Design, synthesis, and biological evaluation of novel dual FFA1 (GPR40)/PPARδ agonists as potential anti-diabetic agents

Article abstract of DOI:10.1016/j.bioorg.2019.103254

The free fatty acid receptor 1 (FFA1) and peroxisome proliferator-activated receptor δ (PPARδ) were considered as potential anti-diabetic targets, and the dual FFA1/PPARδ agonists might provide synergistic effect in insulin secretion and sensibility. Herein, we further develop dual agonists by screening 7 series of heterocycles, resulting in the discovery of compound 19 with considerable oral pharmacokinetic profile. Compound 19 exhibited a balanced potency between FFA1 and PPARδ, and high selectivity over PPARα and PPARγ. Moreover, compound 19 exerted improved glucose-lowering effects and insulin sensitivity in a dose-dependent manner, which might be attributed to its dual effects to simultaneously regulate insulin secretion and resistance. Our results extended the existing chemical space, and provided a potent tool compound 19.

Full text of DOI:10.1016/j.bioorg.2019.103254

This article has been accepted for publication in a future issue of this journal, but has not been fully edited. Content may change prior to final publication. Citation information: DOI 10.1109/TPWRS.2019.2935325, IEEE
Transactions on Power Systems
TPWRS-00050-2019
1
A Dual-Adaptivity Inertia Control Strategy for
Virtual Synchronous Generator
Meiyi Li, Student Member, IEEE, Wentao Huang, Member, IEEE, Nengling Tai, Member, IEEE,
Liuqing Yang, Fellow, IEEE, Dongliang Duan, Member, IEEE, Zhoujun Ma
Abstract—The virtual synchronous generator (VSG) improves
the robustness of the inverter-interfaced distributed generator
(IIDG) against instability by introducing a virtual inertia. However,
the transient response of the active power and the angular
frequency conflict with each other for the IIDG with fixed inertia
control. It is necessary to adopt adaptive control to improve overall
performances of power and frequency as the operating condition
changes. This paper analyzes the impact of the inertia on power and
angular frequency. A dual-adaptivity inertia control strategy is
proposed to offer a responsive and stable frequency support and also
achieve the balance between power regulation and frequency
regulation according to different operating conditions. The principle
of parameter design is given to obtain the range of adaptivity.
Quantitative assessment considering the cumulative effect of the
output deviation and its duration is also presented to evaluate the
proposed strategy intuitively. The strategy is further verified based
on PSCAD/EMTDC and a hardware-in-loop experiment platform
based on RTDS. Results confirm that the proposed strategy not only
achieves rapid frequency response with slight dynamic deviations
under disturbances but also strikes a balance between the frequency
and power and leads to improved overall control.
the VSG is playing an important role in the large-scale
integration of IIDGs [4].
Although the VSG control strategy is to imitate the behavior
of a real synchronous generator, the control parameters as
inertia are virtual. The flexibility of VSG control opens a gate
to a broader range of parameters. Many researchers have
reported on the virtual inertia control to meet the operation
requirements. An inertial control scheme using adaptive gains
is proposed in [10] and a disturbance-adaptive control scheme
in [8] for a doubly fed induction generator to support the
frequency control of a power system. Reference [11] proposes
an adaptive VSG control strategy by establishing the optimal
model of the response time to alleviate the fluctuation of
frequency and reduce the latency of the transient response.
Reference [12] compares the stability of the VSG-IIDG to the
power-angle curve of SGs and proposes a Bang-bang control
algorithm with alternating inertia to achieve fast oscillation
damping and reference [13] further proposes a frequency
stability control strategy with adaptive inertia. Currently, most
VSG control strategies concentrate mainly on the frequency
stabilization [1-3,5,6-8,10-15] when analyzing the dynamic
mechanism. The proposed control strategies promote the
dynamic performance of the IIDG by offering a stable,
responsive and accurate angular frequency support.
