Sigma modified power-control_and_parametric_adaptation_in_a_grid-integrated_pv_for_ev_charging_architecture (2)

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Transactions on Energy Conversion
Sigma-Modified Power Control and Parametric
Adaptation in a Grid-Integrated PV for EV
Charging Architecture
Debasish Mishra, Student Member, IEEE, Bhim Singh, Fellow, IEEE and B.K.Panigrahi, Senior Member, IEEE
Abstract— This paper presents a sigma-modified adaptive
control algorithm to enhance the charging profile in a multi-
objective electric vehicle (EV) charging installation. The
present algorithm takes care of multiple parametric
uncertainties and grid non-idealities to provide an
instantaneous control updation in order to achieve well-
regulated charging dynamics. With the support of renewable
energy and battery energy storage (BES), the present algorithm
also ensures an uninterrupted charging profile with controller
robustness and stability for bi-directional EV charging. The
sigma-mod adaptive controller provides an iterative error
convergence at each clock interval of supply voltage dynamics
to guarantee improved power quality operation in presence of
grid distortions. To further improve the reliability of EV
charging opportunities, a solar photovoltaic (PV) array in
conjunction with the battery energy storage supports the
ancillary services through maximum power point operation.
Multivariable sliding mode control and rule-based phase-shift
adaptation at different stages of power transformation assure
faster convergence, parameter uncertainty and controller
stability for the bi-directional EV charging operation. A 3.3kW
PV-integrated off-board charging facility is designed and
developed as a laboratory prototype to validate the multi-mode
charging architecture with minimal grid dependency.
Keywords— Power quality, PV-grid integration, bi-directional
EV charging, grid frequency estimation
I. INTRODUCTION
The increasing awareness towards sustainable
transportation globally with efficient and environment
supportive EVs are further assisted by rapid advancements in
battery technology and adorable government policies. The
high energy density in battery powered EVs (BEV) are more
preferred for fast charging and in present day scenario 50kW
charging within less than an hour of charging time is a
reality [1]. However, a substantial increase in charging load
demand, with larger penetration of EVs and un-regulated
charging have largely affected the distribution grid [2]. The
power quality is anticipated to ruin further with more EVs,
dependent on the distribution grid during peak hour charging
[3]. The unregulated EV charging with poor grid coordination
further worsens during grid abnormality and multi-objective
charging can be considered as one of the potential solutions
in this aspect [4],[5]. A coordinated charging with minimal
grid dependency through considerable support from
renewables and battery energy storage (BES) has certainly
strengthened the charging profile to a great extent.
Common architectures of dual-stage EV charging
architecture consist of a front-end bridge rectifier with an
intermediate PFC stage, followed by a secondary DC-DC
conversion stage. The selection of PFC converter at the
primary stage of charging architecture largely depends upon
the source current ripple, switching frequency, zero voltage
switching (ZVS) in case of interleaved or asymmetrical
architecture and demands a careful evaluation of circuit
parameters [6]. Boost-derived converter architectures are
commonly used in PFC stage converters for their control
implementation and simple architecture. However, switching
transients, higher current ripples and large inrush current
confines the operational viability within a limited range of
source voltage peaks [7]. In order to minimize the input
current ripple and to provide an extended duty operation,
hybrid DC-DC converters such as SEPIC, Cuk and Zeta
converters significantly improve PFC dynamics. However,
passive component counts, and double line frequency highly
affect the component lifetime with the introduction of even
harmonics. Further improvement in the switching dynamics
with an extended discontinuous mode of conduction (DCM)
is achieved through an asymmetrical front-end converter for
EV charging that achieves a natural commutation with ZVS
[8]. However, critical issues like zero voltage detection can’t
be ignored during source voltage reversal with distorted grid
conditions as explained in [9]. The system dynamics further
worsen in the case of multiple grid intermittency with a lower
short circuit ratio (SCR) and needs a longer restoration time
[10]. In a distribution utility with low SCR, an extended EV
charging during the peak hour of charging further adds hassle
with power quality deterioration and grid intermittency. In
this regard, multi-objective EV charging facility with
renewable support and minimal grid usage is much
anticipated for present and future EV charging solutions.
In order to provide auxiliary load support, local grid
stability and continuous charging solution at the EV supply
equipment (EVSE), a PV-battery-grid integration are
described in [11]. The grid-renewable integration with
additional battery energy storage (BES) significantly reduces
the grid dependency during grid intermittency and peak hour
load demand. Substantial research outcomes have also
illustrated the application of EV chargers in grid power
compensation and utility power factor correction through bi-
directional charging (BDC) architectures. Active front-end
converter and bi-directional DC-DC converter with galvanic
isolation are predominantly used for BDC configurations [6].
However, PV-array and BES integration are realized through
a wide range of power converter configurations based upon
the application and economic consideration. To ensure an
efficient and bi-directional charging power transfer, present-
day EV charging architectures are mostly configured through
an active front-end converter (AFC), with an isolated dual
active bridge (DAB) converter [12]. The presence of AFC at
the grid connected charging outlet extensively supports grid-
to-vehicle G2V and vehicle-to-grid V2G power transfer. The
bi-directional charging (BDC) architecture considers multiple
EV charging units as a potential solution to address various
power quality issues through active and reactive power
compensation [13], [14]. However, to provide an independent
charging solution at EVSE during grid intermittency,
additional energy sources such as renewables, battery energy
storage extensively support the uninterrupted charging with
higher reliability [4]. In certain cases, additional power
demand is also fulfilled from these auxiliary energy sources.
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However, larger penetration of PV sources and higher
