# Oscillations between Grid-Forming Converters in Weakly Connected Offshore
WPPs

Sulav Ghimire1,2,*, Kanakesh V. Kkuni1, Gabriel M. G. Guerreiro1,2,
Emerson D. Guest1, Kim H. Jensen1, Guangya Yang2 1Siemens Gamesa Renewable
Energy A/S, 7330 Brande, Denmark  2Technical University of Denmark, 2800 Kgs
Lyngby, Denmark  *Correspondence via<EMAIL_ADDRESS>
###### Abstract

This paper studies control interactions between grid-forming (GFM) converters
exhibited by power and frequency oscillations in a weakly connected offshore
wind power plant (WPP). Two GFM controls are considered, namely virtual
synchronous machine (VSM) and virtual admittance (VAdm) based GFM. The GFM
control methods are implemented in wind turbine generators (WTGs) of a
verified aggregated model of a WPP and the control interaction between these
GFM WTGs is studied for several cases: cases with the same GFM control
methods, and cases with different GFM control methods. A sensitivity analysis
is performed for the observed oscillations to understand which system
parameter affects the oscillations the most. Several solution methods are
proposed and the inapplicability of some of the conventional solution methods
are elaborated in this paper.

###### Index Terms:

Grid forming, stability, weak grids, oscillations.

##  I Introduction

Type-IV wind turbine generators (WTGs) consist of permanent magnet synchronous
machine (PMSM) and full back-to-back converters. These WTGs have a complex
control and dynamical structure and exhibit different control modes associated
with the different controls and physical devices they have. When the natural
frequencies of the different control modes match with each other, resonances
and/or oscillations can be observed. Similarly, the generator/turbine side
control modes and network converter side control modes can interact/resonate
with each other to lead to torsional vibration modes and torsional
oscillations [1]. Further, the control modes of one WTG can also interact with
that of another WTG leading to power and frequency oscillations. This paper
studies the power and frequency oscillations between two WTGs and investigates
the effect of network and grid parameters on these oscillations.

Conventional power systems exhibited low-frequency oscillations where multiple
synchronous machines form a group and oscillate with or against another group
of synchronous machines [2]. Similarly, low-frequency and sub-synchronous
oscillations in type-IV WTGs have been a topic of discussion in the academic
literature [3], and has also been observed in real-life power systems. For
example, 4 Hz low-frequency oscillations were observed in wind power plants
(WPPs) connected to the ERCOT grid [4], and 30 Hz sub-synchronous oscillations
were observed in WPPs connected to Xinjiang Uygur Autonomous Region, China
[5]. Similar oscillations observed in grid-following (GFL) WPPs were found to
be related to the PLL states and weak grid interconnections [3, 6]. Type-IV
wind turbines with GFM converter also exhibit torsional vibrations which can
be mitigated via a damping filter and this solution can be reinforced by over-
sizing the DC capacitor or by adding storage [1]. Solutions to torsional
vibration via a band pass filter and model-based damper are presented in [7].

Systems such as WPPs with different GFM controls or neighboring WPPs with
different GFM controls can also lead to control oscillations, although this
hasn’t been studied extensively in the academic literature or in the industry.
Fast-acting controls of the WTG converters can interact with each other
leading to power and frequency oscillations, eventually resulting in
oscillatory instability. Avoiding such control interactions is crucial for the
reliable operation of modern power systems. The low-frequency intra-turbine
oscillation modes are usually operating point dependent and can be mitigated
with DC-bus over-sizing [1], PSS, and damping washout filter [8]. However, the
inter-turbine oscillation modes investigated in this paper are near-
synchronous and super-synchronous modes which are highly dependent on system
topology rather than on operating points, and thus require a different
approach. Since the low-frequency intra-turbine oscillation modes are
operating point-dependent, they require extensive study over a wide range of
operating points. However, the less dependency of these high-frequency
oscillation modes on operating points gives an advantage in a number of
studies required to solidify the findings.

Multiple original equipment manufacturers (OEMs,) vendors, and developers
participate in modern power grids. In offshore WPPs, the controls approaches
the different developers and OEMs employ in their GFM WPPs could also be
different in the future. These GFM controls of the different WPPs can thus
have control interactions with each other leading to different oscillatory
behavior. In a system with multiple GFM converters, this paper provides an
insight into how these control methods interact with each other in weak grids.
This paper presents studies under several cases of control interaction: cases
illustrating control interactions between identical GFM controls, cases with
same GFM control with different control tunings, and cases with different GFM
control architecture. Several methods to solve the arising oscillations are
proposed in this paper.