Index Terms—Dual-adaptivity Inertia Control, Virtual
Synchronous Generator (VSG), Inverter interfaced distributed
generator (IIDG), Dynamic performance, Virtual Inertia,
Quantitative assessment
However, existing studies show that the transient response of
the active power and the angular frequency conflict with each
other for the IIDG. For example, the simulation results in [14]
show that small virtual inertia results in a remarkable
performance in terms of the output power with fast response
and small overshoot in the transient process. On the other hand,
the frequency stability of grid-connected VSG is studied in [15]
and the results therein indicate that large inertia leads to smooth
and steady frequency output. It means the angular frequency
stability prefers larger inertia, while the active power response
would be better with smaller inertia. Apart from enhancing
frequency stability, a basic function of an IIDG is to supply
power for the local loads and compensate for the power shortfall
between generating units in the grid and the local loads [14][16].
If the control only considers the angular frequency, it may lead
to violent fluctuations of the output power in certain cases such
as the grid-connected mode, where the frequency has been
supported by the host grid [17]. Difficulties arise in determining
whether to give priority to power regulation or frequency
regulation. However, the tradeoff is only shown by some
simulation results in existing studies, and the joint analysis of
dynamic response mechanism of both power and frequency are
I. INTRODUCTION
HE increasing penetration of distributed generation (DG)
Tbrings direct impacts on the stability of the distribution
network due to the lack of inertia [1]. Conventional
synchronous generators (SGs) with inherent rotating inertia are
able to inject the stored kinetic energy under disturbances to
ensure operation robustness against instability [2]. Inspired by
this concept, the virtual synchronous generator (VSG) control
scheme was proposed for inverter-interfaced distribution
generators (IIDG). By incorporating the swing equation, the
VSG responds like the SG and will inject balancing energy
within proper time scales during disturbances due to the virtual
inertia [5,6,7]. Impedance analysis in [9] shows that VSG
improves the performance of IIDG in the very weak ac grid
condition. Further, the VSG-IIDGs can help the voltage and
frequency regulation of the connected distribution network [3].
With the combined advantages of SGs and power electronics,
This work was supported in part by Shanghai Sailing Program [grant
number (17YF1410200)], National Natural Science Foundation of China
[grant number (51807117)], National Key Research and Development
Program of China [grant number (2017YFB0903202)].
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This article has been accepted for publication in a future issue of this journal, but has not been fully edited. Content may change prior to final publication. Citation information: DOI 10.1109/TPWRS.2019.2935325, IEEE
Transactions on Power Systems
TPWRS-00050-2019
2
yet to be studied. Further, current studies on the design of VSG
controller hasn’t taken the tradeoff into consideration and there
is a need to balance the tradeoff between power regulation and
frequency regulation to improve overall performances when the
operating condition changes.
Time-domain simulations are valuable in evaluating the
effectiveness of a proposed control strategy, and most of the
existing studies of VSG control strategies are simulation based.
Overshoot and resettling time are two key indices of the
dynamic characteristics which can reflect the speed and
accuracy of tracking, respectively [15]. However, there is a
certain limitation when it comes to the assessment of a
responsive output with sharp overshoot and sluggish response
with sustained oscillations. In order to evaluate the behavior of
IIDGs in a more intuitive and precise manner, this paper puts
forward a comprehensive evaluation index integrating the
deviation and its duration, as inspired by [26]. This method
estimates both the output frequency and the active power and
provides a holistic quantitative assessment of the output
characteristics.
Fig. 1 VSG-IIDG control scheme
d