participation of distributed energy sources during light-load
conditions also causes adverse effects with load-frequency
mismatch [15]. In addition, a higher concentration of non-
linear EV charging with distorted voltage conditions poses a
severe threat to auxiliary load management. In this context,
supervisory control is much essential to integrate all the
energy sources at a common DC link voltage with minimal
voltage perturbation. A decoupled control with dq-axis
current regulation is depicted in [14]. However, multiple
reference frame transform and control bandwidth limitation
with fixed-gain control implementation significantly affects
the controller robustness during disturbance rejection.
To provide a dynamic controller gain with a faster
convergence rate, a model predictive control (MPC) is
implemented for AFC switching control [16]. However, the
convergence rate largely depends upon the controller weight
updation within the interrupt sampling speed and hence noise
cancellation is difficult to eliminate. In addition, parameter
robustness can’t be ascertained with controller stability. In
view of these, Mukherjee et. al. [17] have described a power
reference adaptive control to adapt the filtering parameter
deviation in the control algorithm. However, the contribution
from the external control loop and information of state
variable deviation can’t be ignored during real-time
implementation and needs each step updation. To provide a
more robust control for grid-connected DC distribution
system, a back-stepping adaptive control is described in [18]
that considers the state variable updation in control
architecture. A combination of both state variable updation
and parametric variation with external DC loop elimination is
described in [19] with decoupled current control and
Lyapunov stability analysis. The adaptive control considers
the current in ideal grid conditions and continues to operate
with the similar controller gain even at smaller error
dynamics. However, none of above-described controls
consider a frequency variation as a major contributor of
external disturbance in state variable dynamics and assume
an ideal grid. Additional estimation parameters are essential
to determine grid frequency variation during non-ideal grid
conditions and thereof EV charging. Grid non-idealities with
parameter uncertainty have been considered in [20] through
an adaptive sliding mode controller (ASMC) gain adjustment.
However, the sliding gain with a signum function provides a
high-frequency oscillation with a longer error settling time
during reference tracking. Although multiple research works
have demonstrated higher-order integral filters to estimate
quadrature axis source voltage fundamental components, they
are limited to a certain order of harmonic multiples. In
addition, longer signal wires, measurement port offset error
and larger driving loop stray inductances introduce
dominating noise level frequencies that need a regular
updation in the estimation loop.
Input harmonics distortion at the utility during non-linear
charging operation at EVSE is inevitable without affirming
the complete elimination of asymmetrical switching,
decoupled parameters and lower order switching harmonics
[21]. In addition, the presence of multi-source power
integration with the EVSE needs a coordinated control
architecture to operate with minimal grid utilization and
enhanced power factor operation. This paper explores a
multi-objective prioritized control algorithm to provide a
seamless charging operation at EVSE facility. The charging
algorithm ensures BDC operation during G2V and V2G
mode transition with enhanced power quality operation. A
gain adaptive controller based multi-objective EVSE
charging architecture is described to implement bi-directional
charging operation with grid non-idealities and parametric
variation. The present bi-directional EV charging architecture
is well associated with a seamless bi-directional charging
operation and a multi-objective renewable integration to
provide continual charging operation with least grid
dependency. The major contribution of this work is
summarized as follows.
1. Implementation of a variable adaptive gain control
architecture with a direct power control algorithm to
minimize parametric uncertainties in a multi-objective EV
charger during grid distortions. The sigma modification in the
control law significantly improves the charging current
quality and convergence time during reference tracking.
2. A common mode G2V and V2G control architecture with
renewable and storage unit support is depicted to facilitate
uninterruptible charging support at EVSE.
3. A detailed proof of controller convergence and stability is
presented with Lyapunov function analysis and state
parameterization by incorporating cascaded control.
4. A supervisory control algorithm is illustrated to establish
an intelligent shift over, among multiple active energy
sources, in order to minimize grid dependency.
5. Frequency estimation through adaptive gain control is
presented to iteratively update source abnormalities at each
sampling instant of grid voltage input.
This paper is organized as follows: Section-II depicts
complete bi-directional EV charging system. Control
modeling of each stage converter unit is presented in Section-
III. The effectiveness of multi-stage controller, power
variation algorithm, and detailed case studies are depicted in
Section-IV with experimental validation through a charging
prototype, whereas conclusions are described in Section-V.
II. CHARGING ARCHITECTURE
The EV charging facility with grid-integrated multi-
objective control architecture is described in Fig. 1. The off-
board charging installation is well equipped with PV-BES
integration to support an isolated low voltage battery
charging facility and auxiliary DC load connectivity. The
auxiliary load can be considered as a battery swapping outlet
where GB/T connectivity can be accessed. A common DC
link with a fixed voltage Vdc coordinates the multi-source
integration through a supervisory control algorithm both in
standalone and grid-connecting mode. A double stage boost-
configured PV array is integrated with the BES for bi-
directional charging implementation. The BES unit comprises
of PbO3 battery bank of 204V and 100Ah capacity and
supports the intermediate DC link during V2G operation. A
string of PV-array with open circuit voltage Voc of 300V and
short circuit current Isc of 25A constitutes PV-array support
with a boost converter to the DC link bus voltage.
ib
s1
lr
n:1
lb
ic
ilr
s3
s6
s11
s12
s13
s14
s21
s22
s23
s24
Cdc
HFT
isr
s5
s4
load
Point
Line filter
vs
s7
VPV
lp
IPV
Vb
Auxiliary CP
PV
array
Vdc
lb
cf
ls
lsg
lsg
lsg
ls
ls
rf
BES
s2
s8
s9
Cb
ica
ibh
Vb
Fig.1 Schematic of multi-objective bi-directional EV charging architecture

