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Conference Paper

NREL/CP-5D00-74790

July 2020

Impact of Aggregated PV on 

Subsynchronous Torsional Interaction

Preprint

Rasel Mahmud, Andy Hoke, and Jonathan White

National Renewable Energy Laboratory

Presented at the 47th IEEE Photovoltaic Specialists Conference (PVSC 47) 

June 15–August 21, 2020
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Conference Paper

NREL/CP-5D00-74790

July 2020

Impact of Aggregated PV on 

Subsynchronous Torsional Interaction

Preprint

Rasel Mahmud, Andy Hoke, and Jonathan White

National Renewable Energy Laboratory

Suggested Citation 

Mahmud, Rasel, Andy Hoke, and Jonathan White. 2020. Impact of Aggregated PV on 

Subsynchronous Torsional Interaction: Preprint. Golden, CO: National Renewable Energy 

Laboratory. NREL/CP-5D00-74790. https://www.nrel.gov/docs/fy20osti/74790.pdf.
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Impact of Aggregated PV on Subsynchronous

Torsional Interaction

Rasel Mahmud

National Renewable Energy Laboratory

Golden

Colorado 80401

rasel.mahmud@nrel.gov

Andy Hoke

National Renewable Energy Laboratory

Golden

Colorado 80401

andy.hoke@nrel.gov

Jonathan White

National Renewable Energy Laboratory

Golden

Colorado 80401

jonathan.white@nrel.gov

Abstract—This paper investigates induced oscillation (specifically subsynchronous torsional interactions) in power systems

arising from photovoltaic (PV) power modulation. Time domain

simulations of a modified IEEE first-benchmark system are

presented and analyzed. In the IEEE benchmark system, a PV

generator was added at the same bus where the synchronous

generator is connected. The impact of different parameters of

the PV inverters’ volt-volt-ampere reactive (volt-var) curve on

SSTI is examined. The most severe impact found arises from

the time response of the inverter’s reactive power change. A

second-order time response with natural frequency matching

the rotor speed deviation oscillation frequency and low-damping

ratio quickly drives the system to an unstable region. Although

it is highly unlikely that conditions necessary for distributed

energy resource-induced oscillations would occur in the field,

with knowledge of this vulnerability in mind, inverters’ control

parameters can be designed to avoid it.

I. INTRODUCTION

The impact of inverter-based resources on power system

stability has recently gained attention [1], [2] as the percentage of inverter-based renewable generation is increasing

rapidly [3]. Evaluations of voltage source converters used in

inverter-based resource and their circuit parameters, control

strategies, and control parameters for power system stability

analysis have been addressed in several publications [4]. Most

published literature dealing with inverter-based resources and

power system stability have mainly considered wind power

plant and grid stability issues. Similarly, high-voltage DC

[5] and flexible AC transmission systems [6] have also been

studied extensively. There exists a gap, however, in studies

related to power system stability in the presence of photovoltaics (PV). The reason for this could be comparatively less

penetration of PV than other energy sources as well as the

location of PV connections, which are mainly on distribution

circuits. PV penetration is also increasing very fast [7], so the

impact of aggregated PV on power system stability can no

longer be ignored. This situation could be more critical when

instantaneous energy supplied by PV approaches 50% of total

energy supplied by the grid in some locations.

It is known that inverter-based resources under certain

conditions can provide negative damping to a subsynchronous

resonance (SSR) mode, of which subsynchronous torsional

interaction (SSTI) is a subset, thus increasing oscillatory

behavior [8], [9], [10]. In an SSTI, torsional modes of the

generator and turbine masses and shafts oscillate with external

drivers such as series-connected line-compensation capacitors

or power electronic devices. This can push the grid into a

critically unstable state. In this paper, we investigate whether

grid support functions of aggregated PV inverters impact SSTI.

In that regard, we consider SSTI mitigation techniques using

inverter-based resources and explore potential impacts of voltvar function of PV on SSTI.

II. MODEL BACKGROUND

A modified IEEE first-benchmark system [11], as shown in

Fig. 1, can be used to verify the effectiveness of aggregated

PV in mitigating SSTI. The steam turbine model of the synchronous generator has a two-stage steam turbine consisting

of a shaft connecting two masses: low pressure and high

pressure. The shaft is coupled with the synchronous machine

by a second shaft, for a total of three masses. The IEEE

benchmark system was modified by adding a PV generator at

the same bus where the synchronous generator is connected.

The PV generator can be taken to represent a single large

PV plant or an aggregation of many distributed PV plants.

