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Characterization of the Grid-forming function of a power source based on its external frequency smoothing capability

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In the upcoming converter dominated power system, some of the devices will be required to function as grid forming to ensure the stability of the power system. Several control schemes have been proposed in the literature and system operators might use a mixture of these candidates, attending that they fulfill grid codes to be defined. Here is presented a method that derives a simple model based on basic properties expected from grid forming devices from a system point of view. This model serves to define necessary conditions on local frequency smoothing capability to claim grid-forming function in a power system. One application case is proposed to discriminate the so-called "grid forming control" from "grid following control", on external behavior basis rather than from control structure a priori. Eventually, a cost implication in terms of storage size requirement is discussed. This novel point of view on grid-forming control will certainly help TSOs to specify their needs and anticipate their costs for the upcoming transition.
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Characterization of the Grid-forming function of a
power source based on its external frequency
smoothing capability
Debry Marie-Sophie, Denis Guillaume, Prevost Thibault
R´
eseau de Transport d’Electricit´
e (Research and Development Department)
La D´
efense
marie-sophie.debry / guillaume.denis / thibault.prevost @rte-france.com
Abstract—In upcoming converter dominated power systems,
some devices will be required to function as grid forming to
ensure stability. Several control schemes have been proposed in
the literature and future systems might include a mixture of
them, attending that they fulfill grid codes to be defined. Here is
presented a method that derives a simple model based on basic
properties expected from grid forming devices from a system
point of view. This model serves to define necessary conditions
on local frequency smoothing capability to claim grid-forming
function in a power system. One application case is proposed
to discriminate between the so-called ”grid forming controls”
and ”grid following controls”, on the basis of their external
behavior rather than from their control structure. Eventually, a
cost implication in terms of storage size requirement is discussed.
This novel point of view on grid-forming control will certainly
help TSOs to specify their needs and anticipate the costs for the
upcoming transition.
Index Terms—converter controls, frequency dynamic, power
system dynamic, grid forming, droop control.
I. INTRODUCTION
The share of inverter-interfaced generation from renewable
sources is now greater than 100% of the electrical demand
in some countries [1]. In such systems, TSOs are mainly con-
cerned about the remaining level of inertia and about frequency
stability [2]. Indeed, lower inertia implies higher Rate of
Change of Frequency (RoCoF) and faster frequency transients.
With faster frequency dynamics, frequency-based protections
(e.g. load shedding) may be triggered, endangering system
stability. To allow stable operation of electrical systems with a
high share of converter interfaced generation, some of present
or future inverters will need to upgrade their classical grid
following controls into grid forming controls [3]. Amongst
others, the grid forming function characterizes the ability of
an electrical source to contribute to frequency stability by
making its variation throughout the system smoother. Several
control designs claim to provide a grid forming function to
This work is part of the MIGRATE project (Massive InteGRATion of
power Electronic devices). This project has received funding from the Eu-
ropean Unions Horizon 2020 research and innovation programme under grant
agreement No 691800. This article reflects only the authors views and the
European Commission is not responsible for any use that may be made of
the information it contains.
systems (VSM [4], Power Synch. [5], Virtual oscillator control
[7], [8], Matching control [9], Droop filtered [10], SEBIR
[6], Direct voltage [11]) but their effective contribution to
frequency stability has not been highlighted from the system
operator perspective. The present paper proposes to list general
properties expected from grid forming sources to derive a
generic model that embed all the necessary functions for
proper operation. The model can then serve for quantitative
comparison of the grid forming function of different types of
inverter controls when they are connected to a grid. The main
goal of the suggested method is to be not intrusive, so that
only measurements at the point-of-common coupling will be
necessary on an experimental setup to draw conclusions on the
grid forming nature of a source. The method has been only
tested yet by samples from small signal simulations.
The remainder of the paper is organized as follows. The
simplified model of an ideal grid forming source is derived
in section II. The condition for proper parallel operation are
verified in section III. The method proposed to assess the
grid forming function provided by an inverter is detailed
in section IV. Section V focuses on simulation results for
different controls existing in the literature. A discussion on
the cost of grid forming function associated with the frequency
smoothing capability is added in VI. Section VII concludes the
paper.