1
(1)
2H
 P  P -k(

-

grid ) 
(ref
-
grid
)
ref
o
dt
D
where Po is the active power output of the VSG-IIDG,

is the
grid
virtual angular frequency of the IIDG,
is the angular
P
ref
frequency measurement of the common coupling point,
are the reference active power and frequency,
respectively. H, k and D represent the virtual inertia, damping
ref
and
factor and droop coefficient, respectively.
This paper analyzes the dynamic response mechanism of the
VSG-IIDG theoretically and revealed the conflicting influence
of the inertia on power and angular frequency by establishing
the small-signal model. Then a dual-adaptivity inertia control
strategy is developed to enhance frequency stability and also
balance the tradeoff between frequency and power. Besides, the
principle of parameter design for the proposed strategy is put
forward for a reasonable selection of the virtual inertia. The
proposed strategy is verified by the quantitative assessment,
simulation based on PSCAD/EMTDC and a hardware-in-loop
experiment platform based on RTDS.
The contributions of the paper are:1)This paper analyzes the
joint dynamic characteristics of IIDG. 2) This paper proposes a
dual-adaptivity inertia control strategy to offer stable frequency
support and also adjust the regulation priority between power
and frequency adapting to different conditions.3) The principle
of parameter design and a quantitative assessment method are
proposed to provide guidance for the design and optimization
of the control system.
Fig. 2 VSG controller
The VSG controller is shown in Fig.2, and Table I
summarizes how the classical VSG controller operates. The
virtual inertia H in VSG controller is half of the time required
to reach the reference active power at the reference frequency
[18]. The selection of the virtual inertia in a VSG is more
flexible than in a conventional SG. Smaller or larger values are
allowed, and one can also adaptively change the inertia over
time to obtain a faster and more stable output of the IIDG [19].
TABLE І
OPERATING MODES OF THE VSG CONTROLLER
Section II gives the structure of the VSG-IIDG system.
Section III presents the mechanism of the virtual inertia on the
output characteristics. A dual-adaptivity inertia control strategy
is proposed in section IV and the parameter design strategy is
given in section V. Section VI introduces an evaluation index
for quantitative assessment of the proposed strategy. The
simulation results and experimental results are illustrated in
section VII and section VIII, respectively.
Steady-state
frequency
Regulating
term
Function
Modes
track the
frequency of the
network in
synchronism
provide
Grid-
connected
mode
k(

-
grid
ability of the SG
ref grid ) / D , the
)
, the damping
ref grid
(
-
frequency
primary frequency
modulation of
conventional bulk
power plants
Islanded
mode
support for the
island IIDG
system
 grid
I. VSG-IIDG CONTROL STRUCTURE
The control scheme of the VSG-IIDG is shown in Fig. 1
where an IIDG is connected to the network via a feeder. By
incorporating the swing equation of the SG as (1), the IIDG
achieves the dynamic properties of the SG [17].
II. IMPACTS OF VIRTUAL INERTIA ON THE DYNAMIC
RESPONSES OF ANGULAR FREQUENCY AND POWER
OUTPUT UNDER DISTURBANCES
A. Transfer Functions of the VSG Controller
According to (1), the small-signal model of the VSG
controller is obtained as Fig. 3 by linearizing around the
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Transactions on Power Systems
TPWRS-00050-2019
3

 P / 

|
 s ,EEs
,
E
and
S
operating point where
are
s
the phase angle and voltage magnitude of the VSG-IIDG when
the output power is at the reference value, respectively. The
P
ref
VSG controller is considered a system with two inputs:

grid
P
and
, and two outputs:
and
.

o
Fig. 4 The power deviation under different values of virtual inertia.
4 H
tp 
(6)
(7)
8
H  k2
k


8
H k2
P (tp ) 
 e
o
Fig. 3 Small-signal model of VSG controller
2) A sudden change in the angular frequency of the common
coupling point
When the distribution network is subject to disturbances,
there will be a sudden change in the angular frequency of the
common coupling point as described in (8), and the output
angular frequency deviation is obtained in (9).

grid  0
1) When
, namely the angular frequency of the
grid
ref
common coupling point
transfer function of the active power is established as:
is a constant at
, the
P

o
G (s) 
=
(2)
1
2Hs2  ks  
P
ref
P  0

grid
=

u(t) u(t 0
)
(8)


ref
2) When
, the transfer function of the angular
frequency is as:

1
0
2
k
2
(k )(1e
)
8

H  k
4H
D
4H
1
(t) 
e t sin(
t) (9)
(k  )s
2
8H k

grid

D
G2 (s) 

(3)
2Hs2  ks 


where 0 is the time duration of the disturbance.
According to the transfer function in (3), the response of
(t) is presented in Fig.5 and the peak time and the
corresponding output are given in (10) and (11), respectively. It
H5

For the transfer functions (2) and (3) obtained above, the
transfer function in (2) can be used as an analytical tool when
the active power of the VSG-IIDG changes and the transfer
function in (3) investigates how the frequency fluctuates when
the IIDG system is subjected to frequency disturbances from
the network via the lines and the common coupling point.
According to the above transfer functions, the VSG controller
is a second-order system. As indicated in section V, the control
system should be underdamped. Thus the analysis below is
based on an underdamped VSG control system.


