# Locational Aspect of Fast Frequency Reserves in Low-Inertia Systems -
Control Performance Analysis

Georgios Misyris, Deepak Ramasubramanian, Parag Mitra, Vikas Singhvi  Grid
Operations & Planning Group,
Electric Power Research Institute,
Knoxville, Tennessee, USA
<EMAIL_ADDRESS>
###### Abstract

This paper evaluates the frequency performance of an AC system when primary
frequency response is provided by inverter-based resources located at remote-
areas. Due to potentially larger wave propagation constants over longer lines,
fast active power response from inverter based resources may have a negative
impact on the system frequency response. Within this context, this paper
presents a control performance analysis is presented in order to identify
limitations for improving the frequency stability when inverter-based
resources in remote locations use local frequency measurements. Our results
suggest that there exists a trafeoff between disturbance rejection and
stability robustness when allocating primary frequency control. In particular,
fast frequency control can have a negative impact on the damping ratio of
poorly damped electromechanical modes.

###### Index Terms:

Low-inertia, primary frequency response, inverter-based resources, droop-based
control.

##  I Introduction

The replacement of synchronous generators with power electronics-interfaced
devices decreases the available inertia in the system and can lead to much
faster frequency dynamics in the grid [1, 2, 3]. As a result, the dynamic
behavior can endanger the system by stressing the control and protection
schemes [4], e.g. (i) when frequency drops by unacceptable amounts, it results
in the disconnection of production units and loads and producing a cascade
effect that can lead to widespread power outages [5] and (ii) rate of change
of frequency based loss-of-main protection and under-frequency load shedding
[6].

There are various ways to mitigate the impact of reduced level of inertia on
the frequency dynamics, with the main focus being on utilizing the fast action
of inverter-based resources. This is realized by adding a frequency controller
in the outer control loops of power electronic devices. Various frequency
control schemes have been proposed, such as virtual inertia and droop-based
frequency control [7, 8, 9, 10]. To evaluate their impact on frequency
performance of the system after a large disturbance, system operators mainly
use the maximum frequency deviation and the rate of change of frequency of the
Center Of Inertia (COI) frequency [11, 12, 13, 14]. One common assumption that
system planners make in these studies is that nodal frequencies are equal to
the center of inertia frequency. This assumption simplifies the control design
and the process of deciding the amount of fast frequency reserves. However, as
generation sources interconnect to weak areas of the network and move farther
away, the local frequency measurements might differ from the center of inertia
frequency, since inertia are inhomogeneously distributed across the grid.
Consequently, it is necessary to evaluate the frequency performance in low-
inertia power grids and the ability of inverter-based resources to provide
fast and secure primary frequency control.

Metrics such as $H_{2}$-norms have been used in order to evaluate the
frequency performance of the system without the need for time-domain analysis
[15, 16, 17]. However, in the aforementioned studies the impact of the
location of the active power regulation units have been neglected. As
presented in [18], weak electrical ties, i.e. long transmission lines, prevent
the delivery of frequency response from adjoining areas, thus inverter-based
resources cannot improve the frequency performance of the system.

To this end, this paper is to evaluate how much frequency droop response over
long transmission lines is needed for improving the frequency stability for a
power system with low inertia. Motivated by ongoing research on how inertia
location and slow network modes determine how disturbances propagate in power
grids [19], we try to tackle the problem of how fast frequency droop response
affects the dynamic performance of the system. Within this concept, this paper
provides a framework for evaluating the robust performance of inverter-based
resources frequency controllers. The disturbance response ratio is chosen as a
performance metric that allow to evaluate the impact of parameters on the
local and center of inertia frequency dynamics. The contributions of this
paper are summarized as follows. A theoretical background that enables to
analyze the robust performance of frequency controllers in low-inertia systems
with active power regulating units located in remote areas. Insights are
provided concerning the control design of frequency droop-based controllers.
Time-domain studies are performed to further analyze locational impact of
delivering fast frequency response.

The reminder of this paper is organized as follows. First, a motivation is
given to highlight the problems that might arise when delivering primary
frequency response over long transmission paths. Then, a framework is
presented that allows to analyze the frequency performance of the system.
Time-domain studies are performed to further analyze locational impact of
delivering fast frequency response.

