IEEE Electrification - March 2021 - 55

the risks of IBR-related stability problems. The impacts of
IBRs on system stability must be properly evaluated to
maintain the reliability of power systems and to plan
future investments in the transmission system.

Stability Analysis Tools
Commercial eigenvalue analysis tools along with positivesequence phasor-domain simulations are commonly used
for evaluating the stability of bulk power systems. These
tools depend on open-box (i.e., publicly available) models
of synchronous generators and the transmission network;
however, they cannot be applied to evaluate the impact of
IBRs on system stability because of the following reasons:
1)	IBRs use diverse and nonstandardized control methods,
and they cannot be represented using generic and simple models as is possible with synchronous generators
2)	IBRs must be represented using detailed electromagnetic
transient (EMT) models because their complex dynamics
cannot be captured in positive-sequence phasor models
3)	manufacturers only supply the black-box EMT models
of IBRs that do not disclose internal details on the
control system architecture and parameters
4)	IBRs have complex dynamic behavior because of the
large number of nonlinearities, such as PLL, limiters,
and different control modes, which limits the applicability of eigenvalue analysis for understanding the stability problems associated with IBRs.
These limitations of the model-based tools can be
addressed by data-driven stability-analysis approaches.
Impedance-based stability analysis is one such datadriven tool that has proven effective in evaluating

Subsynchronous Resonance
2.2-MW Storage Inverter

20

The impedance-based stability-analysis method was
originally introduced in 1976 by Prof. R. D. Middlebrook
to evaluate the dynamic interactions between a converter-based dc power supply and its source with an
electromagnetic interference filter. Figure 4 demonstrates the method for the stability analysis of a gridconnected IBR: The interconnection of an IBR with a
grid forms a negative feedback loop whose loop gain is
given by the impedance ratio, Z g (s) / Z i (s), where Z g (s) is
the grid impedance as seen from the IBR terminals,
and Z i (s) is the internal impedance of the IBR. The stability of the interface between the IBR and the grid can
be analyzed by applying linear system-analysis tools to
the loop gain, Z g (s) / Z i (s). Either the Nyquist stability
criterion is applied to the loop gain, Z g (s) / Z i (s), or the

Supersynchronous Resonance

4-MW Type 3 Wind Turbine
100

2-MW Type 3 Wind Turbine
20

0

-10

(kV)

50
(A)

0

0

-50

-20
9

9.1

9.2

9.3

9.4

-100
30 30.5 31 31.5 32
58.8 Hz

15 Hz
8 Hz
1 Hz

60 Hz

10 Hz

100

1.9-MW Wind Turbine

0

-50
-100
4

4.5

5

0.01

0.02

0.03

61.2 Hz
3.57 kHz

554 Hz
1 kHz

100 Hz

1.5
1
P
0.5
0
Q
-0.5
-1
1.2 Hz
-1.5
30 30.5 31 31.5 32

(MW)

50

-20
0

20

10 kHz

430-kW PV Plant

10
(A)

(A)

Impedance Method for Stability Analysis

Near-Synchronous Resonance

10

(A)

stability problems involving IBRs. It can use the frequency-domain impedance responses of IBRs-obtained
using either actual measurements or from black-box
EMT models-for analyzing the stability impacts of IBRs
without requiring internal details on power hardware,
control architecture, and parameters. The objectives of
this article are to present historical and modern developments in impedance methods, show their applications for stability analysis of wind and PV power plants
as well as high-voltage direct current (HVdc) transmission networks, and provide recent developments that
make impedance methods suitable for grid-level studies
used for analyzing the stability of future grids with high
levels of IBRs.

0

-10
-20
7.5

7.55

7.6

Figure 2. The stability problems in power systems with high levels of IBRs. All waveforms in this figure are real measurements.

	

IEEE Electrific ation Magazine / MARCH 2 0 2 1

55
IEEE Electrification - March 2021

Table of Contents for the Digital Edition of IEEE Electrification - March 2021
