Download Adaptive predictive error filter-based maximum power point tracking

Adaptive predictive error filter-based maximum power point tracking algorithm for a
photovoltaic system
Bidyadhar Subudhi1, Raseswari Pradhan2
1
Department of Electrical Engineering, National Institute of Technology, Rourkela, India
Department of Electrical Engineering, Veer Surendra Sai University of Technology, Sambalpur-769008
E-mail: [email protected]
2
Published in The Journal of Engineering; Received on 16th December 2015; Accepted on 2nd February 2016
Abstract: This study presents a new adaptive predictive error filter-based maximum power point tracker (MPPT) for a photovoltaic (PV)
system. This MPPT is developed using the concept of an adaptive predictive filter (APEF) that consists of a one-tap finite impulse response.
The filter step-size of the APEF is adapted using a recursive least-square (RLS) algorithm with an adaptive forgetting factor. The specialty of
this MPPT is that it performs MPP tracking operation in a single step. It performs two functions: namely, MPP estimation adjusting operating
point of a boost converter at MPP and then filtering of the PV voltage fluctuation after MPPT action. Thus, the proposed MPPT is compact and
efficient with less computational complexities than existing MPPTs such as perturb and observe (P&O) and incremental conductance. The
filter part of the proposed RLS-APEF-MPPT is a discrete PID-controller, where PD-part is tuned using pole-placement strategy and integral-term is fixed. The performances of the proposed RLS-APEF-MPPT were verified using experimentation on a prototype PV system.
Its performances were compared with that of P&O, adaptive-P&O-MPPTs. From the observed results, it is confirmed that the proposed
MPPT exhibits superior performance.
1
Introduction
In a photovoltaic (PV) system, maximum power point tracker
(MPPT) is employed to estimate MPP voltage. A number of
MPPT algorithms such as perturb and observe (P&O), incremental
conductance, P&O with adaptive perturb size etc. [1] are proposed
and implemented for PV applications. However, one measure
concern in using these MPPT algorithms is that the estimated
MPP fluctuates around the actual reference MPP voltage depending
on the perturbation size [2]. Therefore, the PV voltage vpv fluctuates
with higher magnitude which is adjusted to be equal to MPP voltage
using a DC/DC boost converter due to internal uncertainties of nonlinear boost converter or external disturbances in the power flow of
the PV system. The objective of this paper is to design a controller
that should tolerate these internal uncertainties or external disturbances such that the voltage fluctuation in vpv can be reduced in
view of obtaining a controller for harvesting maximum available
power in a PV system.
It is observed that PI and proportional integral and derivative (PID)controller are very popular controllers that are used in PV system
because of their simplicity in design and ease in implementation [3].
An adaptive controller can handle wider range of uncertainties in
the PV system and provides dynamic responses quickly by online
tuning of the controller parameters during variations in environmental
conditions. Adaptive PID-controllers that tune their parameters online
have been suggested in [4]. Adaptive auto-tuned PID-controllers use
system identification methods to identify the plant parameters and
then update the controller parameters using the estimated plant parameters [4, 5]. Design and operation of such controllers require accurate
estimation of plant parameters in a short period hence may be inappropriate to cope of with quick weather variations.
A filter reshapes the input signal according to some specific rules
to generate an output signal. An adaptive filter is a digital filter that
changes its characteristics (frequency response) automatically by
optimising its internal parameters. In a linear adaptive filter, the
adaptation algorithm follows the principle of superposition [6].
Adaptive linear finite impulse response filters are very popular
because they are easy to analyse and implement [7].
In case of PEF used in controlling a switching converter, future
control variable of the converter can be derived from the past and
J Eng 2016
doi: 10.1049/joe.2015.0195
present values of converter state variables (converter output
voltage, inductor current etc.) and control signal (u). In an adaptive
predictive filter controller (APEFC), the filter parameters are set in
such as a way that its output tries to minimise an objective function
involving the desired signal [8]. An APEFC is usually constructed
using one of the following adaptation approaches such as Weiner
filter theory or recursive least-square (RLS) theory. Weiner filter
theory is based on stochastic frame work as the optimum set of coefficient of the linear filter is obtained by minimisation of its mean
square error. APEFC with least-mean-square (LMS) algorithm is
based on this Weiner filter theory. LMS algorithm is always the
first choice in APEFC as it is easy to implement as its weight adaptation step-size is fixed [9]. Though LMS algorithm has simple
structure but its main disadvantage is its slow convergence in
case of large range of eigen value of the regressor covariance
matrix [10].