The synchronous generator is rated for 600 MVA, and the

aggregated rating of the PV is 300 MVA. The synchronous

generator and the aggregated PV are connected to the rest

of the network via a transformer and a series-compensated

transmission line. This very simple model does not represent any specific real system, so the simulations presented

here should be considered preliminary. An electromagnetic

transient model of this benchmark system was developed

in MATLAB/Simulink. The rotor speed oscillates around its

steady-state value when there is an SSTI. These oscillations

can be triggered by a disturbance, such as a fault in the

transmission line, especially in a series-compensated line [12].

III. DAMPING SSTI WITH AGGREGATED PV

R. K. Verma et al [13] showed that a large-scale PV

plant can be used as a PV static synchronous compensator

to mitigate SSR. Building on that work, we demonstrate that

the voltage regulation feature of smart inverters could possibly

impact SSTI if configured improperly. The approach proposed

by [13] uses the generator rotor speed deviation from nominal

This report is available at no cost from the National Renewable Energy Laboratory (NREL) at www.nrel.gov/publications. 1
Fig. 1. Modified IEEE first-benchmark model for testing SSTI induced by

aggregated PV

Fig. 2. SSTI damping controller

(∆ω) to generate a reference reactive current command (iqref )

to nullify the rotor speed deviation, thus mitigating the SSTI.

Fig. 2 shows the SSTI damping controller as proposed by

[13]. A simulation test was performed to verify that aggregated

PV can suppress SSTI when a fault in the transmission line

triggers it. Fig. 3 shows the simulation result. At t = 0.022 s,

an SSTI event is initiated because of a fault in the transmission

line. The reactive current from the aggregated PV is controlled

by the damping controller shown in Fig. 2. Within 2 s, the rotor

speed deviation is completely damped because of the reactive

current injection from the aggregated inverter.

IV. IMPACT OF VOLT-VAR CONTROL ON SSTI

In this example, the aggregated PV uses the information

of rotor speed deviation in real time to modulate the inverter

reactive power. In practice, obtaining real-time information on

rotor speed deviation could be very difficult. Nonetheless, it

is evident that the reactive power output of aggregated PV

has a significant impact on the stability of the synchronous

generator. We, therefore, investigate the effects of other PV

reactive power modulation techniques on the SSTI. A widely

adopted method for PV reactive power regulation is volt-var

control, in which reactive power is modulated in response to

local voltage measurements. We examine different parameters

of volt-var curves and their impact on the stability of the

synchronous generator. Fig. 4(a) shows a regular volt-var

curve that can be implemented in most smart inverters. The

parameters of the volt-var curves can be changed to have

altered forms of volt-var curves, as shown in Fig. 4(b) and

Fig. 4(c). The impact of horizontal shifts of the volt-var curve

deadband along the voltage axis and vertical shifts of the voltvar deadband along the VAR axis are examined. The recently

published IEEE 1547-2018 [14] standard specifies a range of

allowable settings for different volt-var curve parameters. By

changing the volt-var curve parameters within the allowable

(a)

(b)

Fig. 3. SSTI mitigation using aggregated PV: (a) power, voltage, and

current measurements of aggregated PV output; and (b) synchronous generator

response; the top curve shows the rotor speed deviations of different masses

of the synchronous generator, and the lower plot shows the torques, in p.u.,

transmitted by masses of the generator, low-pressure, and high-pressure side

of the turbine.

range, the altered forms of the volt-var curves shown in

Fig. 4 can be achieved. The impact of the altered volt-var

curves on SSTI is measured by the maximum deviation of

the synchronous generator rotor speed from nominal. Fig.

5(a) shows the baseline case when there is no reactive power

generation or absorption by the aggregated PV. A fault in

the transmission line triggers an SSTI event, as evident in

Fig. 5(b). Any impact from reactive power modulation by

aggregated PV will result in a change in rotor speed deviation.

Thus, the maximum rotor speed deviation from nominal will

be a good indicator to assess the impact. To complete all

the simulations in a reasonable duration, each simulation is

run for a 5-s window, unless some other stopping criterion is

met. (Details of the stopping criteria are discussed later.) Fig.

5(b) shows that rotor speed deviation continues to grow in the

baseline case, indicating the potential for SSTI exists without

PV. The maximum rotor speed deviation metric used in this

paper represents the maximum rotor speed deviation reached

during the 5-s window, or in a shorter duration window when

the simulation is stopped sooner. Larger rotor speed deviations

represent an increased magnitude of SSTI.