H
to 1 , the overshoot
can be seen that as H decreases from
of
(t) becomes larger and the peak time shortens. In other


words, large inertia depresses the overshoot of
small inertia shortens the response time.

(t) , yet
4

tp 
(10)
8
H  k2
1
0
(k  )(1e
)
k

2

8
H k2
B. Influence of the Virtual Inertia on the Response of the VSG-
IIDG
D
8H

(tp ) 
e
(11)
1) A sudden change in the active power
When there is a sudden change in the active power reference
as (4), the output active power deviation can be given as (5).
P =u(t)
(4)
ref
k

t
8H  k2
4H
4H
P (t)    e
sin(
t  )
(5)
o
2
k
1
8H
Fig. 5 The angular frequency deviation under different virtual inertia
values.
where
function, and
According to the transfer function in (2), the response of
P (t) H5 H1
is

is the amplitude of the change, u(t) is the unit step
To sum up, smaller inertia leads to a faster response for both
the angular frequency and the active power. However, the
effects of H on the overshoot of power and frequency are
different. Larger inertia decreases the overshoot of power, yet
it results in more fluctuations of the angular frequency.

 arccos(k / 8 H )

.
with the virtual inertia decreasing from
to
o
shown in Fig. 4. The time for the power deviation to reach its
peak and the corresponding output can be obtained as (6) and
(7), respectively. It can be seen that as H decreases, the
overshoot, as well as the peak time, become smaller. Therefore,
a smaller H results in a better output active power dynamic
performance with faster response and lower oscillations.
III. DUAL-ADAPTIVITY INERTIA CONTROL STRATEGY
The difference in the impacts on the overshoot indicates that
a well-designed VSG controller should consider both the
characteristics of the active power and the frequency to obtain
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Transactions on Power Systems
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4
B. Adaptive Priority Setter
a satisfactory dynamic performance. Therefore, this paper
proposes a dual-adaptivity inertia control strategy of IIDG with
an adaptive deviation regulator and an adaptive priority setter
The basic ideas are:
1) When considering power regulation only, small inertia
should be adopted.
Thus, separate frequency regulation or power regulation has
been conducted separately so far. To achieve a balance between
the frequency regulation and power regulation, the sensitivity
kg
ka
factor
constant.
is adaptive as (13) where
is a predesigned
2) When considering frequency regulation only, the inertia
should be adaptive: When the frequency deviation is small, the
controller could underplay overshot and small inertia
accentuates rapidity ensuring the IIDG to recuperate as quickly
as possible. Once the deviation grows large, the first thing is to
restrain the deviation and large inertia is in need. Therefore, the
controller should also adjust inertia in a timely manner
according to the frequency deviation to implement frequency
regulation.

2

ref





ref

ka2  kg kd  kg
(13)

2

2


ref
P  P
o ref

1












ref
P
ref
kd
As the output deviation of VSG-IIDG varies, the variable
varies from zero to one and reflects the weight of angular
kd
frequency deviation.
increases when the weight of
3) The controller should be able to balance the power and
frequency regulation stated above depending on the operating
conditions.
frequency deviation is large and decreases when the weight of
power deviation is large. Therefore, when the output active
power runs away from the reference value to a large degree,
ka
A. Adaptive Deviation Regulator

gets closer to zero. The actual control curve is closer to 4 , for
3
2
instance, curve
. The VSG controller prioritizes power

 ref
2 




regulation in this case. On the other hand, a large deviation of
Hhka
+H0
 1
ref
k
the output frequency results in larger a . The actual control
2

(12)
H 
2

curve is closer to curve 1 , for instance, curve
In other words, the actual control curve changes between the
1 4
under different conditions. Besides,
.



ref
2 




ka
ref
curve
and curve

the inertia also changes along the control curve according to the
deviation. As a result, not only can the control system adjust
inertia according to the output deviation, but also set the priority
of power and angular frequency adaptively. The control block
of the dual-adaptivity inertia control strategy is given in Fig.7.
The expression of the proposed dual-adaptivity inertia is
H0
given in (12) and the control curve is shown in Fig.6. Here
Hh
is the lower limit of virtual inertia and
is the upper limit.
According to (12), when the angular frequency deviation
1/ ka H  (H  H ) / 2
ka
is called the
reaches
,
. Thus,
h
0
sensitivity factor which divides the range of inertia.
Fig. 7 Dual-adaptivity inertia control
IV. THE PARAMETER SETTING FOR DUAL-ADAPTIVITY
INERTIA CONTROL STRATEGY
Fig. 6 The control curve of the dual-adaptivity inertia.
ka
There are four control curves in Fig.6 with
decreasing
k
A wider range of the virtual inertia leads to better adaptivity
of the control system. The parameter design method for dual-
adaptivity inertia control strategy is given below to obtain the
range of adaptivity.
1

