The 9th Iranian Conference on Renewable Energy & Distributed Generation - ICREDG2022 23&24 February, 2022, Mashhad, Iran.
Closed-Loop MPPT Control in PV System Based on Step-Up Interleaved DC-DC Converter
Hamed Javaheri Fard 1, Seyed Mohammad Sadeghzadeh 2
1 Shahed University, Faculty of Engineering, Tehran; [email protected]
2 Shahed University, Faculty of Engineering, Tehran; [email protected] Abstract
In this paper, using the proposed converter modeling and presenting a proposed control scheme, the maximum power point tracking (MPPT) is developed to lead to its optimization. The photovoltaic energy conversion system generates energy with the help of a step-up interleaved DC-DC converter. In photovoltaic systems, controllers are commonly used to manage the power injected into the grid or load. MPPT is one of the features that some of these controllers are equipped to it and increase power efficiency by up to 30% compared to conventional controllers. In fact, the main purpose of this study is to improve the incremental conductance (InC) algorithm by the state-space averaged model and PI controller. The signals generated in the closed-loop control scheme, including input and output currents and voltages, are accurate and have very low ripples.
Experimental results were analyzed using Arduino Due and the effective performance of the proposed control scheme was verified on the proposed DC-DC converter.
Keywords: Step-up DC-DC converter, MPPT, InC, Interleaved
Introduction
Renewable energy sources have become one of the most important components of electricity generation in today's world industry. They are more attractive to researchers and designers in this field due to the harmful effects of greenhouse gases and fossil fuels such as environmental pollution [1-2].
Despite the advantages of renewable energy conversion systems such as fuel cells (FC) and photovoltaic (PV) power plants, their major drawback is the very low output voltage level [3-5]. Therefore, according to this issue, it is necessary to use an interface that transmits energy to the load stage or grid by increasing the voltage level and desired power density.
This link will be provided by a DC-DC boost converter.
Therefore, it is clear that power electronic equipment plays an important role in renewable energy conversion systems, and such equipment with the above applications is used in many industries [6].
In general, conventional DC-DC converters cannot meet the demand for increased voltage gain. The reason for this is that although they are simple in structure and easy to implement, due to the additional duty cycle, power losses will naturally increase and the converter efficiency will decrease as a result. In this regard, step- up DC-DC converters are one of the most important elements of PV power plants because the acquisition of a high voltage conversion ratio is absolutely required in them [7-9].
Thanks to the evolution of voltage boosting techniques and their integration together in boost-based converters with the aim of increasing the output voltage, Step-up DC-DC converters were developed. There are well-known voltage boosting techniques in various studies, each of which has its own advantages and disadvantages. The techniques of switched-capacitor cells, voltage multiplier modules, coupled inductors, interleaved, quasi-impedance and etc., all in the design of proposed structures can be mentioned as voltage gain enhancement solutions. The above techniques are described in more detail in [10]. At present, the combination of these techniques and the production of novel structures has become more attractive. For example, in [11], a proposed structure is introduced that uses the integration of coupled inductors and voltage multiplier modules. The output voltage increased dramatically in the proposed topology, instead, the input current ripple is extremely high. The solution is to use the interleaved structure.
Another problem of PVs is the extraction of the power point, which changes with variations in radiation, and it is necessary to track and obtain its maximum point with control algorithms such as perturbation and observation (P&O) and InC. Other techniques for MPPT are mentioned in [12]. For a PV module, MPPT tracks the voltage and current to achieve maximum power and thus absorb it. The MPPT algorithm adjusts the voltage for the optimal charge. The role of the DC-DC converter is to isolate the DC input from the DC output in such a way that maximum power is extracted. MPPT control is usually implemented with a microprocessor. The output current of a PV module changes directly with the amount of radiation. Conventional MPPT techniques come with drawbacks that can be improved by a combination of advanced linear or non-linear control methods applied to DC-DC converter power switches. For example, in [13], the InC algorithm is used with the variable step-size method. This algorithm alone has disadvantages such as fluctuations in the steady-state and low speed of dynamic response. In [14], the above shortcomings have been fixed with the improved InC algorithm by the adaptive Kalman filter. In general, using InC has the following disadvantages: 1) due to the constant search of the operating point by this algorithm, there will be a slight power fluctuation at the MPP of the PV cell. 2) If partial shading is present, this algorithm may not be able to detect the desired peak.