During higher solar insolation and higher power demand, the
PV array operates in maximum power point tracking (MPPT)
mode to energize both EV charging operation as well as the
V2G operation. A single EV charging unit of 48V and 50Ah
LiFePO4 is considered in this architecture with a dual active
bridge (DAB) configuration. The DAB converter is able to
transfer bi-directional charging power with phase-leading and
phase-lagging operation. A multi-objective EV charging
algorithm is presented with the charging configuration to
achieve seamless power management with various grid non-
idealities through the design of a laboratory prototype.
III. SYSTEM MODELLING AND CONTROLLER DESIGN
This section describes the detailed system modeling and
control operation among power converter units of the BEV
charger. The effectiveness of the controller is demonstrated
by considering the following grid distortions.
1. Flat-topped and peaky sinusoidal waveforms are
considered individually, with multiple lower order harmonic
phase and frequency distortions. These types of waveforms
are most predominant in commercial charging points where
a fleet of EVs are connected with EVSE installation [22].
2. Frequency variation of 49.5 Hz to 50.5 Hz is
considered as a reference, although Indian grid codes raise a
trip signal within 3% of nominal frequency variation.
An experimental set-up is designed and developed, in
order to validate the EVSE architecture with grid non-
idealities, harmonic distortions and auxiliary load support.
A. Design and Control of Grid-connected Converter
The grid connected AFC is regulated through a three-
phase active bridge configuration to facilitate a constant DC
link voltage at the intermediate electrolytic capacitor Cdc. The
AFC maintains the utility power quality during peak mode of
EV charging. During the G2V charging operation, the front-
end controller establishes UPF operation irrespective of the
PCC power quality and voltage distortion. The design of the
AFC controller can be described by considering the source
current and voltage dynamics which is represented as,
 
 
 
1
1
1
sd
sd d s sd
s
sq
sq q s sq
s
dc s
dc loss o
dc dc
di
v u r i
dt l
di
v u r i
dt l
dV P
V P P
dt C C
  
  
  
(1)
where Ploss represents the power loss across the grid
connected inductive filter and P0 is sending-end power from
the DC link for EV charging operation. The decoupled
control inputs are defined as ud and uq.
The output power from the front-end converter serves as
input to DAB converter, BES unit and the auxiliary power
terminal. Replacing (1) with the decoupled power dynamics
of a three-phase grid-interactive converter, a new set of state
variables 2
( ) ( )
2
T
dc
s s dc
C
p t q t V
 
 
 
are deduced as [16],
2
2 2
( ) ( )
2 2
( ) ( )
2
2
s s m m
d
s s s
s s m
q
s s
dc dc
dc dc l
dp r V V
p t q s e
dt l l l
dq r V
q t p s e
dt l l
dV V
P
dt C V r


    
   
 
 
 
 
(2)
Considering rs and ls as α1, α2 and 2/rl as α3, the above
expression in (2) can be presented as the following state-
space presentation.
2
2
1 1
1
1 1 1
2
2 2 2
1 1
3 3
3
1
0 0
2
1
0 0 0
2
0
0 0
1 0
m
m
loss
dc
V
x x u
V
x x u
x x P
C


 



 

     
 
     
   
       
    
       
   
   
       
   
      
       
     

     
 
 



(3)
where [x1, x2, x3]T
are the state vectors that represent
ps(t),qs(t) and Vdc
2
with u1 and u2 as the input vectors. The
tracking error dynamics (ED) with a desired state reference
vector of xim can be presented as,
i i im
x x x
 
 , for i=1, 2 and 3. (4)
The reactive power error dynamics ( )
q t
 is presented as,
2 2 2m
x x x
 

   (5)
Substituting the ( )
q t
 dynamics from (2) into (5), the ED can
be derived as [21],
2 2
2 2 2 2 2 1 2 2
1 1
m
u
x k x k x x x x


 
      

    (6)
A linearized control law for the reactive power controller u2
can be designed as,
2 21 1 22 2
ˆ ˆ
u    
   (7)
where, 21 2 2 1 2m
k x x x
 
  
  and 22 2
x
   (8)
Substituting the gains of (7), (8), in the expression in (6), the
x2 dynamics is derived as,
1 2
2 2 21 22
1 1
x kx
 
 
 
   
 

  (9)
In similar manner, the reference active power x1m, which is a
function of DC link voltage dynamics is derived from (2) as,
 
1 3 3 3 3 3
ˆ
m m
x k x x  
   
  (10)
Where, 3
3
dc
x
C
 

Substituting the above expression of (10), in (3), the DC
voltage dynamics is expressed as,
3 3 3 1 3 3
x k x x  
   
 
   (11)
Considering the above reference inputs from (9)-(11), the
active power dynamics can be written as,
2
2 1
1 1 1 1 1 1 2 1
1 1 1
2
m
m
V u
x k x k x x x x


  
       

    (12)
A linearized active power control input u1, can be derived
from (12) as,
1 11 1 12 2
ˆ ˆ
u    
   (13)
where 11 1 1 2 3 3 3 3 3
ˆ m m
k x x x k x
   
    

  
and 12 1
x
 
Substituting the gain coefficients as described in (13) in (12),
the active power ED can be written as,
3 3
1 2
1 1 1 11 12 3
1 1 1
k
x k x

 
  
  
    
 
 
  (14)
The closed-loop error dynamics of the state vectors from (3)
to (14) can be rearranged as,

1
1
1 1 1 11 12 1
2
2 2 2 21 22
1
3 3 3 3
3
0 0
0 0 0
1 0 0 0
x k x
x k x
x k x


  

