Steady State Power Flow Calculations

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Presentation transcript:

Steady State Power Flow Calculations Kevin Schneider, Chen-Ching Liu University of Washington Department of Electrical Engineering

Power Flow Information Method used: Newton-Raphson Assumptions: 1) Constant voltage at the shore stations 2) Constant direct current power loads 3) Constant system topology

Convergence Criteria Sum of the differences of all node voltages between two iterations Example: Node # Voltage at Iteration n Iteration n+1 Difference 1 9423.8 9423.6 .2 2 9416.4 9416.1 .3 3 9412.1 9411.9 4 9405.0 9404.9 .1 5 9399.8 9399.4 .4 Total Difference= .2+.3+.2+.1+.4= 1.2V

Voltage Collapse If PL exceeds the point of maximum power transfer the powerflow solution will not converge. Operation beyond the Maximum Power Transfer Region must be avoided

Sample Power Flow Calculations Using the shown network topology 1) All nodes at 2.65 kW 2) All nodes at 4.3 kW 3) All nodes at 4.8 kW

Results 1: 2650Watts per Node Voltage (V) 1 8273.4 13 8248 25 8888 37 8180.7 2 8284.2 14 8318.1 26 8798.7 38 8159.1 3 8306 15 8333.1 27 8714.7 39 8222.9 4 8288.2 16 8418.4 28 8578.6 40 8271.5 5 8282.2 17 8558.2 29 8453.2 41 9304.2 6 8228.5 18 8715.2 30 8334.2 42 9762.3 7 8182.9 19 8824.3 31 8294.3 43 9118 8 8154.9 20 8697.7 32 8292.1 44 9306.6 9 8143.3 21 8583.5 33 8305.5 45 9597.2 10 8146.8 22 8484.5 34 8818.4 46 9793 11 8158.6 23 8399 35 8947 47 10000 12 8194.7 24 8332.9 36 9042.6 48 Shore Station Output Power (watts) 1 53130 2 99616

Results 2: 4300 Watts per Node Voltage (V) 1 6514.2 13 6455.9 25 7771.9 37 6317.9 2 6536.5 14 6602.6 26 7595.2 38 6272.3 3 6581.4 15 6633.9 27 7427.4 39 6406.8 4 6543.8 16 6810.2 28 7146.9 40 6508.8 5 6530.5 17 7098.1 29 6887.1 41 8608.9 6 6417.3 18 7419.9 30 6639.8 42 9526.2 7 6320.6 19 7643.5 31 6556.5 43 8254.1 8 6260.9 20 7386.8 32 6551.4 44 8632.1 9 6236.1 21 7153.6 33 6578 45 9209.8 10 6243.1 22 6950.2 34 7642.6 46 9595.6 11 6267.9 23 6773.5 35 7906.9 47 10000 12 6343.7 24 6636.2 36 8101.7 48 Shore Station Output Power (watts) 1 103780 2 198520

Results 3: 4800 Watts per Node Voltage collapse occurs; the powerflow solution does not converge

Questions?