4
from
to 4 , among which
refers to a zero a . Take
as an example. When the frequency deviation is small
1/ k
1
curve
and less than
a , the corresponding inertia is small and it is
in the responsive area. The IIDG underplays overshot but is able
to respond to the disturbances as quickly as possible. Once the
frequency deviation grows large and is greater than
system goes into the overshoot reduction area. The large
deviation is restrained by the large inertia. As a result, frequency
regulation is achieved.
A. Damping Ratio ζ of the Second-Order System
According to (2) and (3), the VSG controller is a second-
order system with the damping ratio as:
1/ k
a , the
k
(14)
 
2 2H
The damping coefficient ζ determines whether the control
system is underdamped or overdamped. Small values of ζ yield
excessive overshoot in the transient response and a system with
a large value of ζ responds sluggishly. In order to obtain a
desirable response, the damping ratio should be less than one
4
In terms of the power regulation, consider curve
which
k
refers to a zero a . The corresponding inertia is always small
H
and equal to the lower limit
regulation ability.
0 , which results in good power
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Transactions on Power Systems
TPWRS-00050-2019
5
[20]. In this case, the control system is under-damped and the
response is relatively fast.
1

2H
(k 
)

2H
D

2H
A(t )  A（
）=
(20)
B. Droop Coefficient D
k
Droop coefficient D is determined by standards in
accordance with the frequency and it reflects how much the
active power output changes with the frequency [21]. Generally,
a relatively large droop coefficient results in better transient
stability [22] yet brings more fluctuations to the system.
t
where
is the frequency where the phase angle of the
A(t t
)
transfer function is -180°, and
is the magnitude at
.
The principle of parameter design is summarized in Table II
and the suggested values are also given according to [25].
TABLE II
%P
P

ref
(15)
D 

PARAMETER SETTING FOR DUAL-ADAPTIVITY INERTIA
CONTROL STRATEGY
2
Contributing factor
damping ratio
Condition
0.4   0.6
C. Damping Factor k


According to (1), when a VSG-IIDG is connected to the
network and operates at the steady state, the term
grid standards: D  (10%P ) / 2

droop coefficient D
damping factor k
phase margin
ref
commensurate with 1/D
(
ref
-grid ) / D
is equal to zero, while in the islanded mode,
40 
10  20lg(1/ A(
around CDCUD2C / 2Sn

( jg ) 180  60
k(

grid
)
is equal to zero. However, in transient
the term
t ))  20
gain margin
progress, there may be some time that neither of the terms is
zero. If 1/D and k are incommensurate, the far greater one will
overshadow the other, and the controller can’t act accurately.
Hence, to ensure the control signals reflect the frequency
deviation reasonably, the order of the magnitude of 1/D and k
should be the same.
lower limit of inertia
H0
V. QUANTITATIVE ASSESSMENT INDEX FOR THE OUTPUT
CHARACTERISTICS OF VSG-IIDG
H
D. Lower limit of inertia
0
When the VSG-IIDG operates in the steady state, the inertia
value is calculated for the VSG-IIDG by making equal the
stored energy and the kinetic energy [23][24]:
(a)
(b)
(c)
J2
Fig. 8 Three typical types of the response curve.
The relative quality of the response characteristics can be
observed from time-domain simulation results, but it is difficult
to make a quantitative assessment. The quantitative assessment
of dynamic performance usually relies on overshoot and
settling time. However, when there is a tradeoff between these
indicators [15], it is hard to judge which performs better
between a responsive output with a sharp overshoot in Fig.8(a)
and a sluggish response with sustained oscillations in Fig.8(b).
Hence, the concept of integration [26] is introduced. Since
integration reports both the magnitude and the time duration of
deviation, it universally reflects the dynamic performance of the
VSG-IIDG.
(16)
 SE
2
Sn
where J is the moment of inertia and H  J2 / 2Sn
,
is the
rated capacity of the VSG-IIDG. SE is the stored energy of
the IIDG and SE  CDCUD2C / 2 in the paper. Since when the
VSG-IIDG operates in the steady state, the inertia value
adopted in the adaptive controller is just a little bit larger than
H0
the lower limit of inertia,
should be around
CDCUD2C / 2Sn
.
E. Phase and Gain Margin
According to the distribution of characteristic roots, the VSG
control system is a minimum phase system. Based on the design
principles of this kind of system [20], the phase margin should
be in a specific range:
Define the evaluation index η based on the concept of
integration as:
(y  ycr )dt



