Synthetic inertia versus fast frequency response: a definition

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IET Renewable Power Generation
Research Article
Synthetic inertia versus fast frequency
response: a definition
ISSN 1752-1416
Received on 31st May 2017
Revised 16th August 2017
Accepted on 13th September 2017
doi: 10.1049/iet-rpg.2017.0370
www.ietdl.org
Robert Eriksson1 , Niklas Modig1, Katherine Elkington1
1Svenska kraftnät, Sundbyberg, Sweden
E-mail: robert.eriksson@svk.se
Abstract: This study discusses synthetic inertia from the perspective of a transmission system operator and compares it to fast
frequency response based on frequency deviation. A clear distinction of the meanings between these concepts is discussed, the
basis of which is a description of their characteristics. A contribution and the purpose is the clarification of these concepts in
addition to share the perspectives of a transmission system operator. The frequency response of a power system based on the
Nordic system is examined for future scenarios with large amounts of wind power. Conclusions are drawn regarding the benefit
of synthetic inertia compared with fast frequency response based on frequency deviation.
1 Introduction
The frequency of a power system is a continuously changing
quantity whose derivative indicates the balance between consumed
and produced power. A momentary imbalance between these
results in a change of system frequency where kinetic energy is
stored or released in rotating masses in the system. When a
disturbance in the form of disconnection of load or production
occurs, the frequency response of the system depends on size of
disturbance, inertia and response of controlled frequency responses
[1]. Inertia prevents system frequency from experiencing sudden
changes which can in turn cause stability issues. Today the bulk of
inertia in power systems is made up of rotating masses in
synchronous generators. With more non-synchronous generation
such as wind and solar power in the power system, inertia is
reduced. The inertial response from different generator types has
been thoroughly investigated in literature, for example [2], and
there are many challenges related to operation of systems with low
inertia [3–5]. Examples of systems which operate with relatively
small levels of inertia include the power systems in Ireland, New
Zealand [5] and Gotland, in Sweden.
Since non-synchronously connected production units, such as
modern wind turbine generators, are connected via power
converters, their rotational speed is isolated from the system
frequency. They do not therefore deliver a natural inertial response
and do not contribute to the inertia of the system. We refer to
synthetic inertia as the contribution of additional electrical power
from a source which does not inherently release energy as its
terminal frequency varies, but which mimics the release of kinetic
energy from a rotating mass. This provides an electrical torque
which is proportional to the rate of change of frequency (RoCoF),
which resists changes in frequency. Note that by the term synthetic
inertia we mean synthetic inertial response. The first term is the
most frequently used in the literature and is therefore used here as
well.
To operate a power system securely, the frequency of the
system must remain within a narrow band. Momentary imbalances
are regulated by primary control responses to provide an immediate
balancing action to contain frequency deviations. In the Nordic
system, these reserves are called frequency containment reserves.
The accepted minimum instantaneous frequency is in the Nordic
system 49.0 Hz.
The frequency containment reserves in the Nordic system are
currently being re-evaluated. The reason for this is reduced
frequency quality and the expected increase of wind power
penetration which may, if no actions are taken, cause the system
frequency to deviate outside acceptable limits [6, 7]. To mitigate
large frequency deviations after disturbances, wind turbines have
been proposed as an abundant source of frequency support, and
several approaches have been discussed in the literature [1, 3, 8–
10]. One such type of frequency support from wind turbines is
synthetic inertia.
Supply of synthetic inertia requires energy stored in systems
behind power electronic interfaces, such as batteries, rotating
masses in wind turbines or even other power systems connected
through high voltage dc (HVDC) connections. To supply synthetic
inertia, supplementary control of these sources is required, as there
is usually no direct relation between power output of these sources
and the frequency of the system. Control of wind turbines to supply
synthetic inertia has been proposed in literature, and much research
has focused on developing controllers which respond to frequency
disturbances [9, 11–16]. Much of this research focuses on
describing the initial dynamic response of power systems after loss
of generation, with indices such as minimum instantaneous
frequency, also known as minimum instantaneous frequency, and
RoCoF. However, with more HVDC connections, the dimensioning
fault may be loss of power export, which could lead to frequency
increases.
