An Adaptive Control Scheme for Flexible Power Point Tracking in Photovoltaic Systems

Abstract

One of the major concerns associated with the increasing penetration of grid-connected photovoltaic (PV) power plants is the operational challenges (e.g., overloading and overvoltage), imposed due to the variability of PV power generation. A flexible power point tracking (FPPT), which can limit the PV output power to a specific value, has thus been defined in grid-connection regulations to tackle some of the integration challenging issues. However, the conventional FPPT algorithm based on the perturb and observe method suffers from slow dynamics. In this paper, an adaptive FPPT algorithm is thus proposed, which features fast dynamics under rapidly changing environmental conditions (e.g., due to passing clouds), while maintaining low power oscillations in steady-state. The proposed algorithm employs an extra measured sampling at each perturbation to observe the change in the operating condition (e.g., solar irradiance). Afterwards, the voltage-step is adaptively calculated following the observed condition (e.g., transient or steady-state) in a way to improve the tracking performance. Experimental results on a 3-kVA grid-connected single-phase PV system validate the effectiveness of the proposed algorithm in terms of fast dynamics and high accuracy under various operational conditions.

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University Library, Singapore.
Title An adaptive control scheme for flexible power point
tracking in photovoltaic systems
Author(s) Dehghani Tafti, Hossein; Sangwongwanich, Ariya; Yang,
Yongheng; Pou, Josep; Konstantinou, Georgios;
Blaabjerg, Frede
Citation
Dehghani Tafti, H., Sangwongwanich, A., Yang, Y., Pou,
J., Konstantinou, G., & Blaabjerg, F. (2018). An adaptive
control scheme for flexible power point tracking in
photovoltaic systems. IEEE Transactions on Power
Electronics. doi:10.1109/TPEL.2018.2869172
Date 2018
URL http://hdl.handle.net/10220/46007
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© 2018 IEEE. Personal use of this material is permitted.
Permission from IEEE must be obtained for all other
uses, in any current or future media, including
reprinting/republishing this material for advertising or
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resale or redistribution to servers or lists, or reuse of any
copyrighted component of this work in other works. The
published version is available at:
[http://dx.doi.org/10.1109/TPEL.2018.2869172].

1
An Adaptive Control Scheme for Flexible
Power Point Tracking in Photovoltaic Systems
Hossein Dehghani Tafti1∗,Member, IEEE, Ariya Sangwongwanich2,Student Member, IEEE,
Yongheng Yang2,Senior Member, IEEE, Josep Pou1,Fellow, IEEE,
Georgios Konstantinou3,Senior Member, IEEE, Frede Blaabjerg2,Fellow, IEEE,
1School of Electrical and Electronic Engineering, Nanyang Technological University, Singapore.
2Department of Energy Technology, Aalborg University, Denmark.
3School of Electrical Engineering and Telecommunications, University of New South Wales, Australia.
∗hossein002@e.ntu.edu.sg
Abstract
One of the major concerns associated with the increasing penetration of grid-connected photovoltaic (PV) power
plants is the operational challenges (e.g., overloading and overvoltage), imposed due to the variability of PV power
generation. Aflexible power point tracking (FPPT), which can limit the PV output power to a specific value, has
thus been defined in grid-connection regulations to tackle some of the integration challenging issues. However, the
conventional FPPT algorithm based on the perturb and observe method suffers from slow dynamics. In this paper,
an adaptive FPPT algorithm is thus proposed, which features fast dynamics under rapidly changing environmental
conditions (e.g., due to passing clouds), while maintaining low power oscillations in steady-state. The proposed
algorithm employs an extra measured sampling at each perturbation to observe the change in the operating condition
(e.g., solar irradiance). Afterwards, the voltage-step is adaptively calculated following the observed condition (e.g.,
transient or steady-state) in a way to improve the tracking performance. Experimental results on a 3-kVA grid-
connected single-phase PV system validate the effectiveness of the proposed algorithm in terms of fast dynamics and
high accuracy under various operational conditions.
Index Terms
Adaptive voltage-step calculation, constant power generation, photovoltaic systems, photovoltaic panel power-
voltage curve, voltage reference calculation
NOMENCLATURE
pref Power reference.
vp-ref Corresponding voltage to the constant power reference.
ppv(k)Instantaneous PV power at calculation time-step k.
dp1PV power change between t= (k−1)Tand t= (k−1/2)T.
dp2PV power change between t= (k−1/2)Tand t=kT .
dp∗PV power error between pref and ppv(k).
dv PV voltage change between t= (k−1)Tand t=kT .

2
Tstep Calculation time-step.
Vstep Voltage-step.
Vstep-bOptimal voltage-step for the MPPT operation.
Vstep-tr Transient voltage-step.
Vref PV panel voltage reference.
k1,k2Voltage-step calculation proportional gains.
αParameter for differentiating operation modes.
dpth Threshold power.
T hr. Threshold dp/dv.
pmpp PV panel maximum power.
vmpp PV panel maximum power-point voltage.
impp PV panel maximum power-point current.
impp PV panel maximum power-point current.
F F PV panel filling factor.
vdc dc-bus voltage.
Cpv PV-side capacitor.
Cdc dc-link capacitor.
fsw Converter switching frequency.
vgGrid voltage.
igGrid current.
Irr. Solar irradiance.
T emp. Temperature.
T.E. Tracking error.
pavai Instantaneous maximum available power from the PV panels.
I. INTRODUCTION
The increasing installation of grid-connected photovoltaic power plants (GCPVPPs) may lead to overvoltages
in the power infrastructure during peak power generation periods (e.g., noon time in a day), if the grid power
capacity remains the same [1]. In order to tackle potential challenging issues for the power system, grid codes
and/or standards are continuously updated [2], [3]. For instance, the Danish grid code requires that a GCPVPP
with a power output above 11 kVA should be able to limit the output power to a certain constant value if required
[2]. By limiting the power output of the GCPVPP, the additional available power can be used to provide ancillary
functions, such as frequency support [2]. Furthermore, the power limiting control (also known as constant power
generation) [1], [4], [5], power reserve control [6], and power ramp-rate control [7] requirements are imposed by
various grid codes on GCPVPPs. Therefore, the existing maximum power point tracking algorithms in GCPVPPs,
should be replaced by flexible power point tracking (FPPT) algorithms in GCPVPPs in order to comply with these
demands.

