Maximum power point tracking of photovoltaic systems based on the sliding mode control of the module
admittance
Daniel Gonz´alez Montoya
Departamento de Electr´onica y Telecomunicaciones Instituto Tecnol´ogico Metropolitano
Medell´ın, Colombia Email: [email protected]
Carlos Andr´es Ramos Paja
Facultad de Minas Universidad Nacional de Colombia
Medell´ın, Colombia Email: [email protected]
Roberto Giral
Departament d’Enginyeria Electr`onica, El`ectrica i Autom`atica
Universitat Rovira i Virgili Tarragona, Spain Email: [email protected]
Abstract
Photovoltaic (PV) grid-connected applications use an adaption stage to extract the maximum power from the PV module matching its optimal operating point with the load operation. This paper presents a sliding mode control based on the admittance of the PV module to follow a reference provided by an external Maximum Power Point Tracking (MPPT) algorithm, and at the same time, to mitigate the perturbations generated by the load. The sliding mode controller is mathematically analyzed, and a design process is proposed to ensure the desired performance in all the operation range. Finally, simulations and exper- imental results are used to demonstrate the efficiency of the proposed solution in presence of both changes in the irradiance level and load perturbations.
Keywords: Sliding mode control, maximum power point tracking, PV module
admittance
1. Introduction
Photovoltaic (PV) systems represent a good alternative to produce clean energy since they can be dimensioned for a wide range of power ratings in both stand-alone and grid-connected applications [1, 2]. A typical PV system is composed by a PV module, an adaption stage to transform the power provided
5
by the PV source, and a DC load as depicted in Fig. 1 [1, 3, 4, 5, 6, 7].
The PV module is characterized by a non-linear behavior that depends on the ambient conditions, which makes difficult to predict the voltage and current to guarantee the maximum power production [8]. The operating point in which the PV array provides its maximum power is named maximum power point (MPP)
10
[2, 3, 9]. Then, the main objective of the control strategy in a PV system is to ensure the system operation around its MPP (Maximum Power Point Tracking - MPPT operation) in whichever environmental condition [1]. Moreover, the DC load is characterized by a function that depends on the current and voltage outputfo(ib, vb) with its associated impedance [4, 5]. Therefore, to extract the
15
maximum power from a PV module, an adaption stage regulated by an MPPT algorithm system should be inserted in order to match the optimal operating point of the PV module with the load operation [4, 5, 6, 7, 8, 10] .
Adaption Stage
and MPPT
PV module iPV
vPV
Load f0
f1
f2
vPV
+
-
+
-
vb iPV
ib ib
vb
Figure 1: Adaption stage between a PV module and a DC load.
The most commonly used MPPT solutions are the incremental conductance (IC) and the perturb and observe (P&O) methods: The IC method tracks the
20
operating point in which the PV power derivative with respect to the voltage is
zero, since such a condition corresponds to the MPP [7, 11]. The main problem of the IC method is associated to the noise, measurement and quantization er- rors, which could introduce oscillations that degrade the MPPT operation [3].
The P&O algorithm operates by periodically perturbing the control variable
25
and comparing the instantaneous PV powers after and before the perturbation [6, 7, 10] . This algorithm is composed by two critical parameters: the sampling interval (Ta) in which the algorithm perturbs the control variable, and the am- plitude of such perturbation (∆vref) [3]. Due to its simple implementation the P&O is widely adopted in commercial applications [3, 11].
30
The main requirement in PV grid connected applications is to convert the generated DC power into suitable AC power by means of an inverter device.
Hence, the DC voltage provided by the PV module is usually required to be boosted up to the level required by the inverter. However, the direct connection between the DC/DC converter and the inverter causes voltage oscillations since
35
the power delivered by the PV array is DC, while the power requested by the inverter is AC. If such oscillations are not well-mitigated the MPPT performance is reduced, which also reduce the energy delivered to the load [12]. The typical solution to this problem is to connect a large electrolytic capacitor as DC- link (Cb) between the DC/DC converter and the inverter, but such a solution
40
decreases the reliability of the system due to the high failure rate of electrolytic capacitances [13]. Many solutions adopt the previous non-reliable condition [1, 2, 6, 9, 14] , where the MPPT algorithm is designed to extract the maximum power of the PV module without accounting for oscillations at the DC/DC converter output terminals. However, a grid-connected PV system must to
45
include the MPPT design and the mitigation of the DC-link voltage oscillations using suitable control strategies to improve the system reliability.
