High Frequency Grid Impedance Analysis by Current Injection

A. Knop, F.W. Fuchs, Senior Member

Institute of Power Electronics and Electrical Drives,

Christian-Albrechts-University of Kiel, D-24143 Kiel, Germany,

ank@tf.uni-kiel.de, fwf@tf.uni-kiel.de

Abstract—The impedance of the electrical grid is frequencyand time depending. Therefore it is very useful to know itsvalue in the frequency range between grid fundamental frequencyand frequencies in the kHz-range. The proposed grid impedanceanalysis contributes to optimize energy feed especially fromdecentralized converter equipped renewable sources. This paperpresents an advanced impedance measurement system with ahigh frequency range for the energized electrical low voltagegrid. A sinusoidal current of predetermined frequency is injectedinto the grid. The grid impedance at that frequency is calculatedfrom the measured magnitude and phase of the injected currentand resulting voltage. The measurements are executed at nearbyfrequencies to produce nearly continuous impedance versusfrequency characteristic. The basic concept and a prototype oftest equipment are presented.

I. INTRODUCTION

Within the European Union the amount of regenerative

energy should be increased up to 20% of the total generated

energy by 2020 [1], [2]. Energy from big conventional power

plants which is nearly free of pollution of the electrical grid

will be substituted by more or less perturbated energy of

decentralized producers.

The application of non-linear and asymmetrical loads

or sources increases more and more because of converter

equipped and decentralized difficult controllable renewable

energy sources. The result is the reduction of the power quality

of the grid.

For a grid friendly connection of regenerative energy sys-

tems it is necessary to determine the fed in system perturba-

tions. These system perturbations can be calculated by the

grid impedance of the electric distribution network which

depends on time and frequency and the fed in current including

harmonics. By changing the grid loads this grid impedance

shows high variations over the day or season. Additionally

the load density is locally different. In the city areas the

grid is designed for a higher load density than in rural

areas. Hence the impedance of an electric distribution network

is time dependent and varies locally. Therefore, the same

regenerative systems or regenerative plants at different places

cause different system perturbations.

A simple grid constellation is shown in Fig. 1. This consists

of different low-voltage loads like for example domestic and

industrial loads and decentralized energy producers as for

example wind turbine generators. These are connected with

distributed low-voltage transformers at medium voltage level.

At the point of common coupling (PCC) on the medium

voltage level side the line voltage is influenced by other loads

low voltage medium voltage

Wind turbinef =2kHzR

lin. load

VARf =R 0,5...5kHz

Wind turbinef =1.7kHzR

nonlin. loadf =4kHzR

FACTSf =0,5...5kHzR

high voltage

lin. load

PCC

Fig. 1. Exemplary grid with domestic and industrial user and decentralizedenergy producers

in dependence of grid impedance. A estimation of the power

system impedance could be made by using the short circuit

power associated with the point of connection [3]. If wiring

diagrams are available, a more accurate evaluation may be

carried out. However, knowledge of the loads connected at

remote points will be unavailable and affects the accuracy.

Online measurement is the only practical solution as it requires

no a priori knowledge because of the grid and no connected

loads.

The proposed concept offers the accurate calculation of

system perturbation at the switching frequency.

By repeated measurement over time significant changes

in impedance may also be traced [4]. This yields to better

performance and improved power quality. The system becomes

more grid-friendly by taking into account of the system

perturbations in the control such as changing the switching

frequency. Hence maybe more decentralized energy production

units (wind turbine generators as well as the sun and biomass

plants) can be connected to the grid, i.e. a higher number of

decentralized energy production units can be connected to the

grid.

Furthermore changes in the grid impedance can lead to

performance degradation or even trigger system stability prob-

lems in LCL-based grid converter systems or when harmonics

compensators are employed [5], [6]. Information about the

actual grid impedance could be used for making the controller

adaptive in order to avoid these problems.