##  II Problem formulation

In larger power networks, along long transmission lines, electromechanical
waves have a finite and discernible propagation time. Consider an electrical
event such as a change in generation/load. If this change were to occur at one
end of a long tranmission line, then the magnitude of this disturbance seen at
the other end is not only lower but it is alose seen later in time [18, 19].
This behavior is described as weak electrical link and could possibly have a
large impact on the frequency response of a power system dominated by
inverter-based resources. In this section, we present the theory that will be
used in this paper for analyzing the robust performance of the system when
primary frequency response is provided by inverter-based resources located far
from the disturbance location.

###  II-A Control performance analysis

Figure 1: Left figure: Block diagram for general control configuration, Right
figure: droop-based inverter-based controller.

Fig. 1 shows the closed system configuration, where $G(s)$ is the transfer
function mapping the plant input $u$ to the plant outputs $y$ and performance
variables $z$. The transfer function $C(s)$ is the system controller described
as $u=-C(s)y$. The performance variables $z$ specify the desired
characteristics of the closed loop system and play crucial role on the control
design.

If the performance variables $z$ are also the measured outputs $y$, the
stability robustness of the system can be analyzed as follows. The transfer
function $G(s)C(s)=L(s)$ is the open loop gain, which can be used to
investigate how a sinusoidal signal propagates through the feedback loop. One
could analyze the stability of the system by evaluating the Nyquist plot of
the transfer function $L(s)$. To ensure that the system is stable, one needs
to ensure that the Nyquist curve of $L(s)$ not to encircle the point (-1,0)
[20]. This is done by appropriately designing the plant controller C(s). The
further the Nyquist curve is from the (-1,0) point, the more stable the system
is. A way to ensure that r is sufficiently large is by checking the maximum
value of the magnitude of the sensitivity function, i.e. $|S|$. The
sensitivity function is defined as:

$S=\frac{1}{1+L(s)}$ (1)

and indicates how a signal affects the output of the system. It holds that the
sensitivity matrix should be 1 when $s\rightarrow\infty$ and 0 when
$s\rightarrow 0$. Based on the selection of the control gain and the bandwidth
of the controller a reduction of the sensitivity function can be achieved at
some angular frequencies, but this has to be compensated by amplification in
other frequencies. Small $|S|$ is desirable at low frequencies in order to
minimize the impact of disturbances on the steady state error.

The above procedure for achieving robust performance of the closed system is
followed whenever the performance variables $z$ are similar to the measured
outputs $y$. However, in most applications the performance variables differ
from the measured outputs.

#### Application to frequency stability

To monitor the power imbalances in the system and reserve a sufficient amount
of frequency response, the center of inertia frequency of the system has been
used as a metric, i.e. the center of inertia frequency is considered as the
performance variable z of the system. The COI frequency is calculated as the
inertia weighted (where all inertias are on a common system base) sum of all
generator frequencies in the system and the basis for this is outlined in and
the expression for $N$ generators is given below:

$f_{\rm COI}=\frac{\sum_{i=1}^{N}H_{i}f_{i}}{\sum_{i=1}^{N}H_{i}}$ (2)

where $H_{i}$ is the inertia constant of the generator and $f_{i}$ is the
generator frequency. One common assumption that system planners make in order
to decide the frequency response of the system, is that center of inertia
frequency, which is the performance variable can be considered as a measured
output $y=f_{\rm COI}$. This means that the nodal frequencies are equal to the
center of inertia frequency. By making this assumption, robust frequency
performance can be achieved by setting constraints on the sensitivity function
$S$. This approach is followed by Nordic system operators in Europe for
ensuring robust frequency performance in the system [11] .

This simplifies the control design of $C(s)$ (see Fig. 1), which represents
the required frequency response in order to ensure frequency stability of the
system. However, as inertia level decreases and active power regulating units
are located in remote areas, the nodal frequencies differ from the global one.
This introduces control limitations for improving the frequency performance of
the system, since the performance variables differ from the measured outputs.
Consequently, a different control performance analysis is required for
assessing the frequency performance of the system and designing fast primary
frequency control.

