(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. 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.
2. 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.

Divergence Continued

In Part 1, we discussed divergence of the power flow solution. Below is our previous list of reasons for divergence, and additional comments.

Bread and Butter

The power flow is the bread-and-butter tool of power system analysts of large and small-scale transmission systems. It is used in the day-to-day operations of the grid to determine potential congestion, transmission loading relief and need for generation re-scheduling, among others. It is likewise used in short-term and long-term planning to study the potential for thermal overloads, voltage violations and voltage collapse. So it would be disconcerting if a tool of this importance and widespread application should fail, which on occasion it does.

The cyclical nature of customer demand on large scale interconnected networks is a well known phenomena.  Demand varies by time of day and responds to many factors that influence electric usage, including weather, seasonal activities and business cycles. Composite electric load generally behaves in a cyclical fashion for periods of a day and a year.  With the influx of larger amounts of  wind power, another cyclical characteristic is applied to the power system, that of the available wind generation.  Wind that drives turbines for wind farms varies continuously and generally behaves in a cyclical fashion for periods of a day and a year, just like demand.  The output capacity of a wind farm varies according to the prevailing wind.

Whereas demand tends to peak in either winter or summer, wind capacity tends to peak in spring and fall.  Furthermore, while demand tends to be highest at the hottest time of the day (for summer peaking areas), wind capacity tends to be lower during hot and sunny daylight hours.

Both demand and wind capacity have an impact on the thermal loading of transmission systems, and the non-coincidence of their cyclical behavior leads to interesting transmission usage patterns.

For use in power system stability simulations, utilities and system operators may desire to derive accurate model parameters of generators, excitation systems, governor controls and other control equipment. The utility may have found that actual events have not been accurately simulated by computer models or that individual equipment characteristics do not seem to match the manufacturer data. Further, adjustments may have been made by field or operating personnel that have altered the response of the equipment. In these situations, there is a need to obtain more accurate models for simulation. This Techblog provides an overview of the methodology for obtaining more accurate model response from measurements of the actual equipment and appropriate derivation of parameters for the model.

In the accelerated environments of today’s electric energy markets, fast analyses of power flows are a must. Emerging real-time and day-ahead markets require that analysis of infrastructure capacity be performed in a compressed timeframe. Whereas the electric demand of consumers and industry may retain its well-known cyclical nature, varying by time of day, by season and by local weather and social patterns, the supply side of the equation has drastically changed. Competition has engendered even the traditional suppliers of energy to be more flexible and anticipatory to pricing and demand signals, affecting operating and bidding strategy in timeframes that range from the next operating hour to when the next new generation facility can be interconnected. In addition, newer energy sources such as wind and solar power introduce new dependencies which vary hour-to-hour to the supply mix.

When the physicians of the power system (planners and operators) treat for resource inadequacy, congestion, instability and all the modern-day maladies of competitive power markets, their regimen may come with an increasingly common side effect – harmonics.  The utilization of static var compensators (SVC), induction generators, source converters, underground and submarine cables, direct current converters, to name a few, to provide solutions to power system problems can lead to increasing harmonic penetration in the power system.  Harmonic generating equipment coupled with system resonance conditions effects are cumulative and can be detrimental to system operations if not mitigated.

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.

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.)

Ricardo Austria, “The Voltage Ledge,” California ISO Monthly Technology Seminar, April 27, 2007, Folsom, CA

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