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Voltage Stability: The Voltage Ledge Seen Close-Up

Conventional wisdom says that the more motors connected to a feeder, the faster voltage will collapse when there is a reactive deficiency. This is true to the extent that voltages do drop faster, but the voltage may not fall all the way — so a voltage collapse does notoccur. A different and more common state is reached when the feeder is in a quasi-equilibrium state at a low per unit voltage. This is the Voltage Ledge.

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Rising Out of the Trench: Insight from the Voltage Response Curve

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 afault 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.

techbl17A sample VRC is shown at right.  Before the fault occurs, the voltage is atnominal, 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 deepdrop in voltage, followed by a short duration at very low voltage, then arecovery 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 transientperiod 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 adifferent system configuration and dispatch, load model and contingency.  But we can make somegeneral observations about those systems by considering the shape of the VRC.


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.


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.


  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.
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Observability and Controllability in Highly Compensated Systems

Pterra Consulting

Shunt compensation, in the form of capacitor banks and static var devices (SVD), are commonly used to provide voltage support in heavily loaded systems.  Shunt devices offer a relatively cheap andeasy-to-implement solution to providing reactive power to load pockets or remote load areas of the grid.  In concept, one can add a combination of switched and controlled shunt compensation toincrease import capacity up to the thermal limit of the transmission system.  The savings from deferred investment in new transmission or congestion costs can justify the implementation of large shunt devices.  (The largest existing SVDs are a +500/-150 MVAR behemoth in the Allegheny Power service territory in Pennsylvania, USA, and the Chamouchouane SVC (actually two SVCs at one site) rated +330/-330 MVAR in Quebec, Canada.)

But, the impact …

The impact of static shunt devices on system operations can be a concern.  One such impact is a high operating voltage that may show only a small dip before the demand reaches a voltage collapse condition.  This effect can be viewed from the perspective of the P-V curve.  The P-V curve is a plot of voltage at a monitored bus as load or transfer is increased.  A typical curve is shown below.  The curve has a “knee” shape and voltage collapse eventually occurs at a level of load or transfer referred to as the MW or voltage collapse limit.



Observability is the aspect of the power system that provides operators with indicators to anticipate potential problems, in this case, voltage instability. The indicators need to be of a form that operators can observe and monitor in order to have sufficient time to respond to a system disturbance. For voltage stability, the traditional observed quantities are voltages at various nodes of the power system. However, when operating a system with high compensation levels, the pre-contingency voltage can be high, and voltage may not be a sufficient monitored parameter to observe the voltage stability of the grid.

Compatibility is the aspect of the power system that provides operators with sufficient control and response capability to maintain reliability, or in this specific case, voltage stability. The controls available to the operators of today include dispatch, voltage schedules and switching of capacitors and lines, and load adjustments. At high levels of shunt compensation, the sensitivity of voltage to the controls is quite high, i.e., small shifts in dispatch and voltage schedules may result in significant shifts in the voltage stability of the system. The primary causes of this sensitivity are shunt compensation devices in SVCs and capacitor banks whose reactive output vary as the square of the terminal voltage. As voltage shifts take place, the total reactive output from the static devices changes, and needs to be balanced by the reactive output from rotating devices.


To enhance observability, additional monitored parameters are required. One of the most commonly used indicators is the reactive reserve. This is a measure of the level of reactive output of generators and static devices. Although this measure is typically determined from Q-V curves, dynamic simulation offers a better alternative in identifying optimal levels of reactive output from various reactive sources. Other indicators that have been used in Europe and the United States include

  • the rate of voltage change per MW change in load,
  • the rate of reactive output change per MW change in load, and
  • online dynamic security assessment tools.

To improve controllability, additional supervisory and supplementary controls may be specified.  these my take the form of wide-area monitoring or control, or a centralized reactive power controller.



The result of high levels of shunt compensation added to a power system is a loss of observability and controllability.  But there is a certain economic incentive in adding shunt compensation in place of other alternatives, including constructing new transmission.  In concept, switched and controlled shunt devices can be added to increase transmission capacity up to the exiting thermal limit.  Hence, some very large SVCs, in the rating size above 500 MVA, have been implemented, are under construction or are in the planning stages.

