This article has been accepted for publication in a future issue of this journal, but has not been

fully edited. Content may change prior to final publication. Citation information: DOI
10.1109/TPEL.2014.2301463, IEEE Transactions on Power Electronics

Reactive Power Control for Distributed Generation

Power Plants to Comply with Voltage Limits
During Grid Faults
Antonio Camacho, Miguel Castilla, Jaume Miret, Member, IEEE, Ramon Guzman and Angel Borrell

Abstract—Grid faults are one of the most severe problems for alleviate the adverse effects of grid faults, grid codes from the
network operation. Distributed generation power plants can help network system operators dictate the behaviour of DG plants.
to mitigate the adverse effects of these perturbations by injecting The evolution of these codes for DG during grid faults started
reactive power during the sag and the post-fault operation. Thus,
the risk of cascade disconnection and voltage collapse can be with low-voltage ride-through, which demands withstanding
reduced. The proposed reactive power control is intended to voltage sags. As the penetration level of DG sources was
regulate the maximum and minimum phase voltages at the point increased, reactive power injection was included in grid codes
of common coupling within the limits established in grid codes to support the grid voltage and to reduce the possibility of
for continuous operation. In balanced three-phase voltage sags, voltage collapse [5]. The next generation of grid codes could
the control increases the voltage in each phase above the lower
regulated limit by injecting positive sequence reactive power. In require negative sequence current injection [6] and voltage
unbalanced voltage sags, positive and negative sequence reactive support control [7]–[9] in steady-state and transient. The aim
powers are combined to flexibly raise and equalize the phase is to regulate the point of common coupling (PCC) voltage
voltages; maximum phase voltage is regulated below the upper to a safety range, preventing damage in the equipment while
limit and the minimum phase voltage just above the lower limit. improving voltage support services.
The proposed control strategy is tested by considering a distant
grid fault and a large grid impedance. Selected experimental In a real distribution power system, the capacity of voltage
results are reported in order to validate the behavior of the restoration is obviously limited by the power rating and the
control scheme. grid stiffness. Grid codes are demanding more reactive power
Index Terms—Reactive power control, grid fault, voltage sag, capacity to improve the contingency against faults [8], [10].
voltage support, positive and negative sequence control. The use of these extra resources can be adapted to implement
smart voltage support services during distant grid faults. A
smart voltage support service, as proposed below, should
I. I NTRODUCTION regulate the phase voltages within the limits established in grid
codes for continuous operation [11]. The safety limit strategy
T HE high penetration level of renewable energy sources
and distributed generation (DG) plants faces new
challenges in the operation of transmission and distribution
depends on particular grid codes, and each code provides
its own specification for continuous operation, although most
networks [1]–[3]. The growing installed power from DG plants of them state the maximum voltage limit at 1.10 per unit
has led to a change in the requirements for ancillary services, (p.u.), and the minimum at 0.85 p.u. In type I voltage sags
particularly during grid faults. Among these new services, (one dropped phase) or type II (two dropped phases), the
voltage control in wind plants, photovoltaic parks and other reactive power strategy should be different than the strategy
large-scale power plants is gaining increasing attention due to for type III (three dropped phases) sags [12]. Balanced type
its capability to improve grid efficiency, safety and reliability III sags only require positive sequence reactive power to raise
in a distributed manner. the phase voltages above the lower limit, since this type of
A voltage sag is a perturbation in the grid voltages grid fault lacks negative sequence voltage. On the other hand,
characterized by a short-time reduction in the magnitude of unbalanced type I and II sags require a flexible combination of
one or several phases. The effects of such disturbances are positive and negative sequence reactive power to avoid under-
important in terms of economic losses, malfunction of devices voltage in the faulted phase(s) and over-voltage in the non-
connected to the grid and in extreme cases, black-outs [4]. To faulted phase(s) [13].
Advanced control algorithms to ride through different
This work was supported by the Spanish Ministry of Economy and types of voltage sags are mainly based on symmetric
Competitiveness under Grant ENE2012-37667-C02-02.
A. Camacho, M. Castilla and J. Miret are with the Department of Electronic sequences [13]–[29]. Some of these studies have been
Engineering, Technical University of Catalonia, 08800 Vilanova i la Geltrú, proposed to achieve particular control objectives related to
Spain (e-mail: antonio.camacho.santiago@upc.edu; miquel.castilla@upc.edu; power oscillations, total harmonic distortion, power factor, dc-
jmiret@eel.upc.edu)
R. Guzman is with the Department of Signal Theory and Communications, link ripple, or peak current limitation during balanced and
Technical University of Catalonia, 08800 Vilanova i la Geltrú, Spain (e-mail: unbalanced grid faults [16]–[23]. However, little work has
guzman@tsc.upc.edu) been developed for voltage support control during unbalanced
A. Borrell is with the Department of Electrical Engineering, Escola
Universitària Salesiana de Sarrià, Autonomous University of Barcelona, 08017 voltage sags [24]–[29], and they are based on voltage sequence
Barcelona, Spain (e-mail: aborrell@euss.es) amplitudes as voltage targets. Hence, to further improve

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V
V

Vc
Va

Vb

1p.u. 1p.u. 1p.u. 1p.u.

