Content uploaded by Federico Milano
Author content
All content in this area was uploaded by Federico Milano on Jan 19, 2022
Content may be subject to copyright.
2168-6777 (c) 2021 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission. See http://www.ieee.org/publications_standards/publications/rights/index.html for more information.
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/JESTPE.2021.3101123, IEEE Journal
of Emerging and Selected Topics in Power Electronics
1
Modelling of Smart Transformers for Power System
Transient Stability Analysis
Junru Chen, Member, IEEE, Muyang Liu, Member, IEEE, Terence O’Donnell, Senior Member, IEEE, Federico
Milano, Fellow, IEEE
Abstract— The Smart Transformer (ST) has been proposed to
enable bidirectional power flows among the several subsystems
that compose the smart grid. For an accurate and efficient
analysis of the power system dynamic response, a proper ST
model must be developed. Starting from the detailed ST model,
this paper proposes reduced-order models according to the time
scale of the ST dynamics and the simulation objective. The
proposed models are classified based on the level of complexity
and dynamic order and are compared by means of relevant
scenarios, namely, fault (rotor angle stability analysis), DC power
exchange (power management) and system contingencies (voltage
and frequency stability analysis). Finally, case studies based on
the IEEE 39-bus system discuss the features and adequateness
of the proposed models in a scenario of an interconnected grid
with multiple STs.
Index Terms— Smart Transformer (ST), modeling, power sys-
tem simulation.
I. INTRO DUC TIO N
A. Motivation
Power systems are migrating to converter-interfaced gener-
ation, mostly based on renewable energy resources [1]. An
advantage of converter-based generation and control is the
ability to develop “smart” solutions that, if properly imple-
mented, can lead to increase the flexibility of the grid. In this
context, customers can become “prosumers,” i.e., they not only
consume but also actively control and produce energy transac-
tions. On the down side, electronic converters introduce more
complexity and lead to a mixture of AC and DC subsystems
where power flows now are not simply from the feeder to
the consumer but are bidirectional among these subsystems.
In this new scenario, transformers must be able to manage
these bidirectional power flows and, thus, the traditional Low-
Frequency Transformer (LFT) is no longer adequate [2]. The
ST based on controllable power-electronics converters [3]
appears as an ideal energy router [4]. This device can in
fact integrate communication networks and smart controllers
to provide several services, i.e., power management [5], [6],
demand control [7], [8], load identification [9], [10], neutral
current control [11], [12] and reactive power compensation
[13] as shown in Fig. 1.
Time-domain simulation is a general method for the Tran-
sient Stability Assessment (TSA) of the Transmission System
This work is funded by the Science Foundation Ireland (SFI) under grant
numbers SFI/15/SPP/E3125.
Junru Chen and Muyang Liu are with the School of Electrical Engi-
neering, Xinjiang University, China. Terence O’Donnell and Federico Mi-
lano are with the School of Electrical and Electronic Engineering, Univer-
sity College Dublin, Ireland. E-mails: {junru.chen, muyang.liu}@xju.edu.cn,
{terence.odonnell, federico.milano}@ucd.ie
Electric
Vehicle
Reactive Power
Compensation
DC Droop
Control
Load Identification;
Deman d Contro l;
Neutral Cu rrent Co ntrol
Power
Managemen t
Electrical Power Flow
Communi cation Flow
==
~
=
Wind
Turbine Roof
PV DC
Loads Electric
Storage ~=
Wind Farm PV Plant
AC Loads Motor/Generator
Utility Grid
LVDC
MVDC
MVAC
LVAC
Fig. 1: ST in the power system.
Operation (TSO). The configuration of the ST, in general, is 3-
stage consisting of MVAC-MVDC, MVDC-LVDC and LVDC-
LVAC converters [2]. Because of this complex nature of the
ST system, capturing the response of the ST precisely for
power system simulations is a challenge. In particular, an over-
detailed ST model would increase the computational burden of
power system simulations and would typically be unfeasible
for large system simulations. To speed up the simulation with-
out loosing accuracy, adequate simplified models are needed.
Since approximated models inevitably neglect some dynamic
aspect of the ST, this paper focuses on the definition and
classification of ST dynamic models based on different levels.
A systematic taxonomy is lacking in the literature. This paper
fills this gap by proposing simplified ST models and classifies
then into 3×3levels according to their conditions of usage.
B. Literature Review
A classification of the deepness level for modelling general
power electronics converters has been proposed in [14], where
the level ranges from the simplest phasor model suitable
for the optimal power flow use to the complex switching
model suitable for harmonics studies. For power system time-
domain dynamic simulations, where a TSO may require a fast
computation of the TSA, it is not feasible to use switching
models for the converters or to model each online generators
in detail. As mentioned in [14], for the analysis of transient
Authorized licensed use limited to: Xinjiang University. Downloaded on December 16,2021 at 07:03:26 UTC from IEEE Xplore. Restrictions apply.
2168-6777 (c) 2021 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission. See http://www.ieee.org/publications_standards/publications/rights/index.html for more information.
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/JESTPE.2021.3101123, IEEE Journal
of Emerging and Selected Topics in Power Electronics
2
rotor angle stability, and voltage and frequency stability, an
appropriate simplification of the power electronics modelling
can speed up the simulation while maintaining a certain level
of accuracy. As regards conventional generator modelling, the
generators in one power plant are aggregated into a single
generator and the electrical equipment is modelled in the
form of Differential-Algebraic Equation (DAE). Even for the
DAE model of the synchronous generator, it can be classified
according to different levels of complexity from a classical 2nd
order including only electrical transients to 8th order, including
detailed magnetic sub-transients [15]. Another approach which
has been used to achieve a better trade-off between accuracy
and computational speed, is the use of co-simulation between
a detailed Electro-Magnetic Transients (EMT) model of parts
of the system and a simplified phasor model for most of the
system [16]. For example, an EMT model can be used for the
devices close to a fault while a phasor model can be used for
those far away from the fault. This provides an idea that even
for a multistage power electronic system such as ST, some
parts must be precisely modelled while other parts may be
simplified depending on the considered system contingencies.
Specifically for the ST, several models have been proposed
in the literature. Reference [17] and [18] proposes a static
ST model focusing on the power exchanges among the utility
grid and ST-fed internal subsystems. However, this model is
developed for economic dispatch studies and power system re-
liability analysis, thus neglecting all the transients. References
[19]–[22] propose a full-order DAE model of a typical three-
stage ST with inclusion of detailed control dynamics. These
models focus on the power delivery from the primary to the
secondary side of the ST. References [23] and [24] extend the
full-order DAE model above in order to take into account the
DC power integration and the bidirectional power flow. This
model can capture the DC voltage dynamics due to the power
exchange at the DC ports. However, this model is too detailed
to use in a large power system simulation, especially with a
very high ST penetrations.
C. Contributions
As discussed above, the existing ST models are either too
detailed to satisfy the TSA computational requirement or too
simple to capture the dynamics. Intermediate models between
the full-order and the purely static can achieve a certain
accuracy and meanwhile lower the computational burden. For
this purpose, this paper proposes a set of ST DAE models
with various levels of approximations for the three stages that
compose the ST.
Similarly to the variety of dynamic models that exist for
synchronous machines, the usage of the model depends on the
timescale of the response of interest and the focus of the study.