###  II-B Disturbance response ratio

To analyze the ability of a controller to attenuate external disturbance, the
following transfer function can be defined as a metric:

$\centering
T_{zd}(s)=G_{zd}(s)-G_{zu}(s)C(s)\Big{(}1+G_{yu}(s)C(s)\Big{)}^{-1}G_{yd}(s)\@add@centering$
(3)

where $T_{zd}(s)$ is the closed-loop system from the disturbance d to the
performance variable $z$. The transfer function $G_{zd}(s)$ is the open-loop
system from the disturbance d to the performance variable $z$. It should be
mentioned that the performance variable does not have to be the same with the
measured output of the system. In case the performance variable is the system
with the measured variable it holds that $G_{zd}(s)$=$G_{yd}(s)$. The transfer
functions $G_{zu}(s)$ and $G_{yu}(s)$ show the relationships from the
disturbance d to the performance variable $z$ and measured output $y$,
respectively. The transfer function C(s) is the plant controller, which takes
as an input the measured output $y$ and gives as an output the input to the
plant $u$.

Good disturbance attenuation can be achieved if the amplitude of the closed-
loop system $T_{zd}(s)$ is smaller compared to the amplitude the open-loop one
$G_{zd}(s)$. This means that the controller K(s) should be designed so that
$|T_{zd}(s)|<|G_{zd}(s)|$. How well the controller is able to attenuate an
external disturbance applied to the system depends on the bandwidth of the
controller but more importantly on the measured output that is used as a
feedback signal. Multiplying the $T_{zd}(s)$ with $G_{zd}(s)^{-1}$ yields the
following expression:

$\centering
R_{zd}(s)=1-G_{zu}(s)C(s)\Big{(}1+G_{yu}(s)C(s)\Big{)}^{-1}G_{yd}(s)G_{zd}(s)^{-1}\@add@centering$
(4)

which is defined as the disturbance response ratio and it can be used as a
metric to quantify the ability of the controller to attenuate disturbances.
The aim is to design the feedback controller so that $|R_{zd}(s)|<1$ [21]. To
limit the effect of external disturbances $\boldsymbol{d}$ to the performance
variables $\boldsymbol{z}$, we need to increase to increase the volume of the
region in which $|R_{zd}(s)|<1$. By doing that, we can limit the impact of the
disturbance on the frequency dynamics of the system, i.e. reducing the maximum
frequency deviation. Moreover, the disturbance response ratio acts as a
replacement of the sensitivity function for improving the damping of the
system. By constraining the peak of $|R_{zd}|$, one can limit the disturbance
amplification over the whole frequency range and improve the damping of the
system.

###  II-C State space representation

Power system dynamics can be described by a set of non-linear differential and
algebraic equations. Since a power system is a highly non-linear dynamical
system, to perform the study a linearization of the system needs to be
performed. After the linearization, the system takes the following state space
form:

$\displaystyle\centering\boldsymbol{\dot{x}}\@add@centering$
$\displaystyle=\boldsymbol{A}\boldsymbol{x}+\boldsymbol{B_{u}}\boldsymbol{u}+\boldsymbol{B_{d}}\boldsymbol{d}$
$\displaystyle\boldsymbol{y}$
$\displaystyle=\boldsymbol{C_{y}}\boldsymbol{x}+\boldsymbol{D_{yu}}\boldsymbol{u}+\boldsymbol{D_{yd}}\boldsymbol{d}$
(5) $\displaystyle\boldsymbol{z}$
$\displaystyle=\boldsymbol{C_{z}}\boldsymbol{x}$

where $x$ is the state vector containing the state variables of the system, u
is a vector containing the controlled input variables, $d$ contains the
external disturbances to the system, y contains the measured outputs that can
be used as feedback signals and $z$ contains the performance variables that
can be used to evaluate the control and system performance. Using Laplace
transformation, the system can be expressed in frequency domain, in order to
use the theoretical background presented above. Figure 1 shows the block
diagram for general control configuration. $G(s)$ is the system expressed in
frequency domain and $C(s)$ is the plant controller, which for this report is
considered as a frequency droop-based controller that can be placed in
different locations in the system. In the context of this report, the input
vector $u$ contains the active power outputs of the units that participate in
frequency regulation, the output vector $y$ contains the measured quantities
used by the active power regulation units, such as the local frequencies, $d$
is a vector of active power imbalances (modeled as step changes) that can
occur at different locations in the network and the vector $z$ contains the
center of inertia frequency. From a physical standpoint, an unexpected active
power imbalance (step change of $d$), will result in variation of the local
and center of inertia frequencies both during and steady state conditions. The
control should be designed such that: (i) the maximum and steady-state
frequency deviations are limited and (ii) excitation of local and inter-area
modes is avoided. This means that the controller should be designed, in order
to reduce the impact of external disturbances to the system.