In such a way, some solutions used to avoid large electrolytic capacitors have been published in literature, a large number of them, adding a PWM-based controller to regulate the PV voltage in agreement with the MPPT command
50
[1, 12, 14]. Traditionally, the previous alternative consists into designing a linear controller (PI, PID or lead-lag) to guarantee a correct tracking of the voltage
reference generated by the MPPT controller, and to mitigate the perturbations generated by the load and by the irradiance changes [12]. The main problem associated to this kind of controllers is the requirement to use a linearized model
55
of the PV system, which makes impossible to ensure the same performance in all the operating conditions [12]. Other types of controllers have been proposed in the literature to ensure a correct behavior of the system without requiring a linearization process [15, 16, 17, 18]. Those works, which are based on the Sliding Mode Control (SMC) of the inductor or capacitor current of the converter, offer
60
a good performance in both the mitigation of the dc-link voltage oscillations and the tracking of the reference provided by the MPPT controller. However, those solutions also involve the use of PV voltage linear controllers that reduce the bandwidth of the system and compromising the global stability, it also affecting the time response in presence of perturbations. Thus, it is necessary
65
to design a single controller, based on techniques like the SMC, to ensure a correct performance in all operation range, without reducing the bandwidth of the system and ensuring global stability.
On the light of the previous analysis, a SMC should be designed to im- pose a desired PV impedance in concordance with the MPPT requirements as
70
presented in [4, 5, 19, 20]. Those works propose an adaption stage based on a DC/DC converter regulated by a SMC technique connected to an external MPPT algorithm, which gives the optimal reference to the controller following the structure presented in Fig. 2. However, those works do not present the com- plete design process for the MPPT algorithm in terms of the characteristics of
75
the PV module and DC/DC converter. In contrast, other works dealing with the complete design of the MPPT algorithm do not considers the DC/DC converter load perturbations [1, 2, 6, 9, 14, 21]. Therefore, a unified solution dealing with both the MPPT algorithm design and the mitigation of the DC-link voltage oscillations is needed to improve the PV system efficiency and reliability.
80
This paper proposes a new SMC solution to impose the optimal admittance to the PV module by tracking the reference provided by an external admittance- based MPPT algorithm, and at the same time, to mitigate the oscillations in the
Load
PV module iPV
vPV
DC/DC Converter
vPV iPV
MPPT
&
SMC Adaption Stage
u
Figure 2: Impedance matching of a PV module and a load by means of a DC/DC converter controlled by a SMC and an MPPT algorithm.
DC-link without using additional voltage controllers based on a linearized model.
The DC/DC converter adopted consists in a step-up topology to increase the PV
85
voltage to the level required by a classical grid-connected inverter. The analysis of the new sliding surface to demonstrate the stability and correct behavior is presented in Section 2. The admittance-based MPPT algorithm is designed and presented in Section 3. Then, Section 4 presents the summary of the design process to implement the proposed control system. Section 5 illustrates the
90
performance of the solution using simulation results accounting for both load and environmental perturbations. The experimental validations are presented in Section 6, and Section 7 closes the paper with the conclusions.
2. Proposed sliding surface
As presented in the previous section, control the PV impedance (or admit-
95
tance) by means of an SMC linked to an external MPPT algorithm is a good alternative [4, 5, 19, 20]. However, such works do not present the complete de- sign process for the MPPT algorithm. As will be explained afterwards, basing the SMC in controlling admittance, instead of impedance, enables to reduce the hardware implementation, in comparison with [4, 5, 19].
100
The PV system presented in Fig. 3, which is based on the step-up boost topology, exhibits in node (a) the current law presented in (1). Tacking into account that the charge balance principle [22] guarantees an average current equal to zero to any capacitor in a steady-state DC/DC converter, i.e.hiCini= 0 for the input capacitorCin, then in node (a) the average PV current is equal
105
to the average inductor current, i.e. hiP Vi = hiLi. Therefore, the average value of the admittanceiL/vP V is equal to the average value of the PV module admittance iP V/vP V, i.e. hiLi/hvP Vi = hiP Vi/hvP Vi. On the basis of the previous analyses, this paper proposes the switching function Ψ and surface Φ given in (2) to regulate the average value of the admittanceiL/vP V following an
110
external reference given by the MPPT algorithm (Yref), as presented in Fig. 3.
This strategy ensures that the average PV admittance is imposed by the MPPT algorithm, i.e. hiP Vi/hvP Vi=Yref.
PV admittance
control PV array
x
Inverter GRID
Cb Cin
L
Inverter controller vPV
pPV iL
vb
vgrid
igrid MPPT Yref
u
iPV
DC/DC Converter Node (a)
Figure 3: PV system based on the proposed SMC
iP V =iL+iCin (1)
Ψ = iL
vP V
−Yref ∧ Φ ={Ψ = 0} (2)
To analyze the system with the selected surface, and to prove the effective- ness of the proposed solution, the equations that model the boost converter
115
behavior are presented in (3) and (4), wherevbandurepresent the bulk voltage and the converter discrete control variable, respectively.