  


 
 
  
       
         
  
         
       

       
 
 
 


 


 

 

(15)
where 3
1 3
1
k

 
 
  
 
In a generalized parametric form, the expression (15) can be
represented as,
 
ˆ
, ,
T
x x x t

  
 
 
  (16)
To prove the asymptotic convergence and stability of the
above state dynamics in (16) about the equilibrium point, a
Lyapunov function candidate (LFC) is considered as,
1
1 1
( )
2 2
T T
v x Px tr 
 

  
 
  (17)
The dynamics of the LFC in (17), is derived as,
 
1 1
1
ˆ
2
T T T
v x Qx x P tr
   
 
      
 
    (18)
where Q is a symmetric positive definite matrix and Σ is the
damping gain. An updation law is derived from (18) as,
ˆ Px

  
  (19)
such that,
1
( , ) 0
2
T
v x t x Qx
  
   (20)
The asymptotic convergence of the controller functions u1
and u2 at the equilibrium point is also verified due to the
negative semi definiteness (NSD) of the expression in (20)
[23]. The adaptive gains k= [k1 k2 k3]T
effectively control the
current dynamics with quick reference tracking. However, in
case of additional noise at the input u(t), the expression in
(20), is no longer NSD and requires a higher Σ-gain to
cancel it out. The higher gain may impact the convergence
time and to get the updation faster, a modified damping term
e
 is introduced the new updation rule is presented as,
 
ˆ ˆ
e
Px

 
   
  (21)
where e
 represents the sigma modified gain. The gain e

provides a faster convergence during large system dynamics.
However, the present algorithm proposes a gain adaptation
with respect to the error amplitude, which is given as,
2
( 1) ( ) ( )
e e i i i
k k e sign e x

     (22)
where μ provides a faster convergence during large error ei
magnitude. The μ value is considered as 0.03 from the
simulation performances.
Proof of stability: The controller stability as in (19) can be
proved by considering the dynamics of LFC from (18).
Substituting (19) into (18), it can be derived as,
1
( , ) 0
2
T
v x t x Qx
  
   (23)
Since v(t) is positive definite, radially bounded and
decrescent, it is defined in terms of infinity norm L∞ as,
 
1 2 3
( , )
T
v x t L x x x L
 
  
   (24)
The expression in (24) can be further extended as,
   
1 2 3
ˆ ˆ ˆ ˆ
, ,
T
T
x t L L
    
 
    (25)
From the above, it can be said the control laws u1 and u2 are
also bounded by L∞ and hence continuous. The above LCF
dynamics is also square-integrable and according to
Barbalet’s lemma [2], it can be said that,
 
1 2 3 2
T
x x x L

   (26)
Combining the above error perturbation terms, it can be
concluded that, i
x
 is continuous. Hence the error dynamics
converge to zero as the time approaches towards a longer
value that proves the controller’s asymptotical stability. The
simulated performance of error convergence in presence of
error adaptive sigma-mod control and fixed gain adaptive
implementation is shown in Fig. 2. The sigma-mod adaptive
controller provides a faster error convergence during severe
grid distortion as compared to a fixed gain adaptive
controller. The control parameters for various constants
during the stability analysis are presented in Table-I. A
comparative analysis of noise cancellation at lower order
harmonics distinctly identifies the advantage of the sigma-
mod algorithm against the conventional gain adaptation
technique as shown in Fig. 3. The sinusoidal current
convergence at different values of k1,2 is shown in Fig. 3(a)
with supply voltage harmonics. To identify the rate
convergence with sigma-mod adaptation and fixed gain
control a comparative result analysis is shown in Figs. 3 (b),
(c) for lower-order frequency distortions. The adaptive
sigma-mod control illustrates a better error minimization as
compared to the conventional adaptive control [19]. A
detailed comparison of system dynamics with conventional
control architectures is presented in Table-II.
To achieve further accuracy in frequency estimation,
applications of integral filters are depicted in substantial
research work [20]. However, most of these filters are based
on a fixed frequency feed-forward parameter and are often
irresponsive towards higher input distortion. In this paper, a
gradient descent algorithm [24] is implemented to extract the
fundamental voltage components that iteratively update the
grid frequency at each sample of source voltage variation. A
distorted PCC voltage with symmetric periodicity is
comprised of a summation of hth
order harmonic extension
and by the application of Fourier series it can be written as,
Fig. 2 Performances of error convergence with utility voltage distortion

2 1
0
1
( ) sin( ), 0,1,2..
k
s o sh h
h
v t V V h t for k n
 


   
 (27)
An error function ε can be derived by considering the
distorted grid voltage and α-axis component that is
expressed as,
 
0 0
1
( ) cos( ) sin( )
N
sh sh s
h
t V h t V h t v 
  

  
 (28)
Minimizing the above expression in (25), by the negative
gradient of ε(t), the new frequency ω(t) is derived as,
1 0 0
, 1
( ) . cos( ) sin( )
N
sn sm
n m
t V n t V n t
    

 
  
 
 

 (29)
where γ1 is converging constant and a value closer to 0.5
results faster convergence during error minimization.
Considering, fundamental component of supply voltage
only, the above expression in (29) is modified as,
 
1
( ) . s s
t v v
 
  
  