In particular, the larger the time scale of interest, the simpler
the model of the ST. In addition, similarly to the concept of the
co-simulation method, based on the study focus, the ST stage
which has most influence may require a precise model while
other stages may be simplified. Based on this, the model of the
ST can be simplified and classified in different complexities
for the different usage conditions. The specific contributions
of this paper are:
•To propose and classify appropriate simplified ST DAE
based models according to the simulation time scale of
interest and the study focus of interest (e.g. fault response,
DC power exchange, frequency or voltage support). It is
highlighted that different levels of simplification for the
different ST stages may be used depending on the study.
•To present benchmark use cases for the proposed simpli-
fied ST models.
D. Organization
The remainder of the paper is organized as follows. Section
II introduces the full-order DAE model of the ST. Section
III presents the proposed simplified ST models and classifies
according to their complexity, time scales and parameter
sensitivity analysis. Section IV defines the applications for the
the proposed ST models. Section V verifies the accuracy of
the proposed models based on the IEEE benchmark 39-bus
system. Finally, Section VI draws relevant conclusions.
II. MO D EL ING O F THE SM ART TRA NSF OR M ER
Figure 2 shows the configuration of a 3-stage ST, consisting
of an MVAC-MVDC Primary Side Converter (PSC) linking to
the utility grid; an MVDC-LVDC Dual-Active-Bridge (DAB)
with a high frequency transformer; and an LVDC-LVAC Sec-
ondary Side Converter (SSC) feeding the distribution system.
This provides a link to integrate different kinds of load and
generations. In its basic configuration, each stage regulates
its port voltage. Additionally the ST can provide primary
frequency and voltage support to the system.
For each stage, the model consists of the electric circuit, the
basic control functions (e.g. current and voltage) and upper
controls for system services. The link between each stage is
represented via the dynamics of the power conversion and
the voltage control achieved by the upstream converter. The
remainder of this section describes the detailed ST model. The
notations are explained in Table I and marked in Fig.2.
A. MVAC-MVDC Primary Side Converter Model
The PSC is an interface of the ST to the MVAC utility grid
or transmission system. Its purpose is to feed the total power
from the ST-fed subsystems.
The electric circuit in this stage includes the grid power
exchange at the Point of Common Coupling (PCC) as shown
in Fig. 2 and by the following equations:
Pg=Vgcos(δg−δpll)Id,psc +Vgsin(δg−δpll )Iq,psc ,
Qg=Vgsin(δg−δpll)Id,psc −Vgcos(δg−δpll )Iq,psc ,
Vd,psc =Vgcos(δg−δpll)−ωpll LgIq,psc ,
Vq,psc =Vgsin(δg−δpll ) + ωpllLgId,psc ,(1)
and the power conversion from the MVAC to the MVDC via
the converter modulation and L-filter:
Lpsc ˙
Id,psc = 0.5md,pscVdcm −Vd,psc
+ωpllLpsc Iq,psc −rpsc Id,psc ,
Lpsc ˙
Iq,psc = 0.5md,pscVdcm −Vq ,psc (2)
−ωpllLpsc Id,psc −rpsc Iq,psc ,
Authorized licensed use limited to: Xinjiang University. Downloaded on December 16,2021 at 07:03:26 UTC from IEEE Xplore. Restrictions apply.
2168-6777 (c) 2021 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission. See http://www.ieee.org/publications_standards/publications/rights/index.html for more information.
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/JESTPE.2021.3101123, IEEE Journal
of Emerging and Selected Topics in Power Electronics
3
Fig. 2: ST configuration.
TABLE I: ST notations.
Notation Description
ωg/ω∗Grid/reference frequency
ωpll/ωf ,pll PLL/filtered frequency
SnST capability
VgGrid voltage
Vpsc/Vssc MVAC/LVAC voltage
Vdcm/Vdcl MVDC/LVDC voltage
V∗
psc/V∗
ssc MVAC/LVAC voltage ref
V∗
dcm/V∗
dcl MVDC/LVDC voltage ref
Ipsc/Issc PSC/SSC output current
I∗
psc/I∗
ssc PSC/SSC current ref
Imvdc/Ilv dc MVDC/LVDC current to ST
Ppsc/Pssc Converted power in PSC/SSC
Pdab Converted power in DAB
P∗
psc/Q∗
psc PSC power reference
mpsc/mdab /mssc PSC/DAB/SSC modulation
Lpsc/rpsc and Lssc /rssc/Cssc PSC and SSC filter
Cdcm/Cdcl Capacitor at MVDC/LVDC
nDAB Transformer ratio
fmDAB Transformer frequency
LmDAB Transformer inductance
Kp,pll/Ki,pll PLL parameter P/I
Kp,dc/Ki,dc DAB voltage controller P/I
Kpv,psc/Kiv ,psc SSC voltage controller P/I
Kpc,psc/Kic,psc PSC current controller P/I
Kpc,ssc/Kic,ssc SSC current controller P/I
Kvand Kd/KmVoltage and frequency support gain
LPfLow pass filter gain
−CdcmVdcm ˙
Vdcm =Ppsc + (Vd,pscId,psc +Vq,psc Iq,psc ).
The basic control of the PSC is to maintain the synchroniza-
tion at the PCC at the MVAC side by means of a Phase-Locked
Loop (PLL):
˙
δpll = ∆ωpll ,
ωpll =Kp,pll∆ωpll +µpll ,
˙µpll =Ki,pll∆ωpll ,
∆ωpll =ωg−ωpll ,
(3)
and to regulate the voltage at the MVDC side:
P∗
psc =−Kp,dcm(V∗2
dcm −V2
dcm) + Ki,dcm γdcm −Ppsc ,
˙γdcm =V∗2
dcm −V2
dcm .(4)
The PSC itself uses the outer power inner current control
which is defined by:
I∗
d,psc =P∗
psc/V ∗
psc ,and I∗
q,psc =−Q∗
psc/V ∗
psc ,(5)
to determine the modulation, which links to the electric circuit
model, as follows:
0.5Vdcmmd,psc =Kpc,psc (I∗
d,psc −Id,psc)
+Kic,pscd,psc −ωpll Lpsc Iq,psc ,
0.5Vdcmmq,psc =Kpc,psc (I∗
q,psc −Iq,psc )
+Kic,pscq,psc +ωpllLpsc Id,psc ,
˙d,psc =I∗
d,psc −Id,psc ,
˙q ,psc =I∗
q,psc −Iq,psc .
(6)
The system service provided by the PSC is to support
the MVAC voltage at the PCC by means of reactive power
compensation:
Q∗
psc =qSn
2−P∗2
psc(V∗
psc −Vd,psc
V∗
psc
)Kv.(7)
Note that the principal role of the PSC is to deliver the active
power. Thus, the reactive power compensation is limited by
the PSC capacity, which determines the power reference of
the PSC basic control.
B. MVDC-LVDC Dual-Active Bridge Model
The MVDC-LVDC converter or DAB reduces the voltage
level and integrates the DC sources and loads. The electric
circuit in this stage includes the power exchange at the MVDC
side amongst the PSC, DAB and the MVDC sources and loads:
Ppsc =ImvdcVdcm +Pdab ,(8)
and the voltage reduction via a high/medium-frequency trans-
former:
Cdcl ˙
Vdcl =mdab(1 −mdab )n Vdcm
2fmLm
−Pdab
Vdcl
.(9)
Authorized licensed use limited to: Xinjiang University. Downloaded on December 16,2021 at 07:03:26 UTC from IEEE Xplore. Restrictions apply.
