Based on the inherent relationship between dcbus voltage and grid feeding active power, two dcbus voltage regulators with different references are adopted for a gridconnected PV inverter operating in both normal grid voltage mode and low grid voltage mode. In the proposed scheme, an additional dcbus voltage regulator paralleled with maximum power point tracking controller is used to guarantee the reliability of the low voltage ridethrough (LVRT) of the inverter. Unlike conventional LVRT strategies, the proposed strategy does not require detecting grid voltage sag fault in terms of realizing LVRT. Moreover, the developed method does not have switching operations. The proposed technique can also enhance the stability of a power system in case of varying environmental conditions during a low grid voltage period. The operation principle of the presented LVRT control strategy is presented in detail, together with the design guidelines for the key parameters. Finally, a 3 kW prototype is built to validate the feasibility of the proposed LVRT strategy.
I. INTRODUCTION
Low voltage ridethrough (LVRT) and dynamic voltage supporting (DVS) of gridconnected PV systems are increasingly becoming important along with the increasing penetration of photovoltaic (PV) systems. A sudden disconnection of all PV systems from a power grid triggers severe problems, such as power outages and voltage flickers
[1]
,
[2]
. To enhance the stability of a power grid during a sudden grid voltage drop, some relevant standards require largecapacity PV systems to allow LVRT
[3]

[5]
. The LVRT standard of China for PV systems is shown in
Fig. 1
(a). Evidently, all generating plants are required to remain connected with the grid when the grid voltage is within the shaded area known as LVRT. Aside from maintaining connection, the PV system is required to provide reactive power to participate in grid voltage control during fault period and during the recovery process of the afterfault period known as DVS
[6]
,
[7]
. The E.ON code requires the PV system to provide a linearly proportional active/reactive current output when the grid voltage varies in the range of 50% to 90% nominal voltage. When the grid voltage drops below 50%, the PV system should produce 100% reactive current. The required percentage of reactive current during LVRT is illustrated in
Fig. 1
(b).
LVRT requirement. (a) China: Q/GDW 617C201. (b) E.ON code for LVRT.
When connected to a power grid, PV inverters are susceptible to electrical disturbances, such as grid voltage variations, harmonic resonance, and waveform distortions
[8]
,
[9]
. Grid voltage sag is one of the most challenging among these disturbances. During grid voltage sag, the grid feeding active power generally decreases suddenly, whereas the input PV power remains constant. Consequently, the surplus PV power should be absorbed entirely by the dcbus capacitor, which causes the drastic increase of dcbus voltage. If no actions are taken to address the power imbalance during the grid voltage sag period, the dcbus overvoltage protection of the PV inverter is triggered. Subsequently, the PV inverter is disconnected from the grid.
Many methods have been developed in literature to enhance the LVRT capability of twostage gridconnected PV inverters, especially in threephase systems. Switching from a dualloop control to a singleloop control transfers the control system to a constant gridconnected current control for LVRT in low grid voltage mode (LGVM) from a constant power control in normal grid voltage mode (NGVM)
[10]
. However, such switching cannot ensure the stability of the dcbus voltage without the outer dcbus voltage loop in LGVM. The control system is switched to voltage control mode from the maximum power point tracking (MPPT) control mode according to the dcbus voltage
[11]
. However, the different outputs of both control modes at the instant of transfer may cause current and/or voltage spikes during the switching process. The grid voltage is monitored and used to adjust the duty ratio when the ratio is reduced below the threshold
[12]
. Nevertheless, the grid voltage is an openloop control and is susceptible to environmental conditions. LVRT performance is improved with a fast energy storage system based on super capacitors, but LVRT increases hardware cost significantly
[13]
.
The aforementioned LVRT strategies in threephase PV systems can be introduced into singlephase PV systems in terms of LVRT. Similar to Ref.
[11]
, the control system is switched from MPPT mode to nonMPPT mode by comparing the grid feeding active power before grid voltage sag fault with the allowed maximum grid feeding active power during the fault period
[14]
. However, as mentioned earlier, the switching operation may cause voltage and/or current spikes at the instant of transfer. In addition, varying environmental conditions, such as the sudden decrease of solar insolation, are not considered in Ref.
[14]
. The LVRT strategies used for onestage PV systems in Refs.
[15]
and
[16]
are intuitive by implementing a singlephase power control method. However, the LVRT schemes in onestage PV systems cannot be applied to twostage PV systems because the former do not consider the abovementioned dcbus overvoltage problem when dealing with LVRT.
