Formulation and Analysis of an Approximate Expression for Voltage Sensitivity in Radial DC Distribution Systems
Abstract
:1. Introduction
2. Power Flow and Voltage Sensitivity Analysis for a DC Distribution System
2.1. Definition of the G-Bus Matrix
2.2. Power Flow Analysis in a DC Distribution System
2.3. Voltage Sensitivity Calculation in a DC Distribution System
3. Approximate Expression for the Voltage Sensitivity in a Radial DC Distribution System
3.1. Derivative of the General Voltage Equation
3.2. Formulation of an Approximate Expression for Voltage Sensitivity with Respect to Real Bus Power
3.3. Approximate Expression for Voltage Sensitivity with Respect to the Slack Bus Voltage
4. Verification of the Approximate Voltage Sensitivity Equation
Bus No. | Bus Type | Load Capacity (kW) |
---|---|---|
1 | Slack | 0 |
2 | Load | 0 |
3 | Load | 200 |
4 | Load | 150 |
5 | Load | 80 |
6 | Load | 120 |
7 | Load | 200 |
8 | Load | 90 |
9 | Load | 300 |
10 | Load | 0 |
11 | Load | 80 |
12 | Load | 60 |
13 | Load | 100 |
From Bus | To Bus | Resistance (Ω) | Maximum Current (A) |
---|---|---|---|
1 | 2 | 0.02940 | 1318 |
2 | 3 | 0.03460 | 760 |
2 | 5 | 0.03951 | 655 |
2 | 7 | 0.01358 | 1091 |
3 | 4 | 0.02195 | 655 |
5 | 6 | 0.06120 | 726 |
7 | 8 | 0.01730 | 760 |
7 | 10 | 0.03512 | 655 |
7 | 13 | 0.04390 | 655 |
8 | 9 | 0.01730 | 760 |
10 | 11 | 0.03073 | 655 |
10 | 12 | 0.03951 | 655 |
4.1. Verification of the Approximate Expression of Voltage Sensitivity with Regard to Bus Injected Power
4.2. Verification of the Approximate Expression of Voltage Sensitivity with Regard to the Slack Bus Voltage
5. Analysis of Voltage Sensitivity
5.1. Analysis of the Approximate Expression of Voltage Sensitivity with Regard to Bus Injected Power
5.2. Analysis of the Approximate Expression for Voltage Sensitivity to Slack Bus Voltage
6. Conclusions
Acknowledgments
Author Contributions
Conflicts of Interest
Abbreviation
Conductance of the line between bus i and bus j | |
Conductance of a constant resistive load at bus i | |
Number of buses in the DC distribution system | |
The load power of constant power load at bus i | |
Jacobian matrix for the DC power system | |
Net bus real power (i.e., generation minus the load consumption) | |
Element of an R-Bus matrix at i-th row and k-th column | |
Set of line resistances located on the shortest path between the slack bus and bus i | |
The sum of elements at the intersection of and |
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Jeong, H.-Y.; Choi, J.-C.; Won, D.-J.; Ahn, S.-J.; Moon, S.-i. Formulation and Analysis of an Approximate Expression for Voltage Sensitivity in Radial DC Distribution Systems. Energies 2015, 8, 9296-9319. https://doi.org/10.3390/en8099296
Jeong H-Y, Choi J-C, Won D-J, Ahn S-J, Moon S-i. Formulation and Analysis of an Approximate Expression for Voltage Sensitivity in Radial DC Distribution Systems. Energies. 2015; 8(9):9296-9319. https://doi.org/10.3390/en8099296
Chicago/Turabian StyleJeong, Ho-Yong, Jong-Chan Choi, Dong-Jun Won, Seon-Ju Ahn, and Seung-il Moon. 2015. "Formulation and Analysis of an Approximate Expression for Voltage Sensitivity in Radial DC Distribution Systems" Energies 8, no. 9: 9296-9319. https://doi.org/10.3390/en8099296