage drop will be 2 x 100 x 0.0016 = 0.32V (= 1.3%).  

  • And at 48V the current will be 50A. The voltage drop is 0.16V (= 0.3%).

voltage_drop_circuits.png

How much voltage drop is allowed?

This leads to the next question; how much voltage drop is allowed? The opinions vary somewhat, but we advise aiming for a voltage drop no bigger than 2.5%. This is indicated in the below table for the different voltages:

System voltage

Percentage

Voltage drop

12V

2.5%

0.3V

24V

2.5%

0.6V

48V

2.5%

1.2V

Not just the cable resistance, but other factors create resistance as well:

It is important to realise that resistance does not only occur in the cable itself. Additional resistance is created by any items in the path the current has to flow through.

A list of possible items that can add to the total resistance:

  • Cable length and thickness.

  • Fuses.  

  • Shunts. 

  • Switches or circuit breakers.

  • The quality and suitability of the cable terminals and how well they have been crimped to the cable. 

  • The quality and tightness of all electrical connections.

And especially watch out for:

  • Loose connections.

  • Dirty or corroded contacts.

  • Bad cable lug crimps.

Resistance will be added to the electrical circuit each time a connection is made, or if something is placed in the path between the battery and the inverter.

A list of possible items that can add to the total resistance:

  • Each cable connection: 0.06mΩ.

  • A 500A shunt: 0.10mΩ.

  • A 150A fuse: 0.35mΩ.

  • A 2-meter 35mm² cable: 1.08mΩ.

Cable_resistance_schematic.PNG

2.8. The negative effects of cable voltage drop

We now know what we need to do to keep resistance in a circuit low in order to prevent a voltage drop. But what are the negative effects if there is a high voltage drop in a system?

These are the negative effects of a high voltage drop:

  • Energy is lost, and the system is less efficient. Batteries will be discharged quicker.

  • The system current will increase. This can lead to DC fuses blowing.

  • High system currents can lead to premature inverter overloads.

  • Voltage drop during charging will cause batteries to be undercharged.

  • The inverter receives a lower battery voltage. This can potentially trigger low-voltage alarms.

  • The battery cables heat up. This can cause melting wiring insulation or cause damage to the cable conduits or to the connected equipment. In extreme cases, cable heating can cause a fire.

  • All the equipment that is connected to the system will have a reduced lifetime.

This is how to prevent voltage losses:

  • Keep cables as short as possible.

  • Use cables with sufficient cable thickness.

  • Make tight connections, but not too tight. Follow the torque recommendations in the manual.

  • Check that all contacts are clean and not corroded.

  • Use quality cable lugs and crimp these with the appropriate tool.

  • Use quality battery isolation switches.

  • Reduce the number of connections within a cable run.

  • Use DC distribution points or busbars.

  • Follow wiring legislation.

It is good practice to measure the system voltage drop once you have completed an electrical installation that contains batteries. Remember that a voltage drop typically occurs during a high current event. The voltage drop becomes larger when the current increases. This is the case when an inverter is loaded with maximum load or when a battery charger is charging at full current.

How to measure voltage drop, for example, in a system with an inverter:

  • Load the inverter with maximum power.

  • Measure the voltage across the negative cable between the inverter connection and the battery pole.

  • Repeat this for the positive cable.

Measure_voltage_drop_A.png

How to measure voltage drop when the battery is too far away or in a different room or enclosure:

  •  Load the inverter with maximum power.

  • Measure the voltage across the DC connections inside the inverter.

  • Measure the voltage across the battery poles

  • Compare these readings. The difference between the two readings is the voltage drop.

Measure_voltage_drop_B.png

2.9. Ripple voltage

One of the negative effects of a high voltage drop in a system is ripple.

Ripple occurs in systems with an inverter:

Ripple appears in a system where the power source is a battery (DC) and the load is an AC device. This is always the case in a system with an inverter. The inverter connects to batteries, but it powers an AC load.

inverter_connected_to_battery.png

Voltage drop is the mechanism behind ripple:

The mechanism that causes ripple is directly related to the voltage drop over the DC cables when a system is under load, and the battery currents are high. A high current causes a high voltage drop, this becomes particularly exaggerated when thin cables have been used.