Notably, most conventional LVRT strategies rely on the detection of grid voltage sag fault. However, the nearly constant time delay in fault detection is adverse for LVRT, especially in drastic and deep voltage drop cases. Mode switching operations in conventional LVRT schemes may also cause system instability. In previous LVRT approaches, the PV inverter still abandons the MPPT function of the inverter, and then the inverter takes several minutes to restart after the fault even if the voltage sag fault only remains for several grid cycles
[14]
. The inverter does not only reduce solar energy harvesting, but also degrades the stability of the power system because of sudden active power drops. Furthermore, some LVRT methods cannot be used in varying environmental conditions in LGVM.
This study proposes two dcbus voltage regulators with different references to enhance the LVRT capability of the twostage PV system. Without detecting the voltage sag fault, no constant detection delay occurs for the realization of LVRT. Moreover, no abrupt mode switching operations exist regardless of the grid voltage sag in the presented LVRT method. Therefore, a smooth transition from NGVM to LGVM or from LGVM to NGVM is achieved in this research. The proposed LVRT technique can also adapt to varying environmental conditions in LGVM. Hence, the stability of the PV power system can be ensured even though solar insolation decreases suddenly in LGVM.
This paper is organized as follows. The proposed LVRT control scheme is illustrated in Section II. Analysis of the dcbus voltage control in LGVM is presented in Section III, and the design of the key parameters is discussed in Section IV. The simulation and experimental results are shown in Sections V and VI respectively. The conclusion is presented in Section VII.
II. PROPOSED LVRT CONTROL SYSTEM
 A. Description of Control System
A singlephase twostage gridconnected PV system that comprises a boost chopper and a fullbridge inverter is used in this study to illustrate the proposed LVRT method, as shown in
Fig. 2
(a). The whole control system includes a boost chopper control system and an inverter control system, as shown in
Figs. 2
(b) and
2
(c) respectively. As shown in
Fig. 2
(b), the MPPT control of PV panels and the added dcbus voltage loop for LVRT are implemented in the boost chopper control system. Decouple control module (DCM) is adopted to decouple the MPPT controller and the PI_LVRT controller. When the output of PI_LVRT is positive, the output
S_{pv}
of DCM is zero, otherwise the output is one. As shown in
Fig. 2
(c), the classical dualloop control is applied to the inverter control. The outer loop forces the dcbus voltage
V_{dc}
to track the reference
with the proportionalintegral (PI) controller PI_NOR. In the inner current loop, the proportionalresonant (PR) controller is adopted for the high tracking capability of the sinusoidal reference of this controller. Secondorder generalized integratorbased singlephase locked loop (SPLL) is implemented to measure the grid voltage amplitude and phase
[17]
. The gridconnected current reference is generated in the current reference generation unit (CRGU). Notably,
G_{I}
(
s
) s is the fullbridge model. As stated in Ref.
[18]
, considering
G_{I}
(
s
) as united when the dcbus voltage is more than 311 V is reasonable in this study.
(a) Singlephase twostage gridconnected PV system. (b) Proposed boost chopper control system. (c) Inverter control system. (d) Linearized model of the dcbus voltage control in LGVM.
 B. GridConnected Current Reference and PV Voltage Reference
1) Generation of GridConnected Current Reference in CRGU:
The grid voltage is assumed to be:
where
V_{grms}
is the grid voltage
V_{g}
in RMS, and
ω_{f}
is the grid angular frequency. In NGVM, the inverter delivers all the generated PV power to the grid and maintains the dcbus voltage at the voltage reference
. Generally, the PV inverter supplies no reactive power for the unity power factor in normal operational modes. Therefore, the gridconnected current reference
I_{ref}
in NGVM is only determined by the dcbus voltage loop and can be expressed as
where
I_{vdc}
is the output of the dcbus voltage controller PI_NOR. In particular, the CRGU in
Fig. 2
(c) should be united in NGVM. Nevertheless, as mentioned in the Introduction, the gridconnected PV inverter is required to provide reactive power under grid voltage sag faults. According to
Fig. 1
(b), the ratio
Q_{ratio}
between the required reactive current and the rated current
I_{r}
of the inverter can be described as
where
V_{nor}
is the nominal grid voltage in RMS. To prevent the inverter from triggering the overcurrent protection function at the presence of grid voltage sag, the ratio
P_{ratio}
between the active current of the inverter to the rated current can be expressed as
On the one hand, to satisfy the LVRT standard of
Fig. 1
(b) and protect the inverter during LVRT, the required reactive current and the allowed maximum active current in LGVM should be
I_{r}P_{ratio}
and
I_{r}Q_{ratio}
respectively. On the other hand, the gridconnected active current command should be able to stabilize the dcbus voltage in LGVM. Consequently, the active current command should be the minimum current of
I_{r}P_{ratio}
and the output
I_{vdc}
of PI_NOR. Notably, the upper limit of
I_{vdc}
is equal to the rated current
I_{r}
of the inverter. If
I_{vdc}
is less than
I_{r}P_{ratio}
, then the active current command is
I_{vdc}
; otherwise, the command is
I_{r}P_{ratio}
. In addition,
I_{vdc}
,
I_{r}P_{ratio}
, and
I_{r}Q_{ratio}
are all RMS values. Hence, the gridconnected current reference in LGVM can be achieved through
where
represents the gridconnected current reference in RMS,
I_{p}
and
I_{q}
are the active and reactive current references respectively, and
φ
is the phase difference between the current reference and the grid voltage.
