An integrated rule-based power
management and dynamic feed-forward
low voltage ride through scheme for a gridconnected hybrid energy system
Cite as: J. Renewable Sustainable Energy 12, 056303 (2020); https://doi.org/10.1063/5.0019254
Submitted: 23 June 2020 . Accepted: 19 September 2020 . Published Online: 19 October 2020
Amit Kumar Roy
, Gyan Ranjan Biswal
, and Prasenjit Basak
J. Renewable Sustainable Energy 12, 056303 (2020); https://doi.org/10.1063/5.0019254
© 2020 Author(s).
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Journal of Renewable
and Sustainable Energy
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scitation.org/journal/rse
An integrated rule-based power management and
dynamic feed-forward low voltage ride through
scheme for a grid-connected hybrid energy system
Cite as: J. Renewable Sustainable Energy 12, 056303 (2020); doi: 10.1063/5.0019254
Submitted: 23 June 2020 . Accepted: 19 September 2020 .
Published Online: 19 October 2020
Amit Kumar Roy,1
Gyan Ranjan Biswal,2
and Prasenjit Basak1,a)
AFFILIATIONS
1
Electrical and Instrumentation Engineering Department, Thapar Institute of Engineering and Technology, Patiala 147004, Punjab,
India
2
Department of Electrical and Electronics Engineering, Veer Surendra Sai University of Technology, Burla 768018, Odisha, India
a)
Author to whom correspondence should be addressed: prasenjit@thapar.edu
ABSTRACT
Power generation from a grid-integrated renewable energy generator embedded with backup sources to form a hybrid energy system possesses convincing features of high efficiency and zero emissions. Control for felicitating apt power sharing and for providing ancillary services
such as low voltage ride through (LVRT) is necessary for the compliance of grid codes. However, the simultaneous control coordination for
meeting these control objectives is challenging due to the dynamic nature of renewable generators and utility grid. Hence, this paper proposes
an integrated power management strategy (PMS) and LVRT control scheme for such systems. A wind energy conversion system backed up
by a battery energy storage system, proton exchange fuel cell, and electrolyzer is considered in this work. A reduced rule-based power management control scheme is proposed for the considered system where the request made by the grid operator is kept in priority. Further, a
dynamic current feed-forward based LVRT control scheme based on negative sequence current minimization is presented for the gridinterfaced inverter. The inverter control is coupled with an inherent mode selection capability between the grid feeding mode and LVRT
mode in order to realize the proposed integrated control objectives. The validation of the proposed PMS and LVRT control is justified by
detailing relevant mathematical control models and also by realizing practical case scenarios such as variable wind speed, load demand, grid
power request, and occurrences of balanced and unbalanced voltage sag. The obtained simulation results show the cordial response of the
system with the proposed control strategies.
Published under license by AIP Publishing. https://doi.org/10.1063/5.0019254
I. INTRODUCTION
The idea of harnessing power from more than one distributed
generation source is an attractive solution to meet the power demand
of an islanded region or the demand imposed by the utility grid in the
case of grid-connected distributed generators. The resultant system is
termed as a hybrid energy system (HES) which offers the benefits of
high reliability due to uninterruptible operations, good power quality,
and economic benefits due to the use of renewable sources.1 In hybrid
generation, the backup sources may be classified as short-term and
long-term backup systems.2 In general, a typical grid-connected sustainable micro-grid architecture uses photo-voltaic (PV) and wind
generators as the primary generation sources3,4 due to its availability
in abundance and favorable government policies. In primary backup
systems, the use of battery storage is widely acceptable where solar PV
is used as the prime source of power generation.5,6 On the other hand,
J. Renewable Sustainable Energy 12, 056303 (2020); doi: 10.1063/5.0019254
Published under license by AIP Publishing
diesel generator sets are also widely adopted as backup systems for residential electricity distribution systems or as remote area power systems as they provide reliable power. However, these diesel generators
mainly suffer from the issues of environmental pollution and noise,
while batteries suffer from the problem of high maintenance, low
power density, and issues of safe disposal. On the other hand, energy
backup can also be created in the form of hydrogen storage. With
proven technology and storage techniques, hydrogen proves to be a
convincing way for creating long-term energy backup. An added flexibility imposed by hydrogen energy is that the excess energy generated
from the renewable generators can be used to run an electrolyzer to
generate hydrogen which may be further stored in hydrogen tanks in a
controlled manner with the help of process automation.7 The stored
hydrogen is used by fuel cells (FC) to meet the deficit power
demanded from the load or grid. In this way, a non-polluting, reliable,
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and long-term backup system can be created. Use of more than one
backup source can be used to further enhance the reliability of the
storage systems; the resultant system is termed as hybrid storage.7
Hybrid storage systems using battery and hydrogen can complement
each other by overcoming the technical barriers of each other during
transient and steady state conditions, respectively. In Refs. 8 and 9, it is
established that FC are hybridized with batteries, where the function
of battery is to suffice the transient load demand while the steady state
power demand is met by FC. For long-term operation, it is essential to
maintain the lifetime of the battery and FC. The same can be ensured
by the proper control of DC–DC converter interfaces between FC, battery, and the dc-bus. Moreover, an appropriate control logic is
required for DC–DC converters as it attributes to a suitable control
capability for the quantum of power exchange from FC and
batteries.10
HES can be grid interfaced or non-grid interfaced depending on
the constraints of power demand, location of generation, and existing
right of way infrastructure. Standalone systems are well investigated by
the researchers and, in fact, numerous combinations of sources are
suggested in the existing works.11–18 In order to determine the appropriate sharing of power from various sources, the design of a power
management controller (PMC) is very significant. The existing literature solves the power management aspect by considering specific
objectives, like load leveling,11 peak power balancing,12 and unbalanced load compensation.13 Power sharing strategy is demonstrated
using a battery- and supercapacitor in Ref. 14 where the hybrid storage
topology is used, while a hydrogen storage is also considered for the
purpose of backup in Ref. 15. Most importantly, in HES the aspect of
power coordination between the hybrid storage is achieved by employing supervisory control based on states or by using droop-based control. Besides the conventional approach, intelligent controllers like
fuzzy logic and adaptive neuro-fuzzy-based control are also applied for
performing the energy management and inverter control in a microgrid.16–19 These intelligent controllers show cordial performance under
various system dynamics like sudden change in generation, load
demand, or the grid side dynamics, etc.
