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1 Transient analysis of transformers and cables for offshore wind connection Bjørn Gustavsen SINTEF Energy Research Trondheim, Norway Wind power R&D seminar deep sea offshore wind: Trondheim, Norway, January, SINTEF Energy Research

2 Outline Modeling of transformers and cables High-frequency transformer-cable resonance Wind power SINTEF Energy Research 2

3 PART I : Modeling of transformers and cables SINTEF Energy Research 3

4 High-frequency transformer modeling (black box) 1. Characterize the transformer by its frequency domain behavior at its external terminals 2. Identify a model which emulates the behavior of the transformer, as seen from the terminals. SINTEF Energy Research 4

5 Terminal characterization by admittance matrix external terminals i = Y v n I ( ω) ( ) 1 1 I ( ω) 2 I ( ) V ω n ω n( ) I1( ω ) Y11( ω) Y12( ω) Y1n ( ω) V1( ω) I ( ω ) Y ( ω) Y ( ω) Y ( ω) V ( ω) = In ( ω ) Yn1 ( ω ) Yn2 ( ω ) Ynn ( ω ) Vn ( ω ) V ω V ( ω) 2 : Transformer SINTEF Energy Research 5

6 Measurement e e of admittance matrix Network analyzer Connection box Coaxial cables Current sensor Built-in current sensor (Pearson) SINTEF Energy Research 6

7 Modeling via rational functions I ( ω) V ( ω) 1 1 I ( ω) 2 V 2 ( ω ) : Transformer I ( ω ) V ( ) n ω n Measurement I1( ω ) Y11( ω) Y12( ω) Y1n ( ω) V1( ω) I 2( ω ) Y21( ω) Y22( ω) Y11( ω) V2( ω) = In ( ω ) Yn 1 ( ω ) Yn 2 ( ω ) Ynn ( ω ) Vn ( ω ) Y n Model extraction (fitting) Y n ( ω) N m + R jω a m= 1 m D Rational model The rational model is compatible with EMTP-type circuit simulators SINTEF Energy Research 7

8 Procedure for rational fitting 1. Calculate a rational model using Vector Fitting Y( ω) N m + R j ω a m= 1 m D 2. Enforce passivity by residue perturbation N Δ m R m= 1 s am ΔY= +ΔD 0 N ΔR m R m= 1 s am eig(re{ Y+ }) > 0 eig ( D+ Δ D) > 0 Matrix Fitting Toolbox SINTEF Energy Research 8

9 High-frequency cable modeling 1. Characterize the cable by its per-unit-length series impedance matrix Z and shunt admittance matrix Y Z ( ω ) = R ( ω ) + j ω L ( ω ) Y( ω) = G( ω) + jωc( ω) 2. From Z and Y, calculate l parameters for a frequencydependent traveling wave model. This modeling capability is available in EMTP-type programs Main challenge: calculate Z Analytical expressions Finite it Element SINTEF Energy Research 9

10 PART II : Cable-transformer high-frequency resonance B. Gustavsen, Study of transformer resonant overvoltages caused by cable-transformer high-frequency interaction, IEEE Trans. Power Delivery, vol. 25, no. 2, pp , April SINTEF Energy Research 10

11 Demonstrate that transients on the high-voltage side of a transformer can cause excessive overvoltages on the lowvoltage side. Identify critical cable-transformer configurations that lead to high h overvoltages SINTEF Energy Research 11

12 Voltage ratio, from high to low kv 230 V kva At high frequencies, the voltage ratio is governed by stray capacitances and inductances, not ampere-winding balance. 50 Hz voltage ratio MHz voltage ratio 2 A 2 MHz sinusoidal id voltage would produce a 100 p.u. overvoltage SINTEF Energy Research 12

13 Laboratory measurement Step voltage 30 Ω Cable (27 m) High- voltage Low- voltage Before connecting cable to transformer After connecting cable to transformer ~24 p.u. overvoltage!! SINTEF Energy Research 13

