A dynamic wind farm aggregate model for the simulation of power fluctuations due to wind turbulence

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Abstract

An important aspect related to wind energy integration into the electrical power system is the fluctuation of the generated power due to the stochastic variations of the wind speed across the area where wind turbines are installed. Simulation models are useful tools to evaluate the impact of the wind power on the power system stability and on the power quality. Aggregate models reduce the simulation time required by detailed dynamic models of multiturbine systems.

In this paper, a new behavioral model representing the aggregate contribution of several variable-speed-pitch-controlled wind turbines is introduced. It is particularly suitable for the simulation of short term power fluctuations due to wind turbulence, where steady-state models are not applicable.

The model relies on the output rescaling of a single turbine dynamic model. The single turbine output is divided into its steady state and dynamic components, which are then multiplied by different scaling factors. The smoothing effect due to wind incoherence at different locations inside a wind farm is taken into account by filtering the steady state power curve by means of a Gaussian filter as well as applying a proper damping on the dynamic part.

The model has been developed to be one of the building-blocks of a model of a large electrical system, therefore a significant reduction of simulation time has been pursued. Comparison against a full model obtained by repeating a detailed single turbine model, shows that a proper trade-off between accuracy and computational speed has been achieved.

Introduction

In a power system, the balance between produced and consumed power has to be continuously maintained. Imbalance results in frequency deviations of the system voltages and currents from the nominal value, which must be controlled in order to prevent instability phenomena and guarantee the power quality [1], [2], [3]. In the future, the power system will be coping with large scale wind energy integration [4], wind energy becoming a more and more significant fraction of the total produced power. In this scenario, wind power fluctuations, due to the stochastic nature of the wind, may significantly affect the system balancing and frequency stability. In particular, power fluctuations due to the wind turbulence may impose a limit to the amount of wind power which can be installed [5], [6]. Simulation models are therefore of paramount importance to evaluate these effects and design effective control systems.

A modern wind turbine is a complex non-linear dynamical system. Detailed simulation models describing the dynamical behavior of a single wind turbine have been developed at Energy research Center of the Netherlands (ECN) [7], [8], [9] as well as at other research institutes and companies, e.g. [10], [11].

The models are typically developed in simulation environments which enable a graphical representation of the model components as interconnected blocks. In this section we introduce state space representations for discussion purposes. A wind turbine generator is a (time-invariant) dynamical system which admits the state space representation:dx_dt=f˜_[x_(t),u¯(t)],y˜(t)=h˜[x_(t),u¯(t)],where x_ is the state vector, y˜ is the output and u is the input. In this work we assume that y˜ is the (active) power, whereas u is the rotor-effective wind speed acting on the turbine.

Nowadays, wind turbines are typically part of farms consisting of tens to hundred turbines. Assuming that the output y of a wind farm including N turbines can be obtained by adding the outputs y˜i of the single turbine models [7], [8], the detailed wind farm model is:dx_idt=f˜_[x_i(t),u¯i(t)],i=1Ny˜i(t)=h˜[x_i(t),u¯i(t)],i=1Ny(t)=iy˜i(t).

However, this repetition of an individual turbine model is not computationally efficient. A behavioral model can reduce the computational cost of simulations, while preserving, at the same time, the fundamental characteristics of the full model dynamic response. It is a model of reduced complexity which approximates (2) such that ya(t)y(t), ya(t) being the output of the approximated model.

Aggregate models are behavioral models obtained by modelling several identical subsystems (e.g. the turbines of a wind farm) by means of a single instance of the subsystem model [3], [12], [21]. Aggregation may be partial or full. Examples of partially aggregated models are the cluster and compound representations [12]. Their description is omitted in this paper due to a lack of space. This class of models can satisfactorily reproduce the time domain response of the full model. On the other hand, in the single machine representation all the different turbines of the full model are represented by means of a single instance of a turbine model. In this work, we introduce a new single machine model by extending the model proposed in [9] to variable-speed-pitch-controlled wind farms. As in [9], our aim is to approximate just the power spectral density of the full model's output, instead of the time domain response.

A typical single machine equivalent [18], [19], [20] uses “equivalent” parameters. This means that the physical parameters of the single turbine model are rescaled to take into account the presence of multiple turbines (e.g. the rated power of the equivalent electrical machine is the sum of the rated powers of the single electrical machines). The state space representation is:dx_dt=f_[x_(t),u¯(t)],ya1(t)=h[x_(t),u¯(t)],where the effect of parameters rescaling is taken into account in the functions f_ and h which replace f˜_ and h˜ of the single turbine model.

Other (single machine) aggregate models (e.g. [14], [15], [16], [17]) are steady state models, which give the output power as an instantaneous function of the wind speed (power curves):yas(t)=y[u(t)].

The proposed model differs on the models [14], [15], [16], [17] because it relies on the full dynamic turbine behavior. Furthermore, it differs on the models [18], [19], [20] because it retains the physical parameters of the single turbine dynamic model and produces the aggregate model's output by filtering its output (see also [9], [17]):dx_dt=f˜_[x_(t),u¯(t)],ya2(t)=h[x_(t),u0,u¯(t)],where u¯(t)=u0+u(t), u0 is the mean wind speed in a given time interval (e.g. 10 min) and u usually is a stochastic function, known as turbulence.1 It is remarked that the function f˜_ in the first of (5) is the same one used in the first of (1).

