maximum power point tracking of photovoltaic systems using
TRANSCRIPT
Maximum Power Point Tracking of Photovoltaic Systems Using Sensorless Current-Based Model
Predictive Control
Morcos Metry1, Student Member, IEEE, Mohammad B. Shadmand2, Student Member, IEEE, Yushan Liu3, Member, IEEE, Robert S. Balog4, Senior Member, IEEE, and Haitham Abu Rub5, Senior Member, IEEE
Renewable Energy & Advanced Power Electronics Research Laboratory1, 2&4
Dept of Electrical & Computer Engineering, Texas A&M University, College Station, USA1, 2&4 Dept of Electrical & Computer Engineering, Texas A&M University at Qatar, Doha, Qatar3&5
Qatar Environment and Energy Research Institute, Qatar Foundation, Doha, Qatar1&5 [email protected], [email protected], [email protected], [email protected],
Abstract — Variability in the behavior of solar energy made Maximum Power Point Tracking (MPPT) of photovoltaic (PV) required to ensure continuous harvesting of maximum power. This paper presents a current sensorless version of MPPT algorithm using Model Predictive Control (MPC). The main contribution of this paper is to use model based predictive control principle to eliminate the current sensor that is usually required for perturb and observe (P&O) MPPT technique. By predicting the PV system states in horizon of time, the proposed method becomes an elegant, embedded controller that has faster response than the conventional P&O technique under rapidly changing atmospheric conditions and without requiring expensive sensing and communications equipment and networks to directly measure solar insolation changes. Comparison of the proposed sensorless current MPC-MPPT (SC MPC-MPPT) technique with previously introduced MPC-MPPT will be discussed in this paper. The proposed technique for a flyback converter is implemented in real time on dSPACE DS1007.
I. INTRODUCTION The cost reduction in photovoltaic cells has further
increased an interest in solar electricity generation, which continued to gain popularity worldwide with a growth factor of 68 from 2010 to 2013 [1]. However the low conversion efficiency of PV cells is still the significant obstacle for their widespread use [2]. Therefore, Maximum Power Point Tracking (MPPT) is required to ensure that maximum available solar energy is harnessed from the solar panels [3-6]. In common power converter architectures, the PV array is connected to a DC-DC converter that boosts/bucks the input dc voltage and allows the control of the current from PV arrays [5, 7]. An MPPT controller and power converter can efficiently track and convert the maximum available solar energy to increase the overall conversion efficiency of the PV, without relying on an improvement in the solar cell itself.
Many MPPT methods have been suggested recently; the relative merits of these various approaches are discussed in [8]. The critical operating regime is low insolation
conditions. Capturing all of the available solar power during low insolation periods can significantly improve system performance. A high effective MPPT can significantly increase the amount of energy produced from the same foot print area of installed PV system.
The MPPT techniques in [8] can be classified into four categories: Incremental Conductance (INC) [9], Perturb-and-Observe (P&O) [10], fractional Open-Circuit Voltage (Voc) [11], and Best Fixed Voltage (BFV) [12]. Each approach has certain advantages and disadvantages for the present application. P&O is a well-known technique with relatively good performance; however, P&O method cannot always converge to the true maximum power point [8]. Also, P&O is relatively slow, which limits its ability to track transient insolation conditions.
These MPPT algorithms require sensing the PV voltage and current, which necessitates both a voltage and current sensor. This paper investigates a highly efficient MPPT technique using model based predictive controller to eliminate the current sensor. Since the essence of sensorless current control is to use a surrogate signal for the input current without actually measuring it, the concept fits well with model predictive control in that both techniques rely on models of the converter to perform the control actions.
Researchers have investigated sensorless current techniques for MPPT for cost reduction purposes [13-18]. Although these techniques eliminate the cost associated with the current sensor, which tends to be more expensive than the voltage sensor, they suffer in performance due to the extra calculations needed in each sampling period to estimate the PV current [13, 14, 16].
The main characteristic of the model predictive control (MPC) technique is to predict the error one step ahead in the horizon of time. This property can be used to obtain a better-estimated current in the SC MPC-MPPT algorithm. The main contribution of this paper is to introduce a sensorless
978-1-4673-7151-3/15/$31.00 ©2015 IEEE
PV M
odul
e
Vc
-
1:n
VPV
+
-
Switch
C
Snubber Circuit
Transformer
Lm
I sIPV
VPV
IPV
Model-Based Design
Switching signal
+
VcMPPT
Optimization of cost function g
VPV (k+1)~
Current Sensorless Algorithm
Predictive Model of the System
Vref-PV (k+1)
(k)
(k)
~
~
(k)
R
Fig. 1 Flyback converter with snubber circuit for PV application.
k k+1 k+2 k+3 k+4 k+5
u(k)
u(k)
u(k+1)
u(k+1)
u(k+2)
u(k+2)
k k+1 k+2 k+3 k+4 k+5
k k+1 k+2 k+3 k+4 k+5 Fig. 2 Moving in horizon of time principle (N=3).
current technique, as illustrated on Fig. 1, on the already developed MPC P&O method [19-22]. This paper is organized as follows: Section II introduces the principle of Model Predictive Control (MPC). Section III derives the relation for the SC MPC-MPPT algorithm and discusses the Maximum Power Point (MPPT) technique. Then real time simulation results are shown in Section IV.