The grid integration of HES provides the flexibility of balancing
the load demand when the power generated by the distributed generators in less than the power demand of the load. However, with the
changing power system paradigm, there might be a scenario where a
grid is heavily dependent on the power generated by a specific region’s
micro-grid. In such cases, the grid is controlled by a system operator
who can make a request of power demand from the interconnected
micro-grid based on the energy dispatch schedule. In such case, a
power management logic requires special design and considerations
which are elucidated in the work of Refs. 19–29 These works present
the power coordination in a grid-connected micro-grid by considering
specific objective cases. Criteria like dc-link voltage regulation, ac voltage regulation at the point of common coupling (PCC), and appropriate power sharing from individual sources under grid connection
remain as common objectives in most of the works. With the changing
grid codes and architecture of the power system, if renewable energy
generators participate in bulk toward the injection of power to the
grid, then these renewable generators must stay connected with the
grid for a specific duration. This aspect is termed as low voltage ride
through (LVRT) capability.30,32–35 Generally, the simultaneous objective of power management and LVRT capability is rarely attempted in
J. Renewable Sustainable Energy 12, 056303 (2020); doi: 10.1063/5.0019254
Published under license by AIP Publishing
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previous works. Although in Ref. 31 the power management and
LVRT control is proposed for a fuel-cell, supercapacitor, and battery
system, the interconnection of the battery with dc-bus is performed
directly without any interfacing DC–DC converter. Such integration is
not desirable since the charging and discharging cycle of the battery is
affected, and this hampers its lifetime. Looking into the previous literature gaps, the following modalities are performed in this paper where
the authors tried to contribute toward the coordination control strategy for a grid connected HES consisting of wind/fuel-cell/battery/electrolyzer system with an improved control logic in the following way:
1. A new simplified PMC is proposed for the considered gridconnected wind/fuel-cell/battery/electrolyzer system which
accounts for the power request made by the grid operator and
power demand of the loads at PCC simultaneously.
2. Particularly, the proton exchange membrane fuel cell (PEMFC)
is used to improve the overall generation efficiency for the hybrid
system and it has favorable impact on the reduction in greenhouse gas emission.
3. An effort is made to reduce the number of if-else case for making
decision on the power-references for the FC, battery, and electrolyzer in the proposed PMC. This enhances the transient response
of the considered HES.
4. Objectives like minimum dc-link voltage fluctuation, low active
power fluctuations for generation, and loading transients are
ensured with the proposed power management algorithm.
5. Along with the power sharing control, a dynamic feed-forwardbased LVRT control scheme is embedded with the gridinterfaced voltage source inverter (VSI).
6. The proposed LVRT control scheme uses less computations, and
it is based on the positive sequence power tracking scheme so as
to mitigate the negative sequence current profiles in the PCC.
The remaining paper is organized as follows: Sec. II describes the
architecture of the designed HES and the logic of deciding the power
ratings of individual sources along with their brief modeling. The proposed PMC used in the work is explained in Sec. III, while the suggested converter controllers for the wind energy conversion system
(WECS), PEMFC, battery, electrolyzer, and VSI are described in
Sec. IV. Section V presents the detailed validation of the proposed integrated rule-based PMC along with the discussion on exchange capacities. The section also presents the validation of the dynamic feedforward LVRT control for 50% and 90% voltage sag conditions with
the support of extensive simulations. Finally, the concluding remarks
of the paper are deliberated in Sec. VI.
II. SYSTEM ARCHITECTURE, UNIT SIZING, AND
MODELING OF SYSTEM COMPONENTS
In this paper, the HES is considered as per Fig. 1 which consists
of permanent magnet synchronous generator (PMSG) based WECS as
the primary source of power generation. An uncontrolled bridge rectifier and DC–DC boost converter-1 arrangement felicitates the conversion of an uncontrolled AC voltage generated at the PMSG terminal to
a controllable DC voltage. The storage system consisting of battery
acts as the primary storage system which is designed to meet the load
transition for shorter duration, while a FC–electrolyzer combination is
used as the secondary back-up system for long-term backup in the
case of worst-case power outage. A H2 storage system is assumed as
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FIG. 1. Schematic of the considered grid connected hybrid generation system.
indicated in red color, and the corresponding channel of the H2 circuit
is shown in a dotted red line. For the ease of simulation-based modeling, the dynamics and the modeling of H2 storage system has not been
considered in this work. However, it is ensured that the working of FC
and the electrolyzer must complement each other with the proposal of
a new power management algorithm. An appropriate power sharing
logic is designed so as to safeguard the life span of the battery and FC.
The same is elucidated in Sec. IV B where the battery system’s life span
is ensured by keeping its state of charge (SOC) within 20% to 80%,
whereas for the PEMFC system, the prolonged life span is confirmed
by restricting its utilization factor within 80% to 90%. A DC–DC
buck-boost converter is interfaced with the battery system, whereas a
DC–DC boost converter-2 is interfaced with the PEMFC system. A
brief detail regarding the unit sizing and modeling of individual system
components is provided in Secs. II A and II B.
A. Unit sizing
The work considers a situation where the grid is accessible and
the available wind potential enables the WECS to meet an average
annual load of 14-kW. Hence, the sizing of WECS is done by considering its plant load factor (PLF). In general, the wind power plants operate at a PLF of 35%; hence, as per (1), the power rating for the wind
generator is estimated as 40 kW,
J. Renewable Sustainable Energy 12, 056303 (2020); doi: 10.1063/5.0019254
Published under license by AIP Publishing
Plant capacity ¼
Average annual load 14 000
¼
¼ 40 kW:
PLF
0:35
(1)
The rating of FC is based on the grid side peak demand; it is intended
to meet the peak grid demand of 15 kW. Hence, in this work, a total of
12 number of 1.2 kW PEMFC units are connected in series to get the
rated power of 15 kW, while the sizing of the battery is done by considering the grid operator’s demand. The battery backup system
intends to support the load demand of 40 kW for a minimum span of
15 min. Considering an ideal depth of discharge of 60% and battery
terminal voltage as 300 V, the A h rating of the battery is determined
from the following equation:
Load demand Backup time
Battery terminal voltage Depth of discharge
40 000 0:25
55 A h:
(2)
¼
300 0:6
Battery rating ¼
Further, the rating of the electrolyzer is done on the basis of the
available surplus power.4 Assuming an ideal generation of 40 kW from
the WECS and a constant demand of 20 kW, the surplus power is
20 kW. Looking into the aspect of high cost associated with an aqua
electrolyzer, the final rating of the electrolyzer is selected as 60% of the
available surplus power available in the system which is calculated as
per the following equation:
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Electrolyzer rating ¼ 60% ðsurplus powerÞ
¼ ð40 20Þ 0:6 ¼ 12 kW:
ARTICLE
(3)
B. Modeling of the proposed hybrid sustainable
energy system
In this section, a brief modeling of the proposed HES is explicated which is a combination of PMSG based WECS, PEMFC, battery
bank, and electrolyzer, respectively.