II. MO DE L OF A N ID EA L GRID FORMING SOURCE
A. Necessary properties of source for islanded operation
When a power source is feeding a passive network au-
tonomously, it must comply with electrical quality standards
in terms of voltage and frequency range, so that the connected
load can operate under almost nominal conditions. These
quantities must be contained but also be controllable so that the
system operator can adapt the voltage and the frequency to the
operational situation. For slow dynamics referred traditionally
to quasi-static behavior, a grid forming source must embed
the following basic requirements, simplified and adapted from
french grid-codes [18] :
(i) The output RMS voltage at the source terminal must
track a reference Vwithin a time response of 10
seconds.
(ii) The frequency must track an adjustable reference ω,
within a time response of 15 seconds.
For fastest dynamics, the grid forming source must behave
as closed as possible to a voltage source with limited voltage
magnitude and frequency variations. The voltage source be-
havior has never been specified in grid-codes, because it was
guaranteed by the physics and the design of synchronous gen-
erators, with no need for extra control loop. Observing that the
voltage magnitude response to rated load increase is limited by
the sub-transient reactance of synchronous generators, and that
the frequency dynamics are limited by the mechanical inertia
of rotors, it is proposed here to define additional requirements
for generic grid forming sources [3]:
(iii) The output voltage magnitude drop following rated load
connection must be contained within ±0.2 pu before the
aforementioned quasi-static control reacts.
(iv) The frequency dynamics at the source output must be
limited. By calling ωm(t)the instantaneous frequency
of the ideally produced voltage waveform, this time limit
will be represented by the time constant Tω.
m
dt ωn
Tω
(1)
It corresponds to an initial RoCoF limitation.
The value of the frequency dynamics limit should be fixed
according to criteria detailed later in this paper. One can
already note that the RoCoF level needn’t be as high as
the level ensured by the mechanical inertia of synchronous
generators.
The reason to make the frequency a variable quantity
with limited dynamics, even in the absence of synchronous
generator is three fold. First, it anticipates the fact that grid
forming sources will eventually operate in parallel, and that
they cannot rely on external signals for synchronization. Thus
the frequency cannot be fixed to a single value, but must vary
so that all the frequency references of units stably converge to
a common value. The link between frequency dynamics and
stable synchronization process is discussed in the next section.
Second, the definition of an observable frequency is pre-
cious to give information on the state of the power system
everywhere on the grid. Taking the present system as an
example, the frequency deviation provides information on
system unbalance, which triggers the support of dispatchable
sources. Therefore, the frequency must be locally defined as a
continuous quantity, i.e. with limited derivative. Furthermore,
if the frequency is expected to be independent from voltage
amplitude, then frequency dynamics are expected to be 5 to
10 times lower than the electrical period [3]. For example, a
limitation of frequency dynamics to 1% of nominal frequency
over one cycle yields (Tac=20 ms):
m
ωn
<dt
100Tac
(2)
Considering eq. 1, this limit is equivalent to Tω=100 Tac=2 s.
Third, the limitation of dynamics has regard to measurement
conditions. To ensure fast and common frequency estimation
by sensors and protections, the frequency signal variations
must be limited over the time. The accuracy of present pro-
tection devices is guaranteed for frequency variations slower
than 2 Hz.s1, which is equivalent to Tω=25 s.
B. Simplified model of an inverter-based grid-forming source
Fig. 1 represents the assumed minimal model that can be
derived from the necessary conditions (i) to (iv) above. The
model will be later used to assess the grid-forming capability
in grid-connected conditions. The considered assumption are
the following :
Vm
VSC based converter model
Load
e
g
v
src
L
vsrc
vm
Ls
  
 
w
m
V*
w
*E
Islanded
Fig. 1. Minimal grid-forming source model under islanded condition
1) The voltage regulation integration time is set to Tv= 10 s.
The voltage Vmwill be considered constant for dynamics
under 1 s.