3
In the past, the focus of most research studies in the literature was the maximum power point tracking (MPPT)
from PV strings to increase the overall power conversion efficiency and energy utilization [8]–[15]. In addition to
the conventional MPPT algorithms, like perturb & observe (P&O) and incremental conductance (I.C.) [8], several
advanced algorithms like model-predictive [9], particle swarm optimization method [14] and dual-Kalman filter
method [15] are also introduced to extract the maximum power from PV strings. Furthermore, the operation of
PV strings under partial shading conditions is considered in [13]. With the introduction of FPPT requirements,
several FPPT algorithms have also been introduced for different configurations of GCPVPPs. There are mainly two
categories of methods to achieve the FPPT operation:
i) Modifying the dc-dc converter controller in two-stage or dc-ac inverter controller (e.g., Proportional Integral - PI
controller) in single-stage GCPVPPs [16]–[24]. The fundamentals of the FPPT are introduced in [16]–[20] with
focus on stability issues. A voltage reference calculation method is also introduced in [18], [21], based on the P&O
algorithm to calculate the voltage reference related to the required active power. However, moving the operation
point to the right-side of the maximum power point (MPP) reduces the robustness of these algorithms, as the
operation point may go beyond the open-circuit voltage of the PV panel under fast irradiance reductions. These
algorithms apply multi-mode operations to regulate the output power of the PV panels. Clearly, the controller
initialization during the operational mode transitions is required and thus slow dynamics are observed.
ii) Adjusting the voltage reference of PV strings per the required power reference according to the power-voltage
(P-V) characteristics of the PV panels [1], [4]–[6], [25]. Such approaches do not require any modifications in the
dc-dc or dc-ac converter controllers.
Since the second category of FPPT algorithms do not require any changes in the controllers and can achieve fast
dynamics, they are chosen in this study for the generation of constant power from GCPVPPs. These algorithms
perform well during constant environmental conditions (e.g., irradiance and temperature). However, the power and
voltage characteristic of the PV arrays can vary considerably due to environmental changes. Thus, the previous
solutions can encounter issues in the calculation of the voltage reference under rapid irradiance changes. Several
studies are available in the literature to enhance the operation of MPPT algorithms during rapid environmental
changes [26]–[28]. In that case, the performance of FPPT algorithms can be highly affected by environmental
condition changes, especially when the operating point is far away from the MPP, because:
•MPPT operating range is narrow around the MPP, while the FPPT operating range covers the entire region of
the P-V curve. Therefore, it is more challenging to adapt the control parameters according to the environmental
conditions.
•The impact of environmental changes on the PV power during the FPPT operation could be more pronounced
compared to the MPPT operation, because the change of the voltage during FPPT has greater impact on the
power compared to the MPPT operation.
Furthermore, it is not only environmental changes that can influence the FPPT operation, but also sudden changes
of the desired constant power reference (pref ), due to the grid requirements. Hence, the FPPT operation under
transients is more challenging compared to the MPPT operation. However, this has not been addressed in the

4
vpv
Linv
Grid
ipv
Lg
Cr
C
vgig
vdc
Cpv
PV String Boost
Converter Full-bridge
Inverter LCL Filter
PWMinv
PWMb
Grid-Side Control
Flexible Power
Point Tracking
dc-Link Voltage Controller
Grid Support (e.g., LVRT)
Current Controller
Grid Synchronization
PV-Side Control
Zg
pref
(Calculated by grid-side
controller and grid regulations)
Fig. 1. Circuit configuration and overall control structure of a two-stage GCPVPP.
literature yet.
In light of the above, this paper proposes an adaptive FPPT algorithm for GCPVPPs. The proposed algorithm is
an adaptation of the P&O method considering the P-V characteristics of PV panels. The main contributions of the
proposed algorithm in this paper are:
•The key contribution is the proposed adaptive voltage-step calculation strategy for a novel FPPT algorithm,
which can achieve fast dynamics during transients, and low power osculations in steady-state. In the proposed
algorithm, the operation mode of the converter and the current operation point of the PV panel are considered
in the calculation of the voltage-step in each calculation step. This feature adaptively adjusts the voltage-step in
order to enhance the transient and steady-state performances.
•Furthermore, the proposed algorithm is highly robust to fast environmental changes. An extra sampling is used in
the proposed controller to differentiate the effect of the intentional voltage changes in the P&O algorithm from
environmental changes on the PV panel power. By doing so, wrong movements of the operation point under
rapid changing conditions can be avoided.
The proposed FPPT algorithm in this paper can also be used to extract the maximum power from the PV strings,
while it is able to limit the PV power to a required value upon demands. While the proposed algorithm achieves
fast dynamics during the power-limiting operation mode, it can obtain similar performance when operating in the
MPPT mode as the conventional MPPT algorithms. The calculation time-step is fixed for all operational modes,
which reduces the complexity of the controller design for different operation states. Additionally, the proposed
adaptive FPPT algorithm is able to move the operation point of the PV panel to the right- or left-side of the
MPP. It can be implemented in both single- and two-stage GCPVPPs. The performance of the proposed algorithm
is evaluated on a 3-kVA two-stage single-phase GCPVPP, as shown in Fig. 1. The two-stage GCPVPP system
consists of a grid-connected full-bridge inverter, which provides the grid connection requirements. The dc-dc boost
converter provides the FPPT control for the system, while the required power reference (pref ) is calculated from
the grid-side controller. The detailed description of this configuration can be found in [6].
The remaining of the paper is organized as following. The principles of the proposed adaptive FPPT algorithm are
described in Section II. The detailed explanation of the proposed adaptive FPPT algorithm, including the proposed

