ESMOGrid validation: Load flow case 1

Usually the very first aspect electric power engineers have to evaluate when analyzing transmission, distribution or industrial power system is load flows. What is more, nowadays, load flow analysis become a powerful tool for designing domestic scale microgrids with renewable energy power plants.

Load flow study results depict steady – state system components and lines loading, bus voltage profiles, real and reactive power flows, power losses, optimal transformer tap settings.

To verify ESMOGrid load flow module calculations accuracy, case studies are run before each software update. In this article, six – bus system with 2 generators and 3 loads is analyzed. All lines are modeled with their capacitance, inductance and active resistance. One line diagram of analyzed system is presented in Fig. 1. System data is presented in Table 1.

Fig. 1 One line diagram of analyzed 6 bus system

Fig. 1 One line diagram of analyzed 6 bus system

Table 1 System data

Title Resistance Reactance Capacitance
Bus 1 – Bus 2 52,9 Ω 105,8 Ω 240,81 nF
Bus 2 – Bus 3 26,45 Ω 132,25 Ω 361,22 nF
Bus 1 –  Bus 4 26,45 Ω 105,8 Ω 240,81 nF
Bus 1 – Bus  5 42,32 Ω 158,7 Ω 361,215 nF
Bus 2 – Bus 4 26,45 Ω 52,9 Ω 120,4 nF
Bus 2 – Bus 5 52,9 Ω 158,7 Ω 240,81 nF
Bus 2 – Bus 6 37,03 Ω 105,8 Ω 301,01 nF
Bus 3 – Bus 5 63,48 Ω 137,54 Ω 301,01 nF
Bus 3 – Bus 6 10,58 Ω 52,9 Ω 120,41 nF

 

Results are presented and compared to ones from reference in Tables 1 and 2.

Table 2. Bus voltage calculation results comparison with reference

  ESMOGrid Reference ESMOGrid Reference Difference
Bus title U, kV U, kV δ δ ΔU δ
Bus 1 230 230 0 0 0,00% 0,00%
Bus 2 226,381 226,4 -3,9 -3,9 0,01% 0,00%
Bus 3 230,221 230,2 -4,7 -4,7 -0,01% 0,00%
Bus 4 212,03 212 -4,4 -4,4 -0,01% 0,00%
Bus 5 207,33 207,3 -5,8 -5,8 -0,01% 0,00%
Bus 6 214,805 214,8 -6,7 -6,7 0,00% 0,00%

 

Table 3. Branch power flow calculation results comparison with reference

  ESMOGrid Reference Difference
Title Sij, MVA Pij, MW Qij, MVar Sij, MVA Pij, MW Qij, MVar ΔPij ΔQij
Bus 1 – Bus 2 31,382 30,304 -8,153 31,380 30,304 -8,145 0,00% -0,10%
Bus 2 – Bus 3 11,043 4,085 -10,259 11,040 4,085 -10,256 0,00% -0,03%
Bus 1 – Bus 4 50,732 42,447 27,783 50,734 42,447 27,789 0,00% 0,02%
Bus 1 – Bus 5 42,675 36,826 21,563 42,678 36,826 21,569 0,00% 0,03%
Bus 2 – Bus 4 54,546 30,478 45,236 54,543 30,478 45,233 0,00% -0,01%
Bus 2 – Bus 5 26,044 16,997 19,734 26,046 16,997 19,735 0,00% 0,01%
Bus 2 – Bus 6 30,748 27,788 13,164 30,749 27,787 13,167 0,00% 0,02%
Bus 3 – Bus 5 33,32 20,025 26,631 33,320 20,025 26,631 0,00% 0,00%
Bus 3 – Bus 6 72,69 44,024 57,842 72,690 44,024 57,842 0,00% 0,00%

 

Differences between results are less then 0.1%.

Reference

Allen. J. Wood and Bruce F. Wollenberg, “Power Generation, Operation, and Control, 2nd Edition”, pp. 104, 112, 119, 123-124, John Wiley & Sons , NY,  Jan 1996

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