The voltage drop in a system as a whole can be even bigger, especially if lead acid batteries are used that are too small, too old or damaged. The voltage drop will not only occur over the cables but also within the battery itself.   Ripple is related to the phenomenon that when an inverter is powering a large load, the system DC voltage drops. But the system voltage recovers once the load has been turned off.  This process is depicted in the below image.

  1. The voltage measured at the inverter is normal. In this example it is 12.6V.

  2. When a large load is turned on, the battery voltage drops to 11.5V

  3. When the load is turned off, the battery voltage usually recovers back to 12.6V

Voltage_drop_basics.png

How is ripple created?

The following steps follow the sequence of how ripple is created:

1. The inverter converts a DC voltage into an AC voltage.

Ripple_step_1.png

2. The load connected to the inverter creates an AC current in the inverter.

Ripple_step_2.png

3. This AC current causes (via the inverter) a fluctuating DC current on the battery.

Ripple_step_3.png

4. The result of this fluctuating DC current is the following:

  • When the DC current peaks the battery voltage will drop.

  • When the DC current drops the battery voltage recovers

  • When the DC current peaks the battery voltage will drop again.

  • And so on and so forth.

Ripple_step_4.png

The DC voltage will keep going up and down and is not constant anymore. It now is fluctuating. It will go up and down 100 times per second (100Hz). The amount the DC voltage is fluctuating is called ripple voltage.

Ripple_graph.png

How to measure ripple:

When measuring ripple, remember that this only occurs when the system is under full load. Ripple can only be detected when the inverter is powering a full load or when a charger is charging at a high current. The same applies when measuring the voltage drop,

Ripple can be measured in these two ways:

  • Use a multimeter. Select AC mode on the multimeter. Measure across the inverter’s DC connections. You are now measuring the AC component of the DC voltage. This AC voltage is the ripple voltage.

  • Use VEConfigure, it keeps track of ripple.

Ripple_measurement.PNG

The negative impacts of ripple:

A small amount of ripple can exist with no measurable impact. However, excessive ripple can have a negative impact.

The negative impact of excessive ripple:

  • The lifetime of the inverter will be reduced. The capacitors in the inverter will try to flatten the ripple as much as possible and as a result, the capacitors will age faster.

  • The lifetime of the other DC equipment in the system will be reduced as well. They too suffer from ripple in the same way inverters do.

  • The batteries will age prematurely. Each ripple acts as a mini cycle for the battery and the battery lifetime will reduce due to the increase in the number of battery cycles.

  • Ripple during charging will reduce the charge power. It will take longer for the batteries to charge.

Ripple alarms:

Inverters or inverter/chargers have a built-in ripple alarm. There are two ripple alarm levels:

  • Ripple pre-alarm: Both the overload and the low battery LEDs blink and the unit will turn off after 20 minutes.

  • Full ripple alarm:  Both the overload and low battery LEDs are on and the unit powers down.

These are the ripple alarm levels for inverter/charger models at the different DC voltages and the MultiPlus Compact regardless of voltage:

System voltage

Ripple pre-alarm (20 min) *

Ripple full alarm (3 sec) *

Charge regulation

12V

1.50V

2.50

1.4

24V

2.25V

3.75

2.1

48V

3.00V

5.00

2.8

MultiPlus Compact only (regardless of DC voltage)

1.50V

2.5V

0.8V

*) All voltages are RMS voltages.

How to fix ripple:

Ripple will only occur when there is a voltage drop in a system. To fix ripple voltage issues, you will have to reduce the voltage drop. This means that you have to reduce the resistance in the path from the battery to the inverter and back to the battery. For more information, see the Current, cable resistance and voltage drop chapter.  

To fix high ripple in a system do the following:  

  • Reduce long battery cables

  • Use thicker cables.

  • Check fuses, shunts and battery isolation switches for connectivity.

  • Check the specifications of the fuses, shunts and battery isolation switches.

  • Check for loose terminals and loose cable connections.

  • Check for dirty or corroded connections. 

  • Check for bad, old or too small batteries.

  • Always use good quality system components.

Cable_resistance_-_Complex_.png