A number of modified LMS algorithms are available in the literature that can improve the performance of the original LMS algorithm by solving this slow convergence problem. They have
solved this slow convergence problem by varying the LMS
step-size with a step-size adaptation rule. Figs. 1a and b show
generalised view of modified LMS with adaptive step-size.
Different modified LMS algorithms have been proposed and
implemented in signal processing applications such as normalised
LMS [10], variable step-size LMS (VSLMS), correlation-based
VSLMS (CVSLMS), robust CVSLMS (RCVSLMS), gradient adaptive (GA)-step-size LMS and GA-limited SLMS (GA-LSLMS).
In [11], a comparison of VSLMS, CVSLMS, RCVSLMS and
GA-LSLMS has been made and it is observed that GA-LSLMS
is better than LMS algorithms in terms of low steady-state error
and good tracking performance in presence of noise terms.
Though these modified LMS algorithms are found to be better
than LMS algorithms in terms of faster convergence rate and low
steady-state error but become expensive owing to the cost of additional computational complexities [10].
Using RLS algorithm, the filter coefficients are determined recursively by minimising a weighted linear least-squares cost function
relating to the input signals. RLS algorithm is better than that of
all LMS-based algorithms with respect to its quick convergence
and less tracking error natures [12].
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Fig. 1 Generalised view of modified LMS with adaptive step-size
a Studied PV system
b Proposed RLS-APEFC-MPPT for MPP tracking
c Inverter control of the PV system
The PV system having RLS-APEFC designed without integral
component has slow control response. Since, this is very sensitive
to measurement error in PV system parameters such as panel
voltage, current, inductor current of boost converter etc. In this
case, the operating point of the PV system may not reach MPP
[13]. Furthermore, any plant having RLS-APEFC designed with
constant forgetting factor may experience slow convergence for
variable external and internal conditions [14].
Therefore, in this paper we proposed a new RLS-APEFC-MPPT
with variable forgetting factor for a PV system. This new MPPT has
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following merits: (i) can perform dual operations such as MPP
tracking and filtering of voltage fluctuation, (ii) fast response, (iii)
robust and stable operation, (iv) can handle wide range of MPP,
(v) less computational complexity and (vi) efficient with negligible
tracking error.
This paper is organised as follows. In Section 2, the design of the
proposed RLS-APEFC-MPPT is discussed. The results and discussion are provided in Section 3 and the concluding remarks are
included in Section 4.
2.2.2 Tuning of PID-parameters: Using the RLS adapted error
ê(k ) from (2) and actual error e(k) from (1) in a summer, it yields
prediction error ep(k) using (3). This ep(k) is then applied to tune
proportional derivative (PD)-parameter such as KP and KD of the
PID-controller using pole-placement law as follows (KI of the
PID-controller has been empirically chosen). The prediction error
ep(k) in z-domain can be written as
2 Description of the PV system with the proposed
RLS-APEFC-MPPT
Equation (4) can be rewritten as
The proposed RLS-APEFC-MPPT consists of an adaptive predictive error filter-based controller. This controller can suppress voltage
fluctuation better than that of a fixed step PID-controller. It can
reduce the effect of disturbances such as sudden temporary
change in input solar irradiance. It adapts its parameters such as
filter step-size, RLS forgetting factor etc. by predicting PV
system parameters such as panel voltage and current. Since this
RLS-APEFC-MPPT consists of a filter, it can perform dual operation such as MPP tracking and filtering of voltage fluctuation.
Hence, this MPPT can be applied directly to a PV system without
adding any additional controller or filter.
Ep ( z) = Ppv ( z) 1 + w1 z−1 + . . . + wN z−N
Ep ( z)
= 1 + w1 z−1 + . . . + wN z−N
Ppv (z)
UD ( z )
= 10 + 11 z−1
Ppv ( z)
2.2.1 Predictive MPPT error calculation: For MPPT operation,
the controller has to generate a control signal u(k) such that the
PV power is maximum available power for given environmental
condition. The proposed RLS-APEFC-MPPT operates according
to the PV power error signal e(k) which is calculated by comparing
current kth sampled PV power ppv(k) with that of one step back PV
power sample ppv(k − 1) as follows
D ppv (k )
e(k ) =
Dvpv (k )
(1)
where Δppv(k) = ppv(k) − ppv(k − 1) and Δvpv(k) = vpv(k) − vpv(k −
1). This RLS-APEF controller consists of a one-tap RLS linear predictor and a summer. The RLS linear predictor estimates the
required error value ê(k ). Here, ê(k ) is generated as follows
ê(k ) = v(k )e(k − 1)
(2)
where ω(k) is the tap-weight. ω(k) is updated cycle-by-cycle under
the influence of prediction error ep(k) and one step back error e(k−1)
as shown in Fig. 1b.