Assuming that the gridconnected current
I_{g}
can respond to the current command
I_{ref}
accurately is reasonable. Therefore, from Eqs. (1) and (5), the steadystate grid feeding active power
P_{g}
and reactive power
Q_{g}
of the PV inverter in LGVM can be obtained through
and the allowed maximum grid feeding active power
P
_{g max}
in LGVM is expressed as
2) Generation of PV Voltage Reference:
Clearly, the PV system usually operates in the MPPT mode for maximum solar energy harvesting in NGVM. However, two operational modes for PV panels in LGVM are found in this study. If the allowable maximum grid feeding active power
P
_{g max}
is more than the present maximum power of PV panels, then the PV panels can still operate in the MPPT mode. Therefore, the whole system can operate this way in NGVM in terms of the regulation of active power (which is not the focus of this study, and is thus skipped). This study mainly focuses on analyzing the case where
P
_{g max}
is smaller than the present maximum power of PV panels. This observation implies that the dcbus voltage is forced to increase because of the surplus PV power if the PV panels work in MPPT mode. Therefore, to ensure the power balance in LGVM, the PV panels should operate in nonMPPT mode in this case.
In NGVM, to obtain the maximum PV power, the MPPT controller should be able to track the MPP of the PV characteristic curve of the PV panels shown in
Fig. 4
. Owing to its simplicity and excellent performance, perturbation and observation (P&O) method is adopted in this study to determine the MPP by perturbing the terminal voltage of PV panels
[19]
. The flow chart of the P&O method is depicted in
Fig. 3
. If a given perturbation ∆
V
leads to the increase (decrease) of PV power, the next perturbation is made in the same (opposite) direction. This way, the MPPT controller continuously seeks the maximum power point (MPP). Once the MPP is achieved, the output
V_{pv _ mppt}
of the MPPT controller approaches the PV voltage
V_{m}
of MPP, as shown in
Fig. 4
.
P&O flow chart.
PV characteristic curve of PV panels.
As shown in
Fig. 2
(b), the PV voltage reference
can be presented as
Given that the output
V_{pv _ dc}
of PI_LVRT is ensured to be zero in NGVM (as explained in Section II.C), the PV voltage reference equates
V_{pv _ mppt}
and eventually approaches
V_{m}
once the MPP is determined in NGVM.
As mentioned earlier, to guarantee the power balance in LGVM, the MPPT function of the PV inverter should be disabled, and the steadystate PV power should match with the gridfeeding active power
P_{g}
calculated through Eq. (6). Therefore, the PV panels cannot operate at the MPP, but should operate at the intersection points of the
P_{g}
curve and the PV characteristic curve in
Fig. 4
.
Fig. 4
clearly shows that the
P_{g}
curve and the PV characteristic curve intersect at two points B and C. Theoretically, both points B and C can be used as the steadystate operating point of PV panels in LGVM. However, most traditional DC/DC converters have an inherent negative impedance characteristic because the current of these converters increases when voltage decreases. Hence, if the PV system operates at point C in the left section of the PV characteristic curve, the terminal voltage of PV panels may collapse
[19]
. Given that the right section of the PV characteristic curve is steeper than the left section, the right section may also have faster response to abrupt changes in
P_{g}
[20]
. Therefore, from the above comparison, point B in the right section of the PV characteristic curve is a better choice for the PV system compared with point C in the left section. Thus, forcing the steadystate PV voltage reference
to approach the voltage
V_{pv}
_{2}
corresponding to point B in LGVM is better. The regulation of PV power in LGVM is implemented in the right section of the PV characteristic curve in this study. Hence, the PV voltage can vary between
V_{m}
nd the opencircuit voltage
V_{oc}
in LGVM.
 C. Operation Principle of the Control System
In NGVM, the dcbus voltage is regulated by PI_NOR to 400 V, which forces zero output for the PI_LVRT. Therefore, based on
Fig. 2
(b), the PV voltage reference
is only determined by the MPPT controller in NGVM. Meanwhile, the output
S_{pv}
of DCM becomes an output that enables the MPPT controller to seek the MPP of PV panels in NGVM.
