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An Adaptive Incremental Conductance MPPT Based
on BELBIC Controller in Photovoltaic Systems
Saeed Azimi, Behzad Mirzaeian dehkordi, Mehdi Niroomand
Department of electrical engineering, faculty of engineering
University of Isfahan, Isfahan, Iran
[email protected], [email protected], [email protected]
Abstract—Many conventional incremental conductance (INC)
methods are used for maximum power point tracking (MPPT) of
photovoltaic (PV) arrays. In these methods the step size
determines the speed of MPPT. Fast tracking can be achieved
with bigger increments but the system might not operate exactly
at the MPP and may oscillate about it instead; so there is a
tradeoff between the time needed to reach the MPP and the
oscillation error. The main purpose of this paper is to present an
adaptive step size in the INC to improve solar array
performance. Conventional proportional integral (PI) controller
is applied the MPP to the PV output voltage terminals; however,
in this paper brain emotional learning based intelligent controller
(BELBIC) is used as an adaptive step size in the INC. This
controller decrease the oscillation error, so there will be a
considerable increase in system accuracy. At the end, the
effectiveness of the proposed method is verified by simulation
results at different operating conditions and comparing them
with simulation results of conventional method.
MPPT focuses on new and more flexible ways for duty ratio
step size changing. In this paper, a new approach of
incremental conductance (INC) algorithm which makes use of
a variable step of desirable voltage change is presented by
based on adaptive method. This algorithm is applied on a
DC/DC boost converter and the subsequently found MPP by
controlling the duty cycle of the boost converter. The whole
system is simulated using PSIM and simulation results verified
the proposed method.
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Keywords—Maximum power point tracking (MPPT),
Incremental conductance (INC), Adaptive incremental conductance
(AINC), Brain emotional learning based intelligent controller
(BELBIC)
I.
II.
Fig. 1 is shown a single diode model of solar cell equivalent
circuit. In this model, open-circuit voltage and short-circuit
current are the key parameters. The short-circuit current
depends on illumination, while the open-circuit voltage is
affected by the material and temperature. In this model, VT is
the temperature voltage expressed as VT=kT/q, which is 25mV
at 25°C. The ideality factor (α) generally varies between 1 and
5 for this model. The equations defining this model are as
bellow [11]:
INTRODUCTION
Solar energy is one of the most important renewable energy
sources that have been gaining increased attention in recent
years. Solar energy is plentiful; it has the greatest availability
compared to other energy sources. The amount of energy
supplied to the earth in one day by the sun is sufficient to
power the total energy needs of the earth for one year [1]
nowadays research on solar power generates great interest in
achieving the only aim to get the maximum energy that PV can
provide. The power generated from a given PV module mainly
depends on solar irradiance and temperature. For optimal
operation of a PV module, its terminal voltage must be equal to
the corresponding MPP value. To achieve these goals, various
conventional MPP tracking (MPPT) algorithms [2],[3] such as
incremental conductance [4], perturbation and observation
(P&O) [5],[6], hill climbing, parasitic capacitance [7], constant
voltage [8] and current algorithm [9],[10] are presented.
Although its complexity, most usual MPPT algorithm is
Incremental Conductance due to several advantages that
presents in comparison with others have been proposed and
used to extract maximum power from PV arrays under
different operating conditions. Current research in the field of
PV MODELS AND EQUIVALENT CIRCUITS
⎡ V PV
⎤
I D = I 0 ⎢⎢e αVT − 1⎥⎥
⎢⎣
⎥⎦
(1)
I PV = I SC − I D
(2)
⎡ I − I PV
⎤
VPV = αVT ln ⎢ SC
+ 1⎥
I
0
⎣
⎦
(3)
I PV = I PH − I D,
⎡ ⎛ q(V + Rs I PV ) ⎞ ⎤ VPV + Rs I PV
= I PH − I 0 ⎢exp⎜
⎟ − 1⎥ −
αkT
RP
⎠ ⎦
⎣ ⎝
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(4)
Figure 1.
Single-diode model of solar cell equivalent circuit
Where IPH is photocurrent (A), ID is diode current (A), RS is
series resistance, and RP is parallel resistance.
III.
INCREMENTAL CONDUCTANCE BASED MPPT
TECHNIQUE
The incremental conductance technique is the most
Commonly used MPPT for PV systems [11]-[13]. The
technique is based on the fact that the sum of the instantaneous
conductance I/V and the incremental conductance ΔI/ΔV is zero
at the MPP, negative on the right side of the MPP, and positive
on the left side of the MPP. Fig. 2 shows the flowchart
algorithm of the incremental conductance technique. If the
change in current and change in voltage is zero at the same
time, no increment or decrement is required for the reference
voltage. If there is no change in voltage while the current
change is positive, the reference voltage should be increased.