 (30)
The gradient of grid angular frequency is updated at each
interval of operation to update any grid abnormalities through
controller gain adaptation. A detailed control architecture of
front-end converter control is shown in Fig. 4. Implementing
the dq-axis voltage and current components, the measured
active and reactive powers ps, qs are calculated and compared
with the reference powers Pm, Qm [16]. For unity power factor
in G2V charging operation Qm is considered as zero.
B. Modelling and Control of BES
The storage unit essentially consists of a stack of PbO3
batteries to support the DC link voltage for bi-directional
charging operation. The BES operates in current control
mode during the grid-connected mode, where the duty cycle
is obtained from the reference charging current Ib
ref
.
However, during standalone operation, a cascaded control
architecture is implemented, where the outer voltage loop
generates the current reference for BDC operation. The
dynamics of inductor current il and output DC link voltage
Vdc with u1 as switching function are represented as,
1 1
1 1
;
l dc dc l dc
B
dc dc
di V dV i V
V
u u
dt l l dt C RC
    (31)
where Vb represents the storage unit battery voltage. The
resistance R represents a virtual load resistance based upon
the extended range of load current demand. To minimize the
closed loop error dynamics (CLED) a pre-defined sliding
trajectory can be defined as,
 
1 2 3
( ) ( ) ( ) ( )
i v i v
s e t e t e t e t dt
  
   
 (32)
where, α1,α2 and α3 are the sliding coefficients. Considering
Ib
ref
and Vref as the current and voltage reference vectors, the
state errors can be defined as,
 
 
( ) ( )
( ) ( )
i ref l
v ref dc
e t I i t
e t V V t
 
 
(33)
However, in a double-stage cascaded control architecture the
reference current is generated from the outer loop DC
voltage reference tracking, through a PI-control regulation.
Hence, Ib
ref
can be represented as,
( ) ( )
ref
b p ref dc i ref dc
I k V V k V V dt
   
 (34)
The first order dynamics of the above expression in (34) can
be presented as,
( ) ( )
ref p v i v
d
i k e t k e t
dt
 
 (35)
Substituting (31) into (35), the dynamics ṡ is presented as,
 
1 2 3
i v i v
s e e e e
  
   
   (36)
Replacing the error dynamics ,
i v
e e
  in (36), and equating the
sliding dynamics ṡ with zero the equivalent control law ueq
can be derived as,
    1
3 3 1 2 1
1
2
1
1
p B
dc
i i v p
dc
eq
l dc l
p
dc dc
k V
V
e k e k
RC l
u u
i V i
k
C l C

    


    
 
 
 
 
 
(37)
The above control law is implemented to maintain a constant
DC link voltage through the bi-directional BES charging
during grid islanded operation as in Mode-I. However,
during Mode-II operation of bi-directional charging, the
current reference Iref can be decided from the battery SOC
status. To implement the constant current charging scenario,
the sliding trajectory can be modified as a function of current
error only and can be represented as,
1 1 3
( ) ( )
i i
s e t e t dt
 
   (38)
Calculation
of λ11-22
Pm
ps
Qm
qs
Vdc
*
Vdc
Estimation of ps
Estimation of qs
Estimation of Ṽdc
Vq
Vd
dq
abc
PWM
s1-2
s3-4
Calculation
α1
^ α2
^ α3
^
of
˜
˜
s5-6
z-1
vβ
2ξ
vs
vα
ʃ
-γ
Estimation
of u1,u1
θest
d
ωest
^
Σ
ωest
^
^
Fig. 4 Control architecture of front-end converter with frequency estimation
(a) (b) (c)
Fig. 3 (a) Performances of variable gain adaptation, disturbance rejection with (b) conventional gain adaptation (c) sigma-modified gain adaptation

By applying the constant rate reaching law [6], the sliding
control law ueqc can be derived as,
1
1 3
1
1
1
sgn( ) B
i
eqc
dc
V
k s e
l
u
V
l
 

  
 (39)
The control algorithms as described in (37) and (39) are
implemented for bi-directional charging control at the BES
to establish constant DC link voltage and CC charging
respectively as shown in Fig. 5. The robustness of the above-
described charging system and the reference tracking largely
depends upon the selection of sliding co-efficient, those are
determined from the analogy of second-order dynamics.
C. Operation and Control of DAB Converter
An isolated dual active bridge (DAB) converter is a
widely adapted DC-DC converter topology for most of the
high power EV charging architectures due to its inherent
zero voltage switching characteristics. DAB converter
achieves the desired bi-directional charging demand by
phase-shift variation between switching legs of either side of
the converter at a fixed duty cycle. A single phase-shift
(SPS) operation is discussed in the present EV charging
architecture with a fixed frequency operation as shown in
Fig. 6. The high voltage (HV) and low voltage (LV) sides of
the DAB converter are isolated through a 6:1 transformation
ratio to charge a 48V EV battery unit. Assuming a
symmetrical and continuous mode of operation, the current
expression at each of the sub-interval can be summed up to
calculate the phase-shift ratio β as [24],
2
0.5 0.25 0
2
0.5 0.25 0
sw r s
s
dc b
sw r s
s
dc b
f l P
for P
nV V
f l P
for P
nV V

  