Cin· dvP V
dt =iP V −iL (3)
L·diL
dt =vP V −vb·(1−u) (4) The PV current can be modeled by the simplified single diode model (5) [8, 9, 23], whereiSC represents the short-circuit current,IRis the diode saturation current and α represents the inverse of the thermal voltage that depends on
120
the array temperature [8, 17]. The parameters of this model can be calculated from the operation condition and datasheet specifications values as described in [8, 9, 23], where the short-circuit current is approximately proportional to the irradiance asiSC =KS·S [24].
iP V =iSC−IR·(eα·vP V −1) (5) Fig. 4 presents the block diagram of the control system including the model
125
of the PV system and the SMC structure, where uis generated using a com- parator centered in zero.
The design of a stable SMC requires to fulfill three conditions: transversality, equivalent control and reachability [25]. In the following, such conditions are used to develop a design procedure for the control system that ensures the
130
desired performance of the PV voltage.
2.1. Transversality condition
The transversality condition (6) guarantees that the manipulated variableu is present in the switching function derivative [15], which is required to modify the system dynamics.
135
ddΨdt
du 6= 0 (6)
iPV(vPV,iSC) 1 s
1 Cin
+-
iPV iCin
_
1 s
1 + L
-
vL
_
iL
vPV
vPV iL
iSC
vb x
-+ 1
u
u Ψ
..
+- Y
Yref
PV System
SMC Ψ
Figure 4: Block diagram of the proposed SMC.
To analyze the SMC properties for the proposed surface, the derivative of Ψ with respect to the time is presented in (7).
dΨ dt =
diL
dt
vP V
−dvP V dt · iL
vP V2−dYref
dt (7)
Replacing (3) and (4) in (7):
dΨ
dt =vP V −vb·(1−u)
vP v·L −iL·(iP V −iL)
vP V2·C −dYref
dt (8)
The transversality condition is analyzed deriving (8) with respect touob- taining (9). Then, the transversality condition is fulfilled sincevP V, vb and L
140
are positive values.
ddΨdt
du = vb
vP v·L 6= 0 (9)
2.2. Equivalent control condition
The next step is to analyze the equivalent control condition, which imposes that the average valueueq of the control variableumust be constrained within the operation range of that control variable [25]. For the DC/DC converter, the
145
correct range is 0< ueq <1. These analyses are illustrated in (10).
dΨ
dt = 0→0< ueq <1 (10) Substitutingubyueq in (8), and inserting such an expression into (10) leads to the following inequality:
0< ueq =dYref
dt ·vP V ·L vb
+vb−vP V
vb
+iL·L·iP V −iL2·L C·vP V ·vb
<1 (11) Taking into account that the reference Yref of this SMC is provided by an MPPT algorithm as in Fig. 3, the reference signal exhibits the following
150
behavior: it remains constant during the perturbation intervalTa; and eachTa
seconds it changes in constant incremental or decremental steps inYref looking for positive changes on the PV power [26]. Then, inequality (11) defines the dynamic limits for the derivatives of the reference, i.e. dYdtref. Therefore, the maximum and minimum values of dYdtref that must be granted to fulfill the
155
equivalent control condition are given by (12) and (13), respectively. Such expressions depend on the operating conditions of both the PV array and the DC/DC converter.
dYref
dt < C·vP V2−iL·L·iP V +iL2
·L
C·vP V2·L (12)
dYref
dt >C·vP V2−C·vP V ·vb−iL·L·iP V +iL2·L
C·vP V2·L (13)
The constraints in (12) and (13) put in evidence that step-like waveforms must be avoided inYref, i.e. dYdtref < k, where kis a finite value.
160
2.3. Reachability conditions
The reachability conditions analyze the ability of the system to reach the desired state Ψ = 0. The work in [25] demonstrated that a system that fulfills
the equivalent control condition also fulfills the reachability conditions. It also showed that the sign of the transversality imposes the value ofufor each reach-
165
ability condition, i.e. the control law. Since the transversality condition in (9) is positive, this imposes the reachability conditions (14) and (15) provided that the control action is implemented asu= 1 for Ψ<0 andu= 0 for Ψ>0 [25].
lim
Ψ→0−
dΨ dt
u=1
= dΨ dt
u=1,Ψ=0
>0 (14)
lim
Ψ→0+
dΨ dt
u=0
= dΨ dt
u=0,Ψ=0
<0 (15)
Then, the reachability conditions are calculated by evaluating (8) in (14) and (15), obtaining (16) and (17). Therefore, ensuring that dYdtref is constrained
170
within the dynamic limits given in (12) and (13) also guarantee that both reach- ability conditions are fulfilled.
lim
Ψ→0−
dΨ dt = 1
L −iL·(iP V −iL)
vP V2·C −dYref
dt >0 (16) lim
Ψ→0+
dΨ
dt =vP V −vb
vP v·L −iL·(iP V −iL)
vP V2·C −dYref
dt <0 (17)
3. Design of the admittance-based MPPT algorithm
As presented in the previous section, the Yref variable is the admittance reference given by an MPPT algorithm. This algorithm is based on the tradi-
175
tional P&O technique [3], which perturbs the manipulated variable (Yref) and observes the changes in the PV power (PP V). Hence, the algorithm manipulates Yref to optimize the power generated by the PV module.