2) The converter is operating far from its current limit which
implies that the mandatory current limiting strategy is
disregarded.
3) The inductance Ls= 0.15 p.u. represents a accepted
value for the VSC filter inductance. This low value
will limit the voltage drop above 0.8 p.u. following the
connection of a rated load.
4) The frequency dynamics limitation is set to the most
constraining limit of the previous paragraph, namely
Tω=25 s.
Note that the second assumption is only valid under small-
signal conditions. Thus, the large-signal or transient studies
are out of the scope of the paper.
In fig. 1, vm=Vmcos (θm(t)) is the sinusoidal voltage
equivalent to the modulated voltage of a generic Voltage
Source Converter, edenotes the terminal voltage, vg, the grid
voltage at the point of common coupling, vsrc is the equivalent
voltage of the Thevenin equivalent of the rest of the system.
In simulation, the transformer can also be represented by a
self inductance of Lc= 0.15 p.u.
The following section will investigate the necessary con-
ditions for operation with other grid-forming sources, i.e. in
grid-connected situation.
III. CONDITION FOR SYNCHRONIZATION OF MULTIPLE
GRID FORMING SOURCES
A. Static convergence to a common frequency
To obtain synchronization among grid-forming units on an
inductive transmission grid, linking the delivered active power
Pwith the frequency reference ωwith a proportional gain mp
can be sufficient, provided there is enough transfer capability
between sources. This additional condition has been added
to our model on fig. 2. Such a simplified droop controlled
inverter presents the sufficient and necessary conditions for a
stable synchronization with others [17].
P*P
VSC based converter model
Load
e
g
v
src
L
vsrc
Ls
Grid-connected
Vm
vm
  
 
w
m
V*
w
*
E
Fig. 2. Full minimal grid-forming source model
Analytically, for small signals and under quasi-static ap-
proximation of the grid, the synchronization mechanism can be
easily explained by the following equation is Laplace domain:
ω(s) = mpP(s)(3)
ωm(s) = mp
1 + TωsP(s)(4)
Where mpis the droop gain and Pis the power vari-
ation. In quasi-static approach, line dynamics are neglected
compared to frequency variation dynamics. Assuming the two
sources initially don’t exchange power, the power variation
under small grid frequency variations can be simplified into:
P(s) = UmUsrc
X
ωm(s)ωsrc(s)
s(5)
Where Umand Usrc are the phase-to-phase RMS voltage,
and Xthe total reactance between the controlled inverter and
the voltage source. Combining (4) and (5) gives the inverter
frequency response to a grid frequency variation:
ωm(s) = 1
XTωs2
UmUsrcmp+X s
UmUsrcmp+ 1 ωsrc(s)(6)
The unity static gain of the eq. (6) is the proof of the
synchronization mechanism of the inverter with the grid.
B. Stability condition for synchronization
To validate the simplified quasi-static approximation above,
we must ensure that frequency variations of the controlled
inverter do not interact with lines dynamics that have been
neglected, and do not interfere with voltage variations.
The first condition is ensured by setting Tωto a sufficiently
high value, the latter condition is ensured by the assumption
1) of the model where the voltage is considered fixed for fast
dynamics.
The sufficient value of Tωis quantified in [8], as the
minimum value that let the time to the electrical transients
to vanish. The value chosen of Tω=25 s, largely fulfills this
last condition. Hence, our grid-forming model is considered to
reach steady-state in an asymptotic way validating the previous
equations.
Interestingly, from a rough analysis, the eq. (6) gives that
one of the basic function of a grid forming control is to
locally filter the frequency variation with, at least, a second
order low pass filter. The filtering cut off frequency given
by νc=fn.qUmUsrcmp
XTω5H z, which quantifies the
grid forming capability regarding frequency stability, or the
frequency smoothing capability. Thus, for islanded and parallel
operation , the frequency dynamics limitation, understood as a
local frequency smoothing capability, is a necessary condition
for providing a grid forming capability to the system.