As discussed above, the dcbus voltage increases at the appearance of grid voltage sag. Concurrently, the output increases continuously until the upper limit is reached by the PI_NOR output. Once the dcbus voltage reaches 430 V, the output
V_{pv _ dc}
of PI_LVRT starts to increase from zero, which forces
S_{pv}
to become zero, turning the input to the MPPT controller into zero. Consequently, according to
Fig. 3
, the MPPT controller stops perturbing and output
V_{pv _ mppt}
remains constant. In particular, the PV voltage reference is only regulated by the PI_LVRT in LGVM. This finding implies that the MPPT and PI_LVRT controllers are decoupled effectively via the DCM and are not affected mutually regardless if in NGVM or LGVM. Notably, the delay time during the transient process, where the dcbus voltage increases from 400 V to 430 V, is harmful for LVRT. However, the voltage decreases as the depth of voltage sag increases. Hence, the dynamic response speed of the proposed LVRT technique increases with the increasing depth of the grid voltage sag, which is impossible in conventional LVRT approaches because of the constant time delay in grid voltage sag detection.
After the grid voltage sag fault is removed, dcbus voltage decreases as grid feeding active power increases. Consequently,
V_{pv _ dc}
decreases and PI_LVRT drops out of the dcbus voltage control when
V_{pv _ dc}
reduces to zero. Maximum PV power is then achieved instantly at the premise of constant environmental conditions because the MPPT controller always remains at the MPP of PV panels during fault period. Concurrently, DCM outputs one and PI_NOR regulates the dcbus voltage again when
V_{dc}
reaches 400 V.
III. DC  BUS VOLTAGE CONTROL IN LGVM
 A. Stability Analysis of the Dcbus Voltage Control in LGVM
The case when the
P
_{g max}
in Eq. (7) is more than the present maximum power of PV panels is used to illustrate the proposed dcbus voltage control method in this study. As mentioned, the steadystate dcbus voltage in LGVM is regulated by the PI_LVRT in this case. Thus, the gridconnected current reference in this case should be
The steadystategenerated PV power
P_{pv}
on the dc side should be identical to the grid feeding active power
P_{g}
in terms of the power balance of the whole PV system while neglecting the power losses of the inverter. Notably, the dcbus voltage contains double line frequency (2
ω_{f}
) voltage ripples caused by the power pulsation on the ac side. However, the voltage ripples are generally limited to a very small size through the selection of a suitable capacitance for the dcbus capacitor
C
_{2}
in practice. Hence, in this section, the double line frequency voltage ripples are not considered in the steadystate stability analysis of the dcbus voltage control in LGVM. The stored energy
W_{c}
in the dcbus capacitor
C
_{2}
can be expressed as
As stated in Ref.
[21]
,
W_{c}
is a nonlinear term. However, when
V_{dc}
is in the neighborhood of the reference
in the steady state,
W_{c}
can be linearized as
where ∆
V_{dc}
is the small difference between
V_{dc}
and
in the steady state. According to Eq. (10), the steadystate dcbus voltage can be presented as
Given that the stored energy of
C
_{2}
is identical to the integral of the power flowing through
C
_{2}
,
W_{c}
can also be achieved as
The inner voltage loop in
Fig. 2
(b) is regarded as united when performing the analysis of the dcbus voltage control in LGVM because of the considerably faster response speed of this loop with respect to the outer dcbus voltage loop. In particular, the PV voltage can respond to the command
accurately. Thus,
with the mathematical model of the PV panels in Ref.
[22]
, the PV power can be expressed in terms of the PV voltage as
where
f
(
V_{pv}
) is the PV characteristic curve of the PV panels, as illustrated in
Fig. 4
. In a small neighborhood of the desired operating point B in
Fig. 4
, which satisfies
f
(
V_{pv}
_{2}
) =
P_{g}
, Eq. (14) can be linearized as
where
K_{pv}
represents the slope tangential to point B of the PV characteristic curve. As shown in
Fig. 4
,
K_{pv}
is negative when B lies in the right region of the PV characteristic curve.
According to Eqs. (11)–(15), the linearized model of the dcbus voltage control around the steadystate operating point B in LGVM can be described by
Fig. 2
(d). The closed loop transfer function
G_{c}
(
s
) of the linearized model in
Fig. 2
(d) can be derived as
As stated in Section II.B, the regulation of PV power for power balancing in LGVM is implemented in the right section of the PV characteristic curve of PV panels in this research. Thus, the PV power should be reduced by increasing the PV voltage
V_{pv}
from
Fig. 4
if
V_{dc}
>
. Hence, according to Eq. (13),
K_{p}
_{2}
and
K_{i}
_{2}
are set as negative, such that
V_{pv _ dc}
can increase when
V_{dc}
>
. Given that
K_{p}
_{2}
,
K_{i}
_{2}
, and
K_{pv}
are all negative values in LGVM, both
a
and
b
in Eq. (16) are positive, which can guarantee the stability of the closedloop system
[21]
. Therefore, the steadystate stability of the dcbus voltage control in LGVM can be ensured in the developed LVRT scheme.
