Fault Models

This document describes the fault data models, and their mathematical formulations.

Transmission

This section describes the data model for faults under the transmission schema, i.e. when using solve_fault_study.

Name	Default	Type	Used	Description
`fault_bus`		`String`	always	id of bus connection
`g`		`Real`	always	Fault conductance
`b`	`0.0`	`Real`	always	Fault susceptance
`status`	`1`	`Int`	always	`1` or `0`. Indicates if component is enabled or disabled, respectively
`fault_type`		`String`		Metadata field that helps users quickly identify type of fault `\in ["lg", "ll", "llg", "3p", "3pg"]`

Distribution

This section describes the data models for the distribution

`ENGINEERING` data model (user-facing)

Name	Default	Type	Units	Used	Description
`bus`		`String`		always	id of bus connection
`connections`		`Vector{Int}`		always	Ordered list of connected conductors, `size=nconductors`
`g`		`Matrix{Real}`	Siemens	always	Fault conductance matrix, `size=(nconductors,nconductors)`
`b`	`zeros(nconductors,nconductors)`	`Matrix{Real}`	Siemens	always	Fault susceptance matrix, `size=(nconductors,nconductors)`
`status`	`ENABLED`	`Status`		always	`ENABLED` or `DISABLED`. Indicates if component is enabled or disabled, respectively
`fault_type`		`String`			Metadata field that helps users quickly identify type of fault `\in ["lg", "ll", "llg", "3p", "3pg"]`

`MATHEMATICAL` data model (internal)

Name	Default	Type	Units	Used	Description
`fault_bus`		`Int`		always	id of bus connection
`connections`		`Vector{Int}`		always	Ordered list of connected conductors, `size=nconductors`
`g`		`Matrix{Real}`	per-unit	always	Fault conductance matrix, `size=(nconductors,nconductors)`
`b`	`zeros(nconductors,nconductors)`	`Matrix{Real}`	per-unit	always	Fault susceptance matrix, `size=(nconductors,nconductors)`
`status`	`1`	`Int`		always	`1` or `0`. Indicates if component is enabled or disabled, respectively

Connections connections: [1,0] Fault admittance matrix g: $ \begin{bmatrix} gf & -gf \ -gf & gf \end{bmatrix} $ Fault admittance matrix b: $ \begin{bmatrix} bf & -bf \ -bf & bf \end{bmatrix} $

Line-Neutral (Ungrounded Neutral, Phase A)

Connections connections: [1,4] Fault admittance matrix g: $ \begin{bmatrix} gf & -gf \ -gf & gf \end{bmatrix} $ Fault admittance matrix b: $ \begin{bmatrix} bf & -bf \ -bf & bf \end{bmatrix} $

Line-Line (Phase A-B)

Line-Line-Ground (Phase A-B)

Connections connections: [1,2,0] Fault admittance matrix g: $ \begin{bmatrix} g{pg} + g{pp} & -g{pp} & -g{pg} \ -g{pp} & g{pg} + g{pp} & -g{pg} \ -g{pg} & -g{pg} & 2g{pg} \ \end{bmatrix} $ Fault admittance matrix b: $ \begin{bmatrix} b{pg} + b{pp} & -b{pp} & -b{pg} \ -b{pp} & b{pg} + b{pp} & -b{pg} \ -b{pg} & -b{pg} & 2b{pg} \ \end{bmatrix} $

Three-Phase Ungrounded

Connections connections: [1,2,3] Fault admittance matrix g: $ 3 \begin{bmatrix} 2gf & -gf & -gf\ -gf & 2gf & -gf \ -gf & -gf & 2gf\ \end{bmatrix} $ Fault admittance matrix b: $ 3 \begin{bmatrix} 2bf & -bf & -bf\ -bf & 2bf & -bf \ -bf & -bf & 2bf\ \end{bmatrix} $

Three-Phase Grounded

Connections connections: [1,2,3,0] Fault admittance matrix g: $ \begin{bmatrix} g{pg} + 2g{pp} & -g{pp} & -g{pp} & -g{pg} \ -g{pp} & g{pg} + 2g{pp} & -g{pg} & -g{pg} \ -g{pp} & -g{pp} & g{pg} + 2g{pp} & -g{pg} \ -g{pg} & -g{pg} & -g{pg} & 3g{pg} \end{bmatrix} $ Fault admittance matrix b: $ \begin{bmatrix} b{pg} + 2b{pp} & -b{pp} & -b{pp} & -b{pg} \ -b{pp} & b{pg} + 2b{pp} & -b{pg} & -b{pg} \ -b{pp} & -b{pp} & b{pg} + 2b{pp} & -b{pg} \ -b{pg} & -b{pg} & -b{pg} & 3b{pg} \end{bmatrix} $