(a) PCC phase voltages without (b) Positive sequence reactive power (c) Negative sequence reactive power (d) Proposed reactive power
reactive power (Q+ = 0, Q− = 0) strategy (Q+ > 0, Q− = 0) strategy (Q+ = 0, Q− > 0) strategy (Q+ > 0, Q− > 0)

Fig. 1. Phase voltages for different reactive power strategies.

voltage support services, phase voltage regulation instead of continuous operation are defined as
voltage sequence regulation is developed in this work, since
V := 1.10 p.u. (1)
this is the main concern to remain connected in some grid
codes during grid faults [30]. V := 0.85 p.u. (2)
In contrast, the reactive power control proposed in this work where V is the upper safety limit and V is the lower one, which
tries to solve the aforementioned problem and extends the correspond to the most stringent limits provided in some grid
contribution of [31] for any type of voltage sag. In [31], only codes to remain connected during grid faults [6]. However,
symmetric sags were considered. However, voltage sags are these limits depend on national grid codes and can take
very complex phenomena [4], [12], [32]. As shown in that different values for different regulations [11]. These voltage
works, some of the recorded sags are asymmetric and time- thresholds define the safety region in which the three-phase
varying. To achieve all these features, a detailed mathematical voltage amplitudes must reside regardless of the fault type.
formulation is developed to set the voltage targets, and a Beyond these limits, the system should disconnect because of
simplified impedance model is used to compute the reactive over-voltage or under-voltage, according to the functionalities
power references. of the power equipment and the trip times established in grid
The paper is organized as follows. Section II formulates the codes [11]. The trip times are needed to avoid unnecessary
problem. Section III introduces the DG plant and the control disconnection by short time transient voltages.
scheme during grid faults. Section IV develops the voltage To meet these limits, a combination of positive Q+ and
support concept. Section V focuses on the proposed solution. negative Q− sequence reactive power [34] can be injected into
Section VI presents a saturation technique to protect against an inductive grid to support the grid voltage. Positive sequence
inverter overcurrent. Section VII shows the experimental reactive power is related to the amplitude of the current 90◦
results. Finally, section VIII presents the conclusions. leading from the positive sequence voltage (i.e. the reactive
current injected via positive sequence). The same applies for
II. P ROBLEM F ORMULATION negative sequence reactive power, although it is shifted from
the negative sequence voltage.
This study is intended to support the grid voltage in medium To understand the proposed reactive power control, Fig. 1
or high rated DG power plants, as for example wind farms or presents different strategies of reactive power injection [13]
photovoltaic parks, which are interfaced to the grid by means during a voltage sag. The figure shows the three-phase voltages
of power electronic converters. These plants are subject to Va , Vb and Vc . The dashed line highlights the safety limits V
very stringent requirements during grid faults depending on and V. The dotted line indicates the nominal voltage. The
the rated power, and the grid operators require huge amounts figure is divided in four parts. On the left, Fig. 1(a), the phase
of reactive power, both steady-state and dynamic to support voltages at the PCC without voltage support are shown. If
the grid voltage [8]. Typically the most stringent requirements the reactive power is injected via positive sequence Q+ > 0,
in grid codes apply for power plants rated above 30MW [33]. Q− = 0, then the voltage in each phase raises equally as
Whenever a sag occurs close to a DG power plant, shown in Fig. 1(b). The phase voltages should raise until the
the circuit breakers isolate the system to prevent damage. minimum phase voltage achieves the lowest voltage limit to
However, if the sag occurs far away, low-voltage ride-through comply with grid codes. The problem with this strategy is that
is mandatory, and grid codes demand reactive current injection the highest phase voltage Va suffers over-voltage. However,
to avoid cascade disconnection and reduce the risk of black- when the reactive power is injected via negative sequence
out. For distant grid faults, if the grid impedance and the Q+ = 0, Q− > 0, the phase voltages tend to be equalized
plant rated current are large enough, then the voltage can be as presented in Fig. 1(c). The problem is that two phase
supported by an appropriate reactive power strategy. As stated voltages, Vb and Vc , suffer under-voltage. From these two
previously, the main objective in voltage support control is figures, it can be concluded that some flexible combination
the avoidance of over-voltage and under-voltage at the PCC of both positive and negative sequence reactive power can
whenever possible. regulate the maximum phase voltage to the safety upper limit
Throughout this paper, the safety voltage limits for V and the minimum phase voltage to the lower one V. This

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inverter
strategy is adopted in this work and can be clearly understood
from Fig. 1(d). power
source
It is worth mentioning that there exist more stringent targets, PCC grid
such as the maximization and minimization of the voltage Lg
sequences or the regulation of the three phase voltages at STATCOM
the nominal pre-fault values (i.e. Va = Vb = Vc ≈ 1 p.u.). i
v vg
However, these strategies require higher currents. Switched transformer
A particular case can occur for low unbalanced sags, i.e. caps.
when the difference between the maximum and minimum
phase voltages is less than the difference between upper
and lower safety limits. In this case, negative sequence
Fig. 2. Simplified scheme of a DG power plant.
voltage is either zero or quite low. In this situation, the best
strategy in terms of reducing the injected current, is to only power facilities are made up of the following VAr devices
supply positive sequence reactive power. Then, the three-phase [7]
voltages will raise equally until the lowest one achieves the
lower safety limit. • power inverters
The problem in complying with voltage limits during grid • STATCOMs
faults can be formulated as: • switched capacitors
Power inverters can be controlled to supply both active and
find Q+ , Q− reactive power. Moreover, full-scale power converters are
such that: max{Va ,Vb ,Vc } ≤ V (3) becoming the preferred choice in wind turbine technology
min {Va ,Vb ,Vc } ≥ V. because of their flexibility [40]. STATCOMs provide some
dynamic reactive power required by grid codes. Steady-state
The solution to the problem consists in finding which are the VAr compensation is mainly operated by switched capacitors
values for the positive and negative sequence reactive power since they present lower investment cost. All these elements
references, Q+ , Q− , such that the maximum amplitude of the allow the power plant to behave as an equivalent power system
phase voltages Va , Vb , Vc is kept below the safety upper limit that exchanges active and reactive power at the PCC [10].
V, and the minimum above the lower voltage limit V. For proper operation, a communication infrastructure with
Some assumptions are needed in order to simplify the networked control schemes is shared among the elements of
theoretical study: the plant; the dependency among the inner elements of the
• the grid impedance is mainly inductive, power plant (P and Q dispatchers) are out of the scope of
• the grid impedance is approximately known, this work. For an in deep analysis of fault operation modes,
• only reactive power is injected during the fault. see [7]. Under this consideration, Fig. 2 shows a simplified
The first assumption holds in transmission and distribution configuration of a grid-connected DG power plant which
networks with high X/R ratio. The second assumption behaves as an active and reactive power source from a system
indicates that the grid impedance can be estimated even if operator point of view.
it changes. To do so, a well known grid model or a proper The complete system is composed of power sources, dc-
grid impedance estimator [35]–[39] is required. The third link capacitors, inverters, filters, and step-up transformer. The
assumption is required in some grid codes for deep voltage plant is connected to the grid at the PCC. The inductance Lg
sags because the reactive power capacity can be strongly is used to model the grid impedance. The grid voltage vg
increased. In shallow voltage sags, active and reactive power represents the fault produced somewhere in the transmission
should be simultaneously injected to support and feed the grid. or distribution network.
However, for the sake of clear demonstration, in this work
active power is set to zero during the sag.
B. Voltage Sag Identification
III. DG P OWER P LANT U NDER G RID FAULTS For a proper control under grid fault, the voltage v at
This section develops three basic aspects to control DG the PCC is of interest. The instantaneous phase voltages
power plants during grid faults. First, the basic architecture need to be processed in order to identify the characteristics
of the plant is presented. Second, the voltage sag is analyzed of the voltage sag based on symmetric sequences. Using
based on symmetric sequences. Finally, the control scheme is Clarke transformation in a three-wire system, the instantaneous
assessed. voltages can be expressed in the stationary reference frame
(SRF) as
A. DG Power Plant Architecture   

