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Control Strategy for Distribution Generation
Inverters to Maximize the Voltage Sup p o rt in the
Lowest Phase During Voltage Sags
Antonio Camacho, Miguel Castilla, Jaume Miret, Member, IEEE, L. García de Vicuña,
Miguel Andrés Garn ica
Abstract —Voltage sags are considered one of the worst
perturbations in power systems. Distributed generation
power facilities are allowed to disconnect from the grid
during grid faults whenever the voltage is below a certain
threshold. During these severe contingencies, a cascade
disconnection could start, yielding to a blackout. To mini-
mize the risk of a power outage, inverter-based distributed-
generation systems can help to support the grid by ap-
propriately selecting the control objective. Which control
strategy performs better when supporting the grid voltage
is a complex decision that depends on many variables. This
paper presents a control scheme that implements a smart
and simple strategy to support the fault: the maximum
voltage support for the lowest phase voltage. Therefore,
the faulted phase that is more affected by the sag can
be better supported since this phase voltage increases
as much as possible, reducing the risk of under-voltage
disconnection. The proposed controller has the following
features: a) maximizes the voltage in the lowest phase, b)
injects the maximum rated current of the inverter, and c)
balances the active and reactive power references to deal
with resistive and inductive grids. The control proposal is
validated by means of experimental results in a laboratory
prototype.
Index Terms—Grid faults, Positive-negative sequence,
Voltage dip, Voltage ride-through, Voltage sag, Voltage sup-
port
I. INTRODUCTION
T
HE high integration of renewable energy sources and
distributed generation (DG) [1] into the grid has changed
the requirements and the operation of power systems [2]. Some
years ago, DG sources represented a low contribution over
the total energy market. At present, the total amount of non-
conventional energy production can achieve up to 50% of the
total electrical comsumption and even more [3], [4]. This new
scenario presents a potential benefit over the classical one,
since DG reduces energy losses and many times provides from
clean and sustainable energy sources [5]. However, the massive
This work has been supported by ELAC2014/ESE0034 from the
European Union and its linked Spanish n a tional project PCIN-2015-
001. We also appreciate the support from the Ministry of Economy and
Competitiveness of Spain and European Regional Development Fund
(FEDER) under project ENE2015-64087-C2-1-R.
A. Camacho, M. Castilla, J. Miret, L. García d e Vicuña
and M. A. Garnica are with the Department of Electronic
Engineering, Technical University of Catalonia, 08800 Vilanova
i la Geltrú, Spain (e-mail: antonio.camacho.santiago@upc.edu;
miquel.castilla@upc.edu; jmiret@eel.upc.edu; vicuna@eel.upc.edu;
miguel.garnica@armada.mil.co)
integration of those systems can compromise the reliability of
the whole system, in particular during voltage sags.
Voltage sags are one of the worst perturbations in power
systems characterized by a short-time voltage drop in one
or several phases [6]. The main causes are short-circuits by
unintentional contact, lightnings and equipment failure [7].
During the fault, DG grid-connected power sources must
withstand the perturbation and operate continuously. However,
in order to protect the installation, when the voltage is low for
a long time, the power facility can be disconnected according
to the voltage profile and trip times defined in grid codes [8]–
[10]. To reduce the risk of disconnection, appropriate low-
voltage ride-through (LVRT) protocols need to be developed
to support the grid voltages.
The conventional LVRT services [11]–[15] are focused on
medium to big power plants above a certain rated power.
The main objective of grid codes is to support the grid
with reactive power during the fault, and to guarantee the
continuous operation to avoid sudden loss of power generation.
The control proposal of this paper should be understood as a
part of the new generation of grid codes that could apply to
any rated power generation source, that is being interfaced
with the grid via flexible power converters, and tied to any
type of grid impedance (inductive and resistive with high or
low values).
Voltage support has become a challenging method to im-
prove the grid reliability during grid faults. The main reason
for this is the huge amount of fast reactive power provisions
available in inverter-based DG systems. How to manage the
current injected by the DG into the grid is the main issue
for the new development of such control strategies. However,
which strategy is appropriate for a given voltage sag is a
complex problem to be solved. This paper presents a voltage
support control scheme that implements one of the simplest
objectives: to maximize the lowest phase voltage. This strategy
is fairly justified by the fact that raising the lowest voltage
could avoid under-voltage disconnection.
The trend in voltage support control is nonetheless dedicated
to mainly inductive grids [16]–[20], while low and medium
voltage grids with some inherent resistive behavior have been
less discussed in the literature [21]–[24]. This study presents
a control scheme that applies for any type of grid impedance,
either inductive, resistive or a combination of both. Indeed, the
proposed solution is also valid for weak or stiff grids since the
optimal solution does not rely on the magnitude of the grid
power
source
dc-link
inverter filter
L
i
L
o
i
C
PCC
v
L R
v
g
grid
Fig. 1. Simplified scheme of a three-phase grid-connected distributed
generation inverter.
impedance, but on the inductive/resistive ratio
p
L
{
R
q
.