This paper provides a complete definition of synthetic inertia
with a distinction from the general term of fast frequency response.
Due to the prevalence of wind power in the power system, focus
has been laid on the frequency control responses of wind turbines.
These responses are shown and discussed from the perspective of a
transmission system operator (TSO). Here the effect of having
limited frequency control reserves, such as in the case of solar
power and wind power, is also demonstrated.
The Australian Energy Market Operator (AEMO), EirGrid and
System Operator for Northern Ireland (SONI) have performed
much work on issues related to operation of low inertia systems. In
[17], EirGrid and SONI investigate the RoCoF in their system for
specific events. They proposed interim Grid Code standards of 1
Hz/s over 500 ms for the Ireland system and 2 Hz/s for the
Northern Ireland system. High RoCoF was experienced in the
South Australian system during the blackout event on 28
September 2016 [18] and issues related to RoCoF are investigated
in the Future Power System Security Program at AEMO.
Simulations are performed to demonstrate the behaviour of the
system for different fast frequency responses from wind turbines.
A model similar to the Nordic system, with primary control
reserves supplied by hydro power units, has been developed in
Matlab/Simulink. Wind turbines are modelled by taking into
account the reduction in mechanical power from the wind as the
rotational speed of the wind turbines is reduced. Simulations are
then run for large disturbances and for normal operation. Practical
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aspects regarding implementation are also discussed from the
perspective of a TSO. The differences in system response for these
frequency control methods are discussed here, but the requirements
of the system to handle disturbances are outside the scope of this
paper.
2 System dynamics
In order to understand what synthetic inertia is, we present the
dynamics of the system which describe system frequency.
The dynamic behaviour of a single synchronous machine i can
be described by
Ji
dωm,i
dt=Tm,i−Te,i(N m)
(1)
where Ji is moment of inertia, ωm,i is angular velocity, Tm,i and Te,i
are the mechanical and electrical torques for generator i. Equation
(1) can also be expressed in terms of inertia constant Hi and power
on a per unit base as
2Hi
dωi
dtωi=Pm,i−Pe,i(p . u . )
(2)
where ωi is the electrical frequency of rotation, Pm,i and Pe,i are the
mechanical and electrical powers for generator i.
The system frequency is the frequency the machines approach
when their individual dynamics have died out. As the dominating
dynamics for power system frequency comprise the aggregated
synchronous generator dynamics and primary frequency control
response, the dynamics of the system can be expressed as the
dynamics of a lumped machine, which has inertia constant Hsys
which is the weighted sum of the inertia constants of the individual
machines
Hsys =∑∀iHiSi
∑∀iSi
(s)
(3)
The initial response to a disturbance and frequency change is
mainly determined by the total system inertia. The RoCoF is the
time derivative of the frequency signal, and relates directly to the
inertial response of the system. RoCoF is given by
RoCoF = df
dt=ΔP f s
2Hsys (Hz/ s)
(4)
where f is frequency of the system, fs is the nominal frequency and
ΔP= (Pm−Pe)(p.u.)
(5)
is the power imbalance of the system. Pe includes changes to both
electrical power production and consumption.
Practical aspects of measuring RoCoF include the choice of a
time window over which to calculate the RoCoF, for which
different choices will result in different values of RoCoF. RoCoF is
an essential measurement that synthetic inertia control depends on.
However, RoCoF measurements are challenging, as they are highly
susceptible to the disturbances experienced in power systems.
Many measurement techniques have been proposed, yet despite the
vital nature of this parameter, no appropriate standardisation for
RoCoF testing exists. Fig. 1 shows the frequency of a system
following a disturbance.
