Aggregation of Wind Farms for Power System Analysis

1. Otto-von-Guericke-University Magdeburg Aggregation of Wind Farms for Power System Analysis Krzysztof Rudion EAWE Seminar on Wind Energy in Europe 04. – 05. October 2006, Roskilde Prof. Z. A. Styczynski

2. Outline • Motivation and Aim of the Work • Description of the Problem • Coherency Approaches for Power System Reduction • Reduction Approaches for Wind Farms • Summary

3. Motivation and Aim of the Work • Still increasing number of WT in power systems • The impact of a single WT on the grid operation can be neglected • But, the impact of large scale wind farms can be crucial to the stable operation of the power system • Consideration of many small WTs in power system analysis is difficult because of the model size what can lead to long simulation times • To analyse the operation of the power system the behaviour of the wind farm in the PCC is important • Therefore, wind farms can be approximated by an equivalent model with similar dynamic behaviour in the PCC

4. Description of the Problem – WT Types Constant Speed WT with Squirrel Cage Induction Generator Variable Speed WT with Doubly Fed Induction Generator Variable Speed WT with Converter Driven Synchronous Generator

5. Description of the Problem – WT Models WT Mathematical Model Drive Train Model Mechanical Power of WT: DFIG Mathematical Model Stator Equations: WT Controllers • Pitch Controller • Machine-Side Converter Controller • Grid-Side Converter Controller Rotor Equations: Equation of Motion:

6. Sub-System 1 Sub-System 2 Coherency Approaches for System Reduction to be reduced

7. Sub-System Iremaining unchanged Voltage-White-Noise G2 G1 G4 G3 G3 Sub-System IIto be reduced G2 G4 G1 Slip G G G G Coherency Approaches for System Reduction

8. Zd (s) Zdeq (s) Coherency Approaches for System Reduction s=1 Zd“ = R“ + jX“ (subtransient) s=.01 Zd‘ = R‘ + jX‘ (transient) s~0 Zd = R + jX (synchronous) Yeq“ = Y1“ + Y2“ + ... + Yn“ Yeq‘ = Y1‘ + Y2‘ + ... + Yn‘ Yeq = Y1 + Y2 + ... + Yn from 1/Yeq , 1/Yeq‘ , 1/Yeq“ :  Raeq, Xhdeq, Rfdeq, Xfdeq, RDdeq, XDdeq Note: q-axis analog

9. Reduction of WT number Description of WT group (or whole wind farm) using a rescaled unit with equivalent parameters (equivalent model preserve the physical structure of WT) Reduction of wind park model order Wind park complexity reduction using mathematical methods (equivalent model can lose physical structure) Approaches of Wind Farm Reduction Reduction Approaches for WF

10. 1 2 3 Methods for Wind Farm Equivalencing Detailed Wind Park PCC Wind Direction “West  East” m ...... 3 2 1 1 2 …………. n Wind Direction “South  North”

11. 1 2 Methods for Wind Farm Equivalencing Equivalent Wind Park PCC PCC Wind Direction “West  East” Power of the Equivalent Wind Turbine: Wind Direction “South  North”

12. Mathematical Reduction Methods • There are many different mathematical approaches for system order reduction, e.g.: • Modal truncation • Balanced reduction techniques • Optimal Hankel-norm approximation • Singular perturbations method • Most of the methods were developed for linear systems • The analysis of non-linear system is difficult and therefore non-linear models are often linearized • Two methods were found that were used for order reduction in correspondence to the wind generation: • Singular perturbations • Optimal Hankel-norm approximation

13. Singular Perturbations Theory • Useful for prediction of steady-state as well as transient behaviour • Method based on the decomposition of the system variables into slow and fast according to their dynamics • The order of the system is reduced through neglecting the fast or slow dynamic phenomena (depending on analysis objective) • The effects of the neglected dynamics are calculated in the separated time scales and are reintroduced as a boundary layer corrections • The reduction retains the physical meaning of the variables • Separation of the slow and fast system variables can be problematic • Method can be used for order reduction of single wind turbine

14. Hankel-norm approximation • Based on the observability and controllability of the system that are defined as:  Controllability gramian  Observability gramian • On the basis of Hankel singular values the influence of state variables on the input – output behaviour of the system can be determined • States that have low influence can be neglected • Advantageous is that the order of the reduced system can be defined a priori • Disadvantage is that reduced models lose the physical interpretation

15. Implementation of Reduced State Space Model

16. Summary - Next Steps • Reduced model of the wind farm is needed • There are many different mathematical reduction methods available • Analysis of the usability of the existing mathematical methods • Test simulations of the chosen methods • It should be checked if combination of mathematical order reduction methods with aggregation methods can be performed

17. Thank You For Your Attention !