Similarly, if there is no change in voltage while the current
change is negative, the reference voltage should be decreased.
If the voltage change is zero while ΔI/ΔV = -I/V, the PV is
operating at MPP. If ΔI/ΔV ≠ -I/V and ΔI/ΔV > -I/V, the
reference voltage should be decreased. However, if ΔI/ΔV ≠ I/V and ΔI/ΔV < -I/V, the reference voltage should be increased
in order to track the MPP. Based on this algorithm, the
operating point is either located in the BC interval or
oscillating among the AB and CD intervals, as it is shown in
Fig. 3. Selecting the step size (ΔVref), is a trade-off between
accurate steady tracking and dynamic response.
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If larger step sizes are used for quicker dynamic responses,
the tracking accuracy decreases and the tracking point
oscillates around the MPP. On the other hand, when small step
sizes are selected, the tracking accuracy will increase. In the
meantime, the time duration required to reach the MPP will be
increased [14].
IV.
BRAIN EMOTIONAL LEARNING BASED INTELLIGENT
CONTROLLER (BELBIC)
BELBIC is abbreviation of brain emotional learning based
intelligent controller. In addition to simpleness, BELBIC is
an adaptive controller with good performance [15]-[17].
Fig. 4 illustrates the structure of the BELBIC and each part
of the system is described briefly [18].
Thalamus: This part is simulation of real thalamus in this
part does some simple initial- processing on sensory brain
input signals.
Figure 2.
Figure 3.
Incremental conductance algorithm flow-chart diagram
Operating point trajectory of INC–based MPPT
Sensory Cortex: The output signals of thalamus enter
sensory cortex. This part is responsible for the subdivision and
discrimination of the coarse output from thalamus.
Orbitofrontal Cortex: The Orbitofrontal Cortex is
supposed to ban inappropriate responses from the Amygdala,
based on the context given by the hippocampus.
Amygdala: The Amygdala is a small structure in the
medial temporal lobe of brain which is thought to be
responsible for the emotional evaluation of stimuli.
BELBIC consist of two main parts, briefly corresponding to
the amygdala and the orbitofrontal cortex (OFC), respectively.
The amygdaloid part receives signals from the thalamus and
cortical areas, while the orbital part receives signals only from
the cortical areas and the amygdale. Reinforcing signal is also
received. As it is shown in Fig. 4, BELBIC receives sensory
input signals via Thalamus.
After initial-processing in Thalamus, processed input signal
will be sent to Amygdala and Sensory Cortex. Amygdala and
Orbitofrontal process their inputs based on Emotional Signal
received from environment.
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Figure 5.
Control system configuration using BELBIC
The connection weights Vi are set proportionally to the
difference between the reinforce (REW) and the accumulation
of the A nodes. The αa term is a constant used to adjust the
learning speed and settable parameter between 0 (no learning)
and 1 (instant adaptation).
Δvi = α a .si . max(0, REW − ∑ Ai )
This is an instance of a simple associative learning system.
The real difference between this system and similar associative
learning systems is the fact that this weight adjusting rule is
monotonic, i.e., the weights V cannot be decreased. The
Orbitofrontal learning rule is very similar to the Amygdala
rule. The only difference is that the Orbitofrontal connection
weight can be increased and decreased as needed to track the
required inhibiting of Amygdala. It also adapts its output
according to the sensory data S and the reinforce (REW).
Likewise, the learning rule in OFC is calculated as the
difference between E' and the reinforcing signal:
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Figure 4.
Structure of BELBIC [18]
Final output is subtraction of Amygdala and Orbitofrontal
Cortex outputs. In the following section, functionality of these
parts and the learning algorithm is discussed based [18].
There is one A node for every stimulus S to amygdala plus
one additional node from thalamic stimulus. There is one single
node for all outputs of the model, called E. This node simply
sums the outputs from the A nodes, and then subtracts the
inhibitory outputs from the O nodes, where O is OFC node for
each of the stimuli:
E = ∑ Ai − ∑ Oi
(including A th )
(5)
Furthermore, E' node sums the outputs from A except
Ath and then subtracts it from inhibitory outputs of the O
nodes:
(9)
E ′ = ∑ Ai − ∑ Oi
Δwi = α o .si .(E ′ − REW )
(10)
where Wi is the weight of OFC connection and αo is OFC
learning rate constant. It is seen that the OFC learning rule is
very similar to the Amygdaloid rule. The only difference in
Amygdaloid and OFC learning is that the OFC connection
weight can both increase and decrease as required tracking the
desired inhibition.
