|
276 | 276 | \end{eqnarray}
|
277 | 277 | $$
|
278 | 278 |
|
| 279 | +### Asym Line |
| 280 | + |
| 281 | +* type name: `asym_line` |
| 282 | + |
| 283 | +`asym_line` is a {hoverxreftooltip}`user_manual/components:branch` with specified resistance and reactance per phase. A cable can be modelled as `line` or `asym_line`. An `asym_line` can only connect two nodes with the same rated voltage. If `i_n` is not provided, `loading` of line will be a `nan` value. The `asym_line` denotes a 3 or 4 phase line with phases `a`, `b`, `c` and optionally `n` for neutral. |
| 284 | + |
| 285 | +#### Input |
| 286 | + |
| 287 | +The provided values will be converted to a matrix representing the line's properties per phase in the following form: |
| 288 | + |
| 289 | +$$ |
| 290 | + \begin{bmatrix} |
| 291 | + \text{aa} & \text{ba} & \text{ca} & \text{na}\\ |
| 292 | + \text{ba} & \text{bb} & \text{cb} & \text{nb}\\ |
| 293 | + \text{ca} & \text{cb} & \text{cc} & \text{nc}\\ |
| 294 | + \text{na} & \text{nb} & \text{nc} & \text{nn} |
| 295 | + \end{bmatrix} |
| 296 | +$$ |
| 297 | + |
| 298 | +This representation holds for all values `r_aa` ... `r_nn`, `x_aa` ... `x_nn` and `c_aa` ... `c_cc`. If the neutral values are not provided, the last row and column from the above matrix are omitted. |
| 299 | + |
| 300 | +| name | data type | unit | description | required | update | valid values | |
| 301 | +| ------ | --------- | ---------- | --------------------------------- | ---------------------------- | :------: | :--------------------------------: | |
| 302 | +| `r_aa` | `double` | ohm (Ω) | Series serial resistance aa | ✔ | ❌ | `> 0` | |
| 303 | +| `r_ba` | `double` | ohm (Ω) | Series serial resistance ba | ✔ | ❌ | `> 0` | |
| 304 | +| `r_bb` | `double` | ohm (Ω) | Series serial resistance bb | ✔ | ❌ | `> 0` | |
| 305 | +| `r_ca` | `double` | ohm (Ω) | Series serial resistance ca | ✔ | ❌ | `> 0` | |
| 306 | +| `r_cb` | `double` | ohm (Ω) | Series serial resistance cb | ✔ | ❌ | `> 0` | |
| 307 | +| `r_cc` | `double` | ohm (Ω) | Series serial resistance cc | ✔ | ❌ | `> 0` | |
| 308 | +| `r_na` | `double` | ohm (Ω) | Series serial resistance na | ✨ for a neutral phase | ❌ | `> 0` | |
| 309 | +| `r_nb` | `double` | ohm (Ω) | Series serial resistance nb | ✨ for a neutral phase | ❌ | `> 0` | |
| 310 | +| `r_nc` | `double` | ohm (Ω) | Series serial resistance nc | ✨ for a neutral phase | ❌ | `> 0` | |
| 311 | +| `r_nn` | `double` | ohm (Ω) | Series serial resistance nn | ✨ for a neutral phase | ❌ | `> 0` | |
| 312 | +| `x_aa` | `double` | ohm (Ω) | Series serial reactance aa | ✔ | ❌ | `> 0` | |
| 313 | +| `x_ba` | `double` | ohm (Ω) | Series serial reactance ba | ✔ | ❌ | `> 0` | |
| 314 | +| `x_bb` | `double` | ohm (Ω) | Series serial reactance bb | ✔ | ❌ | `> 0` | |