This paper describes an impedance measurement system

with a converter injecting a high frequency sinusoidal current

(with an amplitude up to 20 A) into the grid for measuring

the frequency dependent grid impedance in a frequency range

TABLE IOVERVIEW OF GRID IMPEDANCE MEASUREMENT METHODS

Methods passive resonance transient periodical distortions multi frequent

(switch a load) (LCL-Filter) (inrush C and L) (impulse / rectangle) current

Measuring time medium low low low high

Reproducibility always always none always always

Frequency selectivity none none none middle yes

Frequency resolution only harmonics only res. frequ. middle middle high

Online measuring none none none yes yes

Measurable impedance |Z| |Z| |Z(f)|,6 Z(f) |Z(f)|,6 Z(f) |Z(f)|,6 Z(f)

from 75 Hz to 10 kHz and the instrumentation for measuring

line impedance.

The measurement takes place without disrupting normal

system operation. Measurement results are visualized with a

diagram of impedance magnitude and phase depending on

frequency for frequencies between 75 Hz and 10 kHz. The

operation of the instrumentation is verified and illustrated by

exemplary measurements.

This paper is structured as follows: Chapter II comprises the

method of grid impedance measurement; Chapter III describes

the instrumentation of the measurement system and finally

Chapter IV presents measurement results.

II. METHODS OF GRID IMPEDANCE MEASUREMENT -

STATE OF THE ART

Measurement of non-fundamental frequency impedance of

energized power systems has a long history [7], [8]. Primarily,

all kinds of measurement methods differ in the origin of the

non-fundamental frequency signals used for measurement, i.e.

they differ in the measurement frequency band and associated

frequency resolution.

Passive measurement methods use non fundamental fre-

quency signals which are already presented in the literature.

A method derives the impedance at the fundamental and

harmonic frequencies by measuring the line-voltage magnitude

and phase before and after applying a known load in steady-

state [9], [10].

Another possibility is using the excitation of the LCL-filter

resonance in steady state to estimate the grid impedance [11].

This method is for employing the frequency characteristic of

the current-controlled converter in order to have an indication

of the grid impedance value. In fact, the frequency peak

due to the resonance is particularly sensitive to the grid

impedance change. This method can only be measured at the

grid impedance at the resonance frequency. Furthermore, the

system model has to be known exactly.

In [12] one method using transients to estimate line

impedance by spectral estimation is introduced. These tran-

sients can be generated by capacitor switching, transformer

inrush and line energization and de-energization. One draw-

back of this method is that these transients may not sufficiently

excite the line impedance at all necessary frequencies.

Another steady state method injects well known and typi-

cally periodically distortion currents into the grid and allows

an analysis in steady state. This technique is presented in

[13]–[16]. The basic idea is injecting a rectangular waveform

current into the grid and recording the voltage change re-

sponse. Results are processed by means of a Fourier analyses

at the particular injected harmonic. This technique can be

used to obtain the frequency characteristic of the grid if

the measurement is repeated at different nearby frequencies.

The grid-connected converter of the given system can be

used for injecting the disturbance [17]: a harmonic voltage

is injected by the converter and the following current is

analyzed. Hence, the impedance can be calculated as the ratio

between the voltage disturbance and the measured current. The

measured grid impedance is correctly at the frequency with

enough current and following voltage. These methods can fail

when many grid-connected converters are injecting disturbing

signals at the same time.

Another possibility to determine grid impedance can be

reached by injecting a signal at non characteristic frequencies

[7], [8], [18]. Therefore a multi frequent current source (syn-

chronous generator, converter or equivalent) injects a current

into the grid. With the resultant voltage in the same frequency

range it is possible to determine the magnitude and phase

of the frequency dependent impedance. The advantage of

this method is the measurement and calculation of the grid

impedance separately at each frequency. Furthermore, it is

possible to perform measurements with the same current or

the same voltage. When a high no fundamental voltage in the

grid is present, it is possible by two different measurement

currents to compensate this voltage. By variable selection of

the measuring current, it is possible to adapt to any grid

condition. For example high grid impedance required a low

current.