5
ppv
vpv
vpv(k)
ppv(k)
ppv(k-1)
pref ppv(k+1)
vpv(k-1)
vpv(k+1)
vp-ref
(a)
ppv
vpv
Rapid reductrion
of irradiance
vpv(k)
ppv(k-1)
ppv(k)
pref
ppv(k+1)
vpv(k-1) vpv(k+1)
(b)
Fig. 2. Effect of the voltage-reference change of the PV panels during: (a) Steady-state environmental condition and (b) rapid irradiance changes.
adaptive voltage-step calculation method, is provided in Section III. The experimental results are presented and
discussed in Section IV. Finally, concluding remarks are given in Section V.
II. PRINCIPLES OF THE ADAP TIV E FPPT ALGORITHM
The control objective of the FPPT algorithm is to regulate the output power of the PV system to be constant at a
certain set-point. Conventionally, the P&O-based FPPT algorithm, which intentionally perturbs the PV voltage away
from the MPP to reduce the output power, is employed as illustrated in Fig. 2(a). According to the effect of the
voltage perturbation on the PV output power, the next voltage reference is determined. As illustrated in Fig. 2(a),
the PV voltage is vpv(k−1) at t= (k−1)T, with kindicating the kth sampling and Tbeing the sampling period.
The voltage reference is then changed to vpv(k)at t= (k−1)Tand the controller regulates the PV voltage to this
value at t=kT . Accordingly, the instantaneous power of the PV panel changes from ppv (k−1) to ppv (k). In this
condition, a negative voltage change, i.e., ∆vpv =vpv (k)−vpv (k−1) <0, results in a positive power change, i.e.,
∆p =ppv(k)−ppv (k−1) >0. Based on the signs of ∆v and ∆p, the FPPT algorithm decides another voltage
decrement in this calculation-step, leading to an increase of the PV power, closer to the power reference (pref ), as
shown in Fig. 2(a). Under a constant or slow changing solar irradiance condition, the change in the PV power is
mainly induced by the perturbation of the CPG algorithm. Thus, the P&O CPG algorithm can accurately regulate
the PV power according to the set-point.
However, under a fast reduction of irradiance, the above process can result in large tracking errors, which is
demonstrated in Fig. 2(b). As observed in Fig. 2(b), the same scenario has been applied and a voltage decrement is
imposed by the FPPT algorithm at t= (k−1)T. A fast reduction of the irradiance occurs during the time interval
between t= (k−1)Tand t=kT . The absolute value of the power reduction due to the decrease of irradiance
is larger than the absolute value of the power increment due to the change of the PV voltage. In other words, the

6
Time
(a)
(b)
pcpg
vcpg
ppv
Vref,
vpv
ppv
Vref,
vpv
(k-1)TkT
(k-1/2)T
vref(k-1)
ppv(k-1)
vpv(k)
vpv(k-1/2)
ppv(k)
ppv(k-1/2)
(k+1)T
(k+1/2)T
ppv(k+1)
ppv(k+1/2)
Time
(k-1)TkT
(k-1/2)T
ppv(k-1)
vpv(k)
ppv(k-1/2)
(k+1)T
(k+1/2)T
vref(k)
vref(k+1)
vref(k-1)
vref(k)
ppv(k)ppv(k+1/2)
ppv(k+1)
dp1 > 0 dp2 ~ 0
dp > 0
dp1 < 0 dp2 ~ 0
dp < 0
vpv(k-1) vpv(k+1)
vpv(k+1/2)
dp1 < 0 dp2 < 0
dp > 0
dp1 < 0 dp2 < 0
dp > 0
vpv(k-1)
vpv(k-1/2)
vpv(k+1/2) vpv(k+1)
Fig. 3. Extra measurements between consecutive calculation-steps (top: PV voltage, bottom: PV power): (a) Steady-state environmental condition
and (b) rapid irradiance changes.
change in the PV power during the perturbation is imposed by the sudden change in the solar irradiance condition.
Hence, it will result in a negative change of ∆p and the conventional FPPT algorithm may make a wrong decision
for the next perturbation, as it can be seen in Fig. 2(b).
The voltage and power curves of the PV panels during FPPT operation in steady-state are illustrated in Fig. 3.
It can be seen in Fig. 3 that the operation point oscillates around the power reference pref in steady-state. The
corresponding voltage at pref is referred to vp-ref , as illustrated in Fig. 2(a). At t= (k−1)T, the voltage reference
calculation algorithm sets a new voltage reference to vref (k−1), as shown in Fig. 3(a). An extra measurement is
performed to measure the PV voltage and power at t= (k−1/2)T. The controller is then designed to regulate the
PV voltage vpv in half a sampling period T/2. Consequently, the PV voltage vpv is regulated to its reference value
(i.e., vref (k−1)) at t= (k−1/2)T. The PV output power (ppv) increases to ppv (k−1/2). Between t= (k−1/2)T
and t=kT , the voltage reference is not changed through the voltage reference calculation algorithm. Therefore,
the PV output power ppv remains constant during this period.