3 Existing views of synthetic inertia
In existing literature there is no unified definition of synthetic
inertia, which seems sometimes to have different meanings
depending on context. Many interpretations of the concept of
synthetic inertia include delivering power quickly when system
frequency deviates from its nominal value by a certain amount. The
term is also sometimes used to mean the change in control of
power being provided during a disturbance. This paper gives a
strict description of synthetic inertia, defined in terms of the
physical response of a synchronous generator.
Many studies on synthetic inertia do not focus on distinction
between inertia and fast frequency response. From a system
perspective, important measures of frequency stability are the
minimum instantaneous frequency, and RoCoF. A relaxed view on
synthetic inertia might include services which contribute to
improving the response of the system, such as lifting the minimum
instantaneous frequency, and reducing RoCoF. However, a more
strict, unified view of this term would lead to a clearer picture of
services being offered to improve system stability.
With the help of power electronics, power units can be
controlled in many ways to improve frequency quality after
disturbances. The inertial response of a synchronous generator,
however, releases torque in direct proportion to the RoCoF it
experiences. The term synthetic inertial response must therefore
correspond to the controlled response from a generating unit to
mimic the exchange of rotational energy from a synchronous
machine with the power system. Any other form of fast controlled
response can then be termed as fast frequency response. To clarify,
synthetic inertial response is a subset of fast frequency response
which contains different responses based on frequency and RoCoF.
The term inertia is described by the European Network of
Transmission System Operators for Electricity (ENTSO-E) as ‘The
property of a rotating rigid body, such as the rotor of an alternator,
such that it maintains its state of uniform rotational motion and
angular momentum unless an external torque is applied’ [19]. The
interpretation of this is that rotating masses of synchronous
generators resist change of speed, unless there is change in torque.
The term synthetic inertia is described by ENTSO-E as ‘the
facility provided by a power park module or HVDC system to
replace the effect of inertia of a synchronous power generating
module to a prescribed level of performance’ [20]. While this
definition encompasses the definition presented in this paper, many
have interpreted this definition to include what we call fast
frequency response [21].
Assuming Tm,i is constant, we can rewrite the change in
electrical torque ΔTe,i for a synchronous generator i as a function
of an angular velocity change
ΔTe,i= − Ji
dωm,i
dt(N m)
(6)
which can be converted to power, using the per unit system, as
ΔPe,i= − 2Hi
dωi
dtωi(p . u . )
(7)
≃ − 2Hi
dωi
dt(p . u . )
(8)
Fig. 1 Nordic system frequency following a generator trip
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If the electrical frequency ωi is close to nominal, the inertial power
contribution from machine i is approximately linearly dependent
on the RoCoF. Equation (7) describes what we call an inertial
response. Synthetic inertia is therefore a response of a generating
unit to frequency changes, in particular, a power exchange which is
proportional to RoCoF. For synthetic inertia to be implementable
practically, several aspects such as measurement filtering, unit
recovery and endurance of the contribution must be considered.
4 Definition of synthetic inertia
With reference to inertia as resistance to change in frequency and
(6), we have defined synthetic inertia.
Definition of synthetic inertia: synthetic inertia is defined as the
controlled contribution of electrical torque from a unit that is
proportional to the RoCoF at the terminals of the unit. With
reference to (7), the constant of synthetic inertia Hsyn,i for generator
i is defined by the relationship between the terminal frequency ωt
and ΔPe,i.
Definition of the constant of synthetic inertia
ΔPe,i= − 2Hsyn,i
dωt
dtωt
The torque response should be proportional to RoCoF to deliver an
inertial response.
5 Fast frequency response
As mentioned, generators providing synthetic inertial response
should react proportionally to RoCoF. Other units can, however, be
controlled to support the system by reacting to frequency deviation.
Fast frequency response is then the controlled contribution of
electrical torque from a unit that acts rapidly on a frequency
measure. It can react proportionally to the deviation or inject power
according to a pre-determined schedule. We have defined fast
frequency response as follows.
Definition of fast frequency response: fast frequency response is
the controlled contribution of electrical torque from a unit which
responds quickly to changes in frequency in order to counteract the
effect of reduced inertial response.