Finally, the measured response of an injected white noise

signal can be used with spectral estimation to obtain the line

impedance magnitude without phase [7], [19].

The advantages and disadvantages of the methods are sum-

marized in Tab. I.

III. DEVELOPED MEASUREMENT SYSTEM

The measurement method selected in this paper uses a three-

phase grid connected voltage source converter to generate

measurement currents with a variable measurement frequency

range from 75 Hz to 10 kHz. Thus, this is the underlying

Dead-time

3-phasehysterese-control

AD-Converter

+

+φgrid

PI

-

PLL

|I |supply

*

AD-Converter

VD,ref

+

3

3

3cos( )φ

φφ

cos( -120°)cos( -240°)

VD

1/s

φmeas

|I |*

meas FPGA-Controller

3

ΔIωmeas

3

6

LFilter LGrid v (t)Grida

b

c

N

cos( )φφφ

cos( -120°)cos( -240°)

Hardware

GridFilter/Transformer iact

LTransformer

iact,dig

Converter

Fig. 2. Power and control configuration of the high frequency measurement current generator; control implemented in a FPGA

principle for measuring the impedance versus frequency char-

acteristic of the grid. The selected method injects a signal at

non characteristic frequencies, multifrequent current according

to Tab. I. Compared, to earlier publications, the approach

introduced in this paper uses a grid connected converter creates

the measurement current. The measurement system is designed

for measuring the impedance of a 400 V grid and consists of

a fast switching converter, a control unit and a measurement

equipment.

A. Grid Connected Converter for Current Injection

Fig. 2 illustrates the proposed structure of the controlled

converter for measurement current injection - a three-phase

two-level voltage source converter (VSC) which is connected

via inductors and one transformer to the grid. The control of

the converter provides two basic functions. First, it controls

the DC-link voltage VD to be constant at 800 V. The second

function of the control is to regulate accurately the currents

to be injected in the inductors tracking their reference values.

In this way, the converter operates effectively as a controlled

current source and can inject currents into the grid. The current

control method used for the converter is for each phase a

sampled single phase hysteresis control. The control structure

is described in [20]. The control structure leads to a very

accurate control of the injected high frequency current. The

Phase-locked loop (PLL) for calculation the grid angle is very

robust against the injected measurement current. The control

calculations are performed by a field programmable gate array

(FPGA). Tab. II describes the specifications of the converter.

For the high frequency current (up to 10 kHz) a special

three-phase transformer and three-phase inductor are designed

and produced. These consist of several split tape-wound cores

to reduce the iron losses and flex wire to reduce the skin-effect.

These specific designs allow the operating at a frequency from

TABLE IICONVERTER SPECIFICATIONS

DC-Link voltage 800 V

Filter inductance LFilter = 1 mH

Grid voltage VGrid = 230 V

Transoformer ratio 1:1.7

Grid inductance LGrid = 0.4 mH

Rated power P = 10 kVA

Output frequency 50 Hz − 10 kHz

Switching frequency 30 kHz − 60 kHz

50 Hz to 10 kHz with acceptable iron losses. The transformer

and filter inductors designed for a power rating of 15 kVA.

For this application the converter IGBTs have been selected

with fast switching characteristics. To reduce the recovery cur-

rent from the diodes, SiC-Diodes are used in the freewheeling

path. The power semiconductors have a breakdown voltage

of 1200 V. By this configuration the converter can be used

with fast switching frequency, here up to 50 kHz, and reduced

switching losses [21].

In Fig. 3 the prototype of the high frequency measurement

current generator is shown.