However, the above conclusion cannot be obtained if the PV panels operate in the left section of the PV characteristic curve. For example, as discussed above, the PV voltage reference in LGVM increases if
V_{dc}
>
. However, the dcbus voltage may enlarge because of the increasing PV power generated with the increase in PV voltage
V_{pv}
in the left section of the PV characteristic curve. Consequently, the left section of the PV characteristic curve is an unstable region for the proposed LVRT scheme. Although the PV panels may work in the left section of the PV characteristic curve in the transient process because of abrupt changes of solar irradiation, the proposed technique can fortunately ensure that the steadystate operating point of PV panels always lies in the right section of the PV characteristic curve or at the MPP in LGVM.
 B. Transient Analysis of the Dcbus Voltage Control in LGVM
To explore the transient process of the dcbus voltage control in LGVM, all the possible transient cases are classified into eight types, as shown in
Figs. 5
and
6
according to the present PV power
P_{A}
, the present maximum PV power
P_{mpp}
, and the allowed maximum grid feeding active power
P
_{g max}
in Eq. (7). Point A represents the present operating point of PV panels, and point B is the desired steadystate operating point. In the discussion below, PI_NOR functioning means that the output of PI_NOR does not reach the upper limit, while PI_LVRT functioning means the PI_LVRT output is positive.
Cases when A is in the right section of the PV characteristic curve or at the MPP.
Cases when A is in the left section of the PV characteristic curve or at the MPP.
In
Fig. 5
(a), A is in the downhill section of the PV characteristic curve, and A is forced to move forward to the desired equilibrium B if PI_LVRT is regulating the dcbus voltage according to the aforementioned discussion. By contrast, the dcbus voltage increases continuously if the voltage is controlled by PI_NOR because
P_{A}
is bigger than
P
_{g max}
. However, the PI_LVRT starts to regulate the dcbus voltage once the dcbus voltage exceeds 430 V. Subsequently, operating point A moves forward to the anticipated equilibrium B as well.
Point A in
Fig. 5
(b) moves forward to the MPP because of the MPPT control if PI_NOR is functioning. The case of
Fig. 5
(b) can then be converted to the case of
Fig. 5
(a) after
P_{A}
>
P
_{g max}
. Consequently, point A can return to and remain at point B according to the above analysis for
Fig. 5
(a). Clearly, point A of
Fig. 5
(b) can arrive and remain at point B if PI_LVRT is functioning at present.
Fig. 5
(c) is a particular case of
Fig. 5
(a) when A is at the MPP. Therefore, the adjusting process of
Fig. 5
(c) is similar to that in
Fig. 5
(a).
If PI_LVRT is performing its function, the operating point A of
Fig. 6
(a) will undoubtedly transfer to equilibrium B. This transfer is caused by the continuous increase of the dcbus voltage because
P_{A}
>
P
_{g max}
forces the output
V_{pv _ dc}
of PI_LVRT to increase continuously. Subsequently, point A is forced to enter into the right side of MPP. Thus,
Fig. 6
(a) becomes similar to
Fig. 5
(a), where point A is proven to remain at B in the steady state. Assuming that PI_NOR is functioning in the case of
Fig. 6
(a), the dcbus voltage increases because
P_{A}
>
P
_{g max}
and PI_LVRT regulates the dcbus voltage once
V_{dc}
reaches 430 V. Subsequently, point A also moves to point B.
In
Fig. 6
(b), point A travels forward to the MPP under the MPPT control if PI_NOR is performing its role. Once
P_{A}
>
P
_{g max}
, the case of
Fig. 6
(b) becomes similar to that of
Fig. 6
(a). While PI_LVRT is functioning, A moves toward the origin as
V_{dc}
decreases for
P_{A}
<
P
_{g max}
. However, PI_NOR take its role if the dcbus voltage drops to 400 V. Point A then goes to the MPP under the MPPT control, and
Fig. 6
(b) also becomes similar to
Fig. 6
(a).
As shown in
Fig. 5
(d),
6
(c), and
6
(d), the
P
_{g max}
curve is above the MPP. The PV inverter can still deliver the total PV power to the grid even in LGVM. Consequently, the PV system can still work in the MPPT mode during low voltage period for the steadystate operating point of PV panel, which stays at the MPP in such cases. In summary, the steadystate operating point of PV panels in LGVM is in the right section of the PV characteristic curve when
P
_{g max}
<
P_{mpp}
or at the MPP if
P
_{g max}
≥
P_{mpp}
regardless of the present operating point of PV panels. Therefore, the proposed LVRT strategy is adaptable to variations of both grid voltage and environmental conditions.
