Advices how to calculate the power loss inside the LV switchboard

Power loss and heat dissipation

In order to give the necessary indications on the methods intended to calculate power loss and improve the current carrying capacity of the circuit breakers inside LV switchboard, first of all it is necessary to analyze an assembly from a thermodynamic point of view.

A switchboard can be considered as an enclosure housing a series of elements generating heat and able to dissipate heat towards the outside.

The elements generating heat inside the enclosure exchange heat between them (conduction), with the air inside the switchboard (convection) and with the walls of the switchboard itself (radiation) as shown in Figure 1 below.

In its turn, the enclosure exchanges heat towards the external environment. Also this heat exchange occurs by conduction (through the cables connected to the assembly), convection and radiation, as shown in Figure 2 below.

In enclosures with a degree of protection not very high or with ventilation openings, part of the heat is exchanged through a real air circulation between the assembly and the external environment.

All these phenomena of circulation and exchange of internal and external air, together with the structure of the enclosure, affect temperature at each point of the enclosure itself and of each component installed inside it.

These elements are:

• The power loss inside the switchboard (explained below in details)
• The dissipation of the heat produced inside the enclosure (will be explained in 2nd part)
• the dissipation of the heat produced by the terminals (will be explained in 2nd part)

Power loss inside the switchboard

As known, a modification of the temperature may be caused by a power loss due to the current flow. Now, the different components which constitute the main power sources and which consequently represent also heat sources inside a switchboard shall be considered in detail, together with the measures to be taken in order to reduce the power loss and limit its effects.
These elements are:

1. Internal structure
2. Typology of the circuit breaker installed
3. Cross-sectional area of the internal conductors of the switchboard and
4. Current paths

1. Internal structure

The material used to realize structure and partitions inside switchboards is often ferromagnetic and conductive. If the system structure is such as to create a closed configuration embracing the conductors, Joule-effect losses due to eddy currents and hysteresis losses are induced, with consequent local heating of remarkable importance. The same phenomenon occurs in the bus ducts between the enclosure and the conductor bars.
As an example to illustrate the influence of this phenomenon, Table 1 shows the percentage value representing the part of losses developing inside the enclosure related to the power loss inside the conductor bars.

Table 1 – Percentage value representing the part of losses developing inside the enclosure related to the power loss inside the conductor bars

From these data, it results that the increase of the rated current and consequently the number of busbars in parallel per phase and the material used for the separation of the conductor bars may considerably affect heating.

In fact, if a ferromagnetic ring embraces all the three conductors of a three-phase system, as Figure 3 shows (or all the four conductors in a system with the neutral conductor), the sum of the currents shall result into null induction.
On the contrary, if each conductor is enclosed by a single ring (Figure 3a), the total induction is not null, with the consequent circulation of induced current, power loss and therefore heat generation.

LEFT: Figure 3 – Ferromagnetic ring embraces all the three conductors of a three-phase system; RIGHT: Figure 3a – Each conductor is enclosed by a single ring

Also the mechanical fixing of conductors could cause this inconvenient. Therefore it is important that the formation of close rings is prevented by the insertion of insulators or anchor clamps made of a magnetic and/or insulating material (see Figure 4).

Figure 4 – Mechanical fixing of conductors

2. Typology of the circuit breaker installed

Circuit breakers are components of switchboards which cannot be disregarded when calculating total power loss.
To make this evaluation easier, if we take an example of ABB’s tables which are reported below and refer to MCCBs – molded case circuit breakers of their Tmax series and air circuit breakers type Emax.

As we’re not going into details of these tables (you can check it on your own), the power loss of the same circuit breaker varies depending both on its version as well as on the type of protective release installed!

Taking reference to these two variables, it is possible to observe that :

• The power losses of withdrawable circuit breakers are higher than those of the fixed ones
• The power losses of the circuit breakers equipped with thermo-magnetic releases are higher than those of the circuit breakers with electronic releases.

The difference between the power loss of a circuit breaker in three-pole version compared with a four-pole version is not considered, since in a normal circuit the current flowing in the neutral conductor is assumed to be null.

