Current and Voltage Calculations

Cable Sizing

At first the main factor affected on the cables selected can estimated by the following factors:-

1- Load.

2- Voltage Drop.

3- Installation Condition.

4- Cable Length.

5- Short circuit current.

6- Running cost.

7- Mechanical hazard.

Plunging into calculations of cable size is of little value unless the type of cable and its method of installation are known .This, in turn, will depend on the installation's environment. At the same time, we would need to know whether the supply was single or three phases. Basically, There are eight steps to make the selection of underground cables cross sectional area as follows:

1- Determine the design current Ib.

2- Select the rating of the protection in.

3- Select the relevant correction factors (CFs).

4- Divide In by the relevant CFs to give tabulated cable current carrying capacity it.

5- Choose a cable size to suit it.

6- Check the voltage drop.

7- Check for shock risk constraints.

8- Check for thermal constrains.

Design Current:

In many instances the design current Ib is quoted by the manufacturer, but there are times when it has to be calculated.

In many instances the design current Ib is quoted by the manufacturer, but there are times when it has to be calculated. in that case there are two formulae involved, one for single-phase and one for three-phase

Single phase:



Three phase:





If an item of equipment has a power factor (PF) and has moving part, efficiency (eff) will have to be taken into account.

Hence:

Single phase:




Three phase:

(A) Nominal setting of protection

Nominal setting of the Having determined (Ib) we must now select the (Ib) protection such that (In) ,this protection current depend upon the future expandability and protect against fault which may occurs.

In = 1.25Ib

(B) Correction Factors

The common term in use when considering sizing conductors was derating factor even though at temperature below 30°c an increased rating can result. Now the term correction factor can be found in use only.

The factors specifically referred to in the regulation are:

Cg: Grouping factor.

Ca: ambient temperature factor.

Ct: thermal insulation factor.

(i) Ambient temperature factor Ca

The permitted operating temperature of the conductor varies according to the type of conductor insulation. Additionally, the current carrying capacity are based on an ambient temperature of 30%, so a higher ambient temperature will reduce the rate of flow of heat out of conductor, raising the conductor's operating temperature above the value permitted. This means that the current carrying capacity of the conductor has to be reduced to compensate for reduction in the heat lost from the conductor connection for ambient temperature is carried out using the following table:

Table: Ambient temperature (A)

Temp.	25	30	35	40	45	50	55	65	70
PVC cable	1.02	1	0.97	0.94	0.91	0.88	0.86	0.77	0.63
rubber	1.02	1	0.97	0.94	0.92	0.89	0.85	0.77	0.68

(ii) Grouping factor (Cg)

Where conductors are grouped together they interrelate with the heat dissipated from each other. This raise a conductor's operating temperature to a value that could exceed the permitted value. To ensure the operating temperature of the conductor with value not exceed the permitted value, the effective current carrying capacity of the conductor has to be reduction. This reduction is under taken by using correction factors. This factor is dependent upon how the conductors are installed & the number grouped together. The symbol used in the regulations for this factor Cg

Protection by BS 3036 fuses Cf

There are two type of fuses either high speed fuse or low speed.

In case of high speed fuses we can use a derating factor that equals one.

On the other hand for low speed fuses a derating factor that is equal to 0.725 shall be taken.

(iii) Thermal insulation (Ci)

The use of thermal insulation in buildings, in the forms of cavity wall filling, roof space blanketing, and so on. is now standard. Since the purpose of such materials is to limit the transfer of heat, they will clearly affect the ability of a cable to dissipate the heat build up within it when in contact with them.

Where a cable is buried in thermal insulation for 0.5 m (500 mm) or more, a derating factor of 0.5 is applied, which means that the current rating is halved.

Table: Derating factors (Ci) for cables up to 10mm² in cross-sectional

area buried in thermal insulation.

Length in insulation (mm)	Derating factor (CI)
50	0.89
100	0.81
200	0.68
400	0.55
500 or more	0.50

If a cable is totally surrounded by thermal insulation for only a short length (for example, where a cable passes through an insulated wall), the heating effect on the insulation will not be so great because heat will be conducted from the short high-temperature length through the cable conductor.

Clearly, the longer the length of cable enclosed in the insulation the greater will be the derating effect. Table ‎4‑2Table ‎2‑1 shows the derating factors for lengths in insulation of up to 400 mm and applies to cables having cross-sectional area up to 10 mm². The total correction factor will be the product of all previous factors.

C.F. =Ci×Cg×Ca

Voltage drop calculation:

(i) Voltage Drop of Cables

Voltage drop is normally important for cables of voltage rating 600/1000V or below.

The voltage drop within the installation should not exceed a value appropriate to safe functioning of the associated equipment in normal service.

The voltage drop is given in the regulation in the form mV/A/meter, based on the conductor working at the operational given in the current carrying capacity tables.

Values of voltage drop are tabulated for a current of ampere for one meter run, i.e. for a distance of 1 meter along the taken by the cables and represent the effect of the voltage drop in the entire circuit conductor.

And the used law for calculation will be:





Where:

Vd : the voltage drop in mille volts

I : rated current in amperes

L : cable length in meters

mv: approximate volt/ampere/meter

The voltage at the terminals of the equipment shall be such that the safe functioning of the equipment is not impaired. However, these requirements are to be satisfied if the voltage drop from the origin of the installation to the end of the final circuit does not exceed 4% of the declared nominal voltage.

i.e. (8.8 V for 220 V supply, & 15.2 V, for 380 V supply)

Calculation of short circuit current

The short circuit current can be calculated by thus relation.




Where

Is.c: the short circuit current

Vs: the phase source voltage.

Zt: the value of the total impedance from the source to the short circuit place.