IV. PARAMETER DESIGN
 A. Design of Dcbus Voltage Reference
As described in previous sections, two different dcbus voltage references
are used in this paper. The dcbus voltage is regulated to the voltage reference
in NGVM, whereas the voltage is controlled to
if
P
_{g max}
<
P_{mpp}
in LGVM. Given that the dcbus voltage can potentially increase because of the power imbalance at the presence of grid voltage sag,
is set to be larger than
. With a smaller
, PI_LVRT can function earlier, such that the proposed LVRT approach can respond to the grid voltage sag fault more quickly. Hence,
should be as close to
as possible from the perspective of minimum dcbus peak voltage during sudden grid voltage sag. However, as stated above, the dcbus voltage contains double line frequency voltage ripples caused by power pulsation on the ac side. In practice, the ripples are limited to 1%–5% nominal dcbus voltage
by choosing suitable capacitance for the dcbus capacitor
C
_{2}
. In this study,
C
_{2}
= 1500
uF
, and the maximum voltage ripples are about ±10 V when the inverter operates at the rated capacity of the inverter. Thus, the maximum dcbus voltage is 410 V in NGVM. Notably, except for the grid voltage sag fault, the dcbus voltage also increases because of sudden increased solar insolation or other disturbances. To avoid the wrong operation of PI_LVRT, 20 V voltage margin can be chosen for disturbance rejection Therefore, the dcbus voltage reference
is chosen to 430 V (410 V + 20 V = 430 V) in this study.
 B. Design of PI_LVRT
To prevent the inverter from triggering overvoltage protection when grid voltage sag occurs,
K_{p}
_{2}
and
K_{i}
_{2}
should be chosen according to the limited dcbus peak voltage in LGVM. In this study, the limited dcbus peak voltage is set to 460 V (the overvoltage protection threshold of the inverter is 480 V). The output
V_{pv _ dc}
of PI_LVRT in discrete form can be expressed as
where
T_{c}
is the control period of PI_LVRT. From Eq. (17), the dcbus voltage can be obtained as
According to the simulation results, the performance of PI_LVRT is acceptable if
K_{p}
_{2}
= 10
K_{i}
_{2}
. Thus, only one parameter
K_{i}
_{2}
requires adjustment. The maximum dcbus peak voltage appears in the case where the PV panels operate at rated capacity and the grid voltage drops below 50% nominal value. Given that the grid feeding active power becomes zero when the grid voltage is below 50% nominal value according to
Fig. 2
(b), all the generated PV power should be stored in the dcbus capacitor during the transient period. The maximum dcbus peak voltage can be calculated through Eqs. (17) and (18). If the voltage is larger than 460 V, then
K_{i}
_{2}
should be decreased (absolute value of
K_{i}
_{2}
increases because
K_{i}
_{2}
is negative in this study) until the calculated maximum dcbus peak voltage is below 460 V. A smaller dcbus peak voltage can be achieved with a smaller
K_{i}
_{2}
, but the transient process lengthens. Therefore, a bigger
K_{i}
_{2}
is better as long as the maximum dcbus peak voltage is within the limited value.
V. SIMULATION RESULTS
The case study is based on a singlephase twostage gridconnected PV system. The particular parameters of the system are listed in
Table I
.
SIMULATED SYSTEM SPECIFICATIONS
SIMULATED SYSTEM SPECIFICATIONS
Fig. 7
(a) depicts the simulation, where the grid voltage drops to 149 V from 220 V at 0.3 s and is restored at 0.7 s. Obviously, the dcbus voltage
V_{dc}
increases at 0.3 s. Once the dcbus voltage reaches 430 V,
V_{pv _ dc}
starts to increase, while
V_{pv _ mppt}
remains unchanged. Subsequently, the dcbus voltage is regulated to stay at 430 V in the steady state during the fault period. Moreover, the maximum PV power is achieved instantly when the output
V_{pv _ dc}
of PI_LVRT decreases to zero during the recovery process. Afterwards, the PI_NOR controls the dcbus voltage again when
V_{dc}
drops to 400 V. Before 0.3 s, the grid current is in phase with the grid voltage, whereas the grid current lags behind the grid voltage during the low voltage period. As shown in
Fig. 7
(a), the reactive power is 1,427 Var and the corresponding reactive current is 9.6 A, which agrees well with the required reactive current of 9.7 A calculated via Eq. (3).
(a) LVRT simulation I with the proposed LVRT strategy. (b) LVRT simulation II with the proposed LVRT strategy.
