Three-phase modeling

This repository provides MATLAB scripts that construct the bus admittance matrix for the following multi-phase distribution networks

• IEEE 37-bus feeder
• IEEE 123-bus feeder
• 8500-node feeder
• European 906-bus low voltage feeder (ELV 906-bus feeder)

The data files for the aforementioned feeders are downloaded from PES. Benchmark solutions for the IEEE 37-bus feeder and the ELV 906-bus feeder are taken from the EPRI distribution system simulator, OpenDSS. Benchmark solutions for the IEEE 123-bus and the 8500-node feeder are taken from PES.

If you are interested in using this material in your research, we kindly request you to cite the following publication:

M. Bazrafshan and N. Gatsis, "Comprehensive modeling of three-phase distribution systems via the bus admittance matrix," IEEE Trans. Power Syst., to be published, doi: 10.1109/TPWRS.2017.2728618. See the arXiv version.

Code description

An explanation is provided here for the most important scripts of this folder to simplify usage. Some additional scripts are also within the folder that replicate the results of the cited paper.

The modeling presented here takes into account mixed wye and delta ZIP loads, even though the model in the cited paper only assumes wye or delta ZIP loads.

main.m

This script is the starting point. It contains all the necessary steps from modeling, to computation of voltages as well as comparisons between solutions.

setupYbus<NetworkName>.m

This function uses the data files of the folder feeder data provided from PES to create the bus admittance matrix.

List of outputs

• network a structure with the following fields
  • Sbase Network power base
  • Vbase Network voltage base
  • Zbase Network impedance base
  • Ynet Bus admittance matrix including the slack bus
  • Y Bus admittance matrix excluding the slack bus
  • Y_NS The portion of bus admittance matrix relating the network to the slack bus
  • Y_SS The portion of bus admittance matrix relating only to the slack bus

The output of this function should typically be input to the function computeNoLoadVoltage.m.

List of inputs

• regulatorTypes (optional) a string set to either 'ideal' or 'non-ideal' determining whether step-voltage regulators should be modeled as ideal or lossy. If not provided, 'non-ideal' regulators are assumed.
• epsilon (optional) determines the value of the Epsilon needed to adjust the delta-connected transformers to ensure invertibility. If not provided, a default of 1e-5 is assumed.

computeNoLoadVoltage.m

This function computes some required no-load quantities for the network.

List of outputs

• network a structure with the following additional field:
• noLoadQuantities is itself an structure that has the following fields:
• v0mag Vector of magnitude for the slack bus voltage phasor
• v0phases Vector of phases in degrees for the slack bus voltage phasor
• v0 Vector of slack bus complex voltage phasor
• w Vector of no-load complex voltage profile for the network
• w3phase The no-load complex voltage profile organized in an (N+1)*3 matrix where the rows determining the bus numbers and the columns determine the phases.

The output of this function should typically be input to the function setupLoads<NetworkName>.m.

List of inputs

• network a network structure created by setupYbus<NetworkName>.m.
• v0mags (optional) A 3*1 vector of magnitudes for the slack bus voltage phasor.
• v0phases (optional) A 3*1 vector of phases in degrees for the slack bus voltage phasor.

setupLoads<NetworkName>.m

This function updates the network structure created previously with information on loads. The modeling of loads is based on the load type (constant-power, constant-current, constant-impedance, or any combination of these) as well as the connection (delta, wye, or a combination of these). The load model is explicitly given in the calculateIPQII.m function and is highlighted here first. The general load model is as follows:

iL_PQ= c(i,:)*[ fPQ( eVec1.' * v, sL(i,1)); fPQ(eVec2.'*v, sL(i,2))];
iL_I=c(i,:) *[ fI(eVec1.'*v, iL(i,1)); fI(eVec2.'*v, iL(i,2))]; 
iL_Y=c(i,:)*[fY(eVec1.'*v, yL(i,1)); fY(eVec2.'*v, yL(i,2))];
fv(i,1)=g(i,:)*[iL_PQ;iL_I;iL_Y];

The vector $c(i,:)$ has two binary entries. The first binary entry corresponds to wye connection. The second binary entry corresponds to delta. If both are set to 1, then the load connection is a mixed wye-delta connection. The vectors $eVec1$ and $eVec2$ are needed to decide which phases of the voltage at this node plays a role in the load of the assumed current phase. The vector $g(i,:)$ determines whether the load is constant-power, constant-current, or constant-impedance.

List of outputs

• network a structure with the following additional field:
• loadQuantities a structure with the following fields:
• sL_load Vector of 'nominal power' of constant-power loads
• iL_load Vector of 'nominal current' of constant-current loads
• yL_load Vector of 'nominal admittance' of constant-impedance loads
• ePage A page determining which indices of the voltage vector play a role in the considered phase of the current.
• gMat A matrix determining the ZIP load combination.
• CMat A matrix determining the wye, delta, or mixed wye delta connections. (See the above on load modeling)

The output of this function should typically be input to the function performZBus.m.

List of inputs

• network a structure created by computeNoLoadVoltage.m

performZBus.m

Computes the Z-Bus load flow.

List of outputs

• network a structure with the following additional field:
• ZBusResults a structure with the following fields:
• v vector of voltages (all phases in vector format)
• vsol solution computed (similar to v but does not include the slack voltage)
• success success flag
• err the error at the final iteration

The output of this function should typically be input to the function obtainVoltages.m.

List of inputs

• network structure created by
• maxIt (optional) Maximum iterations. If not specified, a default value of 10 is assumed

obtainVoltages.m

This function merely maps the computed voltage vector from the Z-Bus load-flow to appropriate data structure in terms of buses and their phases.

List of outputs

• network an structure with the following additional fields:
• solution an structure with the following fields:
• resultsVMag a Matrix (N+1)-by-3 corresponding to computed voltage magnitudes
• resultsVPhase a Matrix (N+1)-by-3 corresponding to computed voltage phases in radians
• v3phase a Matrix (N+1)-by-3 corresponding to computed voltage phasors
• v3phaseRegs a Matrix (N+1+NREgs)-by-3 corresponding to computed voltage phasors including regulator secondary buses

List of inputs

• network an structure created by performZBus.m