IV. EXTERNAL CHARACTERIZATION ON FREQUENCY
SMOOTHING CAPABILITY
A. Need for external characterization
The terms grid forming and grid following or grid support-
ing have been employed in many papers to specify inverter
control structures or functions [12]–[14]. However, their defi-
nition is not clearly accepted. A very basic definition of a grid
forming inverter is an inverter that can operate in islanded
mode, while a grid following inverter must be connected to
the main grid with synchronous machines and/or grid forming
inverters to behave properly. Grid supporting inverters have
further been defined to contribute to grid stability by providing
some ancillary services like voltage or frequency regulation.
Nevertheless, this definition does not take into account many
other specifications needed for a 100% power electronics
transmission system [15]. In addition, most of the authors
claim that the function of an inverter is defined by its control
structure, such as in [12], [13]. In practice, a grid-forming-
grid-supporting control and a grid-following-grid-supporting
control can exist and have the same objectives in steady-
state but completely different dynamics, mainly based on the
chosen control time constant. In particular, their contribution
to fast frequency stability differs drastically. The functional
definitions of the literature are all the more unsatisfying as
some ”hybrid” controls [11] are neither grid forming nor grid
following.
The rest of the paper aims at describing an assessment
method of the ability of different inverter controls to locally
smooth frequency and thus to contribute to its stability. The
method is meant to contribute to clarify the frontier between
grid forming and grid following converters.
B. Principle of the method
From a test bench of fig. 3, the ratio of a frequency variation
of eand vgare plotted on a Bode diagram and compared
VSC based
converter
Load
dc
u
dc
C
e
source
i
g
v
src
L
vsrc
Freq Freq
w
g
w
e
Fig. 3. Simulated system
with the response of the simulated ideal grid-forming model
of section II. In particular, the grid-forming impact on the
frequency is expected to be quantified by comparison with the
second order low-pass filter behavior of eq. (6).
The test is meant to be experimental, thus frequency mea-
surement devices are placed to accurately measure the voltage
waveforms eand vgand to derive frequency estimation. At
the present time, the method has been only tested based on
simulated data.
C. Simulation set-up
The operating protocol for the simulation is the following:
1) Building a noisy frequency source around the nominal
frequency:
ωg(t) = ωn(Aωcos(νωt)) (7)
2) Obtaining the frequency response a the terminal of the
controlled inverter.
For simplicity, it has been decided as a first approach to evalu-
ate rather the frequency of vm, considering that the frequency
is directly given by the control output before modulation of
the VSC.
In our simplified model of fig 2, the frequency is directly
given by ωm, whereas the tested control were modeled in dq-
frame. We had to take into account the speed of the rotating
frame ωdq and the faster angle variation. Thus :
θm(t) = Zωdq (t) + atan vmq(t)
vmd(t)(8)
ωm(t) = m
dt =ωdq (t) + 1
1 + v2
mq(t)
v2
md(t)
(9)
V. GRID FORMING ASSESSMENT RESULTS
A. Example of existing converter controls to be tested:
Three different inverter controls will be assessed in the
paper. All of them are said to be ”grid-supporting” controls:
a classical grid following based control: synchronization
is ensured using a typical SRF-PLL [16]. The inverter is
controlled as a current source to regulate its active and
reactive power using a PI controller. Outer loops have
been added to provide both reactive power control and
primary frequency control, in both cases using propor-
tional (droop) characteristics.
a grid forming based control: synchronization is done
using a filtered droop control [10], it therefore provides
primary frequency control. The amplitude of output the
voltage of the inverter is regulated as constant.
a hybrid approach called direct voltage control [11]: this
control has been specifically developed for offshore wind
farm to avoid harmonic resonances when the HVDC
inverter of the wind farm switches off for a short period.
It uses a PLL to synchronize to the grid but the voltage,
and not the current, is directly controlled . It is therefore
difficult to classify according to the above definitions.
For comparison with the present dynamics of the system,
the impact of a synchronous machine regulating both voltage
and frequency will also be tested.