 va

DG power plants are considered a key element to improve vα 1 2 √ −1 −1 √
=  vb  . (4)
the grid operation. Wind farms and photovoltaic parks are the vβ 3 0 3 − 3
vc
most widely extended example of DG plants with flexible
operation during grid faults. These medium to high rated The SRF voltages can be separated into positive and

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v vdc i power reference P , which is set to zero during the sag as

assumed previously. Energy storage elements, active crowbars
among other fast active control schemes are required to keep
abc voltage dc-link abc active power balance during short-time grid faults and prevent
αβ support regulator αβ damage in the equipment. These last two blocks constitute the
vα vβ Q+ Q− P iα iβ
power loop, since they provide the active and reactive power
references. All this information passes through the reference
sequence vα+ vα− reference i∗α current dα u1 generator to build the reference currents i∗α and i∗β , which
SVM
extractor vβ+ vβ− generator i∗β loop dβ u6 allow the injection of reactive power via positive and negative
sequences. The current reference generator is implemented as
[13]
Fig. 3. Control diagram of a three-phase inverter. " #
2 vβ+ +
vβ−
iα =
∗
Q + − 2 Q −
(15)
negative sequence as 3 (vα+ )2 + (vβ+ )2 (vα ) + (vβ− )2
" #
vα = vα+ + vα− (5) −2 vα+ + vα−
iβ =
∗
Q + − 2 Q −
(16)
vβ = vβ+ + vβ− (6) 3 (vα+ )2 + (vβ+ )2 (vα ) + (vβ− )2

where vα+ and vβ+ are the instantaneous positive sequence where each channel has a positive and a negative sequence
voltage in the SRF and vα− and vβ− are the negative ones. term.
Positive and negative sequence voltages as a function of The last stages in Fig. 3 correspond to the current loop,
time can be represented as where the references are compared with the measured currents.
The current control loop provides the duty cycles dα and dβ
vα+ = V + cos(ωt + ϕ+ ) (7) that are processed by the space vector pulse width modulator
π (SVM) to drive the switches u1 , u2 , . . . u6 .
vβ+ = V + cos(ωt − + ϕ+ ) (8)
2
vα− = V − cos(ωt − ϕ− ) (9) IV. VOLTAGE S UPPORT C ONCEPT
π
vβ− = V − cos(ωt + − ϕ− ) (10) Inside the voltage support block in Fig. 3, the mathematical
2 computation of the reactive power references is obtained.
where V + , V − are the amplitudes of the positive and negative These references are computed on-line so as to achieve the
sequences respectively, ω is the grid frequency and ϕ+ , ϕ− objective in (3). The voltage support service at the PCC (see
are the initial phase angles of positive and negative sequences. Fig. 2) can be expressed as a function of the grid voltage and
From (7)-(10), the amplitudes V + and V − are obtained as the injected current as
q
V + = (vα+ )2 + (vβ+ )2 (11) diα
vα = vgα + Lg (17)
q dt
V − = (vα− )2 + (vβ− )2 (12) diβ
vβ = vgβ + Lg (18)
dt
and the angle ϕ = ϕ+ − ϕ− between the positive and negative where vgα and vgβ are the grid voltages in the SRF, and vα ,
sequence is obtained from vβ represent the local measures at the PCC. The magnitude of
vα+ vα− − vβ+ vβ− the voltage sag is derived by inserting (5)-(10), (15) and (16)
cos(ϕ) = (13) in (17) and (18)
V +V −
vα vβ + vβ+ vα−
+ −
sin(ϕ) = . (14)
V +V − Vg+ = V + − ωLg I + (19)
Vg− =V −
+ ωLg I −
(20)
C. Control Scheme
where
The behavior of the power plant is determined by the
injected current at the PCC. Thus, a proper current-mode 2 Q+
I+ = (21)
control, capable of riding through voltage sags is required. Fig. 3V+
3 shows a control block diagram for voltage support during 2 Q−
I− = . (22)
grid faults. The inputs of the controller are local measured 3V−
voltages v and currents i and the dc-link voltage vdc . Voltages From (19)-(22), it can be shown that the magnitude of the sag
v and currents i are transformed into SRF values. Voltages Vg+ , Vg− can be estimated based on measured PCC voltages
vα and vβ are split into their symmetric components vα+ , V + , V − and injected power Q+ , Q− . Also, the voltage
vβ+ , vα− and vβ− by using a sequence extractor [41]–[46]. The support concept can be explicitly described from (19)-(22).
voltage support block detects the voltage sag and provides By injecting positive sequence reactive power, the positive
the reactive power references Q+ and Q− to the reference sequence voltage at the PCC raises with respect to that of
generator. The dc-link voltage regulator controls the active the grid. Furthermore, by injecting negative sequence reactive