##  III Limitations Imposed by Local-Frequency measurements & Time Domain
Analysis

This section focuses on the analysis of the control limitations for improving
the overall frequency stability, when using local-frequency measurements.

Figure 2: Test system. Base case scenario with the total kinetic energy in the
network being equal to 110 GWs.

To illustrate the potential problems that may arise, the test system depicted
in Fig. 2 is utilized. More details about the system parameters can be found
in [22]. Two type of synchronous generators are assumed, hydro (located at bus
1, 2 and 3) and thermal generators (located at bus 4 and 5). All generators
are equipped with automatic voltage regulators and power system stabilizers.
It is considered that only hydro generation units are equipped with governor
models. Moreover, inverter-based units are also equipped with frequency
controllers, which can be used for providing frequency response. Since the
objective here is to evaluate the impact of inverter-based resources (IBR)s on
frequency response, it should be mentioned that the inner loop dynamics of the
inverter-based resources are neglected as it is assumed that these control
loops are tuned and designed appropriately. Table LABEL:T:1 depicts the amount
of kinetic energy at each bus in the system and Table LABEL:T:2 the length of
the lines.

TABLE I: Kinetic energy and active power output of generators for the high-
and low-inertia scenarios.

Bus |  $K_{en}$ [GWs] | $P_{out}$ |  $K_{en}$ [GWs] | $P_{out}$
---|---|---|---|---
1 | 34 | 9000 | 11.25 | 3000
2 | 22.5 | 6000 | 22.5 | 6000
3 | 7.5 | 2000 | 7.5 | 2000
4 | 33 | 5000 | 20 | 3000
5 | 13 | 2000 | 13 | 2000

TABLE II: Length of transmission lines.

Lines | 1-2 | 1-4 | 2-3 | 2-4 | 3-5
---|---|---|---|---|---
Length [km] | 300 | 100 | 350 | 220 | 50

###  III-A Locational impact of frequency response from inverter-based
resources

In this part, the locational impact of frequency response from inverter-based
resources is investigated. To evaluate the locational impact of frequency
response, the disturbance response ratio $|R_{zd}(s)|$ is used as a metric.
When $|R_{zd}(s)|<1$, then the control system is able to attenuate any
external disturbance applied to the system. For this study, it is considered
that the performance variable is the center of inertia frequency, the
controlled inputs are the power outputs from the inverter-based resources at
bus 1 and 3. Thus, two disturbance response ratios are defined namely
$R_{zd}^{1}$ and $R_{zd}^{3}$. The inverter-based resources use local
frequency measurements as feedback signal. The fast frequency controller
considered for this analysis is depicted in Fig. 1.

####  III-A1 High inertia case $K_{en}$=110 GWs

Figure 3: Comparison of frequency response trajectory for different locations
of the inverter-based resources. Disturbance response ratio to evaluate the
locational impact of frequency response.

This study explores the behavior of the system for different locations of the
inverter-based resources. A disturbance of 980 MW is applied at bus 2 in the
system, which is the external disturbance to our system, $d_{2}=980MW$ The
total system inertia is equal to 110 GWs. Further, it is considered that 40%
of the total frequency response is provided by inverter-based resources, which
can be located either at bus 1 or bus 3 and 60% of the total droop resposne by
hydro units.

Figure. 3 shows the comparison of frequency response trajectories and
disturbance response ratios considering different locations of the inverter-
based resources. It can be seen that when fast frequency reserves are located
at bus 1 the maximum frequency deviation is lower compared to the case where
primary frequency control is provided by the IBR located at bus 3 (49.7125 Hz
compared to 49.686 Hz). Looking at the disturbance response ratios curves it
can be seen that when fast frequency response is provided by bus 3 (black
curve), the amplitude of the transfer function $|R_{zd}(s)|$ is higher than 1
within a larger frequency range (for $\omega>0.7$ rad/s) compared to the case
where fast frequency response is provided by the IBR located at bus 1. This
means that any disturbances within this range will be amplified and not
attenuated.