Several works have been proposed in the literature for
voltage support during faults [16]–[28]. Most of these works
are based on symmetric sequences to deal with unbalanced
grid voltages, which has been established as the preferred
method to develop advanced voltage support controllers. The
main features investigated in this research area cover: different
voltage support objectives [16]–[20], [27], [28], maximum
current injection during the sag [17], [19], [25], [26] and grid
impedance matching [22]–[24]. However, none of these works
joins these three features at the same time, i.e. improving the
voltage support for any type of grid impedance while injecting
the maximum rated current. To simultaneously accomplish
these objectives, several issues need to be addressed first as
will be shown along the work.
Compared with previous state-of-the-art control strategies,
the main contributions of the proposed work are: a) the
formulation of a new voltage support objective for distribution
generation inverters during grid faults, b) the control scheme
that guarantees the maximum increase in the lowest phase
voltage, subject to the constraint of a safe current injection,
and c) the flexibility of the proposal to deal with inductive and
resistive, weak or stiff grids. This method has the advantage
of increasing as much as possible the lowest phase voltage
in a safe manner. By considering the grid impedance, it is
possible to extend the voltage support range. Thus, the risk of
under-voltage disconnection is reduced.
The paper is organized as follows. Section II formulates the
problem. Section III solves the problem of maximizing the
lowest phase voltage. Section IV deals with the impact of the
grid impedance on the performance of the proposal. Section
V presents the experimental results obtained in a laboratory
prototype. Finally Section VI concludes the paper.
II. PROBLEM STATEMENT
This section starts presenting the basics of the power plant
under control, then the main controller tasks are enumerated,
and the voltage support concept is briefly explained, finally the
control objectives and the problem to be solved are presented.
A. Power Plant
The main objective of the proposed work is to maximize the
lowest phase voltage during grid faults. This proposal applies
to DG inverters and/or static synchronous compensators with
energy storage capacity that are interfaced with the grid
via full-power converters. A generic scheme of this kind of
controlled systems is presented in Fig.1. In the figure, the
primary source is connected to the three-phase inverter. In
TASK : Controller(t
k
)
1
v
abc
, i
abc
= ReadADC()
2
v
α
, v
β
= Clarke(v
abc
)
3
i
α
, i
β
= C larke(i
abc
)
4
v
α
, v
β
, v
α
, v
β
= SequenceExtractor
v
α
, v
β
5 if Sag is detected then
6
i
α
, i
β
= VoltageSupport
v
α
, v
α
, v
β
, v
β
7 else
8
i
α
, i
β
= NormalOperation(
)
9
d
α
, d
β
= PRes
i
α
i
α
, i
β
i
β
10
T
abc
= SpaceVectorPWM
d
α
,d
β
Fig. 2. Pseudo-code of the controller task.
between, a dc-link is needed to balance the power flow from
the source to the grid. The main inverter’s parts are the power
switches and the LCL output filter to reduce the switching
harmonics. The inverter connects to the grid at the point
of common coupling (PCC), which corresponds to the place
where the phase voltages v for the different voltage support
controls should be compared. The grid is modeled as a voltage
source v
g
and an equivalent grid impedance R and L. It should
be mentioned that for developing the control proposal, the L
{
R
ratio need to be known. To this end, two main methods can
be borrowed: the knowledge of the nearby elements close to
the facility, or an on-line grid impedance estimator [29], [30].
In order to simplify the study, along this work it is assumed
that no local load is tied to the DG inverter. By assuming
this, the theoretical analysis becomes simpler and the control
development can be derived in a more intuitive way.
B. Controller
After presenting the main system parts, the controller func-
tionality is briefly reviewed. To control the plant in Fig. 1,
the inverter is set in current-controlled mode. The pseudo-
code that implements the main controller parts is presented in
Fig. 2. The controller task is activated each sampling time,
the first step is to sense the voltages and currents. Then,
by using Clarke transformation, the instantaneous values in
the α-β domain are obtained. A sequence extractor [31] is
needed to decompose the voltage into the symmetric sequence
counterparts (v
α
and v
β
for the positive sequence, and v
α
and v
β
for the negative one). Once the sag is detected, the
proposed voltage support control is launched. This part of
the code will be fully described in Section III-B. For the
case where no sag has been detected, the current references
are selected based on the conventional behavior of a current-
mode inverter [32], depending on the production, desired
power factor, operational and economic constraints. After
computing the reference currents i
α
and i
β
, a proportional-
resonant controller compares the references and the sensed
currents to get the duty cycles of the inverter d
α
and d
β
.