1. Modeling of wind turbine and PMSG
The 40 kW wind turbine is selected as the prime source of energy
generations whose mechanical power is modeled as per the following
equation:
1
Pm ¼ Cp ðk; bÞqA 3 ;
2
(4)
where the mechanical power developed by the wind turbine is denoted
by Pm, air density in kilograms per cubic meter is symbolized by q,
blades swept area in meter square is highlighted by A, the wind speed
in meter per second is represented by v, and the power coefficient
which is function of tip speed ratio (k) and pitch angle (b) is represented by Cp.8 The considered PMSG is a salient pole whose stator
voltage equations are modeled on Parks transformation according to
the following equations:22
disd
þ isd Rs xe Ls isq ;
dt
(5)
disq
þ isq Rs þ xe Ls isd þ xe u:
dt
(6)
vsd ¼ Ls
vsq ¼ Ls
Here, the resistance and inductance of the PMSG stator winding are
designated by Rs and Ls, while the transformed voltages and currents
of the stator winding in dq-reference frame are represented by vsd, vsq,
isd, and isq, respectively. The magnetic flux and the electrical angular
speed are denoted by / and xe, respectively.
2. Modeling of PEMFC
A 1.2 kW PEMFC system is modeled as per (7)–(11). The internal potential ecell generated across the two electrodes is as per the
Nernst equation denoted by the following equation:
"
!#
RT
pH2 pO2 1=2
log
;
(7)
ecell ¼ eo þ
2F
pH2 0
where the standard reference potential under standard condition of
1 atm and 25 C is denoted by eo . The magnitude of ecell depends on
the stack temperature represented by T, universal gas constant R,
Faraday’s constant F, and the partial pressures of H2 , O2 and H2 O
which are denoted by pH2 , pO2 , and pH2 O , respectively. The magnitude
of terminal voltage is always less than ecell due to the presence of activation loss, ohmic loss, and concentration losses inside the PEMFC.
The start-up and regular operation of FC requires the correct tracking
and control of the FC stack current istack such that the operating point
of istack ranges between its upper and lower limit. The partial pressure
of the reactants at the anode and cathode of the FC preliminarily
J. Renewable Sustainable Energy 12, 056303 (2020); doi: 10.1063/5.0019254
Published under license by AIP Publishing
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depends on the molar flow of reactants at the anode–cathode, stack
current of the FC and with various modeling constants. The same is
expressed as per the following equation:
pH2 ¼ zH2 ðqin
H2 2Kr istack Þ;
(8)
pO2 ¼ zO2 ðqin
O2 2Kr istack Þ;
where pH2 and pO2 are the partial pressure (bar) of H2 and O2 at the
in
anode and cathode, respectively, and qin
H2 and qO2 denote the molar
flow (kmol/s) of the reactants at the anode and cathode of the FC,
while zH2 , zO2 , and Kr are the modeling constants. Considering a constant temperature and pressure in the fuel cell’s stack chamber, the
quantity of reacted H2 in the FC denoted by qrH2 (mol/s) is given as per
the following equation:
qrH2 ¼ N0 Istack =2F ¼ 2Kr Istack ;
(9)
where, N0 is the number of series connected cells, F is the Faraday’s
constant (C/mol), and Kr is the modeling constant [mol/(sA)].
3. Modeling of battery
The terminal voltage vterm and battery SOC are the important
parameters for a battery model. The considered 55 Ah battery is modeled as per (10) and (11), respectively,29
Ð
Ah
ð
(10)
vterm ¼ voc þ ib Rb k
þ va eB ib dt ;
A h þ ib dt
0
1
ð
ib dt A
@
SOC ¼ 1 þ
100;
(11)
Ah
where vterm denotes the battery terminal voltage, voc is the open circuit
voltage, ib is battery current, Rb is the battery internal resistance, k is
the polarization voltage, va is the exponential voltage, and B is the
exponential capacity.
4. Modeling of electrolyzer
The 12 kW electrolyzer forms the supporting system for PEMFC
where H2 is generated with the help of excess power from the WECS.
The cell voltage and current relation in an electrolyzer are related as
per (12),21 where vcell is the electrolyzer cell voltage, vtherm is the thermodynamic cell voltage, T is the electrolyzer temperature in C, r1 and
r2 are the ohmic resistance parameters, and t1, t2, t3, and u1 are the
overvoltage parameters, while ielz is the current through the electrolyzer, A is the cell electrode area in m2 and ielz =A is the electrolyzer
current density in A/m2. The number of electrolyzer cells connected in
series, denoted by ns, is decided as per the required electrolyzer power
rating as per (13),
!
r1 þr2 T
t2 t3
ielz
vcell ¼ vthrm þ
ielz þu1 log 1þ t1 þ þ 2
; (12)
A
T T
A
velz ¼ ns vcell :
(13)
The excess power is used by the electrolyzer to generate hydrogen
which is a function of electrolyzer’s current and is deliberated as per
the following expression:
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gF ns ielz
;
(14)
2F
where nH2 is the generated hydrogen from the electrolyzer in (mol/s),
gF denotes the Faraday’s efficiency, and ns represents the number of
series connected cells in the electrolyzer, while F and ielz are the
Faraday’s constant (C/mol) and electrolyzer’s current (A), respectively.
The significance of faradays efficiency is that it conveys the ratio of
practical and theoretical maximum quantity of hydrogen generated in
the electrolyzer. The value of gF is a function of electrolyzer’s current
which is denoted as per the following equation:
nH2 ¼
gF ¼ 96:5 exp ð96:6=ielz 75:5=i2elz Þ:
(15)
As per the proposed design, a 5 kW, 120 A, and 43 V electrolyzer
whose detailed parameters are mentioned in the Appendix is converted to a 12 kW electrolyzer. The rated terminal voltage across the
electrolyzer is fixed at 100 V with the help of a buck converter. The
number of series connected cells is 75 in order to obtain the rated terminal voltage from the electrolyzer model.
III. PROPOSED POWER MANAGEMENT CONTROLLER
The power sharing algorithm is developed among the generators,
backup devices, and the utility grid with the help of proposed PMC.
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The adopted PMC logic is depicted as per Fig. 2 where the control
logic is divided into three sections, namely, input power sensing (IPS),
PMC, and output power reference (OPR) generation unit. The IPS
senses the available power generation of the WECS denoted by Pw ,
ref
power demand from the grid Pg , and power demand of the load connected at the PCC denoted by PL . The PMC performs the arithmetical
and logical computations with the sensed inputs and channelizes its
results to the OPR generation unit.