| 315 | +| `x_ca` | `double` | ohm (Ω) | Series serial reactance ca | ✔ | ❌ | `> 0` | |
| 316 | +| `x_cb` | `double` | ohm (Ω) | Series serial reactance cb | ✔ | ❌ | `> 0` | |
| 317 | +| `x_cc` | `double` | ohm (Ω) | Series serial reactance cc | ✔ | ❌ | `> 0` | |
| 318 | +| `x_na` | `double` | ohm (Ω) | Series serial reactance na | ✨ for a neutral phase | ❌ | `> 0` | |
| 319 | +| `x_nb` | `double` | ohm (Ω) | Series serial reactance nb | ✨ for a neutral phase | ❌ | `> 0` | |
| 320 | +| `x_nc` | `double` | ohm (Ω) | Series serial reactance nc | ✨ for a neutral phase | ❌ | `> 0` | |
| 321 | +| `x_nn` | `double` | ohm (Ω) | Series serial reactance nn | ✨ for a neutral phase | ❌ | `> 0` | |
| 322 | +| `c_aa` | `double` | farad (F) | Shunt nodal capacitance matrix aa | ✨ for a full c matrix | ❌ | `> 0` | |
| 323 | +| `c_ba` | `double` | farad (F) | Shunt nodal capacitance matrix ba | ✨ for a full c matrix | ❌ | `> 0` | |
| 324 | +| `c_bb` | `double` | farad (F) | Shunt nodal capacitance matrix bb | ✨ for a full c matrix | ❌ | `> 0` | |
| 325 | +| `c_ca` | `double` | farad (F) | Shunt nodal capacitance matrix ca | ✨ for a full c matrix | ❌ | `> 0` | |
| 326 | +| `c_cb` | `double` | farad (F) | Shunt nodal capacitance matrix cb | ✨ for a full c matrix | ❌ | `> 0` | |
| 327 | +| `c_cc` | `double` | farad (F) | Shunt nodal capacitance matrix cc | ✨ for a full c matrix | ❌ | `> 0` | |
| 328 | +| `c0` | `double` | farad (F) | zero-sequence shunt capacitance | ✨ without a c matrix | ❌ | `> 0` | |
| 329 | +| `c1` | `double` | farad (F) | Series shunt capacitance | ✨ without a c matrix | ❌ | `> 0` | |
| 330 | + |
| 331 | +For the r and x matrices providing values for the neutral phase is optional. To clarify which input values are required, please consult the tables below: |
| 332 | + |
| 333 | +| r_aa ... r_cc | r_na | r_nb | r_nc | r_nn | result | Validation Error | |
| 334 | +| --------------- | -------- | -------- | -------- | -------- | -------- | ------------------------- | |
| 335 | +| ✔ | ✔ | ✔ | ✔ | ✔ | ✔ | | |
| 336 | +| ✔ | ✔ | ✔ | ✔ | ❌ | ❌ | MultiFieldValidationError | |
| 337 | +| ✔ | ✔ | ✔ | ✔ | ❌ | ❌ | MultiFieldValidationError | |
| 338 | +| ✔ | ✔ | ✔ | ❌ | ❌ | ❌ | MultiFieldValidationError | |
| 339 | +| ✔ | ✔ | ❌ | ❌ | ❌ | ❌ | MultiFieldValidationError | |
| 340 | +| ✔ | ❌ | ❌ | ❌ | ❌ | ✔ | | |
| 341 | +| ❌ | ❌ | ❌ | ❌ | ❌ | ❌ | MultiFieldValidationError | |
| 342 | + |
| 343 | +| x_aa ... x_cc | x_na | x_nb | x_nc | x_nn | result | Validation Error | |
| 344 | +| --------------- | -------- | -------- | -------- | -------- | -------- | ------------------------- | |
| 345 | +| ✔ | ✔ | ✔ | ✔ | ✔ | ✔ | | |
| 346 | +| ✔ | ✔ | ✔ | ✔ | ❌ | ❌ | MultiFieldValidationError | |
