Energy Engineering - Electric Power Systems

Full exam

Exercise 1 0 N Demand data N 20000 300000 PD 0.97 cosphiD - leading N 50 5100 Vsupply Electric line data 3 Rl 10 Xl Namenplate data of SM 5400 Vn Triangle 600000 AnG 5900 E0M 550000 PmaxT 21 Xs 5 Rs Solution Load 75187.09 tan acos cosphiD PD QD 35.01 Vsupply 3 2 QD 2 PD I Solution of the grid part 11032.65 2 I Rl 3 PlossW 36775.51 2 I Xl 3 Qlossvar 5 10 3.11 Ploss PD PGW 38411.58 Qloss QD QG var 5 10 3.13 2 QG 2 PG AG VA 5167.89 I 3AG VGV 3 Feb 2021 18:07:54 - solution_1.sm 1 / 2 Solution of the SM part 20.06 VG 3PG IreG 2.48 VG 3 QG IimG A A i 433.69 5216.17 IimG i IreG Xs i Rs VG E0V 0.97 5400 1 E0 5234.17 E0V 0.08 arg E0 δrad Check Cap curve 64.15 Vn 3AnG In 35.01 2 IimG 2 IreG 3 IG 317161.9041 2 3 IG Rs 3 PG Pm stator limit 1 In IG rotor limit 1 E0M E0 Turbine limit 1 PmaxT Pm 1 2 π δ Stability limit QmaxStator limit 513087.4087 2 PG 2 AnG Qmax_st Rotor limit - approximation 0.9914 asin E0M Xs 3PG δmax 2266791.536 cos δmax VG E0M Xs VG 3 Qmax_rot 513087.4087 min Qmax_rot Qmax_st Qmax 3 Feb 2021 18:07:54 - solution_1.sm 2 / 2 Im x i Re x conj x Exercise 2 0 N Network data N 0.001 0.025 xL1 0.05 xL2 4 PG 1.02 VGref N 0.1 6 PD1 0.94 cosfiD1 - lagging 0.5 PD2 0.94 cosfiD2 - leading N 0.01 1.0 VEGref Y matrix i xL21 0 i xL210 i xL11 i xL11 i xL21 i xL11 i xL21 i xL11 Y i 20 0 i 200 i 40 i 40 i 20 i 40 i 60 Y 60 1 1 Y Y11 40 1 2 Y Y21 20 1 3 Y Y31 40 2 1 Y Y12 40 2 2 Y Y22 0 2 3 Y Y32 20 3 1 Y Y13 0 3 2 Y Y23 20 3 3 Y Y33 1.57 arg 1 1 Y θ11 1.57 arg 1 2 Y θ21 1.57 arg 1 3 Y θ31 1.57 arg 2 1 Y θ12 1.57 arg 2 2 Y θ22 0 0 θ32 1.57 arg 3 1 Y θ13 1.57 arg 3 3 Y θ33 0 0 θ23 3 Feb 2021 18:08:35 - solution_2.sm 1 / 4 Bus types1 - SLACK 1 VEGref v1 0 δ1 2 - PQ 6 PD1 p2 2.1777 tan acos cosfiD1 PD1 q2 3 - PV 3.5 PD2 PG p3 1.02 VGref v3 Starting profile 1 v2_0 0 δ2_0 0 δ3_0 DC PF 20 00 40 Im 3 3 Y 2 3 Y3 2 Y 2 2 Y B 0.175 0.15 p3 p2 1 B δPF Update phases 0.15 1 δPF δ2_0 0.175 2 δPF δ3_0 Newton-Rhapshon Residues 5.9775 cos θ21 δ1 δ2_0 Y21 v1 p2_calc1 13 10 1.400 cos θ22 0 Y22 v2_0 p2_calc2 5.9775 p2_calc2 p2_calc1 v2_0 p2_calc 3 Feb 2021 18:08:35 - solution_2.sm 2 / 4 3.4822 cos θ31 δ1 δ3_0 Y31 v1 p3_calc1 14 10 7.123 cos θ33 0 Y33 v3 p3_calc2 3.5518 p3_calc2 p3_calc1 v3 p3_calc 39.5508 sin θ21 δ2_0 δ1 Y21 v1 q2_calc1 40.00 sin θ22 0 Y22 v2_0 q2_calc2 0.4492 q2_calc2 q2_calc1 v2_0 q2_calc 2.6269 0.0518 0.0225 q2_calc q2 p3_calc p3 p2_calc p2 R Jacobian matrix 39.5508 sin θ21 δ1 δ2_0 Y21 v1 v2_0 dp2_dδ2 0 dp2_dδ3 5.9775 p2_calc2 2 p2_calc1 dp2_dv2 0 dp3_dδ2 20.0884 sin θ31 δ1 δ3_0 Y31 v1 v3 dp3_dδ3 0 dp3_dv2 5.9775 cos θ21 δ1 δ2_0 Y21 v1 v2_0 dq2_dδ2 0 dq2_dδ3 40.4492 q2_calc2 2 q2_calc1 dq2_dv2 3 Feb 2021 18:08:35 - solution_2.sm 3 / 4 40.4492 0 5.97750 20.0884 0 5.9775 0 39.5508 dq2_dv2 dq2_dδ3 dq2_dδ2dp3_dv2 dp3_dδ3 dp3_dδ2dp2_dv2 dp2_dδ3 dp2_dδ2 J 0.0665 0.0026 0.0106 R 1 J Δx 0.1606 1 Δx δ2_0 δ2_1 0.1724 2 Δx δ3_0 δ3_1 0.9335 3 Δx v2_0 v2_1 QG calculation 19.7034 sin θ31 δ1 δ3_1 Y31 v1 q3_calc1 20.40 sin θ33 0 Y33 v3 q3_calc2 0.7105 q3_calc2 q3_calc1 v3 q3_calc 0.1815 tan acos cosfiD2 PD2 qD2 0.529 qD2 q3_calc qg 3 Feb 2021 18:08:35 - solution_2.sm 4 / 4