In the proposed algorithm of PMC, the power demand from the
grid is kept in priority. If the grid demand is not met by WECS, then
the deficit power denoted by Pnet is first supplied by a battery while
keeping its SOC within its upper and lower limits. After the battery
SOC reaches its lower limit, FC is used to supply the deficit power. For
situations when the power produced by WECS is greater than the grid
and load request, the surplus power is first stored in batteries until it
reaches the upper SOC limit, whereas in scenarios where the surplus
power is still available and the battery is fully charged, the extra power
is dumped to the aqua-electrolyzer by controlling switch S9 and buck
chopper together which are connected in series with the electrolyzer. It
is interesting to note that FC and electrolyzers have slow response
time and are not suitable for frequent start and stop operation as compared to batteries. But H2-based storage systems are very suitable for
FIG. 2. Schematic of the proposed power management controller of HES.
J. Renewable Sustainable Energy 12, 056303 (2020); doi: 10.1063/5.0019254
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satisfying the load demand for a long-term basis which can improve
the overall system’s efficiency. In this work, the above technical constraint exhibited by the FC and electrolyzer system has been mitigated
via the adoption of battery storage. The battery storage always helps in
meeting the transient generation and loading power profiles in the system via the adoption of reduced rule-based PMC depicted as per
Fig. 2. In fact, with the help of proposed PMC, the merits of battery
storage have been judiciously used to overcome the slow dynamic
nature of FC and electrolyzer. If we carefully observe the power management controller’s flow chart schematic as per Fig. 2, the battery can
support either the electrolyzer system or the FC system depending on
the criteria of Pnet and SOC of the battery. During excess power generation inside the hybrid system, the electrolyzer consumes this excess
power to generate H2, whereas the battery consumes this excess power
to replenish its SOC if the battery SOC is less than 0.8. Hence, either
the electrolyzer or the battery participates whenever there is an excess
power generation in the considered system, while the FC-battery combination participates in meeting the deficit load demand whenever the
system encounters power deficiency. Thus, in all cases, the support
from the battery either as an energy source or as an energy sink is
available. The SOC criteria for the battery have been intentionally
applied as this will ensure that the battery is always available whenever
the FC and electrolyzer system cease to deliver or absorb their respective power. Moreover, this SOC criteria help in reducing the frequent
start and stop cycles of the H2-based devices (FC and electrolyzer).
The power references generated from the OPR unit are controlled by
the respective interfacing power electronic converters whose control
algorithms are discussed in Sec. IV.
IV. PROPOSED CONTROL SCHEMES OF POWER
ELECTRONIC CONVERTERS
ref
The power references for the PEMFC converter PFC , battery
ref
ref
converter Pbatt , and electrolyzer converter Pelz are generated from
the OPR unit of the proposed PMC as it was deliberated in Sec. III.
Since this paper has a holistic approach for meeting the objective
of power management and also the aspect of LVRT capability in
the system, the design for DC–DC boost converter-1, that is, interfaced with WECS is done by keeping both of these objectives.
Hence, in this regard, a maximum power point tracking (MPPT)
control and OFF-MPPT control is used, and the control methodology of the same is deliberated in Sec. IV A.
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A. Control of WECS converter
The DC–DC boost converter-1 as shown in Fig. 1 is used for
maximum power point tracking (MPPT) from the WECS. This controller senses the wind speed denoted by vw in order to calculate the
opt
optimum value of the rotor speed xr ; this rotor speed corresponds to
the maximum power to be fetched from the turbine. The optimum
rotor speed changes with the instances in wind speed variation and is
tracked via a PI controller bearing proportional and integral gain as
mppt
mppt
kp and ki , respectively. The PI controller adaptively generates a
reference current for the DC–DC boost converter-1 denoted by iL1
containing the information of maximum power. The error between
the generated reference current iL1 and measured current iL1 is applied
to adjust the duty cycle dpmsg of the boost converter via a hysteresis
current controller in order to operate the turbine at optimum speed.
In the case of grid fault, there is a power imbalance generated in
the system as there is a sharp drop in the magnitude of active power at
the PCC, while the power generated from WECS remains unchanged.
If this imbalance is not nullified, then the magnitude of active power
shoots up at the dc-link which is visible in the form of surge of dc-link
voltage. Thus, the PMSG based WECS needs to be disconnected from
the MPPT mode during the detection of fault at the PCC and must be
switched to OFF-MPPT mode. Since this work also aims to integrate
the LVRT capability in the considered system, an OFF-MPPT control
as depicted in Fig. 3 is also proposed in this regard. The toggle switch
opt
(TS) changes the turbine’s reference speed from xr to a new optiopt
mum reference speed denoted by xrnew . The basic idea of generating
the new speed reference is to momentarily increase the speed of the
turbine as per (16) for the time span of the fault where n stands for
quantity of velocity samples, DT denotes the fault/voltage sag span
duration, Tsspeed represents the MPPT controller’s sampling period, Dx
expresses the increase in PMSG’s speed, and H stands for generators’
inertia constant,
9
opt
>
xrnew ¼ xr þ Dkxr ;
>
=
ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
ffi
s
(16)
Dx
DT
DT >
n
; Dx ¼
:>
Dk ¼
1þ
;n ¼
;
100
Ts speed
H
The tracking of the new speed reference as per (16) will enable to
decrease the power generated from the turbine according to the wind
turbine power and rotor speed characteristics. Moreover, some portion
of the energy will be stored in the system in the form of inertia denoted
as per (17),36 where J denotes the moment of inertia of the rotor mass,
FIG. 3. MPPT controller for WECS.
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2
DKE ¼ 0:5J xopt
ðxr Þ2 :
rnew
ARTICLE
(17)
B. Battery converter control scheme
A bidirectional DC–DC buck-boost converter is interfaced
between the battery and dc-link as the battery is expected to release
and absorb its energy for balancing the deficit power as per the power
sharing algorithm. The representation of the controller is shown in
Fig. 4, where the battery is controlled either in buck mode when the
excess power is to be dumped or in boost mode when the deficit power
ref
is to be met. The battery reference power Pbatt which is derived from
the PMC is mathematically divided by the battery terminal voltage in
ref
order to generate the battery reference current ibatt .
This reference current is tracked by the PI controller bearing proportional and integral gain as kbatt
and kbatt
p
p , respectively. The design
of the entire control scheme is such that it is ensured that the battery
operates within its lower and upper SOC limits of 20% and 80%,
respectively. Thus, an additional check loop is added to take care of
the above condition which, ensures that the battery always works in
the specified SOC condition. Additionally, the condition of buck operation or boost operation is ensured by applying a conditional two-way
switch that selects either of the inputs, i.e., I/P1 or I/P2 based on the
value of control input.
