Problem Formulation Optimum Feeder Routing and Distribution Substation Placement and Sizing using PSO and MST.

Ihsan Jabbar Hasan, Chin Kim Gan, Meysam Shamshiri, Mohd Ruddin Ab Ghani and Rosli Bin Omar Indian Journal of Science and Technology 1685 Vol 7 10 | October 2014 | www.indjst.org substations has been selected among the 275 candidate substations. Meanwhile, this igure indicates the num- bers of consumers which assigned to their particular substation.

2.2 Optimum Feeder Routing using MST

As explained in introduction the prim’s algorithm has been utilizes in this paper to ind the optimum feeder routing of LV and MV networks. But the only prim’s algorithm cannot carry out our desire optimal routing. he modiied prim algorithm needs to be performed because of some technical requirement such as, open loop feeders and not allowed branches pass through each other. Figure 6 shows the proposed modiication algorithm using prim’s algorithm in MST in order to ind the optimum feeder routing in distribution network. Figure 7 shows the obtained results ater LV and MV feeder routing using modiied MST algorithm. It depicts the LV feeder path with purple line color and MV con- ductors by black line color. he LV feeders are connected adequately without passing each other as shown in igure. It demonstrated the modiied algorithm has succeeded to solve the feeder routing problem by considering the prob- lem constraints.