The remainder of this paper is as follows. In section II, a study framework is
proposed where an aggregated model of an offshore WPP is chosen as a test
network. A brief description of the system network topology and the GFM
control methods used is also presented. Power and frequency oscillations
between the WTGs with the same GFM controls are presented in Section III.
Section IV presents the oscillation between WTGs with different GFM controls
where studies like fast Fourier transform (FFT) of the oscillations and a
sensitivity analysis against the network parameters are performed. In Section
V, potential solution methods for the mitigation of the presented oscillations
are presented. Finally, the conclusions are drawn and future steps are noted
in Section VI.

##  II System Description and Modelling

A network with two WTGs, each controlled by a GFM algorithm, connected to the
grid with a nominal SCR value of 1.6 and $X_{g}/R_{g}=5$ (shown in Fig. 1) is
considered for this paper. The power system network used here is adapted from
a WPP model with two power trains, each of which is connected to two
aggregated models of WTG arrays with GFM controls. The control interactions
between these WTGs are observed in terms of power and frequency oscillations
and are studied further.

Figure 1: Network layout for GFM control interaction studies.

The control block diagrams of the GFM control methods are presented in Fig. 2:
Fig. 2(a) shows the virtual synchronous machine (VSM) based grid-forming
control method and Fig. 2(b) shows the virtual admittance (VAdm) based grid-
forming control method. The presented GFM control methods are adapted from
[9].

(a) VSM control diagram

(b) VAdm control diagram

Figure 2: Control diagrams for VSM-based and VAdm-based GFM controllers
employed in the WTGs. Source: [9].

The mathematical model of the outer power control loop of both VSM and VAdm
are identical and can be written as:

$\displaystyle\theta$ $\displaystyle=$
$\displaystyle\int\left[\omega_{n}+\frac{1}{Js+D_{p}}(P^{*}-P_{meas})\right]dt,$
(1) $\displaystyle V_{od}^{*}$ $\displaystyle=$ $\displaystyle
V_{n}^{*}-K_{q}(Q^{*}-Q_{meas}),\quad V_{oq}^{*}=0.$ (2)

Here, $\theta$ is the phase defined by the converter control,
$\omega_{n}:=2\pi f$ is the base angular frequency of the power system with
the frequency $f=50$ Hz. $J$ and $D_{p}$ are the virtual inertia constant and
damping constant respectivelpy, and $P^{*}$ and $P_{meas}$ are the active
power references and measurements respectively. Similarly, $Q^{*}$ and
$Q_{meas}$ denote the reactive power references and measurements respectively,
$V_{n}^{*}$ denotes the voltage reference, and $V_{odq}^{*}$ denote the
voltage references generated by the reactive power control loop.

The inner current and voltage control loops of VSM are PI-controller with dq-
axis decoupling and are written as:

$\displaystyle G_{PI}^{(v)}(s)$ $\displaystyle=$ $\displaystyle
K_{pv}+\frac{K_{iv}}{s},$ (3) $\displaystyle I_{ldq}^{*}$ $\displaystyle=$
$\displaystyle
I_{odq}+G_{PI}^{(v)}(s)(V_{odq}^{*}-V_{odq})+j\omega_{n}C_{f}V_{odq},$ (4)
$\displaystyle G_{PI}^{(c)}(s)$ $\displaystyle=$ $\displaystyle
K_{pc}+\frac{K_{ic}}{s},$ (5) $\displaystyle V_{idq}^{*}$ $\displaystyle=$
$\displaystyle
V_{gdq}+G_{PI}^{(c)}(s)(I_{odq}^{*}-I_{odq})+j\omega_{n}L_{f}I_{ldq}.$ (6)

Here, $K_{pv},\ K_{iv}$ and $K_{pc},\ K_{ic}$ are the respective PI-gains of
the inner loop voltage and current controllers, and $V,\ I$ denote the
measured voltage and currents while $V^{*},\ I^{*}$ denote the reference
voltage and currents respectively.

The inner loops for VAdm include a voltage correction via virtual admittance
and proportional current controller and are written mathematically as:

$\displaystyle Y_{virt}(s)$ $\displaystyle=$
$\displaystyle\frac{1}{sL_{v}+R_{v}},$ (7) $\displaystyle I_{ldq}^{*}$
$\displaystyle=$ $\displaystyle I_{odq}+(V_{odq}^{*}-V_{odq})Y_{virt}(s),$ (8)
$\displaystyle V_{idq}^{*}$ $\displaystyle=$ $\displaystyle
V_{gdq}+K_{P}^{(c)}(I_{ldq}^{*}-I_{ldq})+j\omega_{n}L_{f}I_{ldq}.$ (9)

Here, $L_{v},\ R_{v}$ are the virtual inductance and resistance that define
the virtual admittance $Y_{virt}(s).$

##  III WTGs with same GFM controls

This section presents the observed oscillations in a WPP with WTG converters
having same GFM control methods. Cases with matching control tunings and
control parametric variations are presented.