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sequences is analyzed for any type of voltage sag. Finally, the

Vg −
ω reactive power references are derived based on the grid voltage
+ −
estimation.
ϕ−

−
V

ωL
gI −

g
I
I−

+
A. Amplitude of the Phase Voltages

I
+
ωL

By applying the inverse Clarke transformation to (7)-(10),

the amplitude of the phase voltages can be expressed as a
ϕ+ function of the positive and negative sequence amplitudes and
Vg
+ the phase angle jump between them as
p

V
Va = (V + )2 + (V − )2 + 2V + V − cos(ϕ) (23)

+
p
+ 2 2 +
Vb = (V ) + (V ) + 2V V cos(ϕ − /3)
− − 2π (24)
Fig. 4. Phasor representation of the reactive power control. p
+ 2 2 +
Vc = (V ) + (V ) + 2V V cos(ϕ + /3). (25)
− − 2π

power, the negative sequence voltage is lower in the PCC than The expressions (23)-(25) link positive and negative sequence
in the grid. voltages with the phase amplitudes for a given voltage sag
The voltage support concept can be graphically explained angle. In fact, only two of the three expressions are of interest:
as in Fig.4. The grid voltage is characterized by the amplitude max{Va ,Vb ,Vc } and min{Va ,Vb ,Vc }. By defining
of the positive Vg+ and negative sequence voltages Vg− .
According to the symmetric sequences theory, the two phasors x = max{cos(ϕ), cos(ϕ − 2π/3), cos(ϕ + 2π/3)} (26)
rotate in opposite directions. Then, Vg+ represents the positive y = min {cos(ϕ), cos(ϕ − 2π/3), cos(ϕ + 2π/3)} (27)
sequence grid voltage phasor rotating counter-clockwise at ω
rad/s. The initial phase angle is ϕ+ . Similarly, the negative then
sequence grid voltage Vg− rotates clockwise. In this case, the max{Va ,Vb ,Vc } =
p
(V + )2 + (V − )2 + 2V + V − x (28)
initial angle is ϕ− . In nominal grid conditions, the amplitude p
of Vg+ ≈ 1 p.u. and Vg− ≈ 0 p.u. However, during the min{Va ,Vb ,Vc } = (V + )2 + (V − )2 + 2V + V − y. (29)
sag these phasors experience sudden changes in amplitude
The above expressions can be used to regulate the phase
and phase jump. The objective of the voltage support is to
amplitudes to the desired values. Henceforth, these voltage
increase the amplitude of the positive sequence voltage V +
targets will be denoted with a super-index “∗” in order to
at the PCC compared with the grid sequence voltage Vg+ ;
differentiate them from the measured values
and to reduce the negative sequence voltage V − compared q
with the grid one Vg− . If this is accomplished, then the phase 2 2
max{Va∗ ,Vb∗ ,Vc∗ } = [(V + )∗ ] +[(V − )∗ ] +2(V + )∗ (V − )∗ x
voltages are increased and the voltage imbalance reduced.
(30)
Reactive current injection is the key for this voltage support q
objective. To inject positive sequence reactive power Q+ , a 90◦ 2 2
min{Va∗ ,Vb∗ ,Vc∗ } = [(V + )∗ ] +[(V − )∗ ] +2(V + )∗ (V − )∗ y.
current leading from the positive sequence voltage is needed (31)
as obtained from the definition in (15) and (16). On the other
hand, to inject negative sequence reactive power Q− , a 90◦ This means that if the injection of reactive power can help the
current shifted from the negative sequence voltage must be measured positive or negative sequence voltages V + , V − to
injected. When the positive and negative reactive power flow achieve the desired objectives (V + )∗ , (V − )∗ , then the phase
through an inductor, it produces a voltage variation which is voltages Va , Vb and Vc will be regulated to the desired values
proportional to ωLg . In the case of positive sequence reactive Va∗ , Vb∗ , Vc∗ . Normally voltage sags exhibit asymmetrical and
power, the voltage difference is positive, as a result the positive time-varying profiles. Thus, in a real scenario, the max and
sequence voltage at the PCC increases by ωLg I + volts. In the min expressions derived in (30) and (31) are also time-varying
case of the negative sequence reactive power, the voltage drops functions.
by ωLg I − , which helps to reduce the imbalance at the PCC.
By flexibly combining the amounts of positive and negative
reactive power, the desired voltage support strategy at the PCC B. Targets for Positive and Negative Sequence Voltage
can be reached, thus regulating the phase voltages according As previously stated in section II, the goal is to keep phase
to (3). voltages within the limits established in grid codes. Therefore,
an appropriate phase voltage target should be
V. P ROPOSED S OLUTION max{Va∗ ,Vb∗ ,Vc∗ } = V (32)
This section develops the mathematical procedure to solve min{Va∗ ,Vb∗ ,Vc∗ } = V. (33)
the problem stated in (3). To begin with, the amplitude
of phase voltages is obtained from the sag identification. Replacing the phase voltages in (30) and (31) with the
Then, the relationship between the phase voltages and voltage desired objectives (32) and (33), and solving the voltage

