Voltage Security Assessment

 

UW - Electrical Engineering

 APT
  • Why Should anyone be concerned about voltage security in a power system, what's the big deal?

Imagine if you could not rely on constant (or nearly constant) voltage at a wall outlet. Your television would work sometimes, but not always. Maybe the toaster would burn toast on a low setting and then some time later when the voltage changed, it would barely brown the toast on a high setting. Clearly we, as consumers of electric power, need reliable, constant voltage from the utility power system. For other less obvious reasons, a system's voltage must be maintained at a constant or nearly constant level. This is best explained mathematically. The following information is from Power System Analysis by Arthur Bergan and Vijay Vittal and is covered in detail in EE454 and other courses at the UW.

Voltage Security Assessment

Consider a radial transmission line. That is, a line with a source on one end, and a load at the opposite end. At the "near end" there is voltage support, but at the far end of the line there is a complex power load. How will the voltage at the load end vary as the load changes?

For simplicity, assume that the load draws power at a fixed power factor. In this case complex power can be expressed as follows:

Thus as the load is varied, PD varies with B (beta) as a parameter.
By using the Pythagorean identity we can eliminate angle theta 12:
Rearranging we obtain a quadratic equation:
Using the Quadratic formula, the following solution is obtained.
  • Voltage Equation
Notice that there are multiple solutions because of the +/- portion of the result. The physical meaning of this is that there is one stable voltage solution and one unstable voltage solution. We desire to maintain a stable solution. There is one point however, where there will be only one solution. At the point where:
If the V1 and X are fixed to some value, and PD is allowed to vary, "P-V" plot can be obtained.

For a given load, it is desirable to maintain a voltage above the singular point on the curve. The stable solution is at the higher voltage level. If for some reason, voltage falls too low, the voltage may collapse resulting in a blackout. There is a good reason to pay attention to voltage security. Low voltage is not just an inconvenience for the users of electricity; it can result in a catastrophic failure of the whole system. Why? Read on.

Suppose that the load demands P1, and the voltage is at point A'. Next, suppose the load changes and demands P2. Does it make since for the voltage to increase to point B'? Of course not. Remember that if the load demands more power while the voltage of the source is fixed, then the current carried by the line(s) must increase. If the line current increases while the line impedance remains constant then it follows from Ohm's law that the load voltage will decrease. Points A' and B' are not stable solutions. The correct voltage when the load demand is P1 is found at the point A and at point B when the load demand is P2. If voltage falls too low, the voltage will collapse and a blackout will result. The power system's voltage profile must be maintained if the system is to remain in operation.