7
According to the above discussions, two parameters are defined in order to detect environmental changes
(irradiation and temperature). The first parameter dp1calculates the PV power change between (k−1)Tand
(k−1/2)T, and it is given as
dp1=ppv(k−1/2) −ppv (k−1).(1)
During steady-state environmental conditions, dp1shows the power change due to the voltage reference perturbation.
The PV power change dp2between (k−1/2)Tand kT is defined as
dp2=ppv(k)−ppv (k−1/2).(2)
Clearly, in steady-state, i.e., constant solar irradiance condition dp2is close to zero, since the PV voltage reference
is not changed between (k−1/2)Tand kT . A relatively large value of dp2shows that environmental condition
changes are occurring.
The effect of rapid irradiance changes on the above parameters is illustrated in Fig. 3(b). The current operation
point of the PV panel in this case study is kept to the same operation point as in Fig. 3(a). However, a rapid
linear reduction of the irradiance is considered. The voltage reference at t= (k−1)Tis set to vref (k−1), while
the PV power ppv decreases to ppv(k−1/2) at t= (k−1/2)Tdue to the reduction of the irradiance. Between
t= (k−1/2)Tand t=kT , the PV power ppv decreases. However, the voltage reference is not changed during
this period. Consequently, dp1is negative in this condition, while positive in steady-state. Furthermore, dp2is also
negative with a relatively large amplitude, indicating the case of environmental condition changes, although it is
close to zero in steady-state.
It is noted that dp1includes the information of the power change, which is due to the combination of the effect of
irradiation changes and intentional voltage reference changes. The use of the parameter dp1in the voltage reference
calculation can move the operation point to a wrong direction under environmental changes. Thus, the following
parameter is defined to separate the effect of the environmental changes from the effect of the intentional voltage
reference changes as
dp =dp1−dp2(3)
The change of environmental parameters (irradiation and temperature) is assumed to be linear in one calculation
time-step. Any changes in the environmental parameters result in changing the PV power. By assuming the linear
change of environmental changes in one calculation time-step, its effect on the PV power for dp1is equal to dp2.
Because dp is the difference of dp1and dp2, the effect of environmental changes on the parameter dp is eliminated.
As a result, the parameter dp only includes the information about the PV power changes due to the intentional
voltage reference perturbations from the controller. In this way, the voltage reference calculation algorithm does
not track a wrong direction under rapidly changing environmental conditions.

8
Yes
No |dp| > dpth
dp
dv > Thr
Yes
No
dp > 0Yes
No
Start
Measure vpv(k) and ipv(k)
Record ppv(k) and vpv(k)
Calculate dv and dp*
Return
Calculation
Period: T
Sampling
Period: T/2
Operation Mode
Evaluation
Voltage-Step
Calculation
(Equ. 10)
Voltage-Reference
Calculation
Yes
*
Steady-State
α = 1
Transient
α = 0
Operation Mode
Left-side
of MPP
Vref = Vref-old - Vstep
dp 0
>Yes
Op. Region
Right-side
of MPP
Vref = Vref-old - Vstep
Vref = Vref-old + Vstep
No
dp 0
>
dv 0
>
dv 0
>
Vref = Vref-old + Vstep
Vref = Vref-old - Vstep
Vref = Vref-old - Vstep
Yes
Yes
No
No No
Yes
Vref
Operation Mode
Evaluation
Voltage-Reference Calculation
Conventional P&O
Algorithm
*
*
Fig. 4. Block diagram of the proposed adaptive constant power generation algorithm in GCPVPPs.
III. PROP OSE D ADA PT IVE FLEXIBLE POWE R POI N T TRACKING ALGORITHM
The block diagram of the proposed adaptive FPPT algorithm is illustrated in Fig. 4. The parameters vpv and ppv
are measured with a sampling period of T/2. It is noted that this extra sampling does not increase the computational
complexity of the algorithm. It just requires an extra interrupt for sampling the input measurements. The proposed
adaptive FPPT algorithm consists of three parts, which are performed with a calculation period T. Firstly, the
operation mode of the PV system is identified as transient or steady-state. This is required to achieve fast dynamics
during transient and low power oscillations in steady-state modes. The output of the “operation mode evaluation”
block is used as the entry to the “voltage-step calculation” block. Subsequently, the adaptive voltage-step calculation
algorithm is implemented to calculate the voltage-step according to the operation mode and PV power change
parameters, as defined previously. The calculated voltage-step value by this block is used as the entry to the
“voltage reference calculation” block to determine the PV voltage reference for the regulation of the PV power
to its reference value. All the calculations of these blocks are implemented in one calculation period of T.The
implementation of these parts is presented in detail in the following sections. In the proposed algorithm, the PV
voltage change dv between the current and previous calculation-steps is calculated as
dv =vpv(k)−vpv (k−1).(4)