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Sag detector The step by step procedure of this reactive power control is
shown in Fig. 5, from the detection of the sag to the synthesis
Seq. extract. [41] vα+ ,vβ+ ,vα− ,vβ− = f (va ,vb ,vc ) of the power references and the current reference generator.
Sag param. (11)-(14) V + ,V − ,ϕ = f (vα+ ,vβ+ ,vα− ,vβ− ) Once the sag has been detected and the symmetric sequences
obtained, it should be characterized and identified. Then, to
Grid seq. (19),(22) Vg+ ,Vg− = f (V + ,V − ,Q+ ,Q− ,ω,Lg ) implement the proposed control, Vg+ and Vg− need to be
computed based on previous power references Q+ and Q−
Target seq. (32),(36) (V + )∗ ,(V − )∗ = f (V,V,ϕ)
and PCC measurements V + and V − according to (19) and
Power ref. (38),(39) Q+ ,Q− = f (Vg+ ,Vg− ,(V + )∗ ,(V − )∗ ,ω,Lg ) (20). Then the targets (V + )∗ and (V − )∗ are obtained based
on the desired safety values V and V for a given sequence
Saturation (43),(44) Q+ , Q− := f (I + , I − , Imax ) angle ϕ by applying (32)-(36). The new positive and negative
Current ref. (15),(16) i∗α ,i∗β = f (vα+ ,vβ+ ,vα− ,vβ− ,Q+ ,Q− ) reactive power references are derived from (38) and (39). Due
to the dynamic behaviour of sequence extractors, the settling
Fig. 5. Flow diagram of the proposed control scheme. time in perturbed situations last one grid cycle approximately
[42]. For this reason, the power reference block is triggered
sequence targets, the following expressions are obtained once per grid cycle to compute the new values of Q+ and
v
u r Q− , which remain constant in the flow diagram until the new
2  2 2
u xV − yV 2 +
u 2
yV
2
− xV 2
− V − V 2 update. Once the reactive power references are obtained, a
(V + )∗ =
t current saturation strategy ensures that the injected currents
2(x − y) will be safely limited to the maximum rated current of the
(34) inverter Imax . The procedure to saturate the current injection
v
u r is developed in the next section.
 2  2
u xV − yV 2 − 2 2
u 2 2 2
t yV − xV − V − V
(V − )∗ = . VI. C URRENT S ATURATION
2(x − y)
(35) This section is intended for the case of stiff grids where
the voltage limits strategy proposed in (3) could not be
Equations (34) and (35) are the basis for the proposed voltage
achieved. Voltage support in stiff grids require higher reactive
support control because they relate phase voltage targets to
currents. Thus, the required reactive currents can overpass the
sequence voltage targets. Furthermore, the above equations
safety limits of the inverter. To overcome this issue, a current
allow us to obtain the targets for any sag, whether symmetric
saturation strategy is developed. To achieve this objective, the
or asymmetric.
injected currents are mathematically derived and a correction
For the particular case presented in section II in which the
factor is included to limit the maximum injected current to the
sag has low imbalance (i.e. max{Va ,Vb ,Vc }−min{Va ,Vb ,Vc } <
safety limit Imax .
V − V ), the limits in (32) and (33) need to be modified to
Similarly to (23)-(25), the amplitude of the phase currents
acomplish the aforementioned objective as
are
max{Va∗ ,Vb∗ ,Vc∗ } = V + max{Va ,Vb ,Vc } − min{Va ,Vb ,Vc } p
Ia = (I + )2 + (I − )2 + 2I + I − cos(ϕI ) (40)
(36) p
+ 2 2 +
Ib = (I ) + (I ) + 2I I cos(ϕI − /3)
− − 2π (41)
min{Va∗ ,Vb∗ ,Vc∗ } = V (37) p
+ 2 2 +
Ic = (I ) + (I ) + 2I I cos(ϕI + /3)
− − 2π (42)

C. Reactive Power References where ϕI = π − ϕ. Note that from (40)-(42), the maximum
phase current can be identified since the reactive power
Once the desired targets for positive and negative sequence
references and the voltage sequences are all known.
voltage have been established, the formulation for the reactive
Once the theoretical injected currents are characterized,
power references can be easily obtained. The proposed voltage
the limitation process can be started. If the required power
support control to comply with the voltage limits is obtained
references from (38) and (39) induce a current higher than the
by rearranging (19)-(22) with the target values
  maximum allowable current of the inverter max{Ia , Ib , Ic } >
+ 3 (V + )∗ (V + )∗ − Vg+ Imax , then these references should be modified in order to
Q = (38) protect the inverter from overcurrents. A method for doing
2 ωLg
  so is to modify the power references as
3 (V − )∗ Vg− − (V − )∗
Q− = . (39) Imax
2 ωLg Q+ +
sat = Q (43)
max{Ia , Ib , Ic }
By injecting these amounts of positive and negative Imax
sequence reactive power, the positive and negative sequence Q−
sat = Q− (44)
max{Ia , Ib , Ic }
voltage targets will be achieved. These targets have been
computed to keep the maximum and minimum phase voltages and the effective value for positive sequence reactive
within the safety region. power in the reference generator (15) and (16) should be

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This article has been accepted for publication in a future issue of this journal, but has not been fully edited. Content may change prior to final publication. Citation information: DOI
10.1109/TPEL.2014.2301463, IEEE Transactions on Power Electronics

−200
TABLE I

phase voltages (V)

S YSTEM PARAMETERS −100

Symbol Nominal value per unit value 0

base power Sbase 2 kVA 1.0
100
base voltage Vbase 110 V (l-n, rms), 60 Hz 1.0
base current Ibase 6 A (rms) 1.0 200
active power production P 750 W 0.37 (a) Voltage waveforms (50 ms/div).
grid inductor Lg 5 mH 0.10
dc-link voltage vdc 350 V -
1

rms voltage (p.u.)

switching frequency fs 10 kHz -

V
selected as min{Q+ , Q+ sat }, and for the negative sequence as
0.5 a
Vb
min{Q− , Q− sat } V
c
It is worth mentioning that if the current saturation strategy 0
is activated, then the resulting reactive power is lower than 0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5
t(s)
necessary to meet (3). In this case, even if the voltage support (b) Rms voltage.
targets expressed in (32) and (33) cannot be accomplished, the
overcurrent is properly controlled. Fig. 6. Test1: voltages without voltage support control.
−200