In
Fig. 7
(b), the grid voltage drops to 88 V from 220 V at 0.3 s and restores at 0.7 s. The response process in
Fig. 7
(b) is similar to that in
Fig. 7
(a). However, the dcbus voltage increases to and stays at 450 V during the fault period in
Fig. 7
(b). Surplus solar energy during the transient process forces the dcbus voltage to increase to 450 V. Afterwards, the dcbus voltage remains constant at 450 V because the PV inverter provides zero active power to the grid in LGVM. Fortunately, the dcbus voltage at 450 V is within the limited value of 460 V. The design of PI_LVRT is proven to satisfy the requirement. Both
Figs. 7
(a) and
7
(b) also show that the maximum PV power can be achieved quickly after the fault. Most importantly, the outputs of the MPPT controller and the PI_LVRT have no sudden changes during the entire transition period. Therefore, a smooth transition from NGVM to LGVM or from LGVM to NGVM can be realized in this study.
Fig. 8
presents the transient responses to the cases in
Figs. 5
and
6
. Numbers 1, 2, 3, and 4 represent
Figs. 5
(a),
5
(b),
5
(c), and
5
(d), respectively; while numbers 5, 6, 7, and 8 stand for
Figs. 6
(a),
6
(b),
6
(c), and
6
(d). The symbol MPP on the figure represents the PV voltage at the MPP of the PV panels. As shown in
Fig. 8
, the steadystate dcbus voltage always remains at 400 V or 430 V. Moreover, in the steady state, the PV voltage is always in the right section of the MPP even though the transient operating point of the PV panels enters into the left section of the MPP in cases 1, 2, 3, 5, and 6. In cases 4, 7, and 8, the PV panels operate at the MPP in the steady state because the allowable maximum grid feeding active power is more than the present maximum power of the PV panels. The simulation results agree well with the theoretical analysis in Section III(B) and justify that the dcbus voltage can be well controlled with the proposed control method in both NGVM and LGVM.
Transient processes with the proposed LVRT strategy.
VI. EXPERIMENTAL RESULTS
To validate the proposed LVRT technique, the laboratory prototype shown in
Fig. 9
is built. The particular parameters of the prototype are given in
Table I
. In
Fig. 9
(a), the PV array consists of 14 PV panels. Seven PV panels are in a series to form a group of PV arrays, and then two groups are connected in parallel. The opencircuit voltage of each PV panel is about 45 V, the shortcircuit current is about 8 A, and the rated power is about 220 W. DSP chip 56F8037 is used to implement the proposed LVRT strategy.
The experimental setup. (a) 3 kW PV arrays. (b) Inverter.
The PV voltage, current, and power during the MPPT process in NGVM is depicted in
Fig. 10
. Seeking the maximum power of the PV panels clearly takes about 0.4 s.
MPPT process in NGVM.
The present maximum PV power of the PV panels is about 2.2 kW, while the PV voltage and current at the MPP are around 250 V and 8 A respectively.
In
Fig. 11
(a), the grid voltage drops to 149 V from 220 V and restores after 0.7 s, while the voltage drops to 88 V from 220 V and restores after 0.7 s in
Fig. 11
(b). The PV power decreases to 600 W from about 2.3 kW in
Fig. 11
(a), whereas that in
Fig. 11
(b) decreases to 0 kW from 2.6 kW. During the fault period, the steadystate dcbus voltage in
Fig. 11
(a) is well regulated to 430 V, but the voltage remains at 450 V in
Fig. 11
(b). As mentioned earlier, the dcbus voltage cannot be regulated to 430 V during the fault period because the PV inverter provides zero active power in
Fig. 11
(b). Fortunately, the dcbus peak voltage is below the limited value of 460 V. The provided reactive power of the PV inverter during the fault period in
Figs. 11
(a) and
11
(b) are 1,371 Var ( 13
A
× 211
V
÷ 2 = 1371
Var
) and 1,240 Var ( 20
A
×124
V
÷ 2 = 1240
Var
) respectively, which agree well with the simulations. Therefore, the experimental results demonstrate the feasibility of the proposed LVRT method.
(a) Experiment I with the proposed LVRT strategy. (b) Experiment II with the proposed LVRT strategy. (c) Experiment III with the conventional LVRT strategy. (d) Experiment IV with the conventional LVRT strategy.
The experiment with the conventional LVRT strategy when the grid voltage drops to 149 V from 220 V and restores after 0.7 s is described in
Fig. 11
(c). The experiment where the grid voltage drops to 88 V from 220 V and restores after 0.7 s is shown in
Fig. 11
(d). The transient process in
Fig. 11
(a) is much smoother than that in
Fig. 11
(c). Moreover, the power pulsation in
Fig. 11
(c) caused by a sudden grid voltage drop in the conventional LVRT approach does not occur in
Fig. 11
(a). The dcbus voltage drop of about 100 V in
Fig. 11
(d) during the recovery process is also adverse for the stability of the system because the conventional LVRT method has to restart the MPPT control from the nonMPPT control and cannot achieve enough PV power instantly. Given that the auxiliary power system is generally powered by the dcbus, a dcbus voltage drop that is too large may lead to the power outage of the auxiliary power system, which threatens the safety of the PV inverter. Therefore, the recovery process without a dcbus voltage drop in
Fig. 11
(b) is superior to that in
Fig. 11
(c).