9
ppv
vpv
pref
vp-ref
dpth
}
Steady-state
Transient
Transient
(a)
ppv
vpv
pref
vp-ref
MPP
pmpp
pmpp
(b)
ppv
vpv
pref
vp-ref
vpv(k)
pmpp MPP
(c)
Fig. 5. The different operation modes of the PV system in constant power generation: (a) Operation at steady-state, (b) operation at MPP under
steady-state, while pref is larger than the maximum available PV power, and (c) operation at MPP under transient, while pref is smaller than
pmpp.
A. Operation Mode Evaluation Algorithm
There are two main operational modes as depicted in Fig. 5(a). A power threshold dpth is defined to distinguish
between the two operation modes as:





dp∗≤dpth Steady-state
dp∗> dpth T ransient
(5)
in which the error dp∗is defined as:
dp∗=ppv(k)−pr ef ,(6)

10
where ppv(k)is the instantaneous PV power at the current calculation-step k. In steady-state, the error in (6) is
close to zero, while during transients it can be relatively large, due to the change in the solar irradiance condition.
The implementation of the comparison in (5) can result in a wrong selection of operation mode in the condition
that the PV system operates at the MPP. As illustrated in Fig. 5, this condition can happen under two circumstances:
•The controller is set to extract the maximum power from the PV system, instead of operating at FPPT. In
this case, the controller sets the power reference to a value larger than the nominal maximum PV power, as
depicted in Fig. 5(b).
•Due to partial shading or other reasons, the maximum available PV power (pmpp) is smaller than the constant
power reference during the FPPT operation. In this case, the operation mode is also similar to Fig. 5(b).
The proposed voltage reference calculation algorithm is able to calculate the MPP voltage during the above
conditions. In order to achieve similar or smaller power oscillations compared to the conventional MPPT algorithms,
it should be ensured that these conditions are classified as steady-state. It is known that the slope of the PV panels
P-V curve (dp/dv) at MPP is close to zero. Accordingly, the absolute value of dp/dv is compared to a threshold
(T hr) to identify whether the current operation point is close to the MPP. If the operation point is not close to the
MPP (|dp/dv|> T hr ), the PV system is in transient mode. It should be noted that if the current operation point is
close to the MPP, two different conditions can happen:
•The power reference is larger than pmpp, as illustrated in Fig. 5(b). This operation condition should be classified
as steady-state. In this operation mode, dp∗is positive, as calculated from (6).
•The power reference can be smaller than pmpp at the current calculation time-step. However, due to the step
decrease of pref , the operation point is still at the MPP, as demonstrated in Fig. 5(c). This operation condition
results in dp∗<0and should be classified as transient to achieve fast dynamics.
In order to differentiate the two conditions, the sign of dp∗is determined in the proposed algorithm, as it is shown
in Fig. 4. After the detection of the operation mode, the parameter αis defined as:





T ransient α = 0
Steady-state α = 1.
(7)
When the operation mode evaluation algorithm is implemented, it is ensured that all the operation conditions
are classified correctly. The main advantage of this algorithm is to properly classify the operation at the MPP.
It guarantees that the MPPT operation is classified as steady-state, which results in smaller power oscillations
compared to the conventional MPPT algorithms.
B. Adaptive Voltage-Step Calculation Algorithm
The selection of voltage-step (Vstep) is critical in the design of the FPPT algorithm. A large value of Vstep results
in fast dynamics during transients, while it generates large power oscillations in steady-state. On the other hand,
with small values, relatively small power oscillations in steady-state can be achieved. However, such a choice results
in slow dynamics. Thus, an adaptive voltage-step calculation algorithm is introduced in the following to improve
both the dynamic and steady-state performances.

11
One objective of the proposed FPPT algorithm is to provide similar MPPT performance compared to conventional
MPPT algorithms. In this regard, a fixed voltage-step, which is the optimal voltage-step for the MPPT operation,
can be applied in the FPPT algorithm as
Vstep =Vstep-b,(8)
in which Vstep-bis the optimal voltage-step for the MPPT operation, which can be designed by following [29].
When the fixed voltage-step Vstep-bis adopted for the FPPT algorithm, the dynamics of the system under rapidly
changing environments become slow as aforementioned. Note that the change of the voltage in an FPPT operation
vp-ref for a specific constant power reference is larger than that of the voltage changes at MPP vmpp under similar
environmental condition variations. This is due to the fact that the MPPT operating range is concentrated around
the MPP; where the slope of the P-V curve is close to zero. Accordingly, a larger voltage-step should be applied
during transients to improve the dynamics as
Vstep =
Steady-state
z }| {
α×Vstep-b+
Transient
z }| {
(1 −α)×Vstep-tr,(9)
where Vstep-tr is the selected voltage-step for transient operations and it is larger than the optimal voltage-step
Vstep-b. During transients,α= 0 and Vstep =Vstep-tr , which results in faster dynamics, while in steady-state with
α= 1, relatively low power oscillations can be achieved. Nevertheless, this algorithm still has two drawbacks:
•The FPPT operation in the right-side of the MPP with relatively small power references results in large power
oscillations, even considering Vstep-bas the voltage-step, because the slope of the P-V curve (dp/dv) is large. This
means smaller voltage-step values should be applied for operation points with larger dp/dv values to maintain
low power oscillations.
•The dynamic transients can lead to large power deviations from the power reference (power errors). Using small
voltage-step values increases the response time, as depicted in Fig. 6(a). On the other hand, by applying large
voltage-step values during transients, the operation point may go beyond the steady-state region, in which large
power oscillations are observed, as depicted in Fig. 6(b). In this case, the operation point oscillates beyond the
steady-state region.
To solve these drawbacks, an adaptive voltage-step calculation algorithm is proposed as
Vstep =
Steady-state
z }| {
α×1−k1
|dp|
|dv|+
Transient
z }| {
(1 −α)×k2×dp∗×Vstep-b,(10)
in which αis determined by the operation mode evaluation algorithm in the previous subsection, while k1and k2
are scaling factors.
During the transient operation, α= 0, which gives Vstep =k2×dp∗×Vstep-b. In this method, the value of
Vstep depends on the error between the instantaneous power and its reference value. During transients with large
errors, the voltage-step becomes large, which reduces the response time. When the PV power becomes closer to its
reference value, the voltage-step becomes smaller, as illustrated in Fig. 6(c).