C. Fuel cell converter control scheme
The FC converter participates in meeting the deficit power when
the battery SOC reaches its lower value. The control of switch S2 in
DC–DC converter-2 is done is such a manner that the utilization factor of FC stays in the range of 80% to 90% as this criterion ensures the
optimum life span of the FC. The desired limits of utilization factor
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are converted to lower and upper limits of the current to be supplied
up
by the FC denoted by ilow
fc and ifc correspondingly. The value of the
current limits is calculated as per (18) where Kr is the cell constant and
qin
H2 is the quantity of hydrogen which enters the FC,
up
ifc ¼
0:9qin
H2
;
2Kr
ilow
fc ¼
0:8qin
H2
:
2Kr
(18)
ref
The current reference of the FC converter ifc is obtained by dividing
ref
the fuel cell reference power Pfc with FC terminal voltage vfc . The
ref
magnitude of ifc is controlled between its limits with the help of a limiter block and the inductor current iL2 is controlled via a PI controller
fc
fc
whose proportional and integral gains are kp and ki , respectively. The
corresponding duty cycle for the FC converter DFC is generated as per
the control shown in Fig. 5.
D. Electrolyzer converter control scheme
The electrolyzer is controlled by a buck converter as the required
terminal voltage for the electrolyzer is less than the rated dc-link voltage. The control schematic for the switch S9 and buck converter connected in front of the electrolyzer is presented in Fig. 6. The control
ensures the operation of the electrolyzer is in operation only when the
battery upper limit is reached, and at the same time the desired excess
elz
power is absorbed by the electrolyzer. Here, kelz
p and ki represent the
proportional and integral gain constant of the PI controller used in the
electrolyzer converter control.
E. Control scheme for grid connected VSI
for integrating LVRT capability
The control schematic for the grid connected VSI is as per Fig. 7.
The VSI is controlled in grid feeding mode when the preliminary role
FIG. 4. Schematic showing the battery converter control scheme of the proposed HES model.
J. Renewable Sustainable Energy 12, 056303 (2020); doi: 10.1063/5.0019254
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FIG. 5. Model of FC converter control
scheme.
of the converter is to deliver the power generated from the WECS as
per the grid operator’s request. Besides the grid feeding feature, a new
converter control for attaining the LVRT feature is proposed as well.
In fact, when a grid fault is detected, the VSI control does the switching between its generated current references. The calculation of current reference during grid feeding operation mode and during the
LVRT mode is discussed in Secs. IV E 1–IV E 2.
1. Grid feeding mode operation
The power balance in the system is represented as per (19) where
the total generated power from WECS Pw, PEMFC Pfc, and battery
Pbat is distributed among the dc-link Pdc, electrolyzer Pelz, inverter Pinv,
ref
load demand Pl and the grid demand Pg . This power balance helps to
ref
determine the required power reference power of the inverter Pinv
which is translated to a current reference by the current reference generation block as shown in Fig. 7,
Pgref ;
Pw þ Pfc 6Pbat Pelz ¼ Pdc þ Pinv þ Pl þ
ð
ref
vDC Þ þ kvi ðvdc
idc ¼ kvp ðvdc
vdc Þdt;
ref
ref
Pdc ¼ vdc idc :
(19)
(20)
(21)
ref
Pdc
is obtained by the product of dc-link
The dc-link power reference
ref
reference current idc and dc-link voltage vdc which is generated as
and vdc are the reference and
per (20) and (21), respectively, where vdc
actual value of dc-link voltage, and kvp and kvi are the proportional and
integral gain constant of the voltage controller. As the inverter is controlled in dq-reference frame under unity power factor condition, the
ref
reference d-axis current id is obtained as per (22) and the default qref
axis current reference iq is fixed to zero,
!
ref
ref
2 Pw þ Pfc 7Pbat Pelz Pdc Pl Pg
ref
id ¼
:
(22)
3
vd
ref
ref
The current references id and iq are tracked by the PI controllers PI1
and PI2 in order to generate the direct and quadrature axis voltage
references vd and vq .
2. LVRT mode operation
The mode selection switch performs the switching of current reference from the grid feeding current generation block to LVRT current
controller block upon the detection of grid fault; the mathematical
modeling of the LVRT control is described in this subsection. The reference current is generated during LVRT mode via tracking the positive sequence power of the system as per (23), where Phs is the total
power generated from the hybrid system as per (24), vp is the positive
sequence voltage component, and Cdc is the value of dc-link capacitance. As per (23), the reference current ip does not contain the
FIG. 6. Control of switch S9 and buck converter for an electrolyzer.
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FIG. 7. Grid interfaced VSI control.
component of negative sequence power; thus, if this reference current
is successfully tracked by the inverter control, then the fault ride
through (FRT) functionality is effectually unified in the system,
dvdc
Phs vdc Cdc
dt
;
(23)
ip ¼
3 vp
(24)
Pfc þ Pw þ Pbat ¼ Phs :
The current reference in positive sequence component which is
obtained as per (23) is converted to current variables ia , ib , ic of a
three-phase stationary circuit using Fortes-cue operators, a and a2 as
per (25),
dvdc
Phs vdc Cdc
dt
;
(25a)
ia ¼
3 vp
0
1
0
1
dvdc
dvdc
P
v
C
P
v
C
@ hs dc dc dt A
@ hs dc dc dt A
ib ¼ a2
¼ ð0:5 j0:866Þ
:
3 vp
3 vp
(25b)
0
1
0
1
dvdc
dvdc
P
v
C
P
v
C
dc dc
hs
dc dc
@ hs
dt A ¼ ð0:5 þ j0:866Þ@
dt A;
ic ¼ a
3 vp
3 vp
(25c)
2 3
" # rffiffiffi"
# jia j
id
2 cos h cos ðh 120 Þ cos ðh þ 120 Þ 6 7
¼
4 jib j 5:
iq
3 sin h sin ðh 120 Þ sin ðh þ 120 Þ
jic j
(26)
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Since it is intended to regulate the inverter current references by
PI controllers but it is generated in the abc-frame obtained as per (25),
these current references are converted to synchronous reference frame
(SRF) using (26). Moreover, the current references obtained from (25)
are complex terms because of the presence of sequence factors; their
corresponding magnitude is extracted and the same is applied to (26)
for obtaining the further current references in the dq-frame. The current reference terms of d-axis id and that of q-axis iq enable attaining
FRT. The reference current of q-axis iq is compared with the actual qaxis current and the corresponding error is regulated by the PI controllers PI1 and PI2 to generate an intermediate voltage reference term.