2168-6777 (c) 2021 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission. See http://www.ieee.org/publications_standards/publications/rights/index.html for more information.
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/JESTPE.2021.3101123, IEEE Journal
of Emerging and Selected Topics in Power Electronics
4
The basic control of the DAB is to regulate the voltage at
the LVDC side:
mdab =Kp,dcl(V∗
dcl −Vdcl) + Ki,dcl γdcl ,
˙γdcl =V∗
dcl −Vdcl .(10)
The service of the DAB is to support the LVDC voltage by
means of droop control for the purpose of bidirectional power
flow among the subsystems at the LVDC side:
V∗
dcl =Vdcl,max −KdabIlv dc .(11)
C. LVDC-LVAC Secondary Side Converter Model
The SSC links to the distribution system. Its purpose is to
form the distribution system via an active voltage control. The
electric circuit in this stage includes the power exchange at the
LVDC side amongst the DAB, SSC and the LVDC sources and
loads:
Pdab =IlvdcVdcl +Pssc ,(12)
the power conversion from the LVDC to the LVAC via the
converter modulation and the LC-filter:
Lssc ˙
Id,ssc = 0.5Vdclmd,ssc −Vd,ssc
+ωLssc Iq,ssc −rssc Id,ssc ,
Lssc ˙
Iq,ssc = 0.5md,sscVdcl −Vq ,ssc
−ωLssc Id,ssc −rsscIq ,ssc ,
Cssc ˙
Vd,ssc =Id,ssc −Id,lvac +ωCssc Vq,ssc ,
Cssc ˙
Vq,ssc =Iq,ssc −Iq,lvac −ωCssc Vd,ssc
(13)
and the power exchange at the PCC with the entire prosumers
in the distribution system.
The basic control of the SSC is to regulate the LVAC voltage
to determine the modulation and thus, linking to the electric
circuit model. It utilizes the outer voltage control:
I∗
d,psc =Kpv,ssc(V∗
d,ssc −Vd,ssc) + Kiv,sscγd,ssc
−ωCssc Vq,ssc ,
I∗
q,psc =Kpv,ssc (V∗
q,ssc −Vq,ssc ) + Kiv,ssc γq,ssc
+ωCssc Vd,ssc ,
I∗2
m,ssc ≥I∗2
d,ssc +I∗2
q,ssc ,
˙γd,ssc =V∗
d,ssc −Vd,ssc ,
˙γq,ssc =V∗
q,ssc −Vq,ssc .
(14)
and the inner current control:
0.5Vdclmd,ssc =Kpc,ssc (I∗
d,ssc −Id,ssc)
+Kic,sscd,ssc −ωLsscIq ,ssc ,
0.5Vdclmq,ssc =Kpc,ssc(I∗
q,ssc −Iq,ssc )
+Kic,sscq,ssc +ωLssc Id,ssc ,
˙d,ssc =I∗
d,ssc −Id,ssc ,
˙q ,ssc =I∗
q,ssc −Iq,ssc .
(15)
The SSC supports the frequency of the utility grid by the
means of demand control [8]. The load in general is sensitive
to the voltage and using this feature, the SSC can indirectly
regulate demand, by actively regulating the LVAC voltage
according to the grid frequency and its rate of change. This
can be implemented as a higher level control which determines
the voltage reference for its basic voltage control. A filter and
a dead-band on the frequency measurement is considered to
avoid problems with measurement noise. This can be described
by the following equations:
˙ωf,pll =−LPfωf,pll +LPfωf,
V∗
d,ssc = (ωf,pll −ω∗)Kd+ ˙ωf,pllKm+V∗
ssc .(16)
Equations (1)-(16) represent the complete 19th-order DAE
model of the ST.
D. Model Validation via Hardware Experiment
The full-order DAE ST model is validated via a hardware
experiment based on the OPAL-RT platform. A down-scaled
220 V AC to 520 V DC to 245 V AC three phase 2-stage back-
to-back converter is utilized in this experiment. The parameters
of the hardware setup are given in Table II. The corresponding
DAE model is built in Matlab/Simulink. The contingencies are:
(i) a grid frequency drop from 50 Hz to 49 Hz with 1 Hz/s
ramp at 7 s and following recovery at 10.5 s with 0.5 Hz/s
ramp; (ii) a grid voltage step reduction from 1 pu to 0.95 pu
at 14.5 s and following recovery to 1 pu at 16 s.
TABLE II: ST hardware set-up.
Parameter Value
PWM rate 1350
Sn1500 VA
Kpc,psc/Kic,psc 331/1700
Kp,pll/Ki,pll 0.73/13
Lssc/rssc 33 mH/0.12 Ω
Kpc,ssc/Kic,ssc 331/1700
Kv/Kd/Km53/3.9/24.5
Sampling time 14.5µs
Lpsc/rpsc 33 mH/0.12 Ω
Kp,dc/Ki,dc 0.02/0.005
Cdc 1.4mF
Cssc 80 µF
Kpv,ssc/Kiv ,ssc 0.27/300
Loading 163Ω/phase
Figure 3 shows that the DAE model captures the power
variations at the PCC of the PSC accurately. However, since
the converter switching dynamics are neglected, the DAE
model cannot reflect the harmonics at the PWM frequency.
For the downstream subsystems, it is more relevant to ob-
serve the supply voltages, i.e., DC voltage and LVAC voltage,
which are shown in Fig. 4. The DAE model presents the DC
voltage transients during the active and reactive power change
at the AC sides. This transient cannot be well observed in
the hardware results due to the harmonics at PWM frequency.
On the other hand, the DAE model accurately captures the
voltage variation at the AC side of the SSC. Note that the
reactive power compensation of the PSC only has an impact
on the DC voltage but not on the AC voltage of SSC.
E. Model Validation via Simulation
Due to limitations in accessing a fully functional 3 stage
SST prototype, the hardware validation experiment only used
Authorized licensed use limited to: Xinjiang University. Downloaded on December 16,2021 at 07:03:26 UTC from IEEE Xplore. Restrictions apply.
2168-6777 (c) 2021 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission. See http://www.ieee.org/publications_standards/publications/rights/index.html for more information.
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/JESTPE.2021.3101123, IEEE Journal
of Emerging and Selected Topics in Power Electronics
5
6
8 10 12 14 16
400
500
600
700
Time (s)
PSC Active Power (W)
hardware test
full-order DAE
6
8 10 12 14 16
0
200
400
600
800
Time (s)
PSC Rective Power (Var)
hardware test
full-order DAE
drop from 50Hz
to 49Hz @ 1Hz/s
recover
drop from
1 pu to 0.95 pu
recover
Fig. 3: Validation of the detailed ST model: power exchange with the
grid.
6 8 10 12 14 16
518
520
522
Time (s)
DC Voltage (V)
hardware test
full-order DAE
6 8 10 12 14 16
200
220
240
260
280
Time (s)
SSC Voltage (V)
hardware test
full-order DAE
Fig. 4: Validation of the detailed ST model: voltage regulation.
a 2-stage ST. For a further validation, a 3-stage ST EMT model
is built in Matlab/Simulink, the parameters for which are given
in Table IV. The time step of the simulation is 0.1 us and the
switching frequency of the PSC, DAB and SSC are 1650 Hz,10
kHz and 6.3 kHz respectively. The ST experiences an LVAC
load change from 33 Ωto 16.5 Ωat 2 s, an MVAC current
change from 0 A to -0.06 A at 2.5 s and an LVAC current
change from 0 A to 1.5 A at 3 s.