###  III-A WTGs with same GFM controls and same control tunings

In this study case, both GFM-1 and GFM-2 in Fig. 1 are equipped with the same
GFM control method with the same control tunings. The grid SCR is changed from
3.2 to 1.6 at t=1 s. The resulting power and frequency oscillations are
presented in Fig. 3. It was observed that there is no significant oscillation
between the converters, either during steady state or during or following the
SCR change event. As seen in Fig. 3(a), the oscillation magnitude for the case
setup with two VSM controls is of the order of $10^{-7}$ and for the case
setup with two VAdm controls (Fig. 3(b)) oscillations are of the order of
$10^{-11}$.

(a) VSM vs VSM.

(b) VAdm vs VAdm.

Figure 3: Control oscillations in a system with same GFMs. A SCR change from
3.2 to 1.6 is applied at $t=1\ s.$

The results demonstrate that for converters with the same GFM control and
matched control tunings, the power and frequency oscillations are negligible
in magnitude. However, it must be noted that there are no measurement delays
and latency in the control response included in the models used in this paper.
Thus, the presented results do not include the effect of such delays on system
oscillations.

###  III-B WPP with same GFM control and different inertia constant

This section studies the effect of different controller tunings on system
oscillations. Both GFM-1 and GMF-2 in Fig. 1 are equipped with VSM control,
however a parametric modification is performed on the the VSM control of GFM-1
WTG: its inertia component is removed such that $J=0$. i.e. GFM-1 is now VSM0H
or zero-inertia VSM control while GFM-2 is still the nominal VSM control. An
SCR change from 3.2 to 1.6 is applied to the system at $t=1\ s$. The results
in Fig. 4 show the transient response where $\approx$100 Hz power
oscillations, and similar frequency oscillations are observed. However, there
are no sustained oscillations once the transients clear out. The system gets
fully re-synchronized 200-250 ms after the disturbance and becomes frequency-
stable.

Figure 4: Oscillations between VSM and VSM0H controls following a grid SCR
change from 3.2 to 1.6.

##  IV WTGs with different GFM controls

This section investigates the case of multiple GFM control methods in the same
WPP. In the study cases presented herewith, GFM-1 and GFM-2 in the network
topology in Fig. 1 are equipped with VSM and VAdm respectively. The different
studies performed and the results obtained are presented herewith.

####  IV-1 Oscillation FFT during steady state and transients

The system in Fig. 1 is subjected to a SCR change from 3.2 pu to 1.6 pu at
time $t=1$ s. Both the GFM converters shown in Fig. 2 attempt to control the
voltage and frequency at their terminals before the respective turbine
transformers. During steady state operation and also during a transient, these
converters attempt to control the voltage and frequency at the respective
points. However, since the converters are not communicating and they’re both
controlling nodes with high electrical proximity, the power delivered by one
is counterbalanced by the other. Further, due to the high dependency of the
frequency set by the converters on their generated power, the frequency set by
one converter is also counterbalanced by that set by the other leading to
power and frequency oscillations between the converters.

The power and frequency oscillations shown in Fig. 5 and Fig. 6 exhibit an
amplitude of 0.01 pu and 0.01 Hz respectively. They also have some similar
nature in their frequency content as the converter control defines the
converter frequency based on power mismatch.

(a) Power oscillations $P_{1}-P_{2}$.

(b) Frequency oscillations $f_{1}-f_{2}$.

Figure 5: Fourier transform of the selected oscillation signals for two cycles
after the SCR change event.

Fig. 5(a) and Fig. 5(b) show that the sub-synchronous and near-synchronous
oscillation frequencies are prevalent during the fault transient with 25 Hz
component being dominant in both active power and frequency oscillations.

(a) Power oscillations $P_{1}-P_{2}$.

(b) Frequency oscillations $f_{1}-f_{2}$.

Figure 6: Fourier transform of the selected oscillation signals for two cycles
during steady state.

####  IV-2 Sensitivity of oscillations to electrical proximity between
converters

The electrical distance between the two converters in the presented system is
$2(Z_{array}+Z_{tf})$ which includes the array cable impedance and transformer
impedance of each of the power trains respectively. Now, keeping the
transformer impedance $Z_{tf}$ constant, the array cable impedance $Z_{array}$
is varied from a minimum value $Z_{array}=Z_{grid}/20$ to its nominal value
$Z_{array}=Z_{grid}/5$ to study the sensitivity of the oscillations to the
electrical proximity between the two GFM WTGs. Fig. 7 presents the power and
frequency oscillations between these GFM WTGs in each of these cases. It is
evident from the figures that the control oscillations reduce significantly in
amplitude with the reduction in electrical proximity between the WTGs. The
reason is that the converter control systems are now controlling two distant
nodes which facilitates more independent control without the need for
communication, thus leading to less control interactions between the WTG
converter control systems. Appropriate sizing of the array cables to
facilitate the required power flow during all contingent cases without
unnecessarily over-sizing it can alleviate the oscillation issues.

