voltage_source.rst

Voltage Source Elements

Voltage source elements are represented by their internal voltage source with an internal resistance Z_k:

since the voltage source is moved to the fault location for with methodology of the equivalent voltage source, the bus elements can be reduced to a single shunt impedance:

The contribution of loads and shunts are negligible according to the standard and therefore neglected in the short-circuit calculation.

External Grid

When calculating maximum short-circuit currents, the impedance of an external grid connection is given as:

$$\begin{aligned} z_{k, eg} =& \frac{c_{max}}{s\_sc\_max\_mva} \\[1em] x_{k, eg} =& \frac{z_{sg}}{\sqrt{1 + rx\_max^2}} \\[1em] r_{k, eg} =& rx\_max \cdot x_{sg} \end{aligned}$$

where rx_max and s_sc_max_mva are parameters in the ext_grid table and c_max is the voltage correction factor <c> of the external grid bus.

In case of minimal short-circuit currents, the impedance is calculated accordingly:

$$\begin{aligned} z_{k, eg} =& \frac{c_{min}}{s\_sc\_min\_mva} \\[1em] x_{k, eg} =& \frac{z_{sg}}{\sqrt{1 + rx\_min^2}} \\[1em] r_{k, eg} =& rx\_min \cdot x_{sg} \end{aligned}$$

Asynchronous Motor

Asynchronous motors can be considered by setting the type variable of an sgen element to "motor". The internal impedance is then calculated as:

$$\begin{aligned} Z_{k, m} = \frac{1}{k} \cdot \frac{vn\_kv^2 \cdot 1000}{sn\_kva} \\\ X_{k, m} = \frac{Z_{sg}}{\sqrt{1 + rx^2}} \\\ R_{k, m} = rx \cdot X_{sg} \end{aligned}$$

where sn_kva is the rated power of the motor, k is the ratio of nominal to short circuit current and rx is the R/X ratio of the motor. vn_kv is the rated voltage of the bus the motor is connected to.

Synchronous Generator

Synchronous generators are considered with the short-circuit impedance of:

$$\underline{Z}_{k, gen} = K_G \cdot (R''_d + jX''_d)$$

The short-circuit impedance is calculated as:

z_k = xdss

The generator correction factor K_G is given as:

$$K_G = \frac{V_{N, gen}}{V_{N, bus}} \cdot \frac{c_{max}}{1 + x_{dss} \cdot sin(\varphi)}$$

where V_N, bus is the rated voltage of the bus the generator is connected to and V_N, gen is the rated voltage of the generator which is defined by the parameter sn_kva in the gen table. The rated phasor angle φ is given as:

φ = arcos(cos_phi)

where cos_phi is defined in the gen table.