The proposed model aims to model the smoothing effect due to the incoherence of the wind at different locations within the wind farm. In the following of this paper, we show that this goal is pursued by filtering the steady state part of the single turbine model (power curve) by means of a Gaussian filter as well as by properly scaling the output variations due to its dynamic part.

The rest of the paper is organized as follows. Section 2 introduces the power fluctuations as consequence of the wind speed variation and defines the fluctuation width. Section 3 describes the proposed aggregated model and reviews the Gaussian smoothing applied to the steady state part of the model. Section 4 presents the simulation results obtained with the aggregate model (5) and compares them against those obtained by means of the full model (2). Comparison includes both average power, power spectral density and fluctuation width. Conclusions are summarized in Section 5.

Section snippets

Wind speed and power fluctuations

The main cause of wind power fluctuation is the natural variation of the wind speed. As already explained in Section 1, the wind speed is often expressed as the sum of its mean value u0 in a given time interval (e.g. 10 min.) and turbulence u(t) [4]. The term u(t) is usually modelled as a stochastic function. It is characterized by the intensity Iu, which is expressed as the standard deviation σu of u(t) normalized by the mean wind speed:Iu=σu/u0.

Several spectral characterizations of wind

The proposed model

In this work, the focus is on short term simulations [5], [6]. Therefore, the proposed model takes into account both the wind turbulence and the system dynamics. In more long term studies, e.g. [14], [15], [16], the dynamic behavior of the wind turbines is neglected and the output power is averaged over sufficiently long time intervals (1 min in [15], 10–15 min in [16] and 1 h in [14]).

In [9] an aggregate model of fixed speed wind farms was developed in Matlab/Simulink. The model relies on the

Outline

To generate the output power of a wind farm with N wind turbines, we performed N simulations of a single turbine and summed the so obtained outputs. In fact, we assume that the output of a single VSP-DFIG turbine does not influence the output of the others, see equations (2).

In each simulation, the turbine model (1) is fed by a different wind speed. Wind speed realizations, representing the wind at different wind farm locations, have been obtained by means of the ECN Control Design Tool [25].

Conclusions

A new dynamic aggregate model of variable-speed-pitch-controlled wind farms for the simulation of wind power fluctuations has been proposed. The smoothing effect due to incoherence of power fluctuations of different wind turbines has been introduced by applying Gaussian filtering to the steady state turbine model part of the model (power curve) as well as by rescaling the power variations due to the dynamic behavior of the single turbine model.

Comparison against non-reduced model obtained by

Acknowledgements

The work described in this paper is part of the Dynamic State Estimation and Voltage Stability (DEVS) project. DEVS is a joint project of TU Delft, ECN, Alliander and KEMA, financially supported by SenterNovem (agency of the Dutch Ministry of Economic Affairs).

The authors gratefully thank Jan Pierik, Edwin Wiggelinkhuizen and Stoyan Kanev, (all from ECN Wind Energy), Barry Rawn (Delft University of Technology), Klaas Visscher (DEVS project leader) and the other project members, for revising the

References (26)

  • J. Machowski et al.

    Power System Dynamics—Stability and Control

    (2008)
  • IEEE/CIGRE Joint Task Force on Stability Terms and Definitions, Definition and Classification of Power System...
  • L.L. Freris

    Wind Energy Conversion Systems

    (1990)
  • H. Banakar et al.

    Power system response to wind power fluctuations

    IEEE Transmission and Distribution Conference and Exhibition

    (2006)
  • C. Luo et al.

    Strategies to smooth wind power fluctuations of wind turbine generator

    IEEE Transactions on Energy Conversion

    (2007)
  • J.T.G. Pierik, J. Morren, E.J. Wiggelinkhuizen, S.W.H. de Haan, T.G. van Engelen, J. Bozelie, Electrical and Control...
  • J.T.G. Pierik, J. Morren, E.J. Wiggelinkhuizen, S.W.H. de Haan, T.G. van Engelen, J. Bozelie, Electrical and Control...
  • J.T.G. Pierik, Y. Zhou, P. Bauer, Wind Farm as Power Plant—Dynamic Modelling Studies, ECN-E-08-017,...
  • V. Akhmatov

    Variable-speed wind turbines with doubly-fed induction generators. Part I. Modelling in dynamic simulation tools

    Wind Engineering

    (2002)
  • V. Akhmatov

    Variable-speed wind turbines with doubly-fed induction generators. Part II. Power system stability

    Wind Engineering

    (2002)
  • A. Perdana, O. Carlson, Aggregated models of large wind farm consisting of variable speed wind turbines for power...
  • R. Pena et al.

    Doubly-fed induction generator using back-to-back PWM converters and its applications to variable-speed wind-energy generation

    IEE Proceedings of Electrical Power Applications

    (1996)
  • Cited by (0)

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