Figure 5 compares the result from the EMT model and the
DAE model. The DAE model can represent the EMT model
to a certain accuracy as shown by comparing the results of the
MVAC power, MVDC voltage and LVDC voltage in regardless
of the PWM harmonics.
III. APP ROX IMATE D ST MO DEL S
Depending on the time constant of the current controllers,
the time step to properly integrate the full-order ST has to
be in the range of 10 to 100 µs. This leads to a heavy
computational burden when considering angle and voltage
transient stability studies that typically require simulating
2 2.5 3 3.5
Time (s)
4
6
8
10
MVAC Power (kW)
EMT result
full-order DAE
2 2.5 3 3.5
Time (s)
16.9
16.95
17
17.05
MVDC Voltage (kV)
EMT result
full-order DAE
2 2.5 3 3.5
Time (s)
790
800
810
LVDC Voltage (V)
EMT result
full-order DAE
Fig. 5: Comparison of response from EMT model and full order DAE
model of a 3 stage SST for setpoint changes.
several seconds especially in the case of large systems with
multiple STs.
The computation burden can be decreased by reducing
the dynamic order of the ST model with respect to the
system dynamic response (see relevant time scales in Fig. 6).
Depending on the focus of study, some of the ST controls
can be assumed to be ideal, and thus, its dynamic can be
neglected. For example, if one is interested in the system
inertial response, the ST current controller transients can be
neglected. In the same vein, if the interest is in the system
primary response, then only ST higher level controllers and
services need to be retained in the model.
Parameter sensitivity is a method which can be used to iden-
tify the dependence of the ST model dynamics on the various
parameters of the model for any given dynamic response under
evaluation.
Let us consider the following sensitivities:
Sp=
∆P
∆Ψ
=
PΨ,t −P0,t
0.1P0,t
,(17)
Sq=
∆Q
∆Ψ
=
QΨ,t −Q0,t
0.1Q0,t
,(18)
Where Ψrepresents the parameter of interest, P0,t, Q0,t are
the grid power exchange from the ST at the time tusing the
original parameters, whereas PΨ,t, QΨ,t are the powers at the
same time tas obtained by increasing parameter Ψby 10%.
Based on the ST setup used in the hardware experiment,
Fig. 7 shows which parameters the response is most sensitive
to at 1 ms, 10 ms and 100 ms respectively, following a grid
voltage sag of 0.5 pu (graph on the left) or a grid frequency
drop to 49.5 Hz (graph on the right). For the PI parameters,
here we only show the sensitivity result of the proportional
gain.
Authorized licensed use limited to: Xinjiang University. Downloaded on December 16,2021 at 07:03:26 UTC from IEEE Xplore. Restrictions apply.
2168-6777 (c) 2021 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission. See http://www.ieee.org/publications_standards/publications/rights/index.html for more information.
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/JESTPE.2021.3101123, IEEE Journal
of Emerging and Selected Topics in Power Electronics
6
Figure 7 shows that, as expected, faster control dynamics
can be neglected as the time scale increases. At 1 ms, the ST
dynamics is mainly from the PSC current controller, not from
the SSC. This is because the filter and dead-band of the SSC
demand control do not initially allow the state of the SSC
to vary. As the time scale increases, the effect of the current
control dynamics weakens and that of the voltage controller
dynamics increases as does the demand control. At 100 ms,
fast ST dynamics are less relevant and the effect of the services
on ST transient response becomes visible. On the other hand,
Time60-200 ms 5 s30 s15 m in
Prim ary
Response
Secondary
R esponse
Inertia
Response
Tertiary
R esponse
Fault
Power
(a) Power system
Time
0.5-5 ms 10-50 ms
Power
ST service
V SC Current C ontrol
D A B voltage control
SS C V oltage Control
PS C V oltage Control
>50ms
(b) Smart transformer
Fig. 6: Transient response time scales of interest.
(a) Parameter sensitivity at 1 ms
(b) Parameter sensitivity at 10 ms
(c) Parameter sensitivity at 100 ms
∆Ψ = ΔV𝑔
∆Ψ = Δω𝑔
𝑆𝑝
𝑆𝑞
Fig. 7: Smart transformer parameter sensitivity
the transients of the SSC and PSC are decoupled.
The response to the voltage sag is mainly from the PSC with
DC voltage control and voltage support, whereas the response
to the grid frequency drop is from the SSC with demand
control and SSC voltage control. Note that the demand control
changes the ST power flow resulting in the PCC voltage varia-
tion, thus, activating the voltage support. From this parameter
sensitivity analysis, the model can be simplified based on the
time scale of research interest. These approximated models are
presented in the remainder of this section.
A. Approximated Model based on Time Scales
If the time scale of interest is 10 ms, i.e., fast frequency
response, the transients of the current controllers and DAB
voltage controller are negligible as well as line and filter
transients. The relevant models at PSC stage (1)(2)(6), DAB
stage (8)(9) and at SSC stage (13)(15) can be simplified as
follows:
Pg=Vgcos(δg−δpll)I∗
d,psc +Vgsin(δg−δpll)I∗
q,psc ,
Qg=Vgsin(δg−δpll)I∗
d,psc −Vgcos(δg−δpll)I∗
q,psc ,
Vd,psc =Vgcos(δg−δpll)−ωgLgI∗
q,psc ,
Vq,psc =Vgsin(δg−δpll ) + ωgLgI∗
d,psc ,(19)
−CdcmVdcm ˙
Vdcm = (Vd,pscI∗
d,psc +Vq,pscI∗
q,psc) + Ppsc ,
(20)
Vdcl =V∗
dcl ,(21)
Cssc ˙
Vd,ssc =I∗
d,psc −Id,lvac +ωCssc Vq,ssc ,
Cssc ˙
Vq,ssc =I∗
q,psc −Iq,lv ac −ωCssc Vd,ssc .(22)
If the time scale of interest is 100 ms, i.e., primary response,
all the converter related transients are negligible and only the
transients of ST service need to be captured. Based on the
above 10 ms model, PSC and SSC voltages are assumed to
track their references instantaneously:
Vdcm =V∗
dcm ,(23)
and
Vd,ssc =V∗
d,ssc;Vq,ssc =V∗
q,ssc .(24)
The set of equations of the approximated ST models for
the 10 ms and 100 ms time scales are summarized in Table
III. The time step indicated in the last row of the table is set
as 1/10 of the smallest time constant of the controller in the
model.
TABLE III: Summary of the ST models.
ST Stage Full model 10 ms model 100 ms model
PSC (1)-(7) (3)-(5),(7),(19),(20) (5),(7),(19),(20),(23)
DAB (8)-(11) (8),(11),(21) (8),(11)(21)
SSC (12)-(16) (12),(14),(16),(22) (12),(16),(24)
Time step 0.1 ms 1 ms 10 ms
Authorized licensed use limited to: Xinjiang University. Downloaded on December 16,2021 at 07:03:26 UTC from IEEE Xplore. Restrictions apply.
2168-6777 (c) 2021 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission. See http://www.ieee.org/publications_standards/publications/rights/index.html for more information.