To compensate for loss of observability through the classical means of monitoring system voltages, operators need additional observed parameters and/or an online security assessment tool.  Toaddress the increase in difficulty of controlling the power system through the classical methods such as switching and adjusting voltage setpoint, operators need further supplementary controls such wide-area monitoring and control to be able to continue to maintain a reliable, voltage-stable system.

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Application of DVRs in Networks Subject to Reactive Deficiencies

DVRs, or dynamic voltage restorers, are a relatively new static var device that has seen applications in a variety of distribution and subtransmission applications.  DVRs are series compensation devices that protect electric load against voltage sags, swells, unbalance and distortion.  Though these devices may provide good solutions for customers subject to poor power quality, we caution regarding their application in systems that are subject to prolonged reactive power deficiencies (resulting in low voltage conditions) and in systems that are susceptible to voltage collapse.

The reason for the caution is that in many instances the main protection of networks against voltage collapse is the natural response of load to decrease demand when voltage drop.  The implementation of DVRs would act to maintain demand even when incipient voltage conditions are present thus reducing inherent ability to halt a collapse and increasing the risk of cascading outage and blackout.

About DVRs

The first DVR was installed in North America in 1996, a 12.47 kV system located in Anderson, South Carolina.  Since then, DVRs of capacities up to 50 MVA have seen applications to critical loads in food processing, semiconductor and utility supply.  Cost and installation constraints limit these to where there is clear need for constant voltage supply.

Drawing1DVRs are power electronic controllers that use voltage source converters (VSC).  They inject independent phase voltages to the distribution feeder to regulate voltage seen by the critical load.  In various publications, the voltage injection have been termed, “the missing volts.”  A typical DVRs design is shown at right.  The source of the injected volts is the commutation process for reactive power demand and an energy source for real power demand.  The energy source may vary according to the design and manufacturer of the DVR; some examples of energy sources applied are DC capacitors, batteries and drawn from the line.

The capacity of DVRs are determined primarily by theinverter current capability.  Bypass protection would trigger once the current capability is exceeded.

During normal conditions, the DVR operates in stand-by mode.  Since the device is connected in series, there are conduction losses, which can be minimized by usingIntegrated Gate-Commutated Thyristor (IGCT) technology in the inverters.

Note that there is a similarity in the technical approach to DVRs to that of providing low voltage ride-through capability in wind turbine generators.  The dynamic response characteristics, especially for line supplied DVRs are thus similar to LVRT-mitigated turbines.


Characteristic Response

When a fault occurs on a distribution feeder, the voltage sags in neighboring feeders as well in the portion of the feeder itself which remains supplied through a power source.  After the fault is cleared, the voltage recovers in a manner influenced by the number of induction motors connected to the feeder.  In general, the more motors there are, theslower and more oscillatory is the voltage recovery.   This is true whether the fault is the more common single phase fault to any of the variations of fault types, including two-phase, three-phase and open phase faults.

Lightning BoltsStudies (by other researchers) have found that DVRs havesuccessfully provided protection against voltage sags to as low as 0.5 p.u. for durations of up to 0.1 seconds.  However, there is considerablevariation in conditions when response is simulated.  For example, in tests where there is no phase-shift component to the voltage deviation, the DVR performs well over large dips with prolonged durations.  In tests where significant phase-shift is present in the study or assumed system, the size and type of the energy source has a significant impact.  DC capacitor sources tend not to hold voltage well under phase-shifts.  Battery sources are a bit better.  Line-connected sources through a rectifier provided the best phase-shifted voltage deviation response in terms of maintaining voltage at the load.

From the transmission viewpoint, a DVR would extend the voltage range when load behaves as constant power load.  The combination of on-load tap-changing distribution transformers, voltage-switched capacitor banks and direct-connected DVRs lead to more current drawn from the transmission system during periods of reactive deficiency and low voltages.

A Loss of Relief

Volt Meter

As noted in earlier Techblogs, during periods of extremely high demand such as during summer heat storms,  there is a natural relief system that tends to arrest a declining voltage in the distribution system as reactive power deficiency in the transmission system spreads.  Devices such as the DVR tend to mask distribution load from the drop in voltage in the supply side.  Hence, instead of a drop in demand as voltage drops, demand remains at the nominal level.  This can hasten the onset of voltage collapse by removing the mechanism that helps systems reach a Voltage Ledge.

Direct-connected DVRs bring the added concern that as voltage drops and induction motors load require a phase-shifted supply, the DVRs increase demand from the transmission system.  This type of response can accelerate a voltage collapse.


