The Voltage Response Curve (or for purposes of this article, the “VRC“) is what you get when you plot the voltage at or near a system node just before, during and immediately after an event involving a fault and subsequent clearing.  The VRC is a record of the dynamic response of the system.  It can be obtained from computer simulation, a well-isolated system test or a disturbance recorder.  In much the same way that planning and operations personnel look at swing curves (Note 1) to determine if a synchronous system is angularly stable, much can be deduced about the underlying system and its voltage stability by studying the VRC.

A sample VRC is shown at right.  Before the fault occurs, the voltage is at nominal, or 1.0 per unit (pu).  When the fault occurs, voltage drops and remains depressed while the fault is on.  After a few cycles, the fault is cleared by circuit breakers, which may result in loss of a line or other system element.  Immediately after the fault is cleared the voltage recovers.  Seconds later, the voltage would settle at the post-transient value.

The shape of the VRC is that of a trench(note 2), where there is an initial deep drop in voltage, followed by a short duration at very low voltage, then a recovery period.  The shape of the curve, especially for the time period after the fault is cleared, says a lot about the underlying grid’s reactive power supply, including how close the system is to voltage collapse.  Hence, the VRC provides a measure of voltage stability.

Furthermore, the VRC is a system characteristic whose shape is consistent over a certain area of the grid, such as a load pocket,regardless of location of the fault within that area.  Hence, it may be possible to identify the system based solely on the shape of the VRC.  This system characteristic allows operators and planners to set voltage performance criteria that are specific to a system.  And yet, the same criteria that may work so well in one system may not apply to another whose VRC characteristics may be different.

### One Digression …

Before taking a closer look at the shape of the VRC trench, let us note, for example, the initial effort of FERC to specify the low voltage ride through of wind farms.  The proposed criteria is shown in the Figure below (Note 3).

The concept behind this proposed criteria was that in providing wind farms with the low-voltage ride-through capability, the wind farms will be able to withstand the system VRC.  However, there are a wide variety of VRC shapes existing in US power systems.  (The criteria has been replaced.)

### Continuing …

Voltage Stability refers to the ability of a power system to restore and maintain voltage at all buses in the system following a disturbance from a given initial operating state. Voltage instability can occur in heavily loaded systems when reactive power available from power system equipment such as capacitors, transmission lines, generators, and static var devices are less than the demand from loads and the requirement to supply reactive losses.

Voltage stability during the transient period is determined based on the shape of the VRC in the first few seconds following a disturbance.  For instance, see the three VRCs shown at right.  Each of the VRCs is based on a different system configuration and dispatch, load model and contingency.  But we can make some general observations about those systems by considering the shape of the VRC.

### Typology

The Type 1 VRC (shown as the green curve) has an overshoot after the fault is cleared.  The voltage rise indicates that there is available reactive power in the vicinity of the fault, even after the loss of a line or transformer.  This reactive power may come from generators in the local area, and/or generators remote to the area but connected to the area via transmission lines.  This may also come about from fast load shedding occurring during or immediately after the fault is cleared.  The “ringing” at the top of the response curve may come from voltage regulators taking control of field voltage.

The Type 2 VRC (shown as the red curve) has no overshoot and settles to the post-transient voltage immediately after the fault is cleared.  The underlying system may not have much available reactive power following the fault.  The voltage response is defined primarily by the load characteristic.  With more constant impedance or constant current type loads, the post-fault return to voltage will be even sharper than that shown.

The Type 3 VRC (shown as the blue curve) settles at a very low voltage.  In this case, the underlying system does not have access to reactive power to recover the voltage within acceptable limits.  The system probably enters into a Voltage Ledge, where, to compensate for the lack of reactive power, motors are stalling, dropping out or restarting, and ZIP-type loads (Note 4) are at a reduced level.

### Conclusions

As we get used to checking for voltage stability through VRC curves, we develop better insight on the underlying systems that produce such curves.  Such insight leads to better understanding of the nature of any potential voltage instability, and the possible countermeasures that would be effective for each situation.

### Notes

1. Swing curves – plots of rotor angles of rotating equipment interconnected synchronously.  During a contingency, the rotor angles separate and whether the the angles recover and re-synchronize or not determines the angular stability of the system to the disturbance.  The swing curves are the characteristic response of the rotors whose angles appear to swinging against and with each other.
2. Oceanic trenches are narrow topographic depressions of the sea floor. They are also the deepest parts of the ocean floor.
3. Voltage Response nomogram as proposed by the US FERC for wind farm low-voltage ride through characteristics (United States Federal Energy Regulatory Commission, order No. 661, Appendix B, June 2, 2005).  This has since been replaced.
4. ZIP loads – These are loads that respond in a specific voltage characteristic.  Constant Z (impedance) loads vary as the square of voltage. This type of load includes most lighting, most small motors loads.  Constant I (current) loads vary in direct proportion to voltage. This is an approximation of general response from composite loads such as commercial areas and residential load.  Constant P (power) loads are invariant to voltage. These include adjustable speed drive motors, computers, electronic equipment and other loads.