Fig. 5 presents a typical profile for a commercial BP585 PV module. The adopted PV module is simulated using (5) with the following parameters:iSC =
180
5 A,IR = 11.6 nA, α= 0.9009 V−1 and KS = 0.005 A·m2
/W. The figure shows in a continuos black line the behavior of the PV module at standard test conditions (S = 1000W/m2 andT = 25◦ C), note that there exists an unique
point in which the PV module gives its maximum power, named MPP. Moreover, the PV admittance value associated to the MPP condition is represented by
185
YM P P, which is calculated as the division between the current and the voltage at the MPP condition,IM P P andVM P P respectively.
2
PV 2=VPV 2+ IPV
YMPP = I MPP V MPP
∆Arc=∆θ . PV
∆θ
∆P P MPP
θ =tan (Y ) PV -1 PV
γ
γ
Figure 5: PV profile and MPPT admittance-based.
In addition, any point of the PV current-voltage profile could be represented in terms of the radius (γP V), centered into the origin, and the angle formed by the radius and the voltage axis defined asθP V. Tacking into account the
190
previous definitions, the triangle formed by the radiusγP V, the origin and the PV admittanceYP V presents the following trigonometric considerations:
tan(θP V) = IP V VP V
=YP V (18)
γP V2=IP V2+VP V2 (19) Furthermore, the continuos oscillation around the MPP generates steady- state PV power losses represented by ∆P. Usually, those losses are restricted constraining the manipulated variable of the MPPT to a fixed value that guar-
195
antee a maximum PV power loss, e.g. design the manipulated variable to guar- antee a maximum loss of 2% of the power at the MPP (PM P P) withS= 1000 W/m2 [3]. In this proposed MPPT, the manipulated variable that constrain the PV power is named ∆Arc, which represents a portion of the current-voltage curve calculated as (20), where ∆θindicates the maximum angle variations that
200
ensures power losses lower than the desired value.
∆Arc= ∆θ·γP V (20)
Then, the ∆Arc parameter is calculated as the maximum permisible arc in the current-voltage profile to limit the power losses to ∆P. Hence, the de- sign criteria is to obtain a maximum steady-state losses ∆P =PM P P ·(1−β), where β ∈ (0,1] represents the maximum admissible losses percentage. Im-
205
posing a desired β value for a selected irradiance condition enables to cal- culate the ∆P restriction and its associated I∆P, V∆P and Y∆P parameters.
The ∆θ condition is calculated using a mathematical manipulation of (18) as
∆θ=tan−1(YM P P)−tan−1(Y∆P), hence the ∆Arcparameter that satisfies the desired power losses is evaluated in (20) using theγP V at MPP as presented in
210
(21).
∆Arc= q
I∆P2+V∆P2
·(tan−1(YM P P)−tan−1(Y∆P)) (21) Finally, the summary of the MPPT process is presented in Fig. 6, where the flow chart illustrates theYref on-line calculation based on the ∆Arcdefini- tion and the continuos monitoring of theIP V and VP V conditions. Note that, as described previously, this algorithm is based on a P&O technique, hence
215
it includes aTa parameter that represents the sampling interval in which the algorithm perturbs the control variable. In order to guarantee that the input ca- pacitor achieves the desired admittance reference, theTa parameter is assumed as the minimum time required by the input capacitor to be charged. This condi- tion is represented as the time constant for the input capacitor calculated using
220
the expression as given in (22), whereRM P P =YM P P−1[4].
Ta>5·RM P P ·Cin (22)
Begin
P =V I
Sign=Sign (-1)
End
No Yes
Measure: V , I Define: ∆Arc, θ P = 0W, Sign = 1
θ = θ + ∆θ Sign
θ = θ P = P
2
γ PV 2=VPV 2+ IPV old old
PV PV
PV. PV PV
.
For Each Ta
Y = tan (θ) ref
old .
old
old PV
∆θ = ∆Arc γ PV
P <= P PV old
Figure 6: Flow Chart of MPPT admittance-based algorithm.
4. Summary of the design process
As presented in previous sections, the design of the proposed control system depends on the PV module and DC/DC converter characteristics. The first step is to obtain (using data sheet values or measurements) the converter parameters
225
and the PV module operation range. With those parameters, the dYdtref values
that guarantee the correct sliding performance are calculated using (12) and (13). Such a restrictions enable to design a derivative limiter, which constraint the maximum derivative of the MPPT reference to the acceptable dYdtref value.
Finally, the MPPT is designed following the procedure defined in Fig. 6, where
230
the ∆Arcparameter is calculated from a desiredβcondition as reported in (21), andTa is calculated using (22).