II. PRINCIPLE OF MODEL PREDICTIVE CONTROL Literature investigated numerous control techniques for
power converters and drives [23-30]. Model Predictive Control (MPC) applications in power electronics can be found in literature from as early as the 1980’s for high-power systems with low switching frequency [31]. Higher switching frequencies devices were not viable at that time due to the immense calculation time required for the control algorithm. However, powerful microprocessors, which were later developed, have fueled interest in the application of MPC in power electronics considerably over the last decade [19, 32-35].
The main characteristic of MPC is predicting the future behavior of the desired control variables [32] until a predefined step ahead in horizon of time. The predicted variables are used to obtain optimal switching state by minimizing a defined cost function. The model used for prediction is a discrete-time model which can be presented as state space model [36]:
)()()1( kBukAxkx +=+ (1)
)()()( kDukCxky += (2)
Then a cost function that takes into consideration the future states, references and future actuations can be defined:
( ) ( ) ( )( )Nkukukxfg += ,,, ! (3)
The defined cost function g should be minimized for a predefined horizon in time N; the result is a sequence of N optimal actuations:
[ ] gkuuminarg001)( != (4)
Despite the fact that u(k) contains feasible plants inputs over the entire horizon of time only the first element is used in conventional MPC. At next sampling time (k+1), the system states are calculated using the system model, the horizon is shifted by one step, and another optimization is applied. As demonstrated in Fig. 2 for a horizon length N=3, the horizon taken into consideration in the minimization of g slides forward as k increases.
The general scheme of MPC for power electronic converters is illustrated in Fig. 3 [20]. The measured variables, )(KX , are used in the model to calculate predictions, )1(
~+KX , of the controlled variables for each one
of the n possible actuations, that is, switching states, voltages, or currents. Then these predictions are evaluated
using a cost function, which considers the reference values, )1(* +KX , design constraints; and the optimal actuation, S, is selected and applied in the converter. The general form of the cost function, g, subject to minimization can be formulated as
Minimization
of the cost function
Converter Load
Measurements:
S
( )KX
( )KX
( )1* +KX
Plant n
Plant 1( )1
~
1 +KX
( )1~
2 +KX
( )1~
+KXn
Predictive Model
Plant 2
Fig. 3 General MPC schematic for power electronics
converters.
PV M
odul
e Vc
-
1:n
VPV
+
- Switch
C
Lm
IsIPV
+
ILm
ILmn=
R
Fig. 4 Analysis of Flyback converter to obtain PV current surrogate equation.
( ) ( ) ( ) ( )
( ) ( )⎥⎦⎤
⎢⎣⎡ +−+++
⎥⎦⎤
⎢⎣⎡ +−++⎥⎦
⎤⎢⎣⎡ +−+=
11
1111
*~
*22
~
1*11
~
KXKX
KXKXKXKXg
nnnλ
λ
…
(5)
where λ is the weighting factor for each objective. To select the switching state that minimizes the cost function g, all possible states are evaluated and the optimal value is stored to be applied next.
The power converter can be any topology and number of phases, while the generic load shown in Fig. 3 represents an electrical machine, grid, or any other active or passive loads. In this paper the flyback DC-DC converter topology with RCD snubber circuit, Fig. 1, is selected to control the output current and voltage of the PV using the proposed SC MPC-MPPT technique.
III. PROPOSED SENSORLESS CURRENT MAXIMUM POWER POINT TRACKING USING MODEL PREDICTIVE CONTROL
The relation between the inductor current ILM, as in Fig. 4, and the input voltage VPV can be observed from the relations of the flyback DC/DC converter. The flyback converter in Fig.1 is analyzed in continuous conduction mode during two states: when the switch is on, and when the switch is off [37].
When the switch is on
IPV = ILM (2)
Writing down node equations for Fig. 4, a relation for ILM can be developed
ILM (k) = C dVC (k)dt
+VC (k)R
!
"#
$
%&n (3)
IPV is zero when switch is open. Hence, ILM can be used as an approximation in
IPV (k) = C dVC (k)dt
+VC (k)R
!
"#
$
%&n (4)
Therefore, (4) is used as a model for current to eliminate the current sensor, in which case IPV(k) can be applied to equations (5), (6) and (7), mentioned later, to determine the predicted value for VPV at the next sampling time. The implementation of this algorithm is shown in Fig. 5.