VII. E XPERIMENTAL R ESULTS phase voltages (V) −100

Based on the scheme of Fig. 2, a low rated power test
platform has been built using an Amrel SPS-800-12 DC 0

Power Source, a 2 kVA Semikron three-phase IGBT bridge,

100
a Pacific Power AMX AC grid emulator and an inductance
Lg between the PCC and the grid. The nominal values of 200
(a) Voltage waveforms (50 ms/div).
the system parameters are collected in Table I. The control
algorithm is implemented on a Texas Instruments floating-
point TMS320F28335 Digital Signal Processor. Before and 1
rms voltage (p.u.)

after the sag, 750 W of active power feed the grid; this
operating point corresponds to an arbitrary wind or solar power
0.5 V
a
production (0.37 p.u.). During the fault, the proposed voltage Vb
support control is activated. The sequence extractor presented V
c
in [41] has been employed to obtain symmetric sequences at 0
run-time. For the current loop, a proportional-resonant current 0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5
t(s)
controller has been used. (b) Rms voltage.
Based on [12], three tests have been programmed in order
to show the dynamic behavior of the proposed reactive power Fig. 7. Test1: voltages with voltage support control.
control:
• test 1 is a single-phase-to-ground (type II) voltage sag,
The waveforms of the injected currents are presented in
• test 2 is a balanced three-phase (type III) voltage sag,
Fig. 8. Note that before and after the sag, the inverter
• test 3 is a phase-to-phase (type I) sag with slow recovery.
injects balanced active currents, the current amplitudes in this
situation are around 0.37 p.u. However, during the sag, the
A. Test 1 currents increase up to 0.9 p.u. It is worth mentioning that
Test 1 is an unbalanced single-phase-to-ground voltage deeper voltage sags or smaller grid inductances will require
sag which could be caused by a short circuit or lightning higher reactive currents to regulate the phase voltages. Also,
somewhere in the transmission or distribution network. The it should be pointed out that during the sag, there exists an
sag is time-varying to mimic real behavior of grid faults. inherent current imbalance due to the injection of both positive
The PCC voltage waveforms and rms values without voltage and negative sequence reactive currents.
support are presented in Fig. 6(a) and 6(b). These figures Fig. 9 clearly shows the proposed solution to the stated
show the dynamic evolution of the voltage sag when no problem. This figure presents the positive and negative reactive
reactive power is injected. The next two figures, 7(a) and power references. These references are computed on-line
7(b), illustrate the measurements when the proposed voltage according to the flow diagram in section V-C. Fig. 9 also
support control is activated. As can be shown, the voltage at shows the instantaneous reactive power q, plotted in the thinner
the PCC is regulated to the selected voltage limits V = 1.10 line. As expected, a significant oscillation at twice the grid
p.u., V = 0.85 p.u. which is the main objective of the proposed frequency can be observed during the sag due to the imbalance
reactive power control. in the system.

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This article has been accepted for publication in a future issue of this journal, but has not been fully edited. Content may change prior to final publication. Citation information: DOI
10.1109/TPEL.2014.2301463, IEEE Transactions on Power Electronics

−10

1
phase currents (A)

rms voltage (p.u.)

−5

0
0.5 V
a
5 V
b
Vc
10 0
0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5
Fig. 8. Test 1: inverter current waveforms (50 ms/div). t(s)
3 Fig. 11. Test 2: rms voltages without voltage support.
Q+
Reactive power (kVAr)

−
2 Q
q 1

rms voltage (p.u.)

1
0.5 Va
V
0 b
V
0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5 c
t(s) 0
0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5
Fig. 9. Test 1: Positive and negative reactive power references, and t(s)
instantaneous total reactive power. Fig. 12. Test 2: rms voltages with voltage support.
Voltage seq. amplitude (V)

150 3
Q+

Reactive power (kVAr)

+
V Q
−
2
100 V+ q
g
−
Vg
50 − 1
V

0 0
0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5
0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5
t(s)
t(s)
Fig. 10. Test 1: positive and negative sequence amplitude. Fig. 13. Test 2: Positive and negative reactive power references, and
instantaneous total reactive power.

Fig. 10 shows the measured positive voltage sequence V +

and the calculated positive sequence grid voltage Vg+ when 1
rms voltage (p.u.)

the voltage support strategy is implemented. The negative grid

sequence Vg− and the PCC measure V − are shown below in V
0.5 a
the graph. As desired, to raise the voltage in all the phases, V
b
the PCC positive sequence voltage should be increased. On the V
c
other hand, the negative sequence voltage is decreased, which 0
0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5
helps to equalize the phase voltages. t(s)
Fig. 14. Test 3: rms voltages without voltage support.

B. Test 2
1
rms voltage (p.u.)

Test 2 presents a balanced three-phase voltage sag caused

by a motor starting with high inrush current. Balanced voltage
sags have no negative sequence voltage, therefore the control 0.5 V
a
strategy should inject positive sequence reactive power until Vb
the minimum safety voltage V is achieved in the three phases. V
c
The rms voltages without voltage support are shown in Fig. 0
0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5
11. The effect of the voltage support control at the PCC can t(s)
be appreciated in Fig. 12. With this strategy, the PCC voltages Fig. 15. Test 3: rms voltages with voltage support.
are within the safety region, which is the main objective of
the proposed control scheme.
are present because no imbalance exists in this type of voltage
In Fig. 13, positive and negative reactive power references
sag.
are shown. As stated above, only positive sequence reactive
power is injected during the sag. Therefore, the negative
sequence reactive power reference is set to zero. The C. Test 3
instantaneous total reactive power is represented by the thinner Test 3 is a voltage sag with slow recovery. Fig. 14 presents
line. Note that the instantaneous reactive power follows the the rms voltages without voltage support. The sag begins as a
reference and that no oscillations at twice the grid frequency type I (t = 0.1 s), evolving to a type II (t = 0.3 s), then the