Figure 7: Inter-converter oscillations with change in electrical distance
between the converters.

####  IV-3 Sensitivity of oscillations to grid SCR

Similarly, the grid SCR was increased from the nominal value of $SCR=1.6$ to
$SCR=8$ keeping the electrical proximity between the GFM WTGs at their nominal
value. The effect of five different SCR values on power and frequency
oscillations is presented in Fig. 8. It is evident that the control
interactions depend heavily on grid SCR: as the grid SCR increases, the
oscillations grow in magnitude. High grid SCR representing a strong grid
suggests that the ideal voltage source of the grid (noting that the grid is
modelled as a Thevenin-equivalent source) is in close electrical proximity to
the controlled nodes of both converters. Now, although any disturbance in the
system will mostly be counteracted by the grid, the GFM WTGs will still try to
control their respective control nodes which are now in closer electrical
proximity to the grid. Thus, the GFM WTGs now attempt to control a point close
to the stiff-voltage source which is not possible, and instead end up
oscillating against each other.

Figure 8: Inter-converter oscillations with change in Grid SCR.

It must be noted that although the very high oscillations seen in cases with
$SCR\geq 4.8$ in Fig. 8 are not seen in practical cases as the WTG protective
controls like current limiting and FRTs become active. The results presented
are based on WTG control models with disabled current limiting and FRT
controls to facilitate the demonstration of the severity of the oscillations
in a strong grid connected case.

##  V Potential Solution Methods

Conventional inter-area and inter-machine oscillations in electrical power
systems had a different nature than the inter-converter oscillations in modern
power systems. As demonstrated here, the frequency components of the
oscillations are dominantly super-synchronous and their dependence is mostly
on system parameters and control systems rather than operating points. Since
tools like power system stabilizers (PSS) and frequency washout filters –
which were quite useful to solve oscillations and instability in conventional
power systems – operate on low-frequency oscillations, they are unable to
solve the oscillation issues observed in modern power systems and demonstrated
herewith. Thus, methods like proper parameter tuning based on eigenvalue
analyses and mode participation factors, and system design to maintain a safe
electrical distance between different GFM-controlled WTG can aid in resolving
these issues. Regarding the sensitivity of SCR on system stability, instead of
modelling the grid as a stiff grid behind an impedance, an inertial model of
the grid can be beneficial to properly understand and address the oscillation
issues. Further, small-signal frequency domain models to pinpoint the states
participating in any particular oscillation modes can help tuning the related
control parameters and stabilize the system. Regarding the oscillations not
severe in weak grids, but severe in the strong grids in Fig. 8, different
parameter type selection frameworks could be employed, however, this requires
technological advancements to estimate grid SCR during operation. Designing
and testing controls parameters which can withstand a wide range of grid SCR
and electrical proximity of other sources could help select an appropriate
control tuning which is robust to all those tests of grid SCR and electrical
proximity with other sources.

##  VI Conclusion

Power and frequency oscillations between the same and different GFM converters
were studied in an aggregated model of an offshore wind power plant. The
results showed that the same GFM converters with matching tuning do not
exhibit significant oscillations. The order of magnitude of the observed
oscillations in such cases were infinitesimally small, thus negligible.
However, parameter tunings can affect the system in such a way that they
exhibit power and frequency oscillation. Further, systems with different GFM
converters exhibited mild to severe levels of power and frequency oscillations
depending on several network parameters. It was observed that the electrical
proximity between the converters had a significant effect on oscillation
amplitudes. Grid SCR had an even stronger effect on these oscillations: the
converters exhibited higher amplitude oscillations in a strong-grid connected
case. Thus appropriate parametric tuning and matching control and parameter
selection is recommended for WTGs in the same WPP or for WPPs in close
electrical proximity.

## Legal Disclaimer

Figures and values presented in this paper should not be used to judge the
performance of Siemens Gamesa (SGRE) technology as they are solely presented
for demonstration purposes. Any opinions or analyses contained in this paper
are the opinions of the authors and are not necessarily the same as those of
SGRE.

## Acknowledgement

The authors would like to acknowledge the support of Siemens Gamesa Renewable
Energy (SGRE), Technical University of Denmark (DTU), and Innovation Fund
Denmark. The work of S.G. was supported by Innovation Fund Denmark under the
project Ref. no. 0153-00256B.

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