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/JESTPE.2021.3101123, IEEE Journal
of Emerging and Selected Topics in Power Electronics
7
B. Approximated Model based on Research Focus
Only the active power is passed from one port to another
in the ST while the reactive power in each port is decoupled
as are the voltages. It can be seen in Fig. 4 and Fig. 5 that
the DC voltage has a transient response to the power variation
but this transients barely affect the response of the PSC at
the MVAC side. Due to this feature, according to the research
focus, only the ST stage of interest to the study needs to be
precisely modelled while other stages may be simplified or
even neglected.
For example, in Fig. 7, when the grid voltage sags, the
functional stage is the PSC while the SSC barely reacts. In
this case, the model of the SSC could be neglected. However,
when the grid frequency drops, the functional stage is the SSC,
while the PSC only needs to detect the frequency via the PLL.
In this case, the model of the PSC may be simplified.
Here we should highlight that a precondition of the model
simplification in a particular stage is that the operation of the
other stages is stable. Otherwise the voltage of the unstable
converter collapses and its power oscillates, so that this oscil-
lating power will affect the stage of interest and its dynamic
response. If there are doubts regarding stability of any stage
then a full model must be used.
IV. USE CA S ES
This section defines the use cases of the ST models pro-
posed in this paper. These consider the following scenarios:
faults, power exchange and provision of system services. A 3-
stage ST model built in Matlab/Simulink is utilised to obtain
simulation results. The complete set of parameters of the ST
is given in Table IV, where a large grid impedance is selected
here in order to purposely trigger the transient instability of the
ST during the fault; a large filter of the PSC is then selected for
a stable operation under the normal conditions; the parameters
of the PI controller in the outer voltage and inner current are
set up based on reference [25].
A. Fault Response
According to grid codes, a fault should be cleared within 40
to 100 ms. The response of the converter to the fault is very
fast, on the order of ms. The synchronization stability analysis
of the converter consists in identifying whether the converter
can ride through the fault. This section discusses the accuracy
of the three ST models of Table III following a fault occurring
in either the transmission or the distribution system.
1) Fault in the Transmission System: In this scenario, the
fault occurs at the transmission side, i.e., the grid voltage sags
from 1 pu to 0.34 pu at 2 s. Figure 8 shows the active power
response of the ST at the MVAC side in the first 100 ms
after the fault. The full model shows a peak power at the
instant of the fault and an unstable response after, while the
simplified models fail to capture such instability but represent
a stable response. This is because although the PSC uses
constant power control, ultimately it is a voltage source con-
verter, whose terminal voltage cannot change instantaneously
following the fault occurrence. This give raise to a high fault
current and a peak power. In this case, neglecting the converter
TABLE IV: ST parameters and settings.
Parameter Value
V∗
psc 10 kV
V∗
dcl 800 V
Sn 50 MVA
Kpc,psc/Kic,psc 2000 / 20000
Kp,pll/Ki,pll 0.022 / 0.39
K/fm/Lm20/10 kHz / 15 mH
Lssc/rssc 6.9 mH / 0.012 Ω
Kpc,ssc/Kic,ssc 69 / 553
Kv/Kdab 0.0000059 / 5
V∗
dcm 17 kV
V∗
ssc 330 V
Lg/Lpsc/rpsc 0.5 H / 1 H / 0.1 Ω
Kp,dc/Ki,dc 0.001 / 0.0002
Cdcm/Cdcl 13.6 µF / 0.2 mF
Kp,dcl/Ki,dcl 0.41 / 0.15
Cssc 0.2 mF
Kpv,ssc/Kiv ,ssc 1 / 1100
Kd/Km/LPf0.05 / 0.05 / 628
Initial Value
P∗
psc/Q∗
psc -4.1 MW / 0 MW
Ilvdc 1 A
Imvdc 2 A
loading 26 Ω
current controller dynamics results in an inaccurate transient
behavior of the ST. Comparing with the 10 ms model, the 100
ms model only captures the PLL dynamics at the instant of
the fault occurrence and, thus, reaches the steady-state faster
than the 10 ms model.
2 2.02 2.04 2.06 2.08 2.1
−50
0
50
MVAC Power (kW)
Time (s)
full model
10 ms model
100 ms model
Fig. 8: Transmission system fault: time-scale model comparison.
The response of the ST with respect to the fault in the
transmission system is mainly due to the PSC transients, thus,
the DAB and SSC model can be simplified. Figure 9 shows
the ST response using a detailed PSC model and simplified
SSC and DAB models. Since the PSC model is not simplified,
all models show the same response on the active power at the
MVAC side and the voltage at the MVDC as shown in the
first and second panels of Fig. 9. Neglecting the dynamic of
the DAB voltage in the model “DAB 100 ms mode” worsens
the accuracy at the LVDC side. The LVDC voltage, in fact,
fails to capture the oscillations due to the instability of the
PSC. The simplification of the SSC and DAB models make
them unable to capture the interactions among the ST stages
as shown in the lower panel of Fig. 9. These interactions, in
fact, depend on the filter capacitance on the MVDC, LVDC
and LVAC ports.
Since the instability is attributed to the PSC at the MVAC
Authorized licensed use limited to: Xinjiang University. Downloaded on December 16,2021 at 07:03:26 UTC from IEEE Xplore. Restrictions apply.
2168-6777 (c) 2021 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission. See http://www.ieee.org/publications_standards/publications/rights/index.html for more information.
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/JESTPE.2021.3101123, IEEE Journal
of Emerging and Selected Topics in Power Electronics
8
side, the DAB and SSC lose stability stage by stage in
sequence as shown in Fig. 9. During this process, as long
as the modulation does not hit the limitation, the downstream
converter is in the control. Thus, the LVDC and LVAC voltage
are still in a safe operation range even the MVAC and MVDC
voltage collapsed. As a consequence, the transient power
delivered through DAB, Pdab, barely has an effect on the PSC,
that is the reason that “DAB 100 ms model”, although loses
the accuracy and shows a fixed voltage response at the LVAC
and LVDC side, still can capture the response at the MVDC
and MVAC side similar to the full model. In this situation, if
the focus is solely on the transmission system over a small-
time scale, the ST can be modelled by a detailed PSC with
a constant Pdab to represent the total loading from the DAB.
However, over a longer time, when the corresponding port
voltage collapses, the power would change significantly, and
then the full model must be used for a precise reflection of
ST dynamics.
2 2.02 2.04 2.06 2.08 2.1
−50
0
50
MVAC Power (kW)
Time (s)
full model
SSC 10 ms model
SSC 100 ms model
DAB 100 ms model
2 2.02 2.04 2.06 2.08 2.1
10
12
14
16
MVDC Voltage (kV)
Time (s)
full model
SSC 10 ms model
SSC 100 ms model
DAB 100 ms model
2 2.02 2.04 2.06 2.08 2.1
745
750
755
LVDC Voltage (V)
Time (s)
full model
SSC 10 ms model
SSC 100 ms model
DAB 100 ms model
2 2.02 2.04 2.06 2.08 2.1
329.98
329.99
330
330.01
LVAC Voltage (V)
Time (s)
full model
SSC 10 ms model
SSC 100 ms model
DAB 100 ms model
Fig. 9: Transmission system fault: stage model comparison.
2) Fault in the Distribution System: In this scenario, the
fault occurs at the distribution system side. The loading
impedance changes from 26 Ωto 1 Ω. The current limiter
is set to be 30 A. Figure 10 shows the voltage response of the
ST at the LVAC side and the active power at the MVAC side.