To test the stability of the dcbus voltage in LGVM, the sudden decrease in solar insolation during the fault period is applied to both developed LVRT approach; the conventional strategy and experimental results are presented in
Figs. 12
(a) and
12
(b) respectively. The power drop from the decrease in solar insolation is about 800 W in both
Figs. 12
(a) and
12
(b). According to
Fig. 12
(a), the dcbus voltage can still be regulated to stay at 400 V although the voltage decreases from 430 V as the solar insolation decreases. Nevertheless, the dcbus voltage can no longer be maintained at the reference of 400 V during the fault period in
Fig. 12
(b). The dcbus voltage drop in
Fig. 12
(b) is about 65 V, which increases as the PV power drop grows, threatening the safety of the PV inverter as well. In summary, the conventional LVRT strategy can effectively address the dcbus overvoltage problem during grid voltage sag. However, this strategy cannot guarantee the stabilization of the dcbus voltage in cases of decreasing solar insolation in LGVM. With adaptability to varying environmental conditions, the LVRT scheme created can thus regulate the dcbus voltage effectively and guarantee the safety of PV inverters in LGVM.
(a) Experiment V with the proposed LVRT strategy. (b) Experiment VI with the conventional LVRT strategy.
VII. CONCLUSION
A smooth LVRT control method for singlephase twostage gridconnected PV inverters was presented in this paper. With the proposed LVRT approach, the LVRT capability of the singlephase twostage gridconnected PV inverter can be enhanced with better transient performance and stability. The detailed analysis of the developed LVRT strategy was given. Finally, the simulation and experimental results corroborated the feasibility of the proposed LVRT technique.
BIO
Furong Xiao was born in Jiangxi, China, in 1989. He received his B.S. degree in Electrical Engineering from Beijing Institute of Technology, China, in 2011. He is currently pursuing his Ph.D. degree in the School of Automation, Beijing Institute of Technology. His research interests include power electronic converters, control of inverters, renewable energy systems, and microgrids.
Lei Dong was born in China in 1967. He received his B.S. and Ph.D. degrees from Nanjing University of Aeronautics and Astronautics, China, in 1990 and 2000 respectively. He worked as a postdoctoral in Tsinghua University, China, from 2000 to 2002. He joined AVIC–The First Aircraft Institute as an Engineer from 1990 to 1995. At present, he is an associate professor in the Beijing Institute of Technology China and the director of the Power Electronics and Motion Control Research Center of the university. His research interests include power electronics and motion control, microgrids, and renewable energy.
Shahnawaz Farhan Khahro was born in Hyderabad, Sindh, Pakistan. He received his B.E. (Electronics) and M.E. (CSN) degrees from Mehran University of Engineering and Technology, Jamshoro Sindh Pakistan in 2002 and 2007, respectively. He received his Ph.D. degree in Renewable Energy Conversion and Control Strategies from the Beijing Institute of Technology (BIT), Beijing, PR China in 2014. From 1999 to 2004, he worked in the Civil Aviation Authority in Pakistan, and from 2004 to 2008, he worked at Pakistan Telecommunication Company Ltd. In November 2008, he joined the Environment and Alternative Energy Department, Government of Sindh, Pakistan, as Assistant Director. Since January 2015, Mr. Khahro has been serving as the Deputy Director (Alternative Energy) of the Energy Department, Government of Sindh in Pakistan. His research interests include renewable energy power conversion systems, DC–DC converters, power electronic converters, and application of power electronics in renewable energy systems.
Xiaojiang Huang was born in China in 1985. He received his B.S. degree in Electrical Engineering and Automation from Beijing Institute of Technology, Beijing, China in 2009. He is currently pursuing his Ph.D. degree in the School of Automation, Beijing Institute of Technology. His research interests include power electronics and control, renewable energy systems, and smart grids.
Xiaozhong Liao was born in China in 1962. She received her B.S. and M.S. degrees in Electrical Engineering from Tianjin University, Tianjin, China, in 1982 and 1984 respectively. She received her Ph.D. degree in Control Sciences and Engineering from Beijing Institute of Technology, Beijing, China, in 2004. She was a visiting researcher in the Department of Electrical and Electronic Engineering, University of Central Lancashire, Preston, U.K., from 1995 to 1996. She is now the associate dean and a fulltime professor at the School of Automation, Beijing Institute of Technology, Beijing, China. Her research interests are in the fields of power electronics, motor drives, and renewable energy power conversion.
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