Fast frequency response based on frequency deviation can
significantly improve the minimum instantaneous frequency.
Careful investigations are required in order to ensure that these
responses do not cause instability, overshoot or larger frequency
deviations shifted in time as released power is restored to
supporting units. For wind turbines, the implementation of the
speed recovery has a large impact on the overall system response.
The main focus is on the fast response. The duration of the delivery
will highly depend on the source and other parameters. Required
duration must be coordinated with other frequency reserves
installed in the system.
5.1 Mechanical and electrical power of wind power plants
The power that can be extracted from the wind is a function of
several parameters and is characterised by its performance
coefficient Cp. The mechanical power is described by
PMech(ωwind) = 1
2Cp(λ,θ)ρr2πνw
3(W)
(9)
where ρ is air density, r is the length of the rotor blades and νw the
wind speed. Cp is a function of blade tip speed ratio λ and blade
pitch angle θ. The tip speed ratio
λ=rωwind
νw
(10)
relates the rotor speed ωwind in radians/s to the wind speed νw in
m/s. The function Cp depends on several constants, given by [22]
Cp(λ,θ) = c1
c2
λ−c3θ−c4θc5−c6e−c7((1/λ+c8θ) − (c9/(θ3+ 1)))−1 .
(11)
When the blades of the wind turbine are not pitched the electrical
power output of the turbine follows the maximum mechanical
power extracted from the wind, shown in Fig. 2. Maximum power
point tracking control ensures the maximal power output by
varying the electrical output as a function of rotor speed, according
to the maximum power curve. For a constant wind speed, any
deviation from the curve results in an imbalance between electrical
and mechanical power, which accelerates or decelerates the rotor
such that peak power is retained.
6 Model and control function description
In order to examine the differences between synthetic inertial and
fast frequency response based on frequency deviation, the model
shown in Fig. 3 was built in Matlab/Simulink. It consists of a one-
mass model of the power system and wind power plants
represented as a lumped variable speed turbine. The plants are
controlled to produce the maximum power available at a constant
wind speed, implying that the electrical power output Pe(ωwind) is
then a function of the rotor speed of the turbine. Supplementary
controllers implementing synthetic inertia and another fast
frequency response, which is proportional to frequency deviation,
are added. Both of these use a first-order measurement filter with a
time constant of 300 ms. By adding the supplementary control
function to the maximum power point tracking function, speed
recovery is possible. To fully recover the rotor speed the function
assumes the RoCoF or frequency returns to the nominal value. If
there is a steady-state frequency deviation after a disturbance, the
speed recovery function will find a new stable operating point with
a lower rotation speed. Note that speed recovery is only relevant in
applications where rotating machines are connected to the power
system by power electronics, such as wind turbine systems.
The assumption is that a wind turbine can deliver about 10%
additional power during 10 s. The synthetic inertia is adjusted such
that Hsyn = 7 s, and the gain of the fast frequency response
controller is tuned such that the output power peaks for both
synthetic inertia and proportional control without speed recovery
are approximately the same. See peaks of functions 1 and 3 in
Fig. 4.
The dynamics for primary control in the system are based on
the dynamics of a hydro power plant. Parameters for primary
control, inertia and frequency dependency D of the load have been
estimated using a measured frequency disturbance that has
occurred in the Nordic system. The primary control is modelled
without dead band and power headroom limitation.
Two scenarios are defined, one with 20% wind power
production and one with 80% wind power production, which has
Fig. 2 Power curves as function of rotor speed and different wind speeds
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low inertia. These are described in Table 1. The wind power plants
are assumed to operate with a blade pitch angle of zero and a
constant wind speed. No pitch control is used in order to not have
interference between the control functions and the pitch control.
