Symmetrical Components

In electrical engineering, the method of symmetrical components simplifies analysis of unbalanced three-phase power systems under both normal and abnormal conditions. Using the mathematical method developed by Fortescue this app calculates the symmetrical components for 3 unbalanced phasors as well as the reverse. The app displays both graphical and digital results for the symmetrical components and unbalanced phasors.

GRAPHICAL INPUT

Use the touch screen to drag the unbalanced phasors to the desired values. The same can be done with the symmetrical components (on touch down the app will select the closest red phase of the symmetrical components for input). The digital output values for unbalance and symmetrical components at the bottom of the graphical screen will update automatically.

The keys at the bottom of the graphical screen perform the following functions:

1) Settings (cog symbol): opens the settings menu and allows the user to select rectangular or polar coordinates, angular units (degrees or radians) as well as grid scale, font sizes and other settings.

2) Zoom (magnifying glasses): These buttons cause the graphical display to zoom in and out.

3) Vector summation (greek sigma): Displays the symmetrical components as a vector summation on the unbalanced phasor display.

4) Labels (tags symbol): Display identifying labels on all vectors on both unbalanced and symmetrical components displays.

5) Phases (recycle symbol): Cycle the symmetrical components digital display through all phases.

6) Reset (undo symbol): Return the phasors to a balanced state. (the magnitude upon reset can be specified in the settings page, grid settings.

7) Exit app (power button symbol): Exit the app.

DIGITAL INPUT

Digital input can be carried out by tapping on the digital output at the bottom of the graphical screen. A window will then slide open for input. This window also incorporates a complex number calculator.

The digital input screen will accept complex numbers in rectangular, polar, exponential and trigonometric form. Upon pressing the "=" button the expression is calculated and the answer given in either rectangular, polar, exponential or trigonometric form depending on the setting selected on the menu bar at the top of the screen. This setting can also be used to convert answers from one format to another.

Radians/Degrees key - expressions are evaluated based on the angular units shown in the menu bar. The rad/deg key on the keypad will change this setting and also convert any angles in the digital display (as designated by an angle symbol) from radians to degrees and visa versa. the angular units setting can also be changed via the menu bar without converting any angles currently in the digital display. (Note: if the graphical display is set to Polar then this setting also changes the units on the graphical display).

The calculator can add, subtract, multiply and divide complex numbers in polar form. All complex number forms can be used in the one expression. The calculator will give the solution in the form selected in the menu bar at the top of the screen. This setting does not affect the format of the graphical screen which can be set to Polar or Rectangular coordinates on the settings page.

MISCELLANEOUS

The app evaluates operators in the following order of precedence ^,trig,ln,/,*,-,+. Use brackets to ensure that the input expression is evaluated in the way that you expect.

For example:

-1^(1/2) will result in the answer -1 because the app will first calculate the square root of 1 and then apply the minus sign. To calculate the square root of minus one put the minus one in brackets as below.

(-1)^(1/2) will result in the answer "j" i.e. an imaginary number

Other examples where the use of brackets are required are:

-1-(-2)=1

ln(-2)=0.693+j3.142

sin(pi/4)