Moreover, when the fast frequency reserves are located at bus 1, the value of
the crossover frequency of $R_{zd}$ (frequency at which $|R_{zd}|=1$) is equal
to 0.87 rad/s and it is larger compared to the case where fast frequency
response comes from the IBRs at bus 3. Thus, primary frequency control on bus
1 can better attenuate active power disturbances. This renders IBRs located at
bus 1 more suitable for limiting the maximum frequency deviation in the
system. Finally, since the frequency controller is droop-based, there is no
contribution to the inertial frequency response, thus the rate of change of
frequency is the same in both cases. Thus, it can be concluded when the
inverter-based resources that provide fast frequency response are located
close to the disturbance location, the frequency nadir of the center of
inertia frequency has lower value.

####  III-A2 Low inertia case $K_{en}$=74.25 GWs

The same comparison is conducted considering lower inertia level in the
system. The total system inertia is equal to 74.25 GWs. Further, it is
considered that 40% of the total frequency response is provided by inverter-
based resources, which can be located either at bus 1 or bus 3, and 60% of the
total droop response by hydro units.

Figure 4: Lower inertia scenario. Comparison of frequency response trajectory
for different locations of the inverter-based resources. Disturbance response
ratio to evaluate the locational impact of frequency response.

Figure. 4 shows the comparison of frequency response trajectories and
disturbance response ratios considering different locations of the fast
primary frequency control. It can be noticed that the reduction of system
inertia influences the magnitude of $R_{zd}$ more, when primary frequency
control is provided by active power regulating units located at bus 3. In
particular, the maximum value of $R_{zd}$ is close to 1.3, which means that
the frequency controller cannot attenuate well the active power disturbance
occurring at bus 2. This is translated to higher maximum frequency deviation
compared to the scenario with higher inertia level. Moreover, the region in
which $|R_{zd}|$ is less than one, i.e. $|R_{zd}|<1$, is larger when fast
frequency reserves are located at bus 1. This means that the maximum frequency
deviation is smaller when fast frequency reserves are located at bus 1. This
is confirmed from the time-domain analysis. when fast frequency reserves are
located at bus 1 the maximum frequency deviation is lower compared to the case
where frequency response is provided by the IBR located at bus 3 (49.6742 Hz
compared to 49.6374 Hz). Notice that the difference between the frequency
nadirs is higher for the lower-inertia scenario, since the difference in the
amplitude of $R_{zd}$ increased considering the different fast frequency
reserves’ locations. This comes to show that the lower becomes the inertia
level, the higher the locational impact becomes on the frequency response.
Thus, to achieve the same frequency response and reduce the frequency nadir,
system operators would have to procure more frequency reserves if the fast
active power regulating units were located at bus 3.

###  III-B Impact of increased frequency droop response by inverter-based
resources

Figure 5: System response to an increased total frequency droop dominated by
inverter-based resources.

This study explores the behavior of the system for an increased droop response
provided by inverter-based resources. A disturbance of 560 MW is applied at
bus 2 in the system. The total system inertia is equal to 110 GWs. For this
study the performance variable is the center of inertia frequency, i.e.
$z=f_{\rm COI}$, and the measured output is the local frequency at bus 3, i.e.
$y=f_{3}$. The external disturbance to the system $d$ is equal to the active
power disturbance applied at bus 2. Moreover, 20% of the primary frequency
response is provided by the generator connected to bus 2 and the remaining 80%
by inverter-based resources connected to bus 3.

Figure 5 depicts the system response for increased total frequency droop and
the response provided primarily by inverter-based resources and the amplitude
of the disturbance response ratio. It can be seen that the peak of the
sensitivity function is higher compared to all the previous scenarios, i.e.
$|R_{zd}|_{\rm max}\approx 2$. It can be inferred that for very large
frequency droop response provided by active power regulating units at bus 3,
that the frequency controller amplifies disturbances in regions where
$|R_{zd}|>1$. This can cause excitation of local modes associated with
electromechanical dynamics, since the peak of the sensitivity function is
larger and consequently deteriorate the damping of the system. As it can be
seen from the time-domain analysis, although the maximum frequency deviation
is lower compared to the previous case, it can be noticed that frequency at
bus 3 experiences oscillations of constant amplitude. Further increase of the
frequency droop response by the inverter-based resources will result in small-
signal instability of the system. It is interesting to notice that the
frequency of oscillations is equal to 0.81 Hz, frequency at which $|R_{zd}|$
takes its maximum value.