B. Grid Impedance Measurement Method

The measured current iact and voltage vact waveforms are

transferred to AD converters which sample the waveforms. A

micro-controller performs a single frequency discrete Fourier

transform (DFT) with a Blackman window to find the real and

imaginary components of current iact and voltage vact at mea-

surement frequency fmeas [22]. With this components the line

impedance Z(fmeas) and associated magnitude |Z(fmeas)|and phase 6 Z(fmeas) at the measurement frequency fmeas

Converter with FPGA

transformer

inductor

Fig. 3. Prototype of the high frequency measurement current generator -converter, filter inductance and transformer

V

AD AD

DFT|i|i

DFT|v|

v

|Z(f )|meas

Z(f )meas

fmeas Imeas

controlunit

meas. current gen.L1

L2

L3

N

i ( )tact v ( )tact

grid withnon-linear

loads

Fig. 4. Setup for the grid impedance measurement

are calculated as

|Z(fmeas)| =|v(fmeas)||i(fmeas)|

(1)

6 Z(fmeas) = 6 v(fmeas) − 6 i(fmeas). (2)

The measurement is repeated at all frequencies in range of

interest to a complete characterization of the line impedance

as a function of frequency.

When the measurement frequency fmeas is close to the

harmonics from the 50 Hz fundamental the large grid voltage

superposes the component vmeas of the results from injecting

current imeas. To avoid this problem the harmonic frequency

values are calculated by linear interpolation by the nearby

valid measurements at ±5 Hz. The setup of the grid impedance

measurement is shown in Fig. 4.

C. Measurement setup

The measurement setup is summarized in Fig. 4. The

measurement connection is directly on the power connector.

The line voltages are measured by using voltage transform-

ers with a quoted bandwidth of 40 MHz, the accuracy is 1 %.

The line current is measured using hall effect devices with a

quoted bandwidth of 200 kHz, the accuracy is 1 %.

100 200 300 400 500 600 700 800 900 1000

1

2

3

4

|Z| (Ω

)

100 200 300 400 500 600 700 800 900 10000

50

100

∠ Z

( °

)

100 200 300 400 500 600 700 800 900 10000

0.5

1

L (

mH

)

100 200 300 400 500 600 700 800 900 10000

0.5

1

R (

Ω)

f (Hz)

0.0 mH 0.5 mH 0.2 mH

Fig. 5. Grid impedance with different inductors in series to the grid

The AD conversion is done with a maximum sample rate

of 500 kHz and an accuracy of 16 bit. The sample time is 10

periods of the measurement frequency fmeas.

IV. MEASUREMENT RESULTS

The grid impedance measurement setup, as shown in Fig. 4,

and the high frequency measurement current generator of Fig.

3 are used to a exemplary characterization of the impedance

of a 400 V three-phase electric power system located in

the institute of the authors. The institute has two medium

voltage transformer each with a power rating of 500 kVA.

Unfortunately, the transformer was inaccessible and no other

nameplate data were obtained.

To test the measurement, additionally the impedance char-

acteristics for various circuit components were determined by

the grid impedance analyzer.

A. Method Verification

The measurement method verified in experiments, whereas

many ”test supply impedance” configurations were used. Cir-

cuits which illustrate typical results are presented in this paper.

Further several experiments were performed to verify the

quality of the impedance measurement. These are explained

in the following.

In the first experiment, serial inductors with given values

were added to the line output. The measured impedance and

the calculated resistance and inductance for different inductors

are given in Fig. 5. In this case the grid with the inductors is

simplified as a series circuit of inductance and resistance. The

resistance and inductance are simplified calculated as

R = |Z| · cos6 Z (3)

L =1

2π · fmeas

|Z| · sin6 Z. (4)

According to expectations, the measured inductance varied

with the connected inductance. The resistance increasing with

frequency illustrates the iron losses of the serial inductors.