The final voltage reference in the dq-frame is obtained by including
the cross coupling voltage terms which finally generates the dq-axis
reference voltages vd and vq according to (27) and (28), respectively. kci
and kcp denote the integral and proportional gains of PI-regulators PI1
and PI2; the entire control schematic is included in Fig. 7. The method
described above is one of the significant contributions done in terms
of the system modeling,
ðn
o
n
o
ref
ref
vd ¼ kcp ðid or id Þ id þ kci ðid or id Þ id dt þ vd xLf iq ;
(27)
vq
¼
kcp ðiq or iref
q
iq Þ þ
kci
ð
ðiq or iref
q
iq Þdt þ vq þ xLf id :
(28)
V. RESULTS AND INTERPRETATIONS
The validation of the proposed system modeling and its control
is validated by considering series of simulation experimentation in
MATLAB/Simulink platform.
The detailed simulation parameters are presented in the
Appendix. The following case studies are undertaken to validate the
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dynamic and transient performance of the system under various
power generation and demand scenarios.
A. Case-1: WECS generated power greater than
the grid request
A situation is considered where the power generated from the
wind generator Pw remains constant at 18.3 kW per Fig. 8(a) due to
fixed wind speed. The battery SOC is considered greater than 80%,
while the produced power from the WECS is larger than the power
demand of the grid operator. The power demand of the grid denoted
ref
by Pg as shown in Fig. 8(e) varies in the following way: a demand of
3 kW for the span of 0–0.5 s, 7 kW from 0.5–1.5 s, 15 kW for the peak
demand span of 1.5–3 s, and 10 kW for the remaining duration. The
demand from the grid acts as the input power reference for the grid
connected inverter controller. As presented in Fig. 8(d), net power Pnet
is negative which implies the presence of excess power in the system.
The efficacy of the PMC is seen where the excess power is stored in
the electrolyzer as per Fig. 8(b), and dc-link is regulated near its reference value. Further, the power injected into the grid by the inverter follows the grid demand reference as evident from Fig. 8(f). The PCC
voltages are well regulated at 1 PU by the inverter control, while the
currents at the PCC are regulated as per the grid power demand as
inferred from Figs. 8(g) and 8(h). The generated H2 (mol/s) profile of
the electrolyzer is shown as per Fig. 8(i). The profile of generated H2
clearly gives an inference that H2 production is directly related to the
availability of the excess power in the system whose profile is as per
Fig. 8(d). During instances, when the system has excess power, the H2
generation is more, while in the situation when the magnitude of
excess of power decreases, the generation of H2 also decreases.
B. Case-2: WECS generated power less than the grid
request and load demand
In this case, a situation is considered where the power generated
from the WECS is constant, but the load demand and the demand
coming from the grid operator are constantly varying. The variation of
ref
Pg is as per the previous case, while the load power PL varies as 5 kW
for the span of 0 to 2.1 s, 10 kW for the time range of 2.2 to 3 s, and
30 kW from 3.1 to 4 s.
For this criterion, the net power constantly varies and takes the
positive and negative values as shown in Fig. 9(b). The profile of wind
power, load demand, grid demand, and the response of the inverter
Pinv are depicted as per Fig. 9(a), where it is seen that the inverter
responds according to the demand of load and grid. For instance, durref
ing 3 to 4 s, the total demand of the system (PL þ Pg ) is 40 kW which
is delivered by the inverter. The power delivered by the inverter is
derived by the participation of the battery and electrolyzer in the
power sharing which is evident from Fig. 9(c). The PMC directs
the battery to participate in meeting the deficit power of 21.7 kW in
the system since the generation from WECS is only 18.3 kW at that
instant. The SOC of the battery is considered in the range of 20% to
80%. As per the zoomed version of the active power response of the
electrolyzer and battery as per Fig. 9(c), before 1.5 s the excess power
in the system is absorbed by the electrolyzer; however, after 1.5 s, the
electrolyzer goes to shut-down mode, and due to the slow dynamics of
the electrolyzer, it switches off completely (Pelz ¼ 0 W) at 1.55 s. The
battery storage instantly supports the system at 1.5 s itself, and thus it
J. Renewable Sustainable Energy 12, 056303 (2020); doi: 10.1063/5.0019254
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mitigates the power imbalance in the system created due to the slower
dynamics of the electrolyzer. Although the system experiences transition at 0.5, 1.5, 2, and 3 s, respectively, proper regulation is performed
by the proposed DC–AC converter control. The dc-link voltage is regulated around its reference value of 690 V, while the PCC voltages are
maintained at 1 PU and the PCC currents react as per the load
demand. The profiles of the discussed parameters are depicted as per
Figs. 9(d)–9(f), respectively.
C. Case-3: Variable power generated by WECS
and variable grid request and load demand
The robustness of the proposed system and its control is validated by considering variable wind generation, variable load demand,
and variable grid demand shown as per Fig. 10(a). The battery SOC is
fixed less than 20% because of variable power profile the system experiences both surplus and deficient power. The profile of net power is
as per Fig. 10(b) while the power shared by the FC and battery is as
per Fig. 10(c). During the time span of 0.5 to 1.5 s, the system possesses excess power but the SOC of battery is less than 20%; hence, the
battery works in charging mode. Power of around 5 kW is received by
the battery during the span 1 to 1.5 s; negative magnitude of battery
power Pbat validates the charging mode. After 1.5 s, net power in the
system shifts from excess power mode to deficient power mode where
the FC starts up and delivers the deficient power according the overall
system demand. For instance, 10 kW of deficit power is conveniently
delivered by the FC during the span of 2 to 3 s as per the PMC logic.
The apt regulation of the dc-link voltage around its reference and regulation of PCC voltage at 1 PU is depicted as per Figs. 10(d) and 10(e),
respectively.
The inset version of PCC currents during the transients encountered at 1.5 and 2.1 s is shown in Fig. 10(f) where it is inferred that the
current regulation is well visualized by the inverter control. The consumed/reacted H2 profile in the FC is as per Fig. 10(g) where corresponding changes in the H2 consumption are observed whenever
there is a change in the fuel cell’s power delivery magnitude. For
instance, the system experiences a power deficiency during the span of
1.5–1.9 s; hence, the H2 consumption also surges and registers a value
of around 0.8 mol/s during this span, while after 1.9 s, the H2 consumption gets regularized within the range of 0.65 and 0.7 mol/s,
respectively, as per the fuel cell’s power delivery requirement.