5. Application example and simulation results
With the aim of illustrating the analysis and the design of the SMC for the PV system presented in Fig. 3, the following conditions are assumed. An ir-
235
radiance operation range within 500 W/m2 ≤ S ≤ 1000 W/m2, the adopted BP585 PV module has the standard test conditions parameters presented in the previous section, and the DC/DC converter elements are L = 22.5 µH, Cin= 66µF andCo= 66µF. In addition, the load perturbations generated by a grid-connected inverter consider an European grid frequency fgrid = 50 Hz
240
and a maximum variation invb equal to 34.5 %, i.e. 24 V≤vb ≤34 V. Finally, the proposed SMC is implemented with hysteresis comparators, which is a com- mon practice for DC/DC converter applications [17], hence an hysteresis band H is imposed to the sliding surface to limit the switching frequency. Concern- ing practical realization, the hysteresis comparators are implemented using the
245
TS555 integrated circuit, which imposes an hysteresis bandH = 1.667V for a 5V supply voltage.
Fig. 7(a) presents the evaluation of the proposed system under changes on the PV admittance reference. The referenceYref is injected as a step-like up and down variations of 0.1 S to validate the proposed SMC performance. The
250
simulation presents the correct behavior of the PV average admittance Y in tracking the reference, it validating the mathematical analysis presented in Sec- tion 2. The bottom of the Fig. 7(a) presents the surface Ψ = 0 under the PV admittance reference changes, where the controller presents good performance forYref stable conditions, but when the reference changes as a step-like varia-
255
tion, the SMC presents a loss of the sliding mode as predicted by expressions (12) and (13) due to the large value of dYdtref.
To avoid this problem, a derivative limiter for the Yref variable must be implemented. Using (12) and (13), and the parameters of the system at the MPP, the maximum permisible derivative limit maxdY
ref
dt
= 2 S/ns is cal-
260
culated, and the simulation including such a dYdtref limiter is presented in Fig.
7(b). As predicted by (12) and (13), the derivative limiter enables to guarantee the correct SMC behavior by constraining the surface into the limits even in case of step-like transients onYref, thus avoiding the loss of the sliding mode by fulfilling the transversality conditions.
265
The MPPT algorithm is designed following the procedure presented in Sec- tion 3. The maximum percent of losses selected for this example is β = 2%
of the PM P P at the lowest irradiance value S = 500 W/m2. Hence, the max- imum permisible arc that guarantee those maximum losses is ∆Arc= 12◦. In addition, the MPPT considers a sampling interval Ta = 1 ms to enable the
270
complete charge of the capacitor. The simulation of the PV system, consid- ering the MPPT implemented as described in Fig. 6, is presented in Fig. 8.
Moreover, the simulation also considers 100 Hz voltage oscillations in the load voltagevb to illustrate the satisfactory mitigation of bulk voltage perturbations at twice the grid frequency generated by a grid-connected inverter. This sim-
275
ulation shows a correct tracking of the MPPT reference in presence of large load voltage variations of 34.5 %. The correct operation of the MPPT is con- firmed by the accurate tracking of the maximum PV power availablepmax. The simulation also considers a PV module exposed to an irradiance variation: at t= 15 ms the irradiance changes fromS = 1000W/m2toS= 500W/m2. The
280
results show the accurate tracking of the MPP given by the proposed algorithm and the satisfactory mitigation of the load perturbations, which demonstrates the effectiveness of the proposed design procedure.
Two zoom of Fig. 8, fromt= 6mstot= 15msand fromt= 28mstot= 35ms, are presented in Fig. 9, which enable to verify the maximum acceptable
285
losses ∆P. Fig. 9(a) presents the zoom when the PV module is irradiated atS =
0.1 0.15 0.2 0.25 0.3 0.35
Admittance [S]
2 2.5 3 3.5 4 4.5 5 5.5 6
−2
−1 0 1 2
Time [ms]
Surface [S]
Y Yref
Ψ Loss of sliding mode
(a) Without the filter
0.1 0.15 0.2 0.25 0.3 0.35
Admittance [S]
2 2.5 3 3.5 4 4.5 5 5.5 6
−2
−1 0 1 2
Time [ms]
Surface [S]
Y Yref
Ψ
(b) With the filter
Figure 7: Simulation of the SMC.
0 0.2 0.4
Admittance [S]
20 40 60 80
Power [W]
5 10 15 20 25 30 35
22 30 36
Time [ms]
Voltage [V]
Y Y
ref
pmax p
PV
−2 0 2
Surface [S]
Ψ
vb
Figure 8: Simulation of the PV system in presence of bulk voltage and irradiance perturba- tions.