ep(k) is calculated using the summer as follows
ep (k ) = e(k ) + ê(k )
J Eng 2016
doi: 10.1049/joe.2015.0195
(3)
(6)
where ɛ0 and ɛ1 are the coefficients of the digital RLS-APEF. For
the boost converter, (5) should be written as follows
Ep ( z)
= 1 + w1 z−1
Ppv ( z)
2.2 Modelling and control of MPPT converter
The MPPT converter is a DC/DC boost converter. The gate pulse
for this MPPT converter is generated by a discrete pulse width
modulation (PWM) (DPWM) generator. The DPWM generator
generates gate pulse (u) by comparing output signal of the proposed
modified RLS-APEFC with a triangular signal. The gate pulse has
the duty-ratio δ (Fig. 1b). The proposed modified RLS-APEFC is a
discrete PID-controller. The integral-term is fixed and empirically
chosen referring [12–14]. Fig. 1c shows the inverter control system.
(5)
The order of this RLS-APEF is application dependent. According to
pole-placement law, the order of the RLS-APEF is one order lower
than that of the DC/DC boost converter used for MPPT operation.
Since, the order of the DC/DC boost converter is equal to 2, the
order of the RLS-PEF would be 1. Let, the RLS-APEF be represented as [8]
2.1 Model and control of PV system
The studied PV system is a stand-alone energy conversion as shown
in Fig. 1a. It consists of PV arrays with a DC/DC boost converter.
This converter is designed with an RLS-APEFC-MPPT. Fig. 1c
shows the inverter control system for PV system.
(4)
(7)
Let UD(z) be KA times of Ep(z), hence UD(z) can be written as
UD ( z) = KA Ep (z)
(8)
where KA is PD-controller as follows
KA = KP + KD z−1
(9)
Using values of UD(z) and EP(z) from (6) and (7), respectively, KA
can be calculated as
KA =
10 + 11 z−1
= 111 + 112 z−1
1 + w1 z−1
(10)
Therefore
KP = 111 ,
KD = 112
(11)
When weather changes, the generated PV power also varies. To
extract maximum PV power in the new condition, the values of
w1, ɛ0 and ɛ1 change. With these variations in w1, ɛ0, ɛ1 and KA
are updated using (10). Hence, the adaptive gain factor is implemented with a single RLS tap. If the filter output signal UD is of
appropriate value depending on the PV system, then the controlling
action would be fast. In context of this, a variable K0 is introduced
in the control loop that helps to limit the filter output in accordance
with the boost converter used in the PV system (Fig. 1b). This K0 is
dependent on the switching frequency fs and inductance L of the
boost converter as follows
K0 = L fs
(12)
To verify superiority of the proposed controller with respect to convergence rate, steady-state error and performance with noise terms,
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tracking behaviour of the studied PV system with the proposed
MPPT is compared with that of RLS-APEFC-MPPT [13]. The absolute percentage errors of voltage ev,mpp for the MPPTs are calculated as follows
ev, mpp =
vMPP, actual − vMPP, calculated
× 100
vMPP, actual
(13)
2.2.3 Tap-weight update with the proposed MPPT: The proposed
MPPT algorithm is described in Fig. 2.
3
Results and discussion
In this paper, the performance of the proposed MPPT controller is
verified on an SSI-M6-205 PV system [15] and prototype PV
system that consists of five PM648 PV panels connected in
series. The parameters of the studied PV system and the connected
boost converter are given in Table 1.
3.1 Simulation results
The simulated I–V and P–V characteristics of the prototype PV
system for two cases of environmental conditions as defined by
condition-I (solar irradiance 540 W/m2 and temperature 36°C)
and condition-II (solar irradiance 970 W/m2 and temperature 43°C)
are shown in Fig. 3a. In condition-I, the MPP voltage, current
and power of the PV system are 91 V, 2.2 A and 200 W, respectively. In condition-II, the MPP voltage, current and power of the PV
system are 88.5 V, 1.1 A and 97.6 W, respectively. The tuned
values of filter weight and PD-parameters KP and KD in case of
the proposed MPPT are demonstrated in Figs. 3b and c, respectively. KI is calculated as 0.92 (Fig. 3d ).