Finally, a space vector PWM computes the switching times
of each inverter branch.
C. Voltage Support
Based on the scheme in Fig. 1, the relations among the
inverter and the grid voltages, the injected currents, and the
grid impedance can be expressed as
v
v
g
Ri
L
di
dt
. (1)
where the voltage support from the grid to the PCC is
∆v
v
v
g
. This voltage increment clearly depends on the
grid impedance as will be shown along this work. Indeed, the
main limitation of the voltage support control schemes is the
magnitude of this impedance. For weak grids, higher voltage
support effects are obtained than for stiff ones.
Also, as previously stated, in order to inject a high-quality
current into the grid, and to deal with unbalanced voltages, the
method of symmetric sequences has become the preferred tool
to develop advanced voltage support controllers. To further
develop the control, some magnitudes based on the symmetric
sequence theory are required. After obtaining the instantaneous
voltage sequences v
α
, v
α
, v
β
and v
β
, the amplitudes of the
positive and negative sequences are computed as
V
b
p
v
α
q
2
p
v
β
q
2
(2)
V
b
p
v
α
q
2
p
v
β
q
2
. (3)
Note that along the text, uppercase is used to indicate am-
plitude variables while instantaneous values are written in
lowercase. Besides, the sag angle between the positive and
negative sequence ϕ, which is needed to derive the solution,
is obtained as [20]
cos ϕ
v
α
v
α
v
β
v
β
V
V
(4)
sin ϕ
v
α
v
β
v
α
v
β
V
V
(5)
ϕ
atan2
p
sin ϕ, cos ϕ
q
(6)
where atan2 is the two-argument arctangent function.
Thanks to the use of symmetric sequences, the inverter can
be viewed (when analyzing the voltage support effects) as
a current source injecting positive sequence active I
p
and
reactive I
q
currents into the grid. This assumption is the basis
for the development of the control proposal, and the derivation
of these active and reactive current references are the goal to
maximize the lowest phase voltage.
In order to detail the proposed voltage support concept, Fig.
3 presents the phasor diagram of the phase voltages for a given
voltage sag. The amplitude of the phases V
a
, V
b
and V
c
is
given in per unit (p.u.). As shown in the phasor graph, phase
A barely suffers the sag while phase C (in blue color) is the
most affected voltage. In the interest of clarity, the angle of
phase C (the lowest voltage) is selected to be 180°. Under this
consideration, the currents decomposition and the associated
angles are better appreciated in the graph.
In order to raise as much as possible the lowest phase
voltage, two requirements are needed, the first one is to inject
the maximum rated current of the inverter through this phase
(i.e. I
c
I
max
), and the second one is that this phase current
0°
30°
60°
90°
120°
150°
180° 0°
30°
60°
90°
120°
150°
1p.u.
I
pc
I
qc
I
c
I
max
θ
V
a
V
b
V
c
Fig. 3. Voltage support concept.
must be injected in a particular angle with respect to the
phase voltage. This angle is represented by θ (which has
been arbitrarily selected to 60° in the phasor diagram). The
first requirement allows for a safe operation and a better
utilization of the inverter capabilities during the sag. The
second requirement is the key point to maximize the voltage
support. Without loss of generality, this injected current can
be decomposed into an active I
pc
and a reactive component
I
qc
which are in-phase and in-quadrature with respect to the
phase voltage respectively. Depending on the magnitudes of
these two currents, θ will be modified and different voltage
variations will be produced depending on the grid impedance.
Assuming a mainly inductive grid, it is clear that injecting a
mainly reactive current I
qc
will produce better voltage support
effects on the grid. In such a case θ
90° . On the contrary, for
a mainly resistive grid, the injected current should be mainly
active I
pc
, and θ
0° . In between these two extreme cases,
the best voltage support solution for any grid impedance must
be obtained, as it will be shown in Section III-A.
D. Control Objectives
Along this work, the control to be implemented during the
sag is based on the transformation of the unbalanced voltages
into the symmetric sequences. Thus, the phase currents I
pc
and I
qc
need to be transformed into the corresponding I
p
and I
q
values, consisting in the in-phase and in-quadrature
currents following the positive sequence voltage V
instead
of the phase voltage V
c
. The current reference generator for
the symmetric sequences that achieves this objective can be
expressed as [19]
i
α
I
p
V
v
α
I
q
V
v
β
(7)
i
β
I
p
V
v
β
I
q
V
v
α
(8)
where it can be seen how the reference currents i
α
and i
β
cause the inverter behave as a positive sequence active and
reactive current source.
It should be highlighted that the proposal deals with positive
sequence voltages, being the negative sequence uncontrolled.