Just a Warning

When implementing DVRs, it is important to take into the account the nature of the loadwhose voltage supply is being secured, as well as the the transmission system which must tolerate the change in voltage-response of the load.  In certain applications, it may be necessary to provide local fast reactive supply sources in order to secure the system, with the DVR added, from voltage collapse and cascading outages.  A careful simulation study which includes the transmission system is highly recommended.


  1. “Dynamic voltage restorer against balanced and unbalanced voltage sags: modelling and simulation,” Nguyen, P.T.; Saha, T.K., IEEE Power Engineering Society General Meeting, 6-10 June 2004.
  2. “Experience with an inverter-based dynamic voltage restorer,” Woodley, N.H.; Morgan, L.; Sundaram, A. Power Delivery, IEEE Transactions, Volume 14, Issue 3, Jul 1999.
  3. “The influence of motor loads on the voltage restoration capability of the dynamic voltage restorer,” Chang, C.S.; Ho, Y.S., Power System Technology, Proceedings: PowerCon 2000.
  4. “Voltage regulation using dynamic voltage restorer for large frequency variations,” Jindal, A.K.; Ghosh, A.; Joshi, A., Power Engineering Society General Meeting, 12-16 June 2005.
  5. “Dynamic Voltage Restorer For Voltage Sag Compensation,” Ramasamy, A.K.; Krishnan Iyer, R.; Ramachandaramuthy, V.K.; Mukerjee, R.N., Power Electronics and Drives Systems, 2005. International Conference, 28-01 Nov. 2005.
  6. “A Novel Technique to Compensate Voltage Sags in Multiline Distribution System—The Interline Dynamic Voltage Restorer,” Vilathgamuwa, D.; Wijekoon, H.M.; Choi, S.S., Industrial Electronics, IEEE Transactions, Volume 53, Issue 5. Oct. 2006, Pages: 1603 – 1611.
  7. “Voltage Sag Compensation With Z-Source Inverter Based Dynamic Voltage Restorer,” Vilathgamuwa, D.M.; Gajanayake, C.J.; Loh, P.C.; Li, Y.W., Industry Applications Conference. 41st IAS Annual Meeting. Oct. 2006.
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Living on the Ledge – Operating Distribution Systems at Low Voltage

Conventional wisdom says that the more motors connected to a feeder, the faster voltage will collapse when there is a reactive deficiency. This is true to the extent that voltages do drop faster, but the voltage may not fall all the way — so a voltage collapse does not occur. A different, and perhaps more problematic state is reached, when the feeder is in equilibrium point at a low per unit voltage.  This is operation on the Voltage Ledge.

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The In-Between Voltage State

Among steady-state techniques, one of the most common methods for evaluating voltage stability is through the venerable P-V curve, also known as the “knee” curve.  This method is used to identify the real power, or megawatt, margin to the point when the transmission grid is no longer able to support voltages, a state the industry has referred to as “voltage collapse.”  Many analysts have long suspected that the P-V curve at best provided an approximate indicator, and that there was a lot more it was not capturing.  Recent indications from near voltage collapse events seem to confirm that there is indeed a lot more, which may perhaps require a re-thinking of the whole process of using steady-state methods for voltage analysis.

Flexing the Knee

In the traditional P-V curve analysis, the power across a set of transmission paths is gradually increased by either increasing load or reducing generation at the receiving end.  This would simulate, for example, the gradual rise in demand over time, such as the weekday load rise, or the adjustments to increase imports into a region.  Several nodes or substations are selected where voltage is monitored as a series of power flow solutions is performed.  The result is the P-V curve with its characteristic “knee” shape.

The power flow solution assumes at least one critical factor that gives analysts concern — generators are modeled by static reactive limits.  For periods of a second to several minutes, generators are capable of delivering reactive power of up to 2 to 3 times the static limits, so-called transient vars [1].  What really happens in the short timeframes?  Is the effect sufficient to alter the P-V curve?

The answer to the second question is apparently “yes.”  But surprisingly, the basis goes beyond just the transient reactive capability of generators.