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This article has been accepted for publication in a future issue of this journal, but has not been fully edited. Content may change prior to final publication. Citation information: DOI
10.1109/TPEL.2014.2301463, IEEE Transactions on Power Electronics

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as a type III (t > 0.3 s). wind farm met ESCOSA’s, NEMMCO’s and ElectraNet’s rigorous
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reactive power control is able to keep the voltages within Rodriguez, M. Milligan, and E. Muljadi, “Participation of wind power
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systems,” IEEE Trans. Ind. Electron., vol. 53, no. 5, pp. 1398–1409, current controller for unbalanced grid-voltage conditions,” IEEE Trans.
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converters in ac microgrids,” IEEE Trans. on Power Electron., vol. 27, fluctuation elimination through a dc-capacitor current control for DFIG
no. 11, pp. 4734–4749, 2012. converters under unbalanced grid voltage conditions,” IEEE Trans.
[3] S.-F. Chou, C.-T. Lee, H.-C. Ko, and P.-T. Cheng, “A low-voltage Power Electron., vol. 28, no. 7, pp. 3206–3218, Jul. 2013.
ride-through method with transformer flux compensation capability of [22] P. Rodriguez, G. Medeiros, A. Luna, M. Cavalcanti, and R. Teodorescu,
renewable power grid-side converters,” IEEE Trans. Power Electron., “Safe current injection strategies for a statcom under asymmetrical grid
vol. 29, no. 4, pp. 1710–1719, 2014. faults,” in IEEE Energy Conversion Congr. and Expo. (ECCE), Sep.
[4] V. Ignatova, P. Granjon, S. Bacha, and F. Dumas, “Classification 2010, pp. 3929 –3935.
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methodology,” in Int. Conf. on Future Power Systems, Nov. 2005. and F. Blaabjerg, “Current control method for distributed generation
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ORNL/CON-453, Oak Ridge National Laboratory, Oak Ridge TN, Rep. on IEEE Ind. Electron. Society (IECON), Nov. 2011, pp. 1262 –1269.
Dec., 1997. [24] Y. Mohamed and E. El-Saadany, “A control scheme for PWM voltage-
[6] Offprint of the Operation Procedure O.P. 12.2: Technical requirements source distributed-generation inverters for fast load-voltage regulation
for wind power and photovoltaic installations and any generating and effective mitigation of unbalanced voltage disturbances,” IEEE
facilities whose technology does not consist on a synchronous generator Trans. Ind. Electron., vol. 55, no. 5, pp. 2072 –2084, May 2008.
directly connected to the grid., Asociación Empresarial Eólica, Oct. [25] H.-S. Song and K. Nam, “Dual current control scheme for PWM
2008, [Online]. Available: www.aeeolica.org. converter under unbalanced input voltage conditions,” IEEE Trans. Ind.
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in IEEE Power and Energy Society General Meeting, Jul. 2011, pp. 1 [26] M. Castilla, J. Miret, A. Camacho, J. Matas, E. Alarcón-Gallo, and
–7. L. Garcı́a de Vicuna, “Coordinated reactive power control for static

0885-8993 (c) 2013 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission. See
http://www.ieee.org/publications_standards/publications/rights/index.html for more information.
This article has been accepted for publication in a future issue of this journal, but has not been fully edited. Content may change prior to final publication. Citation information: DOI
10.1109/TPEL.2014.2301463, IEEE Transactions on Power Electronics