100%, y  yref
1


( j
g ) 180 2
(17)



(yref  ycr )tcr
Sd 100
ycrtcr
 
% 
(21)



4H  k2
2H
(ycr  y)dt
(y  yref )tcr

g 
(18)
100%, y  yref


cr
g
where
is the gain crossover frequency where the
magnitude of the transfer function is unity and
phase angle of the transfer function at
ycr
ycr
yref

( jg )
is the
where y is the response curve,
reference, the upper threshold and the lower threshold of it,
respectively, and
,
and
are the
g
.
ycr  yref  ycr  ycr  yref
Sd
is the area
.
In addition, the gain margin should not go beyond a certain
range:
surrounded by y and the straight line of deviation threshold in
tcr
the observation time window whose width is
Take the response curve c in Fig.8 as an example where
ycr  yref  ycr
.
1  20log10 A(t ) 2
(19)
Sd  S1  S3  S
and
4 . The index η, in this
case, can be given as (22). Similarly, when the response curve
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ycr
Fig. 10 Systematic single line diagram.
TABLE III
PARAMETERS OF THE VSG-IIDG
y is above the upper threshold
, it can be treated as the dual
problem. A large η indicates a more stable output. If η=1, it
means that the output is ideal in a perfect world.
S1  S3  S
Parameters
DC voltageUdc
Value
1kV
 
4 100%
(22)
100μF
400μF
1mH
DC capacitance Cdc
S1  S2  S3
AC filter capacitance Cac
1
2