D. Energy exchange analysis of the grid-connected
hybrid generation system
In order to understand the energy balance in the system, the
dynamics of power associated in the dc-link and inverter is ignored for
simplicity. Hence, the power balance inside the system is stated as per
the following expression:
Pw þ Pfc 6 Pbat Pelz ¼ Pl þ Pgref ;
(29)
where Pw is the power generated from the WECS, Pfc is the power
delivered by the FC, Pbat is the power delivered or absorbed by the battery, Pelz is the power absorbed by the electrolyzer, Pl is the power
demand of the AC load connected at the point of common coupling,
ref
and Pg is the power demand of the grid. The energy balance is
derived from (29) and is expressed as per the following equation:
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FIG. 8. (a) Power generated by WECS, (b) power generated by electrolyzer, (c) dc-link voltage, (d) net power in the system, (e) grid demand reference, (f) power delivered to
the grid, (g) voltage at the PCC, (h) current at the PCC, and (i) hydrogen generated by the electrolyzer.
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FIG. 9. (a) Power generated by WECS, load demand, grid demand, inverter generated power, (b) net power in the system, (c) power shared by battery and electrolyzer along
with its zoomed version, (d) dc-link voltage, (e) voltage at the PCC, and (f) current at the PCC.
ð
ð
ð
ð
ð
ð
Pw dt þ Pfc dt 6 Pbat dt Pelz dt ¼ Pl dt þ Pgref dt or;
avg
avg
(30)
Eelz ¼ Pelz t ¼ 10 kW
4
h ¼ 0:012 kW h:
3600
(31)
Ew þ Efc 6 Ebat Eelz ¼ El þ Eg ;
where Ew is the energy supplied by the WECS, Efc is the energy provided by fuel cell, Ebat is the energy absorbed or supplied by battery, El
is the energy demand of the load, and Eg denotes the energy demand
of the grid. Since the validation of power management algorithm is
performed for a shorter simulation span, the demonstrated values of
energy exchange capacities will be of lower magnitudes. In each simulation case, the energy exchange associated with the battery, FC, and
electrolyzer is discussed on the basis of (30) and the same is enumerated as follows:
Simulation case-1: In this case (discussed as per Sect. V A), the
system has energy abundance as Ew > Eg; hence, the excess energy is
consumed by the electrolyzer (Eelz) to generate more H2. At this condition, the FC and battery does not participate in energy exchange; thus,
Efc ¼ 0 kW h and Ebat ¼ 0 kW h. Considering the average power consumption of the electrolyzer as 10-kW for the duration of 4 s [evident
from Fig. 8(b)], the average energy consumption of the electrolyzer
avg
(Eelz ) is calculated as per the following equation:
J. Renewable Sustainable Energy 12, 056303 (2020); doi: 10.1063/5.0019254
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Simulation case-2: In this case (discussed as per Sec. V B),
the system has energy deficiency since Ew < (EgþEl); hence, the
deficient energy is supplied by the battery storage system. As
per the results of Fig. 9(c), the battery supplies an average
power of 27 kW for the duration of 2.5 s; hence, the average
avg
energy exchanged by the battery (Ebat ) is calculated as per (32),
while the energy exchanged with the fuel cell Efc ¼ 0 kW h,
avg
avg
Ebat ¼ Pbat t ¼ 27 kW
2:5
h ¼ 0:01875 kW h:
3600
(32)
Simulation case-3: In this case (discussed as per Sec. V C), the system encounters variable loading; hence, the condition of energy deficiency and energy surplus is created. During energy surplus condition,
the excess energy is absorbed by the battery, while during the energy
deficiency the FC participates in meeting the demand. As per the
results of Fig. 10(c), the FC supplies an average power of 10 kW for the
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FIG. 10. (a) Power generated by WECS, load demand, grid demand, inverter generated power, (b) net power in the system, (c) power shared by battery and fuel cell, (d) dclink voltage, (e) voltage at the PCC, (f) current at the PCC and its corresponding zoomed versions, and (g) consumed H2 by the fuel cell.
duration of 2.5 s; hence, the average energy exchanged by the FC
avg
(Efc ) is calculated as per (33), while the energy exchanged by the electrolyzer Eelz ¼ 0 kW h,
avg
Efc
¼
avg
Pfc
2:5
h ¼ 0:006944 kW h:
t ¼ 10 kW
3600
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(33)
E. Case-4: LVRT capability of the considered hybrid
power generation
The LVRT capacity is added to the system by appending the proposed LVRT controller discussed in Sec. IV E 2 and also by using the
OFF-MPPT control discussed in Sec. IV A. The validation for the
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LVRT control is undertaken by considering three sub-cases, namely,
one-phase sag, two-phase sag, and three-phase sag. The system
response for all the three voltage sag cases is depicted as per Fig. 11.
For all the cases, PCC voltage (vpcc), PCC current (ipcc), dc-link
voltage (vdc), power delivered by the inverter (Pinv), and the mean
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mean
power from the inverter Pinv
are shown. The voltage sags are simulated for the duration of 2 to 2.15 s, respectively, and the inverter is
operated to meet the grid’s active power demand of 5 kW. The corresponding results of all these cases are depicted as per Figs. 11(a)–11(c),
respectively.
FIG. 11. (a) System parameters under 50% one-phase voltage sag, (b) system parameters under 50% two-phase voltage sag, and (c) system parameters under 50% threephase voltage sag.
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1. One-phase voltage sag
In the case of single-phase sag, a voltage dip of 50% is simulated
at one phase correspondingly; the dynamics of the inverter control
and the OFF-MPPT control are actuated, enabling the ride through
characteristics in the considered system. The overshoot of ipcc is
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controlled within the range of 60.1 P.U., while the profile of vdc is controlled in a smooth manner due to simultaneous actuation of OFFMPPT control, operation of the negative sequence current control,
and also effective power sharing performance with the proposed PMC.
The generation of negative sequence currents attributes to the ripple
content in the instantaneous active power oscillations in the system,
FIG. 12. (a) system parameters under 90% one-phase voltage sag, (b) system parameters under 90% two-phase voltage sag, and (c) system parameters under 90% threephase voltage sag.
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while the proposed FRT control is unable to completely eliminate
these oscillations, but the dip in the active power profile is minimized
mean
profile
to a great extent. This aspect is visible by visualizing the Pinv
delivered by the inverter under various voltage sag conditions where
the mean value of the inverter active power is maintained up to
2.7 kW during the voltage dip span.
2. Two-phase voltage sag
The system is subjected to a double phase sag of 50%, and the
corresponding system’s behavior is projected as per Fig. 11(b). Due to
the increase in quantum of unbalancing, the overshoot of ipcc is within
the increased range of 60.15 P.U., while the profile of dc-link voltage
is well stabilized within its rated value of 690 V with minute number of
ripples. The active power profile delivered by the inverter registers a
dip up to 2 kW from the rated power reference of 5 kW.