B. Expected results
The comparison between frequency variations Bode plot and
the presented model should be read as follows :
If for frequency variations speed greater than νc, the gain
of the transfer function is low: the inverter does not react
to the frequency disturbance of the other source. Instead,
the inverter keeps its local frequency very close to 50 Hz,
and thus, smooths the frequency variations in the system.
If for slow frequency variations under νc, the gain is
close to one: it means that the inverter closely follows the
variation of frequency introduced by the voltage source.
The lower the cutoff frequency, the more the inverter stabilizes
the grid frequency and the more it provides grid forming
function to the system. The method therefore enables to
quantitatively compare the impact of different controls on
frequency stability. If the cutoff frequency is greater than the
nominal frequency of the system, the inverter does not provide
any grid forming function since it only follows the system
frequency even without perturbation.
C. Simulation based results
The Bode plots of the three considered inverter controls and
the one of the synchronous machines are plotted on Fig. 4. The
phase diagram will not be plotted in this article as it does not
bring any additional value for the analysis done below.
As expected, it can be seen on Fig. 4 that the gain of all
transfer functions go to 0 for slow variations of frequency,
which means that the three controlled inverters synchronize to
the grid in steady state. The measured cutoff frequencies are:
for the grid-forming by filtered droop control: 6.5 Hz
for the direct voltage control : 7 Hz
as a reference, for the synchronous machine : 1.5 Hz
The behavior for high frequency may look surprising for the
grid feeding inverter. For frequencies above 70Hz, the PLL
does not capture the change in angle, but the grid voltage
feedforward does it in a grid-feeding based control [16].
Therefore, the gain of the system is close to 1. This inverter
does not impact the behavior of the system for high frequency
events.
Fig. 4. Gain of the transfer function for different inverter controls
On the contrary, the grid forming inverter provides some
damping to the frequency oscillations which frequency is
greater than 6.5 Hz, therefore it limits the rate of change of
frequency. The dynamics that are damped by the synchronous
machine are at even lower frequency.
D. Discussions around the proposed method
The proposed method compares the frequency filtering
effect of different types of generation. This allows a quan-
titative evaluation of the impact of a source, without explicit
knowledge of the control.
If most of the inverters on the grid are grid following
with fast PLL, the frequency dynamics will only be driven
by the remaining synchronous machines as the inverters
perfectly follow the frequency variations for most of
the frequency range. There is a filtering effect only for
frequency variation between 10 and 70Hz.
In the case of grid forming inverters, the frequency
dynamics of the system are limited by these inverters.
Such inverters slow down the frequency deviation that
occurs following a loss of generation. As stated in the
previous section, this would only be true if the inverters
have both some available energy and power, but system
wide, we can consider that not all grid forming inverter
would be close to their saturation.
Direct voltage controlled inverters will also impact the
dynamic of the system, as their cutoff frequency is not so
far from the one of synchronous machines. Their behavior
is quite similar to the grid forming one. Still the slope
the gain of this inverter is less than the one of the grid
forming inverter, which means that for the same cutoff
frequency, it will less filter high frequency variations.
The system operators (SO) could therefore use this method
to assess if an inverter will improve the dynamics of their
system or not, or even to define a required cutoff frequency that
an inverter must at least fulfill (νc(inv)< νc(req)). Of course
depending on the system characteristics, the requirement of
cutoff frequency should not be the same. An island system
already has very fast frequency dynamics, while the continen-
tal Europe system with its multiple big synchronous machines
has slower dynamics. The cutoff requirement will also depend
on load shedding, islanding or governor control protections, or
on the frequency measurement accuracy of other devices. As
the active power flow and the variation of frequency are linked
(see eq. (14) and (15) below), it can easily be understood that
an inverter that makes its frequency change slowly will not
be able to track its power reference fast and accurately. This
trade-off should be judged by the SO depending on its system
configuration and the capacity of sources to be dispatchable
or not.
VI. DISCUSSION ON THE COST OF FREQUENCY
SMOOTHING CAPABILITY
To locally filter the frequency the inverter must have:
Some additional energy buffer to provide to the grid
Available current capability to increase its power output
when there is a frequency deviation.
