Kaiserstraße 2 24143 Kiel

Chair of Power Electronics

Christian-Albrechts-Universität zu Kiel

Kaiserstraße 2

24143 Kiel

Chair of Power Electronics

Christian-Albrechts-Universität zu Kiel

Kaiserstraße 2

24143 Kiel

Prof. Marco Liserre, PhD, IEEE fellow

Head of the Chair of Power Electronics

[email protected]

MV Grid Identification (Impedance and Voltage-sensitivity)

Chair of Power Electronics | Prof. Marco Liserre | [email protected] slide 3

Background (Impedance)

Increase of nonlinear loads and power converters leads to the deterioration of the utility grid

Resonance problem arises due to the increased number of filters and length of cables

Grid impedance is the key factor for the grid stabilization.


Background (Voltage sensitivity)

The Voltage sensitivity describe how a network react to a change in the injected power and viceversa how a variation of voltage change the power absorbed/injected by a grid

The knowledge of voltage sensitivity can help in controlling the grid but also in assessing how much reactive power is needed in case of a grid fault

Sensitivities calculation methods require high computational effort and/or large field measurements/data history


Outline

Impedance analysis approach, vector fitting and applications

MV-Analyzer in the Field

Control for wide-frequency grid impedance measurement

Identification of the Voltage sensitivity

Conclusions


Impedance measurement


Impedance-based stability analysis

The grid impedance measurement is important for stability

problem. The VSC-grid system is stable if the Nyquist plots of

the loop gain:

g oL(s) = Z (s)Y (s)

does not encircle the critical point (-1, j).

Re-shaping of the output virtual admittance

Yo on the bases of the estimated Zg in order

to guarantee the stability in case of grid

variations.

Equivalent network of a grid connected inverter

for small signal analysis.


Resonance Identification inSmart Transformer-fed Grid

• Mono-frequency excitation ranging from 150 Hz to 1500 Hz is implemented together with voltage control and active damping;

• The frequency sweep procedure will be repeatedly carried on in order to obtain the grid characteristics in real time.

Z. Zou, G. Buticchi and M. Liserre, "Grid Identification and Adaptive Voltage Control

in a Smart Transformer-fed Grid," in IEEE Transactions on Power Electronics.


LV Grid Impedance Identification

• By using time-domain data, the transfer function of impedance can be obtained by vector fitting method;

• The main idea is to use a rational function to approximate poles {am};

N is the approximation order,

d and e are optional for the rational functionAn example of measured & estimated grid impedance

in LV German grid


Case of study: Public LV grid Northern Germany

Magnitude and Phase angle of grid impedance versus time and frequency measured in public LV grid northern Germany.

• Night: resonance at 1.8 kHz with a magnitude |Zg|= 1.3Ω

• Day: the magnitude at 1.8 kHz is |Zg|=0.5Ω due to the changing operation of loads and generators by the grid customers.

• The grid impedance angle ψg is about 20° at 50 Hz, grid is predominant resistive at 50 Hz

• The measurements show that the grid impedance phase angle is temporarily capacitive in afrequency range between 1.6kHz and 4.8kHz.

L. Jessen and F. W. Fuchs, "Modeling of inverter output impedance for stability analysis in combination with measured grid

impedances," 2015 IEEE 6th International Symposium on PEDG, Aachen


Adaptive Active Damping

Current sensors on the grid side

• LCL-filter effectiveness changes with the grid stiffness

• If the grid impedance Zg is time variant, it influences the resonance frequency of the LCL filter

• The tuning of the active damping parameters can be online adapted as a tradeoff between robustness and resonance damping

• E.s. Notch filter is tuned at the resonance frequency.

Current sensors on the converter side

J. Dannehl, M. Liserre, F. Fuchs, F.; , "Filter-based Active Damping of Voltage Source

Converters with LCL-filter," IEEE Transactions on Industrial Electronics.