The frequency response such as Bode plot of the prototype PV
system with the proposed MPPT at environmental condition-I is
shown in Fig. 4a. The gain margin (GM) and phase margin (PM)
of these frequency responses at condition-I are 2.35 dB and 140°,
respectively. It can be observed that both GM and PM are positive.
Therefore, it is confirmed that PV system with the proposed MPPT
is stable.
The proposed RLS-APECF-MPPT is now compared with
another adaptive MPPT [13] that is designed with a fixed value
of forgetting factor as 0.9 for our studied PV system. The MPP
tracking result of the prototype PV system at environmental
condition-II is shown in Fig. 4b. From this figure, it can be
clearly observed that though tracking operation in case of the proposed RLS-APECF-MPPT is delayed due to time taken in weight
and forgetting factor adaptation but tracking time in case of the proposed RLS-APEFC-MPPT is less than that of the adaptive MPPT
[13]. Since, after this delay, the adjustment speed of the tracking
voltage increases many times than that of adaptive MPPT [13]
and hence tracking time reduces. Furthermore, tracking error of
proposed RLS-APEFC-MPPT and adaptive MPPT [13] is compared in Fig. 4c.
To test the proposed RLS-APEFC-MPPT for higher power
ratings, the studied PV system is upgraded to 20 same PV
modules connected in cascade. Fig. 5a shows the simulated
results of DC-link voltage of the studied PV system at constant
load condition. Fig. 5b shows the simulated results of DC-link
voltage of the studied PV system at changing loading from 80 to
100%. From these two sets of figures, it is clear that the proposed
MPPT is valid for higher voltage and power ratings.
3.2 Experimental results
This section describes the experimental results obtained by using
prototype PV system as shown in Fig. 6a. The MPP tracking
responses are observed and recorded using a digital storage oscilloscope. The objectives of these experimental results are to crosscheck and validate simulation results obtained using MATLAB.
Fig. 2 RLS-APEF adaptation algorithms for updating weight ω of the filter
For better analysis of the MPP tracking responses of the prototype
PV system, two environmental conditions are such as condition-I
and condition-II as defined earlier in Section 3.1 of this section.
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J Eng 2016
doi: 10.1049/joe.2015.0195
Table 1 Characteristics of studied PV system
Isc, A
Voc, V
Impp, A
Vmpp, V
number of series cells in each PV module
number of series PV module in the PV array
inductance, L and L1, mH
input capacitance, C1, µF
output capacitance, C2, µF
voltage and current limit
load, Ω
2.8
21.6
2.2
18.2
36
5
5, 10
330
380
10 A, 450 V
100
The solar irradiance is varied by intentionally inserting shedding to
the PV panel. Fig. 6b shows comparison of experimental responses
of prototype PV system with the proposed RLS-APEFC-MPPT
Fig. 4 Frequency response
a Bode plot of studied PV system with the proposed MPPT at environmental
condition-I
b Comparison of MPP voltage tracking
with that of an adaptive P&O MPPT with adaptive perturbation
size and adaptive MPPT [13].
It is clearly distinguished that the performance of the proposed
MPPT has lesser voltage fluctuations around the reference. Owing
to the uses of an adaptive filter-based algorithm, the proposed
RLS-APEF-MPPT is capable of both tracking action with adaptive
step-size and filtering action. Therefore, it is better than that of the
adaptive P&O. The fluctuations in case of the P&O and adaptive
P&O algorithm are because of the absence of an adaptive filter
Fig. 3 Simulation results
a Comparison of P–V characteristics of prototype PV system at condition-I
(solar irradiance 540 W/m2 and temperature 36°C) and condition-II (solar
irradiance 970 W/m2 and temperature 43°C)
b Filter weight tuning
c Calculated KP and KD
d KI of prototype PV system with the proposed MPPT
J Eng 2016
doi: 10.1049/joe.2015.0195
Fig. 5 PV panel DC-link output for the same PV system with 20 PV panels
connected in cascade
a At constant load condition
b At load change from 80 to 100%
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Fig. 6 Prototype PV system showing
a System architecture of PV system controller
b Block diagram representation of the prototype PV system
c Experimental results showing MPP tracking responses of prototype PV system with adaptive P&O, adaptive MPPT [13] and the proposed RLS-APEFC-MPPT
when varied from open-circuit to condition-II (solar irradiance 970 W/m2 and temperature 43°C) and (b) comparison of tracking error of prototype PV system
with adaptive MPPT [13] and the proposed RLS-APEFC-MPPT
such as our proposed modified RLS-APEF-MPPT. Hence, MPP
tracking response in case of the proposed RLS-APEF-MPPT is
more accurate and faster than that of adaptive P&O and adaptive
MPPT [13].