Both the full-order model and the 100 ms model show the
LVAC voltage sag following the fault occurrence. Neglecting
the voltage controller dynamics leads to an inaccurate ST
response, because the current limiter is also neglected. On the
other hand, the high power at the instant of the fault occurrence
is due to the constant SSC voltage. If the LVAC voltage
decreases, the total ST power consumption also decreases.
2 2.05 2.1 2.15 2.2 2.25 2.3
0
100
200
300
LVAC Voltage (V)
Time (s)
full model
10 ms model
100 ms model
2 2.05 2.1 2.15 2.2 2.25 2.3
−50
−45
−40
−35
MVAC Power (kW)
Time (s)
full model
10 ms model
100 ms model
Fig. 10: Distribution system fault: time-scale model comparison.
The stage of the ST that is most sensitive to a fault in the
distribution system side is the SSC. Hence the models of the
other stages can be simplified. Figure 11 shows the response
of the ST with full-order SSC model and simplified models
for the PSC and DAB. The results show that as long as the
SSC part is accurately modeled, the LVAC voltage dynamics
can be precisely captured regardless of the modeling of the
other stages. Thus, if the research interest is solely on the
distribution system, the ST can be modelled by a detailed
SSC. However, an accurate DAB model can capture the LVDC
voltage dynamics due to the transient power exchange amongst
DAB and SSC.
B. DC Power Exchange
The ability to regulate the power exchange among the ST
subsystems is a relevant feature of the ST. A proper ST model
has to precisely capture its dynamic behavior during these
power exchanges. Since the power exchange initiated at the
AC ports is discussed in Section IV-C, this section focuses on
the DC power exchange.
Figure 12 shows the ST transient response following a step
increase of the LVDC loading from 1 A to 4 A at 2 s and a
step decrease of the MVDC loading current from 2 A to 1.8
A. Due to the fast reaction of the DAB voltage controller, the
DC power exchange only introduces a small disturbance and
these transients damps quickly within 50 ms. As long as the
DAB voltage controller is precisely modeled, the ST transients
can be well captured regardless the modeling of the SSC and
PSC stages.
C. ST Services
The conventional primary frequency and voltage control
of synchronous machines is in the time scale of seconds.
Correspondingly, the model of the ST for the system services
only needs to retain the dynamics in the time scale of seconds.
This subsection presents the ST model aimed at retaining
the dynamics of the primary frequency and voltage support,
respectively.
Authorized licensed use limited to: Xinjiang University. Downloaded on December 16,2021 at 07:03:26 UTC from IEEE Xplore. Restrictions apply.
2168-6777 (c) 2021 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission. See http://www.ieee.org/publications_standards/publications/rights/index.html for more information.
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/JESTPE.2021.3101123, IEEE Journal
of Emerging and Selected Topics in Power Electronics
9
2 2.05 2.1 2.15 2.2 2.25 2.3
0
100
200
300
LVAC Voltage (V)
Time (s)
full model
PSC 10 ms model
PSC 100 ms model
DAB 100 ms model
2 2.02 2.04 2.06 2.08 2.1
650
700
750
800
LVDC Voltage (V)
Time (s)
full model
PSC 10 ms model
PSC 100 ms model
DAB 100 ms model
2 2.02 2.04 2.06 2.08 2.1
16.98
16.99
17
17.01
17.02
MVDC Voltage (kV)
Time (s)
full model
PSC 10 ms model
PSC 100 ms model
DAB 100 ms model
2 2.02 2.04 2.06 2.08 2.1
−50
−45
−40
−35
MVAC Power (kW)
Time (s)
full model
PSC 10 ms model
PSC 100 ms model
DAB 100 ms model
Fig. 11: Distribution system fault: stage model comparison.
1) Frequency Support: In this scenario, a grid frequency
drop from 50 Hz to 49 Hz occurs at 2 s with 1 Hz/s ramp.
From the grid point of view, only the active power at the
MVAC bus of the ST is of interest. Figure 13 shows that the
active power responses for all ST models are identical. This is
because the power change is smooth and, thus, the dynamics
of the ST current and voltage controllers are immaterial
and can be neglected. Note that the power does not change
instantaneously following the frequency variation because of
the dead-band and low-pass filter in the ST demand control.
2) Voltage Support: In this scenario, a grid voltage drop
from 1 pu to 0.95 pu occurs at 2 s. From the grid point of
view, only the reactive power at the MVAC bus of the ST is
of interest. Figure 14 shows that the reactive power response
of the different ST models is significantly different only in the
first 100 ms after the voltage drop. The transient response of
these models in the first 100 ms is similar to that of a fault on
the transmission system side, where the PSC must be precisely
modeled. However, in this case, the time scale of interest is of
the order of seconds and, thus, the differences in the first 100
ms is negligible. This makes the 100 ms ST model adequate
for this use case.
V. CA SE STU DY
The main purpose of the ST models proposed in this paper is
for the analysis of power system transients. With this aim, this
case study considers different ST models in a modified New
2 2.05 2.1 2.15 2.2 2.25 2.3 2.35 2.4
39
40
41
42
43
44
MVDC Power (kW)
Time (s)
full model
100 ms model
1 s model
DAB 1 s model
2 2.05 2.1 2.15 2.2 2.25 2.3 2.35 2.4
7
7.5
8
8.5
9
9.5
LVDC Power (kW)
Time (s)
full model
100 ms model
1 s model
DAB 1 s model
2 2.05 2.1 2.15 2.2 2.25 2.3 2.35 2.4
700
720
740
LVDC Vo ltage (V)
Time (s)
full model
FSC 100 ms model
FSC 1 s model
DAB 1 s model
full model
PSC 10 ms model
PSC 100 ms model
DAB 100 ms model
full model
PSC 10 ms model
PSC 100 ms model
DAB 100 ms model
full model
PSC 10 ms model
PSC 100 ms model
DAB 100 ms model
Fig. 12: DC power exchange: time-scale and stage model comparison.
2 2.2 2.4 2.6 2.8 3
−41
−40.5
−40
MVAC Power (kW)
Time (s)
full model
10 ms model
100 ms model
Fig. 13: ST frequency support: time-scale model comparison.
England 39-bus system, where 40% of the load is assumed
to be connected to the grid through four STs at buses 4, 8,
20 and 39, as shown in Fig. 15. The New England 39-bus
system includes Automatic Voltage Regulations (AVRs) and
Turbine Governor (TG) for each synchronous machine [15].
The loads are modeled as voltage dependent with its exponent
in the range of 0.1 to 1.5.
In accordance with the use case of the model defined
in Section IV, the case study considers three scenarios: a
fault, a DC generation increase, and a generator outage. All
simulations in this section are solved with DO ME, a Python-
based power system software tool [26]. Simulations are carried
out with a Dell Inspiron with 4 Intel Core i5 2.5 GHz. The
computation time of the full, 10-ms and 100-ms models for the
fault scenario are 197.8 s, 23.65 s and 3.131 s, respectively.
2 2.2 2.4 2.6 2.8 3
0
0.2
0.4
0.6
0.8
MVAC Power (kVar)
Time (s)
full model
100 ms model
1 s model
full model
10 ms model
100 ms model
Fig. 14: ST voltage support: time-scale model comparison.
Authorized licensed use limited to: Xinjiang University. Downloaded on December 16,2021 at 07:03:26 UTC from IEEE Xplore. Restrictions apply.
2168-6777 (c) 2021 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission. See http://www.ieee.org/publications_standards/publications/rights/index.html for more information.