Considering the conditions stated about the InC algorithm and covering its weaknesses, this paper uses the state-space averaged model and PI controller for more precise control in order to improve InC algorithm and the control performance of the PV system.
Figure 1. Schematic of the proposed converter power circuit.
Proposed converter performance
The schematic of the proposed converter power circuit is shown in Figure 1. The converter is designed based on a combination of voltage boosting techniques of coupled inductors in the form of three windings and a voltage multiplier cell (VMC) [15]. Therefore, the use of this topology for applications of high power and high output voltage, including renewable energy sources such as PV is appropriate and effective. The converter has two MOSFET power switches (S1 and S2). Winding cross- coupled inductors can be modeled with leakage and magnetizing inductances (Lk, Lm) to facilitate steady-state analysis. Secondary and tertiary windings are applied to the circuit design as voltage extenders, and the primary windings are parallel in two phases. The structure of the interleaved is used to reduce the input current ripple, and thus the topology of the circuit is symmetric. In the power circuit, there are three electrolyte capacitors in the output stage in series, which include Co1, Co2, and Co3. The VMC is also a combination of diodes D3 - D6 and capacitors C1 - C4 embedded in the topology. The turns ratio of coupled inductors is similar and is defined as follows,
1 1 2 2
1 1 2 2
s t s t
p p p p
n n n n
N n n n n
(1) Closed-loop control procedureFigure 2 illustrates the proposed closed-loop MPPT control block diagram related to the proposed converter connections with PV. Compared to Figure 1, it is obvious that the input voltage source in the converter topology is equal to the voltage of the PV module, i.e. Vi
= Vp. The input current of the converter topology is the same as the current of the PV module, i.e. Ii =IL= Ip. The MPPT algorithm is based on InC method. PV current and voltage signals by sensors form the input of the MPPT.
The output of the MPPT is a reference voltage signal whose function is to regulate the duty cycle. This moves the operation point of the P-V curve in the PV module. A Type-2 PI controller is used to supply the reference voltage. By K-factor method and by determining the phase margin (PM=67°) and crossover frequency (fc=1 kHz), PI controller coefficients are found as follows:
a1 = 990, a2 = 1195, a3 = 32321
In this paper, in order to analyze more precisely the proposed control scheme, the dynamic performance of the converter is also expressed by the state-space averaged model. Finally, with the help of the resulting state equations, a transfer function (G) is found that shows the dynamic nature of the proposed converter.
For small-signal modeling and obtaining state equations, a series of conditions are considered to facilitate the analysis process as follows: 1) in the power circuit, anything semiconductor, including switches and diodes, is considered ideal. 2) The equivalent of voltage multiplier capacitors on the first stage is C1 and on the second stage is C2. 3) Capacitors of Co1 to Co3 as well as coupled inductors are ideal, i.e. their equivalent series resistance (ESR) is zero. 4) The ESR of two capacitors for voltage multiplier stages is called r. 5) Converter is analyzed in steady-state. 6) Leakage inductance and non- continuous current conditions of inductors are not considered. 7) Operation modes that have small time intervals in a period are not considered.
According to the stated conditions, the state space equations of the proposed converterare written as (2)-(4) based on the equivalent circuits of three operation modes for when S1 and S2 are in the form of [ON ON, ON OFF, OFF ON]. Equivalent circuits are also shown in Figure 3a-3b. It is worth noting that due to the symmetric performance of the converter, the equivalent circuit is not shown for the mode where the first switch is OFF and the second switch is ON and only the state equations for this mode are written.
Figure 2. Block diagram of proposed control scheme.
Figure 3. Equivalent circuits for dynamic analysis of the proposed converter.