12
ppv
vpv
0
pref
vp-ref vpv(k+1)
Current
operation point
Intended
operation point
vpv(k)vpv(k+2)vpv(k+3)
(a)
ppv
vpv
0
pref
Current
operation point
vp-ref vpv(k)
vpv(k+1)
vpv(k+2)vpv(k+3)
Oscillation beyond the
steady-state margin
(b)
ppv
vpv
0
pref
Current
operation point
Intended
operation point
vp-ref vpv(k)
vpv(k+1)
vpv(k+2)
(c)
Fig. 6. Principles of the proposed voltage-step calculation algorithm during transients: (a) Constant small voltage-step, (b) constant large
voltage-step, and (c) proposed adaptive voltage-step.
In steady-state, α= 1, which results in Vstep = (1 −k1|dp|/|dv|)×Vstep-b. The P-V curve of the PV panels
and the curve of |dp|/|dv|are illustrated in Figs. 7(a) and (b). The value of |dp|/|dv|is close to zero at the MPP,
while it increases to relatively large values in the right-side of the MPP. The voltage-step values in the proposed
algorithm are plotted in Fig. 7(c). It is seen in Fig. 7(c) that Vstep is equal to Vstep-bat the MPP, while it is reduced
to a minimum value (Vstep-min) in the right-side of the MPP. Additionally, the voltage-step Vstep remains close
to a constant value in the left-side of the MPP due to the linear behavior of the P-V curve in this region. Further
observations in Fig. 7(c) confirm that with the proposed algorithm, the voltage-step is adaptively modified according
to the operation point of the PV panels. Therefore, the voltage oscillations can remain small in steady-state for all
operation points.
C. Voltage Reference Calculation Algorithm
The voltage reference calculation algorithm for the proposed FPPT operation scheme is illustrated in Fig. 4. If
the instantaneous power of the PV system is smaller than the power reference (dp∗<0), a conventional P&O is
applied to move the operation point towards the MPP to increase the power. If the instantaneous power is larger
than the power reference, based on the intended operation region (i.e., right- or left-side of the MPP) the voltage

13
Vstep
vpv
(c)
ppv
vpv
(a)
dp / dv
vpv
(b)
MPP
pmpp
0
0
0
Vstep-b
Vstep-min
Fig. 7. Principles of the proposed voltage-step calculation algorithm in steady-state: (a) The P-V curve of the PV panels, (b) ppv over vpv
derivation, and (c) calculated voltage-step according to (10).
reference increases or decreases, respectively. The details of the voltage reference calculation algorithm for FPPT
operation can be found in [4], [5].
D. Design Guidelines
In terms of design of the proposed adaptive FPPT algorithm, the following should be considered:
•The calculation time-step (Tstep) is selected for the optimal MPPT operation of the PV system. Notice that the
proposed adaptive FPPT algorithm is able to achieve fast dynamics, even with relatively large values of time-steps.
Furthermore, using the same calculation time-step in both MPPT and FPPT algorithms reduces the calculation
complexity of the proposed algorithm. The sampling frequency for MPPT algorithms in commercial systems is
normally 1−10 Hz [30], [31].
•Vstep-bis the optimal voltage-step for the MPPT operation and can be calculated according to the available
algorithms in the literature [29], [32].
•The transient voltage-step (Vstep-tr) is chosen to be two to three times larger than the Vstep-bto achieve fast
dynamics. Since, the slope of the P-V curve in the right-side of MPP is larger than the left-side of MPP, a
smaller value can be chosen for Vstep-tr in the right-side of MPP.
•Since the proposed adaptive FPPT algorithm is based on the P&O algorithm, the effect of the intentional voltage
change is considered in the selection of new voltage references. Therefore, a minimum voltage-step is required

14
PV Simulator
FPGA Controller
AC Grid
(Isolation Transformer)
Two-Stage GCPVPP
Fig. 8. Experimental setup of the 3-kVA two-stage single-phase grid-connected PV system.
in the proposed algorithm. As shown in Fig. 7(c), a minimum voltage-step (Vstep-min) is applied in the proposed
algorithm, which is selected according to the voltage and power rating of the PV system.
•The threshold power (dpth) is chosen between 3% to 5% of the nominal power of the system.
IV. EXP E RI MEN TAL EVAL UATION
The operation and performance of the proposed algorithm are demonstrated experimentally using a two-stage
single-phase grid-connected PV system as shown in Fig. 8. The system parameters of the experimental setup are
given in Table I. The PV-side is emulated using a Chroma 62150H-1000S PV Simulator and its P-V characteristics
are given in Table I. The calculation-step (Tstep) of the proposed FPPT algorithm is selected as 1 s as a typical
calculation step for commercial systems [30]. Four case studies are demonstrated in order to verify the performance
of the proposed adaptive FPPT algorithm under various conditions.
The performance of the proposed adaptive voltage-step calculation algorithm is compared with the conventional
voltage-step algorithms. The fixed voltage-step in (8) is referred to as method 1 (m1), while the conditional voltage-
step in (9) is specified as method 2 (m2) and the proposed adaptive voltage-step algorithm in (10) is named
method 3 (m3). To obtain a numerical comparison between the performance of these algorithms, the average tracking
error (in percentage of the total energy yield) during the FPPT operation is calculated. The tracking error (T.E.) is
calculated from the difference between the actual PV output power and its reference (i.e., |ppv −pref |), and then
divided by the total energy yield as
T.E. =R|ppv −pr ef |
R|ppv|.(11)
The tracking error is calculated during the FPPT period, in which the instantaneous maximum available power from
the PV panels (pavai) is larger or equal to the required power reference pref .
For a fair comparison of the performance of various algorithms, the following are considered: a) The rest of
the control system is identical for all test conditions for different algorithms, and b) the PV emulator is used to
provided similar PV curves for all test conditions.

