# A Methodology for Estimating Potential Curtailment of Wind Farms

Figure 1

A wind farm integrated into a transmission grid is subject to curtailment due to temporary or long-term insufficient capacity on the transmission lines.  Maintenance outage of a nearby line, dispatch of competing wind farms and availability of other generators are examples of system events that may limit injection capacity.  In general, events that increase transmission utilization present potential curtailment conditions for wind farms, and so the daily and seasonal load cycles, and changes to interchange and import/export patterns can influence injection capacity as well.

In measuring the potential curtailment of a wind farm for, say, the incoming year, it is important to take into account the wind availability as well.  It may seem likely that curtailment will occur when the load is highest and transmission use is greatest; however, this condition may occur in summer when wind availability is low.  Hence, we have the common situation that at summer peak, the available transmission is low, but the wind capacity is also low, resulting in no or minimal curtailment.  Some operating wind farms have observed that most curtailments occur in the spring and fall periods where grid use may be relatively low but wind farm capacities are high.

One approach to estimating potential wind farm curtailment is to simulate the hourly chronological performance of the combined generation and transmission system taking into account outages, unit commitment, least cost dispatch and load variations.  This method is widely known as production simulation.  In addition to being data intensive and laborious to setup, the simulation duration can be significant, especially if one chooses to run multiple years in a Monte Carlo simulation.  This Blog presents a methodology that is based on an analytical model that is generally much simpler to develop than production simulation models and provides some unique insight into how and how often curtailments come about.

## Analytical Approach

We begin with the observation that a wind farm does not experience curtailment at all hours of the year.  And when it does, the causes are specifically identifiable either through operations data or scenario reconstruction.  Hence, we can say that  events that do not result in curtailment are of no interest for our present purposes, narrowing down our focus to only those conditions that lead to curtailment.  The fewer the curtailment events and scenarios, the simpler the analytical method will be compared to production simulation.

Another observation is that curtailment will occur due to operating reliability requirements on the transmission system.  (There is a requirement for operating reserve that may lead to curtailment, but such curtailment is not specific to a wind farm but to a group of generators in a control area and is not captured in this methodology.)  Transmission systems are operated to withstand the most credible contingencies, also referred to by various names such as design, first or n-1 contingencies.  Operators use various forms of security constrained dispatch models that specify the acceptable operating mode which may specifically identify the amount of curtailment on a wind farm.  The typical curtailment condition on a wind farm occurs when power flows on the transmission lines and transformers in the vicinity of the wind farm reduce available transmission capacity to less than the wind capacity for that point in time.

Figure 2

The final foundational piece to this  analytical approach is based on the manner in which transmission lines are loaded.  The system intact and post-contingency power that flows on a transmission branch is directly influenced by generation dispatch, customer load, interchanges with neighboring control areas and grid configuration (including planned upgrades) in various combinations.  Some of these factors taken individually may have the same effect on potential curtailment; i.e., increase in generation on the sending end, increase in load at the receiving end, maintenance outage of a parallel line and increasing imports from sending to receiving end — all have the same effect on the transmission branch which is to increase flow from sending to receiving end.  If we can identify the condition that brings the available transmission capacity to just equal the wind farm capacity for a specific period, then we may generalize that all other conditions that increase the flow further on the constraining transmission branch will lead to curtailment.  We can thus ignore all the conditions that reduce flow since these do not result in curtailment.

Combining all of the above observations leads us to the structure of the new analytical method.

## Nuts and Bolts

First we take a power flow model of a typical system condition such as summer peak load.  Next, we measure the available transmission capacity for the subject wind farm using an AC power flow methodology as follows:

In the system state prior to the injection of power from the subject wind farm, the transmission system is in security-constrained dispatch; i.e., generation is scheduled in a manner that no thermal overloads would occur for any credible contingency.  With the wind farm dispatched at the installed capacity level, contingency analysis is conducted to check for thermal overloads.  If overloads are observed, the wind farm generation is reduced until the overloads are resolved representing a system that meets conditions for security-constrained dispatch.  If no overloads are observed, proceed to another season or operating period.

