On Using Aggregate Models of a Wind Farm

(A serialized and expanded version of this article can be found here)

As an increasing number of wind
turbines are connected to the power system, more and more wind farm
interconnection studies are requested. Usually a wind farm consists of
tens
of wind turbines and cables. The wind turbines are mostly the same
type in one particular wind farm, but the cables interconnecting these wind
turbines vary in length, capacity and configuration. A transmission
analyst may need to avoid modeling each turbine and each cable in the wind
farm for the interconnection study for one or more of several possible
reasons:

  1. It is laborious to setup the detailed model. For example, a
    300 MW wind farm would comprise of 200 1.5-MW wind turbines
    interconnected at a distribution level voltage such as 34.5 kV in
    a feeder network similar to that of a suburban housing development.
  2. The simulation software for power flow, short circuit or stability
    analysis may not accommodate carrying detailed models for all the
    existing and proposed wind farms. To consider the dimensions, take the
    case of a system with some 5000 MW of installed wind capacity. Detailed
    modeling of the wind farms would require about 4000 turbine models, 5000
    additional nodes and the same number of additional branches in the
    database.
  3. The detailed model requires representation of distribution level
    feeder circuits that increase the “spread” of branch impedances
    in the power flow model. “Spread” here refers to the range of impedances
    included in the database. (see further discussion about spread or
    diversity in the article, “Converging
    the Power Flow
    ”). Too much spread can lead to difficulties in
    solving, or converging, the power flow.

In view of all the above reasons, it may be sufficient to aggregate
groups of wind turbines into equivalents that capture their net impact on
the transmission system.

Modeling Issues

For a typical interconnection study consisting of power flow calculation,
transient stability and short circuit analysis, the aggregated wind farm
model must effectively represent the behavior of the wind farm during

  • steady-state operation;
  • switching operations or short circuit occurrences;
  • transient period following planned and unplanned events such as a
    fault, line trip, breaker reclose, or trip of a turbine.

The components that need to be considered in the aggregate modeling are:

  • Steady-state, short circuit and stability models of the
    individual turbines
    . Typically, a farm will use the same type and
    manufacture of wind turbine throughout. Aggregating the individual
    turbines is straight-forward in this case. Most turbine models
    have the characteristics of aggregating by capacity. For example, GE1.5
    wind turbine generator model variables are in per unit on the generator
    MVA base. To model the aggregated unit, only the generator MVA base
    need be changed to the sum of the individual turbine MVAs. If the
    turbines are of different types (for types of wind turbines, please see
    article on Wind Farms), a
    more involved process for aggregating is required to obtain a
    good equivalent. In general, interconnection studies assume that each
    turbine sees the same wind speed; however, in reality, the wind
    diversity
    across a farm is such that some turbines may be below the
    wind threshold and delivering zero power while others may be at full
    power.
  • Electrical layout of a wind farm. The layout of a wind farm
    looks much like a suburban housing development where the “houses” or in
    this case, the individual wind turbines, are spread out to minimize wind
    shadows and maximize wind capture. The turbines are
    interconnected by feeders that are arranged and optimized similar to a
    suburban distribution network, only in this case, they are part of the “collector
    system. The more wind turbines there are in the farm, the more complex
    the collector system. For aggregation purposes, if the feeder is
    radial
    , one aggregate may be developed for the whole feeder, as
    shown in Figure 1. For the electrical impedance of the equivalent
    feeder, the two most common practices are: (a) use the sum of the
    feeder impedance to the farthest wind turbine or (b) use a rule-of-thumb
    for the equivalent impedance to be 1/3 of the total feeder
    impedance.
  • Step-up transformer characteristics. These are generally
    modeled explicitly, even if the wind turbines are aggregated.
  • Capacitor banks and static var devices. These are also
    modeled explicitly.

Figure
1A shows a detailed wind farm with 16 turbines arranged in two radial
feeders, and in Figure 1B, a proposed equivalent with two aggregates, one
for each feeder. In the figure, the numbers in the circles represent the
total number of turbines at the corresponding buses. In the detailed model,
each turbine is modeled exactly as it is electrically located in the wind
farm, and each wind turbine bus has only one turbine connected. In the
simplified model, two aggregated wind turbines are modeled at the remote end
of each cable branch, one lumps together twelve wind turbines and the other,
four wind turbines.

Figure 1: (A) Detailed Wind Farm Model and its (B)
Simplified Equivalent

For steady state analysis, the two
models show very similar performance characteristics. Actually, the
difference between these two models comes from some minor power loss
differences on the cables connecting the wind turbines. Since in the steady
state analysis, the wind farm is modeled as seen from the system, only the
effects of the power injection into the system are considered while the
internal wind farm behavior is neglected.

For transient stability analysis, the aggregated model closely
represents the wind farm especially when the cables connecting the wind
turbines are short. However, there are cases where the internal wind farm
responses are different, and these result in significant differences in
impacts on the system.