The OFC nodes values are then calculated as follows:
(not including A th )
(6)
The thalamic connection is calculated as the maximum over
all stimuli S and becomes another input to the amygdaloid part:
Ath = max (si )
(7)
Unlike other inputs to the Amygdala the thalamic input is
not projected into the Orbitofrontal part and cannot be banned.
For each A node, there is a plastic connection weight V. Each
input is multiplied by this weight to make the output of the
node.
Ai = S iVi
(8)
Oi = S iWi
(11)
Note that this system works at two levels: the Amygdaloid
part learns to predict and react to a given reinforce. So, the
OFC output is adjusted to minimize the discrepancy of the
amygdala output and the reinforce, which was exactly desired.
The emotional learning mechanism in mammalians is an
open-loop learning system. This means the living creature
receives stimuli from environment and reacts respectively.
Effectiveness of this reaction is being evaluated in the
reinforcement signal and helps the creature to reproduce better
responses. To use this algorithm for decision making and
control applications a closed-loop scheme must be introduced,
a schematic diagram of closed-loop decision making
mechanism is suggested in Fig. 5.
As it is illustrated in (12), (13) sensory input and reward
signal, generally can be arbitrary function of the reference
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output yr, controller output, u and error signal e, and the
designer must find a proper function for the controller.
Inputs to emotional learning mechanism are a set of sensory
input signals as well as a reinforcing signal. These signals
generally can be arbitrary selected by the designer of the
control algorithm. It is recommended that the reinforcing signal
REW is a function of other signals which can be supposed as a
cost function rationale, specifically award and punishment:
REW = J (si , e, y P )
(12)
where yp is the plant output and e is the error signal. Similarly
the sensory inputs must be a function of plant outputs and
controller outputs as follows:
S i = f (u , e, y P , y r )
(1)
VI.
SIMULATION RESULTS
Simulations were conducted with PSIM to verify the
validity of the purposed method. Table shows the
characteristics of the solar module. In the following, the worst
possible change of the irradiance level-that is a step change- is
observed.
A. Simulation of INC with PI controller
First, the performance of conventional method is illustrated.
Fig. 6 and Fig. 7 show the performance of INC in tracking the
new MPP when there is a rapid change in irradiance level
between 500W/m2 and 1000W/m2. Fig. 6 shows the
performance with a constant Vstep=0.0005 and Fig. 7 shows the
performance with a constant Vstep=0.0001. According to Fig. 6
and Fig. 7, shorter Vstep leads to less oscillation around the MPP
but more needed time to reach the MPP. Longer Vstep result in
less time needed reach the MPP, but more oscillation around
the MPP. In general, neither of these two steps can find the
exact MPP.
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where yr is the reference signal.
V.
Using a PI controller has a good performance [19], generally.
But the accuracy and the speed of adjusting could be improved
using BELBIC controller. BELBIC is an intelligent method, so
it exactly adjusts the VMPP -found by adaptive incremental
conductance- to the output terminals of photovoltaic system,
while, the PI controller cannot perform as accurate as the
BELBIC controller. PI lack of accuracy leads to less efficiency,
because the photovoltaic system is not at the optimized point.
Therefore, we miss some energy.
ADAPTIVE INCREMENTAL CONDUCTANCE (AINC)
BASED ON BELBIC CONTROLLER
A new adaptive method for maximum power point tracking
has been introduced. In the proposed method the Vstep changes
according to the error value or in other words, to the difference
between Vref and VMPP. The more error value leads to greater
step size. Thus, in every iterations the value of Vstep varies. In
the MPP neighborhood the step size is reduced adaptively in
order to avoid fluctuation around the MPP. At the MPP, we
have ΔI/ΔV = -I/V so the difference between ΔI/ΔV and -I/V
gives us the value of error. Using this criterion, the step size
should be changed adaptively based on the gradient descent
algorithm.