1000W/m2: the top of the simulation shows the correct tracking of the reference and the bottom presents the PV power and the calculated maximum power at this condition. Moreover, the maximum acceptable losses are illustrated as a continuos white line, where the system constraint due to the ∆Arcrestriction is
290
effective. In the same way, Fig. 9(b) presents the zoom when the module has a constant irradiance value ofS= 500W/m2. The ∆P condition is well-respected and, since the ∆Arc was calculated for this irradiance value, it validates the analysis presented in Section 3.
The previous simulations show that the proposed sliding-mode controller
295
(2) satisfactorily rejects the main perturbation generated by the grid-connected inverter in the scheme of Fig. 3: a sinusoidal voltage perturbation in vb at double of the grid frequency, which is shown at the bottom of Fig. 8. However, a
0.2 0.25 0.3
Admittance [S]
Y Y
ref
6 7 8 9 10 11 12 13 14 15
83 84 85 86
Time [ms]
Power [W]
pmax p
PV
∆P
(a) Zoom att= 6mstot= 15ms.
0.05 0.1 0.15 0.2
Admittance [S]
Y Y
ref
28 29 30 31 32 33 34 35
40.5 41 41.5 42
Time [ms]
Power [W]
pmax p
PV
∆P
(b) Zoom att= 28mstot= 35ms.
Figure 9: Zoom of Fig 8.
grid-connected inverter also introduces high-frequency harmonics caused by the semiconductors switching. Therefore, a second simulation scheme considering a
300
detailed grid-connected inverter is introduced in Fig. 10 to further evaluate the
proposed solution. The adopted single stage inverter considers a control system to provide a correct power factor and to regulate the voltage on the DC-link connection Cb as reported in [27]. The inverter is designed to operate in the following conditions: the grid voltage is 110 V AC with a frequency of 60 Hz and
305
the average DC-link voltagevb is regulated at 220 V. Moreover, the simulation considers the same MPPT parameters calculated for the previous simulation and a step-down irradiance variation at t = 0.75 s. The simulation results, presented in Fig. 11, show the extraction of the maximum PV power even with the DC-link (bulk) voltage oscillations caused by the grid-connected inverter
310
with the same tracking-time exhibited in Fig. 8 (9ms). In addition, Fig. 11 also shows the AC voltage and the injected current waveforms corresponding to a power factor nearby to one, which put in evidence the correct behavior of the inverter. Finally, the simulation shows the reduction in the injected AC current caused by the reduction in the PV power.
315
PV admittance
control PV array
x
Cb Cin
L
vPV
pPV iL
MPPT Yref u
iPV
DC/DC Converter
Power factor control + driver
DC-link control +-
+ -
+ x - Linv
Cinv Rinv
vac
vdc-ref
Figure 10: Circuital scheme including a single stage grid-connected inverter.
In conclusion, the simulations presented in this section put in evidence the effectiveness of the proposed solution in the tracking of the MPP under the presence of perturbations caused by climatic conditions and by the operation of a grid-connected inverter.
20 40 60 80
Power [W]
0.5 0.6 0.7 0.8 0.9 1 1.1 1.2 1.3
−180
−90 0 90 180
Time [s]
Voltage [V]
pmax p
PV
160 180 200 220 240
Voltage [V]
vb
vac
−1 0 1
Current [A]
iac
Figure 11: Simulation of the PV system with a single stage grid-connected inverter.
6. Experimental validation
320
This section presents experimental validations of the proposed SMC. The experimental test bench consists in a PV module emulator Agilent E4360A, a boost DC/DC converter, an electronic load Kepco BOP72-14MG, a DSP device with a MCP4822 DAC (Digital-to-Analog Converter) to implement the P&O as in [28], and a circuit based on operational amplifiers and a TS555 to implement
325
the Hysteresis comparators. The TS555 and all OpAmps (rail-to-rail TLC2272
& OPA2350) are unipolar 5-V powered. The structure of the experimental platform is presented in Fig. 12, where the PV module emulator is programmed to perform the irradiance variations presented in Section 5.
The DSP executes the previously designed MPPT and it gives the Yref
330
parameter to the controller. For practical implementation, the surface Ψ is
PV emulator Agilent E4360A
Load Kepco BOP72-14MG Cb
Cin
L
vPV
u vPV
+
- iL
Sallen-key Filter iPV
MPPT algorithm
iref = Yref * VPV
iL
DSP Yref
u Flip-Flop S-R
S
R Q +- +- -H/2
H/2
-+
TS555 iref
Figure 12: Scheme implementation.
mathematically adjusted to avoid the analog divisionviL
P V: the solution adopted consists in computing the multiplication ofvP V with the reference given by the MPPT and constrained by the derivative limiter. The result of this operation is converted to an analog value using the MCP4822 and injected to a circuit
335
based on operational amplifiers, which performs the control action by means of the TS555 device. This implementation gives the advantage of computing the high frequency signals by means of analog circuits and the low frequency signals in a digital form. In addition, the iP V variable is generated by removing the switching ripple from the input currentiL with a Sallen-Key filter; this avoids
340
the use of an additional current sensor to sense the PV current, it reducing the cost of the system. The laboratory setup is presented in Fig. 13, which shows the real components used in the experiments.
