Interactive Heavily Unbalanced Power System Analysis

In order to see and interact with the case of study open the case_of_study.html file with an internet browser, it should work in all browser but we tested in Google Chrome, Firefox and Safari.

Once the file is open, we will see something like the attached figure. In the next steps, the different variables available and the way of interacting with then will be described.

A heavily unbalanced three-phase system of 11 nodes is represented in the left part, where each phase of a line is represented with a color (red,green,blue) for (a,b,c) respectively, and this can be extended also for the nodes. The white number in the center of the nodes represent the node numbers. The movement of the yellow ball on the lines represents the convention of positive power flow. The power flow in a line will be positive if it flows in the same direction of the movement of the ball.  Voltages are expressed in V, currents in A and power in kW, kVAr or kVA.

The power flow in this system has been solved and all the results, included the power dividers are available. Nodal variables, like voltage, current injections, active, reactive and apparent power can be represented in the nodes by selecting them using the drop-down menu labeled as “Node Variable”.  Next to this drown menu we can see a tick labeled as “Angle”, if it is marked, complex nodal variables are shown with angle, if not, only module. The size of the colored circles inside the node will be proportional to the module of the variable represented.  Positive active power means consumption, negative active power injection. When clicking a node of the scheme a phasor diagram with the injected currents and the voltages in the nodes appears in the right side of the screen. Also, the power triangles are represented.

The “Line variable” drop-down menu allow us to represent variables in the lines, basically, currents, powers and losses. I12t is the total current (considering also the shunt current, if it exists), flowing from the starting point to the ending point while I21t the total current flowing from the ending point to the starting point. It must be remarked that the yellow ball is always moving from the starting point to the ending point.  Shunt currents are represented by I1s and I2s and the currents flowing through the lines without considering shunt currents are expressed as I12 and I21. Same criteria apply to active, reactive and apparent power through the lines. The line losses can be represented selecting “Line_losses” in this very same drop-down menu. The width of the colored lines representing the phases is proportional to the module of the variable represented. When clicking in a specific line, all the currents through that line are represented in the right part of the screen in the so called “Line details” diagram.

The power dividers of the expression (21) of the paper P(m,n) and P(m,n) as well as the P(m,n)loss can be analyzed using the “drop-down” menu labeled as “Pdivs”, there we can select Pdiv12t and Pdiv21t representing respectively P(m,n) and P(m,n).  Pdiv_losses represent P(m,n)loss.

We recommend the next set up for analysis:

Node variable drop-down menu: P

Line variable drop-down menu: Line_losses

Pdivs drop-down menu: Pdiv_losses