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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.

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