The proposed SMC and MPPT algorithm were validated by reproducing the simulation tests presented in Section 5 using the experimental platform of Fig.
345
13. In that way, Fig. 14 shows the experimental behavior of the PV system in presence of step-like perturbations injected to the referenceYref, similar to the simulations presented in Fig. 7. This test verifies the requirement of the
DSP F28335 controlCARD
Sallen-key Filter +
TS555
Boost Converter
To the load
From the Agilent PV
emulator
Current sensor DSP
Voltage Supply
Figure 13: Laboratory setup.
derivative limiter to ensure the system operation inside the sliding hysteresis band. Moreover, the experimental test validates the mathematical expressions
350
proposed in Section 2.
Two additional experiments were made to validate the performance of the proposed cascade admittance-based MPPT algorithm connected to the SMC.
In both tests the electronic load was configured to impose a 100 Hz oscillation at the output port of the DC/DC converter to emulate a disturbance of 34.5
355
% generated by a grid-connected inverter. The first test is presented in Fig.
15, which considers the PV module irradiated at a constant value S = 500 W/m2 , where the P&O exhibits a stable 3-point profile in presence of the load voltage perturbations, which indicates the satisfactory performance of the proposed design procedure.
360
In the second case, the PV emulator is configured to perform the irradi- ance transient simulated in Fig. 8. That experiment presented in Fig. 16, where the P&O accurately tracks the new MPP in presence of the load voltage perturbations, which verifies again the satisfactory performance of the design
(a) Without filter
(b) With filter
Figure 14: Experimental verification of the SMC performance.
Figure 15: Experimental performance of PV system.
procedure.
365
Finally, the experimental results presented in this section validate the cor- rectness of the SMC performance in agreement with the requirements of the admittance-based MPPT algorithm.
7. Conclusion
This paper has presented a different control architecture for PV systems
370
based on a sliding mode control technique aimed at avoiding the use of elec- trolytic capacitors that degrade the system reliability. The sliding surface was implemented to follow an external reference provided by an MPPT algorithm to guarantee the operation at the maximum power point for the PV module. The MPPT algorithm was based on detecting the optimal PV admittance using a
375
mathematically considerations on the PV profile, which guarantee the tracking of the MPP. The SMC and the MPPT algorithm were evaluated by means of
Figure 16: Experimental performance of PV system with irradiance variations.
simulations and experimental tests in presence of both environmental and grid- connection perturbations. Finally, further developments using the same SMC analysis and design can be applied to PV systems based on other converter
380
topologies (e.g. buck, buck-boost, inverters).
Acknowledgments
This work was supported by the Automatic, Electronic and Computer Sci- ence research group of the Instituto Tecnol´ogico Metropolitano under the projects P14215 and P14220 and the Universidad Nacional de Colombia and Colcien-
385
cias (Fondo Nacional de Financiamiento para la Ciencia, la Tecnolog´ıa y la Innovaci´on Francisco Jos´e de Caldas) under the project MicroRENIZ-25439 (Code 1118-669-46197) and the doctoral scholarship 2012-567. In addition, the Spanish Ministerio de Economia y Competitividad and FEDER under Projects TEC2012-30952 and DPI2013-47437-R.
390
References
[1] A. Mellit, S. A. Kalogirou, Mppt-based artificial intelligence techniques for photovoltaic systems and its implementation into field programmable gate array chips: Review of current status and future perspectives, Energy 70 (2014) 1–21.
395
[2] E. Mamarelis, G. Petrone, G. Spagnuolo, A two-steps algorithm improving the p&o steady state mppt efficiency, Applied Energy 113 (2014) 414–421.
[3] N. Femia, G. Petrone, G. Spagnuolo, M. Vitelli, Optimization of perturb and observe maximum power point tracking method, IEEE Transactions on Power Electronics 20 (2005) 963–973.
400
[4] R. Haroun, A. E. Aroudi, A. Cid-Pastor, G. Garca, C. Olalla, L. Martnez- Salamero, Impedance matching in photovoltaic systems using cascaded boost converters and sliding-mode control, IEEE Transactions on Power Electronics 30 (2015) 3185–3199.
[5] A. Cid-Pastor, L. Martinez-Salamero, A. El Aroudi, R. Giral, J. Calvente,
405
R. Leyva, Synthesis of loss-free resistors based on sliding-mode control and its applications in power processing, Control Engineering Practice 21 (2013) 689–699.
[6] R. Arulmurugan, N. Suthanthiravanitha, Model and design of a fuzzy-based hopfield nn tracking controller for standalone pv applications, Electric
410
Power Systems Research 120 (2015) 184–193.