This report is available at no cost from the National Renewable Energy Laboratory (NREL) at www.nrel.gov/publications. 2
(a) (b)

(c)

Fig. 4. Different volt-var curves: (a) regular volt-var curve, (b) horizontal shift

of deadband from nominal voltage along the voltage axis, and (c) vertical shift

of deadband along the var axis

(a)

(b)

Fig. 5. Baseline case when the aggregated PV is not generating or absorbing

any power: (a) power, voltage and current measurements of aggregated PV

output and (b) synchronous generator response

Fig. 6. Baseline volt-var curve

Fig. 7. Impact of shifting volt-var curve horizontally and changing volt-var

controller delay time on rotor speed deviation

A. Baseline Volt-var Modulation

Various simulation tests are conducted to investigate the

sensitivity of the SSTI to volt-var control parameters. Fig. 6

shows the baseline volt-var curve used for the simulations. In

these tests, the PV output is controlled based on only local

information (i.e., without using the rotor speed information).

The PV generator voltage-trip settings are not implemented,

allowing testing across a wider range of voltage settings.

B. Worst-Case Analysis: Horizontal Volt-var Shifting

For a first set of tests, the middle point of the volt-var

deadband is horizontally shifted in 0.02-p.u. increments from

0.1 p.u. below nominal voltage to 0.1 p.u. above nominal

voltage. The middle point of the deadband is initially set

to 0.9 p.u. voltage, then it is incrementally moved toward

1.1 p.u. voltage in 0.02-p.u. voltage steps. This process is

repeated for different values of delays in the volt-var control

response, from 0.0002 s to 0.4802 s, with 0.02-s incremental

steps. Fig. 7 shows the maximum rotor speed deviation for

each test in this set. A total of 275 simulations are performed

for this set of tests. It is found that shifting the volt-var

curve 0.1 p.u. above nominal voltage and using the lowest

delay produces maximum rotor speed deviation, although the

overall differences in maximum rotor speed deviation are not

particularly significant.

C. Worst-Case Analysis: Vertical Volt-var Shifting

The goal of the simulation is to find the worst condition

that produces maximum rotor speed deviation. The volt-var

set points that produced the greatest rotor speed deviation in

the previous step are used in subsequent tests. Starting from

those settings, the volt-var curve is shifted vertically to see

This report is available at no cost from the National Renewable Energy Laboratory (NREL) at www.nrel.gov/publications. 3
Fig. 8. Impact of shifting volt-var vertically on rotor speed deviation

Fig. 9. Impact of change of volt-var Deadband and Steepness on rotor speed

deviation

the impact on rotor speed deviation. In this case, the vertical

shift happens only on the deadband; other points of the curve

are kept constant. Fig. 8 shows a summary of the simulation

results. Vertical shifting of the deadband above the baseline

position yields maximum rotor speed deviation.

D. Worst-Case Analysis: Deadband and Steepness of Volt-var

Curve

Once the worst position of the vertically and horizontally

shifted volt-var curve is found, simulations are conducted to

find how the deadband width and the steepness of the volt-var

curve slope impact the rotor speed deviation. Fig. 9 shows

a summary of the simulation results. Results show that a

steeper slope generally produces more rotor speed deviation.

Deadband width is found to have a less significant impact on

the rotor speed deviation.

Examination of Fig. 7 through Fig. 9 show that although

different values of the parameters defining the volt-var curve

have different impacts on the rotor speed deviation, the maximum rotor speed deviation does not greatly change for any

of these settings.

V. IMPACT OF VOLT-VAR TIME RESPONSE

Further investigation of the issue includes consideration of

the time response of the volt-var controller. It was previously

observed by the authors that the volt-var time-domain dynamics of most commercially available inverters can be modeled

with reasonable accuracy using one of three types of time

responses: first-order responses, second-order responses, and

ramp rate-limited responses [15]. A series of simulation tests

is performed on the aggregated inverter to find the impact of

Fig. 10. Impact of damping coefficient in the second-order time response on

rotor angle stability

different second-order volt-var responses on the rotor speed

deviation; the second-order response can be defined as (1):

H(s) = ω

2

n

s

2 + ζωns + ω2

n

(1)

where ωn, and ζ are the natural frequency and damping

coefficient of the response, respectively. The previously found

worst-case volt-var settings are used while running the tests

with different time response parameters. The simulations find

that if the natural frequency of the second-order time response

matches the frequency of the rotor speed deviation, the resulting SSTI could cause the synchronous machine to become

unstable. Whether the SSTI becomes unstable depends on the

damping coefficient for the time response and the capacity of

the aggregated inverter. For the setup used in these simulations,

the frequency of the rotor speed deviation was found to be

around 25 Hz. A summary of the simulation results for varying

damping coefficients on the rotor angle stability is presented

in Fig. 10. All the simulations are set to run for 5 s; however,

a stop criterion was set in the simulation to check for rotor

speed deviation and output power from the aggregated inverter.