3. Three-phase voltage sag
The systems investigation for the LVRT capability is performed for a symmetrical fault case study where a uniform voltage
dip by 50% is created in the utility grid in order to observe the ride
through performance in the system. The corresponding parameters are showcased in Fig. 11(c) where the current surge is limited
within the range of 60.1 P.U. Further, the dc-link voltage profile
and the instantaneous active power profile do not register any
double frequency oscillations due to the absence of negative and
zero sequence components of current and voltage. Since such type
of sag condition is considered to be the most severe one, the dip in
the mean value of active power profile is up to 1 kW from the
rated value of 5 kW.
4. Severe voltage sag ride through capability
In general, a typical electric power system mostly registers a onephase voltage sag, and the magnitude of voltage at the PCC or at the
inverter terminals generally lies within 0.9 to 0.5 P.U. This typical
range of voltage magnitude at the PCC during the voltage sag span is
due to inherent availability of impedance existing between the line
connecting the utility grid and inverter terminals. In this work, the
robustness of the proposed LVRT algorithm is also brought out by validating it for the considered system during 90% voltage sag events
where the magnitude of respective PCC voltages is registered up to 0.1
P.U. The system ride through performance is portrayed as per Fig. 12
where the respective considered subcases of 90% one-phase, twophase, and three-phase voltage sag are depicted as per Figs.
12(a)–12(c), respectively. As seen from Fig. 12, there is a gradual
increase in the magnitude of PCC current from 0.3 to 0.5 P.U as the
voltage sag events shift from one-phase, two-phase, and three-phase
sag, respectively. Hence, in all the cases, the magnitude of PCC currents ipcc is within the range of rated current carrying capability of the
inverter’s power electronic switches. The profile of dc-link voltage
registers oscillation during one-phase and two-phase voltage sag due
to presence of negative sequence currents. However, similar to the
response of 50% voltage sag event, the registered oscillation in vdc has
negligible peaks and does not portray the magnitude surge due to
effective action of the proposed feed-forward LVRT control action in
the VSI control discussed as per Sec. IV E 2.
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As far as the profile of instantaneous power at the inverter terminal Pinv is concerned, the double frequency oscillations persist during
one-phase and two-phase sag, while steep spike is visualized during
the end of three-phase sag which can be considered as a limitation of
the adopted LVRT strategy. Nevertheless, the mean value of inverter’s
mean
lies above 1500-W for all the cases which is
active power profile Pinv
due to effective support from the OFF-MPPT control of the PMSGWECS discussed as per Sec. IV A.
VI. CONCLUSION
This paper has addressed the simultaneous power management and LVRT control of a grid connected hybrid WECS-based
renewable energy generation system backed up by battery and
PEMFC. The behavior of the proposed reduced rule-based power
management control is found satisfactory for various power generation and demand scenarios. The proposed PMC takes into
account the request of grid, power demand of the loads at PCC,
and available generation from the WECS during the entire system’s operation. Most importantly in all cases, the dc-link voltage and PCC voltages are regulated around 690 V and 1-PU,
respectively. The proposed PMC also ensures the apt energy balance in the system. Further, the life span enhancement of the
storage devices is ensured with the proposed PMC by the allocation of proper coordination control and current limits within the
various interfacing DC–DC converter control. As an added feature of the system, a dynamic current feed-forward control based
on the regulation of negative sequence PCC current is appended
in the inverter control which ensures the LVRT functionality.
The ride through functionality is found satisfactory for 50% and
90% one-phase, two-phase, and three-phase voltage sag cases.
The profiles of PCC voltages, currents, and the dc-link voltage
exhibit firm regulation under all the considered transient events.
Overall, the proposed system and its control are well suitable
where the grid operator is dependent on fetching reliable and
clean power. As a limitation of the work, the system performance
has been investigated on a simulation-based platform available to
the scientific community, and the studies are conducted for
shorter span of power generation and demand profiles. As a part
of future work, it will be interesting to investigate the discussed
system’s performance by considering a real time yearly power
generation and demand profile and also by considering variety of
non-linear and dynamic loads at the PCC.
APPENDIX: PARAMETERS OF THE SUBSYSTEMS
AND CONTROLLERS IN HES
The detailed parameters of the simulated system of Fig. 1 are
presented below.
Parameters of the system used for simulation
Rated power of the wind turbine
Rated electromagnetic torque of the PMSG
Rated speed of the PMSG
40 kW
126 N m
314 rad/s
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APPENDIX (Continued.)
APPENDIX (Continued.)
Parameters of the system used for simulation
Parameters of the system used for simulation
Base wind speed of the turbine
Pitch angle (b)
Optimal tip speed ratio (kopt) for MPPT
mppt mppt
kp , ki
of the DC–DC MPPT
converter (boost converter-1)
12 m/s
0
8.1
82, 650
Lithium ion
55 A H
300 V
0.1 X
0.0153, 2
PEMFC system
Power rating of individual stack
eo
Rated voltage of a single stack
Rated stack current
Number of cells in a single stack
Nominal stack efficiency
Operating temperature
Universal gas constant
Faradays constant
Cell constant
Nominal supply pressure of H2
Nominal supply pressure of O2
Number of series connected stacks
Overall rating of the PEMFC array
fc fc
kp , ki of the DC–DC boost converter
(boost converter-2)
1.2 kW
1.229 V
26 V
46 A
48
46%
55 C
8314.47 J/(k mol K)
96 485 C/mol
9.94 10–7
1.5 Bar
1 Bar
12
15 kW
3.5, 350
Parameters of the inverter control system
Base voltage (peak of line to ground)
Switching frequency
dc-link voltage reference; vdc
12 kW
1.5 10–5 X m2
6.019 106 X m2 C
0.214 A1 m2
9.870 A1 m2 C
119.1 A1 m2 C2
75
1.1647 V
70 C
873 cm2
6, 82
338 V
20-kHz
690 V
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20-lS
0.02, 267
2.67, 0.002
DATA AVAILABILITY
Battery Bank
Type
Rating
Rated terminal voltage
Internal resistance
batt
kbatt
of the DC–DC buck-boost
p , ki
converter
Electrolyzer system
Rating of the electrolyzer
r1
r2
t1
t2
t3
N
vtherm
T
A
elz
kelz
p , ki of the DC–DC buck converter
Simulation sample time
Voltage controller parameters; kvp , kvi
Current controller parameters; kcp , kci
The data that support the findings of this study are available
within the article.
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