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Reactive power injection strategies for wind energy regarding its statistical nature Joaquín Mur M.P. Comech joako@unizar.es mcomech@unizar.esjoako@unizar.esmcomech@unizar.es

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I. Introduction: presentation layout II. Wind site resource III. Turbine power curve IV. Farm power curve V. Farm electric model VI. Nearby wind farms VII. Limits on reactive power VIII. Reactive Power Policy Constant power factor Automatic voltage control Scheduled Reactive control Reactive power under centralized control IX. Effect on power losses X. Uncertainty Analysis XI. Conclusions

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II. Wind site resource (Weibull distribution) Chart for shape parameter = 2 Solid red => wind speed = 5 m/s Dashed pink=> wind speed = 5,5 m/s Dark blue => wind speed = 6 m/s Light blue => wind speed = 6,5 m/s Dotted green=> wind speed = 7 m/s Yellow => wind speed = 7,5 m/s

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III. Wind turbine (IEC 61400-12-1) Power curve measured at a pitch regulated turbine (from IEC 61400-12-1)

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III. Snapshoot of turbines in a farm Power curve measured at a pitch regulated turbine (from IEC 61400-12-1)

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IV. Wind farm curve ( IEC 61400-12-3 ) Declared (calculated) wind farm power curve by directional sector (from IEC 61400-12-3, annex C)

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IV. Wind farm (4 parameters adjusted curve) w off w 25% w 75% w off wf is the farm mean efficiency factor (referred to “unperturbated wind” of the site).

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IV. Farm power distribution

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Chart for shape factor k = 2 Solid red => wind speed = 5 m/s Dashed pink=> wind speed = 5,5 m/s Dark blue => wind speed = 6 m/s Light blue => wind speed = 6,5 m/s Dotted green=> wind speed = 7 m/s Yellow => wind speed = 7,5 m/s Dashed red => wind speed = 8 m/s

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V. Model of the wind farm with one medium voltage circuit

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V. Model of the wind farm with several medium voltage circuits

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V. Approximated equivalent model of the wind farm Averaged model

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V. Fourth pole model & parameters of the farm

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VI. Power of nearby farms Nearby wind farms are supposed to be closely correlated a linear regression can be precise enough P i and P j are the average power output in park “j” (estimated farm) and “i” (reference farm); r ij is the experimental correlation coefficient; s i and s j are the standard deviation of power in farms i and j. Q i and Q j must be estimated based on each farm reactive control

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VII. Limits on reactive power Limits provided by the turbine manufacturer. Second edition of IEC 61400-21 will include a section devoted to the reactive power capability and the ability to participate in an automatic voltage control scheme. Allowable voltage at the turbines. The wind turbine that is electrically farer from PCC will suffer the greatest voltage deviations of the wind farm. Voltage at turbines is dependent on U PCC Current limit in series elements (lines, transformers, etc) and grid bottlenecks. Slow thermal dynamics, grid congestion… Usually, some degree of overload is allowed.

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VII. Voltage at electrically farer turbine Estimation of parameters from power flows:

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VII. Loci of allowable power

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VIII. Reactive power policy Centralized control: stabilize voltage, power losses, balance reactive power flows… Constant power factor regulation Automatic voltage control Scheduled reactive control Current model in Spain, power factor depending on hours Improvement if weekdays and holidays would be considered Improvement if target is based on reactive power, not on power factor

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Peak hours 4 h/day (Capacitive behaviour) Mediu m hours 12 h/day (unity power factor) Valley hours 8 h/day VIII. Voltage deviation due to scheduled power factor (Spain)

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Peak hours 4 h/day (Capacitive behaviour) Valley hours 8 h/day VIII. Reactive power injection due to scheduled power factor (Spain)

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VIII. Reactive power under centralized control Simplistic example of realizable reactive power at a wind turbine

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VIII. Availability of reactive power INJECTION for the example Probability of being able to INJECT capacitive power up to Q wt Chart for shape parameter = 2 Solid red => wind speed = 5 m/s Dashed pink=> wind speed = 5,5 m/s Dark blue => wind speed = 6 m/s Light blue => wind speed = 6,5 m/s Dotted green=> wind speed = 7 m/s Yellow => wind speed = 7,5 m/s

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VIII. Availability of reactive power ABSORPTION for the example Probability of being able to ABSORB inductive power up to Q wt Chart for shape parameter = 2 Solid red => wind speed = 5 m/s Dashed pink=> wind speed = 5,5 m/s Dark blue => wind speed = 6 m/s Light blue => wind speed = 6,5 m/s Dotted green=> wind speed = 7 m/s Yellow => wind speed = 7,5 m/s

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IX. Effect on power losses Parameters a P, a Q, b P and b Q can be obtained from power flow runs An analogue relationship can be established for losses on reactive power

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X. Uncertainty of the results The main source of errors are: Adjustment of wind resource to a Weibull distribution. The uncertainty of the farm power curve. Simplistic model of the power curve with only two or four parameters. Approximations done in the model of the grid (for example, considering U 0 constant). Availability of turbines and network.

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Conclusions This work shows a statistical model of wind farms and a methodology for adjusting its parameters. This model has been used to assess the grid impact of a wind farm reactive power during normal operation. Several reactive power control strategies are analyzed. The uncertainty of the final data due to the approximations made is studied. The accuracy can be increased if non-parametric models of farm power curve and wind resource is employed.

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