1 2
1 2
1 2
1 1 2 3
1 1 1
2 1 2 3
2 2 2
3 1 2 3
3 3 3
,
0, 0
( )
( )
( )
p p
Lm Lm
m m
C C
Co Co Co Co
L o L o L o
Co Co Co Co
L o L o L o
Co Co Co Co
L o L o L o
V V
di di
dt L dt L
dv dv
dt dt
dv v v v
dt R C R C R C
dv v v v
dt R C R C R C
dv v v v
dt R C R C R C
(2)
(3)
1 2 1
1 2 2
1 1 1
1 1
2 2 1 3
2 2 2
2
1 2 1 2 1
1 1 1 1
2 3
1 1
,
2 2
2 5 1
( )
2
( 1 )
2
p p
Lm Lm Co
m m m
C C Co
C C Co Co
Co Lm C C Co
o o o L o
Co Co
L o L o
V V
di di v
dt L dt L L
dv v Nv
dt rC rC
dv v Nv v
dt rC rC rC
dv i Nv Nv N v
dt C rC rC r R C
v N v
R C r R C
2 1 2 3
2 2 2
3 2 1 2
3 3 3
3 3
( )
( 1 )
2
1 1
( )
2
Co Co Co Co
L o L o L o
Co C Co Co
o L o L o
Co
L o
dv v v v
dt R C R C R C
dv v N v v
dt rC r R C R C
v r R C
(4)
1 1 2
1 1 2
1 1 1 3
1 1 1
2 2 1
2 2
2 1 1 3
2 3 3
2 2
3 1 2 3
3 3 3
,
2 2
( 1 )
2
1 1
( )
2
( )
p p
Lm Co Lm
m m m
C C Co Co
C C Co
Co C Co Co
o L o L o
Co
L o
Co Co Co Co
L o L o L o
V V
di v di
dt L L dt L
dv v Nv v
dt rC rC rC
dv v Nv
dt rC rC
dv v N v v
dt rC r R C R C
v r R C
dv v v v
dt R C R C R C
1 2
1 1
0 0 0 0 0
T
m m
B L L
(6)Figure 4. Flowchart of MPPT control based on InC algorithm.
(5)
0 0 0 0 1 1 1
C
(7)1
2
1 1 1
2 2 2
2
1 1 1 1 1 1 1 1 1 1
2 2
0 0 1 0 0 0 0
0 0 1 0 0 0 0
2( 1) (1 ) 1
0 0 0 0
2 2
2( 1) (1 ) 1
0 0 0 0
2 2
1 1 (1 ) (1 ) 5 ( 1) 1 (1 ) 1 (1 ) 1
2 2
1 (1 ) 1
0 0 0
2
m
m
L L L
o o o o o o o o o o
o o L o
d L d L
d N d d
rC rC rC
d N d d
A rC rC rC
d d N d N d N d N d N d
C C rC rC rC R C rC R C rC R C
d N d
rC rC R C
2 2 2 2
3 3 3 2 2 2
1 1 1
2
1 (1 ) 1 1 1 1
0 0 0
2 2
L o o L o
L L L
o o o o o o
d
R C rC R C
d N d d
rC rC R C rC R C R C
(11)
1 1 1 2
1 1 2
1 1 1
2 1 3
2 2 2
2
1 2 1 2 3
1 1 1 1 1
1 1 2
2 2 2
2 1 3
3 3 3
2
2 2
2
2 2
5
2 2
2 2
2 2
Co m Co m
C Co Co
C Co Co
C C Co Co Co
o o o o o
C Co Co
o o o
C Co Co
o o o
v L v L
v Nv Nv
rC rC rC
v Nv Nv
D rC rC rC
Nv Nv N v Nv Nv
rC rC rC rC rC
v Nv v
rC rC rC
v Nv v
rC rC rC
Then, the matrix form of the state-space equations in (2)-(4) is obtained according to (5)-(7). In the state-space averaged model, in order to find the transmission function, by adding perturbations to the state variables defined by (8), finally, the small-signal model of the converter is obtained according to (9). In this case, the new matrices are defined according to (10)-(11) and according to the duty ratio coefficients in the operation modes which are (d-1/2), (1-d), and (1-d), respectively.
In this way, after performing the stated mathematical operation, the transfer function is described as (12).
(10)
(8)
1 1 1 2 2 2
1 1 1 2 2 2
1 1 1 2 2 2
3 3 3
ˆ , ˆ , ˆ
ˆ , ˆ
ˆ , ˆ
ˆ , ˆ
Lm Lm Lm Lm Lm Lm
C C C C C C
Co Co Co Co Co Co
Co Co Co o o o
d D d i I i i I i
v V v v V v
v V v v V v
v V v v V v
ˆ ˆ ˆ
ˆ ˆ
x A x Dd y Cx
(9)( ) ( )
1G S C SI A
D
(12) Where, I is identity matrix.InC Algorithm is shown in Figure 4. This algorithm determines the change in voltage to achieve MPP by comparing the increase in power to the increase in voltage between two consecutive samples. InC algorithm causes fewer fluctuations than other algorithms and by optimizing it in this study, its effect has increased. The purpose of the InC algorithm is to overcome the limitations of alpha. It is also more complex than P&O.