In this method (AINC) we have a variable Vstep instead of a
constant Vstep, which changes by a coefficient of error.
e = ΔI / ΔV + I / V
Vstep = η * e
(14)
(15)
Where the advantage of using this method is that if we are far
from the MPP, the amount of error is high, so according to (14)
the Vstep is high, too. As we get closer to the MPP, the amount
of error is reduced. So the Vstep will be shortened. Large steps at
the beginning of the process lead to less iteration needed to
reach the MPP neighborhood. Thus, this method is very faster
in the matter of tracking the MPP. In the MPP neighborhood,
the steps are becoming shorter. Therefore, approaching to the
MPP is done more accurately. The proposed algorithm reduces
the time needed to reach the MPP which leads to a boost in the
efficiency of the system. After finding VMPP, we should adjust
this voltage to the output terminals of the photovoltaic system
by changing the duty cycle of the switch in the boost converter.
B. Simulation of AINC with PI controller
Here, an adaptive Vstep is produced according to AINC
instead of a constant Vstep. Fig. 8 shows the performance of the
AINC in tracking the new MPP when there is a rapid change in
irradiance level between 500W/m2 and 1000W/m2. Fig. 8
shows that by applying the adaptive Vstep MPP tracking is
increased as well as the accuracy of tracking in comparison
with INC method. However, there is not the best accuracy in
adjusting the VMPP to the PV output voltage terminals, although
the adaptive method has a good performance in MPP tracking
and its accuracy in comparison to conventional PI controller.
C. Simulation of AINC with BELBIC controller
Here, BELBIC controller is applied for improving the
accuracy of adjustment. Fig. 9 shows the tracking of the MPP
TABLE I.
Number of cells
Ns
Standard light
intensity S0
Ref.
Temperature
Tref
Series resistance
Rs
Shunt resistance
Rsh
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CHARACTERISTICS OF THE SOLAR MODULE
36
Short circuit current
Isc0
3.8 A
1000
Saturation current Is0
2.16e-8 A
25°C
Band energy Eg
1.12 J
0.008 Ω
Identify factor α
1.2
1000 Ω
Temperature
coefficient Ct
0.0024
based on AINC method with BELBIC controller. It is obvious
that BELBIC controller improves the accuracy of adjustment in
comparison with PI controller. Table 2 shows the summary of
the comparison between these three methods (INC with
conventional PI controller, AINC with PI conventional
controller, AINC with BELBIC controller). This table
illustrates that the first method (INC with PI) by choosing
smaller Vstep, the accuracy is increased, while the speed is
decreased. Introducing adaptive Vstep led to a perfect accuracy,
while the speed remained reasonable. The last method (AINC
with BELBIC) resulted in ultimate accuracy with the same
speed. In the AINC method Vstep will not fix and varies as
shown in Error! Reference source not found. but in
conventional methods Vstep is constant, therefore the MPP
cannot be pursued. Variation of Vstep led to have a small Vstep
size near the MPP and result to more accuracy, also far from
MPP by large Vstep size allows to very fast tracking.
Fig. 10 shows the Variation of Vstep in AINC method when
a step change in irradiate is accured (t=0.2 sec). It is obvious
that, at the first Vstep increased to 0.4 in order to fast tracking the
MPP, Then, Vstep decrease to zero for more accuracy in tracking
and elimination the fluctuations around the MPP.
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I.
CONCLUSION
In this paper, different methods in tracking MPP of PV
systems and applying to the PV output voltage terminals are
presented. The drawbacks of INC method, especially in rapid
changes in atmospheric conditions, are the needed time to
reach the MPP and oscillation error.
Figure 7.
PV Power output in INC with constant Vstep=1e-4 ; A)
Magnified figure
The adaptive INC method is introduced in purpose of
increasing the accuracy.
Figure 8.
Figure 6.
PV Power output in INC with constant Vstep=5e-4 ; A)
Magnified figure
PV Power output in AINC with PI controller; A) Magnified
figure
To apply the VMPP to the PV output voltage terminals,
conventional PI controller is applied conventionally; however,
in this paper the BELBIC controller is used instead. This led to
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a more accurate adjustment, which resulted in more efficiency
of the whole system.
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[8]
[9]
[10]
Figure 9.
PV Power output in AINC with BELBIC controller; A)
Magnified figure
[11]
[12]
[13]
[14]
[15]
[16]
Figure 10.
Variation of Vstep in AINC method
[17]
[18]
TABLE II.
SUMMARY OF THE COMPARISON BETWEEN THESE 3 METHODS
Methode
INC with PI Vstep=5e-4
INC wiyh PI Vstep=1e-4
AINC With PI
AINC With BELBIC
Time needed to
reach the MPP
6 msec
18 msec
6 msec
6.7 msec
ΔP/P
0.14
0.013
3.4e-3
2e-6
[19]
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