[7] P. Sivakumar, A. Abdul Kader, Y. Kaliavaradhan, M. Arutchelvi, Analy- sis and enhancement of pv efficiency with incremental conductance mppt technique under non-linear loading conditions, Renewable Energy 81 (2015) 543–550.
415
[8] J. Wang, J. Shieh, Y. Su, K. Kuo, Y. Chang, Y. Liang, J. Chou, K. Liao, J. Jiang, A novel method for the determination of dynamic resistance for photovoltaic modules, Energy 36 (2011) 5968–5974.
[9] N. A. Ahmed, A. K. Al-Othman, M. R. AlRashidi, Development of an effi- cient utility interactive combined wind/photovoltaic/fuel cell power system
420
with mppt and dc bus voltage regulation, Electric Power Systems Research 81 (2011) 1096–1106.
[10] C. R. Snchez Reinoso, D. H. Milone, R. H. Buitrago, Simulation of photo- voltaic centrals with dynamic shading, Applied Energy 103 (2013) 278–289.
[11] T. Esram, P. L. Chapman, Comparison of photovoltaic array maximum
425
power point tracking techniques, IEEE Transactions on energy conversion 22 (2007) 439–449.
[12] A. Trejos, D. Gonzalez, C. A. Ramos-Paja, Modeling of step-up grid- connected photovoltaic systems for control purposes, Energies 5 (2012) 1900–1926.
430
[13] G. Petrone, G. Spagnuolo, R. Teodorescu, M. Veerachary, M. Vitelli, Reli- ability issues in photovoltaic power processing systems, IEEE Transactions on Industrial Electronics 55 (2008) 2569–2580.
[14] K. Ishaque, Z. Salam, A. Shamsudin, M. Amjad, A direct control based maximum power point tracking method for photovoltaic system under par-
435
tial shading conditions using particle swarm optimization algorithm, Ap- plied Energy 99 (2012) 414–422.
[15] S. . Tan, Y. M. Lai, C. K. Tse, General design issues of sliding-mode controllers in dc-dc converters, IEEE Transactions on Industrial Electronics 55 (2008) 1160–1174.
440
[16] E. Bianconi, J. Calvente, R. Giral, E. Mamarelis, G. Petrone, C. A. Ramos- Paja, G. Spagnuolo, M. Vitelli, Perturb and observe mppt algorithm with a current controller based on the sliding mode, International Journal of Electrical Power and Energy Systems 44 (2013) 346–356.
[17] E. Bianconi, J. Calvente, R. Giral, E. Mamarelis, G. Petrone, C. A. Ramos-
445
Paja, G. Spagnuolo, M. Vitelli, A fast current-based mppt technique em-
ploying sliding mode control, IEEE Transactions on Industrial Electronics 60 (2013) 1168–1178.
[18] I. . Kim, Sliding mode controller for the single-phase grid-connected pho- tovoltaic system, Applied Energy 83 (2006) 1101–1115.
450
[19] Y. Levron, D. Shmilovitz, Maximum power point tracking employing slid- ing mode control, IEEE Transactions on Circuits and Systems I: Regular Papers 60 (2013).
[20] D. G. Montoya, C. A. R. Paja, R. Giral, Maximum power point track- ing based on the sliding mode control of the average pv admittance, in:
455
19th IEEE International Conference on Emerging Technologies and Factory Automation, ETFA 2014, 2014.
[21] M. C. Di Piazza, G. Vitale, Photovoltaic field emulation including dynamic and partial shadow conditions, Applied Energy 87 (2010) 814–823.
[22] R. Erickson, D. Maksimovic, Fundamentals of Power Electronics, Kluwer
460
Academic Publishers, New York, 2004.
[23] G. Petrone, C. Ramos-Paja, Modeling of photovoltaic fields in mismatched conditions for energy yield evaluations, Electric Power Systems Research 81 (2011) 1003–1013.
[24] U. Eicker, Solar Technologies for Buildings, Wiley, 2003.
465
[25] H. Sira-Ramirez, Sliding motions in bilinear switched networks., IEEE transactions on circuits and systems CAS-34 (1987) 919–933.
[26] N. Femia, G. Petrone, G. Spagnuolo, M. Vitelli, A technique for improving p&o mppt performances of double-stage grid-connected photovoltaic sys- tems, IEEE Transactions on Industrial Electronics 56 (2009) 4473–4482.
470
[27] G. Petrone, G. Spagnuolo, M. Vitelli, A multivariable perturb-and-observe maximum power point tracking technique applied to a single-stage pho-
tovoltaic inverter, IEEE Transactions on Industrial Electronics 58 (2011) 76–84.
[28] R. Mastromauro, M. Liserre, A. Dell’Aquila, Control issues in single-stage
475
photovoltaic systems: Mppt, current and voltage control, IEEE Transac- tions on Industrial Informatics 8 (2012) 241–254.