2 2

2 2

2( )

2

z NF NFNF

p NF NF

s sG s

s s


EEMSWEA:Medium Voltage Grid Analyser

• Aim: Analysis of the electrical properties

of medium-voltage networks with regard

to an optimization at high feed-in from

wind energy plants and improvement of

the harmonic load

• Realization: Development of a mobile

measurement and analysis system for

feeding harmonic currents and

measuring the network impedance

• Project volume: € 3.8 million (overall)

• 2.9 million € (Kiel University)


MV Analyzer System Description

Pos. Description

A MV-switchgear room

B Auxiliary power transformer

C MV-transformer room

D Inverter room

E Measurement room

F Cooling System

Transformer Container

Inverter Container

3D-Rendering of the MV Analyzer System


Specifications of the single Transformer

Rated power per transformer 1000 kVA

Rated current per transformer 1077 A

Rated voltage 20 kV / 536 V

Rel. short-circuit voltage 2.5 %

Number of transformers 2

Rated current (overall) 2154 A

Rated power (overall) 2000 kVA

Transformer Container

Two MV-transformers MV-Switchgear


Inverters Container

6 NPC-Inverters Control CabinetSpecifications of the single inverter

Nominal power 478 kVA

Nominal voltage (interl.) 920 V

Nominal current 300 A

Inductive filter 25 µH

DC link voltage 1500 V

DC link capacity 55.2 µF/A (2x)

Power feed 265 kVA

Switching frequency (nom.) 15 kHz

max. Switching frequency 30 kHz

Dimensions (100 x 200 x 80) cm


EEMSWEA-PROJEKT

MITTEL SPANNUNGS NETZ ANALYSATOR

Grid impedance identification

-High-frequency current injection (100 Hz…10 kHz)

-Total system: 1.6 MVA; single inverter: 480 kVA

-FPGA-based control system (master-slave configuration)

Inverter Filter Cable Transformer MV-Grid

Overall Power: 2 MVA


Impedance Identification through mono-Frequency Current Injection

MV grid impedance analyzer uses mono-frequency current injection in a wide rangebetween 100 Hz÷10 kHz to excite the MV grid.

, 2

cos cos

2 cos 1

s res res res s

RES

res s

T z z TG z

z z T

Internal Model Principle

To track a sinusoidal reference the harmonic model of the reference need to be added in the direct branch of the current loop.

Discretization method

Resonant controller must have infinite gain at thedesired frequency: deviation leads to tracking error.

Computation and PWM delay compensation

2 2 ( )

32 ( )

2 2

res res s res co s

res res s res co s

T f T

T f T

Phase lead compensation φres due to the delay phase lag: stability and robustness


Resonant Discretization for High Frequency Current Control

P+RES Controller

2 2P RES p i

res

sG s K K

s

1

f fL s R

+

-

*

g si kT

PWM

gi

RES

convv *

conv sv kT

RESG z

pK+

+

g si kTDigital Controller

skT

Filter

iK

Plant model in Z – time domain

1 f S f

f S f

R T Ln

T R T L

f

z eG z

R z e

Discretization Z


Resonant Discretization for High Frequency Current Control

SOGI

Gain/phase deviation at high frequency

Simple implementation

Impulsive invariant

Perfect tracking at every frequency

More computational burden


Experimental Results

αβ grid current and current error at 1kHz injection with

SOGI

αβ grid current and current error at 1kHz injection with Z {cos(ωRest)}

S. Brüske, S. Pugliese, S. Flacke and M. Liserre, "High-Frequency Grid Current Control of Parallel Inverters," IECON 2018 - Washington


Computation and PWM delayphase compensation

Kp tradeoff between high bandwidth and optimal damping

Kp =Lf /3Ts damping factor ξ=0.7

PM = 60° crossover frequency fco=1/6πTs.

System delay causes instability when the resonant frequency is over the bandwidth of the system!

φres should compensate the delay introduced by the plant GT(z)

φres = -GT(z)

2-sample phase lead

3 2

,2 2

4cos 3cos 1 2cos

2 cos 1

s res s res s s res s

RES Ts

res s

T z T T T TG z

z z T

3

2 2res res sT

Linear phase compensation of GT(z)

moving the zero of the transfer function with a two-step prediction

for frequencies higher than f90 = 5Rf /πLf


Nyquist Stability Criterion in Open-Loop Bode Diagram

Open-loop Bode diagram with linear phase delay compensation.Open-loop Bode diagram with 2-sample phase delay compensation.

