# Dynamic Braking Resistors

## General Dynamic Braking Resistors

Case resistors are mostly used for overload operation, such as precharge of capacitors, dynamic braking of VFD, crowbar operations.

We can distinguish between 3 typical overload conditions: one is the isolated single pulse (emergency braking, precharge in case of short circuit or abnormal duty), the second one is the cyclic work load (i.e. braking of a lift), and the third one is a long overload (i.e. due to a fault in the system).

In all 3 cases, we can state that for pulses of duration less than 30 s, the mass of the wire must be taken in account to define the admissible overload. The mass of the wire depends on the ohmic value.

Unless the pulse is very short (<0,5 s), the mass of the quartzite sand inside, plays an important role for the calculation of the global thermal capacity. The longer is the duration of pulse, the higher is the multiplier of the thermal capacity of the wire.equation:

## Constructive Characteristics

Fairfild’s dynamic braking resistors are made in three different ways:

wire wound on mica plates, not filled and not sealed (RFX)

wire wound on mica plates, filled with quartzite sand and sealed (RFD, RFK, RFH, RFP)

wire coiled as a spring and put inside a ceramic filled with quartzite sand and sealed (RFZ/C, RAF, RDF)

## Thermal characteristics Transient

Thermal constant is higher in filled resistors, since there are more components than in not-filled ones, so total thermal capacity is higher. Thus, transient thermal dynamics are faster on not-filled ones: for example, if two different resistors are supplied by duty cycle, the gap between the highest and the lowest temperature of the wire is higher in not-filled ones. Meanwhile, average temperature is lower (see the following graph).

Considering two different resistors, with the same dimensions and the same working conditions, useful life is almost the same, since in the two cases thermal stresses on the wire are equivalent. We may state that the two effects (higher oscillations of temperature in not-filled ones, higher average temperature in filled ones) compensate each other. The average temperature on the external case is approximately the same (oscillations larger in the not-filled ones).

## Steady State

In steady state condition, the rated power of a resistor depends essentially on the external surface for heat transfer with the ambient.

The with the ambient are convection (forced or natural) and radiation. Since the power transferred from a surface to the ambient depends quite linearly on temperature for convection mode and on the fourth power (math) of absolute temperature (Kelvin) for radiation mode, we can state that if surface temperature is not very high, convection mode is predominant; meanwhile, if surface reaches high temperatures, the rate of power transferred to the ambient by radiation prevails on the rate of power transferred by convection. That can easily explain why in graphs reporting the relationship between temperature and power the gradient decreases with power (see the following graph).

Obviously, the rate of power dissipated by means of radiation is strongly related to the emissivity of radiating surface (black surfaces are very emissive; oxidation increases emissivity; polished surfaces have low emissivity).

However, the using case temperature , to select a resistor, is not enough. Actually, when the diameter of the wire is very thin (high ohmic values), thermal constant of the wire is very low, so the temperature increases very quickly: the resistor might not reach steady state, since it might reach melting point before. Also thicker windings have higher mechanical stresses and are not able to dissipate as much energy by conduction as thinner wires because their surface area is low. Therefore there is a defined maximum current density for thick )low resistance windings).

## Pulses

Electrical pulses can be adiabatic (Not gaining or losing heat to the surroundings) or non-adiabatic.

Generally, we define a pulse as adiabatic when its duration is less than 0.5secs.

Obviously, adiabatic is an ideal condition, but it can properly approximate reality if the duration of the pulse is so quick that active mass (wire) cannot transfer its own heat, generated by Joule effect, to its coating (for filled resistors), or to the external case (for not-filled resistors). Thus, energy absorbable is proportional to the active mass (m), to its specific heat (cp) and to the max variation of temperature required (ΔT).

When the duration of the pulse is not so fast, we cannot idealize the condition as adiabatic. In this situation, a certain percentage of the energy given to the active mass, after the pulse, has already transferred to its coating or/and to the external case. So, we can state that the adiabatic approximation is as conservative as long the duration of the pulse is.

The shorter a pulse is, the more closely it approximates to adiabatic.

In every Fairfild DBR datasheet is given the appropriate graph to find the relationship between max absorbable energy for a single pulse (all using 500°C of temperature rise of the resistance element), and ohmic value. As a general rule by increasing ohmic value, absorbable energy decreases, since active mass decreases. While we can obtain the same ohmic value (on the same model) by several diameter values, in our calculations we maximize the mass of the wire (i.e. its diameter), to absorb the max available energy.

## Duty Cycle

With this working condition, it is possible to supply the resistor with a higher power than rated nominal power: that is related to duty cycle ratio (i.e. the ratio between the duration of voltage pulse (Ton) and the duration of the cycle (T)).

Of course, there are some restrictions about increasing applied power respect to the rated nominal power: for example, the duration of the cycle cannot exceed a certain value, i.e. the duration of the cycle cannot be too high, or the wire would overheat and break before the resistor reaches the periodic steady state condition.

Main formulas for duty cycle calculations

When the resistor is supplied with duty cycle power, after a certain time it will reach the periodic steady state condition. Thus, we can usefully consider the following formulas:

(2.1)

(2.2)

where:

(2.3)

P = pulse power

h = film coefficient (considering only convection heat transfer, or, in general, considering heat transfer as proportional to the difference of temperature between external surface an the ambient)

A = area of the external surface

ton = duration of the pulse power

T = duration of the cycle