15
TABLE I
PARAMETERS OF THE TWO-STAG E GRID-CON NE CT ED PV SY ST EM .
Parameter Symbol Value
PV panel maximum power*pmpp 3 kW
PV panel maximum
power-point voltage*vmpp 350 V
PV panel maximum
power-point current*impp 8.5 A
PV panel filling factor F F 0.68
DC-bus voltage vdc 450 V
PV-side capacitor Cpv 1000 µF
DC-link capacitor Cdc 1100 µF
Converter switching frequency fsw
dc-dc: 16 kHz
Inverter: 8 kHz
Calculation time-step Tstep 1 s
Optimal voltage-step
for the MPPT operation*Vstep-b2 V
Transient voltage-step Vstep-tr
Right-side: 4 V
Left-side: 6 V
Voltage-step calculation
parameters in right-side
k1
k2
0.015
0.003
Voltage-step calculation
parameters in left-side
k1
k2
0.008
0.006
Threshold power dpth 100 W
Threshold dp/dv T hr. 4 W/V
*Irr. = 1000 W/m2and T emp. = 25◦C.
Case I: The performance of the proposed adaptive FPPT algorithm under rapid irradiance changes with the
movement of the operation point to the right-side of the MPP is evaluated in this case study and the results are
presented in Fig. 9. Two test cases are demonstrated with pref = 2 kW and pref = 1 kW. Before t= 10 s,
the irradiance is constant and the available power pavai is 1 kW. A rapid increase of irradiance occurs between
t= 10 s and t= 25 s, in which pav ail increases from 1 kW to the nominal maximum power of the PV panels,
i.e., 3 kW. The output power of the PV system during the FPPT operation with the implemented voltage-step
calculation algorithms under pref = 2 kW is illustrated in Fig. 9(a). In the results, ppv -m1is the PV power with
method 1, while ppv-m2is the power related to method 2 and ppv-m3is related to method 3, which is the proposed
adaptive FPPT algorithm. The PV voltages related to these algorithms are shown in Fig. 9(b). A rapid decrement
of the irradiance occurs between t= 65 s and t= 80 s, which reduces pavail to 1 kW. The dynamic performance
of method 2 is faster than method 1, while the proposed adaptive FPPT algorithm (method 3) is the best among the
three in terms of fast dynamics. The tracking error of the proposed algorithm is also smaller than other algorithms
(T.E.-m3 = 18.2%), as shown in Fig. 9.

16
(a)
(b)
(c)
T.E.-m1 = 4.7%
T.E.-m2 = 4.2%
T.E.-m3 = 3.3%
Time (s)
(d)
T.E.-m1 = 23.4%
T.E.-m2 = 20.7%
T.E.-m3 = 18.2%
pref
pref
l
l
Fig. 9. Experimental results of Case I, i.e., FPPT operation with the movement of the operation point to the right-side of the MPP: (a) PV
power with pref = 2 kW, (b) PV voltage with pref = 2 kW, (c) PV power with pref = 1 kW, and (d) PV voltage with pref = 1 kW.
The performance of the proposed algorithm operation with pref = 1 kW, under similar environmental conditions,
is illustrated in Figs. 9(c) and (d). The proposed adaptive FPPT algorithm is able to regulate the PV power to its
reference value under such rapid environmental changes. Notice that the tracking errors in this test condition are
larger, compared to the test condition with pref = 2 kW, because of the smaller power reference in this test
condition. Furthermore, the settling time of the proposed algorithm is shorter compared to the other two algorithms.

17
(a)
(b)
(c)
T.E.-m1 = 20.3%
T.E.-m2 = 12.5%
T.E.-m3 = 6.4%
Time (s)
(d)
T.E.-m2 = 24.8%
T.E.-m3 = 14.4%
T.E.-m1 = 45.8%
pref
pref
l
l
Fig. 10. Experimental results of Case II, i.e., FPPT operation with the movement of the operation point to the left-side of the MPP: (a) PV
power with pref = 2 kW, (b) PV voltage with pref = 2 kW, (c) PV power with pref = 1 kW, and (d) PV voltage with pref = 1 kW.
Case II: The performance of the proposed FPPT algorithm for the movement of the operation point to the
left-side of the MPP is investigated under similar test conditions as Case I and the results are illustrated in Fig. 10.
The FPPT operation in the left-side of the MPP requires larger voltage adjustment under environmental changes.
Therefore, the FPPT algorithm with a fixed voltage-step (method 1) is not able to regulate the power to its reference
value under such rapid environmental changes, as depicted in Fig. 10(a) and (c). Notice that larger voltage-step
values are calculated with the proposed adaptive voltage-step algorithm in Fig. 10(b) and (d), which result in a