| 347 | +| ✔ | ✔ | ✔ | ✔ | ❌ | ❌ | MultiFieldValidationError | |
| 348 | +| ✔ | ✔ | ✔ | ❌ | ❌ | ❌ | MultiFieldValidationError | |
| 349 | +| ✔ | ✔ | ❌ | ❌ | ❌ | ❌ | MultiFieldValidationError | |
| 350 | +| ✔ | ❌ | ❌ | ❌ | ❌ | ✔ | | |
| 351 | +| ❌ | ❌ | ❌ | ❌ | ❌ | ❌ | MultiFieldValidationError | |
| 352 | + |
| 353 | +For the c-matrix values there are two options. Either provide all the required c-matrix values i.e. `c_aa` ... `c_cc` or provide `c0`, `c1`. Whenver both sets are supplied the powerflow calculations will use `c0`, `c1`. |
| 354 | +The table below provides guidance in providing valid input. |
| 355 | + |
| 356 | +| c_aa ... c_cc | c0 | c1 | result | Validation Error | |
| 357 | +| ------------- | -------- | -------- | -------- | ------------------------- | |
| 358 | +| ✔ | ✔ | ✔ | ✔ | | |
| 359 | +| ✔ | ✔ | ❌ | ✔ | | |
| 360 | +| ✔ | ❌ | ❌ | ✔ | | |
| 361 | +| ❌ | ✔ | ❌ | ❌ | MultiFieldValidationError | |
| 362 | +| ❌ | ✔ | ✔ | ✔ | | |
| 363 | + |
| 364 | +#### Electric Model |
| 365 | + |
| 366 | +The cable properties are described using matrices where the $Z_{\text{series}}$ matrix is computed as: |
| 367 | + |
| 368 | +$$ |
| 369 | + Z_{\text{series}} = R + \mathrm{j} * X |
| 370 | +$$ |
| 371 | + |
| 372 | +Where $R$ and $X$ denote the resistance and reactance matrices build from the input respectively. |
| 373 | + |
| 374 | +Whenever the neutral phase is provided in the $Z_{\text{series}}$, the $Z_{\text{series}}$ matrix will first be reduced to a 3 phase matrix $Z_{\text{reduced}}$ with a kron reduction as follows: |
| 375 | + |
| 376 | +$$ |
| 377 | + Z_{\text{aa}} = \begin{bmatrix} |
| 378 | + Z_{\text{0,0}} & Z_{\text{1,0}} & Z_{\text{2,0}}\\ |
| 379 | + Z_{\text{1,0}} & Z_{\text{1,1}} & Z_{\text{2,1}}\\ |
| 380 | + Z_{\text{2,0}} & Z_{\text{2,1}} & Z_{\text{2,2}} |
| 381 | + \end{bmatrix} |
| 382 | +$$ |
| 383 | +$$ |
| 384 | + Z_{\text{ab}} = \begin{bmatrix} |
| 385 | + Z_{\text{0,3}} \\ |
| 386 | + Z_{\text{1,3}} \\ |
| 387 | + Z_{\text{2,3}} |
| 388 | + \end{bmatrix} |
| 389 | +$$ |
| 390 | +$$ |
| 391 | + Z_{\text{ba}} = \begin{bmatrix} |
| 392 | + Z_{\text{3,0}} \\ |
| 393 | + Z_{\text{3,1}} \\ |
| 394 | + Z_{\text{3,2}} |
| 395 | + \end{bmatrix} |
| 396 | +$$ |
| 397 | +$$ |
| 398 | + Z_{\text{bb}}^{-1} = \frac{1}{Z_{\text{3,3}}} |
| 399 | +$$ |
| 400 | +$$ |
| 401 | + Z_{\text{reduced}} = Z_{\text{aa}} - Z_{\text{ba}} \otimes Z_{\text{ab}} \cdot Z_{\text{bb}}^{-1} |
| 402 | +$$ |
| 403 | + |
| 404 | +Where $Z_{\text{i,j}}$ denotes the row and column of the $Z_{\text{series}}$ matrix. |
| 405 | + |
279 | 406 | ## Branch3
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280 | 407 |
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281 | 408 | * type name: `branch3`
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