Five different types of supplementary wind power control are
modelled, wind turbines which do not contribute to frequency
support, wind turbines which contribute with synthetic inertia and
those which contribute with fast frequency response proportional to
frequency deviation. Both synthetic inertia and fast frequency
response are active all the time and will provide a response
according to the measured RoCoF and frequency deviation. If the
speed of the rotor decreases by 10%, support from synthetic inertia
or other fast frequency response is withdrawn, and maximum
power point tracking is resumed. For the control schemes which
contribute to frequency stability, the schemes are modelled both
with and without speed recovery functions. The five types have the
following functions:
•Base case: In this case wind power provides a constant power,
but does not contribute to frequency support.
•Function 1: Synthetic inertia without speed recovery.
•Function 2: Synthetic inertia with speed recovery.
•Function 3: Fast frequency response proportional to frequency
deviation, without speed recovery.
•Function 4: Fast frequency response proportional to frequency
deviation, with speed recovery.
Functions 1 and 3 are studied without any speed recovery
during the frequency disturbance to avoid interference between the
speed recovery and the frequency control. Speed recovery for
energy storage is not needed for non-rotating units such as
batteries. Functions 1 and 3 can be used without any consideration
of rotor speed for such energy sources. Practically the type 4 wind
power turbines have speed control. In functions 1 and 3 the speed
control is disabled in order to show the concept of the two
frequency controls.
In functions 2 and 4 the speed recovery function is active all the
time. The function is one example of a speed recovery and is not
optimised in any way. The speed recovery function uses the current
rotor speed of the turbine to calculate a new active power set point
based on the maximum power point tracking curve. When the rotor
speed decreases, the power set point also decreases, resulting in a
stabilising effect. When the supplementary control signal is
reduced to zero the rotation speed will return to the initial value.
There are also other possible solutions to implement frequency
control from wind turbines. For example, measured signals can be
further processed in order to reduce the interaction between speed
and frequency control. Research on how to practically implement
frequency control on wind turbines is ongoing.
7 Large disturbance: generator trip
This section provides the results of a simulated generator trip. The
model and control functions are described in Section 6.
Fig. 3 Overview of simulation model
Fig. 4 Electrical power from wind for different combinations of wind
power control with 20% wind power production
Table 1 Scenario parameters
system load 30 GW
primary regulation strength 2972 MW/Hz
frequency-dependent load 300 MW/Hz
number of wind power plants 4000
wing length 50 m
Scenario 1
wind power production 6 GW
wind speed 8.6 m/s
initial rotational speed 1.22 rad/s
system inertia 177 GWs
Scenario 2
wind power production 24 GW
wind speed 13.7 m/s
initial rotational speed 1.93 rad/s
system inertia 44 GWs
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The two defined scenarios are simulated with a 1450 MW
generator trip. To represent the worst case the frequency before the
disturbance is set to 49.9 Hz, which is the lowest allowed system
frequency in normal operation.
7.1 Results – scenario 1: 20% wind power production
The system frequency for scenario 1 is shown in Fig. 5. Compared
with the base case, the minimum instantaneous frequency is
improved by all of the supplementary frequency support functions,
except for function 3. For function 3, the nadir is even lower than
in the base case. This is because the rotational speed is reduced so
much that normal operation has to be interrupted and speed
recovery activated. For this function wind power is reduced by
1700 MW, as shown in Fig. 4. A similar event could also be seen
for function 1 beyond the simulation time, and is indicated by the
slow reduction of rotor speed in Fig. 6. Function 2 reduces the
RoCoF of the system but the minimum instantaneous frequency is
similar to the nadir of the base case. The fast frequency response
functions based on frequency deviation do not improve the system
RoCoF significantly.
Electrical power output is activated more quickly for the
synthetic inertia functions but support is also reduced more quickly
compared with the fast frequency response functions based on
frequency deviation, as shown in Fig. 4. Function 2 has a more
oscillatory behaviour compared with function 1 because it uses
speed recovery. Without the recovery function however, it becomes
impossible to maintain rotor speed. When rotor speed decreases,
the mechanical power to the wind turbine also decreases, and the
rotor speed continues to decrease even faster. This is shown in
Fig. 6. For both of the functions without speed recovery, rotor
speed continues to decrease until the lower limit for the rotor speed
is reached. Rotor speed for a wind turbine with function 4 will
reach another steady-state operation because the frequency of the
system deviates. The rotor speed is lower compared with its level
before the disturbance, but it is a stable operating point. When the
frequency is restored to the nominal frequency the rotor speed will
return to its initial value. For practical implementation a more
sophisticated rotor speed recovery function may be required.