Nyquist stability criterion counts –π crossings, in the open-loop Bode diagram, in the frequency range

where the magnitude is above 0 dB. N+ and N- number of positive/negative crossings.

No unstable open-loop poles and (N- - N+) = 0 Stable system

S. Pugliese, S. Flacke, Z. Zou and M. Liserre, "High-Frequency Harmonic Current Control of Power Converters," 2019 IEEE ECCE, Baltimore


Zone-phase based delay compensation

2 2

32

2 2

res res s res co

res res s res co

T f

T f

High PMs provided by the linear

compensation in high frequencies

Stability provided by the 2-sample delay method in low frequencies

fco = 1/6πTs (crossover frequency)

+

Stability margins at different fres in case of linear, 2-sample and zone-phase delay compensation

Open-loop Bode diagrams with zone-phase delay compensation


MV Grid-Impedance Analyzer Setup

Symbol Description Value

LV (rms) LV grid side 510 V / 50Hz

MV (rms) MV grid side 20 kV

Lf AC Inductor filter 25 uH

Rf AC Resistive filter 2.6mΩ

vDC DC-Link voltage 1200 V

fsw Switching frequency 30 kHz

Kp Proportional gain 0.25

Ki,50 Integral gain at 50Hz 62.5

Ki,res Integral gain at fres 62.5 / 125 / 250 / 375

`

NPC 1-4

Control Cabinet 1, 2

Control Cabinet 3

NPC 5,6

500A/div 4 ms/div

200A/div 500Hz/div

fres = 250Hz

iabc,1

iabc,2

iabc,tot

fres = 5kHz

10A/div 500Hz/div

20A/div 1 ms/div

Single NPC-converter: 30Apeak

at 5kHz grid current injection

2-parallel NPC converters: 800Apeak

at 250Hz grid current injection.

Table: power stage and current controller parameters used in simulations and experiments.

Experimental setup: 1.6 MVA MV grid impedance analyzer based on 6-parallel 3phase-NPC converters.


Simulation and Experimental Results

100A/div 20 ms/div

3

2 2res res sT

2res res sT

50A/div 1 ms/div

3

2 2res res sT

2res res sT

300Apeak /250Hzgrid current injection when switching the delay compensation from the 2-sample based method to the linear formulation.

30Apeak /5kHz grid current injection when switching the delay compensation from the 2-sample based method to the linear formulation.


MV-Analyzer in the Wind-park field

Field measurement on northern Germany's north coast


Messtechnische Einbindung

110 kV 20 kV

𝐼𝜈,𝑀𝑒𝑠𝑠𝑡𝑟𝑜𝑚

𝐼𝜈,𝐿𝑎𝑠𝑡+𝐸𝑟𝑧𝑒𝑢𝑔𝑒𝑟

𝐼𝜈

𝑍𝜈,𝑁𝑒𝑡𝑧

Messeinrichtung

𝑍𝜈,𝐴𝑛𝑙𝑎𝑔𝑒

𝑍𝜈,𝑁𝑒𝑡𝑧 ≪ 𝑍𝜈,𝐴𝑛𝑙𝑎𝑔𝑒


MittelspannungFrequenzgangmessung

Samples during a 250 Hz filter test


MittelspannungFrequenzgangmessung

Frequency response measurement, magnitude values

Frequency response measurement,

phase values

Medium voltage mains impedance measurement


Voltage Sensitivity Measurement


Example: Voltage sensitivity in UK

Tests performed in UK show that the active power sensitivity to voltage varies mostly during the day between constant current and constant impedancebehavior.

A. Ballanti, L. Ochoa, “Off-Line Capability Assessment”, WP2 Part A – Final Report.


𝑃 = 𝑃0𝑉

𝑉0

𝐾𝑝

1 + 𝐾𝑓𝑝𝑓 − 𝑓0𝑓0

𝑄 = 𝑄0𝑉

𝑉0

𝐾𝑞

1 + 𝐾𝑓𝑞𝑓 − 𝑓0𝑓0

The load can be represented with an exponential model for the voltage and with a linear dependency from the frequency

• Independent of initial voltage and does not require initialization

• Only one parameter is needed for active and one for reactive power.

