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

2. 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

3. 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= = 1.2V

4. 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

5. 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

6. 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

7. 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

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

9. Questions?