Single-phase feeders

This repository creates single-phase versions of IEEE 13-bus, IEEE 37-bus, and IEEE 123-bus distribution networks. The load-flow solution using the Z-Bus method. Further, it is demonstrated that the Z-Bus iterations are contracting.

1. M. Bazrafshan and N. Gatsis, "Convergence of the Z-Bus Method for Three-Phase Distribution Load-Flow with ZIP Loads," in IEEE Trans. Power Syst., to be published. doi:10.1109/TPWRS.2017.2703835. See the arXiv version.

2. M. Bazrafshan and N. Gatsis ``Convergence of the Z-Bus method and existence of unique solution in single-phase distribution load-flow," in Proc. Global Conf. Signal & Information Proc., Washington, DC, Dec. 2016. See the Presentation slides.

Code description

The following IEEE networks are modeled:

• The IEEE 13-bus
• The IEEE 37-bus
• The IEEE 123-bus

The required data to model the above networks are downloaded from https://ewh.ieee.org/soc/pes/dsacom/testfeeders/ and are included in the corresponding data folders.

For each network, the scripts setupBusAdmittance<NetworkName>.m and solve<NetworkName>.m are provided and are explained next.

setupBusAdmittance<NetworkName>.m

This script creates a MatFile named <NetworkName>SinglePhase.mat in the directory SinglePhaseMatFiles/. The MatFile contains the following

Output fields

1. Sbase
2. Vbase
3. N (Number of buses without the Slack bus)
4. allNodesActualLabels (Bus labels as given by the IEEE feeders)
5. Av1001 (The voltage gains of the step-voltage regulator)
6. Ytilde (the bus admittance matrix)
7. sL_load (Vector of `nominal power' of constant-power loads)
8. iL_load (Vector of `nominal current' of constant-current loads)
9. yL_load (Vector of `nominal admittance' of constant-impedance loads)
10. gMat (An N*3 binary matrix determining load-type per node.
    For example, gMat(i,:)=[1 0 0] determines constant-power load only, gMat(i,:)=[1,0,1] determines constant-power and constant-impedance loads)
11. Y (the bus admittance matrix removing the slack bus)
12. Y_NS (the portion of Ytilde corresponding to the interface of network and slack bus)
13. yImpedance (the matrix YL corresponding to constant-impedance loads)
14. Ycheck ( Y+YImpedance)
15. w (the no-load voltage profile)
16. Z (inverse of Ycheck)

The MatFile created here is input to the solve<NetworkName>SinglePhase.m

Modeling comments

• The conversion from multi-phase lines to single-phase is as follows:
  1. Three-by-three Nodal admittances YNMn, YMNn, YNMm, YMNm are created first by assuming zero's in their rows and columns corresponding to columns.
  2. The average of non-zero diagonal entires and the non-zero off diagonal entries is computed, denoted respectively by yd and yo.
  3. A symmetrical 3*3 matrix is then constructed YSymmetric=[yd, yo, yo; yo, yd, yo; yo, yo, yd];
  4. A symmetrical component transformation is then applied yielding a diagonal matrix Ydiagonal=diag([y0; y1; y2]).
  5. The representative admittance of the corresponding line is then chosen as y1.
• The conversion from multi-phase loads to single-phase: the sum of loads per bus is divided by three. Of course, this is heuristical since single-phase representation is for balanced networks only.

solve<NetworkName>.m

This script takes in a MatFile named <NetworkName>SinglePhase.mat from the directory SinglePhaseMatFiles/ and computes the Z-Bus method

Contraction mapping

The directory SinglePhaseContraction/ numerically verify that the Z-Bus method is a contraction.