CGI for Impedance Characterization 

of Inverter-Coupled Generation

Shahil Shah, Przemyslaw Koralewicz, and 

Vahan Gevorgian 

Fifth International Workshop on Grid Simulator Testing

Tallahassee, Florida

November 15–16, 2018 

NREL/PR-5D00-72899
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Super-synchronous resonance

Problem: Control Interactions – Resonance

Multifrequency resonance

Sub-synchronous resonance AC/DC hybrid resonance
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Outline

• Challenges of time-domain power-hardware-in-the-loop (PHIL) 

characterization

• Frequency-domain impedance-based characterization

• Impedance measurement using 7 MW grid simulator 

(controllable grid interface: CGI)

– Evaluation of dynamic interactions

– Validation of original equipment manufacturer (OEM) dynamic models.

• Large-signal impedance theory of resonance

– Prediction of resonance-generated harmonics in Type-III wind turbines

– Effect of MOV surge arresters on grid impedance

• Impedance-based characterization of frequency response
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Challenges of Time-Domain Characterization

• PHIL

– Difficult to gain insights for control design

– Shows device behavior only for a specific condition

– Does not support high-fidelity model validation

– Does not excite entire dynamic space of device under test

• Simulation

– All of the above, plus:

– Outcome highly dependent on model accuracy

– Not all dynamics can be captured in simulations

• Parasitic elements, switching artifacts, complex nonlinearities—transformer 

saturation, control saturation, protection functions, thermal/mechanical 

losses
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Impedance-Based Analysis

• Impedance response of converter and grid are compared

– Impedance intersection point gives resonance frequency

– Phase difference at intersection point gives stability margin

Grid

( ) Z s g

Loop gain:

Zg(s)/Zp(s), Zg(s)/Zn(s) 

( )

( )

p

n

Z s

Z s
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100 Hz 300 Hz 1 kHz 2 kHz 4 kHz 150

100

50

0

50

100

100 Hz 300 Hz 1 kHz 2 kHz 4 kHz 20

30

40

50

60

( ) Z s p

Magnitude (dB) Phase (deg.)

( ) Z s g

( ) Z s g

( ) Z s p

SCR: 5

SCR: 2

172o

182o

195o

205o

SCR Grid 

Inductance, Lg

Resonance 

Frequency

Phase 

Margin

5 4.6 mH 641 Hz +8o

4 5.7 mH 584 Hz −2o

3 7.6 mH 512 Hz −15o

2 11.5 mH 441 Hz −25o

• VSC becomes Unstable during 

Weak Grid Operation

– Unstable for SCR<5.0

– Resonance Frequency Decreases with 

SCR and its “Severity” Increases −

−

−

Resonance Frequency and Phase-Margin
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SCR: 4

SCR: 3

SCR: 2

Resonance-Generated Distortions
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Impedance Measurement Using CGI

• 7-MVA, 13.2-kV grid 

simulator (CGI)

+

• Perturbed voltages

• Response currents

Photo by Mark McDade, NREL
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Impedance of 1-MW/13.8-kV Inverter

• Inverter-interfacing 1-MW/

1-MWh battery energy storage 

system

– Voltage perturbation (% of 13.8 kV)

• Impedance response

• Different control 

elements dominate at 

different frequencies.

Photo by Dennis Schroeder, NREL
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Frequency Cross-Coupling

• Voltage perturbation at a frequency produces current 

response also at other frequencies

Perturbed voltages

Response currents
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4-MW Type III Wind Turbine Drivetrain

4-MW DFIG 

generator 

5-MW dyno as 

prime mover

Back-to-back 

converters

Photo from NREL
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Positive-Sequence Impedance of DFIG

• Low-frequency inductive 

behavior because of 

induction machine

– Phase higher than 90o: 

Negative resistance

– Subsynchronous resonance 

(SSR)

• Capacitive behavior 

between 80–250 Hz 

because of current control

• EMI filters dominate highfrequency response

Measurements of 4-MW DFIG
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Blue: Measurements of 4-MW DFIG

Red: PSCAD model from OEM

Impedance for Dynamic Model Validation

• High-fidelity model 

validation

• Validated model can be 

used to evaluate:

– Farm-grid and turbineturbine interactions

– Grid-support functions

– Transient performance

– Control redesign

Magnitude (dB) Phase (DEG.)
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Large-Signal Impedance Theory

• IDEA: Impedance changes with resonance magnitude

Nyquist 

stability 

analysis
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• Impedance analysis

SSR in Type III Wind Turbines

• DFIG output currents

• Control design to mitigate turbineturbine and farm-grid dynamic 

interactions.
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Prediction of SSR-generated harmonics Grid impedance changes with resonance (and 

perturbation) magnitude because of MOVs

Prediction of SSR-Generated Harmonics

( ) Z s g

( ) Z s g
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Frequency Response Characterization

• Transfer function from active power to frequency at the 

point of common coupling
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Characterization of Frequency Response

• Loss of generation

• Applications:

– Real-time estimation of system 

inertia and primary frequency 

response (PFR)

– Design of frequency support by 

inverters

• P (power) to f (frequency) 

transfer function
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Summary

• Adoption of impedance characterization by wind 

industry for dynamic interactions

– Root-cause finding, new grid codes, control design, impedance specs

• Impedance measurement using grid simulator can play 

critical role 

– Covers entire dynamic space of device under test

– High-fidelity model validation

– Control design

– Optimization of dynamic and transient performance.

• New frequency-domain characterization tools for grid- support functions such as frequency and voltage 

support
www.nrel.gov

Shahil.Shah@nrel.gov

Thank You

This work was authored by the National Renewable Energy Laboratory, operated by Alliance for Sustainable Energy, 

LLC, for the U.S. Department of Energy (DOE) under Contract No. DE-AC36-08GO28308. Funding provided by U.S. 

Department of Energy Office of Energy Efficiency and Renewable Energy Wind Energy Technologies Office. The 

views expressed in the article do not necessarily represent the views of the DOE or the U.S. Government. The U.S. 

Government retains and the publisher, by accepting the article for publication, acknowledges that the U.S. 

Government retains a nonexclusive, paid-up, irrevocable, worldwide license to publish or reproduce the published 

form of this work, or allow others to do so, for U.S. Government purposes.