If the rotor speed deviates more than 2% or the aggregated

PV reactive power output exceeds 150% of rated power, the

simulation stops, indicating an unstable condition. Fig. 10

shows that the simulation setup quickly reaches instability

for damping coefficients in the range of 0–0.17. Also note

that IEEE 1547-2018[14] requires distributed energy resources

(DERs) to have adjustable response times. Though a damping

coefficient might not be a directly adjustable parameter, a

very fast response time might set the value of the damping

coefficient within the range that triggers instability. Fig. 11

shows the response of the aggregated PV and synchronous

machine rotor speed when the aggregated PV has a secondorder time response with natural frequency matching the rotor

speed deviation frequency (25 Hz) and damping coefficient

of 0.005. Under this condition, the system becomes highly

unstable and the aggregated PV output shows reactive power

oscillation. The rotor speed deviation also shows increased

deviation. Note that such a low damping ratio is unlikely to

be found in a realistic inverter.

VI. CONCLUSION

Time domain simulations were performed to investigate

induced oscillation arising from aggregated PV response. A

simple IEEE benchmark model with a synchronous generator

This report is available at no cost from the National Renewable Energy Laboratory (NREL) at www.nrel.gov/publications. 4
(a)

(b)

Fig. 11. Simulation result when the natural frequency of aggregated volt-var

response matches rotor speed deviation frequency (25.12 Hz) with a volt-var

damping coefficient of 0.005

was chosen and aggregated PV was added to investigate the

induced oscillation phenomena. It was demonstrated that if

generator rotor speed information is available in real time,

SSTI can be damped by modulating the reactive power of

aggregated PV. Considering that obtaining real-time rotor

speed data could be very difficult, the effect of altered PV

volt-var curves on SSTI was investigated. A large number

of electromagnetic transient simulations were performed in

MATLAB/Simulink to investigate the induced oscillation. The

following observations were made:

• Different parameters of volt-var curves have different

levels of impact on SSTI;

• The most severe impact found so far arises from the time

response of reactive power change; a second-order time

response with natural frequency matching the rotor speed

deviation oscillation frequency and low damping ratio

drives the system quickly to an unstable region.

Although this research identified a potential impact of aggregated PV on the stability of the electric grid, especially on the

ability of aggregated PV to induce oscillations in the power

system, the work was limited in scope, and findings should be

considered preliminary. The models used were simplified, and

the effects of many model parameters were not investigated.

Numerous aspects should be investigated further:

• Developing an analytic (mathematical) understanding of

the effects of advanced inverter functions on induced

oscillations, including SSTI.

• The simplified model used here did not consider

SSTI mitigation techniques commonly deployed by synchronous machines. Additionally, PV generator voltage

trip settings were not implemented. Further investigation

is required to find the impact of such constraints and

protections on SSTI induced by aggregated PV.

• A very simple network model (IEEE first-benchmark

model) was considered here with series compensation.

A more realistic model should be considered in future

investigations. The effects of changing the value of

the series capacitor or eliminating the capacitor should

be investigated. Additionally, the effect of varying the

impedance between the synchronous generator and the

DER should be investigated.

• A single aggregated PV generator was considered here; in

reality, PV systems are often highly distributed. Further

investigation is required to find the impact of distributed

inverter-based resources on SSTI.

• This research was focused on SSTI, but other modes of

oscillations should be investigated.

While it is possible to create the conditions for inverter-based

resources to contribute to SSTI in simulation, it is unlikely that

such conditions would exist in the field, and such conditions

can be avoided through proper selection of inverter control

parameters.

ACKNOWLEDGMENT

This work was supported by the U.S. Department of Energy

under Contract No. DE-AC36-08GO28308 with Alliance for

Sustainable Energy, LLC, the Manager and Operator of the

National Renewable Energy Laboratory. Funding provided

by U.S. Department of Energy Office of Energy Efficiency

and Renewable Energy (EERE) Solar Energy Technologies

Office. The authors acknowledge Dr. Jin Tan of the National

Renewable Energy Laboratory for her invaluable assistance

and inputs.

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