Figs. 7a and b show the MPP tracking responses of prototype PV
system using the proposed RLS-APEFC-MPPT and adaptive
MPPT [13], respectively, during change in solar irradiance from
condition-I to condition-II. Comparing these figures, it is clear
that the tracking behaviour in case the proposed
RLS-APEFC-MPPT is more smooth and faster than that of the
adaptive MPPT [13]. It can also be seen in these figures that the
MPP tracking time in case of the proposed RLS-APEFC-MPPT
is 0.25 s, whereas in case of the adaptive MPPT [13] is around
0.45 s. Therefore, tracking responses in case of the proposed
RLS-APEFC-MPPT is faster and smoother than that of adaptive
MPPT [13].
The MPP tracking performance of the studied PV system in case
of proposed RLS-APEFC-MPPT, adaptive MPPT [13], adaptive
P&O MPPT and P&O MPPT are compared in Table 2. From this
figure, the tracking results of PV system in case of the proposed
RLS-APEFC-MPPT is better in terms of voltage oscillation, tracking time from open-circuit condition and tracking time from
condition-I to condition-II.
Figs. 8a–c show some other experimental responses of prototype
PV system with the proposed RLS-APEFC-MPPT at condition-II.
The duty-ratio of MPPT converter is shown in Fig. 8a. The
DC-link voltage (vdc) which is input to inverter is shown in
Fig. 8b. Fig. 8c shows the gate pulses of inverter, respectively. In
this Fig. 8c, two sets of pulses for inverter switches are shown.
The first set of pulses is for switches S1 and S2, whereas the
second set of pulse is for switches S3 and S4. S1 and S2 are switched
ON and OFF simultaneously and then switches S3 and S4 are
switched ON and OFF simultaneously. However, when S1 and S2
are switched ON, S3 and S4 are switched OFF and vice-versa. The
switching period, ON time and OFF time of switches S1 and S2 are
Tac, t11 and t12 microseconds, respectively. The switching period,
ON time and OFF time of switches S3 and S4 are Tac, t12 and t11
microseconds, respectively. Hence, Tac = t11 + t12.
4
Conclusions
A new MPPT is proposed in this paper. This proposed
RLS-APEFC-MPPT works adaptively where the derivative gain
parameter is tuned online by an APEF. The filter weight is
adapted by an RLS algorithm with variable forgetting factor.
Testing with the prototype PV system, it is found that MPP tracking
with this proposed RLS-APEFC-MPPT provides both fast response
and less steady-state error than that of adaptive MPPT [13]. The effectiveness and accuracy of the proposed RLS-APEFC-MPPT have
been verified by both simulation and experimental studies using a
0.2 kW prototype PV system. This proposed RLS-APEFC-MPPT
is found to be computationally less complex, and effective in tracking MPP of the studied PV system.
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Fig. 7 Experimental results showing MPP tracking responses of prototype
PV system for step change of environmental condition from 690 W/m2
(condition-I) to 958 W/m2 (condition-II)
a In case of Proposed RLS-APEFC-MPPT
b In case of adaptive MPPT [13] (scale in the x-axis: 0.5 s/div and y-axis:
100 V/div)
Table 2 Comparison of experimental tracking behaviour of the prototype
PV system with different MPPTs
MPPT controller
proposed
RLS-APEFC-MPPT
adaptive MPPT [13]
adaptive P&O
P&O
5
Fig. 6 Continued
J Eng 2016
doi: 10.1049/joe.2015.0195
Voltage
oscillation,
V
Tracking time
from
open-circuit
condition, s
Tracking time
from condition-I
to condition-II,
s
1.2
0.4
0.25
2
2.5
4
0.5
0.65
0.75
0.45
1.2
1.6
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Fig. 8 Experimental results showing different responses of prototype PV
system with the proposed RLS-APEFC-MPPT during MPP tracking operation such as
a Gate pulse of MPPT converter
b Load voltage (vac)
c Gate pulses of inverter switches S1, S2, S3 and S4 at condition-II
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