The amount of the energy reserve can easily be estimated
by the following consideration. For the simplified model
of a voltage controlled inverter, subject to grid frequency
variations slower than the nominal frequency (ie, νω< ωn),
the simplified equation of the active power flow between the
inverter and the source is:
P(t) = UmUsrcsin(θm(t)θsr c(t))
X(10)
Let’s assume that the inverter perfectly filters a frequency
oscillation at a given frequency νω1, and that the inverter
frequency is fixed at ωinv =ωn. Further assuming the worse
case where there is no power transfer initially, the phase angle
difference is only provoked by the frequency variation of
the voltage source. Therefore the power exchange can be re-
written as follow:
P(t) = UmUsrcsin(Rt
0ωnAωcos(νωt)dt)
X(11)
P(t) = UmUsrcsin(ωn
νωAωsin(νωt))
X(12)
It is worth noting that as νω>1.5Hz which implies
ωn
νωAω<1
3, validating the following approximation:
P(t) UmUsrc ωn
νωAωsin(νωt)
X(13)
The amount of additional energy reserve ∆Σ that is needed
from the inverter to be able to filter can then be calculated
based on integrating the power on half a period of the
frequency oscillation.
∆Σ = Zπ
νω
0
UmUsrc ωn
νωAωsin(νωt)
Xdt(14)
∆Σ = 2UmUsrc Aω
X
ωn
ν2
ω
(15)
Numerial application in our test case, with Um=Usrc =
225kV ,Aω= 0.01,X= 30Ω and the nominal power Pnof
units equal to 1000MW:
∆Σ = Pn
10.6
ν2
ω
J(16)
The inverter must have enough reserve to operate at Pn
during 10.6
ν2
ωs.
VII. CONCLUSION
This article illustrates a method aiming at evaluating the
impact on power systems’ frequency dynamics of different
types of generation connection, interfaced either by a syn-
chronous generator or by power electronics. In the latter case,
the method determines on whether a converter control can
provide grid forming function to the grid or not. Its main
advantage is that it provides quantitative results that can be
easily interpreted without specific knowledge of the internal
control of the generating units.
The method is based on simulations, the results of which
enable to estimate the Bode magnitude plot of the ratio
between the frequency variations of the voltage imposed by
the considered generating unit and a frequency perturbation
introduced by an ideal voltage source.
The results exhibits that all considered generating units be-
have as low pass filters in the frequency domain but that their
cut off frequency greatly varies. Synchronous machines and
grid forming inverters smooth frequencies greater than a few
Hertz, whereas grid following inverters smooth frequencies
greater than a few tens of Hertz. The level of attenuation
of a given frequency can easily be deducted from the slope
of the Bode magnitude plot. The obtained results fits the
prediction given by the theoretical transfer function of a basic
grid forming control by filtered droop.
From our first view, having a frequency that slowly varies is
of most importance as frequency measurements on short time
scale is very challenging. Having a common frequency that can
be easily and accurately measured would enable any type of
device to help for frequency regulation and would also allow
to keep some operation rules and protection schemes that are
based on frequency measurements.
The method proposed in this paper only covers one of the
aspects of the impact of grid forming inverters on the grid. If
making smoother frequency variations is a necessary condition
for a converter control to be considered as grid forming, it is
however not enough. As mentioned in the paper grid forming
converters must be able to operate in islanded mode and this
is not capture by the frequency characterization. They must be
protected against over currents during large transients which is
out of the scope of small-signal analysis. These two features,
as well as others presented in [10], cannot be detected by
the method proposed in this paper. It should therefore be
completed with other tools to globally characterize the grid
forming behavior of a control.
VIII. ANN EX
A. Parameters of the grid following based inverter
Current loop time response: Tri = 0.01 s, PLL bandwidth:
ωP LL =ωn= 314 rad.s1,
B. Parameters of the grid forming based inverter
Voltage loop time response: Tr v = 0.05 s, Static droop gain:
mp= 4%, Power filter cutoff frequency: ωLP =ωn
10
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