|
2 | 2 |
|
3 | 3 | `BranchLumpedConstant` represents a lumped-parameter EMT transmission line. |
4 | 4 | The nominal $\pi$-model is obtained by spatially discretizing the telegrapher equations over |
5 | | -a segment of length $\Delta x$, with a half shunt placed at each terminal. |
| 5 | +a segment of length $\Delta x$, with a half shunt placed at each port. |
6 | 6 | Series current $\mathbf{i}$ is directed from bus 1 to bus 2. Bus residual |
7 | 7 | current injections are positive into buses. All electrical parameter matrices |
8 | 8 | are $3 \times 3$ and capture self and mutual coupling between phases. |
9 | 9 |
|
10 | 10 | <div align="center"> |
11 | | - <img align="center" src="../../../../../docs/Figures/EMT/lumped_constant_diagram.svg"> |
| 11 | + <img align="center" src="../../../../../../docs/Figures/EMT/lumped_constant_diagram.svg"> |
12 | 12 |
|
13 | 13 | Figure 1: Lumped constant EMT branch model |
14 | 14 | </div> |
@@ -49,16 +49,16 @@ None. |
49 | 49 | ### External Variables |
50 | 50 |
|
51 | 51 | External variables enter component model equations but are owned by |
52 | | -other components. The EMT bus at each terminal owns the voltage |
| 52 | +other components. The EMT bus at each port owns the voltage |
53 | 53 | variable and provides the equation needed to have a balanced system |
54 | 54 | of equations. |
55 | 55 |
|
56 | 56 | #### Differential |
57 | 57 |
|
58 | 58 | Symbol | Units | Description | Note |
59 | 59 | -----------------|--------|--------------------------|------------------ |
60 | | -$\mathbf{v}_1$ | [V] | Terminal voltage at bus 1, owned by bus 1 | $\mathbf{v}_1 = [v_{1,a}, v_{1,b}, v_{1,c}]^T \in \mathbb{R}^3$ |
61 | | -$\mathbf{v}_2$ | [V] | Terminal voltage at bus 2, owned by bus 2 | $\mathbf{v}_2 = [v_{2,a}, v_{2,b}, v_{2,c}]^T \in \mathbb{R}^3$ |
| 60 | +$\mathbf{v}_1$ | [V] | Port voltage at bus 1, owned by bus 1 | $\mathbf{v}_1 = [v_{1,a}, v_{1,b}, v_{1,c}]^T \in \mathbb{R}^3$ |
| 61 | +$\mathbf{v}_2$ | [V] | Port voltage at bus 2, owned by bus 2 | $\mathbf{v}_2 = [v_{2,a}, v_{2,b}, v_{2,c}]^T \in \mathbb{R}^3$ |
62 | 62 |
|
63 | 63 | #### Algebraic |
64 | 64 |
|
|
79 | 79 |
|
80 | 80 | ### Bus Residual Contributions |
81 | 81 |
|
82 | | -The lumped line contributes to the KCL residual at each terminal bus. |
| 82 | +The lumped line contributes to the KCL residual at each port bus. |
83 | 83 | Each expression is accumulated into the owning bus residual. |
84 | 84 |
|
85 | 85 | ``` math |
@@ -119,5 +119,5 @@ DAE consistency: |
119 | 119 | Candidate monitorable outputs include the series branch current components |
120 | 120 | $i_a$, $i_b$, and $i_c$. |
121 | 121 |
|
122 | | -Terminal current injection expressions are documented above as |
| 122 | +Port current injection expressions are documented above as |
123 | 123 | $\mathbf{i}^\text{inj}_1$ and $\mathbf{i}^\text{inj}_2$. |
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