   
(40)
The expression of β in (40), determines the power transfer
limit during charging operation. During CC charging, the
phase-shift ratio is improved from the voltage reference error
in case of a high discharged battery. However, the maximum
phase-shift ratio is limited to 0.5 to accomplish the BDC
charging operation. The schematic control architecture for
DAB converter control is shown in Fig. 6 (a).
D. Operation and Control of Solar-PV Unit
The PV-array serves as an auxiliary power source in the
proposed EVSE charging architecture. The PV-array is
mostly exposed towards a variable solar irradiance and on a
bright sunny day it varies between 700-1000W/m2
[11]. The
PV array thus needs to be weel-regulated to match the load
profile with a step-up converter operation to boost up the
variable input voltage. Although several algorithms are
depicted in literature to operate the PV unit through
maximum power point tracking (MPPT) algorithms, an
incremental conductance (INC) algorithm is implemented in
the present control architecture as shown in Fig. 6 (b) [11].
The algorithm modifies the duty ratio at each sample data
acquisition in order to search the MPP based upon the
positive and negative values of the updated conductance.
The MPP algorithm generates a voltage reference that is
further compared with the DC link reference voltage to
generate desired duty cycle more than a threshold value dth.
V*
b PI
ib
ib
ref
Vb
-
Eq.(37) d s9
-
SMC
Ib
ref
Ib
-
Gv(s)
d
Vb
Vb
ref
CC/CV
Mode selector
Mode-I
Mode-II
0.85p.u < vs <1.1p.u vs(n)
Y
N
SOC
Ib
soc0
Vb
ei
ev
SMC
u1
α1 α2 α3
s8
Gv(s)
Vb
Eq.(39)
s9
s8
Fig. 5 Control schematic for BES bi-directional operation
Phase-shift
Calculation
G2V
V2G
Selector
Vb
V*
b
PI
∆β
β
Vdc
Ps
>0 k
V2G G2V
Leading-edge
PWM carrier
Lagging-edge
PWM carrier
0.5
PI
I*
b
CC Mode
CV Mode
0.2-0.8 SOC
SOC>0.8
Ib
s11
s21
s12
s22
DAB Control
CC CV
CV CC
∆β
(a)
MPPT
InC Algorithm
enable
VPV
IPV
Vpo
Do
Vref
Vdc
d
Vstep
[11]
d=0
dth>0.1
s7
(b)
Ppv > PVT
START
Check the Grid nominal voltage Vp.u.
If
Vp.u< 0.8
If
0.8 < Vp.u< 0.9
If
0.9< Vp.u<1.1
Ppv > 0
Y Pgrid > 0
Check Pcmd
Select EVSC
Y
N
Check Pcmd
Select EVFC
Y
Pgrid > 0 N
Check PPV
Select EVSC
Select V2G
N
Y
Y
PBES >PT
Check PBES
Y
Y
Y
N N N
Ppv > PVT
PBES >PT
N
EVFC-EV Fast Charging EVSC-EV Slow Charging
(c)
Fig. 6 Schematic for (a) control architecture of DAB converter (b) PV-
MPPT control (c) G2V and V2G operational flow-chart
E. EVSE Bi-directional Charging Architecture
A coordinated power control architecture is followed to
operate the EVSE with seamless power flow operation as
shown in Fig. 6 (c). The flow chart describes the selection of
adequate operational modes based upon the grid voltage
information. The PCC voltage information is articulated with
low, medium and normal voltage operation based upon the
per unit voltage magnitude. The subsequent mode selection
command is then initiated to verify the status of grid power
requirement, where a negative command Pcmd, indicates the
requirement of grid-feeding operation. The EV slow
charging operation (EVSC) is initiated during grid feeding
operation with limited availability of auxiliary sources.
However, during an adequate amount of power availability
with PV operations, EV fast charging can be selected.

TABLE I
CONTROL PARAMETERS
Control
Parameters
Simulation
Value
Control
Parameters
Simulation
Value
k1, k2 2150 μ 0.03
k3 240 Σ [0.1 1e-4 30]T
P1,P2 1.26e-6 [α1 α2 α3]T
[2.4e-5 1.8e-2
0.075]T
P3 7.25e-6 k 1.5e-2
IV. RESULTS AND ANALYSIS
To verify the proof-of-concept a 3-phase 230V, 3.3kW
off-board charging facility is developed with a laboratory
prototype. A 3-phase grid simulator and PV emulator are
connected to provide multiple real-time characteristics for
bi-directional EV charging. A high-frequency transformer
(HFT) with EE-65 core, N87 material from TDK is designed
to accomplish power transformer across DAB converter unit.
To establish high-frequency current transfer with reduced
skin effect, a multi-stranded Litz wire with 42 AWG is
utilized for the HFT design. The auxiliary energy sources
such as PV-BES are integrated together at the common DC
link. The DC-link is designed with an electrolytic capacitor
of 2600μF capacitance that effectively eliminates the second
harmonic ripples and maintains a fixed DC voltage across it.
A. Performances with G2V and V2G Operations
To verify the controller adaptability with multiple grid
non-idealities and to assure enhanced power quality
operation, G2V and V2G simulations have been carried out
as shown in Fig. 7. The performances with G2V dynamics
are presented in Fig. 7(a). The input voltage vs is presented
with voltage swell and harmonic distortion. The source
current following is presented with highlighted portion,
where unity power factor operation can be observed. In order
to verify the voltage and current transients, the reference
charging current is increased up to twice the initial battery
current Ib. The source current at both of the charging ends
immediately follows the reference command with a 15V DC
voltage shoot-through. The change in SOC slope can be seen
with variation in charging current. A similar operation has
been carried out with V2G dynamics as shown in Fig. 7(b),
where a phase opposed current tracking is observed with
minimal DC-link voltage ripple. The bi-directional charging
operation is carried out on the similar control architecture,
only by changing the current and voltage reference values.
B. Charging Performances with BES Integration
The charging dynamics of BES is shown in Fig.8. The
auxiliary battery storage operates in both charging and
discharging modes through a non-isolated DC-DC converter.
The positive current magnitude indicates the BES charging
mode, where the grid or PV-array is utilized to charge the
battery. To verify BES charging dynamics, a lower charging
current reference is applied as shown in Fig. 8(a).The source
current demand decreases proportionately with the change in
BES current demand. The converter switching operation is
shown in Fig. 8(b) with inductor voltage and current
dynamics. The grid current dynamics with BES charging and
discharging performances are shown in Fig. 8(c). In order to
support the active power demand during the peak hour
charging at the utility and non-availability of PV energy, the
BES performs the discharging operation, which is reflected
in the source current dynamics. However, at the onset of grid
rated power availability, a mode changing command is
applied to establish the charging operation at BES, which is
illustrated in Fig. 8 (c).
C. Performances with Grid-PV Integration
Performances of grid dynamics during bi-directional
charging and PV integration are presented in Fig. 9. The PV-
array characteristics are emulated through a PV simulator
and implemented with the incremental conductance
algorithm to verify the MPPT operation. The efficacy of the
MPPT algorithm is obtained by recording a wide range of
solar insolation variations within a scheduled time period.
The PV-to-grid, current feeding operation is illustrated
through variable solar insolation to verify multiple dynamics
during charging operation. Fig. 9 (a) demonstrates a test
case, when PV insolation is increased by 300W/m2
. The
change in Vmpp is shown in ch. 4 of the scope parameter that
converges quickly during Ipv variation. The three-phase
source current is and vs are phase-opposing in nature which
depicts the V2G operation. The entire operation is carried
out with the least support from BES. The CC charging
operation at the BES can be identified from Fig. 9 (b), where
PV-array delivers power to the grid. Fig. 9 (c) demonstrates
another test case when PV-energy is utilized for both BES
charging and grid feeding operation with MPP operation.
The MPP operation with boost converter is set to increase
the Vmpp from 300V to 360V with conversion efficiency at
room temperature as shown in ch.5 of Fig. 9 (c). At the
moment the grid requires additional active power, the battery
unit charging is stopped that results an increase in the source
current magnitude. Experimental performance of MPPT with
the average efficiency is shown in Fig. 10.
D. Performance Analysis with DAB Operation
The isolated DAB converter is connected across the DC
link to carry out the charging operation for a lower battery
operating voltage of 48V. The converter operates with a
fixed duty cycle at 25 kHz. switching frequency to generate
symmetrical voltages across the HF transformer as shown in
Fig. 11. The phase-shift is calculated according to desired
power level of charging demand as shown with the control
architecture in Fig. 6(a). Single phase-shift (SPS)
modulation is applied between two full bridges of DAB
converter with the charging power requirement. To
demonstrate battery current Ib dynamics in DAB converter
the power reference is lowered by half of the initial charging
power as shown in Fig. 11 (a).
(a) (b)
Fig. 7 Performance dynamics with (a) G2V (b) V2G charging operations

