**2.Fuse Model**

The fuse model described in this article implements two modelling functions from SPICE derived circuit simulation software; analogue switches and analogue behavioural modelling (**ABM**). The analogue switch has an output resistance which is controlled by either an input current or voltage. For example, when the input voltage is above 1V the switch is on (low resistance), and when below 0V the switch is off (high resistance), with a transition region occurring when the input is between 0 and 1V. **ABM** can describe a circuits operation using equations or tables. For instance, an output current can be generated that is equal to an input current squared.

The fuse model, shown in Figure 2, comprises a current controlled switch **Wfuse**, a voltage controlled voltage source **Efuse**, a voltage controlled switch **Sfuse**, and a current controlled current source **Gfuse**. The model functions by generating a current in **Gfuse** that is equal to the fuse current squared **i**f², and using this current to charge the capacitor **Cfuse**. The voltage developed across **Cfuse** is proportional to **i**²t and is used to operate **Sfuse**. The switch **Wfuse** only allows current to charge **Cfuse** when the fuse current **i**f is above the fuse rated current **i**r. The voltage source **Efuse** operates as a non-linear resistor, modelling the rise in fuse resistance with current due to heating effects. The resistor **R**b models the affects of fuse thermal loss by dissipating the voltage across **Cfuse**. Resistor **R**a provides a current path for **Gfuse** when **Wfuse** is in an open state, and the RC network **R**c/**C**c provides a small time delay to ensure one-way operation of the switch **Sfuse**.

The model accurately represents the following four fuse characteristics: 1) rated current, under which the fuse will not operate; 2) pre-arcing **i**²t, after which time the fuse will start to operate by limiting current; 3) arcing **i**²t, after which time the fuse current has reduced to zero; and 4) resistance increase with current, which includes the affects of thermal loss. The expressions describing the fuse model are now presented and have been developed for the commercial software PSpice.

**Rated Current** : The current controlled switch **Wfuse** starts to turn on when the fuse current exceeds rated current **i**r, and is fully on when the fuse current reaches 110% of **i**r. The model expression for **Wfuse** is,

.model name iswitch(ION=1.1 **i**r , IOFF=**i**r )

**Pre-arcing i²t** : The voltage developed across **Cfuse** is,

By making the capacitor **Cfuse** value equal to (**i**²t)p, in A²s, the voltage developed across **Cfuse** at the end of the pre-arcing time is normalised to 1V. When the voltage across **Cfuse** reaches 1V the voltage controlled switch **Sfuse** starts to turn off, and is fully off when the voltage reaches 1.2V. The model expression for the switch **Sfuse** is,

.model name vswitch ( VON=1V VOFF=1.2V )

The **Rc/Cc** network introduces a small time delay to ensure one-way operation of the switch, and the delay can typically be minimised to an insignificant time of less than 0.1msec.

**Arcing i²t** : The time duration **t**a for the current to reduce to zero after the onset of arcing can be modelled by the turn-off characteristic of the switch **Sfuse**. Varying the transition range of the switch **Sfuse** controlling voltage (VOFF-VON) adjusts the arcing time **t**a and hence the arcing **i**²t, (i²t)a.

**Resistance Increase and Thermal Loss** : During the application of a fault current, the fuse resistance increases with current level as the temperature of the fuse element increases towards the melting point. The resistance increase and resulting voltage drop across the fuse can be substantial. If the fault current is reduced before the **i**²t level reaches the pre-arcing level (**i**²t)p , then the fuse element cools and resistance reduces back to the nominal resistance at ambient temperature **R**F.

The fuse resistance is modelled by a combination of the constant resistance of the switch Sfuse, and the non-linear resistance of the voltage source **Efuse**. The model expression for the switch **Sfuse** including resistance is,

.model name vswitch ( RON=**R**F VON=1V VOFF=1.2V)

The ABM model expression for the voltage source **Efuse** is,

Efuse <+node> value = { if * vCfuse * (Rf – RF)}

where **i**f is the fuse current, **v**Cfuse is the voltage across the capacitor **Cfuse**, and **R**f is a fuse parameter equal to the fuse resistance at the end of the pre-arcing time.

The thermal loss of the fuse element is modelled by the resistor **R**b, which discharges the voltage across capacitor **Cfuse**. Reducing the value of **R**b increases the thermal loss, returning the fuse to its pre-fault state in a faster time.

**Parameter Acquisition** : The parameters **i**r, (**i**²t)p, **t**p, **i**p, (**i**²t)a and **t**a are readily obtained from manufacturer’s data for the fuse operating in a circuit with a given time constant and prospective current.

The nominal resistance of the fuse **R**F at ambient temperature can be measured using a 4 terminal milliohm meter or measured in a suitable test circuit, as described in the next section. A measurement of the fuse resistance **R**f taken at the end of the pre-arcing time can be made using the test circuit described in the next section.

The inclusion of resistor **R**b in the model is optional, as it does not affect fuse operation during a fault leading to fuse operation in a short duration. The affect of **R**b is significant only for low levels of fault current or where repetitive fault currents occur with the individual fault level below (**i**²t)p.

**Circuit Breaker Adaptation** : The fuse model can be used without modification to represent the operation of circuit breakers, however certain circuit breaker characteristics can only be included by adapting the fuse model. For example, to include the characteristics of minimum operating time, and other special current-time responses, may require the use of **ABM** using a lookup table.