3. Cross-section of the conductors within switchboards

In primary distribution switchboards, the power loss of the connection systems (busbars or cables) is usually from 20% to 40% of the total power loss of the switchboard.
The Std. IEC/TR 60890 includes a series of tables which give the power loss of cables and busbars inside switchboards per unit length, making reference to the current carrying capacity. By applying these tables (here defined as Tables 3, 4 and 5) it is possible to point out how a reduction in the power loss corresponds to an increased cross-section.
In addition, it is important to remark how the cables entering the enclosure give a contribution not negligible to power loss, whereas they are often not considered since they are not “strictly” part of the switchboard.

Table 2 – Operating current and power losses of insulated conductors and conductors for auxiliary circuits

Table 2 – Operating current and power losses of insulated conductors and conductors for auxiliary circuits

1) Any arrangement desired with the values specified referring to six cores in a multi-core bundle with a simultaneous load 100%
2) single length

Table 3 – Operating current and power losses of bare conductors, in vertical arrangement, without direct connections to the apparatus

Table 3 – Operating current and power losses of bare conductors, in vertical arrangement, without direct connections to the apparatus

*) one conductor per phase
**) two conductors per phase
1) single length

Table 4 – Operating current and power losses of bare conductors used as connections between the apparatus and the main busbars

Calculation the total power loss inside the switchboard

This example has the purpose of evaluating as first approximation – the total power loss inside the switchboard of which Figure 5 shows the arrangement of the components, the dimensions, the structure and the relevant single- wire diagram.

Figure 5 – Arrangement of the switchboard components

The components which form the switchboard are circuit breakers, busbars and cables. The power loss is calculated for each component and then the total power loss is determined.

Circuit breakers

As regards circuit breakers, the power loss can be determined on the basis of the dissipated power “Pn ” at the rated current “In_CB” referred to the current which really flows through the circuit breaker “Ib” – full load current of the circuit.
The formula linking these three quantities is the following :
P_CB = Pn_CB × (Ib / In_CB)²
Then, according to the type of apparatus installed inside the switchboard, the contribution to the load current in terms of power loss of the individual circuit breaker and the total power loss are reported in the following table:

Tabl

e 5 – Total power loss of the circuit breakers [W]

Busbars

As regards main busbars, distribution busbars and the busbars connecting circuit breakers and cables, the effective power loss can be determined from the dissipated powers, at the nominal current and per unit length, as shown in the previous Tables 3 and 4.
The formula to relate the data in the table to the characteristics (load current and length) of the busbars installed in the switchboard is the following:
P_SB = Pn_SB (Ib / In_SB)² × 3 × L_SB
Therefore, with reference to the typology, the length “L” and the load current of the busbars installed inside the switchboard, the contribution in terms of power loss of the single length and the total power loss are reported in Table 6 below:

Table 6 – Total power loss of the connection busbars [W]

Cables

As regards cables, taking reference to Table 3 above, the same method used for the busbars can be applied and the relevant results are reported in Table 7.

T

able 7 – Total power loss of the connection busbars [W]

Then, the total power dissipated inside the switchboard is given by the sum of the three contributions already determined above, therefore:
P_TQ = 234 + 68 + 332 = 784 W
It is important to note how the total power loss would be equal to 452W and therefore the estimated temperature would be much lower than the effective one if the cable contribution (332W) were not taken into account.

4. Paths of the current

The positioning of apparatus and conductors may result into a different power loss inside the switchboard. It is a good rule to position the circuit breakers as shown in Figure 5, so that the paths of the highest currents are as short as possible.

Thus, contrary to what occurs in a type of installation as that of Figure 5a, the dissipated power inside the switchboard is reduced and unquestionable advantages from the thermal point of view are achieved.

LEFT: Figure 6 – Suggested positioning: The highest current (500 A) flows through the shortest path; RIGHT: NOT suggested positioning: The highest current (500 A) flows through the longest path

In case of switchboards with many columns, whenever possible, it is advisable that the main circuit breaker is installed in the middle column or, however, in barycentric position with respect to the load distribution, as shown in Figure 6.
Thus, by dividing the current into the two branches of the switchboard busbar system, a remarkable reduction in the power loss is obtained with the same cross-section – in comparison with a configuration having the incoming feeder at both ends of the switchboard as in Figure 6a, which is a solution implying the circulation of highest currents.

LEFT: Figure 6 – Main circuit breaker is installed in the middle column; RIGHT: Dividing the current into the two branches of the switchboard busbar system

Reference // ABB circuit breakers inside LV switchboards – Technical application paper