• The exponent is equal to load sensitivity to voltage.

G. De Carne, M. Liserre, C. Vournas, "On-Line Load Sensitivity Identification in LV Distribution Grids," in IEEE

Transactions on Power Systems, vol. 32, no. 2, pp. 1570-1571, March 2017.

Voltage Sensitivity Identification


𝑃0 = 𝑃𝐿 − 𝑃𝐺 > 0 (7)

Let us suppose that the DG works at unity power factor and that the following assumption holds:

Where P0 is the net power, PL is the passive load power and PG is the DG power.The passive load has a normalized sensitivity equal to:

𝐾𝑝 =Τ∆𝑃𝐿 𝑃𝐿Τ∆𝑉 𝑉0

∆𝑃=∆𝑃𝐿 = 𝐾𝑝,𝐿 Τ∆𝑉 𝑉0 𝑃𝐿

Considering that the DG power output is invariant to the voltage, the previous equation becomes:

(8)

(9)

Voltage Sensitivity Identification: Influence of DG on the identification


Integrating eq. (9) in eq. (4) we obtain:

𝐾𝑝 =Τ∆𝑃 𝑃0Τ∆𝑉 𝑉0

= 𝐾𝑝,𝐿𝑃𝐿

𝑃𝐿 − 𝑃𝐺(10)

The net load reacts in different way depending on the presence of DG.

Example:

𝐾𝑝 = 11

1 − 0= 1

𝑃𝐿 = 1, 𝑃𝐺 = 0 → 𝑃0 = 1𝐾𝑝,𝐿 = 1

𝑃𝐿 = 1.5, 𝑃𝐺 = 0.5 → 𝑃0 = 1𝐾𝑝,𝐿 = 1

𝐾𝑝 = 11.5

1.5 − 0.5= 1.5

𝑃 = 𝑃0𝑉

𝑉0

1

𝑃 = 𝑃0𝑉

𝑉0

1.5Linear

responseMore than linear

response

Voltage Sensitivity Identification: Influence of DG on the identification


The Voltage sensitivity can beevaluated applying a controlledvoltage disturbance and measuringthe power or the opposite

Simple and low-computationalcost

Updates in real time (every few minutes)

Consider the power influence ofDG

Helps in assessing how muchpower need really to be injected

Main grid

0

1.0 ind

Q (

p.u

.)

Time0.95

1.0

P (

p.u

.)Time

0.95

1

V (

p.u

.)

Time

0

1.0 ind

Q (

p.u

.)

Time

0.95

1.0

P (

p.u

.)

Time

0.95

1

V (

p.u

.)

Time

Voltage Sensitivity Potential


The load sensitivity to voltage can be used to shape the load consumption varying the ST voltage output

𝑽

𝑉0= 1 +

∆𝑷

𝑃𝑲𝒑

Sensitivity coefficients for each phase

ST bus

0.93 pu

Furthest bus

0.90 pu

ST voltage and lowest grid voltage

5%

Load reduction (%)

Desired power

variation

Active power

sensitivity to voltage

New voltage

set-point

Voltage Sensitivity Potential in ST application


This features enables the Smart Transformer to offer services to the grid, such as primary frequency supportH

V F

req

uen

cy

+200mHz

Voltage Sensitivity Potential in ST application

Sensitivity coefficients for each phase

ST bus

0.93 pu

Furthest bus

0.90 pu

ST voltage and lowest grid voltage

5%

Load reduction (%)


Impedance knowledge helps in Wind Turbine park integration

Active filter, active damping and Low Voltage Ride Through could be improved

EEMSWEA Project: 2MVA MV-grid impedance analyzer

Impedance Identification through mono-Frequency Current Injection in MV grid is analyzed:

- the effects of the discretization in the accuracy of current control

- the effects of computation/PWM delay compensation in the stability of current control.

Voltage sensitivity can be used by influencing load consumption and in defining the power to be injected into the grid for supporting the voltage and the primary frequency

Conclusions

Documents

Kaiserstraße 2 24143 Kiel