# Short Circuit Algorithm Details This page provides detailed mathematical descriptions of the short circuit algorithms implemented in power-grid-model. For a summary and guidance, see [Calculations](../user_manual/calculations.md#short-circuit-calculation-algorithms). ## Short Circuit Equations In the short circuit calculation, the following equations are solved with border conditions of faults added as constraints. $$ I_N = Y_{bus}U_N $$ This gives the initial symmetrical short circuit current ($I_k^{\prime\prime}$) for a fault. This quantity is then used to derive almost all further calculations of short circuit studies applications. ```{note} Short-circuit calculations are currently implemented in the phase (abc) domain and therefore require a grounded network, similar to asymmetric power flow calculations. Note that this limitation does not exist in the sequence (0-1-2) domain but is present in the phase domain calculation. ``` ## IEC 60909 short circuit calculation Algorithm call: {py:class}`CalculationMethod.iec60909 ` The assumptions used for calculations in power-grid-model are aligned to the ones mentioned in [IEC 60909](https://webstore.iec.ch/publication/24100). - The state of the grid with respect to loads and generations are ignored for the short circuit calculation. (Note: Shunt admittances are included in calculation.) - The pre-fault voltage is considered in the calculation and is calculated based on the grid parameters and topology. (Excl. loads and generation) - The calculations are assumed to be time-independent. (Voltages are sine throughout with the fault occurring at a zero crossing of the voltage, the complexity of rotating machines and harmonics are neglected, etc.) - To account for the different operational conditions, a voltage scaling factor of `c` is applied to the voltage source while running short circuit calculation function. The factor `c` is determined by the nominal voltage of the node that the source is connected to and the API option to calculate the `minimum` or `maximum` short circuit currents. The table to derive `c` according to IEC 60909 is shown below. | Algorithm | c_max | c_min | | -------------- | ----- | ----- | | `U_nom` <= 1kV | 1.10 | 0.95 | | `U_nom` > 1kV | 1.10 | 1.00 | ```{note} In the IEC 609090 standard, there is a difference in `c` (for `U_nom` <= 1kV) for systems with a voltage tolerance of 6% and 10%. In power-grid-model we only use the value for a 10% voltage tolerance. ``` There are {py:class}`4 types ` of fault situations that can occur in the grid, along with the following possible combinations of the {py:class}`associated phases `: - Three-phase to ground: `abc` - Single phase to ground: `a`, `b`, `c` - Two phase: `ab`, `bc`, `ac` - Two phase to ground: `ab`, `bc`, `ac` ## Prefault voltages IEC 60909 prescribes use of rated voltage of the fault node on the Thevenin equivalent of the grid impedance for calculation of $I_k^{\prime\prime}$. This isolates the short circuit calculations from the actual loading conditions of the grid. PGM extends IEC 60909 to support simulation of multiple simultaneous faults for advanced use cases. Since IEC 60909 does not prescribe a method for this scenario, PGM deviates slightly from the standard to accommodate it. Prefault voltages and corresponding $I_k^{\prime\prime}$ deviate by an "equivalent transformation ratio" from all transformers. An example is shown below to demonstrate this effect. In the following grid, lets say we assumed the rated voltage of the source and fault node is $u_{rated-1}$ and $u_{rated-2}$ respectively. The transformer has a $u1$/$u2$ transformation ratio. Let $z_k$ and $z_t$ denote the source and transformer impedances, respectively. ```{tikz} :alt: transformer \draw (0,3) node[gridnode, anchor=east]{} to (1,3); \draw [black, ultra thick] (1,2) -- (1,4); \draw (1,3) to (2,3) [oosourcetrans] to (5,3); \draw [black, ultra thick] (5,2) -- (5,4); \draw[thick, ->] (5,1.4) +(0.05,0.5) -- +(-0.1,-0.1) -- +(0.1,0.1) -- +(0,-0.5); ``` IEC 60909 calculation should give $I_k^{\prime\prime} = \frac{u_{rated-2}}{ \sqrt{3} \cdot (z_k + z_t)}$ PGM calculates short circuit by setting source voltage as $u_{rated-1}$ instead. Hence $I_k^{\prime\prime} = \frac{u_{rated-1} \cdot k}{ \sqrt{3} \cdot (z_k + z_t)}$ where $k =\frac{u1 \cdot u_{rated-2}}{u2 \cdot u_{rated-1}} $ When the voltage rating of the transformer matches the rated voltage of the nodes, this factor is exactly `1.0`. In radial grids, it can be easily accumulated by multiplying the transformation ratios of all transformers ($k_{t1} \cdot k_{t2} \cdot k_{t3} ...$) along the fault path to the source. However, when multiple sources and meshed networks are involved, the calculation becomes complex. This factor is roughly `0.97` to `1.03` on a practical grid. An easy approach is then to simply leave a margin of ~`1.03` in the maximal short circuit current.