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 | Units | 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 |
Connection Examples
Line-Ground (Phase A)
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)
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-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} $
Formulation
Depending on fault type, the constraints between networks are as follows
LG
\[I_{f1} = I_{f2} = I_{f0} = \frac{V_{f1} + V_{f2} + V_{f0}}{Z_f}\]
LL
\[I_{f1} = - I_{f2} = \frac{V_{f1} - V_{f2}}{Z_f}\]
LLG
\[V_{f1} = V_{f2}\]
\[I_{f0} = \frac{V_{f1} - V_{f2}}{Z_f}\]
3P
\[I_{f1} = \frac{V_{f1}}{Z_f}\]
\[I_{f2} = I_{f0} = 0\]