InC has the ability to specify the relative distance to reach the MPP, therefore when the MPP is reached is determined. Most of the techniques whose main pillar is the InC algorithm are based on fixed-size iteration steps.
High accuracy and ideal speed in tracking play an important role in step size. These two factors have the opposite effect on step size. It should be noted that if the step size is reduced to increase accuracy, the convergence speed of the algorithm is lost. To solve this problem, the InC algorithm with variable step size must be used.
1
2
1 1 1
2 2 2
2
1 1 1 1 1 1 1 1 1 1
2 2
0 0 1 0 0 0 0
0 0 1 0 0 0 0
2( 1) (1 ) 1
0 0 0 0
2 2
2( 1) (1 ) 1
0 0 0 0
2 2
1 1 (1 ) (1 ) 5 ( 1) 1 (1 ) 1 (1 ) 1
2 2
1 (1 ) 1
0 0 0
2
m
m
L L L
o o o o o o o o o o
o o L
D L D L
D N D D
rC rC rC
D N D D
A rC rC rC
D D N D N D N D N D N D
C C rC rC rC R C rC R C rC R C
D N D
rC rC R C
2 2 2 2
3 3 3 2 2 2
1 1 1
2
1 (1 ) 1 1 1 1
0 0 0
2 2
L L
o o o o
L L L
o o o o o o
D
R C rC R C
D N D D
rC rC R C rC R C R C
Real-time validation
After analyzing the performance of the converter and the proposed control scheme applied to it, laboratory tests were performed to validate the effectiveness of a 400 W prototype. The experimental results of the tests are shown in Figures 5 and 6. The pulses of the power switches at the gate are obtained by programming an Arduino Due based on the Atmel SAM3X8E ARM Cortex-M3 CPU microcontroller board, which consists of a 32-bit core. NCV33152 MOSFET driver, which is used in DC-DC converter applications, is used here to boost the start-up signal of the gates. The HANTEK oscilloscope DSO4202C model with two digital channels with a frequency of 70 MHz and high voltage and current probes (T3100 & HT8100) has been used to obtain voltage and current waveforms.
Due to the limitations of the PV module, such as the lack of space in the laboratory, an emulator, which is Agilent E4360A here, can be used as a power source.
MOSFETs are with the number IPA075N15N3. Diodes are also with numbers of MUR1560 and MUR1540, which have ultrafast 35 and 60 nanosecond recovery times. Figures 5a and 5b show the current and voltage of the PV system as well as the current and voltage of the load, respectively. In order to confirm the effectiveness of the proposed control scheme, the voltage and current of the PV system and the voltage and current of the load in the state without the proposed controller and only with a simple InC algorithm have been tested, which are illustrated in Figures 6a and 6b. This comparison shows that the system provides more accurate results with less current ripple and fewer fluctuations by applying the proposed controller.
Figure 5. Current and voltage with the proposed control scheme. (a) PV system voltage and current (b) Load voltage and current
Figure 6. Current and voltage without the proposed control scheme. (a) PV system voltage and current (b) Load voltage and current
Conclusions
This paper presents a closed-loop control scheme to improve MPPT performance. This controller is designed and proposed to cover the shortcomings of the InC algorithm such as increased fluctuations and current ripple, slow responses, poor convergence to achieve MPP, and low accuracy. For this purpose, in this study, the method of the state-space averaged model and Type- 2 PI controller has been used to improve the InC algorithm. In addition, a proposed converter is used to interface between the PV energy conversion system and the resistive load, and the device is fully integrated into the control design by the control signals generated and applied to the power switches. In order to validate and evaluate the effectiveness of the proposed control scheme on the proposed converter, the experimental results were tested in the laboratory on a 400 W prototype and analyzed. These results showed that compared to when the InC algorithm is applied without any improvement, it has high fluctuations and ripples.
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