This facts allows for a simpler and easier implementation, pro-
ducing balanced injected currents, which is of interest during
unbalanced voltage sags. As a drawback, voltage imbalance
cannot be mitigated with the proposed method.
Along this work, the lowest phase voltage will be denoted
as V
x
in order to deal with any voltage sag. For this purpose,
the following is defined
V
x
min
t
V
a
, V
b
, V
c
u
. (9)
Resuming the main control goals, i.e.
1) maximize the lowest phase voltage V
x
2) inject the maximum current of the inverter I
max
,
the problem can be formulated as
max
x
Pt
a,b,c
u
V
x
I
p
, I
q
subject to: I
x
I
max
.
(10)
The solution relies on finding a combination of active and
reactive currents
p
I
p
, I
q
q
that simultaneously maximizes the
lowest phase voltage by injecting the maximum permissible
current of the inverter I
max
. As can be inferred from (10), the
optimal solution comprises several stages. First, to evaluate
the voltage support effect of an injected phase current into a
generic R-L grid for any given voltage sag. Then, to find the
current to voltage angle that maximizes the voltage support.
And finally, to translate these expressions from the phase
values into the symmetric sequence values. These three steps
are fundamental to develop the solution to (10) as will be
shown in next Section, and constitutes the main contributions
of this work.
III. PROBLEM SOLUTION
This section will be devoted to solve (10). The solution is
developed in two steps: firstly, the active and reactive phase
currents that maximizes the lowest phase voltage are obtained
and, secondly, the positive sequence active and reactive cur-
rents are derived.
A. Maximization of the Lowest Phase Voltage
Proposition 1. Let I
px
be the active phase current associated
with the lowest phase voltage, and let I
qx
be the reactive phase
current. Under this consideration, by selecting
I
px
I
max
R
a
R
2
p
ωL
q
2
(11)
I
qx
I
max
ωL
a
R
2
p
ωL
q
2
(12)
then the lowest phase voltage V
x
is maximized and the injected
phase current equals the rated current of the inverter I
x
I
max
, for a given grid frequency ω, and for any grid impedance
R and L.
Proof. The optimal active and reactive phase currents that
maximize the voltage in the lowest phase are obtained by using
the method of the Lagrange multipliers. The problem consists
in building the Lagrange function L based on the objective
function f and the restriction g so that
L
p
y
1
, y
2
, λ
q
f
p
y
1
, y
2
q
λg
p
y
1
, y
2
q
(13)
where λ is the Lagrange multiplier, and y
1
, y
2
are the
dependent variables.
Using (1) and the graphical projection of each phasor as
shown in Fig. 3, the voltage support effects can be quantified.
To this end, the phase current is decomposed into the active
and reactive parts. Arranging the involved terms into a single
equation, and after some mathematical manipulations, the
theoretical amplitude of the phase voltage at the PCC side
can be obtained. As a result, the PCC voltage is related to the
voltage amplitude at the grid side, the injected currents and
the grid impedance as
V
x
ωLI
qx
RI
px
b
p
V
gx
q
2
p
ωLI
px
RI
px
q
2
(14)
where V
x
is the amplitude of the supported phase voltage, V
gx
is the phase voltage at the grid side, and I
px
and I
qx
are the
unknown variables.
Once the objective function to be maximized f
p
y
1
, y
2
q
V
x
p
I
px
, I
qx
q
presented in (14) is derived, a constraint should
be included to keep the inverter currents safely controlled.
Resuming the current in phase C from Fig. 3, the restriction is
straightforward since both components in the phase current I
px
and I
qx
are 90 ° delayed. Thus, the constraint can be written
as
g
p
y
1
, y
2
q
b
p
I
px
q
2
p
I
qx
q
2
I
max
0. (15)
Each involved term in the Lagrange function (13) has been
identified for the problem stated. To obtain the optimal solu-
tion, the next step is the computation of the gradient with
respect to the involved variables I
px
, I
qx
and λ. Finally,
solving the gradient to zero gives the optimal solution
∇L
p
y
1
, y
2
, λ
q
B
L
B
I
px
,
B
L
B
I
qx
,
B
L
B
λ
0. (16)
Developing (16), the optimal currents
p
I
px
, I
qx
q
that maxi-
mizes the lowest phase voltage are (11) and (12).
Alternatively, by using trigonometric identities, (11) and
(12) can be rewritten as
I
px
I
max
cos θ (17)
I
qx
I
max
sin θ (18)
where
θ
atan2
p
ωL, R
q
. (19)
B. Phase Currents to Symmetric Sequence Currents
Proposition 2. Let
s
ϕ be the rotation angle that translates
the optimal active I
px
and reactive I
qx
phase currents in
(17) and (18) to the symmetric sequence counterparts I
p
and
I
q
. Under such consideration the active and reactive current