3. Problem Formulation

In distribution system planning, the geographical dis- tribution of loads density and allocation of feasible candidate substations are the important information in the study year. Based on optimization point of view, Figure 3. he optimum substation placement lowchart using PSO. START Initialization Create random solution, considering the maximum number of substation Evaluate the solutions by substituting in objective function Determining the personal and global bests Update position and velocity Population number? Check the stop condition END Population and iteration numbers. Consumer coordinates and etc. Distance calculation between consumers and candidate substations. Iteration= Iteration+1 Yes Yes No No Figure 4. Consumers and candidate substation. 200 400 600 800 1000 200 400 600 800 1000 X [m] Y [m] Consumers Candidate Substation Figure 5. Selected MVLV substations ater optimization. 200 400 600 800 1000 100 200 300 400 500 600 700 800 900 X [m] Y [m] Indian Journal of Science and Technology Vol 7 10 | October 2014 | www.indjst.org 1686 Figure 6. he lowchart of modiied MST algorithm in order to solve the optimum feeder routing in distribution network. START Initialization of MST algorithm Distance calculation between all graph points and create the graph Calculate the weight of each branch Prim Algorithm Is there any branch cross the other branches? Extract the obtained tree to the OpenDSS file as the Line data connections END Repeat the algorithm to find the non-cross minimum branch Consumers and Substations Coordinates X,Y Does the graph nodes finished? Yes Yes No No Figure 7. Obtained network ater optimum feeder routing for LV and MV in 164 consumers distribution network. 200 400 600 800 1000 100 200 300 400 500 600 700 800 900 1 7 8 10 13 14 16 23 34 42 45 79 121 164 175 187 200 205 228 233 242 245 265 297 307 309 340 349 358 433 437 4 11 18 25 84 101 103 109 127 134 153 163 168 183 212 260 273 337 344 367 438 463 476 20 29 32 48 57 70 78 82 90 107 115 120 124 126 131 135 149 151 165 167 184 195 230 250 254 257 274 302 339 370 392 448 35 37 40 44 47 49 50 52 54 62 81 94 112 128 137 143 150 152 166 179 185 189 281 298 321 330 347 355 363 364 371 390 417 420 428 430 434 440 444 447 451 460 496 41 58 63 72 73 75 86 88 96 100 111 118 139 144 148 171 182 227 261 272 299 325 328 368 377 389 393 409 412 423 431 435 458 462 466 482 498 67 74 92 97 105 106 130 132 138 142 146 154 178 197 253 262 263 276 285 310 312 315 343 365 383 385 400 401 402 427 454 468 470 479 481 486 499 157 160 161 162 174 188 191 196 217 218 220 223 229 234 236 238 241 246 247 258 264 266 268 277 279 286 289 317 327 351 360 382 384 388 418 421 436 446 456 457 464 485 488 492 2 9 22 30 55 56 60 61 71 80 117 169 172 190 201 222 248 271 284 305 332 334 359 362 375 381 478 490 15 24 26 33 87 102 110 113 199 214 225 235 239 293 294 426 432 461 194 231 232 249 251 252 255 275 288 300 319 352 369 373 387 391 410 441 471 474 483 3 5 6 38 43 46 51 77 85 89 91 98 108 141 155 180 209 210 211 215 221 240 244 259 267 270 283 303 314 326 331 333 336 398 453 459 469 487 497 17 27 28 31 36 39 59 64 65 76 83 93 95 99 104 119 123 133 145 186 193 203 204 256 287 290 296 311 329 348 350 366 376 379 394 405 413 414 424 425 455 493 12 19 21 53 66 68 116 122 158159 176 198 207 208 216 224 226 243 291 301 304 313 318 338 341 345 354 372 386 395 399 403 404 406 415 422 429 439 445 452 465 472 477 480 278 308 322 342 353 357 380 419 489 495 114 125 136 156 170 173 181 202 213 219 237 269 280 282 295 306 316 324 346 356 361 374 396 407 408 411 416 442 443 449 473 475 491 494 500 69 129 140 147 177 192 206 292 320 323 335 378 397 450 467 484 X [m] Y [m] bus, c Maximum load capacity of all substation, and d cost minimization of new substation construction. Accordingly, the objective functions of substation place- ment and sizing can be formulated as follows: CL C P L Loss i i nlb = = Â . .8760 1 2 where, CL is the total losses cost for a study year, C L [kWh] is the cost of real power losses which is provided in 12 C L =168 kWyear], P Loss i [kW] is the real power losses at consumer i and nlb is the number of consumers. he investment cost of substation should be annui- tized to able to accumulate with other network costs 13 . hus, to annuitize the investment cost of distribution net- work, the following economical consideration should be performed. VC C j d j i S j ns lb i nlb = Ê Ë Á ˆ ¯ ˜ = = Â Â var . , 1 1 3 FC C j S fix j ns = = Â 1 4 C VC FC S S S = + 5 where VC s is the total substation variable cost, C var j is the cost of substation j per MVA, d lb j,i is the consumer demand i which connected to substation j. FC s repre- sents the total ixed cost of substations and C ix j is the ixed cost of substation j. he variable cost of substation included the cost of operation and maintenance, and the ixed cost consists of installation and other related ix cost of substation such as land and equipment prices and etc. IC C C S j l j ns = = Â 1 6 CC IC d d d T T = + + - 1 1 1 7 where IC stand for Investment Cost [], C S is the total substation installation and operation costs [], C l is the total cost of the lines [], CC is the annuitized capital cost [year], d is the discount rate and T is the number of operation years. the following constraints must be satisied in order to optimal distribution substation allocation and feeder routing, which are: a supplying all the consumers of the networks, b acceptable voltage drops at the receiving Ihsan Jabbar Hasan, Chin Kim Gan, Meysam Shamshiri, Mohd Ruddin Ab Ghani and Rosli Bin Omar Indian Journal of Science and Technology 1687 Vol 7 10 | October 2014 | www.indjst.org hus, the main objective function that needs to be minimized can be written as follows: Min Z CL CC PF = + + 8 where Z is the total cost function and PF is the penalty factor which is calculated by the optimization constraints. For instance, if the voltage is out of the deined range, therefore the violation amount of voltage will multiply to the constant ine rate Beta which can be written as follows: PF Violation i i nv = ¥ = Â b 1 9 where, nv is number of violations and β is the ine rate. he irst constraint of distribution network planning is acceptable voltage drop at receiving bus V i which volt- age should be within the speciied range. 0 95 1 05 . . £ £ V i 10 he next constraint of distribution network planning is the longest distance of each consumer from the distri- bution substation which introduced by substation radius based on standard. To consider this constraint the follow- ing condition must be considered: D R j i j £ max 11 where D j i is stand for distance between substation j to consumer i and R j max is the maximum acceptable radius of substation j that can supply the consumers. Based on the standard, in LV feeder the maximum length of feeder can be up to 0.5–1 km. In urban networks, the length of 11 kV feeders in generally up to 3 km and for rural networks is up to 20 km.

4. Result and Discussion