synchronous compensators under unbalanced voltage sags,” in IEEE Int. Antonio Camacho received the B.S. degree in
Symp. on Industrial Electronics (ISIE), May 2012, pp. 987 –992. chemical engineering in 2000 and the M.S. degree
[27] M. Castilla, J. Miret, A. Camacho, J. Matas, and L. de Vicuna, “Voltage in automation and industrial electronics in 2009,
support control strategies for static synchronous compensators under both from the Technical University of Catalonia,
unbalanced voltage sags,” IEEE Trans. Ind. Electron., In press. Barcelona, Spain. Currently, he is pursuing the Ph.D.
[28] T. Lee, S. Hu, and Y. Chan, “D-STATCOM with positive-sequence degree in electronic engineering also at the Technical
admittance and negative-sequence conductance to mitigate voltage University of Catalonia. His research interests
fluctuations in high-level penetration of distributed generation systems,” include networked and embedded control systems,
IEEE Trans. Ind. Electron., vol. 60, no. 4, pp. 1417–1428, Apr. 2013. industrial informatics, and power electronics.
[29] S. Chaudhary, R. Teodorescu, P. Rodriguez, P. Kjaer, and A. Gole,
“Negative sequence current control in wind power plants with VSC-
HVDC connection,” IEEE Trans. Sustainable Energy, vol. 3, no. 3, pp.
535 –544, Jul. 2012.
[30] “Resolution-P.O.12.3-Response requirements against voltage dips in
wind installations,” Red Electrica (REE), Operat. Proced., Oct. 2006.
[31] J. Miret, A. Camacho, M. Castilla, L. Garcı́a de Vicuna, and Miguel Castilla received the B.S., M.S. and Ph.D.
J. Matas, “Control scheme with voltage support capability for distributed degrees in telecommunication engineering from the
generation inverters under voltage sags,” IEEE Trans. Power Electron., Technical University of Catalonia, Barcelona, Spain,
vol. 28, no. 11, pp. 5252–5262, Nov. 2013. in 1988, 1995, and 1998, respectively.
[32] J. Mora, J. Melndez, D. Llanos, J. Colomer, and X. Snchez J., Corbella, Since 2002, he has been an Associate Professor in
“Classification of sags measured in a distribution substation using a the Department of Electronic Engineering, Technical
fuzzy tool,” in ICREPQ Int. Conf. on Renewable Energy and Power University of Catalonia, where he teaches courses on
Quality, 2003, pp. 1–7. analog circuits and power electronics. His research
[33] Procedimiento de operación 7.4: Servicio complementario de control interests are in the areas of power electronics,
de tensión de la red de transporte, Red Eléctrica de España, Oct. 2000, nonlinear control, and renewable energy systems.
[Online]. Available: www.ree.es.
[34] “IEEE standard definitions for the measurement of electric power
quantities under sinusoidal, nonsinusoidal, balanced, or unbalanced
conditions,” IEEE Std 1459-2010, pp. 1–40, Mar. 2010.
[35] L. Asiminoaei, R. Teodorescu, F. Blaabjerg, and U. Borup,
“Implementation and test of an online embedded grid impedance
estimation technique for PV inverters,” IEEE Trans. Ind. Electron., Jaume Miret (M01) received the B.S. degree in
vol. 52, no. 4, pp. 1136 – 1144, Aug. 2005. telecommunications and the M.S. and Ph.D. degrees
[36] A. Moallem, D. Yazdani, A. Bakhshai, and P. Jain, “Frequency domain in electronics from the Technical University of
identification of the utility grid parameters for distributed power Catalonia, Barcelona, Spain, in 1992, 1999, and
generation systems,” in 26th Ann. IEEE Applied Power Electronics Conf. 2005, respectively.
and Expo. (APEC), Mar. 2011, pp. 965 –969. He is currently an Associate Professor with the
[37] A. Timbus, R. Teodorescu, and P. Rodriguez, “Grid impedance Department of Electronic Engineering, Technical
identification based on active power variations and grid voltage control,” University of Catalonia, Vilanova i la Geltrú, Spain,
in 42nd Ann. Meeting. Conf. Record of the 2007 IEEE Industry where he teaches courses on digital design and
Applications Conference (IAS), Sep. 2007, pp. 949 –954. circuit theory. His research interests include dc–ac
[38] S. Cobreces, E. Bueno, D. Pizarro, F. Rodriguez, and F. Huerta, converters, active power filters, and digital control.
“Grid impedance monitoring system for distributed power generation
electronic interfaces,” IEEE Trans. Instrum. Meas., vol. 58, no. 9, pp.
3112 –3121, Sep. 2009.
[39] N. Hoffmann and F. W. Fuchs, “Minimal invasive equivalent grid
impedance estimation in inductive-resistive power-networks using
extended kalman-filter,” IEEE Trans. Power Electron., In press. Ramon Guzman received the B.S. and M.S. degrees
[40] K. Ma and F. Blaabjerg, “Thermal optimised modulation methods of in telecomunications engineering from the Technical
three-level neutral-point-clamped inverter for 10 MW wind turbines University of Catalonia, Barcelona, Spain in 1999
under low-voltage ride through,” IET Power Electron., vol. 5, no. 6, and 2004, respectively. He is currently working
pp. 920 –927, Jul. 2012. toward the Ph.D. degree in the Power and Control
[41] F. Rodriguez, E. Bueno, M. Aredes, L. Rolim, F. Neves, and Electronics Systems (SEPIC) group.
M. Cavalcanti, “Discrete-time implementation of second order Since 2001, he is an Associate Professor of the
generalized integrators for grid converters,” in 34th Annu. Conf. of IEEE Comunications and Signal Theory Department at the
Ind. Electron., Nov. 2008, pp. 176–181. Technical University of Catalonia, Barcelona, Spain.
[42] J. Matas, M. Castilla, J. Miret, L. Garcia de Vicuna, and R. Guzman, His current research interests are in the area of
“An adaptive prefiltering method to improve the speed/accuracy tradeoff nonlinear and adaptive control for three phase power
of voltage sequence detection methods under adverse grid conditions,” converters.
IEEE Trans. Ind. Electron., vol. 61, no. 5, pp. 2139–2151, 2014.
[43] F. Neves, H. Souza, E. Bueno, M. Rizo, F. Bradaschia, and
M. Cavalcanti, “A space-vector discrete fourier transform for detecting
harmonic sequence components of three-phase signals,” in 35th Annu.
Conf. of IEEE Ind. Electron., Nov. 2009, pp. 3631–3636.
[44] P. Rodriguez, A. Luna, R. Muñoz Aguilar, I. Etxeberria-Otadui, Angel Borrell received the B.S. degree in
R. Teodorescu, and F. Blaabjerg, “A stationary reference frame grid electrical engineering, M.S. degree in automation
synchronization system for three-phase grid-connected power converters and industrial electronics engineering and PhD
under adverse grid conditions,” IEEE Trans. Power Electron., vol. 27, in electronics engineering from the Technical
no. 1, pp. 99–112, 2012. University of Catalonia, Barcelona, Spain, in 1993,
[45] P. Rodriguez, A. Luna, I. Candela, R. Mujal, R. Teodorescu, 2006 and 2012 respectively.
and F. Blaabjerg, “Multiresonant frequency-locked loop for grid Since 1994, he has been an Associate Professor
synchronization of power converters under distorted grid conditions,” in the Department of Electrical Engineering, Escola
IEEE Trans. Ind. Electron., vol. 58, no. 1, pp. 127–138, Jan. 2011. Universitària Salesiana de Sarrià, where he teaches
[46] P. Roncero-Sánchez, X. del Toro Garcı́a, A. Parreno Torres, and courses on electrical machines and automation.
V. Feliu, “Fundamental positive- and negative-sequence estimator for His research interest are in the areas of power
grid synchronization under highly disturbed operating conditions,” IEEE electronics, electric motor drives and renewable energy systems.
Trans. Power Electron., vol. 28, no. 8, pp. 3733–3746, Aug. 2013.

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