Activation of the primary control reserves is shown in Fig. 7.
The lowest output power peak of the primary control output is
achieved with function 4 but the steady-state value is somewhat
higher because of the new operating point of the wind power.
7.2 Results – scenario 2: 80% wind power production
The frequency of the system for the low inertia scenario is shown
in Fig. 8.
As there is less inertia in the system in scenario 2, the damping
of the oscillatory behaviour for function 2 is reduced. In this
scenario, the minimum instantaneous frequency is significantly
improved with both functions 1 and 4. Since there is 60% more
wind power in this scenario, the contributions from both synthetic
inertia and fast frequency response based on frequency deviation
are greater than they are in scenario 1, and there is a larger
difference between the base case and the other controllers.
The speed of the wind turbine is shown in Fig. 9. Apart from
the increased oscillations in the case with function 2, the results
show similar behaviour of the wind turbines compared with
scenario 1.
Fig. 5 System frequency for different types of supplementary frequency
support functions for wind turbines with 20% wind power production
Fig. 6 Wind turbine rotor speed for different combinations of wind power
control with 20% wind power production
Fig. 7 Primary control reserves for different combinations of wind power
control with 20% wind power production
Fig. 8 System frequency for different combinations of wind power control
with 80% wind power production
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7.3 Discussion
Simulations show that both the synthetic inertial response and the
fast frequency response, which are proportional to frequency
deviation, improve the minimum instantaneous frequency,
however, only synthetic inertia improves the RoCoF. For the
synthetic inertia with a speed recovery function based on maximum
power point tracking, the minimum instantaneous frequency is not
improved compared with the base case. From the results it is
obvious the design of the speed recovery is of great importance to
avoid interactions between the synthetic inertia control and the
speed recovery. Further work may include analysing how the speed
recovery function can be better designed. Synthetic inertia without
speed recovery improves both frequency deviation and RoCoF
significantly and if a slow acting speed recovery is implemented
this response would be possible from a wind power turbine. It is
important that the contribution of energy to the power system is
positive before the minimum instantaneous frequency is reached,
and improvements to system performance could be gained by not
starting any speed recovery process until after the minimum
instantaneous frequency has been reached. If the recovery starts too
quickly, there is a risk of two minimum instantaneous frequencies,
as for the fast frequency response function, shown in Fig. 5.
Studies indicate that synthetic inertia has some benefits over
other types of fast frequency responses that have previously been
proposed. One benefit is that synthetic inertia emulates
synchronous generators whose response does not need to be
adjusted for different operating points and the natural development
of the power system over longer periods of time. It can also
improve the RoCoF after a disturbance. Fast frequency response
based on frequency deviation can also, however, improve the
minimum instantaneous frequency after disturbances. The chosen
method for doing this should be chosen in such a way to reduce
societal costs, and should take into account the dynamics of the
primary frequency control.
With a measurement filter the initial RoCoF directly after the
disturbance is not affected as there is latency in the supply of
electrical torque. It is important to know how fast and accurate
both frequency and RoCoF can be measured when using these as
control signals as a longer measurement time and dead band will
impact the result with a slower response. In this paper, the
calculation of the RoCoF assumes symmetrical operation. In
practice, the measurement must also be able to account for
unbalanced faults.
After a disturbance has occurred, supplying the system with
energy during the first few seconds can help to mitigate the
resulting frequency deviation. The imbalance between production
and consumption results in a certain RoCoF, and the integral of this
imbalance over time results in the instantaneous frequency of the
system. It is therefore important to lower this imbalance over time,
to reduce the minimum instantaneous frequency. The ability of
supporting units to provide energy then becomes important for
preventing large frequency dips.