The flyback DC-DC converter, in Fig. 1, is used for purpose of adjusting the current drawn from PV array by adjusting the converter operation. By using the system model as an input to P&O technique, the reference current/voltage for the MPC is determined. The procedure for determination of reference current/voltage by P&O and finally minimization of MPC cost function are detailed in Fig. 5.
This technique predicts the error of the next sampling time and based on optimization of the cost function g, the switching state is determined. The inputs to the predictive controller are the PV system voltage, output voltage, and the PV current surrogate algorithm.
By deriving the set of discrete-time equations, the behavior of control variable can be predicted at next sampling time k+1. The proposed methodology is based on the fact that the slope of the PV array power curve is zero at the predicted MPP, positive on the left and negative on the right of the predicted MPP.
The discrete-time equations of the predicted voltage for the flyback converter of Fig. 1 are given in (5) when the switch is closed and (6) when the switch is open:
VPV (k +1) = Vc (k)−TSRC"
#$
%
&'Vc (k)
(
)*
+
,-1−DnD
"
#$
%
&' (5)
VPV (k +1) =DTSnC
IPV (k)−TSRC
Vc(k)+Vc(k)"
#$%
&'1−DnD
(
)*
+
,- (6)
The average model of VPV (k+1) becomes as in (7):
Inputs : VPV (k), VC(k)
Start
Current Surrogate Equation
Model Based Prediction of Vpv(k+1)
S=0
S=1
Return
⎟⎠
⎞⎜⎝
⎛ −⎥⎦
⎤⎢⎣
⎡⎟⎠
⎞⎜⎝
⎛ −+−
=+nDDkV
RCTkI
nCSTkV C
SPV
SPV
1)(1)()1()1(
nRkV
dtkdVCkI CC
PV ⎟⎠
⎞⎜⎝
⎛ +=)()()(
)1()( −−=Δ kIkIi PVPVPV
)1()( −−=Δ kVkVv PVPVPV
0=Δ PVv
)()(kVkI
vi
PV
PV
PV
PV −=Δ
Δ0=Δ PVi
0>Δ PVi
)()(kVkI
vi
PV
PV
PV
PV −>Δ
Δ
α−= )()( kVkV PVref α+= )()( kVkV PVref
)()( kVkV PVref = )()( kVkV PVref =
)1()1(1,01,0 +−+=
== kVkVg refPVS S
10 == < ss ggYES
NO
NO
YES
NO
NO
YES
YES
YESNO
NO
YES
MPPT Algorithm
Model BasedDesign
Cost FunctionMinimization
Fig. 5 SC MPC MPPT procedure to determine reference voltage, and determination of switching state using cost function minimization.
VPV (k +1) =TS (1− S)nC
IPV (k)+ 1−TSRC
"
#$
%
&'VC (k)
(
)*
+
,-1−DnD
"
#$
%
&' (7)
After determination of the next step reference voltage using the procedure shown in Fig. 3, the cost function subject to minimization can be obtained as in (8):
)1()1(1,01,0 +−+=
== kVkVg refPVS S (8)
The final switching states is the state that minimizes (8), the complete procedure of the controller is summarized in Fig. 5.
IV. SIMULATION RESULTS The SUNPOWER SPR-305-WHT is used as PV module.
The PV module characteristics under standard test condition (STC: solar irradiance = 1 kW/m2, cell temperature = 25 deg. C) are as presented in Table 1.
Table 1 System model parameter table
System Model Parameter Table Switching Frequency (F) 5 kHz Sampling Time (TS) 10 µs Load Value (R) 10 ohm Output Capacitor (C) 470 µF Open-circuit voltage (VOC) 64.2 V Short-circuit current (ISC) 5.96 A Voltage at MPP (VMP) 54.7 V Current at MPP (IMP) 5.58 A
0 10 20 30 40 50 60 700
5
10
1 kW/m2
0.75 kW/m2
0.5 kW/m2
0.25 kW/m2
Voltage (V)
Cur
rent
(A)
0 10 20 30 40 50 60 700
200
400
6001 kW/m2
0.75 kW/m2
0.5 kW/m2
0.25 kW/m2
Voltage (V)
Pow
er (W
)
Fig. 6 I-V and P-V characteristics of the PV array.
Irradiance(W
/m2 )
Time(s)
Fig. 7 Irradiance data for simulation.