Fig. 10 PV-array MPPT operation with INC algorithm
The current Ib starts immediately following the reference
command by lowering the phase-shift ratio in the DAB
operation. The performances of DAB converter primary and
secondary voltages vTp, vTs and current dynamics iTp, iTs are
shown in Fig. 11 (b). In the case of lower SOC at the battery
terminals, an internal phase shift is applied between the
adjacent legs of DAB converter as shown in Fig. 11 (c).
E. Performance with Grid Voltage Distortion
The effectiveness of the present controller dynamics at
grid distortions is verified with two distinct test cases as
shown in Fig. 12. In Fig. 12 (a), the dynamic performance is
analyzed with BES charging operation in presence of lower-
order voltage harmonic dominance. The source current
remains sinusoidal even at grid distortion and maintains UPF
operation with minimal DC-link voltage shoot through. The
test case is carried out without PV support, where the entire
charging operation is current-controlled. In order to verify
the controller reliability, a critical case is considered, where
the EVSE restricts additional feed-through power from
renewables and the PV insolation is entirely utilized in DAB
converter charging operation. The controller maintains the
grid current as desired by the distribution operator through
variable reference command. In this case, additional current
feed from the renewables is utilized to charge the EV storage
unit. Fig. 12 (b) describes the above described performances
with variable solar irradiance, with a constant grid dynamics.
The experimental prototype for the present EV charging
architecture is shown in Fig. 13.
F. Performance Analysis of BEV Charger
Performance indices of the present control algorithm and
the effectiveness of the charging operation are verified by
considering a distorted grid operation as shown in Fig. 14.
The lower harmonic performance indices ensure the entire
charging and discharging operation with improved power
quality conditions. The total harmonic distortion (THD) and
each harmonic content are limited within a range of 5% as
per the IEEE reference guidelines [25]. The performance is
verified with ideal and non-ideal grid conditions by
implementing the present adaptive control architecture with
the sigma-modified algorithm. The bi-directional operation
with G2V and V2G dynamics is shown in Figs. 14. (a), (b)
with ideal grid voltage condition. The distorted charging
dynamics is shown in Fig. 14 (c), where a THD as low as
3.53% is obtained with peaky source voltage distortions.
V. CONCLUSION
The integrated operation of PV-BES supported multi-
objective EV charging operation is investigated in the
present work with a gain adaptive control implementation.
An updated sigma-mod control is demonstrated to be
efficient under a wide range of supply voltage distortion.
The robustness of the dynamic control is proven analytically
with the Lyapunov candidate function to prove the
convergence of the present control algorithm against the
parametric uncertainty and frequency distortion. A multi-
mode charging algorithm with minimal grid dependency is
demonstrated at a wide range of charging dynamics to
evaluate the efficacy of the controller implementation. A
rule based sliding control algorithm at the non-isolated DC
converter stage and phase-shift control at DAB converter is
established to support multi-mode power exchange at
various grid dynamics. A coordinated control algorithm is
proposed and verified by considering various grid dynamics
for enhanced power quality operation. As illustrated through
the experimental validation, the present architecture is
suitable to establish multi-objective charging and ancillary
power support at EVSE installation.
Decrease in charging current
change in is
Ch.1:1A/div.
Ch.2-4: 5A/div. Time:40ms/div.
change in Ib
is
Time: 40µs/div.
Ch.1: 100V/div. Ch.3: 1A/div.
Ch.4: 250V/div.
Mode transition
vlb
iBES
VBES
Change in current
Ch.1: 50V/div.
Ch.4: 2A/div.
Ch.2: 250V/div. Ch.3: 5A/div.
V2 G Mode G2 V Mode
Ib
Charging mode transition
V2G to G2V
v s i s
V dc
(a) (b) (c)
Fig. 8 Charging performances with (a) source current dynamics (b) BES charging current variation (c) mode transition

