Fig. 1.
Fig. 2.
Fig. 3.
Fig. 4.
Fig. 5.
Fig. 6.
Fig. 7.
Fig. 8.
Fig. 9.
Fig. 10.
Fig. 11.
Fig. 12.
Fig. 13.
Fig. 14.
Fig. 15.
Results for nods comparison
| Parameter | Unit | 041 | 042 | 043 | 044 |
|---|---|---|---|---|---|
| viHPSS | p.u. | 0.989 | 0.973 | 0.950 | 1.006 |
| viSPS | p.u. | 0.990 | 0.969 | 0.947 | 0.965 |
| viSim | p.u. | 0.990 | 0.969 | 0.947 | 0.965 |
| viSPSLF | p.u. | 0.990 | 0.969 | 0.947 | 1.001 |
| vSimLF | p.u. | 0.990 | 0.969 | 0.947 | 1.002 |
| viAn | p.u. | 0.990 | 0.965 | 0.943 | 0.997 |
| PiHPSS | W | 367 | 347 | 343 | 130 |
| PiSPS | W | 384.71 | 368.68 | 363.79 | 154.35 |
| PiSim | W | 384.73 | 368.69 | 363.82 | 154.41 |
| PiSPSLF | W | 387.75 | 371.60 | 366.69 | 155.57 |
| PiSimLF | W | 387.8 | 372.0 | 367.1 | 155.8 |
| PiAn | W | 384.6 | 368.58 | 363.71 | 154.30 |
| QiHPSS | var | -130 | 20 | 49 | 0 |
| QiSPS | var | -118.75 | 48.72 | 73.69 | -0.001 |
| QiSim | var | -118.87 | 48.62 | 73.61 | 0.001 |
| QiSPSLF | var | -119.78 | 54.19 | 91.18 | 0 |
| QiSimLF | var | -119.80 | 49.10 | 74.30 | 0 |
| QiAn | var | -118.80 | 48.71 | 73.10 | 0 |
Results for branches errors comparison
| Parameter | Unit | L0412 | L0423 | L0434 |
|---|---|---|---|---|
| δΔPiSPS | % | -19.86 | 22.01 | -36.51 |
| δΔPiSim | % | -19.85 | 21.99 | -41.16 |
| δΔPiSPSLF | % | -19.25 | 22.75 | -40.14 |
| δΔPiSimLF | % | -21.0 | 22.5 | -34.0 |
| δΔPiAn | % | -19.88 | 21.85 | -37.09 |
| δΔQiSPS | % | 11.64 | -13.90 | 0.093 |
| δΔQiSim | % | 11.66 | -13.83 | 0.35 |
| δΔQiSPSLF | % | 15.98 | 27.56 | 3.41 |
| δΔQiSimLF | % | 12.6 | -13.10 | 11.50 |
| δΔQiAn | % | 11.68 | -13.87 | 0.088 |
Power lines parameters
| Parameter | Unit | L0412 | L0423 | L0434 |
|---|---|---|---|---|
| RLa | Ω | 16.8 | 5.2 | 16.8 |
| RLb | Ω | 16.9 | 5.1 | 16.8 |
| RLc | Ω | 16.8 | 5.1 | 16.8 |
| LLa | H | 0.289 | 0.076 | 0.289 |
| LLb | H | 0.287 | 0.075 | 0.293 |
| LLc | H | 0.291 | 0.072 | 0.284 |
| CLa(1) | F | 1.03 · 10−6 | 2.43 · 10−7 | 1.04 · 10−6 |
| CLb(1) | F | 1.08 · 10−6 | 2.43 · 10−7 | 1.09 · 10−6 |
| CLc(1) | F | 1.02 · 10−6 | 2.41 · 10−7 | 1.08 · 10−6 |
| CLa–b(1) | F | 5.25 · 10−7 | 1.02 · 10−7 | 5.10 · 10−7 |
| CLb–c(1) | F | 5.20 · 10−7 | 9.95 · 10−8 | 5.20 · 10−7 |
| CLc–a(1) | F | 5.45 · 10−7 | 1.01 ·10−7 | 5.08 · 10−7 |
| CLa(2) | F | 1.09 · 10−6 | 1.84 · 10−7 | 1.04 · 10−6 |
| CLb(2) | F | 1.08 · 10−6 | 1.82 · 10−7 | 1.09 · 10−6 |
| CLc(2) | F | 1.07 · 10−6 | 1,81 · 10−7 | 1.08 · 10−6 |
| CLa–b(2) | F | 5.22 · 10−7 | 1.02 · 10−7 | 5.31 · 10−7 |
| CLb–c(2) | F | 5.37 · 10−7 | 1.00 · 10−7 | 5.22 · 10−7 |
| CLc–a(2) | F | 5.40 · 10−7 | 1.01 ·10−7 | 5.51 · 10−7 |
Results for terminal voltages errors comparison
| Parameter | Unit | 041 | 042 | 043 | 044 |
|---|---|---|---|---|---|
| δviSPS | % | 0.001 | -0.433 | -0.342 | -4.148 |
| δviSim | % | 0.001 | -0.424 | -0.332 | -4.136 |
| δviSPSLF | % | 0.005 | -0.427 | -0.338 | -0.544 |
| δviSimLF | % | 0.015 | -0.386 | -0.285 | -0.435 |
| δviAn | % | 0.015 | -0.836 | -0.744 | -0.950 |
Loads parameters
| Parameter | Unit | Load_1 | Load_2 |
|---|---|---|---|
| Ria | Ω | 220.853 | 1052 |
| Rib | Ω | 220.072 | 1036 |
| Ric | Ω | 221.389 | 1003 |
| Lia | H | 1.022 | 0 |
| Lib | H | 1.009 | 0 |
| Lib | H | 1.054 | 0 |
Results for branches comparison
| Parameter | Unit | L0412 | L0423 | L0434 |
|---|---|---|---|---|
| ΔPiHPSS | W | 20 | 4 | 7 |
| ΔPiSPS | W | 16.03 | 4.88 | 4.44 |
| ΔPiSim | W | 16.03 | 4.88 | 4.12 |
| ΔPiSPSLF | W | 16.15 | 4.91 | 4.19 |
| ΔPiSimLF | W | 15.8 | 4.9 | 4.62 |
| ΔPiAn | W | 16.02 | 4.87 | 4.40 |
| ΔQiHPSS | var | -150 | -29 | -226 |
| ΔQiSPS | var | -167.46 | -24.97 | -226.21 |
| ΔQiSim | var | -167.49 | -24.99 | -226.79 |
| ΔQiSPSLF | var | -173.97 | -36.99 | -233.71 |
| ΔQiSimLF | var | -168.9 | -25.2 | -252.0 |
| ΔQiAn | var | -167.52 | -24.99 | -226.20 |
Average values of errors for all methods
| Parameter | Unit | ∂vAV | δΔPAV | δΔQAV |
|---|---|---|---|---|
| Specialized Power Systems | % | -1.231 | -11.453 | -0.722 |
| Simscape | % | -1.223 | -13.007 | -0.607 |
| SPS Load Flow | % | -0.326 | -12.213 | 15.650 |
| Simscape Load Flow | % | -0.273 | -10.833 | 3.667 |
| Analytical | % | -0.629 | -11.707 | -0.701 |