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/JESTPE.2021.3101123, IEEE Journal
of Emerging and Selected Topics in Power Electronics
10
DC
DC
DC
DC
33
30
15
16
31
24
11
6
38
Gen 3
7
Gen 2
32
Gen 6
35
Gen 1
39
37
Gen 8
25 26 28 29
27
17 Gen 9
21
183
1
2
12
13
10
9
8
5
14
19
23
22
36
Gen 10 4
ST1
ST2
34
20
Gen 4
Gen 7
Gen 5
ST3
ST4
Fig. 15: Modified New England 39-bus system.
A. Scenario 1: Fault
This scenario considers a fault on line 1-2 occurring at
1 s and cleared in 40 ms. Figure 16 shows the response of
the power of ST4 and the system response, namely the grid
frequency and the voltage at bus 39. At the instants of the fault
occurrence and clearance, the full model shows a transient
peak in the power. These peaks corresponds to voltage tran-
sients at ST PCC buses. However, this phenomenon can only
be captured via the full model. The simplified models cannot
reproduce these transients as they do not retain the dynamics
of converter currents. On the other hand, the response of the
system frequency is similar for the three models as it is mainly
driven by the synchronous machines and their controllers.
B. Scenario 2: ST DC power generation
This scenario considers the DC current of the STs following
a DC power generation step increase from 0 to 1 pu at 1 s.
Figure 17 shows the ST4 power response, the grid frequency
and the voltages bus 39. As shown in the use case of DC power
exchange in Section IV-B, the transients of the DC power is
very small and damps quickly. The power decrease following
the current step change is due to the ST demand control in
response to the frequency increase. The system frequency and
voltage response are similar and independent from the ST
model.
C. Scenario 3: Generator Outage
This scenario considers the outage of the generator at bus
34 at 1 s. Figure 18 shows the grid frequency and the voltage
at Bus 39. Similarly to the use case discussed in Section IV-C,
all ST models are equivalent in the time scale of frequency
and voltage stability analysis. This means that the simplest ST
model can be utilized without loss of information.
0.95 1 1.05 1.1 1.15
Time [s]
8.5
9.0
9.5
10.0
10.5
11.0
11.5
12.0
12.5
ST 4 MVAC Power [pu(MW)]
full model
10 ms model
100 ms model
0.95 1 1.05 1.1 1.15
Time [s]
0.80
0.85
0.90
0.95
1.00
1.05
1.10
1.15
Bus 39 voltage [pu(kV)]
full model
10 ms model
100ms model
0246810
Time [s]
49.998
50.000
50.002
50.004
50.006
50.008
grid frequency [Hz]
full model
10 ms model
100 ms model
Fig. 16: New England 39-bus system, Scenario 1: fault.
VI. CO N CL USI ON
This paper proposes a 3×3set of ST models according to
the time scales, and classifies these models based on a set of
use cases. The following relevant conclusions are supported
by simulation results.
•For the analysis of the transients following a fault occur-
ring in the transmission system, the PSC of the ST must
be precisely modelled. A simplification of the PSC cur-
rent dynamics erroneously increases the ST operational
region and fails to capture the voltage transients. On the
other hand, the DAB and SSC model can be simplified or
even neglected, depending on the fault duration without
loss of accuracy, if the LVDC and LVAC voltage is not
of interest.
•For the analysis of the transients following a fault oc-
curring in the distribution system, the SSC of the ST
must be precisely modelled. A simplification of the SSC
current dynamics disables the current limitation thus fails
to capture the voltage transients. On the other hand, the
PSC and DAB model can be neglected without loss of
accuracy, if the LVDC, MVDC and MVAC voltage are
not of interest.
•The simplest ST model is adequate for frequency and
voltage stability analysis.
Authorized licensed use limited to: Xinjiang University. Downloaded on December 16,2021 at 07:03:26 UTC from IEEE Xplore. Restrictions apply.
2168-6777 (c) 2021 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission. See http://www.ieee.org/publications_standards/publications/rights/index.html for more information.
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/JESTPE.2021.3101123, IEEE Journal
of Emerging and Selected Topics in Power Electronics
11
0 10 20 30 40 50
Time [s]
11.0
11.5
12.0
12.5
13.0
13.5
14.0
14.5
ST 4 MVAC Power [pu(MW)]
full model
10 ms model
100 ms model
0 10 20 30 40 50
Time [s]
1.028
1.029
1.030
1.031
1.032
1.033
Bus 39 voltage [pu(kV)]
full model
10 ms model
100 ms model
0 10 20 30 40 50
Time [s]
48.2
48.4
48.6
48.8
49.0
49.2
49.4
49.6
49.8
50.0
grid frequency [Hz]
full model
10 ms model
100 ms model
Fig. 17: New England 39-bus system, Scenario 2: DC generation.
REF ER E NC ES
[1] F. Milano, F. D ¨
orfler, G. Hug, D. J. Hill, and G. Verbiˇ
c, “Foundations
and challenges of low-inertia systems (invited paper),” in 2018 Power
Systems Computation Conference (PSCC), 2018, pp. 1–25.
[2] X. She, A. Q. Huang, and R. Burgos, “Review of solid-state transformer
technologies and their application in power distribution systems,” IEEE
Journal of Emerging and Selected Topics in Power Electronics, vol. 1,
no. 3, pp. 186–198, 2013.
[3] M. Liserre, G. Buticchi, M. Andresen, G. De Carne, L. F. Costa,
and Z. Zou, “The smart transformer: Impact on the electric grid and
technology challenges,” IEEE Industrial Electronics Magazine, vol. 10,
no. 2, pp. 46–58, 2016.
[4] A. Q. Huang, M. L. Crow, G. T. Heydt, J. P. Zheng, and S. J. Dale, “The
future renewable electric energy delivery and management (freedm)
system: The energy internet,” Proceedings of the IEEE, vol. 99, no. 1,
pp. 133–148, 2011.
[5] X. Yu, X. She, X. Zhou, and A. Q. Huang, “Power management for
dc microgrid enabled by solid-state transformer,” IEEE Transactions on
Smart Grid, vol. 5, no. 2, pp. 954–965, 2014.
[6] X. Gao, F. Sossan, K. Christakou, M. Paolone, and M. Liserre, “Con-
current voltage control and dispatch of active distribution networks
by means of smart transformer and storage,” IEEE Transactions on
Industrial Electronics, vol. 65, no. 8, pp. 6657–6666, 2018.
[7] Z. Zou, G. De Carne, G. Buticchi, and M. Liserre, “Smart transformer-
fed variable frequency distribution grid,” IEEE Transactions on Indus-
trial Electronics, vol. 65, no. 1, pp. 749–759, 2018.
[8] J. Chen, M. Liu, G. De Carne, R. Zhu, M. Liserre, F. Milano, and
T. O’Donnell, “Impact of smart transformer voltage and frequency
support in a high renewable penetration system,” Electric Power
Systems Research, vol. 190, p. 106836, 2021. [Online]. Available:
http://www.sciencedirect.com/science/article/pii/S0378779620306362
[9] G. De Carne, G. Buticchi, M. Liserre, and C. Vournas, “Load control
using sensitivity identification by means of smart transformer,” IEEE
Transactions on Smart Grid, vol. 9, no. 4, pp. 2606–2615, 2018.