Finally, this study highlights the fact that the stability margins might vary
for different allocation of primary frequency control and the importance to
evaluate the disturbance response ratio.

###  III-C Mitigation strategy

Considering that the peak of $|R_{zd}|$ is considerably higher when fast
frequency reserves are located at bus 3, one could limit its primary frequency
contribution by setting a constraint on the maximum value of $|R_{zd}|$ and
allocate primary frequency control at buses with smaller peak of $|R_{zd}|$.
Consider the previous scenario, in which a disturbance of 560 MW applied at
bus 2 in the system and the total system inertia is equal to 110 GWs. The
objective is to allocate the 80% of the total frequency droop control between
buses 1 and 3 so that the maximum $|R_{zd}|$ reduces and the system becomes
better damp. A maximum value of 1.35 is considered for the $R_{zd}$. The value
1.35 was empirically selected. Similarly to the previous cases, it is
considered that the performance variable is the center of inertia frequency,
the controlled inputs are the power outputs from the inverter-based resources
at bus 1 and 3. Thus, two disturbance response ratios are defined namely
$R_{zd}^{1}$ and $R_{zd}^{3}$.

Figure 6 demonstrates the system response considering different allocation of
fast primary frequency response between buses 1 and 3. We start from the case,
in which 80% of the total frequency droop control is provided by IBRs located
at bus 3, which is similar to the previous scenario (80% of total droop
response is provided by IBRs and 20% from generators). As shown in the figure,
the system is marginally stable. Then, we gradually reduce the participation
of the active power regulating units at bus 3 in primary frequency control
until $R_{zd}^{3}$ becomes smaller than 1.35 (see Fig. 7). This results in 8%
of the total droop response being provided by IBRs at bus 3 and 72% by IBRs at
bus 1. It can be seen in Fig 6 that when 72% of the total frequency droop
response is provided by IBRs located at bus 1, the local frequencies $f_{1}$
and $f_{3}$, as well as the COI frequency, are better damped. This is expected
since the maximum value for both disturbance response ratios $R_{zd}^{1}$ and
$R_{zd}^{3}$ are lower than 1.35 (see Fig. 7). Thus, we realize that by
allocating fast frequency response we can limit the maximum disturbance
response ratios and avoid disturbance amplification and excitation of poorly
damped modes in the system.

Figure 6: Comparison of system response considering different allocation of
fast primary frequency response between buses 1 and 3. Figure 7: Comparison of
disturbance response ratios $R_{zd}^{1}$ and $R_{zd}^{3}$ considering
different allocation of fast primary frequency response between buses 1 and 3.

It should be mentioned that a more sophisticated approach, such as
$H_{\infty}$/$H_{2}$ optimization or control design of a typical feedback
damping controller, could be considered in order to achieve a more robust
solution be achieved. However, this is not in the scope of this paper,
therefore it is intended as future work.

##  IV Conclusion

As inertia level decreases and active power regulating units are located in
remote areas, the nodal frequencies differ from the global one. This
introduces control limitations for improving the frequency performance of the
system, since the performance variables differ from the measured outputs. This
paper assesses the impact of delivering fast primary frequency response. Using
the disturbance response ratio of the system, the locational aspect of fast
frequency reserves can be evaluated by means of screening the frequencies in
which fast primary frequency control amplifies or attenuates disturbances in
the system. The disturbance response ratio allows to evaluate how well the
center of inertia frequency can be controlled by remotely placed active power
regulating units. The results show that fast primary frequency reserves
located at areas far from the disturbance location in combination with low-
inertia scenarios can result in an unstable response due to excitation of
poorly damped modes. In this case, careful consideration should be given on
the selection of the total droop response provided by these reserves, as their
increased frequency droop response can significantly deteriorate the small-
signal stability margins of the system. A possible mitigation strategy for
system operators would be to procure fast frequency reserves located in the
electrical vicinity of disturbance location. Finally, our results show that
fast primary frequency response is most effective in terms of reducing the
frequency nadir and preserving the small-signal stability of the system, when
it is provided from areas that are close to the location of disturbance.

Future work will focus on utilizing the disturbance response ratio for
allocating primary frequency response in large power systems and robustly
designing primary frequency controllers in future power systems.

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