Generators deliver extra vars at the expense of thermal heating.  Oversized generators such as steam turbines in coal and nuclear plants are able to deliver more transient vars since they are able to tolerate more heating than smaller units such as gas turbines.  However, in a timeframe of minutes, rotor temperature control requires the reduction of transient vars through either overexcitation limiter protection or operator action.  When generators reduce var output, voltages drop.  At this point, the action shifts away from the observation of transmission network operators over to the distribution system!

Tap-changing transformers serving distribution circuits mask dropping voltages in the transmission network by maintaining setpoint voltages at customer loads.  The tap-changers will do this until they exhaust the available tap steps, at which point customer loads are exposed to a rapidly deteriorating voltage.  Capacitors do not help during this time as they themselves are losing reactive output at the rate of square of the drop in voltage.  In addition, the following effects seek to push voltages further downwards:

  • Loads that have low voltage tolerance that allow them to recover to their normal demand level at lower terminal voltages, such as variable speed motors, or thermostat-controlled loads

  • Motor loads that stall, causing an increase in reactive demand

However, there are other effects that help curb the deterioration of voltage:

  • The natural response of loads to decrease power demand as terminal voltages decrease

  • The dropout of contactors due to low voltage, most notably in motors, such as air conditioners and pumps

The combined effects of the above, as seen from the transmission system, produce a quasi-equilibrium characterized by voltages holding steady at the transmission level, somewhere in the .9 to 1.0 per unit range, while distribution voltages experience widely fluctuating and damaging voltages.  This condition may remain in place over an extended range of transfers and load levels, and thus prevail over several hours.  The net effect is a sort of voltage “ledge” in the P-V curve where transmission voltages appear to be “normal.”  One could liken this to the Brownian movement that occurs in the molecules of a liquid that from all outward appearances is sitting still.

Case Study

In July 1999, a situation characterized as a “near voltage collapse event” provides a good, practical example of the voltage ledge.

On this particular summer day, extremely high temperatures were projected along the Eastern US seaboard.  By noon, emergency dispatch conditions and a 5% voltage reduction (where the distribution voltage setpoints are reduced by 5%) had been called for.  At about 1 PM, voltages at the 500 kV network had dropped to 1.0 per unit, an unusual event, perhaps the first time ever, and yet not outside acceptable operating limits.  This condition remained for about 3 hours until load outages and cooling outside temperatures allowed voltages to recover.  During 3 hours on the voltage ledge, over a thousand pole-top distribution transformers failed, numerous motors stalled and re-started, some repeatedly, primarily air conditioners, and reports of damaged computers and TV sets and other sensitive equipment clogged call centers.  Distribution connected gas turbines failed to startup because of low terminal voltage conditions.

In the aftermath of this event, root cause analysis indicated the need for certain critical measures including more accurate modeling of generator reactive capability, the need for static var devices, must-run generators and possibly undervoltage load shedding and a broader study of the conditions that led to the disturbance.

Additional Comments

There is no doubt that the transient effects have an impact on the P-V curve.  Most of the time, the steady-state results are more conservative in terms of providing margin to voltage instability.  However, it is significant to note that the voltage ledge starts around 1.0 per unit voltage, above where most P-V curves would consider voltage collapse.

Clearly, dynamic simulation techniques provide a clearer view of grid response during the transient period.  Models for self-restoring loads, overexcitation limiters, motor stall and re-start and tap-changing transformers extend the reach of simulations beyond a few seconds to the minutes timeframe that is needed to see how systems behave in the voltage ledge.


The following references provide additional information on the concepts and events described in this article.

  1. A. Murdoch, G.E. Boukarim, B.E. Gott, M.J. D’Antonio and R.A. Lawson, “Generator Overexcitation Capability,” Panel Session Summary for the IEEE/PES 2001 WPM, Columbus, OH, jointly sponsored by the Excitation System Subcommittee and the
    Power System Stability Controls Subcommittee.
  2. Ricardo Austria, et al,Voltage Stability Assessment of the National Grid System Using Modern Analytical Tools,” presented at the 2001 Transmission and Distribution Conference and Exposition, October 28 – November 2, 2001, Atlanta, Georgia, USA.
  3. Robert T. Eynon, Thomas J. Leckey, and Douglas R. Hale, “The Electric Transmission Network: A Multi-Region Analysis,” EIA, DOE.
  4. Report of the U.S. Department of Energy’s Power Outage Study Team, Findings and Recommendations to Enhance Reliability from the Summer of 1999,” Washington, DC, March 2000.

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