Two modules are connected in parallel with the I-V and P-V characteristics of the string, illustrated in Fig. 6. In this paper, SC MPC-MPPT is compared to MPC-MPPT published in [20, 21]. The sampling time is 10 µs which corresponds to a sampling frequency of 100 kHz. The actual switching frequency of the power semiconductor is 5 kHz. This gives a 20x oversampling for the proposed digital controller. The irradiance profile in Fig. 7 is applied to both the MPC-
MPPT and the SC MPC-MPPT. The system is tested under three irradiance level changes. Fig. 8 illustrates the simulation results for power, voltage, duty cycle and current of the proposed SC MPC-MPPT, and compared to the MPC MPPT with current sensor. As shown in the figures, the performance of the SC MPC-MPPT tracks the maximum power with some ripple. To illustrate the performance of the SC MPC-MPPT, steady state voltage and current ripple plots are shown in Fig. 9 at 500 W/m2 irradiance level. Voltage
(a)MPC-MPPTPVVoltage.
(c)MPC-MPPTPVCurrent.
(b)SCMPC-MPPTPVVoltage.
(e)MPC-MPPTPVPower.
(g)MPC-MPPTDutyCycle.
(d)SCMPC-MPPTPVCurrent.
(f)SCMPC-MPPTPVPower.
(h)SCMPC-MPPTDutyCycle.
Time(s)
Time(s)
Time(s)
Time(s)
Time(s)
Time(s)
Curren
tIPV(A
)
Volta
geV
PV(V
)
Volta
geV
PV(V
)
Time(s)
Curren
tIPV(A
)
Power(W
)Du
tyCycle
DutyCycle
Power(W
)
Time(s)
Fig. 8 PV current and voltage simulation results for MPC-MPPT (left) and SC MPC-MPPT (right).
80
82
84
86
88
90
92
94
96
98
100
98
98.2
98.4
98.6
98.8
99
99.2
99.4
99.6
99.8
100
200 300 400 500 600 700 800 900 1000
Cur
rent
Sen
sorl
essM
PC-M
PPT
Con
trol
E
ffec
tiven
ess [
%]
MPC
-MPP
T C
ontr
ol E
ffec
tiven
ess [
%]
Solar Insolation [W/m^2]
MPC-MPPT Control EffectivenessCurrent sensorless MPC-MPPT Control Effectiveness
Fig. 10 Control Effectiveness of MPC-MPPT versus SC MPC-MPPT
IPV
VPV
Solar Irradiance =500 W/m^2
Solar Irradiance =750 W/m^2
Fig. 11 Step change response
IPV
VPVSolar Irradiance =750 W/m^2
Fig. 12 PV current and voltage ripple at 750 W/m^2 solar irradiance level
IPV
VPV
Solar Irradiance =500 W/m^2
Solar Irradiance =750 W/m^2
Transient change in solar irradiance
Fig. 13 Transient change response
ripple in Fig. 9a is 1.92%, while current ripple in Fig. 9b is 1.34%. The control effectiveness of both techniques from 200 W/m2 to 1000 W/m2 is illustrated in Fig. 10. It can be seen that the SC MPC-MPPT control effectiveness is 99.9% at irradiance level 750 W/m2 and 99.1% at irradiance level 500 W/m2. Comparing the plots for the MPC SC-MPPT to MPC-MPPT, it shows that the SC MPC-MPPT has sacrificed some of the performance advantages of the MPC-MPPT, yet it may be a viable option to cut down on equipment costs. The detail descriptive plots are illustrated in Fig. 8 to Fig. 10 using Matlab/Simulink, then dSPACE DS1007 is used for the experimental implementation. The real time
implementation of MPC SC-MPPT illustrated in Fig. 11, Fig. 12 and Fig. 13 confirm the simulation results.
V. CONCLUSION This paper presented an improved MPPT technique by
predicting the error at next sampling time before applying the switching signal using MPC. Then it proposed applying a sensorless current algorithm to eliminate the cost of the current sensor. The proposed SC MPC-MPPT technique tracked the maximum power by using only voltage sensors with some ripple, and presented comparable dynamic response to the MPC-MPPT under rapidly changing
5.49 5.495 5.5 5.505 5.51 5.515 5.52
5.55
5.6
5.65
5.49 5.495 5.5 5.505 5.51 5.515 5.5251
51.5
52
52.5
Time (s) Time (s)(a) SC MPC-MPPT PV Voltage Ripple. (b) SC MPC-MPPT PV Current Ripple.
Vol
tage
(V)
Cur
rent
(A)
Fig. 9 PV current and voltage ripple for SC MPC-MPPT
atmospheric conditions. Results presented in this paper indicate a relatively similar performance of both techniques in steady state as well as dynamic response. Moreover, the reduced sensor controller approach results in a lower system cost. The dSPACE DS1007 was used for implementing of the control technique experimentally.
ACKNOWLEDGMENT This publication was made possible by the NPRP award
[NPRP-EP X-033-2-007] (Sections II and IV) and the NPRP award [NPRP 7-299-2-124] (Section III) from the Qatar National Research Fund (a member of Qatar Foundation). The statements made herein are solely the responsibility of the authors.
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