Measurement-based model of transformer 11 kv 230 V 1 2 3 4 5 6 300 kva Frequency sweep measurements

14 Measurement-based model of transformer 11 kv 230 V kva Frequency sweep measurements of Y(ω) Model extraction by Matrix Fitting Toolbox Y( ω) N m R m= 1 jω a + D m SINTEF Energy Research 14

15 Measurement-based model of 27-m cable A R v v 1 2 S Cable A R S ˆv 1 ˆv 2 Cable 50 Ω y b = b b R ( 1) a y a = y b a Model extraction by Matrix Fitting Toolbox N m Y( ω) R ω + D m= 1 j a m y a,y b SINTEF Energy Research 15

16 Simulation vs. measurement High- Low- 30 Ω voltage voltage 1 Step voltage Cable (27 m) Before connecting cable to transformer After connecting cable to transformer SINTEF Energy Research 16

17 Max. overvoltage vs. cable length State-of-the art frequency-dependent traveling-wave type model obtained from geometry. Compute max. overvoltage on low-voltage side for alternative cable lengths SINTEF Energy Research 17

18 Ground fault. Max. overvoltage vs. cable length ideal Step voltage 30 Ω Cable (27 m) Overvoltage in p.u. of applied voltage Highvoltage Lowvoltage m cable (open LV) ~43 p.u. overvoltage!! SINTEF Energy Research 18

19 Switching overvoltages (1) 1 p.u m overhead line 300 m cable 20 m cable t=0 Several parallel cables connected to bus Combined characteristic impedance much lower than that of connection cable Bus appears as stiff voltage seen from connection cable Closing CB results in oscillating voltage on cable SINTEF Energy Research 19

20 Switching overvoltages (1) 1pu p.u m overhead line 300 m cable A 20 m cable t=0 ~20 p.u. overvoltage!! SINTEF Energy Research 20

21 Switching overvoltages (2) Two cables of equal length coupled to the same busbar One cable is live 1 p.u m overhead line t=0 20 m cable 20 m cable T1 T2 T1 ~25 p.u. overvoltage!! SINTEF Energy Research 21

22 Switching overvoltages (3) 1 p.u m overhead line 20 m cable close 1 t=0 ~43 p.u. overvoltage!! SINTEF Energy Research 22

23 Note: Other transformers may have resonances at much lower frequencies. Overvoltages will occur with longer cables. Voltage ratio for a 410 MVA generator transformer (434 kv / 21 kv) SINTEF Energy Research 23

24 PART III : Relevance to wind power SINTEF Energy Research 24

25 Switching overvoltages Radials of nearly equal length Energizing a branch oscillating overvoltage on WT transformer HV side In the case of short radials (< 1km), the oscillating overvoltage has frequency above 50 khz High overvoltages may result on WT transformer LV side by resonance SINTEF Energy Research 25

26 Ground fault initiation Ground fault initiation can cause an oscillating overvoltage in the cable. Frequency depends on fault location High overvoltages may result on WT transformer LV side by resonance SINTEF Energy Research 26

27 Notes The actual overvoltage on the WT LV side is strongly dependent on the network on the LV side A complete model must be developed SINTEF Energy Research 27

28 Conclusions High-frequency interaction between the wind turbine transformers and the cables can lead to excessive overvoltages the transformer LV side. The phenomenon can be triggered by ground fault initiation and by switching. SINTEF Energy Research 28

29 Electromagnetic Transients in Future Power Systems. Phenomena, Component Stresses, Modeling A JIP project (KMB) between SINTEF and industry partners ( ) 2015) New partners are welcome! Contact: bjorn.gustavsen@sintef.no SINTEF Energy Research 29

30 Objective SINTEF Energy Research

Enforcing Passivity for Admittance Matrices Approximated by Rational Functions

IEEE TRANSACTIONS ON POWER SYSTEMS, VOL. 16, NO. 1, FEBRUARY 2001 97 Enforcing Passivity for Admittance Matrices Approximated by Rational Functions Bjørn Gustavsen, Member, IEEE and Adam Semlyen, Life