18
(a)
(b)
Time (s)
T.E.-m1 = 15.2%
T.E.-m2 = 14.3%
T.E.-m3 = 8.9%
pref
Step 1
Step 2
Step 3
Fig. 11. Experimental results of Case III, i.e., FPPT operation with the movement of the voltage reference to the right-side of the MPP under
changes of the constant power reference: (a) PV power, and (b) PV voltage.
fast dynamic response. Furthermore, the smaller voltage-step value in steady-state reduces the power oscillations,
as observed in Fig. 10(a) and (c). The tracking error of the proposed adaptive FPPT algorithm for pref = 1 kW
is 14.4%, which is significantly reduced compared to the tracking error for the algorithm with a fixed voltage-step
(T.E.-m1 = 45.8%). It is noted that method 1 is not able to regulate the PV power to its reference during this
period, while method 2 shows a longer settling time compared to the proposed algorithm in method 3.
Case III: The performance of the proposed FPPT algorithm under changes of the constant power reference
when moving the operation point to the right-side of the MPP is investigated in this case study and the results are
presented in Fig. 11. In these tests, the irradiance is equal to Irr = 1000 W/m2. Before t= 40 s, the central
controller imposes the MPPT operation to the GCPVPP. Consequently, the proposed algorithm regulates the PV
voltage to the MPP voltage, by applying a power reference, which is greater than the nominal maximum power of
the PV system (i.e., pref = 3.5 kW), as shown in Fig. 5(b).
At t= 40 s, the FPPT operation with pref = 2.2 kW is imposed by the external controller. The power reference
is reduced to 1.5 kW at t= 60 s, while it has a step decrease to 0.5 kW at t= 80 s. Finally, there is a step
increase in the power reference to 1.5 kW at t= 100 s. The PV power with the implementation of the mentioned
three methods of FPPT operation is illustrated in Fig. 11(a). The proposed adaptive FPPT algorithm (method 3)
shows a faster dynamic response compared to the other two conventional FPPT algorithms with smaller tracking
errors. The PV voltage under such conditions is depicted in Fig. 11(b), in which it can be seen that the calculated
voltage-step in steady-state with the proposed adaptive voltage-step is smaller than other algorithms.

19
(a)
(b)
Time (s)
T.E.-m1 = 30.5%
T.E.-m2 = 10.8%
T.E.-m3 = 7.9%
pref
Step 1
Step 2
Step 3
Fig. 12. Experimental results of Case IV, i.e., FPPT operation with the movement of the voltage reference to the left-side of the MPP under
changes of the constant power reference: (a) PV power, and (b) PV voltage.
TABLE II
COM PARI SO N OF E XP ER IM EN TAL R ES ULTS B AS ED O N TH E TR ACK IN G ER RO R.
Test Condition method 1 method 2 method 3
Case I pref = 2 kW 4.7% 4.2% 3.3%
pref = 1 kW 23.4% 20.7% 18.2%
Case II pref = 2 kW 20.3% 12.5% 6.4%
pref = 1 kW 45.8% 24.8% 14.4%
Case III 15.2% 14.3% 8.9%
Case IV 30.5% 10.8% 7.9%
Case IV: The performance of the proposed adaptive FPPT algorithm with the movement of the operation
point to the left-side of the MPP under power reference changes, similar to Case III, is studied and the results are
illustrated in Fig. 12. It can be seen that the proposed adaptive FPPT algorithm is able to regulate the PV power
to the required power reference under all operating conditions. In contrast, the other two algorithms either cannot
achieve an accurate constant power generation or will have slow dynamics, as shown in Fig. 12.
Numerical comparisons of experimental results for the tracking error and settling-time are provided in Tables II
and III. The tracking error of the proposed FPPT algorithm with an adaptive voltage-step is smaller compared to
the obtained tracking error from the other two algorithms. Additionally, the settling time of the proposed algorithm
is shorter in all of the test conditions, which proves the effectiveness of the proposed FPPT algorithm. That is, it

20
TABLE III
COM PARI SO N OF E XP ER IM EN TAL R ES ULTS B AS ED O N TH E SE TT LI NG T IM E.
Test Condition method 1 method 2 method 3
Case III
Step 1 8.6s4.9s2.6s
Step 2 3.2s3.1s1.2s
Step 3 8.8s6.1s2.7s
Case IV
Step 1 N.A. 11.1s9.0s
Step 2 N.A. 11.2s10.7s
Step 3 N.A. 16.2s10.5s
can achieve fast, accurate, and flexible active power tracking of grid-connected PV systems.
V. CONCLUSION
An adaptive flexible power point tracking (FPPT) algorithm for calculating the voltage reference of PV panels,
which regulates the output power to a certain power reference, has been introduced in this paper. The main target
of the proposed algorithm is to tackle the power system challenges (i.e., overvoltage), which may occur due to the
increasing growth of the installation of GCPVPPs. Fast dynamics under rapid environmental changes were obtained
by adaptively calculating the voltage-step based on the instantaneous power error. The effect of the intentional voltage
reference change of the PV string on the PV power was differentiated from the effect of environmental changes
by adding an extra measurement sampling in the controller. The calculation of the voltage-step according to the
operation point of the PV string reduces the power oscillation during steady-state. Also, it has been shown that if the
target power reference is larger than the maximum available power of the PV string, the proposed algorithm operates
at the maximum power point, with performance comparable to conventional MPPT algorithms. The flexibility of
the proposed adaptive FPPT algorithm has been demonstrated experimentally on a 3-kVA laboratory setup under
different conditions. The tracking error of the proposed algorithm has been reduced significantly in all experimental
tests, while the settling has also been decreased. The results demonstrated the applicability and effectiveness of the
proposed FPPT algorithm as an additional function for existing MPPT algorithms in GCPVPPs.
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