We now review the variations in load, import/export energy and interchange power for those conditions which tend to exacerbate violations for the limiting conditions (also referred to as flowgates or congestions).  By modeling each of the critical contributing factors in the power flow, we can confirm the impact on the wind farm injection capacity by repeating the AC power flow methodology above.

Finally, we group the contributing factors by magnitude of potential impact on curtailment and apply probability theory. And that’s basically it.

## Case Study

As a case study to illustrate the mothodology we use a 350 MW wind farm interconnected to a transmission grid at 138 kV.  We start with four power flow models representing each of the seasons for the incoming year.  The wind farm’s injection capacity for the summer peak power flow is 150 MW.  First we check for sensitivity of the injection capacity to load.  Then we correlate the average wind capacity by load level and the result is shown in Figure 1.  The graph shows that wind capacity is likely to exceed transmission capacity when load is between 68-88% of peak.   The magnitude of curtailment varies as the load level as shown by the purple line in Figure 1. Next we check for sensivity to generation dispatch.  One competing wind farm has an impact on the limiting conditions.  The competing wind farm shares use of the available transmission capacity with the study wind farm.   The resulting curtailment characteristic is shown in Figure 2.  The magnitude of curtailments are larger now with the competing wind farm and occurs

Figure 3

over a wider range of load levels.  A check of import/export impacts shows that injection capacity has no sensitivity to this factor.  The final check is on the impact of line maintenance outages.  These are generally scheduled during the spring period.  However, to maintain a comparison with the previous figures, we assume a summer outage.  The resulting curtailment characteristic is shown in Figure 3.   Curtailments are seen to occur at all load levels while the line is out on maintenance with up 180 MW of wind capacity curtailed. With just load variations, the summertime curtailment is about 3 % of available wind capacity.  This increases to 29% when the competing wind farm is in service; and to 65% with a line out on maintenance.

## Further Considerations

This is a very raw introduction to the new analytical method that includes only “deterministic” models; i.e., pre-defined values of load and dispatch.  The main characteristic of the method is that it uses a significantly smaller data set to conduct the assessment compared to production simulation methods.  The computational demand is also significantly smaller since all the processes are based on algebraic equations.  Hence, set-up and run times are generally short.

However, the method is also amenable to handling “probabilistic” models of the power system.  Examples of probabilistic events include: projected demand may change due to variations in weather and temperature, power system facilities may become unavailable due to planned or unplanned outages, and failure bunching during extreme weather conditions.  A forthcoming Blog describes this aspect of the methodology.

A more rigorous presentation of the method is included in a forthcoming technical paper.

## Conclusions

An analytical method is proposed to determine the potential curtailments for a wind farm interconnected to a transmission system.  The methodology differs from production simulation in that it does not use the full generation-transmission representation but rather applies offline analysis using power flow models to develop operating polygons to identify conditions for curtailments.   The methodology was applied to a sample 350 MW wind farm and successfully identifed the critical factors that lead to curtailments and the magnitude of impact of each.  The methodology was also simpler to apply and can be used to underpin a heuristic method for estimating curtailments.

## References:

(1) “Wind Farm Integration: On the Use of Agreggate Models“, By J. Chen, M. Gutierrez, R. Austria, Pterra Tech Blog, Oct 14, 2009.

(2)”Wind Farm Integration: Analytical Requirements“, Pterra Tech Blog, Oct 26, 2009.

(3) “High Voltage Concern at Wind Farms?” Pterra Tech Blog, May 18, 2010.

(4) “On the Use of Aggregate Models of a Wind Farm,” J. Chen, M. Gutierrez, R. Austria, October 2009.

(5) “The Coincidence of Wind,” Pterra Consulting, May 2009.

(6) “On Using Linear Approximation and Distribution Factors,” Pterra Consulting, April 2008.

(7) “The Renewables: Part 1 – Wind Farms,” May 2006.