To conclude, both the simulated synthetic inertia and the fast
frequency response improve the minimum instantaneous frequency.
The RoCoF is only improved by the synthetic inertia. The
implemented speed recovery reduces the effectiveness of the
controls because of the interactions with frequency control.
8 Normal operation: stochastic net power
variations
To study how the synthetic inertial response and fast frequency
response based on frequency deviation contribute in normal
operation analysis is performed using the same model as in the
large disturbance study, with a 24 h imbalance power series
injected to the system, where here an imbalance refers to the
momentary difference in power between production and
consumption. The power series represents the imbalance in the
Nordic power system for a typical day in May. The imbalance
shown in Fig. 10 was estimated in a Nordic project where the
frequency was used to derive the system power imbalance [23]. In
order to analyse how the supplementary frequency control of wind
power affects the frequency quality, the index time outside normal
frequency band (TONFB) is used. This index is used today in the
Nordic system, and is the number of minutes that the system
frequency is outside the normal operating band 49.9–50.1 Hz.
Due to the small size of the data series, the relative change of
TONFB compared with the base case will be analysed.
As functions 1 and 3 are implemented without the speed
recovery, these control methods will result in a rotor speed which
exceeds the limits and the control is shifted to the maximum power
point tracking in the same was as seen in Fig. 6. Due to this fact
functions 1 and 3 are excluded from the normal operation study.
The study is performed for scenario 2 with 80% wind production.
The models use the same parameters as in the Large disturbance
study except for the measurement filter time constant which is
increased from 300 ms to 2 s. This is done to make the controller
less aggressive compared with the controller in the Large
disturbance study.
8.1 Results – scenario 2: 80% wind power production
The resulting system frequencies for functions 2 and 4 are shown
in Fig. 11 for the power imbalance shown in Fig. 10.
The relative change of the TONFB from the base case was:
•Function 2: 6.4%.
•Function 4: −10.7%.
Fig. 9 Wind turbine rotor speed for different combinations of wind power
control with 80% wind power production
Fig. 10 Estimated imbalance in the Nordic power system during a day in
May
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In order to better compare the system frequencies for the
different alternatives, a frequency distribution graph is shown in
Fig. 12.
Function 2 increases TONFB compared with the base case,
whereas function 4 decreases the TONFB, which can be clearly
seen in the lower frequency distribution.
Another way of looking at the frequency is by looking at the
frequency distribution of the RoCoF in Fig. 13. Function 2 makes
the peak of the distribution around 0 Hz/s higher than the base case
and function 4, which also makes the peak higher than the base
case. Both of these functions improve upon the RoCoF
characteristics of the base case.
The electrical output power and rotor speed of the wind turbine
are shown in Figs. 14 and 15. The electrical output power can, at
first glance, look small compared with the system imbalance. The
reason the activation is small is that the stored kinetic energy is
limited. When the controller activates, the speed starts to decrease
and the set point is changed in order to recover the rotor speed.
This allows the controller to only respond to short term changes in
power imbalance. The simulated power imbalance contains mainly
slower dynamics, making the response from the wind turbine
small.
8.2 Discussion
Simulations show that function 2 increases the TONFB compared
with the base case but moves the RoCoFs toward 0 Hz/s. Function
4 reduces the variance of the frequency deviation seen in both the
TONFB and the frequency distribution of the system frequency,
however it does not improve the RoCoF as much as function 2.
The reason for the higher TONFB using function 2 is that
RoCoF is reduced by using synthetic inertia resulting in longer
frequency restoration times. Additionally, due to the low inertia in
scenario 2, damping of the slow frequency oscillatory behaviour
for function 2 is reduced. When the damping is lower the impact of
Fig. 11 System frequency for different types of supplementary frequency
support functions for wind power control in normal operation with 80%
wind power production
Fig. 12 Distribution of system frequency for different types of
supplementary frequency support functions for wind power control in
normal operation with 80% wind power production
Fig. 13 Distribution of RoCoF for different types of supplementary
frequency support functions for wind power control in normal operation
with 80% wind power production.