TABLE IIITEST WITH TWO SERIAL HARMONIC FILTERS

calculated measured

shunt 1 (0.50 mH, 16 µF) 1.454 kHz 1.4 kHz

shunt 2 (5.58 mH, 240 nF) 4.35 kHz 4.3 kHz

Next, two harmonic shunt filters (series-resonant circuit)

have been connected in series to the grid, close to the grid

impedance analyzer. These resonant frequencies are calculated

by

fR =1

2π

1√L · C

. (5)

The first harmonic filter (L = 0.5 mH, C = 16µF) has a

resonance frequency at fR1 = 1454 Hz and the second filter

(L = 5.58 mH, C = 240 nF) has a resonance frequency

at fR2 = 4350 Hz. The filter resonant peaks appear in the

grid impedance at the calculated frequency (Fig. 6). With the

measurement there exists a relatively good correspondence

between the calculated and measured data (Tab. III).

1 2 3 4 5 6 7 8 9 10

0.4

0.6

0.8

1

1.2

1.4

1.6

|Z| (Ω

)

1 2 3 4 5 6 7 8 9 100

10

20

30

40

50

60

∠ Z

( °

)

f (kHz)

with Filter without Filter

fR2

=4.3 kHz

fR1

=1.4 kHz

Fig. 6. Grid impedance with and without two serial harmonic filters (fR1 =1454 Hz, fR2 = 4350 Hz)

1 2 3 4 5 6 7 8 9 100

2

4

V (

V)

1 2 3 4 5 6 7 8 9 100

5

10

I (A

)

1 2 3 4 5 6 7 8 9 100

1

2

|Z| (Ω

)

1 2 3 4 5 6 7 8 9 100

20

40

∠ Z

( °

)

f (kHz)

Fig. 7. Grid impedance with different injected currents

In Fig. 7 measurements at the same connection point nearly

at the same time with different injected currents is presented.

It is shown that the results are almost independent from the

injected current.

B. Measured Grid Impedance

Fig. 8 shows the measured grid impedance of the institute,

the magnitude and the phase angle for a frequency range from

75 Hz to 10 kHz. The measurements are taken at different

days and times. At a frequency of nearly 3 kHz a resonance

is detected. As expected, the characteristics have no linear

dependency on the frequency. In these measurements it’s

clearly shown that, in many cases, the R-L model of the grid

is inadequate because the effective values of R and L depend

on frequency because of other components (C-compensators)

are part of the grid.

Finally in Fig. 9 the measurement results are presented of

the various grid impedance magnitudes over a 10-hour period.

This figure shows the fluctuations of the grid impedance over

a time.

1 2 3 4 5 6 7 8 9 10

0.5

1

1.5

|Z| (Ω

)

1 2 3 4 5 6 7 8 9 100

20

40

60

∠ Z

( °

)

1 2 3 4 5 6 7 8 9 100

0.05

0.1

L (

mH

)

1 2 3 4 5 6 7 8 9 100

0.5

1

R (

Ω)

f (kHz)

Fig. 8. Measured grid impedance with magnitude and phase at different days

09:00

12:00

18:00 1005.000

10.000

0,5

1

1,5

2

f (Hz)time

Z (

Ω)

Fig. 9. Measured grid impedance at different times within 10 hours

V. CONCLUSION

A practical and non-disruptive technique and prototype sys-

tem for measuring grid impedance as a function of frequency

for an energized low voltage grid in normal operation is

presented and evaluated.

Function and accuracy of the applied method are evaluated.

A sinusoidal current of predetermined frequency is injected

into the grid, and the grid impedance at that frequency is

calculated from the measured magnitude and phase of the

injected current and resulting voltage. The measurements are

executed at ascending nearby frequencies to produce nearly

continuous impedance versus frequency characteristic.

This complete characterization of power system impedance

for a wide frequency range provides valuable data for power

quality calculations.

The measured grid impedance provides accurate data as a

starting point for many power system calculations. This offers

the possibility to optimize the power of decentralized energy

production units that can be fed to the grid.

ACKNOWLEDGMENT

This work has been funded by the Innovation Fond of

the state Schleswig-Holstein (Germany). This work has been

carried out in the frame of CEwind (competence center for

wind energy of universities of Schleswig-Holstein) together

with Prof. Hinrichs, University of Applied Science, Kiel.

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