(
f

P
)
(23)
L
AC filter impedance
f
311V
U
AC voltage
g
The index η reflects the severity of deviation in the
tcr
0.3MW+j0.1MVar
P
 jQ
ref
Power reference
ref
observation window with a width
in the dynamic response.
In each case study, the same scenario is applied to the VSG-
IIDG with fixed inertia H=0.1 (small inertia), H=1 (large
inertia), the classical Bang-bang control with alternating inertia
[12] and the proposed dual-adaptivity control.
For the angular frequency, the integral calculation is the phase
angle. The index η reflects the output angle deviation of the
IIDG from the common coupling point. For the output power,
the integral calculation is the energy. The index η reflects the
difference between the output energy of VSG-IIDG and the
A. Disturbances in the Grid-Connected Mode
energy consumed by the load. Furthermore, since η is the
To analyze the effect of the adaptive inertia strategy in the
grid-connected mode, frequency oscillation begins at the time
of 4s in the grid and ends at 4.2s. Besides, there is a step change
in the power reference from 0.3MW to 0.4MW at 6.2s. The
simulation results are shown in Fig.11. The threshold deviation
yref
ycr
tcr
standard value, the results based on different [
,
,
]
are comparable [26]. Hence as indicated in (23), the
 f
comprehensive index is the mean of
and P , the
evaluation index of frequency response and power response
respectively. The flow diagram of figuring out η is summarized
in Fig.9.
ycr
10%yref
is given as
in the quantitative assessment and
the comprehensive assessment results are shown in Table IV.
As observed, the trends of output with different control
strategies are similar to each other. When subjected to
frequency oscillations from the external network, the VSG-
IIDG is affected and the output frequency fluctuates. When the
power reference increases, VSG output power follows the
power command after experiencing damped oscillations. The
output finally reaches the reference value and the deviation
reduces to zero.
There are obvious differences in the control effects of four
different strategies. The oscillating time is extremely short with
small inertia, whereas the overshoot of frequency is large. The
fluctuation is slighter using large inertia. Whereas with large
inertia, several periodic oscillations can be observed and the
dynamic performance is not so good. It is confusing to
determine which performs better. The comprehensive
assessment facilitates the analysis. The index η using Bang-
bang control and adaptive control is much larger than others.
The Bang-bang control improves the stability of the VSG-IIDG.
Yet the overall performance is even better using the adaptive
control. The response time is relatively short with the adaptive
inertia and the output follows the reference value closely.
Compared with other control strategies, a fast response and a
stable output of power and frequency are not mutually exclusive
when adopting the adaptive strategy. The proposed control
Fig. 9 Flow diagram of figuring out the evaluation index η.
VI. CASE STUDIES
Simulations based on PSCAD/EMTDC are performed to
evaluate the proposed strategy and the systematic single line
diagram is shown in Fig.10. The parameters of the VSG-IIDG
are listed in Table III, where the control parameters are
determined according to the principle in section V. The droop
coefficient D is 0.016, and the damping factor k is 0.01.
10000, and the upper and lower limit of the inertia is 1 and 0.1
respectively.
kg
is
strategy achieves a better overall dynamic performance.
TABLE IV
ASSESSMENT RESULTS IN GRID-CONNECTED MODE
Control
Small H
Evaluation index
0.9578
Large H
0.9559
Bang-bang
Adaptive inertia
0.9676
0.9684
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(a) Output of VSG-IIDG
(b) Inertia of different control strategies
Fig. 11 Simulation results in the grid-connected mode.
The quantitative assessment of the output characteristics is
somewhat different from the grid-connected mode. The index
of adaptive control is the best. Whereas the index with small
inertia is even larger than that using Bang-bang control. This is
due to the fact that the resettling time of small inertia is so short
B. Disturbances in the Islanded Mode
The simulation results and quantitative assessment of the
islanded mode (with break 2 open) are presented in Fig.12 and
Table V. The VSG-IIDG is subjected to a step change in the
power reference from 0.4MW to 0.3MW at 4s. Besides, due to
the output fluctuation of DG1, there is a sudden change in the
angular frequency of the common coupling point from 7.2s to
7.4s.
As shown in Fig.12, the adaptive inertia control strategy
forces the output frequency to converge more effectively and
quickly with fewer oscillations. The output active power using
adaptive inertia control strategy recuperates faster than that
using Bang-bang control or large inertia. Also, the overshoot is
suppressed.
despite larger overshot.
TABLE V
ASSESSMENT RESULTS IN THE ISLANDED MODE
Control
Small H
Evaluation index
0.9905
Large H
0.9770
Bang-bang
Adaptive inertia
0.9794
0.9909
(a) Output of VSG-IIDG
(b) Inertia of different control strategies
Fig. 12 Simulation results in the islanded mode.
is introduced to represent the arc fault.
C. Arc fault in grid-connected mode
At first, when both utility source and DGs feed the fault, the
arc is modeled as a primary arc with low arc resistance as seen
from Fig.13(a). Once relay 1 responds at 5.03s to isolate the
fault from the utility side, the rest of the system becomes
islanded. During the islanded operation, the arc is modeled as a
It has been found that around 90% of the faults in the power
system are transient arc faults [27]. To investigate the effect of