0 10 20 30 40 50
Time [s]
1.027
1.028
1.029
1.030
1.031
1.032
1.033
Bus 39 voltage [pu(kV)]
full model
10 ms model
100 ms model
0 10 20 30 40 50
Time [s]
49.2
49.3
49.4
49.5
49.6
49.7
49.8
49.9
50.0
grid frequency [Hz]
full model
10 ms model
100 ms model
Fig. 18: New England 39-bus system, Scenario 3: system contingency.
[10] G. De Carne, M. Liserre, and C. Vournas, “On-line load sensitivity
identification in lv distribution grids,” IEEE Transactions on Power
Systems, vol. 32, no. 2, pp. 1570–1571, 2017.
[11] J. Chen, T. Yang, C. O’Loughlin, and T. O’Donnell, “Neutral current
minimization control for solid state transformers under unbalanced loads
in distribution systems,” IEEE Transactions on Industrial Electronics,
vol. 66, no. 10, pp. 8253–8262, 2019.
[12] J. Chen, R. Zhu, I. Ibrahim, T. O’Donnell, and M. Liserre, “Neutral
current optimization control for smart transformer-fed distribution sys-
tem under unbalanced loads,” IEEE Journal of Emerging and Selected
Topics in Power Electronics, vol. 9, no. 2, pp. 1696–1707, 2021.
[13] D. Shah and M. L. Crow, “Online volt-var control for distribution
systems with solid-state transformers,” IEEE Transactions on Power
Delivery, vol. 31, no. 1, pp. 343–350, 2016.
[14] G. De Carne, M. Langwasser, M. Ndreko, R. Bachmann, R. W.
De Doncker, R. Dimitrovski, B. J. Mortimer, A. Neufeld, F. Rojas,
and M. Liserre, “Which deepness class is suited for modeling power
electronics?: A guide for choosing the right model for grid-integration
studies,” IEEE Industrial Electronics Magazine, vol. 13, no. 2, pp. 41–
55, 2019.
[15] F. Milano, Power System Modelling and Scripting. London: Springer,
2010.
[16] F. Plumier, P. Aristidou, C. Geuzaine, and T. Van Cutsem, “Co-
simulation of electromagnetic transients and phasor models: A relaxation
approach,” IEEE Transactions on Power Delivery, vol. 31, no. 5, pp.
2360–2369, 2016.
[17] J. Chen, R. Li, A. Soroudi, A. Keane, D. Flynn, and T. O’Donnell,
“Smart transformer modelling in optimal power flow analysis,” in
IECON 2019 - 45th Annual Conference of the IEEE Industrial Elec-
tronics Society, vol. 1, 2019, pp. 6707–6712.
[18] J. Miao, N. Zhang, C. Kang, J. Wang, Y. Wang, and Q. Xia, “Steady-
state power flow model of energy router embedded ac network and its
application in optimizing power system operation,” IEEE Transactions
on Smart Grid, vol. 9, no. 5, pp. 4828–4837, 2018.
[19] T. Zhao, J. Zeng, S. Bhattacharya, M. E. Baran, and A. Q. Huang, “An
average model of solid state transformer for dynamic system simulation,”
in 2009 IEEE Power Energy Society General Meeting, 2009, pp. 1–8.
[20] A. A. Milani, M. T. A. Khan, A. Chakrabortty, and I. Husain, “Equi-
librium point analysis and power sharing methods for distribution
systems driven by solid-state transformers,” IEEE Transactions on Power
Systems, vol. 33, no. 2, pp. 1473–1483, 2018.
[21] Y. Tu, J. Chen, H. Liu, and T. O’Donnell, “Smart transformer modelling
and hardware in-the-loop validation,” in 2019 IEEE 10th International
Symposium on Power Electronics for Distributed Generation Systems
(PEDG), 2019, pp. 1019–1025.
[22] M. Lee, J. Kim, and J. Lai, “Small-signal modeling of three-level boost
rectifier and system design for medium-voltage solid-state transformer,”
Authorized licensed use limited to: Xinjiang University. Downloaded on December 16,2021 at 07:03:26 UTC from IEEE Xplore. Restrictions apply.
2168-6777 (c) 2021 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission. See http://www.ieee.org/publications_standards/publications/rights/index.html for more information.
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/JESTPE.2021.3101123, IEEE Journal
of Emerging and Selected Topics in Power Electronics
12
in 2019 10th International Conference on Power Electronics and ECCE
Asia (ICPE 2019 - ECCE Asia), 2019, pp. 1–7.
[23] Q. Ye, R. Mo, and H. Li, “Impedance modeling and dc bus voltage sta-
bility assessment of a solid-state-transformer-enabled hybrid ac–dc grid
considering bidirectional power flow,” IEEE Transactions on Industrial
Electronics, vol. 67, no. 8, pp. 6531–6540, 2020.
[24] M. T. A. Khan, A. A. Milani, A. Chakrabortty, and I. Husain, “Dynamic
modeling and feasibility analysis of a solid-state transformer-based
power distribution system,” IEEE Transactions on Industry Applications,
vol. 54, no. 1, pp. 551–562, 2018.
[25] A. Yazdani and R. Iravani, Voltage-Sourced Converters in Power Systems
: Modeling, Control, and Applications. New Jersy: John Wiley & Sons,
Inc., 2014.
[26] F. Milano, “A Python-based software tool for power system analysis,”
in IEEE PES General Meeting, 2013, pp. 1–5.
Junru Chen (S’17, M’20)received the ME and
Ph.D. degree in Electrical Energy Engineering from
University College Dublin in 2016 and 2019. He was
exchanging student at Kiel University (Germany)
in 2018 and at Tallinn University of Technology
(Estonia). He was a Senior Researcher in Univer-
sity College Dublin and visiting scholar in Aalborg
University (Denmark) in 2020. Since 2020 he is an
Associate Professor at Xinjiang University, China.
His current research interests include power elec-
tronics control, modeling, stability and application.
Muyang Liu (S’17, M’20) received the ME and
Ph.D. in Electrical Energy Engineering from Univer-
sity College Dublin, Ireland in 2016 and 2019. From
December 2019 to December 2020, she was a se-
nior researcher with University College Dublin. She
joined Xinjiang University, Urumqi, China in 2019
and is currently an Associate Professor in Electrical
Engineering. Her current research interests include
power system modeling and stability analysis.
Terence O’Donnell (M’95, SM’20) is an Associate
Professor in the School of Electrical and Electronic
Engineering, University College Dublin. He is a
principle investigator within the UCD Energy In-
stitute where his research interests are focused on
the use of power electronics converters in power
systems and in particular on the interfacing of power
electronics to the grid. Specific interests include
the grid applications of solid-state transformers, the
control of converters for distributed energy resources
and the use of power hardware in the loop testing
methods.
Federico Milano (S’02, M’04, SM’09, F’16) re-
ceived from the University of Genoa, Italy, the ME
and Ph.D. in Electrical Engineering in 1999 and
2003, respectively. From 2001 to 2002, he was with
the Univ. of Waterloo, Canada. From 2003 to 2013,
he was with the Univ. of Castilla-La Mancha, Spain.
In 2013, he joined the Univ. College Dublin, Ireland,
where he is currently Professor of Power Systems
Control and Protections. His research interests in-
clude power systems modeling, control and stability
analysis.
Authorized licensed use limited to: Xinjiang University. Downloaded on December 16,2021 at 07:03:26 UTC from IEEE Xplore. Restrictions apply.
