
Fig. 1.
The view of hardware power system simulator used for studies

Fig. 2.
Test grid structure

Fig. 3.
Line model scheme according to 3rd type scheme
Tab. 1.
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 |
Tab. 2.
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 |

Fig. 4.
Specialized Power Systems based model scheme

Fig. 5.
Simscape library based model scheme

Fig. 6.
Specialized Power Systems model scheme for load flow analysis tool

Fig. 7.
Simscape model scheme for load flow analysis tool
Tab. 3.
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 |
Tab. 4.
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 |
Tab. 5.
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 |
Tab. 6.
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 |
Tab. 7.
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 |

Fig. 8.
Voltage levels in following grid terminals

Fig. 9.
Active power in following grid terminals

Fig. 10.
Reactive power in following grid terminals

Fig. 11.
Active power losses in grid lines comparison

Fig. 12.
Reactive power losses in grid lines comparison

Fig. 13.
Voltage level error comparison

Fig. 14.
Active power losses error comparison

Fig. 15.
Reactive power losses error comparison