Ch.2: 2A/div.
Ch.5:200V/div. Ch.8:5A/div. Ch.6:5A/div.
Ch.4:50V/div.
Ch.1: 5A/div.
Ch.3: 200V/div.
Ch.7:5A/div.
Constant Vdc
Increase in
is
Constant Ib
Increase inPVinsolation
Constant DC link
Ch.4: 50V/div.
Ch.2:5A/div.
Ch.5: 200V/div.
Ch.6:5A/div.
Change in Ib
Constant Vmpp
Ch.1:5A/div.
Constant Impp
Ch.8:5A/div. Increase inis
(a) (b) (c)
Fig. 9 PV-grid-BES dynamics with (a) variable solar insolation (b) CC operation at BES unit (c) V2G operation

(a)
vTp
vTs
iTs
iTp
180
phase-shift
Higher Ib
(b)
(c)
Fig. 11 DAB dynamics with (a) charging current variation (b) voltage and
current response across HF transformer (a) internal phase modulation
(a)
(b)
Fig. 12 Charging dynamics in presence of grid distortions with (a) G2V
operation (b) V2G operation
Fig. 13 Experimental prototype for 3.3kW bi-directional EV charger
ACKNOWLEDGMENT
The authors are grateful to the DST, Government of India
for FIST scheme under grant no. RP03195G, SERB-NSC
Fellowship and SIEVE grand challenge project by IIT Delhi.
TABLE II
PERFORMANCE COMPARISON
Topology Control
strategy
Non-idealities Performance
vs fs vsh Error settling
time
Convergence
rate
Control
gain
Memory
Utilization
[11] PI Yes No Yes (40-60) ms. Low Fixed Low
[14] Adaptive Yes No No (20-40) ms. Moderate Fixed High
[16] MPC No No No (40-60) ms. Low Variable High
[17] Adaptive No Yes No 30ms Low Fixed Medium
[19] Adaptive No No No 30ms High Variable Low
[20] ASMC Yes No Yes (30-40) ms. Moderate Variable Medium
Present Adaptive Yes Yes Yes (10-20) ms High Variable Low

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(a)
(b)
(c)
Fig. 14 Performance indices with (a) G2V dynamics (b) V2G dynamics in ideal voltage condition (c) G2V dynamics with grid distortions

Debasish Mishra (S,16) was born in Bhubaneswar,
Odisha, India, in 1983. He received the B.Tech degree
in electrical engineering with first class and Hons.
from Biju Patnaik University of Technology (BPUT),
Rourkela, India and M.Tech degree in power
electronics from Indian Institute of Technology
(BHU), Varanasi, India, in 2006 and 2012
respectively. He is currently working towards the
Ph.D. degree in the Department of Electrical
Engineering at Indian Institute of Technology Delhi,
New Delhi, India. His research interests include power electronic converter
for electric vehicle applications, power quality enhancement, controller
applications for renewable energy based grid interactive systems.
Bhim Singh (SM’99, F’10) has received his B.E.
(Electrical) from the University of Roorkee (Now
IIT Roorkee), India, in 1977 and his M.Tech.
(Power Apparatus & Systems) and Ph.D.
(Electrical) from the IIT Delhi, India, in 1979 and
1983, respectively. In 1983, he joined the
Department of Electrical Engineering, University of
Roorkee, as a Lecturer. He became a Reader there
in 1988. In December 1990, he joined the
Department of Electrical Engineering, IIT Delhi,
India, as an Assistant Professor, where he has
become an Associate Professor in 1994 and a Professor in 1997. He has
been Head of the Department of Electrical Engineering at IIT Delhi from
July 2014 to August 2016. He has been Dean, Academics at IIT Delhi,
August 2016 to August 2019. He has been JC Bose Fellow of DST,
Government of India from December 2015 to June 2021. He has been CEA
Chair Professor from January 2019 to June 2021. He is SERB National
Science Chair since July 2021. Prof. Singh has guided 103 Ph.D.
dissertations, and 171 M.E./ M.Tech./M.S.(R) theses. He has filed 96
patents. He has executed ninety sponsored and consultancy projects. His
areas of interest include solar PV grid interface systems, micro grids, power
quality monitoring and mitigation, solar PV water pumping systems,
improved power quality AC-DC converters.
Bijaya Ketan Panigrahi (Senior Member,
IEEE) received the Ph.D. degree in power
systems from Sambalpur University,
Sambalpur, India, in 2004. He is currently a
Professor with the Department of Electrical
Engineering, IIT Delhi, New Delhi, India,
where he is also the Head of the Center for
Automotive Research and Tribology (CART).
His research interests include soft computing,
signal processing, power quality, renewable
energy systems, power system protection,
electric vehicles and charging infrastructure, cyber security of power systems,
and the Internet of Things. Prof. Panigrahi is an Associate Editor for IET
Smart Grid and Editor for IETE Journal of Research.

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