For short circuit analysis, the two models’ differences in the
interconnection study vary. For those wind turbines that do not contribute
short circuit current , the modeling choice does not matter. For example,
Clipper’s permanent magnet wind turbine generator has no shirt
circuit current contribution. For those wind turbines that contribute short
circuit current, the detailed model might have higher current than that of
the simplified model.

Test Case

In our test case, a wind
farm, sized 32MW and shown in Figure 1(A), is proposed for
interconnection to an existing 115 kV line rated 105 MVA. In the simplified
model, the feeder branches are modeled with full equivalent impedances,
i.e. the corresponding largest impedance of the feeder.

  • Performance in the steady-state: The power injections at POI (point
    of interconnection) for the detailed model and simplified model are
    31.6MW and 31.5MW respectively, and the corresponding reactive demands
    and voltages at the POI are 0.7MVAR, 1.020p.u. and 0.2MVAR, 1.022p.u.,
    respectively. The active and reactive power differences are due to the
    minor power loss and voltage profile differences on the interconnecting
    cables. The difference in power delivered at the 115 kV POI constitute
    less than 1% of the line rating and will not have a significant
    impact on the steady-state thermal performance. The 0.5MVAR difference
    in reactive power demand likewise will not significantly change the
    steady-state voltage performance of the models. (The farm is small
    enough
    that it may be interconnected to a 69 or 34.5 kV system. If
    this is the case, the thermal and voltage impacts from the difference in
    modeling can be more significant.)
  • Short circuit performance. For this test case, the wind turbine
    generator has no short circuit contribution. As such, the maximum fault
    current level with the addition of the wind project will not change.
  • Transient stability performance. The models show very similar
    performance for most disturbance except for those close to the POI.
    When a three-phase fault is applied at the POI, the terminal voltage of
    the wind turbine next to the step-up transformer in the detailed model
    (at units marked as “N1” and “M1” shown in Figure 1A) is less than that
    of the corresponding aggregated turbine in the simplified model. The
    voltage difference might cause the situation that some wind turbines in
    the detailed model are tripped due to low voltages while the aggregated
    turbines in the simplified model are all online. Figure 2 shows
    simulation results for the test case for a 3 phase fault at the POI, (A)
    for the detailed model and (B) for the simplified or aggregated model.
    In Figure 2, the active power (pbr), current (ibr) through the
    transformer and the voltage (vbus) on the low side of the transformer
    are monitored. In the detailed model case, the four turbines on the
    right branch (units “M1” to “M4”in Figure 1) are all tripped due to low
    voltages, while the aggregated turbines in the simplified model all stay
    online. The simulation of the detailed model shows that the terminal
    voltages for units “M1” to “M4” dip low enough and for long enough to
    trip the wind turbines’ voltage protection. On the other hand, the
    terminal voltages of the aggregated units are above the limits.

Figure 2: Different Responses of the (A) Detailed Model
and the (B) Simplified Model (Output from PSLF software; PSLF is a
commercial product of General Electric Energy)

For test purposes, a partial equivalent feeder impedance
equal to 1/3 of the full impedance is applied to the simplified
model.  This model is more conservative with respect to the voltage
profile during the fault than the model with the full equivalent impedance.
Applying the same fault at the POI, with 1/3 of the corresponding maximum
feeder impedance, the lumped unit with 4 turbines is tripped.  This is
a similar result to the case with detailed model.

Another observation of note in the test case: when re-dispatching
involving the wind farm is required, it is easier switch on/off turbines in
a detailed model than to calculate the new equivalent in the aggregated
model.

Conclusions

  • In general, an aggregated model provides a good enough
    approximation
    of the wind farm performance for use in
    interconnection studies.
  • There are certain situations when a detailed model is
    required.

    • When the size of the wind farm to be interconnected is
      significant relative to the network; for example, a 30 MW wind farm
      to a 34.5 kV network
    • When the fault is applied at or close to the POI for
      transient stability performance
  • To avoid inaccuracies, a detailed model is preferred when
    simulating close-in faults for transient stability.  All other
    faults can be simulated with acceptable accuracy using a
    simplified model.  When applied to interconnection studies, it is
    usually sufficient to model other wind farms which are not the subject
    of the assessment using a simplified model.

References

  1. J.G.Slootweg, W.L. Kling, “Aggregated Modeling of Wind Parks in
    Power System”, Power Engineering Society Summer Meeting, 2002 IEEE,
    Volume 1, 25-25 July 2002 Page(s):503 – 508 vol.1
  2. M. Poller, S. Achilles, “Aggregated Wind Park Models for Analyzing
    Power System Dynamics”, online:

    http://www.digsilent.de/Consulting/Publications
  3. K. Elkington, V. Knazkins, M. Ghandhar, “On the Rotor Angle
    Stability of Power Systems with Doubly Fed Induction Generators”, Power
    Tech, 2007 IEEE Lausanne, 1-5 July 2007 Page(s):213 – 218
  4. PSLF Users’ Manual, August, 2006
  5. Clipper Liberty Brochure.

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