Fig. 14 Electrical power from wind for different types of supplementary
frequency support functions for wind power control in normal operation
with 80% wind power production
Fig. 15 Wind turbine rotor speed for different types of supplementary
frequency support functions for wind power control in normal operation
with 80% wind power production
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7

interactions between measurement filter, implemented speed
recovery and the system frequency is more prominent. It is
important that speed recovery is implemented in order to not
decrease the stability margin of the system. One goal of minimising
RoCoF levels in the system is to reduce wear and tear in the turbine
governor actuator. Wear and tear of the turbine governor actuator is
related to two indices. One is the accumulated travelled distance by
the actuator and the other is the number of directional changes of
the actuator [24]. Lower RoCoFs make the governor actuator
experience smoother and fewer directional changes. Synthetic
inertia may be used to achieve this.
These results are not surprising since the TONFB in many cases
is a result of the frequency slowly diverging from 50 Hz. In such
cases, function 4 will provide stronger support as the frequency is
further away from 50 Hz. Function 2 will not be able to offer as
much support unless frequency changes are fast. The results are in
line with the results from the large disturbance study.
Differences in electrical power magnitude for functions 2 and 4
for the normal operation disturbances are explained by the use of
the same gains as in the large disturbance study. Function 2 uses
more power on average compared to Function 4 but for shorter
durations, resulting in low usage of the wind turbine kinetic energy.
This is also reflected in the angular frequency where function 2
results in an angular frequency which stays closer to the nominal
compared with function 4. Since function 2 does not exchange as
much energy with the power system as function 4, the effect on the
frequency quality is low. The gains for the functions could be
chosen differently and for normal operation, but that has not been
done here.
9 Additional stability aspects
This paper addresses issues related to the frequency of the system.
The synthetic inertial response and proportional fast frequency
response contribute to synchronising and damping torques in the
system. The change in electrical torque of a synchronous machine i
followed a perturbation can be divided into two components as
[25]
ΔTi= ΔTs,i+ jΔTd,i=Ks,iΔδi+ jKd,iΔωi
(12)
where ΔTi is change in electrical torque of synchronous machine i,
ΔTs,i and ΔTd,i are synchronising and damping torque aligned with
the change in electrical rotor angle Δδi and speed Δωi, respectively.
Ks,i and Kd,i are the coefficients of the synchronising and damping
torque, respectively. Thus, controlled response contributes to
electrical torque where synthetic inertial response is aligned with
RoCoF, and therefore contributes with synchronising torque.
Similarly proportional fast frequency response contributes with
damping torque to the system. The contributions can be derived
from a linearisation of the power system equations and are not
examined further here. These may, however, be important to
consider as all stability aspects have to be considered in the design
and operation.
10 Conclusions
This paper presents a complete definition of synthetic inertia which
separates it from other fast frequency response. Synthetic inertia is
related to the supply of electrical torque in proportion to RoCoF. To
improve the RoCoF of a system, electrical power needs to be
controlled in response to the RoCoF. A simulation study shows that
both synthetic inertia and fast frequency response based on
frequency deviation can improve the minimum instantaneous
frequency after a disturbance compared with a system without any
frequency support from wind power. It has been shown that both
synthetic inertia and fast frequency response based on frequency
deviation can improve the minimum instantaneous frequency after
a disturbance compared to a system without any support from wind
power. It has also been shown that fast frequency response based
on frequency deviation improves normal operation frequency
quality and reduces absolute RoCoF, and that synthetic inertia does
not improve the frequency quality but reduces the absolute RoCoF.
10 Acknowledgment
The authors thank Per-Olof Lindström for his thoughtful feedback
on this paper.
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8IET Renew. Power Gener.
This is an open access article published by the IET under the Creative Commons Attribution License
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