the adaptive control on arc faults, an arc fault is created at 5 s
on Line 1. As Fig.10 shows, relay 1 is on the utility source side
of Line 1 and relay 2 is on the DG side. The arc model in [28]
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secondary arc. Relay 2 responds at 5.05s to isolate the fault
from the DG side (Fig.13(b)). The isolation of the faulted
segment results in the islanded mode of operation containing all
the three DGs. Then, the system recovers.
TABLE VI
ASSESSMENT RESULTS OF ARC FAULT
Control
Small H
Evaluation index
0.9725
Large H
0.9486
(a) Arc resistance
(b) Relay response
Bang-bang
Adaptive inertia
0.9783
Fig. 13 System behavior for an arc fault
0.9788
(a) Output of VSG-IIDG
(b) Inertia of different control strategies
Fig. 14 Simulation results of arc fault
The simulation results are presented in Fig.14 and they show
that the output of VSG-IIDG experiences excursion under arc
fault. Using adaptive control, the dynamic performance is more
responsive with shorter resettling time. The assessment results
(Table VI) also indicates the result. The comprehensive index
using adaptive control is the largest.
D. Sensitive load
To analyze how frequency-sensitive loads respond to the
adaptive inertia strategy, we replace load 1 in Fig.10 with a
motor load. There is a step change in the power reference of the
VSG-IIDG from 0.2MW to 0.3MW at 6s. The simulation
results and the comprehensive assessment results are shown
below.
(a) Output of VSG-IIDG
(b) Inertia of different control strategies
Fig. 15 Simulation results of sensitive load
As shown in Fig. 15, the output of the VSG-IIDG fluctuates overall dynamic performance of frequency and active power.
when the power reference increases. Compared with the As indicated in Table VII, the comprehensive index using
simulation results shown in Fig. 11, the frequency overshot with adaptive control is still the largest.
TABLE VII
frequency sensitive-load is larger than that with a resistor-
inductance load. The proposed strategy also improves the
ASSESSMENT RESULTS OF SENSATIVE LOAD
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Control
Small H
Large H
Evaluation index
0.9604
0.9368
Bang-bang
Adaptive inertia
0.9531
0.9679
In summary, the proposed strategy has a strong robustness in
adapting to different conditions. The dual-adaptivity inertia
control achieves a better dynamic performance when taking
both the power and the frequency into consideration.
(b) frequency of the VSG-IIDG
VII. EXPERIMENTAL RESULTS
The proposed strategy is verified by applying to a real-time
controller hardware-in-loop experiment platform. The overall
system configuration is shown in Fig. 16. The droop coefficient
kg
D is 0.05, and the damping factor k is 0.04.
is 10000. The
H
H0
upper limit inertia
1.5.
h is 10, and the lower limit inertia
is
(c) adaptive inertia
Fig.16 Experimental results of the islanded mode
(a) Overall design
(a) active power of the VSG-IIDG
(b) frequency of the VSG-IIDG
(b) experimental devices
Fig. 16 Controller hardware-in-loop experiment platform
The experimental results of the islanded mode are shown in
P
Figs. 17 where
abruptly changes from 1 MW to 0.75MW
ref
at 7s. Replace the local load in Fig.16(a) with a motor load.
P
When the system operates in the grid-connected mode,
ref
increases from 0.8 MW to 1MW at 7s. The experimental results
are shown in Figs. 18. The assessment results are in Table VIII.
(c) adaptive inertia
Fig.17 Experimental results of the grid-connected mode
TABLE VIII
QUANTITATIVE ASSESSMENT INDEX FOR THE OUTPUT
CHARACTERISTICS OF THE VSG-IIDG
Islanded mode
Control
Grid-connected mode
Control
Index
0.9704
0.9453
0.9652
0.9790
Index
0.9689
0.9301
0.9603
0.9751
Fixed inertia(H0)
Fixed inertia(Hh)
Bang-bang control
Adaptive inertia
Fixed inertia(H0)
Fixed inertia(Hh)
Bang-bang control
Adaptive inertia
(a) active power of the VSG-IIDG
P
When
abruptly changes, the VSG output power
ref
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Transactions on Power Systems
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VIII. CONCLUSIONS
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The virtual synchronous generator is a promising method to
enhance the stability of the IIDG by introducing the virtual
inertia. Fixed inertia causes a transient response conflict
between the power and the angular frequency. In order to
improve the overall performance of IIDG, a dual-adaptivity
inertia control is presented to optimize both the power and
frequency transient response under different operation conditions.
A quantitative assessment considering the cumulative effect of
the output deviation and its duration is also presented to
evaluate the proposed strategy.
Small inertia leads to a fast response for both the angular
frequency and the active power. Large inertia decreases the
overshoot of active power, yet it results in more fluctuations of
the angular frequency. The proposed strategy decreases the
inertia when power deviation is large. Whereas when frequency
deviation is large, the controller adjusts the inertia dynamically:
Large inertia is adopted to facilitate small overshoot and small
inertia to achieve fast frequency response. The proposed
strategy not only offers a responsive and stable frequency
support, but also balances frequency regulation with power
regulation as operating condition changes.
According to the simulation and the experiments, the
proposed strategy achieves
a
better overall dynamic
performance adapting to different conditions. It is a preferable
candidate strategy for the application of renewable energy
generation and storage system.
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